Automating Manufacturing Systems - Process Control and ...

ST1 

B 

T2 

A 

T1 

C * B 

T3 

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ST3 

T4 

FS = first scan 

T1 

T2 

= 

= 

ST2 ⋅ A 

ST1 ⋅ B 

T3 = ST3 ⋅ ( C ⋅ B) 

T4 = ST2 ⋅ ( C+ 

B) 

ST1 = ( ST1 + T1) ⋅ T2 + FS 

ST2 

C + B 

ST2 = ( ST2 + T2 + T3) ⋅T1 ⋅T4 

ST3 = ( ST3 + T4 ⋅ T1) ⋅ T3 

ST2 

A 

T1 

ST1 B 

Automating Manufacturing Systems 

ST3 C B 

with PLCs 

T2 

T3 

ST2 

C 

T4 

B 

T2 

(Version 5.0, May 4, 2007) 

ST1 

ST1 

T1 

first scan 

T1 

T4 

ST2 

Hugh Jack 

T2 

ST2 

T3 

T3 

ST3 

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Copyright (c) 1993-2007 Hugh Jack (jackh@gvsu.edu). 

Permission is granted to copy, distribute and/or modify this document under the 

terms of the GNU Free Documentation License, Version 1.2 or any later version 

published by the Free Software Foundation; with no Invariant Sections, no 

Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included 

in the section entitled "GNU Free Documentation License". 

This document is provided as-is with no warranty, implied or otherwise. There 

have been attempts to eliminate errors from this document, but there is no doubt 

that errors remain. As a result, the author does not assume any responsibility for 

errors and omissions, or damages resulting from the use of the information provided. 

Additional materials and updates for this work will be available at http://claymore.engineer.gvsu.edu/~jackh/books.html 

www.PAControl.com

page i 

1.1 TODO LIST 1.3 

2. PROGRAMMABLE LOGIC CONTROLLERS . . . . . . . . . . . . . 2.1 

2.1 INTRODUCTION 2.1 

2.1.1 Ladder Logic 2.1 

2.1.2 Programming 2.6 

2.1.3 PLC Connections 2.10 

2.1.4 Ladder Logic Inputs 2.11 

2.1.5 Ladder Logic Outputs 2.12 

2.2 A CASE STUDY 2.13 

2.3 SUMMARY 2.14 

2.4 PRACTICE PROBLEMS 2.15 

2.5 PRACTICE PROBLEM SOLUTIONS 2.15 

2.6 ASSIGNMENT PROBLEMS 2.16 

3. PLC HARDWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 


3.2 INPUTS AND OUTPUTS 3.2 

3.2.1 Inputs 3.3 

3.2.2 Output Modules 3.7 

3.3 RELAYS 3.13 

3.4 A CASE STUDY 3.14 

3.5 ELECTRICAL WIRING DIAGRAMS 3.15 

3.5.1 JIC Wiring Symbols 3.18 





4. LOGICAL SENSORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 


4.2 SENSOR WIRING 4.1 

4.2.1 Switches 4.2 

4.2.2 Transistor Transistor Logic (TTL) 4.3 

4.2.3 Sinking/Sourcing 4.3 

4.2.4 Solid State Relays 4.10 

4.3 PRESENCE DETECTION 4.11 

4.3.1 Contact Switches 4.11 

4.3.2 Reed Switches 4.11 

4.3.3 Optical (Photoelectric) Sensors 4.12 

4.3.4 Capacitive Sensors 4.19 

4.3.5 Inductive Sensors 4.23 

4.3.6 Ultrasonic 4.25 

4.3.7 Hall Effect 4.25 


page ii 

4.3.8 Fluid Flow 4.26 





5. LOGICAL ACTUATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 


5.2 SOLENOIDS 5.1 

5.3 VALVES 5.2 

5.4 CYLINDERS 5.4 

5.5 HYDRAULICS 5.6 

5.6 PNEUMATICS 5.8 

5.7 MOTORS 5.9 

5.8 OTHERS 5.10 





6. BOOLEAN LOGIC DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 


6.2 BOOLEAN ALGEBRA 6.1 

6.3 LOGIC DESIGN 6.6 

6.3.1 Boolean Algebra Techniques 6.13 

6.4 COMMON LOGIC FORMS 6.14 

6.4.1 Complex Gate Forms 6.14 

6.4.2 Multiplexers 6.15 

6.5 SIMPLE DESIGN CASES 6.17 

6.5.1 Basic Logic Functions 6.17 

6.5.2 Car Safety System 6.18 

6.5.3 Motor Forward/Reverse 6.18 

6.5.4 A Burglar Alarm 6.19 





7. KARNAUGH MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 






page iii 


8. PLC OPERATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 


8.2 OPERATION SEQUENCE 8.3 

8.2.1 The Input and Output Scans 8.4 

8.2.2 The Logic Scan 8.4 

8.3 PLC STATUS 8.6 

8.4 MEMORY TYPES 8.6 

8.5 SOFTWARE BASED PLCS 8.7 





9. LATCHES, TIMERS, COUNTERS AND MORE . . . . . . . . . . . . 9.1 


9.2 LATCHES 9.2 

9.3 TIMERS 9.6 

9.4 COUNTERS 9.14 

9.5 MASTER CONTROL RELAYS (MCRs) 9.17 

9.6 INTERNAL BITS 9.19 

9.7 DESIGN CASES 9.20 

9.7.1 Basic Counters And Timers 9.20 

9.7.2 More Timers And Counters 9.21 

9.7.3 Deadman Switch 9.22 

9.7.4 Conveyor 9.23 

9.7.5 Accept/Reject Sorting 9.24 

9.7.6 Shear Press 9.26 





10. STRUCTURED LOGIC DESIGN . . . . . . . . . . . . . . . . . . . . . . . 10.1 


10.2 PROCESS SEQUENCE BITS 10.2 

10.3 TIMING DIAGRAMS 10.6 


10.5 SUMMARY 10.9 





page iv 

13.11 

11. FLOWCHART BASED DESIGN . . . . . . . . . . . . . . . . . . . . . . . 11.1 


11.2 BLOCK LOGIC 11.4 

11.3 SEQUENCE BITS 11.11 

11.4 SUMMARY 11.15 




12. STATE BASED DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 


12.1.1 State Diagram Example 12.4 

12.1.2 Conversion to Ladder Logic 12.7 

Block Logic Conversion 12.7 

State Equations 12.16 

State-Transition Equations 12.24 

12.2 SUMMARY 12.29 




13. NUMBERS AND DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 


13.2 NUMERICAL VALUES 13.2 

13.2.1 Binary 13.2 

Boolean Operations 13.5 

Binary Mathematics 13.6 

13.2.2 Other Base Number Systems 13.10 

13.2.3 BCD (Binary Coded Decimal) 13.11 

13.3 DATA CHARACTERIZATION 13.11 

13.3.1 ASCII (American Standard Code for Information Interchange) 

13.3.2 Parity 13.14 

13.3.3 Checksums 13.15 

13.3.4 Gray Code 13.16 

13.4 SUMMARY 13.17 




14. PLC MEMORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 


14.2 PROGRAM VS VARIABLE MEMORY 14.1 


page v 

14.3 PROGRAMS 14.3 

14.4 VARIABLES (TAGS) 14.3 

14.4.1 Timer and Counter Memory 14.6 

14.4.2 PLC Status Bits 14.8 

14.4.3 User Function Control Memory 14.11 

14.5 SUMMARY 14.12 




15. LADDER LOGIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . 15.1 


15.2 DATA HANDLING 15.3 

15.2.1 Move Functions 15.3 

15.2.2 Mathematical Functions 15.5 

15.2.3 Conversions 15.10 

15.2.4 Array Data Functions 15.11 

Statistics 15.12 

Block Operations 15.13 

15.3 LOGICAL FUNCTIONS 15.15 

15.3.1 Comparison of Values 15.15 

15.3.2 Boolean Functions 15.21 


15.4.1 Simple Calculation 15.22 

15.4.2 For-Next 15.23 

15.4.3 Series Calculation 15.24 

15.4.4 Flashing Lights 15.25 

15.5 SUMMARY 15.25 




16. ADVANCED LADDER LOGIC FUNCTIONS . . . . . . . . . . . . . 16.1 


16.2 LIST FUNCTIONS 16.1 

16.2.1 Shift Registers 16.1 

16.2.2 Stacks 16.3 

16.2.3 Sequencers 16.6 

16.3 PROGRAM CONTROL 16.9 

16.3.1 Branching and Looping 16.9 

16.3.2 Fault Handling 16.14 

16.3.3 Interrupts 16.15 

16.4 INPUT AND OUTPUT FUNCTIONS 16.17 

16.4.1 Immediate I/O Instructions 16.17 


page vi 

16.5 DESIGN TECHNIQUES 16.19 

16.5.1 State Diagrams 16.19 


16.6.1 If-Then 16.24 

16.6.2 Traffic Light 16.25 

16.7 SUMMARY 16.25 




17. OPEN CONTROLLERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.1 


17.2 IEC 61131 17.2 

17.3 OPEN ARCHITECTURE CONTROLLERS 17.3 

17.4 SUMMARY 17.4 




18. INSTRUCTION LIST PROGRAMMING . . . . . . . . . . . . . . . . . 18.1 


18.2 THE IEC 61131 VERSION 18.1 

18.3 THE ALLEN-BRADLEY VERSION 18.4 

18.4 SUMMARY 18.9 




19. STRUCTURED TEXT PROGRAMMING . . . . . . . . . . . . . . . . 19.1 


19.2 THE LANGUAGE 19.2 

19.2.1 Elements of the Language 19.3 

19.2.2 Putting Things Together in a Program 19.9 

19.3 AN EXAMPLE 19.14 

19.4 SUMMARY 19.16 




20. SEQUENTIAL FUNCTION CHARTS . . . . . . . . . . . . . . . . . . . 20.1 


20.2 A COMPARISON OF METHODS 20.16 

20.3 SUMMARY 20.16 


page vii 




21. FUNCTION BLOCK PROGRAMMING . . . . . . . . . . . . . . . . . . 21.1 


21.2 CREATING FUNCTION BLOCKS 21.3 

21.3 DESIGN CASE 21.4 

21.4 SUMMARY 21.4 




22. ANALOG INPUTS AND OUTPUTS . . . . . . . . . . . . . . . . . . . . 22.1 


22.2 ANALOG INPUTS 22.2 

22.2.1 Analog Inputs With a PLC-5 22.9 

22.3 ANALOG OUTPUTS 22.13 

22.3.1 Analog Outputs With A PLC-5 22.16 

22.3.2 Pulse Width Modulation (PWM) Outputs 22.18 

22.3.3 Shielding 22.20 


22.4.1 Process Monitor 22.22 

22.5 SUMMARY 22.22 




23. CONTINUOUS SENSORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.1 


23.2 INDUSTRIAL SENSORS 23.2 

23.2.1 Angular Displacement 23.3 

Potentiometers 23.3 

23.2.2 Encoders 23.4 

Tachometers 23.8 

23.2.3 Linear Position 23.8 

Potentiometers 23.8 

Linear Variable Differential Transformers (LVDT)23.9 

Moire Fringes 23.11 

Accelerometers 23.12 

23.2.4 Forces and Moments 23.15 

Strain Gages 23.15 

Piezoelectric 23.18 

23.2.5 Liquids and Gases 23.20 


page viii 

Pressure 23.21 

Venturi Valves 23.22 

Coriolis Flow Meter 23.23 

Magnetic Flow Meter 23.24 

Ultrasonic Flow Meter 23.24 

Vortex Flow Meter 23.24 

Positive Displacement Meters 23.25 

Pitot Tubes 23.25 

23.2.6 Temperature 23.25 

Resistive Temperature Detectors (RTDs) 23.26 

Thermocouples 23.26 

Thermistors 23.28 

Other Sensors 23.30 

23.2.7 Light 23.30 

Light Dependant Resistors (LDR) 23.30 

23.2.8 Chemical 23.31 

pH 23.31 

Conductivity 23.31 

23.2.9 Others 23.32 

23.3 INPUT ISSUES 23.32 

23.4 SENSOR GLOSSARY 23.35 

23.5 SUMMARY 23.36 

23.6 REFERENCES 23.37 




24. CONTINUOUS ACTUATORS . . . . . . . . . . . . . . . . . . . . . . . . . 24.1 


24.2 ELECTRIC MOTORS 24.1 

24.2.1 Basic Brushed DC Motors 24.3 

24.2.2 AC Motors 24.7 

24.2.3 Brushless DC Motors 24.15 

24.2.4 Stepper Motors 24.17 

24.2.5 Wound Field Motors 24.19 

24.3 HYDRAULICS 24.23 

24.4 OTHER SYSTEMS 24.24 

24.5 SUMMARY 24.25 




25. CONTINUOUS CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.1 



page ix 

25.2 CONTROL OF LOGICAL ACTUATOR SYSTEMS 25.4 

25.3 CONTROL OF CONTINUOUS ACTUATOR SYSTEMS 25.5 

25.3.1 Block Diagrams 25.5 

25.3.2 Feedback Control Systems 25.6 

25.3.3 Proportional Controllers 25.8 

25.3.4 PID Control Systems 25.12 


25.4.1 Oven Temperature Control 25.14 

25.4.2 Water Tank Level Control 25.17 

25.4.3 Position Measurement 25.20 

25.5 SUMMARY 25.20 




26. FUZZY LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26.1 


26.2 COMMERCIAL CONTROLLERS 26.7 


26.4 SUMMARY 26.7 




27. SERIAL COMMUNICATION . . . . . . . . . . . . . . . . . . . . . . . . . . 27.1 


27.2 SERIAL COMMUNICATIONS 27.2 

27.2.1 RS-232 27.5 

ASCII Functions 27.9 

27.3 PARALLEL COMMUNICATIONS 27.13 


27.4.1 PLC Interface To a Robot 27.14 

27.5 SUMMARY 27.15 




28. NETWORKING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.1 


28.1.1 Topology 28.2 

28.1.2 OSI Network Model 28.3 

28.1.3 Networking Hardware 28.5 

28.1.4 Control Network Issues 28.7 

28.2 NETWORK STANDARDS 28.8 


page x 

28.2.1 Devicenet 28.8 

28.2.2 CANbus 28.12 

28.2.3 Controlnet 28.13 

28.2.4 Ethernet 28.14 

28.2.5 Profibus 28.15 

28.2.6 Sercos 28.15 

28.3 PROPRIETARY NETWORKS 28.16 

28.3.1 Data Highway 28.16 

28.4 NETWORK COMPARISONS 28.20 


28.5.1 Devicenet 28.22 

28.6 SUMMARY 28.23 




29. INTERNET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29.1 


29.1.1 Computer Addresses 29.2 

IPV6 29.3 

29.1.2 Phone Lines 29.3 

29.1.3 Mail Transfer Protocols 29.3 

29.1.4 FTP - File Transfer Protocol 29.4 

29.1.5 HTTP - Hypertext Transfer Protocol 29.4 

29.1.6 Novell 29.4 

29.1.7 Security 29.5 

Firewall 29.5 

IP Masquerading 29.5 

29.1.8 HTML - Hyper Text Markup Language 29.5 

29.1.9 URLs 29.6 

29.1.10 Encryption 29.6 

29.1.11 Compression 29.7 

29.1.12 Clients and Servers 29.7 

29.1.13 Java 29.9 

29.1.14 Javascript 29.9 

29.1.15 CGI 29.9 

29.1.16 ActiveX 29.9 

29.1.17 Graphics 29.10 


29.2.1 Remote Monitoring System 29.10 

29.3 SUMMARY 29.11 





page xi 

30. HUMAN MACHINE INTERFACES (HMI) . . . . . . . . . . . . . . . 30.1 


30.2 HMI/MMI DESIGN 30.2 


30.4 SUMMARY 30.3 




31. ELECTRICAL DESIGN AND CONSTRUCTION . . . . . . . . . . 31.1 


31.2 ELECTRICAL WIRING DIAGRAMS 31.1 

31.2.1 Selecting Voltages 31.8 

31.2.2 Grounding 31.9 

31.2.3 Wiring 31.12 

31.2.4 Suppressors 31.13 

31.2.5 PLC Enclosures 31.14 

31.2.6 Wire and Cable Grouping 31.16 

31.3 FAIL-SAFE DESIGN 31.17 

31.4 SAFETY RULES SUMMARY 31.18 


31.6 SUMMARY 31.20 




32. SOFTWARE ENGINEERING . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 


32.1.1 Fail Safe Design 32.1 

32.2 DEBUGGING 32.2 

32.2.1 Troubleshooting 32.3 

32.2.2 Forcing 32.3 

32.3 PROCESS MODELLING 32.3 

32.4 PROGRAMMING FOR LARGE SYSTEMS 32.8 

32.4.1 Developing a Program Structure 32.8 

32.4.2 Program Verification and Simulation 32.11 

32.5 DOCUMENTATION 32.12 

32.6 COMMISIONING 32.20 

32.7 SAFETY 32.20 

32.7.1 IEC 61508/61511 safety standards 32.21 

32.8 LEAN MANUFACTURING 32.22 


32.10 SUMMARY 32.23 


page xii 




33. SELECTING A PLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.1 


33.2 SPECIAL I/O MODULES 33.6 

33.3 SUMMARY 33.9 




34. FUNCTION REFERENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34.1 

34.1 FUNCTION DESCRIPTIONS 34.1 

34.1.1 General Functions 34.1 

34.1.2 Program Control 34.3 

34.1.3 Timers and Counters 34.5 

34.1.4 Compare 34.10 

34.1.5 Calculation and Conversion 34.14 

34.1.6 Logical 34.20 

34.1.7 Move 34.21 

34.1.8 File 34.22 

34.1.9 List 34.27 

34.1.10 Program Control 34.30 

34.1.11 Advanced Input/Output 34.34 

34.1.12 String 34.37 

34.2 DATA TYPES 34.42 

35. COMBINED GLOSSARY OF TERMS . . . . . . . . . . . . . . . . . . . 35.1 

35.1 A 35.1 

35.2 B 35.2 

35.3 C 35.5 

35.4 D 35.9 

35.5 E 35.11 

35.6 F 35.12 

35.7 G 35.13 

35.8 H 35.14 

35.9 I 35.14 

35.10 J 35.16 

35.11 K 35.16 

35.12 L 35.17 

35.13 M 35.17 

35.14 N 35.19 

35.15 O 35.20 


page xiii 

35.16 P 35.21 

35.17 Q 35.23 

35.18 R 35.23 

35.19 S 35.25 

35.20 T 35.27 

35.21 U 35.28 

35.22 V 35.29 

35.23 W 35.29 

35.24 X 35.30 

35.25 Y 35.30 

35.26 Z 35.30 

36. PLC REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36.1 

36.1 SUPPLIERS 36.1 

36.2 PROFESSIONAL INTEREST GROUPS 36.2 

36.3 PLC/DISCRETE CONTROL REFERENCES 36.2 

37. GNU Free Documentation License . . . . . . . . . . . . . . . . . . . . . . . 37.1 

37.1 PREAMBLE 37.1 

37.2 APPLICABILITY AND DEFINITIONS 37.1 

37.3 VERBATIM COPYING 37.2 

37.4 COPYING IN QUANTITY 37.3 

37.5 MODIFICATIONS 37.3 

37.6 COMBINING DOCUMENTS 37.5 

37.7 COLLECTIONS OF DOCUMENTS 37.5 

37.8 AGGREGATION WITH INDEPENDENT WORKS 37.6 

37.9 TRANSLATION 37.6 

37.10 TERMINATION 37.6 

37.11 FUTURE REVISIONS OF THIS LICENSE 37.6 

37.12 How to use this License for your documents 37.7 


plc wiring - 1.1 

PREFACE 

Designing software for control systems is difficult. Experienced controls engineers 

have learned many techniques that allow them to solve problems. This book was written to 

present methods for designing controls software using Programmable Logic Controllers 

(PLCs). It is my personal hope that by employing the knowledge in the book that you will 

be able to quickly write controls programs that work as expected (and avoid having to 

learn by costly mistakes.) 

This book has been designed for students with some knowledge of technology, 

including limited electricity, who wish to learn the discipline of practical control system 

design on commonly used hardware. To this end the book will use the Allen Bradley ControlLogix 

processors to allow depth. Although the chapters will focus on specific hardware, 

the techniques are portable to other PLCs. Whenever possible the IEC 61131 

programming standards will be used to help in the use of other PLCs. 

In some cases the material will build upon the content found in a linear controls 

course. But, a heavy emphasis is placed on discrete control systems. Figure 1.1 crudely 

shows some of the basic categories of control system problems. 

CONTROL 

CONTINUOUS 

DISCRETE 

LINEAR NON_LINEAR CONDITIONAL SEQUENTIAL 

EVENT BASED 

e.g. MRAC 

TEMPORAL 

e.g. PID 

BOOLEAN 

e.g. FUZZY LOGIC 

e.g. COUNTERS 

EXPERT SYSTEMS e.g. TIMERS 

Figure 1.1 

Control Dichotomy 

• Continuous - The values to be controlled change smoothly. e.g. the speed of a car. 

• Logical/Discrete - The value to be controlled are easily described as on-off. e.g. 

the car motor is on-off. NOTE: all systems are continuous but they can be 

treated as logical for simplicity. 

e.g. “When I do this, that always happens!” For example, when the power 

is turned on, the press closes! 



• Linear - Can be described with a simple differential equation. This is the preferred 

starting point for simplicity, and a common approximation for real world 

problems. 

e.g. A car can be driving around a track and can pass same the same spot at 

a constant velocity. But, the longer the car runs, the mass decreases, and 

it travels faster, but requires less gas, etc. Basically, the math gets 

tougher, and the problem becomes non-linear. 

e.g. We are driving the perfect car with no friction, with no drag, and can 

predict how it will work perfectly. 

• Non-Linear - Not Linear. This is how the world works and the mathematics 

become much more complex. 

e.g. As rocket approaches sun, gravity increases, so control must change. 

• Sequential - A logical controller that will keep track of time and previous events. 

The difference between these control systems can be emphasized by considering a 

simple elevator. An elevator is a car that travels between floors, stopping at precise 

heights. There are certain logical constraints used for safety and convenience. The points 

below emphasize different types of control problems in the elevator. 

Logical: 

1. The elevator must move towards a floor when a button is pushed. 

2. The elevator must open a door when it is at a floor. 

3. It must have the door closed before it moves. 

etc. 

Linear: 

1. If the desired position changes to a new value, accelerate quickly 

towards the new position. 

2. As the elevator approaches the correct position, slow down. 

Non-linear: 

1 Accelerate slowly to start. 

2. Decelerate as you approach the final position. 

3. Allow faster motion while moving. 

4. Compensate for cable stretch, and changing spring constant, etc. 

Logical and sequential control is preferred for system design. These systems are 

more stable, and often lower cost. Most continuous systems can be controlled logically. 

But, some times we will encounter a system that must be controlled continuously. When 

this occurs the control system design becomes more demanding. When improperly controlled, 

continuous systems may be unstable and become dangerous. 

When a system is well behaved we say it is self regulating. These systems don’t 

need to be closely monitored, and we use open loop control. An open loop controller will 

set a desired position for a system, but no sensors are used to verify the position. When a 



system must be constantly monitored and the control output adjusted we say it is closed 

loop. A cruise control in a car is an excellent example. This will monitor the actual speed 

of a car, and adjust the speed to meet a set target speed. 

Many control technologies are available for control. Early control systems relied 

upon mechanisms and electronics to build controlled. Most modern controllers use a computer 

to achieve control. The most flexible of these controllers is the PLC (Programmable 

Logic Controller). 

The book has been set up to aid the reader, as outlined below. 

Sections labeled Aside: are for topics that would be of interest to one discipline, 

such as electrical or mechanical. 

Sections labeled Note: are for clarification, to provide hints, or to add 

explanation. 

Each chapter supports about 1-4 lecture hours depending upon students 

background and level in the curriculum. 

Topics are organized to allow students to start laboratory work earlier in the 

semester. 

Sections begin with a topic list to help set thoughts. 

Objective given at the beginning of each chapter. 

Summary at the end of each chapter to give big picture. 

Significant use of figures to emphasize physical implementations. 

Worked examples and case studies. 

Problems at ends of chapters with solutions. 

Glossary. 

1.1 TODO LIST 

- Finish writing chapters 

* - structured text chapter 

* - FBD chapter 

- fuzzy logic chapter 

* - internet chapter 

- hmi chapter 

- modify chapters 

* - add topic hierarchies to this chapter. split into basics, logic design techniques, 

new stuff, integration, professional design for curriculum design 

* - electrical wiring chapter 

- fix wiring and other issues in the implementation chapter 

- software chapter - improve P&ID section 

- appendices - complete list of instruction data types in appendix 

- small items 



- update serial IO slides 

- all chapters 

* - grammar and spelling check 

* - update powerpoint slides 

* - add a resources web page with links 

- links to software/hardware vendors, iec1131, etc. 

- pictures of hardware and controls cabinet 



2. PROGRAMMABLE LOGIC CONTROLLERS 

Topics: 

• PLC History 

• Ladder Logic and Relays 

• PLC Programming 

• PLC Operation 

• An Example 

Objectives: 

• Know general PLC issues 

• To be able to write simple ladder logic programs 

• Understand the operation of a PLC 

2.1 INTRODUCTION 

Control engineering has evolved over time. In the past humans were the main 

method for controlling a system. More recently electricity has been used for control and 

early electrical control was based on relays. These relays allow power to be switched on 

and off without a mechanical switch. It is common to use relays to make simple logical 

control decisions. The development of low cost computer has brought the most recent revolution, 

the Programmable Logic Controller (PLC). The advent of the PLC began in the 

1970s, and has become the most common choice for manufacturing controls. 

PLCs have been gaining popularity on the factory floor and will probably remain 

predominant for some time to come. Most of this is because of the advantages they offer. 

• Cost effective for controlling complex systems. 

• Flexible and can be reapplied to control other systems quickly and easily. 

• Computational abilities allow more sophisticated control. 

• Trouble shooting aids make programming easier and reduce downtime. 

• Reliable components make these likely to operate for years before failure. 

2.1.1 Ladder Logic 

Ladder logic is the main programming method used for PLCs. As mentioned 

before, ladder logic has been developed to mimic relay logic. The decision to use the relay 



logic diagrams was a strategic one. By selecting ladder logic as the main programming 

method, the amount of retraining needed for engineers and tradespeople was greatly 

reduced. 

Modern control systems still include relays, but these are rarely used for logic. A 

relay is a simple device that uses a magnetic field to control a switch, as pictured in Figure 

2.1. When a voltage is applied to the input coil, the resulting current creates a magnetic 

field. The magnetic field pulls a metal switch (or reed) towards it and the contacts touch, 

closing the switch. The contact that closes when the coil is energized is called normally 

open. The normally closed contacts touch when the input coil is not energized. Relays are 

normally drawn in schematic form using a circle to represent the input coil. The output 

contacts are shown with two parallel lines. Normally open contacts are shown as two 

lines, and will be open (non-conducting) when the input is not energized. Normally closed 

contacts are shown with two lines with a diagonal line through them. When the input coil 

is not energized the normally closed contacts will be closed (conducting). 



input coil 

OR 

normally 

closed 

normally 

open 

OR 

Figure 2.1 

Simple Relay Layouts and Schematics 

Relays are used to let one power source close a switch for another (often high current) 

power source, while keeping them isolated. An example of a relay in a simple control 

application is shown in Figure 2.2. In this system the first relay on the left is used as normally 

closed, and will allow current to flow until a voltage is applied to the input A. The 

second relay is normally open and will not allow current to flow until a voltage is applied 

to the input B. If current is flowing through the first two relays then current will flow 

through the coil in the third relay, and close the switch for output C. This circuit would 

normally be drawn in the ladder logic form. This can be read logically as C will be on if A 

is off and B is on. 



115VAC 

wall plug 

relay logic 

input A 

(normally closed) 

input B 

(normally open) 

output C 

(normally open) 

A B C 

ladder logic 

Figure 2.2 

A Simple Relay Controller 

The example in Figure 2.2 does not show the entire control system, but only the 

logic. When we consider a PLC there are inputs, outputs, and the logic. Figure 2.3 shows a 

more complete representation of the PLC. Here there are two inputs from push buttons. 

We can imagine the inputs as activating 24V DC relay coils in the PLC. This in turn drives 

an output relay that switches 115V AC, that will turn on a light. Note, in actual PLCs 

inputs are never relays, but outputs are often relays. The ladder logic in the PLC is actually 

a computer program that the user can enter and change. Notice that both of the input push 

buttons are normally open, but the ladder logic inside the PLC has one normally open contact, 

and one normally closed contact. Do not think that the ladder logic in the PLC needs 

to match the inputs or outputs. Many beginners will get caught trying to make the ladder 

logic match the input types. 



push buttons 

power 

supply 

+24V 

com. 

PLC 

inputs 

ladder 

logic 

A B C 

outputs 

115Vac 

AC power 

light 

neut. 

Figure 2.3 

A PLC Illustrated With Relays 

Many relays also have multiple outputs (throws) and this allows an output relay to 

also be an input simultaneously. The circuit shown in Figure 2.4 is an example of this, it is 

called a seal in circuit. In this circuit the current can flow through either branch of the circuit, 

through the contacts labelled A or B. The input B will only be on when the output B 

is on. If B is off, and A is energized, then B will turn on. If B turns on then the input B will 

turn on, and keep output B on even if input A goes off. After B is turned on the output B 

will not turn off. 



A 

B 

B 

Note: When A is pushed, the output B will turn on, and 

the input B will also turn on and keep B on permanently 

- until power is removed. 

Note: The line on the right is being left off intentionally 

and is implied in these diagrams. 

Figure 2.4 

A Seal-in Circuit 

2.1.2 Programming 

The first PLCs were programmed with a technique that was based on relay logic 

wiring schematics. This eliminated the need to teach the electricians, technicians and engineers 

how to program a computer - but, this method has stuck and it is the most common 

technique for programming PLCs today. An example of ladder logic can be seen in Figure 

2.5. To interpret this diagram imagine that the power is on the vertical line on the left hand 

side, we call this the hot rail. On the right hand side is the neutral rail. In the figure there 

are two rungs, and on each rung there are combinations of inputs (two vertical lines) and 

outputs (circles). If the inputs are opened or closed in the right combination the power can 

flow from the hot rail, through the inputs, to power the outputs, and finally to the neutral 

rail. An input can come from a sensor, switch, or any other type of sensor. An output will 

be some device outside the PLC that is switched on or off, such as lights or motors. In the 

top rung the contacts are normally open and normally closed. Which means if input A is on 

and input B is off, then power will flow through the output and activate it. Any other combination 

of input values will result in the output X being off. 



HOT 

A B X 

NEUTRAL 

C 

D 

G 

Y 

E 

F 

H 

INPUTS 

OUTPUTS 

Note: Power needs to flow through some combination of the inputs 

(A,B,C,D,E,F,G,H) to turn on outputs (X,Y). 

Figure 2.5 

A Simple Ladder Logic Diagram 

The second rung of Figure 2.5 is more complex, there are actually multiple combinations 

of inputs that will result in the output Y turning on. On the left most part of the 

rung, power could flow through the top if C is off and D is on. Power could also (and 

simultaneously) flow through the bottom if both E and F are true. This would get power 

half way across the rung, and then if G or H is true the power will be delivered to output Y. 

In later chapters we will examine how to interpret and construct these diagrams. 

There are other methods for programming PLCs. One of the earliest techniques 

involved mnemonic instructions. These instructions can be derived directly from the ladder 

logic diagrams and entered into the PLC through a simple programming terminal. An 

example of mnemonics is shown in Figure 2.6. In this example the instructions are read 

one line at a time from top to bottom. The first line 00000 has the instruction LDN (input 

load and not) for input A. This will examine the input to the PLC and if it is off it will 

remember a 1 (or true), if it is on it will remember a 0 (or false). The next line uses an LD 

(input load) statement to look at the input. If the input is off it remembers a 0, if the input 

is on it remembers a 1 (note: this is the reverse of the LD). The AND statement recalls the 

last two numbers remembered and if the are both true the result is a 1, otherwise the result 

is a 0. This result now replaces the two numbers that were recalled, and there is only one 

number remembered. The process is repeated for lines 00003 and 00004, but when these 

are done there are now three numbers remembered. The oldest number is from the AND, 

the newer numbers are from the two LD instructions. The AND in line 00005 combines the 

results from the last LD instructions and now there are two numbers remembered. The OR 

instruction takes the two numbers now remaining and if either one is a 1 the result is a 1, 

otherwise the result is a 0. This result replaces the two numbers, and there is now a single 



number there. The last instruction is the ST (store output) that will look at the last value 

stored and if it is 1, the output will be turned on, if it is 0 the output will be turned off. 

00000 

00001 

00002 

00003 

00004 

00005 

00006 

LDN 

LD 

AND 

LD 

LD 

AND 

OR 

ST 

END 

A 

B 

C 

D 

00007 X 

00008 

A 

the mnemonic code is equivalent to 

the ladder logic below 

B 

X 

C 

D 

END 

Note: The notation shown above is 

not standard Allen-Bradley 

notation. The program to the 

right would be the A-B equivalent. 

SOR 

BST 

XIC A 

XIO B 

NXB 

XIO C 

XIO D 

BND 

OTE X 

EOR 

END 

Figure 2.6 

An Example of a Mnemonic Program and Equivalent Ladder Logic 

The ladder logic program in Figure 2.6, is equivalent to the mnemonic program. 

Even if you have programmed a PLC with ladder logic, it will be converted to mnemonic 

form before being used by the PLC. In the past mnemonic programming was the most 

common, but now it is uncommon for users to even see mnemonic programs. 



Sequential Function Charts (SFCs) have been developed to accommodate the programming 

of more advanced systems. These are similar to flowcharts, but much more 

powerful. The example seen in Figure 2.7 is doing two different things. To read the chart, 

start at the top where is says start. Below this there is the double horizontal line that says 

follow both paths. As a result the PLC will start to follow the branch on the left and right 

hand sides separately and simultaneously. On the left there are two functions the first one 

is the power up function. This function will run until it decides it is done, and the power 

down function will come after. On the right hand side is the flash function, this will run 

until it is done. These functions look unexplained, but each function, such as power up 

will be a small ladder logic program. This method is much different from flowcharts 

because it does not have to follow a single path through the flowchart. 

Start 

power up 

Execution follows 

multiple paths 

power down 

flash 

End 

Figure 2.7 

An Example of a Sequential Function Chart 

Structured Text programming has been developed as a more modern programming 

language. It is quite similar to languages such as BASIC. A simple example is shown in 

Figure 2.8. This example uses a PLC memory location i. This memory location is for an 

integer, as will be explained later in the book. The first line of the program sets the value 

to 0. The next line begins a loop, and will be where the loop returns to. The next line 

recalls the value in location i, adds 1 to it and returns it to the same location. The next line 

checks to see if the loop should quit. If i is greater than or equal to 10, then the loop will 

quit, otherwise the computer will go back up to the REPEAT statement continue from 

there. Each time the program goes through this loop i will increase by 1 until the value 

reaches 10. 



i := 0; 

REPEAT 

i := i + 1; 

UNTIL i >= 10 

END_REPEAT; 

Figure 2.8 

An Example of a Structured Text Program 

2.1.3 PLC Connections 

When a process is controlled by a PLC it uses inputs from sensors to make decisions 

and update outputs to drive actuators, as shown in Figure 2.9. The process is a real 

process that will change over time. Actuators will drive the system to new states (or modes 

of operation). This means that the controller is limited by the sensors available, if an input 

is not available, the controller will have no way to detect a condition. 

PROCESS 

Feedback from 

sensors/switches 

Connections to 

actuators 

PLC 

Figure 2.9 

The Separation of Controller and Process 

The control loop is a continuous cycle of the PLC reading inputs, solving the ladder 

logic, and then changing the outputs. Like any computer this does not happen 

instantly. Figure 2.10 shows the basic operation cycle of a PLC. When power is turned on 

initially the PLC does a quick sanity check to ensure that the hardware is working properly. 

If there is a problem the PLC will halt and indicate there is an error. For example, if 

the PLC power is dropping and about to go off this will result in one type of fault. If the 

PLC passes the sanity check it will then scan (read) all the inputs. After the inputs values 

are stored in memory the ladder logic will be scanned (solved) using the stored values - 

not the current values. This is done to prevent logic problems when inputs change during 

the ladder logic scan. When the ladder logic scan is complete the outputs will be scanned 



(the output values will be changed). After this the system goes back to do a sanity check, 

and the loop continues indefinitely. Unlike normal computers, the entire program will be 

run every scan. Typical times for each of the stages is in the order of milliseconds. 

PLC program changes outputs 

by examining inputs 

Read inputs 

THE 

CONTROL 

LOOP 

Set new outputs 

Power turned on 

Process changes and PLC pauses 

while it checks its own operation 

Figure 2.10 

The Scan Cycle of a PLC 

2.1.4 Ladder Logic Inputs 

PLC inputs are easily represented in ladder logic. In Figure 2.11 there are three 

types of inputs shown. The first two are normally open and normally closed inputs, discussed 

previously. The IIT (Immediate InpuT) function allows inputs to be read after the 

input scan, while the ladder logic is being scanned. This allows ladder logic to examine 

input values more often than once every cycle. (Note: This instruction is not available on 

the ControlLogix processors, but is still available on older models.) 



x 

Normally open, an active input x will close the contact 

and allow power to flow. 

x 

Normally closed, power flows when the input x is not open. 

IIT 

x 

immediate inputs will take current values, not those from 

the previous input scan. (Note: this instruction is actually 

an output that will update the input table with the current 

input values. Other input contacts can now be used to 

examine the new values.) 

Figure 2.11 

Ladder Logic Inputs 

2.1.5 Ladder Logic Outputs 

In ladder logic there are multiple types of outputs, but these are not consistently 

available on all PLCs. Some of the outputs will be externally connected to devices outside 

the PLC, but it is also possible to use internal memory locations in the PLC. Six types of 

outputs are shown in Figure 2.12. The first is a normal output, when energized the output 

will turn on, and energize an output. The circle with a diagonal line through is a normally 

on output. When energized the output will turn off. This type of output is not available on 

all PLC types. When initially energized the OSR (One Shot Relay) instruction will turn on 

for one scan, but then be off for all scans after, until it is turned off. The L (latch) and U 

(unlatch) instructions can be used to lock outputs on. When an L output is energized the 

output will turn on indefinitely, even when the output coil is deenergized. The output can 

only be turned off using a U output. The last instruction is the IOT (Immediate OutpuT) 

that will allow outputs to be updated without having to wait for the ladder logic scan to be 

completed. 



When power is applied (on) the output x is activated for the left output, but turned 

off for the output on the right. 

x 

x 

An input transition on will cause the output x to go on for one scan 

(this is also known as a one shot relay) 

x 

OSR 

When the L coil is energized, x will be toggled on, it will stay on until the U coil 

is energized. This is like a flip-flop and stays set even when the PLC is turned off. 

x 

x 

L 

U 

Some PLCs will allow immediate outputs that do not wait for the program scan to 

end before setting an output. (Note: This instruction will only update the outputs using 

the output table, other instruction must change the individual outputs.) 

IOT 

x 

Note: Outputs are also commonly shown using parentheses -( )- instead of 

the circle. This is because many of the programming systems are text 

based and circles cannot be drawn. 

Figure 2.12 

Ladder Logic Outputs 

2.2 A CASE STUDY 

Problem: Try to develop (without looking at the solution) a relay based controller 

that will allow three switches in a room to control a single light. 



Solution: There are two possible approaches to this problem. The first assumes that any 

one of the switches on will turn on the light, but all three switches must be off for the 

light to be off. 

switch 1 

light 

switch 2 

switch 3 

The second solution assumes that each switch can turn the light on or off, regardless of 

the states of the other switches. This method is more complex and involves thinking 

through all of the possible combinations of switch positions. You might recognize 

this problem as an exclusive or problem. 

switch 1 

switch 2 

switch 3 

light 

switch 1 

switch 2 

switch 3 

switch 1 

switch 2 

switch 3 

switch 1 switch 2 switch 3 

Note: It is important to get a clear understanding of how the controls are expected to 

work. In this example two radically different solutions were obtained based upon a 

simple difference in the operation. 

2.3 SUMMARY 

• Normally open and closed contacts. 

• Relays and their relationship to ladder logic. 

• PLC outputs can be inputs, as shown by the seal in circuit. 

• Programming can be done with ladder logic, mnemonics, SFCs, and structured 

text. 

• There are multiple ways to write a PLC program. 



2.4 PRACTICE PROBLEMS 

1. Give an example of where a PLC could be used. 

2. Why would relays be used in place of PLCs? 

3. Give a concise description of a PLC. 

4. List the advantages of a PLC over relays. 

5. A PLC can effectively replace a number of components. Give examples and discuss some good 

and bad applications of PLCs. 

6. Explain why ladder logic outputs are coils? 

7. In the figure below, will the power for the output on the first rung normally be on or off? Would 

the output on the second rung normally be on or off? 

8. Write the mnemonic program for the Ladder Logic below. 

A 

Y 

B 

2.5 PRACTICE PROBLEM SOLUTIONS 

1. To control a conveyor system 

2. For simple designs 

3. A PLC is a computer based controller that uses inputs to monitor a process, and uses outputs to 

control a process using a program. 



4. Less expensive for complex processes, debugging tools, reliable, flexible, easy to expand, etc. 

5. A PLC could replace a few relays. In this case the relays might be easier to install and less 

expensive. To control a more complex system the controller might need timing, counting and 

other mathematical calculations. In this case a PLC would be a better choice. 

6. The ladder logic outputs were modelled on relay logic diagrams. The output in a relay ladder 

diagram is a relay coil that switches a set of output contacts. 

7. off, on 

8. Generic: LD A, LD B, OR, ST Y, END; Allen Bradley: SOR, BST, XIO A, NXB, XIO B, 

BND, OTE Y, EOR, END 

2.6 ASSIGNMENT PROBLEMS 

1. Explain the trade-offs between relays and PLCs for control applications. 

2. Develop a simple ladder logic program that will turn on an output X if inputs A and B, or input 

C is on. 



3. PLC HARDWARE 

Topics: 

• PLC hardware configurations 

• Input and outputs types 

• Electrical wiring for inputs and outputs 

• Relays 

• Electrical Ladder Diagrams and JIC wiring symbols 

Objectives: 

• Be able to understand and design basic input and output wiring. 

• Be able to produce industrial wiring diagrams. 


Many PLC configurations are available, even from a single vendor. But, in each of 

these there are common components and concepts. The most essential components are: 

Power Supply - This can be built into the PLC or be an external unit. Common 

voltage levels required by the PLC (with and without the power supply) are 

24Vdc, 120Vac, 220Vac. 

CPU (Central Processing Unit) - This is a computer where ladder logic is stored 

and processed. 

I/O (Input/Output) - A number of input/output terminals must be provided so that 

the PLC can monitor the process and initiate actions. 

Indicator lights - These indicate the status of the PLC including power on, program 

running, and a fault. These are essential when diagnosing problems. 

The configuration of the PLC refers to the packaging of the components. Typical 

configurations are listed below from largest to smallest as shown in Figure 3.1. 

Rack - A rack is often large (up to 18” by 30” by 10”) and can hold multiple cards. 

When necessary, multiple racks can be connected together. These tend to be the 

highest cost, but also the most flexible and easy to maintain. 

Mini - These are smaller than full sized PLC racks, but can have the same IO 

capacity. 

Micro - These units can be as small as a deck of cards. They tend to have fixed 

quantities of I/O and limited abilities, but costs will be the lowest. 

Software - A software based PLC requires a computer with an interface card, but 



allows the PLC to be connected to sensors and other PLCs across a network. 

rack 

mini 

micro 

Figure 3.1 

Typical Configurations for PLC 

3.2 INPUTS AND OUTPUTS 

Inputs to, and outputs from, a PLC are necessary to monitor and control a process. 

Both inputs and outputs can be categorized into two basic types: logical or continuous. 

Consider the example of a light bulb. If it can only be turned on or off, it is logical control. 

If the light can be dimmed to different levels, it is continuous. Continuous values seem 

more intuitive, but logical values are preferred because they allow more certainty, and 

simplify control. As a result most controls applications (and PLCs) use logical inputs and 

outputs for most applications. Hence, we will discuss logical I/O and leave continuous I/O 

for later. 

Outputs to actuators allow a PLC to cause something to happen in a process. A 

short list of popular actuators is given below in order of relative popularity. 

Solenoid Valves - logical outputs that can switch a hydraulic or pneumatic flow. 

Lights - logical outputs that can often be powered directly from PLC output 

boards. 

Motor Starters - motors often draw a large amount of current when started, so they 

require motor starters, which are basically large relays. 

Servo Motors - a continuous output from the PLC can command a variable speed 

or position. 



Outputs from PLCs are often relays, but they can also be solid state electronics 

such as transistors for DC outputs or Triacs for AC outputs. Continuous outputs require 

special output cards with digital to analog converters. 

Inputs come from sensors that translate physical phenomena into electrical signals. 

Typical examples of sensors are listed below in relative order of popularity. 

Proximity Switches - use inductance, capacitance or light to detect an object logically. 

Switches - mechanical mechanisms will open or close electrical contacts for a logical 

signal. 

Potentiometer - measures angular positions continuously, using resistance. 

LVDT (linear variable differential transformer) - measures linear displacement 

continuously using magnetic coupling. 

Inputs for a PLC come in a few basic varieties, the simplest are AC and DC inputs. 

Sourcing and sinking inputs are also popular. This output method dictates that a device 

does not supply any power. Instead, the device only switches current on or off, like a simple 

switch. 

Sinking - When active the output allows current to flow to a common ground. This 

is best selected when different voltages are supplied. 

Sourcing - When active, current flows from a supply, through the output device 

and to ground. This method is best used when all devices use a single supply 

voltage. 

This is also referred to as NPN (sinking) and PNP (sourcing). PNP is more popular. 

This will be covered in detail in the chapter on sensors. 

3.2.1 Inputs 

In smaller PLCs the inputs are normally built in and are specified when purchasing 

the PLC. For larger PLCs the inputs are purchased as modules, or cards, with 8 or 16 

inputs of the same type on each card. For discussion purposes we will discuss all inputs as 

if they have been purchased as cards. The list below shows typical ranges for input voltages, 

and is roughly in order of popularity. 

12-24 Vdc 

100-120 Vac 

10-60 Vdc 

12-24 Vac/dc 



5 Vdc (TTL) 

200-240 Vac 

48 Vdc 

24 Vac 

PLC input cards rarely supply power, this means that an external power supply is 

needed to supply power for the inputs and sensors. The example in Figure 3.2 shows how 

to connect an AC input card. 

24 V AC 

Power 

Supply 

Hot 

Neut. 

normally open push-button 

PLC Input Card 

24V AC 

00 

01 

02 

03 

04 

normally open 

temperature switch 

05 

06 

07 

COM 

Pushbutton (bob:3:I.Data.1) 

it is in rack "bob" 

slot 3 

Tempsensor (bob:3:I.Data.3) 

Note: inputs are normally high impedance. This means that they will 

use very little current. 

Figure 3.2 

An AC Input Card and Ladder Logic 



In the example there are two inputs, one is a normally open push button, and the 

second is a temperature switch, or thermal relay. (NOTE: These symbols are standard and 

will be discussed later in this chapter.) Both of the switches are powered by the positive/ 

hot output of the 24Vac power supply - this is like the positive terminal on a DC supply. 

Power is supplied to the left side of both of the switches. When the switches are open there 

is no voltage passed to the input card. If either of the switches are closed power will be 

supplied to the input card. In this case inputs 1 and 3 are used - notice that the inputs start 

at 0. The input card compares these voltages to the common. If the input voltage is within 

a given tolerance range the inputs will switch on. Ladder logic is shown in the figure for 

the inputs. Here it uses Allen Bradley notation for ControlLogix. At the top is the tag 

(variable name) for the rack. The input card (’I’) is in slot 3, so the address for the card is 

bob:3.I.Data.x, where ’x’ is the input bit number. These addresses can also be given alias 

tags to make the ladder logic less confusing. 

NOTE: The design process will be much easier if the inputs and outputs are planned first, 

and the tags are entered before the ladder logic. Then the program is entered using the 

much simpler tag names. 

Many beginners become confused about where connections are needed in the circuit 

above. The key word to remember is circuit, which means that there is a full loop that 

the voltage must be able to follow. In Figure 3.2 we can start following the circuit (loop) at 

the power supply. The path goes through the switches, through the input card, and back to 

the power supply where it flows back through to the start. In a full PLC implementation 

there will be many circuits that must each be complete. 

A second important concept is the common. Here the neutral on the power supply 

is the common, or reference voltage. In effect we have chosen this to be our 0V reference, 

and all other voltages are measured relative to it. If we had a second power supply, we 

would also need to connect the neutral so that both neutrals would be connected to the 

same common. Often common and ground will be confused. The common is a reference, 

or datum voltage that is used for 0V, but the ground is used to prevent shocks and damage 

to equipment. The ground is connected under a building to a metal pipe or grid in the 

ground. This is connected to the electrical system of a building, to the power outlets, 

where the metal cases of electrical equipment are connected. When power flows through 

the ground it is bad. Unfortunately many engineers, and manufacturers mix up ground and 

common. It is very common to find a power supply with the ground and common mislabeled. 



Remember - Don’t mix up the ground and common. Don’t connect them together if the 

common of your device is connected to a common on another device. 

One final concept that tends to trap beginners is that each input card is isolated. 

This means that if you have connected a common to only one card, then the other cards are 

not connected. When this happens the other cards will not work properly. You must connect 

a common for each of the output cards. 

There are many trade-offs when deciding which type of input cards to use. 

• DC voltages are usually lower, and therefore safer (i.e., 12-24V). 

• DC inputs are very fast, AC inputs require a longer on-time. For example, a 60Hz 

wave may require up to 1/60sec for reasonable recognition. 

• DC voltages can be connected to larger variety of electrical systems. 

• AC signals are more immune to noise than DC, so they are suited to long distances, 

and noisy (magnetic) environments. 

• AC power is easier and less expensive to supply to equipment. 

• AC signals are very common in many existing automation devices. 



ASIDE: PLC inputs must convert a variety of logic levels to the 5Vdc logic levels 

used on the data bus. This can be done with circuits similar to those shown below. 

Basically the circuits condition the input to drive an optocoupler. This electrically 

isolates the external electrical circuitry from the internal circuitry. Other circuit 

components are used to guard against excess or reversed voltage polarity. 

+5V 

+ 

optocoupler 

DC 

input 

TTL 

COM 

hot 

neut. 

AC 

input 

+5V 

optocoupler 

TTL 

Figure 3.3 

Aside: PLC Input Circuits 

3.2.2 Output Modules 

WARNING - ALWAYS CHECK RATED VOLTAGES AND CURRENTS FOR PLC’s 

AND NEVER EXCEED! 



As with input modules, output modules rarely supply any power, but instead act as 

switches. External power supplies are connected to the output card and the card will 

switch the power on or off for each output. Typical output voltages are listed below, and 

roughly ordered by popularity. 

120 Vac 

24 Vdc 

12-48 Vac 

12-48 Vdc 

5Vdc (TTL) 

230 Vac 

These cards typically have 8 to 16 outputs of the same type and can be purchased 

with different current ratings. A common choice when purchasing output cards is relays, 

transistors or triacs. Relays are the most flexible output devices. They are capable of 

switching both AC and DC outputs. But, they are slower (about 10ms switching is typical), 

they are bulkier, they cost more, and they will wear out after millions of cycles. Relay 

outputs are often called dry contacts. Transistors are limited to DC outputs, and Triacs are 

limited to AC outputs. Transistor and triac outputs are called switched outputs. 

Dry contacts - a separate relay is dedicated to each output. This allows mixed voltages 

(AC or DC and voltage levels up to the maximum), as well as isolated outputs 

to protect other outputs and the PLC. Response times are often greater than 

10ms. This method is the least sensitive to voltage variations and spikes. 

Switched outputs - a voltage is supplied to the PLC card, and the card switches it to 

different outputs using solid state circuitry (transistors, triacs, etc.) Triacs are 

well suited to AC devices requiring less than 1A. Transistor outputs use NPN or 

PNP transistors up to 1A typically. Their response time is well under 1ms. 



ASIDE: PLC outputs must convert the 5Vdc logic levels on the PLC data bus to external 

voltage levels. This can be done with circuits similar to those shown below. 

Basically the circuits use an optocoupler to switch external circuitry. This electrically 

isolates the external electrical circuitry from the internal circuitry. Other circuit 

components are used to guard against excess or reversed voltage polarity. 

optocoupler 

+V 

TTL 

Sourcing DC output 

TTL 

optocoupler 

AC 

output 

TTL 

+V 

relay 

output 

AC/DC 

Note: Some AC outputs will 

also use zero voltage detection. 

This allows the output 

to be switched on when the 

voltage and current are 

effectively off, thus preventing 

surges. 

Figure 3.4 

Aside: PLC Output Circuits 

Caution is required when building a system with both AC and DC outputs. If AC is 



accidentally connected to a DC transistor output it will only be on for the positive half of 

the cycle, and appear to be working with a diminished voltage. If DC is connected to an 

AC triac output it will turn on and appear to work, but you will not be able to turn it off 

without turning off the entire PLC. 

ASIDE: A transistor is a semiconductor based device that can act as an adjustable valve. 

When switched off it will block current flow in both directions. While switched on it 

will allow current flow in one direction only. There is normally a loss of a couple of 

volts across the transistor. A triac is like two SCRs (or imagine transistors) connected 

together so that current can flow in both directions, which is good for AC current. 

One major difference for a triac is that if it has been switched on so that current flows, 

and then switched off, it will not turn off until the current stops flowing. This is fine 

with AC current because the current stops and reverses every 1/2 cycle, but this does 

not happen with DC current, and so the triac will remain on. 

A major issue with outputs is mixed power sources. It is good practice to isolate all 

power supplies and keep their commons separate, but this is not always feasible. Some 

output modules, such as relays, allow each output to have its own common. Other output 

cards require that multiple, or all, outputs on each card share the same common. Each output 

card will be isolated from the rest, so each common will have to be connected. It is 

common for beginners to only connect the common to one card, and forget the other cards 

- then only one card seems to work! 

The output card shown in Figure 3.5 is an example of a 24Vdc output card that has 

a shared common. This type of output card would typically use transistors for the outputs. 



24 V DC 

Output Card 

00 

01 

02 

03 

04 

Relay 

120 V AC 

Power 

Supply 

Neut. 

Motor 

05 

06 

24 V Lamp 

07 

COM 

rack "sue" 

slot 2 

+24 V DC 

Power 

Supply 

COM 

Motor (sue:2.O.Data.3) 

Lamp (sue:2.O.Data.3) 

Figure 3.5 

An Example of a 24Vdc Output Card (Sinking) 

In this example the outputs are connected to a low current light bulb (lamp) and a 

relay coil. Consider the circuit through the lamp, starting at the 24Vdc supply. When the 

output 07 is on, current can flow in 07 to the COM, thus completing the circuit, and allowing 

the light to turn on. If the output is off the current cannot flow, and the light will not 

turn on. The output 03 for the relay is connected in a similar way. When the output 03 is 

on, current will flow through the relay coil to close the contacts and supply 120Vac to the 

motor. Ladder logic for the outputs is shown in the bottom right of the figure. The notation 

is for an Allen Bradley ControlLogix. The output card (’O’) is in a rack labelled ’sue’ in 

slot 2. As indicated for the input card, it is good practice to define and use an alias tag for 

an output (e.g. Motor) instead of using the full description (e.g. sue:2.O.Data.3). This card 



could have many different voltages applied from different sources, but all the power supplies 

would need a single shared common. 

The circuits in Figure 3.6 had the sequence of power supply, then device, then PLC 

card, then power supply. This requires that the output card have a common. Some output 

schemes reverse the device and PLC card, thereby replacing the common with a voltage 

input. The example in Figure 3.5 is repeated in Figure 3.6 for a voltage supply card. 

24 V DC 

Output Card 

V+ 

00 

Power 

Supply 

+24 V DC COM 

01 

02 

03 

04 

Relay 

Motor 

120 V AC 

Power 

Supply 

Neut. 

05 

06 

24 V lamp 

07 

Figure 3.6 

An Example of a 24Vdc Output Card With a Voltage Input (Sourcing) 

In this example the positive terminal of the 24Vdc supply is connected to the output 

card directly. When an output is on power will be supplied to that output. For example, 

if output 07 is on then the supply voltage will be output to the lamp. Current will flow 

through the lamp and back to the common on the power supply. The operation is very similar 

for the relay switching the motor. Notice that the ladder logic (shown in the bottom 

right of the figure) is identical to that in Figure 3.5. With this type of output card only one 

power supply can be used. 

We can also use relay outputs to switch the outputs. The example shown in Figure 



3.5 and Figure 3.6 is repeated yet again in Figure 3.7 for relay output. 

120 V AC/DC 

Output Card 

00 

24 V DC 

Power 

Supply 

01 

02 

03 

04 

Relay 

05 

06 

07 24 V lamp 

in rack 01 

I/O group 2 

Motor 

120 V AC 

Power 

Supply 

Figure 3.7 

An Example of a Relay Output Card 

In this example the 24Vdc supply is connected directly to both relays (note that 

this requires 2 connections now, whereas the previous example only required one.) When 

an output is activated the output switches on and power is delivered to the output devices. 

This layout is more similar to Figure 3.6 with the outputs supplying voltage, but the relays 

could also be used to connect outputs to grounds, as in Figure 3.5. When using relay outputs 

it is possible to have each output isolated from the next. A relay output card could 

have AC and DC outputs beside each other. 

3.3 RELAYS 

Although relays are rarely used for control logic, they are still essential for switch- 



ing large power loads. Some important terminology for relays is given below. 

Contactor - Special relays for switching large current loads. 

Motor Starter - Basically a contactor in series with an overload relay to cut off 

when too much current is drawn. 

Arc Suppression - when any relay is opened or closed an arc will jump. This 

becomes a major problem with large relays. On relays switching AC this problem 

can be overcome by opening the relay when the voltage goes to zero (while 

crossing between negative and positive). When switching DC loads this problem 

can be minimized by blowing pressurized gas across during opening to suppress 

the arc formation. 

AC coils - If a normal coil is driven by AC power the contacts will vibrate open 

and closed at the frequency of the AC power. This problem is overcome by 

relay manufacturers by adding a shading pole to the internal construction of the 

relay. 

The most important consideration when selecting relays, or relay outputs on a 

PLC, is the rated current and voltage. If the rated voltage is exceeded, the contacts will 

wear out prematurely, or if the voltage is too high fire is possible. The rated current is the 

maximum current that should be used. When this is exceeded the device will become too 

hot, and it will fail sooner. The rated values are typically given for both AC and DC, 

although DC ratings are lower than AC. If the actual loads used are below the rated values 

the relays should work well indefinitely. If the values are exceeded a small amount the life 

of the relay will be shortened accordingly. Exceeding the values significantly may lead to 

immediate failure and permanent damage. Please note that relays may also include minimum 

ratings that should also be observed to ensure proper operation and long life. 

• Rated Voltage - The suggested operation voltage for the coil. Lower levels can 

result in failure to operate, voltages above shorten life. 

• Rated Current - The maximum current before contact damage occurs (welding or 

melting). 

3.4 A CASE STUDY 

(Try the following case without looking at the solution in Figure 3.8.) An electrical 

layout is needed for a hydraulic press. The press uses a 24Vdc double actuated solenoid 

valve to advance and retract the press. This device has a single common and two input 

wires. Putting 24Vdc on one wire will cause the press to advance, putting 24Vdc on the 

second wire will cause it to retract. The press is driven by a large hydraulic pump that 

requires 220Vac rated at 20A, this should be running as long as the press is on. The press 

is outfitted with three push buttons, one is a NC stop button, the other is a NO manual 

retract button, and the third is a NO start automatic cycle button. There are limit switches 



at the top and bottom of the press travels that must also be connected. 

SOLUTION 

24VDC 

output card 

V+ 

advance 

O/0 

solenoid 

24VDC 

input card 

I/0 

I/1 

I/2 

I/3 

retract 

O/1 

I/4 

relay for 

hydraulic 

pump O/2 

- 

+ 

24VDC 

com 

Figure 3.8 

Case Study for Press Wiring 

The input and output cards were both selected to be 24Vdc so that they may share 

a single 24Vdc power supply. In this case the solenoid valve was wired directly to the output 

card, while the hydraulic pump was connected indirectly using a relay (only the coil is 

shown for simplicity). This decision was primarily made because the hydraulic pump 

requires more current than any PLC can handle, but a relay would be relatively easy to 

purchase and install for that load. All of the input switches are connected to the same supply 

and to the inputs. 

3.5 ELECTRICAL WIRING DIAGRAMS 

When a controls cabinet is designed and constructed ladder diagrams are used to 

document the wiring. A basic wiring diagram is shown in Figure 3.9. In this example the 

system would be supplied with AC power (120Vac or 220Vac) on the left and right rails. 



The lines of these diagrams are numbered, and these numbers are typically used to number 

wires when building the electrical system. The switch before line 010 is a master disconnect 

for the power to the entire system. A fuse is used after the disconnect to limit the 

maximum current drawn by the system. Line 020 of the diagram is used to control power 

to the outputs of the system. The stop button is normally closed, while the start button is 

normally open. The branch, and output of the rung are CR1, which is a master control 

relay. The PLC receives power on line 30 of the diagram. 

The inputs to the PLC are all AC, and are shown on lines 040 to 070. Notice that 

Input I:0/0 is a set of contacts on the MCR CR1. The three other inputs are a normally 

open push button (line 050), a limit switch (060) and a normally closed push button (070). 

After line 080 the MCR CR1 can apply power to the outputs. These power the relay outputs 

of the PLC to control a red indicator light (040), a green indicator light (050), a solenoid 

(060), and another relay (080). The relay on line 080 switches a relay that turn on 

another device drill station. 



L1 

N 

010 

020 

stop 

start 

CR1 

CR1 

MCR 

030 

L1 

PLC 

N 

040 

050 

060 

070 

080 

CR1 

PB1 

LS1 

PB2 

CR1 

I:0/0 

I:0/1 

I:0/2 

I:0/3 

ac com 

O:0/0 

O:0/1 

O:0/2 

O:0/3 

90-1 

100-1 

110-1 

120-1 

090 

100 

110 

120 

L1 

R 

L2 

G 

S1 

CR2 

090 

90-1 

035 

100 

100-1 

050 

110 

120 

110-1 

120-1 

060 

070 

130 

CR2 

Drill Station 

L1 N 

Figure 3.9 

A Ladder Wiring Diagram 



In the wiring diagram the choice of a normally close stop button and a normally 

open start button are intentional. Consider line 020 in the wiring diagram. If the stop button 

is pushed it will open the switch, and power will not be able to flow to the control 

relay and output power will shut off. If the stop button is damaged, say by a wire falling 

off, the power will also be lost and the system will shut down - safely. If the stop button 

used was normally open and this happened the system would continue to operate while the 

stop button was unable to shut down the power. Now consider the start button. If the button 

was damaged, say a wire was disconnected, it would be unable to start the system, thus 

leaving the system unstarted and safe. In summary, all buttons that stop a system should be 

normally closed, while all buttons that start a system should be normally open. 

3.5.1 JIC Wiring Symbols 

To standardize electrical schematics, the Joint International Committee (JIC) symbols 

were developed, these are shown in Figure 3.10, Figure 3.11 and Figure 3.12. 



disconnect 

circuit interrupter 

(3 phase AC) (3 phase AC) 

normally open 

limit switch 

normally closed 

limit switch 

breaker (3 phase AC) 

normally open 

push-button 


push-button 

double pole 

push-button 

mushroom head 

push-button 

F 

thermal 

overload relay 

fuse 

motor (3 phase AC) 

vacuum pressure 


liquid level 

normally open 

liquid level 


vacuum pressure 

normally open 

Figure 3.10 

JIC Schematic Symbols 



temperature 

normally open 

temperature 


flow 

normally open 

flow 


R 

relay contact 

normally open 

relay contact 


relay coil 

indicator lamp 

relay time delay on 

normally open 

relay time delay on 


relay time delay off 

normally open 

relay time delay off 


H1 

H3 

H2 

H4 

horn buzzer bell 

2-H 

X1 X2 

control transformer 

solenoid 

2-position 

hydraulic solenoid 

Male connector 

normally open 

proximity switch 


proximity switch 

Female connector 

Figure 3.11 




Resistor Tapped Resistor Variable Resistor 

(potentiometer) 

+ 

Rheostat 

(potentiometer) 

Capacitor 

Polarized Capacitor 

+ 

Variable Capacitor 

Capacitor 

Battery 

Crystal Thermocouple Antenna 

Shielded Conductor Shielded Grounded 

Common 

Coil or Inductor 

Coil with magnetic core 

Tapped Coil 

Transformer 

Transformer magnetic core 

Figure 3.12 




3.6 SUMMARY 

• PLC inputs condition AC or DC inputs to be detected by the logic of the PLC. 

• Outputs are transistors (DC), triacs (AC) or relays (AC and DC). 

• Input and output addresses are a function of the card location/tag name and input 

bit number. 

• Electrical system schematics are documented with diagrams that look like ladder 

logic. 


1. Can a PLC input switch a relay coil to control a motor? 

2. How do input and output cards act as an interface between the PLC and external devices? 

3. What is the difference between wiring a sourcing and sinking output? 

4. What is the difference between a motor starter and a contactor? 

5. Is AC or DC easier to interrupt? 

6. What can happen if the rated voltage on a device is exceeded? 

7. What are the benefits of input/output modules? 

8. (for electrical engineers) Explain the operation of AC input and output conditioning circuits. 

9. What will happen if a DC output is switched by an AC output. 

10. Explain why a stop button must be normally closed and a start button must be normally open. 

11. For the circuit shown in the figure below, list the input and output addresses for the PLC. If 

switch A controls the light, switch B the motor, and C the solenoid, write a simple ladder logic 



program. 

200 

201 

202 

100 

A 

203 

204 

205 

206 

207 

com 

solenoid 

valve 

+ 

24VDC 

101 

102 

103 

104 

105 

106 

107 

B 

C 

+ 

12VDC 

com 

12. We have a PLC rack with a 24 VDC input card in slot 3, and a 120VAC output card in slot 2. 

The inputs are to be connected to 4 push buttons. The outputs are to drive a 120VAC light bulb, 

a 240VAC motor, and a 24VDC operated hydraulic valve. Draw the electrical connections for 

the inputs and outputs. Show all other power supplies and other equipment/components 

required. 

13. You are planning a project that will be controlled by a PLC. Before ordering parts you decide 

to plan the basic wiring and select appropriate input and output cards. The devices that we will 

use for inputs are 2 limit switches, a push button and a thermal switch. The output will be for a 

24Vdc solenoid valve, a 110Vac light bulb, and a 220Vac 50HP motor. Sketch the basic wiring 

below including PLC cards. 

14. Add three push buttons as inputs to the figure below. You must also select a power supply, and 



show all necessary wiring. 

1 

com 

2 

com 

3 

com 

4 

com 

5 

com 

15. Three 120Vac outputs are to be connected to the output card below. Show the 120Vac source, 

and all wiring. 

V 

00 

01 

02 

03 

04 

05 

06 

07 

16. Sketch the wiring for PLC outputs that are listed below. 

- a double acting hydraulic solenoid valve (with two coils) 

- a 24Vdc lamp 

- a 120 Vac high current lamp 

- a low current 12Vdc motor 




1. no - a plc OUTPUT can switch a relay 

2. input cards are connected to sensors to determine the state of the system. Output cards are connected 

to actuators that can drive the process. 

3. sourcing outputs supply current that will pass through an electrical load to ground. Sinking 

inputs allow current to flow from the electrical load, to the common. 

4. a motor starter typically has three phases 

5. AC is easier, it has a zero crossing 

6. it will lead to premature failure 

7. by using separate modules, a PLC can be customized for different applications. If a single module 

fails, it can be replaced quickly, without having to replace the entire controller. 

8. AC input conditioning circuits will rectify an AC input to a DC waveform with a ripple. This 

will be smoothed, and reduced to a reasonable voltage level to drive an optocoupler. An AC 

output circuit will switch an AC output with a triac, or a relay. 

9. an AC output is a triac. When a triac output is turned off, it will not actually turn off until the 

AC voltage goes to 0V. Because DC voltages don’t go to 0V, it will never turn off. 

10. If a NC stop button is damaged, the machine will act as if the stop button was pushed and shut 

down safely. If a NO start button is damaged the machine will not be able to start. 

11. 

outputs: 

200 - light 

202 - motor 

204 - solenoid 

inputs: 

100 - switch A 

102 - switch B 

104 - switch C 

100 

102 

104 

200 

202 

210 



12. 

0 

1 

2 

3 

4 

5 

6 

7 

com 

+ 

24VDC 

- 

0 

1 

2 

3 

4 

5 

6 

7 

com 

13. 

0 

1 

0 

1 

+ 

24Vdc 

- 

2 

2 

3 

4 

3 

4 

hot 

220Vac 

neut. 

+ 

24VDC 

- 

5 

6 

7 

com 

5 

6 

7 

hot 

120Vac 

neut. 

Note: relays are used to reduce the total 

number of output cards 



14. 

24Vdc 

+ 

- 

1 

com 

2 

com 

3 

com 

4 

com 

5 

com 

15. 

V 

00 

01 

02 

03 

04 

05 

06 

07 

Load 1 

Load 2 

Load 3 

hot 

120Vac 

neut. 



16. 

relay output card 

00 

+ 

- 

power 

supply 

24Vdc 

01 

02 

03 

hot 

neut. 

power 

supply 

120Vac 

04 

+ 

- 

power 

supply 

12Vdc 


1. Describe what could happen if a normally closed start button was used on a system, and the 

wires to the button were cut. 

2. Describe what could happen if a normally open stop button was used on a system and the wires 

to the button were cut. 

3. a) For the input (’in’) and output (’out’) cards below, add three output lights and three normally 



open push button inputs. b) Redraw the outputs so that it uses a relay output card. 

in:0.I.Data.x 

out:1.O.Data.x 

0 

V 

1 

0 

2 

1 

+ 

- 

+ 

- 

3 

4 

5 

6 

7 

com 

2 

3 

4 

5 

6 

7 

4. Draw an electrical wiring (ladder) diagram for PLC outputs that are listed below. 

- a solenoid controlled hydraulic valve 

- a 24Vdc lamp 

- a 120 Vac high current lamp 

- a low current 12Vdc motor 

5. Draw an electrical ladder diagram for a PLC that has a PNP and an NPN sensor for inputs. The 

outputs are two small indicator lights. You should use proper symbols for all components. You 

must also include all safety devices including fuses, disconnects, MCRs, etc... 

6. Draw an electrical wiring diagram for a PLC controlling a system with an NPN and PNP input 

sensor. The outputs include an indicator light and a relay to control a 20A motor load. Include 

ALL safety circuitry. 


discrete sensors - 4.1 

4. LOGICAL SENSORS 

Topics: 

• Sensor wiring; switches, TTL, sourcing, sinking 

• Proximity detection; contact switches, photo-optics, capacitive, inductive and 

ultrasonic 

Objectives: 

• Understand the different types of sensor outputs. 

• Know the basic sensor types and understand application issues. 


Sensors allow a PLC to detect the state of a process. Logical sensors can only 

detect a state that is either true or false. Examples of physical phenomena that are typically 

detected are listed below. 

• inductive proximity - is a metal object nearby? 

• capacitive proximity - is a dielectric object nearby? 

• optical presence - is an object breaking a light beam or reflecting light? 

• mechanical contact - is an object touching a switch? 

Recently, the cost of sensors has dropped and they have become commodity items, 

typically between $50 and $100. They are available in many forms from multiple vendors 

such as Allen Bradley, Omron, Hyde Park and Turck. In applications sensors are interchangeable 

between PLC vendors, but each sensor will have specific interface requirements. 

This chapter will begin by examining the various electrical wiring techniques for 

sensors, and conclude with an examination of many popular sensor types. 

4.2 SENSOR WIRING 

When a sensor detects a logical change it must signal that change to the PLC. This 

is typically done by switching a voltage or current on or off. In some cases the output of 

the sensor is used to switch a load directly, completely eliminating the PLC. Typical out- 



puts from sensors (and inputs to PLCs) are listed below in relative popularity. 

Sinking/Sourcing - Switches current on or off. 

Plain Switches - Switches voltage on or off. 

Solid State Relays - These switch AC outputs. 

TTL (Transistor Transistor Logic) - Uses 0V and 5V to indicate logic levels. 

4.2.1 Switches 

The simplest example of sensor outputs are switches and relays. A simple example 

is shown in Figure 4.1. 

24 Vdc 

Power 

Supply 

+ 

- 

normally open push-button 

sensor 

V+ 

V- 

relay 

output 


24V DC 

00 

01 

02 

03 

04 

05 

06 

07 

COM 

Figure 4.1 

An Example of Switched Sensors 

In the figure a NO contact switch is connected to input 01. A sensor with a relay 

output is also shown. The sensor must be powered separately, therefore the V+ and V- terminals 

are connected to the power supply. The output of the sensor will become active 

when a phenomenon has been detected. This means the internal switch (probably a relay) 

will be closed allowing current to flow and the positive voltage will be applied to input 06. 



4.2.2 Transistor Transistor Logic (TTL) 

Transistor-Transistor Logic (TTL) is based on two voltage levels, 0V for false and 

5V for true. The voltages can actually be slightly larger than 0V, or lower than 5V and still 

be detected correctly. This method is very susceptible to electrical noise on the factory 

floor, and should only be used when necessary. TTL outputs are common on electronic 

devices and computers, and will be necessary sometimes. When connecting to other 

devices simple circuits can be used to improve the signal, such as the Schmitt trigger in 

Figure 4.2. 

Vi 

Vo 

Vi 

Vo 

Figure 4.2 

A Schmitt Trigger 

A Schmitt trigger will receive an input voltage between 0-5V and convert it to 0V 

or 5V. If the voltage is in an ambiguous range, about 1.5-3.5V it will be ignored. 

If a sensor has a TTL output the PLC must use a TTL input card to read the values. 

If the TTL sensor is being used for other applications it should be noted that the maximum 

current output is normally about 20mA. 

4.2.3 Sinking/Sourcing 

Sinking sensors allow current to flow into the sensor to the voltage common, while 

sourcing sensors allow current to flow out of the sensor from a positive source. For both of 

these methods the emphasis is on current flow, not voltage. By using current flow, instead 

of voltage, many of the electrical noise problems are reduced. 

When discussing sourcing and sinking we are referring to the output of the sensor 

that is acting like a switch. In fact the output of the sensor is normally a transistor, that will 

act like a switch (with some voltage loss). A PNP transistor is used for the sourcing output, 

and an NPN transistor is used for the sinking input. When discussing these sensors the 



term sourcing is often interchanged with PNP, and sinking with NPN. A simplified example 

of a sinking output sensor is shown in Figure 4.3. The sensor will have some part that 

deals with detection, this is on the left. The sensor needs a voltage supply to operate, so a 

voltage supply is needed for the sensor. If the sensor has detected some phenomenon then 

it will trigger the active line. The active line is directly connected to an NPN transistor. 

(Note: for an NPN transistor the arrow always points away from the center.) If the voltage 

to the transistor on the active line is 0V, then the transistor will not allow current to flow 

into the sensor. If the voltage on the active line becomes larger (say 12V) then the transistor 

will switch on and allow current to flow into the sensor to the common. 

physical 

phenomenon 

Sensor 

and 

Detector 

V+ 

Active 

Line 

sensor 

output 

V+ 

NPN 

current flows in 

when switched on 

V- 

V- 

Aside: The sensor responds to a physical phenomenon. If the sensor is inactive (nothing 

detected) then the active line is low and the transistor is off, this is like an open 

switch. That means the NPN output will have no current in/out. When the sensor is 

active, it will make the active line high. This will turn on the transistor, and effectively 

close the switch. This will allow current to flow into the sensor to ground 

(hence sinking). The voltage on the NPN output will be pulled down to V-. Note: the 

voltage will always be 1-2V higher because of the transistor. When the sensor is off, 

the NPN output will float, and any digital circuitry needs to contain a pull-up resistor. 

Figure 4.3 

A Simplified NPN/Sinking Sensor 

Sourcing sensors are the complement to sinking sensors. The sourcing sensors use 

a PNP transistor, as shown in Figure 4.4. (Note: PNP transistors are always drawn with the 

arrow pointing to the center.) When the sensor is inactive the active line stays at the V+ 



value, and the transistor stays switched off. When the sensor becomes active the active 

line will be made 0V, and the transistor will allow current to flow out of the sensor. 

physical 

phenomenon 

Sensor 

and 

Detector 

V+ 

Active 

Line 

sensor 

output 

V+ 

PNP 

current flows out 

when switched on 

V- 

V- 

Aside: The sensor responds to the physical phenomenon. If the sensor is inactive (nothing 

detected) then the active line is high and the transistor is off, this is like an open switch. 

That means the PNP output will have no current in/out. When the sensor is active, it 

will make the active line high. This will turn on the transistor, and effectively close the 

switch. This will allow current to flow from V+ through the sensor to the output (hence 

sourcing). The voltage on the PNP output will be pulled up to V+. Note: the voltage 

will always be 1-2V lower because of the transistor. When off, the PNP output will 

float, if used with digital circuitry a pull-down resistor will be needed. 

Figure 4.4 

A Simplified Sourcing/PNP Sensor 

Most NPN/PNP sensors are capable of handling currents up to a few amps, and 

they can be used to switch loads directly. (Note: always check the documentation for rated 

voltages and currents.) An example using sourcing and sinking sensors to control lights is 

shown in Figure 4.5. (Note: This example could be for a motion detector that turns on 

lights in dark hallways.) 



sensor V+ 

V+ 

NPN 

power 

supply 

sinking 

V- 

V- (common) 

sensor V+ 

V+ 

PNP 

power 

supply 

sourcing 

V- 

V- (common) 

Note: remember to check the current and voltage ratings for the sensors. 

Note: When marking power terminals, there will sometimes be two sets of 

markings. The more standard is V+ and COM, but sometimes you will see 

devices and power supplies without a COM (common), in this case assume 

the V- is the common. 

Figure 4.5 

Direct Control Using NPN/PNP Sensors 

In the sinking system in Figure 4.5 the light has V+ applied to one side. The other 

side is connected to the NPN output of the sensor. When the sensor turns on the current 

will be able to flow through the light, into the output to V- common. (Note: Yes, the current 

will be allowed to flow into the output for an NPN sensor.) In the sourcing arrangement 

the light will turn on when the output becomes active, allowing current to flow from 

the V+, thought the sensor, the light and to V- (the common). 

At this point it is worth stating the obvious - The output of a sensor will be an input 

for a PLC. And, as we saw with the NPN sensor, this does not necessarily indicate where 

current is flowing. There are two viable approaches for connecting sensors to PLCs. The 

first is to always use PNP sensors and normal voltage input cards. The second option is to 

purchase input cards specifically designed for sourcing or sinking sensors. An example of 

a PLC card for sinking sensors is shown in Figure 4.6. 



PLC Input Card for Sinking Sensors 

Internal Card Electronics 

PLC Data Bus 

+V 

00 

current flow 

+V 

NPN 

-V 

NPN 

sensor 

+V 

power 

supply 

-V 

01 Note: When a PLC input card does not have a 

common but it has a V+ instead, it can be 

used for NPN sensors. In this case the current 

will flow out of the card (sourcing) and 

External Electrical we must switch it to ground. 

ASIDE: This card is shown with 2 optocouplers (one for each output). Inside these 

devices the is an LED and a phototransistor, but no electrical connection. These 

devices are used to isolate two different electrical systems. In this case they protect 

the 5V digital levels of the PLC computer from the various external voltages 

and currents. 

Figure 4.6 

A PLC Input Card for Sinking Sensors 

The dashed line in the figure represents the circuit, or current flow path when the 

sensor is active. This path enters the PLC input card first at a V+ terminal (Note: there is 

no common on this card) and flows through an optocoupler. This current will use light to 

turn on a phototransistor to tell the computer in the PLC the input current is flowing. The 

current then leaves the card at input 00 and passes through the sensor to V-. When the sensor 

is inactive the current will not flow, and the light in the optocoupler will be off. The 

optocoupler is used to help protect the PLC from electrical problems outside the PLC. 

4.7. 

The input cards for PNP sensors are similar to the NPN cards, as shown in Figure 



PLC Input Card for Sourcing Sensors 

Internal Card Electronics 

00 

01 

com 

+V 

PNP 

-V 

PNP 

sensor 

current flow 

+V 

power 

supply 

-V 

Note: When we have a PLC input card that has 

a common then we can use PNP sensors. In 

this case the current will flow into the card 

and then out the common to the power supply. 

Figure 4.7 

PLC Input Card for Sourcing Sensors 

The current flow loop for an active sensor is shown with a dashed line. Following 

the path of the current we see that it begins at the V+, passes through the sensor, in the 

input 00, through the optocoupler, out the common and to the V-. 

Wiring is a major concern with PLC applications, so to reduce the total number of 

wires, two wire sensors have become popular. But, by integrating three wires worth of 

function into two, we now couple the power supply and sensing functions into one. Two 

wire sensors are shown in Figure 4.8. 




for Sourcing Sensors 

00 

+V 

-V 

two wire 

sensor 

01 

+V 

power 

supply 

-V 

com 

V+ 

Note: These sensors require a certain leakage 

current to power the electronics. 


for Sinking Sensors 

00 

01 

+V 

-V 

two wire 

sensor 

+V 

power 

supply 

-V 

Figure 4.8 

Two Wire Sensors 

A two wire sensor can be used as either a sourcing or sinking input. In both of 

these arrangements the sensor will require a small amount of current to power the sensor, 

but when active it will allow more current to flow. This requires input cards that will allow 

a small amount of current to flow (called the leakage current), but also be able to detect 

when the current has exceeded a given value. 



When purchasing sensors and input cards there are some important considerations. 

Most modern sensors have both PNP and NPN outputs, although if the choice is not available, 

PNP is the more popular choice. PLC cards can be confusing to buy, as each vendor 

refers to the cards differently. To avoid problems, look to see if the card is specifically for 

sinking or sourcing sensors, or look for a V+ (sinking) or COM (sourcing). Some vendors 

also sell cards that will allow you to have NPN and PNP inputs mixed on the same card. 

When drawing wiring diagrams the symbols in Figure 4.9 are used for sinking and 

sourcing proximity sensors. Notice that in the sinking sensor when the switch closes 

(moves up to the terminal) it contacts the common. Closing the switch in the sourcing sensor 

connects the output to the V+. On the physical sensor the wires are color coded as indicated 

in the diagram. The brown wire is positive, the blue wire is negative and the output 

is white for sinking and black for sourcing. The outside shape of the sensor may change 

for other devices, such as photo sensors which are often shown as round circles. 

NPN (sinking) 

V+ 

brown 

NPNwhite 

blue 

V- 

PNP (sourcing) 

brown 

black 

V+ PNP 

blue 

V- 

Figure 4.9 

Sourcing and Sinking Schematic Symbols 

4.2.4 Solid State Relays 

Solid state relays switch AC currents. These are relatively inexpensive and are 

available for large loads. Some sensors and devices are available with these as outputs. 



4.3 PRESENCE DETECTION 

There are two basic ways to detect object presence; contact and proximity. Contact 

implies that there is mechanical contact and a resulting force between the sensor and the 

object. Proximity indicates that the object is near, but contact is not required. The following 

sections examine different types of sensors for detecting object presence. These sensors 

account for a majority of the sensors used in applications. 

4.3.1 Contact Switches 

Contact switches are available as normally open and normally closed. Their housings 

are reinforced so that they can take repeated mechanical forces. These often have rollers 

and wear pads for the point of contact. Lightweight contact switches can be purchased 

for less than a dollar, but heavy duty contact switches will have much higher costs. Examples 

of applications include motion limit switches and part present detectors. 

4.3.2 Reed Switches 

Reed switches are very similar to relays, except a permanent magnet is used 

instead of a wire coil. When the magnet is far away the switch is open, but when the magnet 

is brought near the switch is closed as shown in Figure 4.10. These are very inexpensive 

an can be purchased for a few dollars. They are commonly used for safety screens and 

doors because they are harder to trick than other sensors. 

Note: With this device the magnet is moved towards the reed switch. As it gets 

closer the switch will close. This allows proximity detection without contact, but 

requires that a separate magnet be attached to a moving part. 

Figure 4.10 

Reed Switch 



4.3.3 Optical (Photoelectric) Sensors 

Light sensors have been used for almost a century - originally photocells were 

used for applications such as reading audio tracks on motion pictures. But modern optical 

sensors are much more sophisticated. 

Optical sensors require both a light source (emitter) and detector. Emitters will 

produce light beams in the visible and invisible spectrums using LEDs and laser diodes. 

Detectors are typically built with photodiodes or phototransistors. The emitter and detector 

are positioned so that an object will block or reflect a beam when present. A basic optical 

sensor is shown in Figure 4.11. 

square wave 

smaller signal 

+V +V 

oscillator 

LED 

lens 

light 

lens 

amplifier 

demodulator 

detector and 

switching circuits 

phototransistor 

Figure 4.11 

A Basic Optical Sensor 

In the figure the light beam is generated on the left, focused through a lens. At the 

detector side the beam is focused on the detector with a second lens. If the beam is broken 

the detector will indicate an object is present. The oscillating light wave is used so that the 

sensor can filter out normal light in the room. The light from the emitter is turned on and 

off at a set frequency. When the detector receives the light it checks to make sure that it is 

at the same frequency. If light is being received at the right frequency then the beam is not 

broken. The frequency of oscillation is in the KHz range, and too fast to be noticed. A side 

effect of the frequency method is that the sensors can be used with lower power at longer 

distances. 

An emitter can be set up to point directly at a detector, this is known as opposed 

mode. When the beam is broken the part will be detected. This sensor needs two separate 



components, as shown in Figure 4.12. This arrangement works well with opaque and 

reflective objects with the emitter and detector separated by distances of up to hundreds of 

feet. 

emitter object detector 

Figure 4.12 

Opposed Mode Optical Sensor 

Having the emitter and detector separate increases maintenance problems, and 

alignment is required. A preferred solution is to house the emitter and detector in one unit. 

But, this requires that light be reflected back as shown in Figure 4.13. These sensors are 

well suited to larger objects up to a few feet away. 

emitter 

reflector 

detector 

reflector 

emitter 

object 

detector 

Note: the reflector is constructed with polarizing screens oriented at 90 deg. angles. If 

the light is reflected back directly the light does not pass through the screen in front 

of the detector. The reflector is designed to rotate the phase of the light by 90 deg., 

so it will now pass through the screen in front of the detector. 

Figure 4.13 

Retroreflective Optical Sensor 



In the figure, the emitter sends out a beam of light. If the light is returned from the 

reflector most of the light beam is returned to the detector. When an object interrupts the 

beam between the emitter and the reflector the beam is no longer reflected back to the 

detector, and the sensor becomes active. A potential problem with this sensor is that 

reflective objects could return a good beam. This problem is overcome by polarizing the 

light at the emitter (with a filter), and then using a polarized filter at the detector. The 

reflector uses small cubic reflectors and when the light is reflected the polarity is rotated 

by 90 degrees. If the light is reflected off the object the light will not be rotated by 90 

degrees. So the polarizing filters on the emitter and detector are rotated by 90 degrees, as 

shown in Figure 4.14. The reflector is very similar to reflectors used on bicycles. 

have filters for 

emitted light 

rotated by 90 deg. 

emitter 

detector 

light reflected with 

same polarity 

object 

reflector 

emitter 

detector 

light rotated by 90 deg. 

reflector 

Figure 4.14 

Polarized Light in Retroreflective Sensors 

For retroreflectors the reflectors are quite easy to align, but this method still 

requires two mounted components. A diffuse sensors is a single unit that does not use a 

reflector, but uses focused light as shown in Figure 4.15. 



emitter 

object 

detector 

Note: with diffuse reflection the light is scattered. This reduces the quantity of light 

returned. As a result the light needs to be amplified using lenses. 

Figure 4.15 

Diffuse Optical Sensor 

Diffuse sensors use light focused over a given range, and a sensitivity adjustment 

is used to select a distance. These sensors are the easiest to set up, but they require well 

controlled conditions. For example if it is to pick up light and dark colored objects problems 

would result. 

When using opposed mode sensors the emitter and detector must be aligned so that 

the emitter beam and detector window overlap, as shown in Figure 4.16. Emitter beams 

normally have a cone shape with a small angle of divergence (a few degrees of less). 

Detectors also have a cone shaped volume of detection. Therefore when aligning opposed 

mode sensor care is required not just to point the emitter at the detector, but also the detector 

at the emitter. Another factor that must be considered with this and other sensors is that 

the light intensity decreases over distance, so the sensors will have a limit to separation 

distance. 



effective beam 

effective 

detector 

angle 

detector 

emitter 

effective 

beam angle 

alignment 

is required 

intensity 

∝ ---- 

1 

r 2 

Figure 4.16 

Beam Divergence and Alignment 

If an object is smaller than the width of the light beam it will not be able to block 

the beam entirely when it is in front as shown in Figure 4.17. This will create difficulties 

in detection, or possibly stop detection altogether. Solutions to this problem are to use narrower 

beams, or wider objects. Fiber optic cables may be used with an opposed mode optical 

sensor to solve this problem, however the maximum effective distance is reduced to a 

couple feet. 

emitter 

object 

detector 

the smaller beam width is good (but harder to align 

Figure 4.17 

The Relationship Between Beam Width and Object Size 

Separated sensors can detect reflective parts using reflection as shown in Figure 

4.18. The emitter and detector are positioned so that when a reflective surface is in position 

the light is returned to the detector. When the surface is not present the light does not 

return. 



emitter 

reflective surface 

detector 

Figure 4.18 

Detecting Reflecting Parts 

Other types of optical sensors can also focus on a single point using beams that 

converge instead of diverge. The emitter beam is focused at a distance so that the light 

intensity is greatest at the focal distance. The detector can look at the point from another 

angle so that the two centerlines of the emitter and detector intersect at the point of interest. 

If an object is present before or after the focal point the detector will not see the 

reflected light. This technique can also be used to detect multiple points and ranges, as 

shown in Figure 4.20 where the net angle of refraction by the lens determines which detector 

is used. This type of approach, with many more detectors, is used for range sensing 

systems. 

emitter 

focal point 

detector 

Figure 4.19 

Point Detection Using Focused Optics 



The optical reflectivity of objects varies from material to material as shown in Figemitter 

lens 

distance 1 distance 2 

detector 2 

detector 1 

lens 

Figure 4.20 

Multiple Point Detection Using Optics 

Some applications do not permit full sized photooptic sensors to be used. Fiber 

optics can be used to separate the emitters and detectors from the application. Some vendors 

also sell photosensors that have the phototransistors and LEDs separated from the 

electronics. 

Light curtains are an array of beams, set up as shown in Figure 4.21. If any of the 

beams are broken it indicates that somebody has entered a workcell and the machine needs 

to be shut down. This is an inexpensive replacement for some mechanical cages and barriers. 

Figure 4.21 

A Light Curtain 



ure 4.22. These values show the percentage of incident light on a surface that is reflected. 

These values can be used for relative comparisons of materials and estimating changes in 

sensitivity settings for sensors. 

Reflectivity 

nonshiny materials 

shiny/transparent materials 

Kodak white test card 

white paper 

kraft paper, cardboard 

lumber (pine, dry, clean) 

rough wood pallet 

beer foam 

opaque black nylon 

black neoprene 

black rubber tire wall 

clear plastic bottle 

translucent brown plastic bottle 

opaque white plastic 

unfinished aluminum 

straightened aluminum 

unfinished black anodized aluminum 

stainless steel microfinished 

stainless steel brushed 

90% 

80% 

70% 

75% 

20% 

70% 

14% 

4% 

1.5% 

40% 

60% 

87% 

140% 

105% 

115% 

400% 

120% 

Note: For shiny and transparent materials the reflectivity can be higher 

than 100% because of the return of ambient light. 

Figure 4.22 

Table of Reflectivity Values for Different Materials [Banner Handbook of 

Photoelectric Sensing] 

4.3.4 Capacitive Sensors 

Capacitive sensors are able to detect most materials at distances up to a few centimeters. 

Recall the basic relationship for capacitance. 



C 

= 

Ak 

----- 

d 

where, C = capacitance (Farads) 

k = dielectric constant 

A = area of plates 

d = distance between plates (electrodes) 

In the sensor the area of the plates and distance between them is fixed. But, the 

dielectric constant of the space around them will vary as different materials are brought 

near the sensor. An illustration of a capacitive sensor is shown in Figure 4.23. an oscillating 

field is used to determine the capacitance of the plates. When this changes beyond a 

selected sensitivity the sensor output is activated. 

electric 

field 

+V 

object 

electrode 

oscillator 

load 

switching 

electrode 

detector 

NOTE: For this sensor the proximity of any material near the electrodes will 

increase the capacitance. This will vary the magnitude of the oscillating signal 

and the detector will decide when this is great enough to determine proximity. 

Figure 4.23 

A Capacitive Sensor 

These sensors work well for insulators (such as plastics) that tend to have high 

dielectric coefficients, thus increasing the capacitance. But, they also work well for metals 

because the conductive materials in the target appear as larger electrodes, thus increasing 

the capacitance as shown in Figure 4.24. In total the capacitance changes are normally in 

the order of pF. 



electrode 

metal 

electrode 

dielectric 

electrode 

electrode 

Figure 4.24 

Dielectrics and Metals Increase the Capacitance 

The sensors are normally made with rings (not plates) in the configuration shown 

in Figure 4.25. In the figure the two inner metal rings are the capacitor electrodes, but a 

third outer ring is added to compensate for variations. Without the compensator ring the 

sensor would be very sensitive to dirt, oil and other contaminants that might stick to the 

sensor. 

electrode 

compensating 

electrode 

Note: the compensating electrode is used for 

negative feedback to make the sensor 

more resistant to variations, such as contaminations 

on the face of the sensor. 

Figure 4.25 

Electrode Arrangement for Capacitive Sensors 

A table of dielectric properties is given in Figure 4.26. This table can be used for 

estimating the relative size and sensitivity of sensors. Also, consider a case where a pipe 

would carry different fluids. If their dielectric constants are not very close, a second sensor 

may be desired for the second fluid. 



Material 

Constant 

Material 

Constant 

ABS resin pellet 

acetone 

acetyl bromide 

acrylic resin 

air 

alcohol, industrial 

alcohol, isopropyl 

ammonia 

aniline 

aqueous solutions 

ash (fly) 

bakelite 

barley powder 

benzene 

benzyl acetate 

butane 

cable sealing compound 

calcium carbonate 

carbon tetrachloride 

celluloid 

cellulose 

cement 

cement powder 

cereal 

charcoal 

chlorine, liquid 

coke 

corn 

ebonite 

epoxy resin 

ethanol 

ethyl bromide 

ethylene glycol 

flour 

FreonTM R22,R502 liq. 

gasoline 

glass 

glass, raw material 

glycerine 

1.5-2.5 

19.5 

16.5 

2.7-4.5 

1.0 

16-31 

18.3 

15-25 

5.5-7.8 

50-80 

1.7 

3.6 

3.0-4.0 

2.3 

5 

1.4 

2.5 

9.1 

2.2 

3.0 

3.2-7.5 

1.5-2.1 

5-10 

3-5 

1.2-1.8 

2.0 

1.1-2.2 

5-10 

2.7-2.9 

2.5-6 

24 

4.9 

38.7 

2.5-3.0 

6.1 

2.2 

3.1-10 

2.0-2.5 

47 

hexane 

hydrogen cyanide 

hydrogen peroxide 

isobutylamine 

lime, shell 

marble 

melamine resin 

methane liquid 

methanol 

mica, white 

milk, powdered 

nitrobenzene 

neoprene 

nylon 

oil, for transformer 

oil, paraffin 

oil, peanut 

oil, petroleum 

oil, soybean 

oil, turpentine 

paint 

paraffin 

paper 

paper, hard 

paper, oil saturated 

perspex 

petroleum 

phenol 

phenol resin 

polyacetal (Delrin TM) 

polyamide (nylon) 

polycarbonate 

polyester resin 

polyethylene 

polypropylene 

polystyrene 

polyvinyl chloride resin 

porcelain 

press board 

1.9 

95.4 

84.2 

4.5 

1.2 

8.0-8.5 

4.7-10.2 

1.7 

33.6 

4.5-9.6 

3.5-4 

36 

6-9 

4-5 

2.2-2.4 

2.2-4.8 

3.0 

2.1 

2.9-3.5 

2.2 

5-8 

1.9-2.5 

1.6-2.6 

4.5 

4.0 

3.2-3.5 

2.0-2.2 

9.9-15 

4.9 

3.6 

2.5 

2.9 

2.8-8.1 

2.3 

2.0-2.3 

3.0 

2.8-3.1 

4.4-7 

2-5 



Material 

Constant 

Material 

Constant 

quartz glass 

rubber 

salt 

sand 

shellac 

silicon dioxide 

silicone rubber 

silicone varnish 

styrene resin 

sugar 

sugar, granulated 

sulfur 

sulfuric acid 

3.7 

2.5-35 

6.0 

3-5 

2.0-3.8 

4.5 

3.2-9.8 

2.8-3.3 

2.3-3.4 

3.0 

1.5-2.2 

3.4 

84 

Teflon (TM), PCTFE 

Teflon (TM), PTFE 

toluene 

trichloroethylene 

urea resin 

urethane 

vaseline 

water 

wax 

wood, dry 

wood, pressed board 

wood, wet 

xylene 

2.3-2.8 

2.0 

2.3 

3.4 

6.2-9.5 

3.2 

2.2-2.9 

48-88 

2.4-6.5 

2-7 

2.0-2.6 

10-30 

2.4 

Figure 4.26 

Dielectric Constants of Various Materials [Turck Proximity Sensors Guide] 

The range and accuracy of these sensors are determined mainly by their size. 

Larger sensors can have diameters of a few centimeters. Smaller ones can be less than a 

centimeter across, and have smaller ranges, but more accuracy. 

4.3.5 Inductive Sensors 

Inductive sensors use currents induced by magnetic fields to detect nearby metal 

objects. The inductive sensor uses a coil (an inductor) to generate a high frequency magnetic 

field as shown in Figure 4.27. If there is a metal object near the changing magnetic 

field, current will flow in the object. This resulting current flow sets up a new magnetic 

field that opposes the original magnetic field. The net effect is that it changes the inductance 

of the coil in the inductive sensor. By measuring the inductance the sensor can determine 

when a metal have been brought nearby. 

These sensors will detect any metals, when detecting multiple types of metal multiple 

sensors are often used. 



metal 

inductive coil 

+V 

oscillator 

and level 

detector 

output 

switching 

Note: these work by setting up a high frequency field. If a target nears the field will 

induce eddy currents. These currents consume power because of resistance, so 

energy is in the field is lost, and the signal amplitude decreases. The detector examines 

filed magnitude to determine when it has decreased enough to switch. 

Figure 4.27 

Inductive Proximity Sensor 

The sensors can detect objects a few centimeters away from the end. But, the 

direction to the object can be arbitrary as shown in Figure 4.28. The magnetic field of the 

unshielded sensor covers a larger volume around the head of the coil. By adding a shield 

(a metal jacket around the sides of the coil) the magnetic field becomes smaller, but also 

more directed. Shields will often be available for inductive sensors to improve their directionality 

and accuracy. 



shielded 

unshielded 

Figure 4.28 

Shielded and Unshielded Sensors 

4.3.6 Ultrasonic 

An ultrasonic sensor emits a sound above the normal hearing threshold of 16KHz. 

The time that is required for the sound to travel to the target and reflect back is proportional 

to the distance to the target. The two common types of sensors are; 

electrostatic - uses capacitive effects. It has longer ranges and wider bandwidth, 

but is more sensitive to factors such as humidity. 

piezoelectric - based on charge displacement during strain in crystal lattices. These 

are rugged and inexpensive. 

These sensors can be very effective for applications such as fluid levels in tanks 

and crude distance measurement. 

4.3.7 Hall Effect 

Hall effect switches are basically transistors that can be switched by magnetic 

fields. Their applications are very similar to reed switches, but because they are solid state 

they tend to be more rugged and resist vibration. Automated machines often use these to 

do initial calibration and detect end stops. 



4.3.8 Fluid Flow 

We can also build more complex sensors out of simpler sensors. The example in 

Figure 4.29 shows a metal float in a tapered channel. As the fluid flow rate increases the 

pressure forces the float upwards. The tapered shape of the float ensures an equilibrium 

position proportional to flowrate. An inductive proximity sensor can be positioned so that 

it will detect when the float has reached a certain height, and the system has reached a 

given flowrate. 

fluid flow out 

metal 

float 

inductive proximity sensor 

fluid flow in 

As the fluid flow increases the float is forced higher. A proximity sensor 

can be used to detect when the float reaches a certain height. 

Figure 4.29 

Flow Rate Detection With an Inductive Proximity Switch 

4.4 SUMMARY 

• Sourcing sensors allow current to flow out from the V+ supply. 

• Sinking sensors allow current to flow in to the V- supply. 

• Photo-optical sensors can use reflected beams (retroreflective), an emitter and 

detector (opposed mode) and reflected light (diffuse) to detect a part. 

• Capacitive sensors can detect metals and other materials. 

• Inductive sensors can detect metals. 

• Hall effect and reed switches can detect magnets. 

• Ultrasonic sensors use sound waves to detect parts up to meters away. 




1. Given a clear plastic bottle, list 3 different types of sensors that could be used to detect it. 

2. List 3 significant trade-offs between inductive, capacitive and photooptic sensors. 

3. Why is a sinking output on a sensor not like a normal switch? 

4. a) Sketch the connections needed for the PLC inputs and outputs below. The outputs include a 

24Vdc light and a 120Vac light. The inputs are from 2 NO push buttons, and also from an optical 

sensor that has both PNP and NPN outputs. 

24Vdc 

outputs 

V+ 

0 

+ 

24VDC 

- 

24Vdc 

inputs 

0 

1 

1 

2 

3 

4 

5 

6 

7 

OR 

2 

3 

4 

5 

6 

7 

com 

b) State why you used either the NPN or PNP output on the sensor. 

5. Select a sensor to pick up a transparent plastic bottle from a manufacturer. Copy or print the 

specifications, and then draw a wiring diagram that shows how it will be wired to an appropriate 

PLC input card. 

6. Sketch the wiring to connect a power supply and PNP sensor to the PLC input card shown 



below. 

00 

01 

02 

+ 

24VDC 

- 

03 

04 

05 

06 

07 

COM 

7. Sketch the wiring for inputs that include the following items. 

3 normally open push buttons 

1 thermal relay 

3 sinking sensors 

1 sourcing sensor 

8. A PLC has eight 10-60Vdc inputs, and four relay outputs. It is to be connected to the following 

devices. Draw the required wiring. 

• Two inductive proximity sensors with sourcing and sinking outputs. 

• A NO run button and NC stop button. 

• A 120Vac light. 

• A 24Vdc solenoid. 



in:2.I.Data.x 

0 


0 

1 

2 

1 

3 

4 

2 

5 

6 

3 

7 

com 

9. Draw a ladder wiring diagram (as done in the lab) for a system that has two push-buttons and a 

sourcing/sinking proximity sensors for 10-60Vdc inputs and two 120Vac output lights. Don’t 



forget to include hard-wired start and stop buttons with an MCR. 

L1 

N 

L1 

PLC 

N 

I.0 

I.1 

I.2 

I.3 

com 

Vac 

O.0 

O.1 

O.2 

O.3 


1. capacitive proximity, contact switch, photo-optic retroreflective/diffuse, ultrasonic 

2. materials that can be sensed, environmental factors such as dirt, distance to object 

3. the sinking output will pass only DC in a single direction, whereas a switch can pass AC and 

DC. 



4. 

24Vdc 

outputs 

V+ 

0 

1 

2 

3 

4 

5 

6 

7 

hot 

120Vac 

neut. 

+ 

24VDC 

- 

24Vdc 

inputs 

0 

1 

2 

3 

4 

5 

6 

7 

com 

b) the PNP output was selected. because it will supply current, while the input card 

requires it. The dashed line indicates the current flow through the sensor and input card. 



5. 

A transparent bottle can be picked up with a capacitive, ultrasonic, diffuse optical sensor. 

A particular model can be selected at a manufacturers web site (eg., www.banner.com, 

www.hydepark.com, www.ab.com, etc.) The figure below shows the 

sensor connected to a sourcing PLC input card - therefore the sensor must be sinking, 

NPN. 

+ 

24VDC 

- 

V+ 

0 

1 

2 

3 

4 

5 

6 

7 



6. 

00 

01 

02 

+ 

24VDC 

- 

03 

04 

05 

06 

07 

COM 



7. 

00 

01 

02 

03 

04 

05 

+ 

24Vdc 

- 

power 

supply 

06 

07 

COM 

V+ 

00 

+ 

24Vdc 

- 

power 

supply 

01 

02 

03 



8. 

+ 

power 

supply 

- 

V+ 

PNP 

V- 

in:2.I.Data.x 

0 

1 

2 

3 

4 


0 

1 

2 

+ 

- 

power 

supply 

120Vac 

power 

neut. supply 

V+ 

PNP 

V- 

5 

6 

3 

7 

com 



9. 

L1 

N 

stop 

start 

MCR 

C1 

C1 

PB1 

PB2 

PR1 

L1 

I.0 

I.1 

I.2 

PLC 

N 

Vac 

O.0 

O.1 

L1 

L2 

C1 

I.3 

com 

O.2 

O.3 

V+ V- 

L1 

N 


1. What type of sensor should be used if it is to detect small cosmetic case mirrors as they pass 

along a belt. Explain your choice. 

2. Summarize the tradeoffs between capacitive, inductive and optical sensors in a table. 

3. Clearly and concisely explain the difference between wiring PNP and NPN sensors. 



4. a) Show the wiring for the following sensor, and circle the output that you are using, NPN or 

PNP. Redraw the sensor using the correct symbol for the sourcing or sinking sensor chosen. 

24Vdc 

inputs 

+ 

24VDC 

V+ 

- 

0 

1 

2 

3 

4 

5 

6 

7 

5. A PLC has three NPN and two PNP sensors as inputs, and outputs to control a 24Vdc solenoid 

and a small 115Vac motor. Develop the required wiring for the inputs and outputs. 


discrete actuators - 5.1 

5. LOGICAL ACTUATORS 

Topics: 

• Solenoids, valves and cylinders 

• Hydraulics and pneumatics 

• Other actuators 

Objectives: 

• Be aware of various actuators available. 


Actuators Drive motions in mechanical systems. Most often this is by converting 

electrical energy into some form of mechanical motion. 

5.2 SOLENOIDS 

Solenoids are the most common actuator components. The basic principle of operation 

is there is a moving ferrous core (a piston) that will move inside wire coil as shown 

in Figure 5.1. Normally the piston is held outside the coil by a spring. When a voltage is 

applied to the coil and current flows, the coil builds up a magnetic field that attracts the 

piston and pulls it into the center of the coil. The piston can be used to supply a linear 

force. Well known applications of these include pneumatic values and car door openers. 

current off 

current on 

Figure 5.1 

A Solenoid 



As mentioned before, inductive devices can create voltage spikes and may need 

snubbers, although most industrial applications have low enough voltage and current ratings 

they can be connected directly to the PLC outputs. Most industrial solenoids will be 

powered by 24Vdc and draw a few hundred mA. 

5.3 VALVES 

The flow of fluids and air can be controlled with solenoid controlled valves. An 

example of a solenoid controlled valve is shown in Figure 5.2. The solenoid is mounted on 

the side. When actuated it will drive the central spool left. The top of the valve body has 

two ports that will be connected to a device such as a hydraulic cylinder. The bottom of the 

valve body has a single pressure line in the center with two exhausts to the side. In the top 

drawing the power flows in through the center to the right hand cylinder port. The left 

hand cylinder port is allowed to exit through an exhaust port. In the bottom drawing the 

solenoid is in a new position and the pressure is now applied to the left hand port on the 

top, and the right hand port can exhaust. The symbols to the left of the figure show the 

schematic equivalent of the actual valve positions. Valves are also available that allow the 

valves to be blocked when unused. 

solenoid 

The solenoid has two positions and when 

actuated will change the direction that 

fluid flows to the device. The symbols 

shown here are commonly used to 

represent this type of valve. 

exhaust out 

power in 

solenoid 

power in 

exhaust out 

Figure 5.2 

A Solenoid Controlled 5 Ported, 4 Way 2 Position Valve 



Valve types are listed below. In the standard terminology, the ’n-way’ designates 

the number of connections for inlets and outlets. In some cases there are redundant ports 

for exhausts. The normally open/closed designation indicates the valve condition when 

power is off. All of the valves listed are two position valve, but three position valves are 

also available. 

2-way normally closed - these have one inlet, and one outlet. When unenergized, 

the valve is closed. When energized, the valve will open, allowing flow. These 

are used to permit flows. 

2-way normally open - these have one inlet, and one outlet. When unenergized, the 

valve is open, allowing flow. When energized, the valve will close. These are 

used to stop flows. When system power is off, flow will be allowed. 

3-way normally closed - these have inlet, outlet, and exhaust ports. When unenergized, 

the outlet port is connected to the exhaust port. When energized, the inlet 

is connected to the outlet port. These are used for single acting cylinders. 

3-way normally open - these have inlet, outlet and exhaust ports. When unenergized, 

the inlet is connected to the outlet. Energizing the valve connects the outlet 

to the exhaust. These are used for single acting cylinders 

3-way universal - these have three ports. One of the ports acts as an inlet or outlet, 

and is connected to one of the other two, when energized/unenergized. These 

can be used to divert flows, or select alternating sources. 

4-way - These valves have four ports, two inlets and two outlets. Energizing the 

valve causes connection between the inlets and outlets to be reversed. These are 

used for double acting cylinders. 

Some of the ISO symbols for valves are shown in Figure 5.3. When using the symbols 

in drawings the connections are shown for the unenergized state. The arrows show 

the flow paths in different positions. The small triangles indicate an exhaust port. 



Two way, two position 


normally open 

Three way, two position 


normally open 

Four way, two position 

Figure 5.3 

ISO Valve Symbols 

When selecting valves there are a number of details that should be considered, as 

listed below. 

pipe size - inlets and outlets are typically threaded to accept NPT (national pipe 

thread). 

flow rate - the maximum flow rate is often provided to hydraulic valves. 

operating pressure - a maximum operating pressure will be indicated. Some valves 

will also require a minimum pressure to operate. 

electrical - the solenoid coil will have a fixed supply voltage (AC or DC) and current. 

response time - this is the time for the valve to fully open/close. Typical times for 

valves range from 5ms to 150ms. 

enclosure - the housing for the valve will be rated as, 

type 1 or 2 - for indoor use, requires protection against splashes 

type 3 - for outdoor use, will resists some dirt and weathering 

type 3R or 3S or 4 - water and dirt tight 

type 4X - water and dirt tight, corrosion resistant 

5.4 CYLINDERS 

A cylinder uses pressurized fluid or air to create a linear force/motion as shown in 

Figure 5.4. In the figure a fluid is pumped into one side of the cylinder under pressure, 



causing that side of the cylinder to expand, and advancing the piston. The fluid on the 

other side of the piston must be allowed to escape freely - if the incompressible fluid was 

trapped the cylinder could not advance. The force the cylinder can exert is proportional to 

the cross sectional area of the cylinder. 

F 

advancing 

Fluid pumped in 

at pressure P 

Fluid flows out 

at low pressure 

F 

retracting 

Fluid flows out 

at low pressure 

Fluid pumped in 

at pressure P 

For Force: 

where, 

P 

= 

F 

-- 

A 

F 

= 

PA 

P = the pressure of the hydraulic fluid 

A = the area of the piston 

F = the force available from the piston rod 

Figure 5.4 

A Cross Section of a Hydraulic Cylinder 

Single acting cylinders apply force when extending and typically use a spring to 

retract the cylinder. Double acting cylinders apply force in both direction. 



single acting spring return cylinder 

double acting cylinder 

Figure 5.5 

Schematic Symbols for Cylinders 

Magnetic cylinders are often used that have a magnet on the piston head. When it 

moves to the limits of motion, reed switches will detect it. 

5.5 HYDRAULICS 

Hydraulics use incompressible fluids to supply very large forces at slower speeds 

and limited ranges of motion. If the fluid flow rate is kept low enough, many of the effects 

predicted by Bernoulli’s equation can be avoided. The system uses hydraulic fluid (normally 

an oil) pressurized by a pump and passed through hoses and valves to drive cylinders. 

At the heart of the system is a pump that will give pressures up to hundreds or 

thousands of psi. These are delivered to a cylinder that converts it to a linear force and displacement. 



Hydraulic systems normally contain the following components; 

1. Hydraulic Fluid 

2. An Oil Reservoir 

3. A Pump to Move Oil, and Apply Pressure 

4. Pressure Lines 

5. Control Valves - to regulate fluid flow 

6. Piston and Cylinder - to actuate external mechanisms 

The hydraulic fluid is often a noncorrosive oil chosen so that it lubricates the components. 

This is normally stored in a reservoir as shown in Figure 5.6. Fluid is drawn from 

the reservoir to a pump where it is pressurized. This is normally a geared pump so that it 

may deliver fluid at a high pressure at a constant flow rate. A flow regulator is normally 

placed at the high pressure outlet from the pump. If fluid is not flowing in other parts of 

the system this will allow fluid to recirculate back to the reservoir to reduce wear on the 

pump. The high pressure fluid is delivered to solenoid controlled vales that can switch 

fluid flow on or off. From the vales fluid will be delivered to the hydraulics at high pressure, 

or exhausted back to the reservoir. 

air filter 

fluid return 

outlet tube 

refill oil filter 

access hatch 

for cleaning 

level 

gauge 

baffle - isolates the 

outlet fluid from 

turbulence in the inlet 



Figure 5.6 

A Hydraulic Fluid Reservoir 

Hydraulic systems can be very effective for high power applications, but the use of 

fluids, and high pressures can make this method awkward, messy, and noisy for other 

applications. 

5.6 PNEUMATICS 

Pneumatic systems are very common, and have much in common with hydraulic 

systems with a few key differences. The reservoir is eliminated as there is no need to collect 

and store the air between uses in the system. Also because air is a gas it is compressible 

and regulators are not needed to recirculate flow. But, the compressibility also means 

that the systems are not as stiff or strong. Pneumatic systems respond very quickly, and are 

commonly used for low force applications in many locations on the factory floor. 

Some basic characteristics of pneumatic systems are, 

- stroke from a few millimeters to meters in length (longer strokes have more 

springiness 

- the actuators will give a bit - they are springy 

- pressures are typically up to 85psi above normal atmosphere 

- the weight of cylinders can be quite low 

- additional equipment is required for a pressurized air supply- linear and rotatory 

actuators are available. 

- dampers can be used to cushion impact at ends of cylinder travel. 

When designing pneumatic systems care must be taken to verify the operating 

location. In particular the elevation above sea level will result in a dramatically different 

air pressure. For example, at sea level the air pressure is about 14.7 psi, but at a height of 

7,800 ft (Mexico City) the air pressure is 11.1 psi. Other operating environments, such as 

in submersibles, the air pressure might be higher than at sea level. 

Some symbols for pneumatic systems are shown in Figure 5.7. The flow control 

valve is used to restrict the flow, typically to slow motions. The shuttle valve allows flow 

in one direction, but blocks it in the other. The receiver tank allows pressurized air to be 

accumulated. The dryer and filter help remove dust and moisture from the air, prolonging 

the life of the valves and cylinders. 



Flow control valve 

Shuttle valve 

Receiver tank 

Dryer 

Filter 

Pump 

Pressure regulator 

Figure 5.7 

Pneumatics Components 

5.7 MOTORS 

Motors are common actuators, but for logical control applications their properties 

are not that important. Typically logical control of motors consists of switching low current 

motors directly with a PLC, or for more powerful motors using a relay or motor 

starter. Motors will be discussed in greater detail in the chapter on continuous actuators. 



5.8 OTHERS 

There are many other types of actuators including those on the brief list below. 

Heaters - The are often controlled with a relay and turned on and off to maintain a 

temperature within a range. 

Lights - Lights are used on almost all machines to indicate the machine state and 

provide feedback to the operator. most lights are low current and are connected 

directly to the PLC. 

Sirens/Horns - Sirens or horns can be useful for unattended or dangerous machines 

to make conditions well known. These can often be connected directly to the 

PLC. 

Computers - some computer based devices may use TTL 0/5V logic levels to trigger 

actions. Generally these are prone to electrical noise and should be avoided 

if possible. 

5.9 SUMMARY 

• Solenoids can be used to convert an electric current to a limited linear motion. 

• Hydraulics and pneumatics use cylinders to convert fluid and gas flows to limited 

linear motions. 

• Solenoid valves can be used to redirect fluid and gas flows. 

• Pneumatics provides smaller forces at higher speeds, but is not stiff. Hydraulics 

provides large forces and is rigid, but at lower speeds. 

• Many other types of actuators can be used. 


1. A piston is to be designed to exert an actuation force of 120 lbs on its extension stroke. The 

inside diameter of the cylinder is 2.0” and the ram diameter is 0.375”. What shop air pressure 

will be required to provide this actuation force? Use a safety factor of 1.3. 

2. Draw a simple hydraulic system that will advance and retract a cylinder using PLC outputs. 

Sketches should include details from the PLC output card to the hydraulic cylinder. 

3. Develop an electrical ladder diagram and pneumatic diagram for a PLC controlled system. The 

system includes the components listed below. The system should include all required safety 

and wiring considerations. 

a 3 phase 50 HP motor 

1 NPN sensor 

1 NO push button 



1 NC limit switch 

1 indicator light 

a doubly acting pneumatic cylinder 


1. A = pi*r^2 = 3.14159in^2, P=FS*(F/A)=1.3(120/3.14159)=49.7psi. Note, if the cylinder were 

retracting we would need to subtract the rod area from the piston area. Note: this air pressure is 

much higher than normally found in a shop, so it would not be practical, and a redesign would 

be needed. 

2. 

cylinder 

V 

00 

S1 

+ 

- 

24Vdc 

01 

02 

03 

S1 

sump 

pressure 

regulator 

release 

pump 



3. 

ADD SOLUTION 


1. Draw a schematic symbol for a solenoid controlled pneumatic valve and explain how the valve 

operates. 

2. A PLC based system has 3 proximity sensors, a start button, and an E-stop as inputs. The system 

controls a pneumatic system with a solenoid controlled valve. It also controls a robot with 

a TTL output. Develop a complete wiring diagram including all safety elements. 

3. A system contains a pneumatic cylinder with two inductive proximity sensors that will detect 

when the cylinder is fully advanced or retracted. The cylinder is controlled by a solenoid controlled 

valve. Draw electrical and pneumatic schematics for a system. 

4. Draw an electrical ladder wiring diagram for a PLC controlled system that contains 2 PNP sensors, 

a NO push button, a NC limit switch, a contactor controlled AC motor and an indicator 

light. Include all safety circuitry. 

5. We are to connect a PLC to detect boxes moving down an assembly line and divert larger 

boxes. The line is 12 inches wide and slanted so the boxes fall to one side as they travel by. 

One sensor will be mounted on the lower side of the conveyor to detect when a box is present. 

A second sensor will be mounted on the upper side of the conveyor to determine when a larger 

box is present. If the box is present, an output to a pneumatic solenoid will be actuated to divert 

the box. Your job is to select a specific PLC, sensors, and solenoid valve. Details (the absolute 

minimum being model numbers) are expected with a ladder wiring diagram. (Note: take 

advantage of manufacturers web sites.) 


plc boolean - 6.1 

6. BOOLEAN LOGIC DESIGN 

Topics: 

• Boolean algebra 

• Converting between Boolean algebra and logic gates and ladder logic 

• Logic examples 

Objectives: 

• Be able to simplify designs with Boolean algebra 


The process of converting control objectives into a ladder logic program requires 

structured thought. Boolean algebra provides the tools needed to analyze and design these 

systems. 

6.2 BOOLEAN ALGEBRA 

Boolean algebra was developed in the 1800’s by James Bool, an Irish mathematician. 

It was found to be extremely useful for designing digital circuits, and it is still 

heavily used by electrical engineers and computer scientists. The techniques can model a 

logical system with a single equation. The equation can then be simplified and/or manipulated 

into new forms. The same techniques developed for circuit designers adapt very well 

to ladder logic programming. 

Boolean equations consist of variables and operations and look very similar to normal 

algebraic equations. The three basic operators are AND, OR and NOT; more complex 

operators include exclusive or (EOR), not and (NAND), not or (NOR). Small truth tables 

for these functions are shown in Figure 6.1. Each operator is shown in a simple equation 

with the variables A and B being used to calculate a value for X. Truth tables are a simple 

(but bulky) method for showing all of the possible combinations that will turn an output 

on or off. 



Note: By convention a false state is also called off or 0 (zero). A true state is also 

called on or 1. 

AND 

A 

B 

X = 

A 

A⋅ 

B 

B 

OR 

NOT 

A 

A 

X B X X 

X 

X = A+ 

B 

A B 

X 

X = 

A 

A 

X 

0 

0 

1 

1 

0 

1 

0 

1 

0 

0 

0 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

1 

1 

0 

1 

1 

0 

NAND 

A 

B 

NOR 

EOR 

A 

A 

X B X B X 

X 

A 

= 

A⋅ 

B 

B 

X 

X = A+ 

B 

A B 

X 

X = A⊕ 

B 

A B 

X 

0 

0 

1 

1 

0 

1 

0 

1 

1 

1 

1 

0 

0 

0 

1 

1 

0 

1 

0 

1 

1 

0 

0 

0 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

1 

0 

Note: The symbols used in these equations, such as + for OR are not universal standards 

and some authors will use different notations. 

Note: The EOR function is available in gate form, but it is more often converted to 

its equivalent, as shown below. 

X = A⊕ 

B = 

A⋅ 

B 

+ 

A⋅ 

B 

Figure 6.1 

Boolean Operations with Truth Tables and Gates 

In a Boolean equation the operators will be put in a more complex form as shown 

in Figure 6.2. The variable for these equations can only have a value of 0 for false, or 1 for 



true. The solution of the equation follows rules similar to normal algebra. Parts of the 

equation inside parenthesis are to be solved first. Operations are to be done in the 

sequence NOT, AND, OR. In the example the NOT function for C is done first, but the 

NOT over the first set of parentheses must wait until a single value is available. When 

there is a choice the AND operations are done before the OR operations. For the given set 

of variable values the result of the calculation is false. 

given 

X = ( A + B⋅ 

C) + A⋅ 

( B+ 

C) 

assuming A=1, B=0, C=1 

X = ( 1 + 0 ⋅ 1) + 1 ⋅ ( 0 + 1) 

X = ( 1 + 0) + 1 ⋅ ( 0 + 0) 

X = ( 1) + 1 ⋅ ( 0) 

X = 0 + 0 

X = 0 

Figure 6.2 

A Boolean Equation 

The equations can be manipulated using the basic axioms of Boolean shown in 

Figure 6.3. A few of the axioms (associative, distributive, commutative) behave like normal 

algebra, but the other axioms have subtle differences that must not be ignored. 



Idempotent 

A 

+ A = A 

A⋅ 

A 

= 

A 

Associative 

( A+ 

B) + C = A+ ( B+ 

C) 

( A⋅ 

B) ⋅ C = A⋅ 

( B ⋅ C) 

Commutative 

A+ B = B+ 

A 

A⋅ 

B 

= 

B⋅ 

A 

Distributive 

A+ ( B ⋅ C) 

= ( A+ 

B) ⋅ ( A+ 

C) 

A⋅ 

( B+ 

C) 

= 

( A⋅ 

B) + ( A⋅ 

C) 

Identity 

A + 0 = A 

A + 1 = 1 

A ⋅ 0 = 0 

A ⋅ 1 

= 

A 

Complement 

A 

+ A = 1 

( A) = A 

DeMorgan’s 

A⋅ A = 0 

1 = 0 

( A+ 

B) = A⋅ 

B 

( A⋅ 

B) = A+ 

B 

Duality 

interchange AND and OR operators, as well as all Universal, and Null 

sets. The resulting equation is equivalent to the original. 

Figure 6.3 

The Basic Axioms of Boolean Algebra 

An example of equation manipulation is shown in Figure 6.4. The distributive 

axiom is applied to get equation (1). The idempotent axiom is used to get equation (2). 

Equation (3) is obtained by using the distributive axiom to move C outside the parentheses, 

but the identity axiom is used to deal with the lone C. The identity axiom is then used 

to simplify the contents of the parentheses to get equation (4). Finally the Identity axiom is 



used to get the final, simplified equation. Notice that using Boolean algebra has shown 

that 3 of the variables are entirely unneeded. 

A = B⋅ 

( C ⋅ ( D + E + C) 

+ F⋅ 

C) 

A = B⋅ 

( D ⋅ C+ E⋅ 

C+ C⋅ 

C+ 

F⋅ 

C) 

A = B⋅ 

( D ⋅ C+ E⋅ C+ C+ 

F⋅ 

C) 

A = B⋅ 

C⋅ 

( D+ E+ 1 + F) 

A = B⋅ 

C⋅ 

( 1) 

(1) 

(2) 

(3) 

(4) 

A 

= 

B⋅ 

C 

(5) 

Figure 6.4 

Simplification of a Boolean Equation 

Note: When simplifying Boolean algebra, OR operators have a lower priority, so they 

should be manipulated first. NOT operators have the highest priority, so they should be 

simplified last. Consider the example from before. 

X = ( A + B⋅ 

C) + A⋅ 

( B+ 

C) 

X 

X 

= ( A) + ( B⋅ 

C) 

+ A⋅ 

( B + C) 

= ( A) ⋅ ( B⋅ 

C) 

+ A⋅ 

( B+ 

C) 

X = A⋅ ( B + C) 

+ A⋅ 

( B+ 

C) 

X = A⋅ 

B+ 

A ⋅ C+ A⋅ 

B+ 

X = A⋅ 

B+ ( A⋅ 

C + A ⋅ C) 

+ 

X = A⋅ 

B+ 

C ⋅ ( A + A) 

+ 

X = A⋅ B+ 

C + A⋅ 

B 

A⋅ 

C 

A⋅ 

B 

A⋅ 

B 

The higher priority operators are 

put in parentheses 

DeMorgan’s theorem is applied 

DeMorgan’s theorem is applied again 

The equation is expanded 

Terms with common terms are 

collected, here it is only NOT C 

The redundant term is eliminated 

A Boolean axiom is applied to 

simplify the equation further 



6.3 LOGIC DESIGN 

Design ideas can be converted to Boolean equations directly, or with other techniques 

discussed later. The Boolean equation form can then be simplified or rearranges, 

and then converted into ladder logic, or a circuit. 

Aside: The logic for a seal-in circuit can be analyzed using a Boolean equation as shown 

below. Recall that the START is NO and the STOP is NC. 

START 

ON 

STOP 

ON 

ON′ = ( START + ON) ⋅ STOP 

ON 

STOP 

START 

ON’ 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

1 

0 

0 

1 

1 

stop pushed, not active 


not active 

start pushed, becomes active 



active, start no longer pushed 

becomes active and start pushed 

If we can describe how a controller should work in words, we can often convert it 

directly to a Boolean equation, as shown in Figure 6.5. In the example a process description 

is given first. In actual applications this is obtained by talking to the designer of the 

mechanical part of the system. In many cases the system does not exist yet, making this a 

challenging task. The next step is to determine how the controller should work. In this 

case it is written out in a sentence first, and then converted to a Boolean expression. The 

Boolean expression may then be converted to a desired form. The first equation contains 

an EOR, which is not available in ladder logic, so the next line converts this to an equivalent 

expression (2) using ANDs, ORs and NOTs. The ladder logic developed is for the second 

equation. In the conversion the terms that are ANDed are in series. The terms that are 

ORed are in parallel branches, and terms that are NOTed use normally closed contacts. 

The last equation (3) is fully expanded and ladder logic for it is shown in Figure 6.6. This 

illustrates the same logical control function can be achieved with different, yet equivalent, 



ladder logic. 

Process Description: 

A heating oven with two bays can heat one ingot in each bay. When the 

heater is on it provides enough heat for two ingots. But, if only one 

ingot is present the oven may become too hot, so a fan is used to 

cool the oven when it passes a set temperature. 

Control Description: 

If the temperature is too high and there is an ingot in only one bay then 

turn on fan. 

Define Inputs and Outputs: 

B1 = bay 1 ingot present 

B2 = bay 2 ingot present 

F = fan 

T = temperature overheat sensor 

Boolean Equation: 

F = T⋅ 

( B 1 

⊕ B 2 

) 

F = T⋅ 

( B 1 

⋅ B 2 

+ B 1 

⋅ B 2 

) 

F = B 1 

⋅B 2 

⋅ T + B 1 

⋅B 2 

⋅ T 

Ladder Logic for Equation (2): 

(2) 

(3) 

B1 

B2 

T 

F 

B1 

B2 

Note: the result for conditional logic 

is a single step in the ladder 

Warning: in spoken and written english OR and EOR are often not clearly defined. Consider 

the traffic directions "Go to main street then turn left or right." Does this or mean 

that you can drive either way, or that the person isn’t sure which way to go? Consider 

the expression "The cars are red or blue.", Does this mean that the cars can be either red 

or blue, or all of the cars are red, or all of the cars are blue. A good literal way to 

describe this condition is "one or the other, but not both". 

Figure 6.5 

Boolean Algebra Based Design of Ladder Logic 



Ladder Logic for Equation (3): 

B1 

B2 

T 

F 

B1 

B2 

T 

Figure 6.6 

Alternate Ladder Logic 

Boolean algebra is often used in the design of digital circuits. Consider the example 

in Figure 6.7. In this case we are presented with a circuit that is built with inverters, 

nand, nor and, and gates. This figure can be converted into a boolean equation by starting 

at the left hand side and working right. Gates on the left hand side are solved first, so they 

are put inside parentheses to indicate priority. Inverters are represented by putting a NOT 

operator on a variable in the equation. This circuit can’t be directly converted to ladder 

logic because there are no equivalents to NAND and NOR gates. After the circuit is converted 

to a Boolean equation it is simplified, and then converted back into a (much simpler) 

circuit diagram and ladder logic. 



A 

B 

C 

B 

A 

X 

C 

The circuit is converted to a Boolean equation and simplified. The most nested terms 

in the equation are on the left hand side of the diagram. 

X = ⎛ 

⎝ 

( A ⋅B ⋅ C) + B⎞ ⎠ 

⋅ B⋅ 

( A+ 

C) 

X = ( A + B+ C+ 

B) ⋅ B⋅ 

( A⋅ 

C) 

X 

X 

X 

= A⋅ B⋅ A⋅ C+ B⋅ B⋅ A⋅ C+ C⋅ B⋅ A⋅ C + B ⋅B ⋅A ⋅C 

= B⋅ A⋅ C+ B⋅ A⋅ C+ 0 + B⋅ 

A⋅ 

C 

= 

B⋅ 

A⋅ 

C 

This simplified equation is converted back into a circuit and equivalent ladder logic. 

B 

A 

C 

X 

B A C X 

Figure 6.7 

Reverse Engineering of a Digital Circuit 

To summarize, we will obtain Boolean equations from a verbal description or 

existing circuit or ladder diagram. The equation can be manipulated using the axioms of 

Boolean algebra. after simplification the equation can be converted back into ladder logic 

or a circuit diagram. Ladder logic (and circuits) can behave the same even though they are 

in different forms. When simplifying Boolean equations that are to be implemented in lad- 



der logic there are a few basic rules. 

1. Eliminate NOTs that are for more than one variable. This normally includes 

replacing NAND and NOR functions with simpler ones using DeMorgan’s theorem. 

2. Eliminate complex functions such as EORs with their equivalent. 

These principles are reinforced with another design that begins in Figure 6.8. 

Assume that the Boolean equation that describes the controller is already known. This 

equation can be converted into both a circuit diagram and ladder logic. The circuit diagram 

contains about two dollars worth of integrated circuits. If the design was mass produced 

the final cost for the entire controller would be under $50. The prototype of the 

controller would cost thousands of dollars. If implemented in ladder logic the cost for each 

controller would be approximately $500. Therefore a large number of circuit based controllers 

need to be produced before the break even occurs. This number is normally in the 

range of hundreds of units. There are some particular advantages of a PLC over digital circuits 

for the factory and some other applications. 

• the PLC will be more rugged, 

• the program can be changed easily 

• less skill is needed to maintain the equipment 



Given the controller equation; 

A = B ⋅ ( C ⋅ ( D + E+ 

C) 

+ F⋅ 

C) 

The circuit is given below, and equivalent ladder logic is shown. 

D 

E 

C 

A 

F 

B 

D 

C 

X 

The gates can be purchased for 

about $0.25 each in bulk. 

Inputs and outputs are 

typically 5V 

E 

C 

X 

B 

A 

An inexpensive PLC is worth 

at least a few hundred dollars 

F 

C 

Consider the cost trade-off! 

Figure 6.8 

A Boolean Equation and Derived Circuit and Ladder Logic 

The initial equation is not the simplest. It is possible to simplify the equation to the 

form seen in Figure 6.8. If you are a visual learner you may want to notice that some simplifications 

are obvious with ladder logic - consider the C on both branches of the ladder 

logic in Figure 6.9. 



A = B⋅ 

C⋅ 

( D+ E+ 

F) 

D 

E 

F 

C 

B 

A 

D 

C 

B 

A 

E 

F 

Figure 6.9 

The Simplified Form of the Example 

The equation can also be manipulated to other forms that are more routine but less 

efficient as shown in Figure 6.10. The equation shown is in disjunctive normal form - in 

simpler words this is ANDed terms ORed together. This is also an example of a canonical 

form - in simpler terms this means a standard form. This form is more important for digital 

logic, but it can also make some PLC programming issues easier. For example, when an 

equation is simplified, it may not look like the original design intention, and therefore 

becomes harder to rework without starting from the beginning. 



A = ( B ⋅C ⋅D) + ( B⋅C ⋅E) + ( B⋅C⋅ 

F) 

B 

C 

D 

A 

E 

F 

B C D A 

B C E 

B C F 

Figure 6.10 

A Canonical Logic Form 

6.3.1 Boolean Algebra Techniques 

There are some common Boolean algebra techniques that are used when simplifying 

equations. Recognizing these forms are important to simplifying Boolean Algebra 

with ease. These are itemized, with proofs in Figure 6.11. 



A+ CA = A+ 

C proof: A+ 

CA 

AB 

( A+ 

C) ( A+ 

A) 

( A+ 

C) ( 1) 

A+ 

C 

+ A = A proof: AB + A 

AB + A1 

AB ( + 1) 

A( 1) 

A + B+ C = ABC proof: A+ B+ 

C 

( A+ 

B) + C 

A 

( A+ 

B)C 

( AB)C 

ABC 

Figure 6.11 

Common Boolean Algebra Techniques 

6.4 COMMON LOGIC FORMS 

Knowing a simple set of logic forms will support a designer when categorizing 

control problems. The following forms are provided to be used directly, or provide ideas 

when designing. 

6.4.1 Complex Gate Forms 

In total there are 16 different possible types of 2-input logic gates. The simplest are 

AND and OR, the other gates we will refer to as complex to differentiate. The three popular 

complex gates that have been discussed before are NAND, NOR and EOR. All of these 

can be reduced to simpler forms with only ANDs and ORs that are suitable for ladder 

logic, as shown in Figure 6.12. 



NAND 

X 

= 

A⋅ 

B 

NOR 

X = A+ 

B 

EOR 

X = A⊕ 

B 

X = A+ 

B 

X 

= 

A⋅ 

B 

X 

= 

A⋅ 

B 

+ 

A⋅ 

B 

A 

X 

A B X 

A B X 

B 

Figure 6.12 

Conversion of Complex Logic Functions 

6.4.2 Multiplexers 

Multiplexers allow multiple devices to be connected to a single device. These are 

very popular for telephone systems. A telephone switch is used to determine which telephone 

will be connected to a limited number of lines to other telephone switches. This 

allows telephone calls to be made to somebody far away without a dedicated wire to the 

other telephone. In older telephone switch boards, operators physically connected wires 

by plugging them in. In modern computerized telephone switches the same thing is done, 

but to digital voice signals. 

In Figure 6.13 a multiplexer is shown that will take one of four inputs bits D1, D2, 

D3 or D4 and make it the output X, depending upon the values of the address bits, A1 and 

A2. 



D1 

D2 

D3 

multiplexer 

X 

A1 A2 X 

0 

0 

1 

1 

0 

1 

0 

1 

X=D1 

X=D2 

X=D3 

X=D4 

D4 

A1 

A2 

Figure 6.13 

A Multiplexer 

Ladder logic form the multiplexer can be seen in Figure 6.14. 

A1 A2 D1 X 

A1 A2 D2 

A1 A2 D3 

A1 A2 D4 

Figure 6.14 

A Multiplexer in Ladder Logic 



6.5 SIMPLE DESIGN CASES 

The following cases are presented to illustrate various combinatorial logic problems, 

and possible solutions. It is recommended that you try to satisfy the description 

before looking at the solution. 

6.5.1 Basic Logic Functions 

Problem: Develop a program that will cause output D to go true when switch A 

and switch B are closed or when switch C is closed. 

Solution: 

D 

= 

( A⋅ 

B) + C 

A 

B 

D 

C 

Figure 6.15 

Sample Solution for Logic Case Study A 

Problem: Develop a program that will cause output D to be on when push button A 

is on, or either B or C are on. 



Solution: 

D = A+ ( B ⊕ C) 

A 

D 

B 

C 

B 

C 

Figure 6.16 

Sample Solution for Logic Case Study B 

6.5.2 Car Safety System 

Problem: Develop Ladder Logic for a car door/seat belt safety system. When the 

car door is open, and the seatbelt is not done up, the ignition power must not be applied. If 

all is safe then the key will start the engine. 

Solution: 

Door Open Seat Belt Key 

Ignition 

Figure 6.17 

Solution to Car Safety System Case 

6.5.3 Motor Forward/Reverse 

Problem: Design a motor controller that has a forward and a reverse button. The 

motor forward and reverse outputs will only be on when one of the buttons is pushed. 



When both buttons are pushed the motor will not work. 

Solution: 

F 

R 

= 

= 

BF⋅ 

BR 

BF⋅ 

BR 

where, 

F = motor forward 

R = motor reverse 

BF = forward button 

BR = reverse button 

BF 

BF 

BR 

BR 

F 

R 

Figure 6.18 

Motor Forward, Reverse Case Study 

6.5.4 A Burglar Alarm 

Consider the design of a burglar alarm for a house. When activated an alarm and 

lights will be activated to encourage the unwanted guest to leave. This alarm be activated 

if an unauthorized intruder is detected by window sensor and a motion detector. The window 

sensor is effectively a loop of wire that is a piece of thin metal foil that encircles the 

window. If the window is broken, the foil breaks breaking the conductor. This behaves like 

a normally closed switch. The motion sensor is designed so that when a person is detected 

the output will go on. As with any alarm an activate/deactivate switch is also needed. The 

basic operation of the alarm system, and the inputs and outputs of the controller are itemized 

in Figure 6.19. 



The inputs and outputs are chosen to be; 

A = Alarm and lights switch (1 = on) 

W = Window/Door sensor (1 = OK) 

M = Motion Sensor (0 = OK) 

S = Alarm Active switch (1 = on) 

The basic operation of the alarm can be described with rules. 

1. If alarm is on, check sensors. 

2. If window/door sensor is broken (turns off), sound alarm and turn on 

lights 

Note: As the engineer, it is your responsibility to define these items before starting 

the work. If you do not do this first you are guaranteed to produce a poor 

design. It is important to develop a good list of inputs and outputs, and give 

them simple names so that they are easy to refer to. Most companies will use 

wire numbering schemes on their diagrams. 

Figure 6.19 

Controller Requirements List for Alarm 

The next step is to define the controller equation. In this case the controller has 3 

different inputs, and a single output, so a truth table is a reasonable approach to formalizing 

the system. A Boolean equation can then be written using the truth table in Figure 

6.20. Of the eight possible combinations of alarm inputs, only three lead to alarm conditions. 



Inputs Output 

S M W A 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

1 

0 

1 

1 

alarm off 

alarm on/no thief 

alarm on/thief detected 

note the binary sequence 

Figure 6.20 

Truth Table for the Alarm 

The Boolean equation in Figure 6.21 is written by examining the truth table in Figure 

6.20. There are three possible alarm conditions that can be represented by the conditions 

of all three inputs. For example take the last line in the truth table where when all 

three inputs are on the alarm should be one. This leads to the last term in the equation. The 

other two terms are developed the same way. After the equation has been written, it is simplified. 



A = ( S⋅ 

M⋅ 

W) + ( S ⋅M⋅ 

W) + ( S ⋅M⋅ 

W) 

∴A 

= S ⋅ ( M ⋅ W + M ⋅ W + M ⋅ W) 

∴A 

= S ⋅ (( M ⋅ W+ 

M ⋅ W) + ( M ⋅ W + M⋅ 

W) 

) 

∴A 

= ( S ⋅ W) + ( S ⋅ M) 

= S⋅ 

( W+ 

M) 

W 

W 

(S*W) 

(S*W)+(S*M) 

S 

A 

M 

(S*M) 

M 

S 

W S A 

Figure 6.21 

A Boolean Equation and Implementation for the Alarm 

The equation and circuits shown in Figure can also be further simplified, as shown 




W 

M 

W 

(M+W) 

S * (M+W) 

= (S*W)+(S*M) 

S 

A 

M 

S 

A 

W 

Figure 6.22 

The Simplest Circuit and Ladder Diagram 

Aside: The alarm could also be implemented in programming languages. The program 

below is for a Basic Stamp II chip. (www.parallaxinc.com) 

w = 1; s = 2; m = 3; a = 4 

input m; input w; input s 

output a 

loop: 

if (in2 = 1) and (in1 = 0 or in3 = 1) then on 

low a; goto loop ‘alarm off 

on: 

high a; goto loop ‘alarm on 

Figure 6.23 

Alarm Implementation Using A High Level Programming Language 

6.6 SUMMARY 

• Logic can be represented with Boolean equations. 

• Boolean equations can be converted to (and from) ladder logic or digital circuits. 

• Boolean equations can be simplified. 

• Different controllers can behave the same way. 

• Common logic forms exist and can be used to understand logic. 



• Truth tables can represent all of the possible state of a system. 


1. Is the ladder logic in the figure below for an AND or an OR gate? 

2. Draw a ladder diagram that will cause output D to go true when switch A and switch B are 

closed or when switch C is closed. 

3. Draw a ladder diagram that will cause output D to be on when push button A is on, or either B 

or C are on. 

4. Design ladder logic for a car that considers the variables below to control the motor M. Also 

add a second output that uses any outputs not used for motor control. 

- doors opened/closed (D) 

- keys in ignition (K) 

- motor running (M) 

- transmission in park (P) 

- ignition start (I) 

5. a) Explain why a stop button must be normally closed and a start button must be normally open. 

b) Consider a case where an input to a PLC is a normally closed stop button. The contact used in 

the ladder logic is normally open, as shown below. Why are they both not the same? (i.e., NC 

or NO) 

start 

motor 

stop 

motor 

6. Make a simple ladder logic program that will turn on the outputs with the binary patterns when 



the corresponding buttons are pushed. 

OUTPUTS 

H G F E D C 

B 

A 

INPUTS 

1 

1 

1 

1 

0 

0 

0 

1 

0 

1 

0 

1 

0 

0 

0 

1 

0 

1 

0 

0 

1 

1 

1 

1 

Input X on 

Input Y on 

Input Z on 

7. Convert the following Boolean equation to the simplest possible ladder logic. 

X = A ⋅ ( A + A⋅ 

B) 

8. Simplify the following boolean equations. 

a) AB ( + AB) b) AB ( + AB) 

c) AB ( + AB) d) AB ( + AB) 

9. Simplify the following Boolean equations, 

a) ( A+ 

B) ⋅ ( A+ 

B) 

b) 

ABCD + ABCD + ABCD + ABCD 

10. Simplify the Boolean expression below. 

(( A⋅ 

B) + ( B+ 

A) 

) ⋅ C + ( B⋅ 

C+ 

B⋅ 

C) 

11. Given the Boolean expression a) draw a digital circuit and b) a ladder diagram (do not simplify), 

c) simplify the expression. 

X = A⋅ 

B⋅ 

C + ( C+ 

B) 

12. Simplify the following Boolean equation and write corresponding ladder logic. 

Y = ( ABCD + ABCD + ABCD + ABCD) + D 

13. For the following Boolean equation, 

X = A+ B( A+ CB+ 

DAC) + ABCD 

a) Write out the logic for the unsimplified equation. 



b) Simplify the equation. 

c) Write out the ladder logic for the simplified equation. 

14. a) Write a Boolean equation for the following truth table. (Hint: do this by writing an expression 

for each line with a true output, and then ORing them together.) 

A B C D Result 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

1 

0 

0 

1 

0 

1 

0 

1 

1 

0 

0 

1 

0 

0 

1 

1 

b) Write the results in a) in a Boolean equation. 

c) Simplify the Boolean equation in b) 

15. Simplify the following Boolean equation, and create the simplest ladder logic. 

⎛ 

⎛ 

Y C A ⎜A + BC⎛ 

⎝ 

A + BC⎞ 

⎝ 

⎛ ⎠⎠ 

⎞ ⎞ 

⎞ 

= ⎜ 

⎜ 

+ 

⎟ 

⎟ 

⎝ 

⎝ 

⎠ 

⎟ 

⎠ 

16. Simplify the following boolean equation with Boolean algebra and write the corresponding 

ladder logic. 

X = ( A + B⋅ 

A) + ( C+ D+ 

EC) 

17. Convert the following ladder logic to a Boolean equation. Then simplify it, and convert it back 



to simpler ladder logic. 

A B D D 

Y 

B 

A 

A C D 

18. a) Develop the Boolean expression for the circuit below. 

b) Simplify the Boolean expression. 

c) Draw a simpler circuit for the equation in b). 

A 

B 

C 

B 

A 

X 

C 

19. Given a system that is described with the following equation, 

X = A+ ( B⋅ 

( A+ 

C) 

+ C) + A ⋅B ⋅( D + E) 

a) Simplify the equation using Boolean Algebra. 

b) Implement the original and then the simplified equation with a digital circuit. 

c) Implement the original and then the simplified equation in ladder logic. 

20. Simplify the following and implement the original and simplified equations with gates and 

ladder logic. 

A+ 

( B + C + D) ⋅ ( B+ 

C) + A⋅ 

B⋅ 

( C+ 

D) 


1. AND 



2. 

A 

B 

D 

C 

3. 

B 

C 

D 

B 

C 

A 

4. 

I 

P 

K 

M 

M 

K 

D 

B 

where, 

B = the alarm that goes "Bing" to warn that the keys are still in the car. 

5. a) If a NC stop button is damaged, the machine will act as if the stop button was pushed and 

shut down safely. If a NO start button is damaged the machine will not be able to start.) 

b) For the actual estop which is NC, when all is ok the power to the input is on, when there is a 

problem the power to the input is off. In the ladder logic an input that is on (indicating all is ok) 



will allow the rung to turn on the motor, otherwise an input that is off (indicating a stop) will 

break the rung and cut the power.) 

6. 

X 

H 

Y 

Z 

X 

G 

Y 

F 

X 

E 

Z 

ETC.... 

7. 

A 

X 

8. 

a) AB b) A+ B c) AB d) A + B 



9. 

a) 

( A+ 

B) ⋅ ( A+ 

B) 

= ( AB) ( AB) = 0 

b) 

ABCD + ABCD + ABCD + ABCD = BCD + ABD = BCD ( + AD) 

10. C 

11. 

X = B⋅ 

( A ⋅ C + C) 

12. 

Y = ( ABCD + ABCD + ABCD + ABCD) + D 

Y = ( ABCD + ABCD + ABCD + ABCD)D 

Y = ( 0 + ABCD + 0 + 0)D 

Y 

= 

ABCD 

A B C D 



13. 

a) 

A 

X 

B 

A 

C 

B 

D A C 

A B C D 

b) A+ 

DCB 

c) 

A 

X 

D 

C 

B 



A 

B 

C 

B 

C 

D 

C 

A 

B 

D 

A 

D 

B 

C 

14. 

ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD 

BCD + ACD + BCD + ABD + BCD + ACD + ABC 

BCD + CD( A + A) + CD( B + B) + ABD + ABC 

BCD + D( C + AB) + ABC 



15. 

⎛ 

⎛ 

Y C A ⎜A + BC⎛ 

⎝ 

A+ 

BC⎞ 

⎝ 

⎛ ⎠⎠ 

⎞ ⎞ 

⎞ 

= ⎜ 

⎜ 

+ 

⎟ 

⎟ 

⎝ 

⎝ 

⎠ 

⎟ 

⎠ 

⎛ 

Y C A + A+ ( BC( A + B+ 

C) 

) 

⎝ 

⎛ ⎠ 

⎞ ⎞ 

= ⎜ 

⎟ 

⎝ 

⎠ 

⎛ 

Y C A + ⎝ 

⎛ A + ( BCABC) 

⎠ 

⎞ ⎞ 

= ⎜ 

⎟ 

⎝ 

⎠ 

Y = C⎛A+ ( A+ 

0) 

⎞ 

⎝ ⎠ 

Y = C⎛A+ ( A+ 

1) 

⎞ 

⎝ ⎠ 

Y = C( A+ ( 1) 

) 

Y = C( A+ 

0) 

C 

A 

Y 

Y 

= 

CA 

Y = C + A 

16. 

X = ( A + B⋅ 

A) + ( C+ D+ 

EC) 

X = ( A + B⋅ 

A) ( C+ D+ 

EC) 

X = 

X = 

( A) ( B⋅ 

A) ( C + D + EC) 

( A) ( B⋅ 

A) ( C + D + EC) 

X = AB( C + D + EC) 

X = AB( C + D + E) 

OR 

X = ( A+ 

B⋅ 

A) + ( C + D + EC) 

X = A + B⋅ 

A+ 

CD( E + C) 

X = A + B+ 

CDE 

X 

= 

AB( CDE) 

X = AB( C+ D+ 

E) 



17. 

D 

A 

Y 

18. 

CAB 

C 

A 

B 

X 

A B C 

X 



19. 

a) X = A+ ( B⋅ 

( A+ 

C) 

+ C) + A⋅ 

B⋅ 

( D+ 

E) 

X = A+ ( B⋅ 

A+ 

B⋅ 

C + C) + A⋅ 

B⋅ 

D+ 

A⋅ 

B⋅ 

E 

X = A⋅ 

( 1 + B⋅ 

D + B⋅ 

E) + B⋅ A+ 

C⋅ 

( B+ 

1) 

X = A+ B⋅ 

A+ 

C 

b) 

ABCDE 

X 

X 



c) A 

X 

B 

A 

C 

C 

A B D 

E 

A 

X 

B 

A 

C 

20. 

A+ 

( B + C + D) ⋅ ( B+ 

C) + A⋅ 

B⋅ 

( C+ 

D) 

A ⋅ ( 1 + B⋅ 

( C+ 

D) 

) + ( B + C + D) ⋅ B + ( B+ C+ 

D) ⋅ C 

A+ ( C + D) ⋅ B + C 

A+ C⋅ 

B+ D⋅ 

B+ 

C 

A+ D⋅ 

B+ 

C 



A+ D⋅ 

B+ 

C 

A 

B 

C 

D 

B 

C 

C 

D 

A 

B 

D 

B 

A 

C 


1. Simplify the following Boolean equation and implement it in ladder logic. 

X = A + BA + BC + D + C 



2. Simplify the following Boolean equation and write a ladder logic program to implement it. 

X = ( ABC + ABC + ABC + ABC + ABC) 

3. Convert the following ladder logic to a Boolean equation. Simplify the equation using Boolean 

algebra, and then convert the simplified equation back to ladder logic. 

C 

A 

B 

D 

X 

B 

A 

D 

D 

4. Use Boolean equations to develop simplified ladder logic for the following truth table where A, 

B, C and D are inputs, and X and Y are outputs. 

A 

B 

C 

D 

X 

Y 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

1 

1 

1 

0 

0 

0 

0 

0 

1 

1 

1 



5. Convert the truth table below to a Boolean equation, and then simplify it. The output is X and 

the inputs are A, B, C and D. 

A 

B 

C 

D 

X 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

1 

0 

0 

0 

1 

0 

0 

0 

1 

1 

1 

1 

1 

6. Simplify the following Boolean equation. Convert both the unsimplified and simplified equations 

to ladder logic. 

X 

= 

( ABC) ( A+ 

BC) 


plc karnaugh - 7.1 

7. KARNAUGH MAPS 

Topics: 

• Truth tables and Karnaugh maps 

Objectives: 

• Be able to simplify designs with Boolean algebra and Karnaugh maps 


Karnaugh maps allow us to convert a truth table to a simplified Boolean expression 

without using Boolean Algebra. The truth table in Figure 7.1 is an extension of the 

previous burglar alarm example, an alarm quiet input has been added. 

Given 

A, W, M, S as before 

Q = Alarm Quiet (0 = quiet) 

Step1: Draw the truth table 

S M W Q A 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

1 

0 

1 



Figure 7.1 

Truth Table for a Burglar Alarm 

Instead of converting this directly to a Boolean equation, it is put into a tabular 

form as shown in Figure 7.2. The rows and columns are chosen from the input variables. 

The decision of which variables to use for rows or columns can be arbitrary - the table will 

look different, but you will still get a similar solution. For both the rows and columns the 

variables are ordered to show the values of the bits using NOTs. The sequence is not 

binary, but it is organized so that only one of the bits changes at a time, so the sequence of 

bits is 00, 01, 11, 10 - this step is very important. Next the values from the truth table that 

are true are entered into the Karnaugh map. Zeros can also be entered, but are not necessary. 

In the example the three true values from the truth table have been entered in the 

table. 

Step 2: Divide the input variables up. I choose SQ and MW 

Step 3: Draw a Karnaugh map based on the input variables 

S Q (=00) 

SQ (=01) 

SQ (=11) 

SQ (=10) 

M W (=00) MW (=01) MW (=11) MW (=10) 

1 1 1 

Added for clarity 

Note: The inputs are arranged so that only one bit changes at a time for the Karnaugh 

map. In the example above notice that any adjacent location, even the top/bottom 

and left/right extremes follow this rule. This is done so that changes are visually 

grouped. If this pattern is not used then it is much more difficult to group the bits. 

Figure 7.2 

The Karnaugh Map 

When bits have been entered into the Karnaugh map there should be some obvious 

patterns. These patterns typically have some sort of symmetry. In Figure 7.3 there are two 

patterns that have been circled. In this case one of the patterns is because there are two bits 

beside each other. The second pattern is harder to see because the bits in the left and right 

hand side columns are beside each other. (Note: Even though the table has a left and right 

hand column, the sides and top/bottom wrap around.) Some of the bits are used more than 

once, this will lead to some redundancy in the final equation, but it will also give a simpler 



expression. 

The patterns can then be converted into a Boolean equation. This is done by first 

observing that all of the patterns sit in the third row, therefore the expression will be 

ANDed with SQ. There are two patterns in the third row, one has M as the common term, 

the second has W as the common term. These can now be combined into the equation. 

Finally the equation is converted to ladder logic. 

Step 4: Look for patterns in the map 

S Q 

SQ 

SQ 

SQ 

M W MW MW MW 

1 1 1 

Step 5: Write the equation using the patterns 

M is the common term 

all are in row SQ 

W is the common term 

A = S⋅Q ⋅ ( M + W) 

Step 6: Convert the equation into ladder logic 

M S Q A 

W 

Figure 7.3 

Recognition of the Boolean Equation from the Karnaugh Map 

Karnaugh maps are an alternative method to simplifying equations with Boolean 

algebra. It is well suited to visual learners, and is an excellent way to verify Boolean algebra 

calculations. The example shown was for four variables, thus giving two variables for 

the rows and two variables for the columns. More variables can also be used. If there were 

five input variables there could be three variables used for the rows or columns with the 

pattern 000, 001, 011, 010, 110, 111, 101, 100. If there is more than one output, a Karnaugh 

map is needed for each output. 



Aside: A method developed by David Luque Sacaluga uses a circular format for the table. 

A brief example is shown below for comparison. 

A 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

B 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

C 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

D 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

X 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

1 

1 

Convert the truth table to a circle using the Gray code 

for sequence. Bits that are true in the truth table are 

shaded in the circle. 

1010 

1011 

1110 

1111 

1001 

1101 

1000 

1100 

0011 

0000 

0001 

0010 

0100 

0101 

0110 

0111 

Look for large groups of repeated patterns. 

1. In this case ’B’ is true in the bottom half of the circle, so the equation becomes, 

X = B ⋅ (…) 

2. There is left-right symmetry, with ’C’ as the common term, so the equation becomes 

X = B⋅ 

C ⋅ (…) 

3. The equation covers all four values, so the final equation is, 

X = B⋅ 

C 

Figure 7.4 

Aside: An Alternate Approach 

7.2 SUMMARY 

• Karnaugh maps can be used to convert a truth table to a simplified Boolean equation. 




1. Setup the Karnaugh map for the truth table below. 

A B C D Result 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

2. Use a Karnaugh map to simplify the following truth table, and implement it in ladder logic. 

0 

0 

0 

1 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

A 

B 

C 

D 

X 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

1 

1 



3. Write the simplest Boolean equation for the Karnaugh map below, 

CD CD CD CD 

AB 

1 

0 

0 

1 

AB 

0 

0 

0 

0 

AB 

0 

0 

0 

0 

AB 

0 

1 

1 

0 

4. Given the truth table below find the most efficient ladder logic to implement it. Use a structured 

technique such as Boolean algebra or Karnaugh maps. 

A B C D X Y 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

0 

1 

0 

0 

0 

0 

1 

1 

0 

1 

0 

0 

0 

0 

1 

1 



5. Examine the truth table below and design the simplest ladder logic using a Karnaugh map. 

D 

E 

F 

G 

Y 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

6. Find the simplest Boolean equation for the Karnaugh map below without using Boolean algebra 

to simplify it. Draw the ladder logic. 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

DE 

1 

1 

0 

1 

0 

0 

0 

0 

DE 

1 

1 

0 

0 

0 

0 

0 

0 

DE 

1 

1 

0 

0 

0 

0 

0 

0 

DE 

1 

1 

0 

1 

0 

0 

0 

0 

7. Given the following truth table for inputs A, B, C and D and output X. Convert it to simplified 



ladder logic using a Karnaugh map. 

A B C 

D 

X 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

1 

0 

1 

0 

0 

0 

0 

1 

1 

1 

1 

8. Consider the following truth table. Convert it to a Karnaugh map and develop a simplified 



Boolean equation (without Boolean algebra). Draw the corresponding ladder logic. 

A 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

B 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

C 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

D 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

E 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

X 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

inputs 

output 



9. Given the truth table below 

A B C D Z 

0 0 0 0 0 

0 0 0 1 0 

0 0 1 0 0 

0 0 1 1 0 

0 1 0 0 0 

0 1 0 1 1 

0 1 1 0 1 

0 1 1 1 1 

1 0 0 0 0 

1 0 0 1 1 

1 0 1 0 0 

1 0 1 1 0 

1 1 0 0 0 

1 1 0 1 1 

1 1 1 0 1 

1 1 1 1 1 

a) find a Boolean algebra expression using a Karnaugh map. 

b) draw a ladder diagram using the truth table (not the Boolean expression). 

10. Convert the following ladder logic to a Karnaugh map. 

A 

C 

A 

X 

B 

D 

11. a) Construct a truth table for the following problem. 

i) there are three buttons A, B, C. 

ii) the output is on if any two buttons are pushed. 

iii) if C is pressed the output will always turn on. 

b) Develop a Boolean expression. 

c) Develop a Boolean expression using a Karnaugh map. 

12. Develop the simplest Boolean expression for the Karnaugh map below, 

a) graphically. 

b) by Boolean Algebra 

A B AB AB AB 

CD 1 

1 

CD 

C D 

CD 

1 

1 1 

1 



13. Consider the following boolean equation. 

X = ( A+ 

BA)A+ ( CD + CD + CD) 

a) Can this Boolean equation be converted directly ladder logic. Explain your 

answer, and if necessary, make any changes required so that it may be converted 

to ladder logic. 

b) Write out ladder logic, based on the result in step a). 

c) Simplify the equation using Boolean algebra and write out new ladder logic. 

d) Write a Karnaugh map for the Boolean equation, and show how it can be used to 

obtain a simplified Boolean equation. 


1. 

CD 

AB AB A B AB 

1 1 1 1 

CD 

1 

1 

0 

1 

C D 

0 

0 

0 

1 

CD 

0 

0 

0 

1 

2. 

00 

CD 

01 11 

10 

AB 

00 

01 

11 

10 

B 

0 

0 

0 

0 

0 

0 

0 

0 

C 

0 

1 

1 

0 

0 

1 

1 

0 

X 

= 

BC 

X 



3. 

AB 

CD CD CD CD 

1 0 0 1 

-For all, B is true 

AB 

AB 

0 

0 

0 

0 

0 

0 

0 

0 

BAD ( + AD) 

AB 

0 

1 

1 

0 

4. 

FOR X 

FOR Y 

00 

CD 

01 11 

10 

00 

CD 

01 11 

10 

AB 

00 

01 

11 

10 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

AB 

00 

01 

11 

10 

0 

0 

0 

0 

1 

0 

0 

1 

0 

1 

1 

0 

0 

1 

1 

0 

X 

= A⋅ 

C 

Y = B⋅C ⋅D+ 

B⋅ 

C 

A C X 

B C D 

Y 

B 

C 



5. 

00 

FG 

01 11 

10 

DE 

00 

01 

11 

10 

0 

0 

0 

0 

0 

1 

1 

1 

0 

1 

1 

1 

0 

0 

0 

0 

Y = G( E+ 

D) 

G 

E 

D 

Y 

6. 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

DE 

1 

1 

0 

1 

0 

0 

0 

0 

DE 

1 

1 

0 

0 

0 

0 

0 

0 

DE 

1 

1 

0 

0 

0 

0 

0 

0 

DE 

1 

1 

0 

1 

0 

0 

0 

0 

AB 

ABCE 

output = AB + ABCE 

A 

B 

output 

A B C E 

7. 

A 

B 

X 

D 

B 



8. 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

ABC 

DE 

0 

0 

0 

0 

0 

1 

0 

0 

DE 

0 

0 

0 

0 

0 

1 

0 

0 

DE 

0 

1 

1 

1 

0 

1 

1 

0 

DE 

0 

1 

0 

1 

0 

1 

0 

0 

X = ABC + D( ABC + ABC + EC) 

A B C 

D A B C 

X 

A B C 

E 

C 



9. 

CD 

AB AB A B AB 

1 0 0 1 

CD 

1 

0 

0 

1 

Z=B*(C+D)+A B C D 

C D 

0 

0 

0 

0 

CD 

1 

1 

0 

1 

A B C D Z 

A B C D 

A B C D 

A B C D 

A B C D 

A B C D 

A B C D 



10. 

11. 

A 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

B 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

C 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

D 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

X 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

1 

0 

0 

0 

1 

0 

AB 

AB 

AB 

AB 

CD CD CD CD 

0 

0 

0 

1 

1 

1 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

A 

0 

0 

0 

0 

1 

1 

1 

1 

B 

0 

0 

1 

1 

0 

0 

1 

1 

C 

0 

1 

0 

1 

0 

1 

0 

1 

out 

0 

1 

0 

1 

0 

1 

1 

1 

C 

A B 

⋅ 

+ 

1 

1 

1 

0 

1 

0 

1 

0 

AB AB A B AB 

C 

C 



12. 

DA + ACD 

ABCD + ABCD + ABCD + ABCD + ABCD + ABCD 

ACD + ACD + ACD 

AD + ACD 

13. 

a) 

c) 

d) 

X = AB+ A + ( C+ 

D) ( C+ 

D) ( C + D) 

X = A+ B + CD 

AB 

CD CD CD CD 

1 

1 

1 

1 

AB 

1 

0 

0 

0 

AB 

1 

1 

1 

1 

AB 

1 

1 

1 

1 


1. Use the Karnaugh map below to create a simplified Boolean equation. Then use the equation to 

create ladder logic. 

CD 

AB AB AB AB 

1 1 1 1 

CD 

1 

0 

0 

1 

CD 

0 

0 

0 

1 

CD 

0 

0 

0 

1 



2. Use a Karnaugh map to develop simplified ladder logic for the following truth table where A, 

B, C and D are inputs, and X and Y are outputs. 

A 

B 

C 

D 

X 

Y 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

1 

0 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

1 

1 

1 

0 

0 

0 

0 

0 

1 

1 

1 

3. You are planning the basic layout for a control system with the criteria provided below. You 

need to plan the wiring for the input and output cards, and then write the ladder logic for the 

controller. You decide to use a Boolean logic design technique to design the ladder logic. 

AND, your design will be laid out on the design sheets found later in this book. 

• There are two inputs from PNP photoelectric sensors part and busy. 

• There is a NO cycle button, and NC stop button. 

• There are two outputs to indicator lights, the running light and the stopped light. 

• There is an output to a conveyor, that will drive a high current 120Vac motor. 

• The conveyor is to run when the part sensor is on and while the cycle button is 

pushed, but the busy sensor is off. If the stop button is pushed the conveyor will 

stop. 

• While the conveyor is running the running light will be on, otherwise the stopped 

light will be on. 



4. Convert the following truth table to simplified ladder logic using a Karnaugh map AND Boolean 

equations. The inputs are A, B, C and D and the output is X. 

A 

B 

C 

D 

X 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

0 

0 

1 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

0 

1 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

0 

1 

1 

1 

0 

0 

1 

1 

0 

0 

1 

0 

1 

0 

1 

0 

1 

0 


plc operation - 8.1 

8. PLC OPERATION 

Topics: 

• The computer structure of a PLC 

• The sanity check, input, output and logic scans 

• Status and memory types 

Objectives: 

• Understand the operation of a PLC. 


For simple programming the relay model of the PLC is sufficient. As more complex 

functions are used the more complex vonNeumann model of the PLC must be used. 

A vonNeumann computer processes one instruction at a time. Most computers operate this 

way, although they appear to be doing many things at once. Consider the computer components 

shown in Figure 8.1. 

Keyboard 

(Input) 

Serial 

Mouse 

(Input) 

x86 

CPU 

SVGA Screen 

(Output) 

1GB Memory 

(Storage) 

30 GB Disk 

(Storage) 

Figure 8.1 

Simplified Personal Computer Architecture 

Input is obtained from the keyboard and mouse, output is sent to the screen, and 

the disk and memory are used for both input and output for storage. (Note: the directions 

of these arrows are very important to engineers, always pay attention to indicate where 

information is flowing.) This figure can be redrawn as in Figure 8.2 to clarify the role of 



inputs and outputs. 

inputs input circuits computer 

output circuits 

outputs 

Keyboard 

Input Uart 

x86 CPU 

Graphics 

card 

Monitor 

Mouse 

Serial Input Uart 

Digital output 

LED display 

Disk Controller 

Memory ICs Disk 

storage 

Figure 8.2 

An Input-Output Oriented Architecture 

In this figure the data enters the left side through the inputs. (Note: most engineering 

diagrams have inputs on the left and outputs on the right.) It travels through buffering 

circuits before it enters the CPU. The CPU outputs data through other circuits. Memory 

and disks are used for storage of data that is not destined for output. If we look at a personal 

computer as a controller, it is controlling the user by outputting stimuli on the 

screen, and inputting responses from the mouse and the keyboard. 

A PLC is also a computer controlling a process. When fully integrated into an 

application the analogies become; 

inputs - the keyboard is analogous to a proximity switch 

input circuits - the serial input uart is like a 24Vdc input card 

computer - the x86 CPU is like a PLC CPU unit 

output circuits - a graphics card is like a triac output card 

outputs - a monitor is like a light 

storage - memory in PLCs is similar to memories in personal computers 



It is also possible to implement a PLC using a normal Personal Computer, 

although this is not advisable. In the case of a PLC the inputs and outputs are designed to 

be more reliable and rugged for harsh production environments. 

8.2 OPERATION SEQUENCE 

All PLCs have four basic stages of operations that are repeated many times per 

second. Initially when turned on the first time it will check it’s own hardware and software 

for faults. If there are no problems it will copy all the input and copy their values into 

memory, this is called the input scan. Using only the memory copy of the inputs the ladder 

logic program will be solved once, this is called the logic scan. While solving the ladder 

logic the output values are only changed in temporary memory. When the ladder scan is 

done the outputs will updated using the temporary values in memory, this is called the output 

scan. The PLC now restarts the process by starting a self check for faults. This process 

typically repeats 10 to 100 times per second as is shown in Figure 8.3. 

Self 

test 

input 

scan 

logic 

solve 

output 

scan 

Self 

test 

input 

scan 

logic 

solve 

output 

scan 

Self 

test 

input 

scan 

logic 

solve 

0 

PLC turns on 

ranges from


input scan takes a snapshot of the inputs, and solves the logic. This prevents potential 

problems that might occur if an input that is used in multiple places in the ladder logic program 

changed while half way through a ladder scan. Thus changing the behaviors of half 

of the ladder logic program. This problem could have severe effects on complex programs 

that are developed later in the book. One side effect of the input scan is that if a change in 

input is too short in duration, it might fall between input scans and be missed. 

When the PLC is initially turned on the normal outputs will be turned off. This 

does not affect the values of the inputs. 

8.2.1 The Input and Output Scans 

When the inputs to the PLC are scanned the physical input values are copied into 

memory. When the outputs to a PLC are scanned they are copied from memory to the 

physical outputs. When the ladder logic is scanned it uses the values in memory, not the 

actual input or output values. The primary reason for doing this is so that if a program uses 

an input value in multiple places, a change in the input value will not invalidate the logic. 

Also, if output bits were changed as each bit was changed, instead of all at once at the end 

of the scan the PLC would operate much slower. 

8.2.2 The Logic Scan 

Ladder logic programs are modelled after relay logic. In relay logic each element 

in the ladder will switch as quickly as possible. But in a program elements can only be 

examines one at a time in a fixed sequence. Consider the ladder logic in Figure 8.4, the 

ladder logic will be interpreted left-to-right, top-to-bottom. In the figure the ladder logic 

scan begins at the top rung. At the end of the rung it interprets the top output first, then the 

output branched below it. On the second rung it solves branches, before moving along the 

ladder logic rung. 



1 2 3 

4 

5 6 

9 

11 

7 8 

10 

Figure 8.4 

Ladder Logic Execution Sequence 

The logic scan sequence become important when solving ladder logic programs 

which use outputs as inputs, as we will see in Chapter 8. It also becomes important when 

considering output usage. Consider Figure 8.5, the first line of ladder logic will examine 

input A and set output X to have the same value. The second line will examine input B and 

set the output X to have the opposite value. So the value of X was only equal to A until the 

second line of ladder logic was scanned. Recall that during the logic scan the outputs are 

only changed in memory, the actual outputs are only updated when the ladder logic scan is 

complete. Therefore the output scan would update the real outputs based upon the second 

line of ladder logic, and the first line of ladder logic would be ineffective. 

A 

X 

B 

X 

Note: It is a common mistake for beginners to unintentionally repeat 

the same ladder logic output more than once. This will basically 

invalidate the first output, in this case the first line will never do 

anything. 

Figure 8.5 

A Duplicated Output Error 



8.3 PLC STATUS 

The lack of keyboard, and other input-output devices is very noticeable on a PLC. 

On the front of the PLC there are normally limited status lights. Common lights indicate; 

power on - this will be on whenever the PLC has power 

program running - this will often indicate if a program is running, or if no program 

is running 

fault - this will indicate when the PLC has experienced a major hardware or software 

problem 

These lights are normally used for debugging. Limited buttons will also be provided 

for PLC hardware. The most common will be a run/program switch that will be 

switched to program when maintenance is being conducted, and back to run when in production. 

This switch normally requires a key to keep unauthorized personnel from altering 

the PLC program or stopping execution. A PLC will almost never have an on-off switch or 

reset button on the front. This needs to be designed into the remainder of the system. 

The status of the PLC can be detected by ladder logic also. It is common for programs 

to check to see if they are being executed for the first time, as shown in Figure 8.6. 

The ’first scan’ or ’first pass’ input will be true the very first time the ladder logic is 

scanned, but false on every other scan. In this case the address for ’first pass’ in Control- 

Logix is ’S:FS’. With the logic in the example the first scan will seal on ’light’, until 

’clear’ is turned on. So the light will turn on after the PLC has been turned on, but it will 

turn off and stay off after ’clear’ is turned on. The ’first scan’ bit is also referred to at the 

’first pass’ bit. 

first scan 

S:FS 

light 

clear 

light 

Figure 8.6 

An program that checks for the first scan of the PLC 

8.4 MEMORY TYPES 

There are a few basic types of computer memory that are in use today. 



RAM (Random Access Memory) - this memory is fast, but it will lose its contents 

when power is lost, this is known as volatile memory. Every PLC uses this 

memory for the central CPU when running the PLC. 

ROM (Read Only Memory) - this memory is permanent and cannot be erased. It is 

often used for storing the operating system for the PLC. 

EPROM (Erasable Programmable Read Only Memory) - this is memory that can 

be programmed to behave like ROM, but it can be erased with ultraviolet light 

and reprogrammed. 

EEPROM (Electronically Erasable Programmable Read Only Memory) - This 

memory can store programs like ROM. It can be programmed and erased using 

a voltage, so it is becoming more popular than EPROMs. 

Hard Disk - Software based PLCs run on top of another operating system (such as 

Windows) that will read and save values to a hard drive, in case power is lost. 

All PLCs use RAM for the CPU and ROM to store the basic operating system for 

the PLC. When the power is on the contents of the RAM will be kept, but the issue is what 

happens when power to the memory is lost. Originally PLC vendors used RAM with a battery 

so that the memory contents would not be lost if the power was lost. This method is 

still in use, but is losing favor. EPROMs have also been a popular choice for programming 

PLCs. The EPROM is programmed out of the PLC, and then placed in the PLC. When the 

PLC is turned on the ladder logic program on the EPROM is loaded into the PLC and run. 

This method can be very reliable, but the erasing and programming technique can be time 

consuming. EEPROM memories are a permanent part of the PLC, and programs can be 

stored in them like EPROM. Memory costs continue to drop, and newer types (such as 

flash memory) are becoming available, and these changes will continue to impact PLCs. 

8.5 SOFTWARE BASED PLCS 

The dropping cost of personal computers is increasing their use in control, including 

the replacement of PLCs. Software is installed that allows the personal computer to 

solve ladder logic, read inputs from sensors and update outputs to actuators. These are 

important to mention here because they don’t obey the previous timing model. For example, 

if the computer is running a game it may slow or halt the computer. This issue and 

others are currently being investigated and good solutions should be expected soon. 

8.6 SUMMARY 

• A PLC and computer are similar with inputs, outputs, memory, etc. 

• The PLC continuously goes through a cycle including a sanity check, input scan, 

logic scan, and output scan. 

• While the logic is being scanned, changes in the inputs are not detected, and the 



outputs are not updated. 

• PLCs use RAM, and sometime EPROMs are used for permanent programs. 


1. Does a PLC normally contain RAM, ROM, EPROM and/or batteries. 

2. What are the indicator lights on a PLC used for? 

3. A PLC can only go through the ladder logic a few times per second. Why? 

4. What will happen if the scan time for a PLC is greater than the time for an input pulse? Why? 

5. What is the difference between a PLC and a desktop computer? 

6. Why do PLCs do a self check every scan? 

7. Will the test time for a PLC be long compared to the time required for a simple program. 

8. What is wrong with the following ladder logic? What will happen if it is used? 

A 

B 

L 

U 

X 

Y 

X 

Y 

9. What is the address for a memory location that indicates when a PLC has just been turned on? 


1. Every PLC contains RAM and ROM, but they may also contain EPROM or batteries. 

2. Diagnostic and maintenance 

3. Even if the program was empty the PLC would still need to scan inputs and outputs, and do a 

self check. 

4. The pulse may be missed if it occurs between the input scans 



5. Some key differences include inputs, outputs, and uses. A PLC has been designed for the factory 

floor, so it does not have inputs such as keyboards and mice (although some newer types 

can). They also do not have outputs such as a screen or sound. Instead they have inputs and 

outputs for voltages and current. The PLC runs user designed programs for specialized tasks, 

whereas on a personal computer it is uncommon for a user to program their system. 

6. This helps detect faulty hardware or software. If an error were to occur, and the PLC continued 

operating, the controller might behave in an unpredictable way and become dangerous to people 

and equipment. The self check helps detect these types of faults, and shut the system down 

safely. 

7. Yes, the self check is equivalent to about 1ms in many PLCs, but a single program instruction is 

about 1 micro second. 

8. The normal output Y is repeated twice. In this example the value of Y would always match B, 

and the earlier rung with A would have no effect on Y. 

9. S2:1/14 for micrologix, S2:1/15 for PLC-5, S:FS for ControlLogix processor 


1. Describe the basic steps of operation for a PLC after it is turned on. 

2. Repeating a normal output in ladder logic should not be done normally. Discuss why. 

3. Why does removing a battery from some older PLCs clear the memory? 


plc timers - 9.1 

9. LATCHES, TIMERS, COUNTERS AND MORE 

Topics: 

• Latches, timers, counters and MCRs 

• Design examples 

• Internal memory locations are available, and act like outputs 

Objectives: 

• Understand latches, timers, counters and MCRs. 

• To be able to select simple internal memory bits. 


More complex systems cannot be controlled with combinatorial logic alone. The 

main reason for this is that we cannot, or choose not to add sensors to detect all conditions. 

In these cases we can use events to estimate the condition of the system. Typical events 

used by a PLC include; 

first scan of the PLC - indicating the PLC has just been turned on 

time since an input turned on/off - a delay 

count of events - to wait until set number of events have occurred 

latch on or unlatch - to lock something on or turn it off 

The common theme for all of these events is that they are based upon one of two 

questions "How many?" or "How long?". An example of an event based device is shown 

in Figure 9.1. The input to the device is a push button. When the push button is pushed the 

input to the device turns on. If the push button is then released and the device turns off, it 

is a logical device. If when the push button is release the device stays on, is will be one 

type of event based device. To reiterate, the device is event based if it can respond to one 

or more things that have happened before. If the device responds only one way to the 

immediate set of inputs, it is logical. 



e.g. A Start Push Button 

Push Button 

+V 

On/Off 

Device 

Push Button 

Device 

Device 

(Logical Response) 

(Event Response) 

time 

Figure 9.1 

An Event Driven Device 

9.2 LATCHES 

A latch is like a sticky switch - when pushed it will turn on, but stick in place, it 

must be pulled to release it and turn it off. A latch in ladder logic uses one instruction to 

latch, and a second instruction to unlatch, as shown in Figure 9.2. The output with an L 

inside will turn the output D on when the input A becomes true. D will stay on even if A 

turns off. Output D will turn off if input B becomes true and the output with a U inside 

becomes true (Note: this will seem a little backwards at first). If an output has been latched 

on, it will keep its value, even if the power has been turned off. 

A 

A 

L 

D 

C 

B 

U 

D 

Figure 9.2 

A Ladder Logic Latch 



The operation of the ladder logic in Figure 9.2 is illustrated with a timing diagram 

in Figure 9.3. A timing diagram shows values of inputs and outputs over time. For example 

the value of input A starts low (false) and becomes high (true) for a short while, and 

then goes low again. Here when input A turns on both the outputs turn on. There is a slight 

delay between the change in inputs and the resulting changes in outputs, due to the program 

scan time. Here the dashed lines represent the output scan, sanity check and input 

scan (assuming they are very short.) The space between the dashed lines is the ladder logic 

scan. Consider that when A turns on initially it is not detected until the first dashed line. 

There is then a delay to the next dashed line while the ladder is scanned, and then the output 

at the next dashed line. When A eventually turns off, the normal output C turns off, but 

the latched output D stays on. Input B will unlatch the output D. Input B turns on twice, 

but the first time it is on is not long enough to be detected by an input scan, so it is ignored. 

The second time it is on it unlatches output D and output D turns off. 

Timing Diagram 

event too short to be noticed (aliasing) 

A 

B 

C 

D 

These lines indicate PLC input/output refresh times. At this time 

all of the outputs are updated, and all of the inputs are read. 

Notice that some inputs can be ignored if at the wrong time, 

and there can be a delay between a change in input, and a change 

in output. 

The space between the lines is the scan time for the ladder logic. 

The spaces may vary if different parts of the ladder diagram are 

executed each time through the ladder (as with state space code). 

The space is a function of the speed of the PLC, and the number of 

Ladder logic elements in the program. 

Figure 9.3 A Timing Diagram for the Ladder Logic in Figure 9.2 



The timing diagram shown in Figure 9.3 has more details than are normal in a timing 

diagram as shown in Figure 9.4. The brief pulse would not normally be wanted, and 

would be designed out of a system either by extending the length of the pulse, or decreasing 

the scan time. An ideal system would run so fast that aliasing would not be possible. 

A 

B 

C 

D 

Figure 9.4 

A Typical Timing Diagram 

A more elaborate example of latches is shown in Figure 9.5. In this example the 

addresses are for an older Allen-Bradley Micrologix controller. The inputs begin with I/, 

followed by an input number. The outputs begin with O/, followed by an output number. 



I/0 

O/0 

I/0 

O/1 

L 

I/1 

O/1 

U 

I/0 

O/2 

I/1 

O/2 

I/0 

I/1 

O/0 

O/1 

O/2 

Figure 9.5 

A Latch Example 

A normal output should only appear once in ladder logic, but latch and unlatch 

instructions may appear multiple times. In Figure 9.5 a normal output O/2 is repeated 

twice. When the program runs it will examine the fourth line and change the value of O/2 

in memory (remember the output scan does not occur until the ladder scan is done.) The 

last line is then interpreted and it overwrites the value of O/2. Basically, only the last line 

will change O/2. 

Latches are not used universally by all PLC vendors, others such as Siemens use 



flip-flops. These have a similar behavior to latches, but a different notation as illustrated in 

Figure 9.6. Here the flip-flop is an output block that is connected to two different logic 

rungs. The first rung shown has an input A connected to the S setting terminal. When A 

goes true the output value Q will go true. The second rung has an input B connected to the 

R resetting terminal. When B goes true the output value Q will be turned off. The output Q 

will always be the inverse of Q. Notice that the S and R values are equivalent to the L and 

U values from earlier examples. 

A 

B 

S 

R 

Q 

Q 

A 

B 

Q 

Q 

Figure 9.6 

Flip-Flops for Latching Values 

9.3 TIMERS 

There are four fundamental types of timers shown in Figure 9.7. An on-delay timer 

will wait for a set time after a line of ladder logic has been true before turning on, but it 

will turn off immediately. An off-delay timer will turn on immediately when a line of ladder 

logic is true, but it will delay before turning off. Consider the example of an old car. If 

you turn the key in the ignition and the car does not start immediately, that is an on-delay. 

If you turn the key to stop the engine but the engine doesn’t stop for a few seconds, that is 

an off delay. An on-delay timer can be used to allow an oven to reach temperature before 

starting production. An off delay timer can keep cooling fans on for a set time after the 



oven has been turned off. 

on-delay 

off-delay 

retentive 

RTO 

RTF 

nonretentive 

TON 

TOF 

TON - Timer ON 

TOF - Timer OFf 

RTO - Retentive Timer On 

RTF - Retentive Timer oFf 

Figure 9.7 

The Four Basic Timer Types 

A retentive timer will sum all of the on or off time for a timer, even if the timer 

never finished. A nonretentive timer will start timing the delay from zero each time. Typical 

applications for retentive timers include tracking the time before maintenance is 

needed. A non retentive timer can be used for a start button to give a short delay before a 

conveyor begins moving. 

An example of an Allen-Bradley TON timer is shown in Figure 9.8. The rung has a 

single input A and a function block for the TON. (Note: This timer block will look different 

for different PLCs, but it will contain the same information.) The information inside 

the timer block describes the timing parameters. The first item is the timer ’example’. This 

is a location in the PLC memory that will store the timer information. The preset is the 

millisecond delay for the timer, in this case it is 4s (4000ms). The accumulator value gives 

the current value of the timer as 0. While the timer is running the accumulated value will 

increase until it reaches the preset value. Whenever the input A is true the EN output will 

be true. The DN output will be false until the accumulator has reached the preset value. 

The EN and DN outputs cannot be changed when programming, but these are important 

when debugging a ladder logic program. The second line of ladder logic uses the timer DN 

output to control another output B. 



A 

TON 

Timer example 

Preset 4000 

Accumulator 0 

(EN) 

(DN) 

example.DN 

B 

A 

example.EN 

example.DN 

example.TT 

B 

example.ACC 0 3 

0 3 6 9 13 14 17 19 

Note: For the older Allen-Bradley equipment the notations are similar, although the 

tag names are replaced with a more strict naming convention. The timers are kept 

in ’files’ with names starting with ’T4:’, followed by a timer number. The examples 

below show the older (PLC-5 and micrologix notations compared to the new 

RS-Logix (5000) notations. In the older PLCs the timer is given a unique number, 

in the RSLogix 5000 processors it is given a tag name (in this case ’t’) and type 

’TIMER’. 

4 

2 

Older 

T4:0/DN 

T4:0/EN 

T4:0.PRE 

T4:0.ACC 

T4:0/TT 

Newer 

t.DN 

t.EN 

t.PRE 

t.ACC 

t.TT 

Figure 9.8 

An Allen-Bradley TON Timer 



The timing diagram in Figure 9.8 illustrates the operation of the TON timer with a 

4 second on-delay. A is the input to the timer, and whenever the timer input is true the EN 

enabled bit for the timer will also be true. If the accumulator value is equal to the preset 

value the DN bit will be set. Otherwise, the TT bit will be set and the accumulator value 

will begin increasing. The first time A is true, it is only true for 3 seconds before turning 

off, after this the value resets to zero. (Note: in a retentive time the value would remain at 

3 seconds.) The second time A is true, it is on more than 4 seconds. After 4 seconds the TT 

bit turns off, and the DN bit turns on. But, when A is released the accumulator resets to 

zero, and the DN bit is turned off. 

A value can be entered for the accumulator while programming. When the program 

is downloaded this value will be in the timer for the first scan. If the TON timer is 

not enabled the value will be set back to zero. Normally zero will be entered for the preset 

value. 

The timer in Figure 9.9 is identical to that in Figure 9.8, except that it is retentive. 

The most significant difference is that when the input A is turned off the accumulator 

value does not reset to zero. As a result the timer turns on much sooner, and the timer does 

not turn off after it turns on. A reset instruction will be shown later that will allow the 

accumulator to be reset to zero. 

A 

RTO 

Timer example 

Preset 4000 

Accum. 0 

(EN) 

(DN) 

A 

example.EN 

example.DN 

example.TT 

example.ACC 0 

3 

4 

0 3 6 9 10 

14 17 19 



Figure 9.9 

An Allen Bradley Retentive On-Delay Timer 

An off delay timer is shown in Figure 9.10. This timer has a time base of 0.01s, 

with a preset value of 3500, giving a total delay of 3.5s. As before the EN enable for the 

timer matches the input. When the input A is true the DN bit is on. Is is also on when the 

input A has turned off and the accumulator is counting. The DN bit only turns off when the 

input A has been off long enough so that the accumulator value reaches the preset. This 

type of timer is not retentive, so when the input A becomes true, the accumulator resets. 

A 

TOF 

Timer example 

Preset 3500 

Accum. 0 

(EN) 

(DN) 

A 

example.EN 

example.DN 

example.TT 

example.ACC 

0 

3 

3.5 

0 3 6 9.5 10 16 18 20 

Figure 9.10 

An Allen Bradley Off-Delay Timer 

Retentive off-delay (RTF) timers have few applications and are rarely used, therefore 

many PLC vendors do not include them. 

An example program is shown in Figure 9.11. In total there are four timers used in 

this example, t_1, t_2, t_3, and t_4. The timer instructions are shown with the accumulator 

values omitted, assuming that they start with a value of zero. All four different types of 

counters have the input ’go’. Output ’done’ will turn on when the TON counter t_1 is 

done. All four of the timers can be reset with input ’reset’. 



go 

TON 

t_1 

delay 4 sec 

go 

RTO 

t_2 

delay 4 sec 

go 

TOF 

t_3 

delay 4 sec 

go 

RTF 

t_4 

delay 4 sec 

t_1.DN 

done 

reset 

RES 

t_1 

reset 

RES 

t_2 

reset 

RES 

t_3 

reset 

RES 

t_4 

Figure 9.11 

A Timer Example 

A timing diagram for this example is shown in Figure 9.12. As input go is turned 

on the TON and RTO timers begin to count and reach 4s and turn on. When reset becomes 

true it resets both timers and they start to count for another second before go is turned off. 

After the input is turned off the TOF and RTF both start to count, but neither reaches the 

4s preset. The input go is turned on again and the TON and RTO both start counting. The 

RTO turns on one second sooner because it had 1s stored from the 7-8s time period. After 

go turns off again both the off delay timers count down, and reach the 4 second delay, and 

turn on. These patterns continue across the diagram. 



go 

reset 

t_1.DN 

t_2.DN 

t_3.DN 

t_4.DN 

done 

0 5 10 15 20 25 30 35 40 

time 

(sec) 

Figure 9.12 A Timing Diagram for Figure 9.11 

Consider the short ladder logic program in Figure 9.13 for control of a heating 

oven. The system is started with a Start button that seals in the Auto mode. This can be 

stopped if the Stop button is pushed. (Remember: Stop buttons are normally closed.) 

When the Auto goes on initially the TON timer is used to sound the horn for the first 10 

seconds to warn that the oven will start, and after that the horn stops and the heating coils 

start. When the oven is turned off the fan continues to blow for 300s or 5 minutes after. 



Start 

Stop 

Auto 

Auto 

Auto 

TON 

Timer heat 

Delay 10s 

TOF 

Timer cooling 

Delay 300s 

heat.TT 

heat.DN 

Horn 

Heating Coils 

cooling.DN 

Fan 

Note: For the remainder of the text I will use the shortened notation for timers 

shown above. This will save space and reduce confusion. 

Figure 9.13 

A Timer Example 

A program is shown in Figure 9.14 that will flash a light once every second. When 

the PLC starts, the second timer will be off and the t_on.DN bit will be off, therefore the 

normally closed input to the first timer will be on. t_off will start timing until it reaches 

0.5s, when it is done the second timer will start timing, until it reaches 0.5s. At that point 

t_on.DN will become true, and the input to the first time will become false. t_off is then set 

back to zero, and then t_on is set back to zero. And, the process starts again from the 

beginning. In this example the first timer is used to drive the second timer. This type of 

arrangement is normally called cascading, and can use more that two timers. 



t_on.DN 

t_off.DN 

t_on.TT 

TON 

Timer t_off 

Delay 0.5s 

TON 

Timer t_on 

Delay 0.5s 

Light 

Figure 9.14 

Another Timer Example 

9.4 COUNTERS 

There are two basic counter types: count-up and count-down. When the input to a 

count-up counter goes true the accumulator value will increase by 1 (no matter how long 

the input is true.) If the accumulator value reaches the preset value the counter DN bit will 

be set. A count-down counter will decrease the accumulator value until the preset value is 

reached. 

An Allen Bradley count-up (CTU) instruction is shown in Figure 9.15. The 

instruction requires memory in the PLC to store values and status, in this case is example. 

The preset value is 4 and the value in the accumulator is 2. If the input A were to go from 

false to true the value in the accumulator would increase to 3. If A were to go off, then on 

again the accumulator value would increase to 4, and the DN bit would go on. The count 

can continue above the preset value. If input B becomes true the value in the counter accumulator 

will become zero. 



A 

CTU 

Counter example 

Preset 4 

Accum. 2 

(CU) 

(DN) 

example.DN 

X 

B 

RES 

example 

Note: The notations for older Allen-Bradley equipment are very similar to the newer 

notations. The examples below show the older (PLC-5 and micrologix notations 

compared to the new RS-Logix (5000) notations. In the older PLCs the counter is 

given a unique name, in the RSLogix 5000 processors it is given a name (in this 

case ’c’) and the type ’COUNTER’. 

Older 

C5:0/DN 

C5:0/CU 

C5:0.PRE 

C5:0.ACC 

C5:0/CD 

Newer 

c.DN 

c.CU 

c.PRE 

c.ACC 

c.CD 

Figure 9.15 

An Allen Bradley Counter 

Count-down counters are very similar to count-up counters. And, they can actually 

both be used on the same counter memory location. Consider the example in Figure 9.16, 

the example input cnt_up drives the count-up instruction for counter example. Input 

cnt_down drives the count-down instruction for the same counter location. The preset 

value for a counter is stored in memory location example so both the count-up and countdown 

instruction must have the same preset. Input reset will reset the counter. 



cnt_up 

cnt_down 

reset 

CTU 

CTD 

RES 

example 

preset 3 

example 

preset 3 

example 

example.DN 

output_thingy 

cnt_up 

cnt_down 

reset 

example.DN 

output_thingy 

Figure 9.16 

A Counter Example 

The timing diagram in Figure 9.16 illustrates the operation of the counter. If we 

assume that the value in the accumulator starts at 0, then the positive edges on the cnt_up 

input will cause it to count up to 3 where it turns the counter example done bit on. It is then 

reset by input reset and the accumulator value goes to zero. Input cnt_up then pulses again 

and causes the accumulator value to increase again, until it reaches a maximum of 5. Input 

cnt_down then causes the accumulator value to decrease down below 3, and the counter 

turns off again. Input cnt_up then causes it to increase, but input reset resets the accumulator 

back to zero again, and the pulses continue until 3 is reached near the end. 



The program in Figure 9.17 is used to remove 5 out of every 10 parts from a conveyor 

with a pneumatic cylinder. When the part is detected both counters will increase 

their values by 1. When the sixth part arrives the first counter will then be done, thereby 

allowing the pneumatic cylinder to actuate for any part after the fifth. The second counter 

will continue until the eleventh part is detected and then both of the counters will be reset. 

part_present 

CTU 

Counter parts_cnt 

Preset 6 

CTU 

Counter parts_max 

Preset 11 

parts_max.DN 

RES 

parts_cnt 

RES 

parts_max 

parts_cnt.DN part present pneumatic 

cylinder 

Figure 9.17 

A Counter Example 

9.5 MASTER CONTROL RELAYS (MCRs) 

In an electrical control system a Master Control Relay (MCR) is used to shut down 

a section of an electrical system, as shown earlier in the electrical wiring chapter. This 

concept has been implemented in ladder logic also. A section of ladder logic can be put 

between two lines containing MCR’s. When the first MCR coil is active, all of the intermediate 

ladder logic is executed up to the second line with an MCR coil. When the first 

MCR coil in inactive, the ladder logic is still examined, but all of the outputs are forced 

off. 

Consider the example in Figure 9.18. If A is true, then the ladder logic after will be 



executed as normal. If A is false the following ladder logic will be examined, but all of the 

outputs will be forced off. The second MCR function appears on a line by itself and marks 

the end of the MCR block. After the second MCR the program execution returns to normal. 

While A is true, X will equal B, and Y can be turned on by C, and off by D. But, if A 

becomes false X will be forced off, and Y will be left in its last state. Using MCR blocks to 

remove sections of programs will not increase the speed of program execution significantly 

because the logic is still examined. 

A 

MCR 

B 

X 

C 

D 

L 

U 

Y 

Y 

MCR 

Note: If a normal input is used inside an MCR block it will be forced off. If the 

output is also used in other MCR blocks the last one will be forced off. The 

MCR is designed to fully stop an entire section of ladder logic, and is best 

used this way in ladder logic designs. 

Figure 9.18 

MCR Instructions 

If the MCR block contained another function, such as a TON timer, turning off the 

MCR block would force the timer off. As a general rule normal outputs should be outside 

MCR blocks, unless they must be forced off when the MCR block is off. 



9.6 INTERNAL BITS 

Simple programs can use inputs to set outputs. More complex programs also use 

internal memory locations that are not inputs or outputs. These Boolean memory locations 

are sometimes referred to as ’internal relays’ or ’control relays’. Knowledgeable programmers 

will often refer to these as ’bit memory’. In the newer Allen Bradley PLCs these can 

be defined as variables with the type ’BOOL’. The programmer is free to use these memory 

locations however they see fit. 

NOTE: In the older Allen Bradley 

PLCs these addresses 

begin with ’B3’ by default. 

The first bit in memory is 

’B3:0/0’, where the first zero 

represents the first 16 bit 

word, and the second zero 

represents the first bit in the 

word. The sequence of bits 

is shown to the right. 

bit 

number 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

memory 

location 

B3:0/0 

B3:0/1 

B3:0/2 

B3:0/3 

B3:0/4 

B3:0/5 

B3:0/6 

B3:0/7 

B3:0/8 

B3:0/9 

B3:0/10 

B3:0/11 

B3:0/12 

B3:0/13 

B3:0/14 

B3:0/15 

B3:1/0 

B3:1/1 

bit 

number 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

etc... 

memory 

location 

B3:1/2 

B3:1/3 

B3:1/4 

B3:1/5 

B3:1/6 

B3:1/7 

B3:1/8 

B3:1/9 

B3:1/10 

B3:1/11 

B3:1/12 

B3:1/13 

B3:1/14 

B3:1/15 

B3:2/0 

B3:2/1 

B3:2/2 

etc... 

An example of bit memory usage is shown in Figure 9.19. The first ladder logic 

rung will turn on the internal memory bit ’A_pushed’ (e.g., B3:0/0) when input ’hand_A’ 

is activated, and input ’clear’ is off. (Notice that the Boolean memory is being used as 

both an input and output.) The second line of ladder logic similar. In this case when both 

inputs have been activated, the output ’press on’ is active. 



hand_A 

(I:0/0) 

A_pushed 

(B3:0/0) 

clear 

(I:0/2) 

A_pushed 

(B3:0/0) 

hand_B 

(I:0/1) 

B_pushed 

(B3:0/1) 

clear 

(I:0/2) 

B_pushed 

(B3:0/1) 

A_pushed 

(B3:0/0) 

B_pushed 

(B3:0/1) 

press_on 

(O:0/0) 

Figure 9.19 

An example using bit memory (older notations are in parentheses) 

Bit memory was presented briefly here because it is important for design techniques 

in the following chapters, but it will be presented in greater depth after that. 

9.7 DESIGN CASES 

The following design cases are presented to help emphasize the principles presented 

in this chapter. I suggest that you try to develop the ladder logic before looking at 

the provided solutions. 

9.7.1 Basic Counters And Timers 

Problem: Develop the ladder logic that will turn on an output light, 15 seconds 

after switch A has been turned on. 



Solution: 

A 

TON 

Preset 15s 

delay 

delay.DN 

Light 

Figure 9.20 

A Simple Timer Example 

Problem: Develop the ladder logic that will turn on a light, after switch A has been 

closed 10 times. Push button B will reset the counters. 

Solution: 

A 

count.DN 

CTU 

Preset 10 

Accum. 0 

Light 

count 

B 

RES 

count 

Figure 9.21 

A Simple Counter Example 

9.7.2 More Timers And Counters 

Problem: Develop a program that will latch on an output B 20 seconds after input 

A has been turned on. After A is pushed, there will be a 10 second delay until A can have 

any effect again. After A has been pushed 3 times, B will be turned off. 



Solution: 

A 

On 

L 

On 

t_0.DN 

TON t_0 

Time base: 1.0 

Preset 20 

Light 

L 

t_0.DN 

t_1.DN 

TON t_1 

Time base: 1.0 

Preset 10 

On 

U 

On 

count.DN 

CTU 

Preset 3 

Accum. 0 

Light 

count 

U 

Figure 9.22 

A More Complex Timer Counter Example 

9.7.3 Deadman Switch 

Problem: A motor will be controlled by two switches. The Go switch will start the 

motor and the Stop switch will stop it. If the Stop switch was used to stop the motor, the 

Go switch must be thrown twice to start the motor. When the motor is active a light should 

be turned on. The Stop switch will be wired as normally closed. 



Solution: 

Motor 

Stop 

C5:0 

RES 

Go 

Motor 

CTU 

Preset 2 

Accum. 1 

count 

count.DN 

Stop 

Motor 

Motor 

Light 

Consider: 

What will happen if stop is pushed and the motor is not running? 

Figure 9.23 

A Motor Starter Example 

9.7.4 Conveyor 

Problem: A conveyor is run by switching on or off a motor. We are positioning 

parts on the conveyor with an optical detector. When the optical sensor goes on, we want 

to wait 1.5 seconds, and then stop the conveyor. After a delay of 2 seconds the conveyor 

will start again. We need to use a start and stop button - a light should be on when the system 

is active. 



Solution: 

Go 

Stop 

Light 

Light 

Part Detect 

TON 

Preset 1.5s 

incoming 

incoming.DN 

TON 

Preset 2s 

stopped 

incoming.DN 

Light 

Motor 

stopped.DN 

stopped.DN 

incoming 

RES 

stopped 

RES 

Consider: What is assumed about part arrival and departure? 

Figure 9.24 

A Conveyor Controller Example 

9.7.5 Accept/Reject Sorting 

Problem: For the conveyor in the last case we will add a sorting system. Gages 

have been attached that indicate good or bad. If the part is good, it continues on. If the part 

is bad, we do not want to delay for 2 seconds, but instead actuate a pneumatic cylinder. 



Solution: 

Go 

Stop 

Light 

Light 

Part Detect 

TON 

incoming 

Preset 1.5s 

incoming.DN 

Part_Good 

TON 

stopped 

Preset 2s 

incoming.DN 

Part_Good 

TON 

rejected 

Preset 0.5s 

stopped.EN 

Light 

Motor 

rejected.EN 

stopped.DN 

rejected.DN 

Cylinder 

incoming 

RES 

stopped.DN 

rejected.DN 

stopped 

rejected 

RES 

RES 

Figure 9.25 

A Conveyor Sorting Example 



9.7.6 Shear Press 

Problem: The basic requirements are, 

1. A toggle start switch (TS1) and a limit switch on a safety gate (LS1) must both 

be on before a solenoid (SOL1) can be energized to extend a stamping cylinder 

to the top of a part. 

2. While the stamping solenoid is energized, it must remain energized until a limit 

switch (LS2) is activated. This second limit switch indicates the end of a stroke. 

At this point the solenoid should be de-energized, thus retracting the cylinder. 

3. When the cylinder is fully retracted a limit switch (LS3) is activated. The cycle 

may not begin again until this limit switch is active. 

4. A cycle counter should also be included to allow counts of parts produced. 

When this value exceeds 5000 the machine should shut down and a light lit up. 

5. A safety check should be included. If the cylinder solenoid has been on for more 

than 5 seconds, it suggests that the cylinder is jammed or the machine has a 

fault. If this is the case, the machine should be shut down and a maintenance 

light turned on. 



Solution: 

TS1 LS1 LS3 part_cnt.DN 

SOL1 

L 

LS2 

SOL1 

U 

extend.DN 

SOL1 

SOL1 

CTU 

Preset 5000 

Accum. 0 

RTO 

Preset 5s 

part_cnt 

extend 

extend.DN 

part_cnt.DN 

LIGHT 

L 

RESET 

extend 

RES 

- what do we need to do when the machine is reset? 

Figure 9.26 

A Shear Press Controller Example 

9.8 SUMMARY 

• Latch and unlatch instructions will hold outputs on, even when the power is 

turned off. 

• Timers can delay turning on or off. Retentive timers will keep values, even when 

inactive. Resets are needed for retentive timers. 

• Counters can count up or down. 

• When timers and counters reach a preset limit the DN bit is set. 



• MCRs can force off a section of ladder logic. 


1. What does edge triggered mean? What is the difference between positive and negative edge 

triggered? 

2. Are reset instructions necessary for all timers and counters? 

3. What are the numerical limits for typical timers and counters? 

4. If a counter goes below the bottom limit which counter bit will turn on? 

5. a) Write ladder logic for a motor starter that has a start and stop button that uses latches. b) 

Write the same ladder logic without latches. 

6. Use a timing diagram to explain how an on delay and off delay timer are different. 

7. For the retentive off timer below, draw out the status bits. 

A 

RTF 

Timer t 

Preset 3.5s 

Accum. 0 

(EN) 

(DN) 

A 

t.EN 

t.DN 

t.TT 

t.ACC 

0 3 6 10 16 18 20 



8. Complete the timing diagrams for the two timers below. 

RTO 

A 

Timer t 

Preset 10s 

Accum. 1 

(EN) 

(DN) 

A 

t.EN 

t.TT 

t.DN 

t.ACC 

0 3 6 9 14 17 19 20 

A 

TOF 

Timer t 

Preset 0.5s 

Accum. 0 

(EN) 

(DN) 

A 

t.EN 

t.TT 

t.DN 

t.ACC 

0 15 45 150 200 225 



9. Given the following timing diagram, draw the done bits for all four fundamental timer types. 

Assume all start with an accumulated value of zero, and have a preset of 1.5 seconds. 

input 

TON 

RTO 

TOF 

RTF 

0 1 2 3 4 5 6 7 sec 

10. Design ladder logic that allows an RTO to behave like a TON. 

11. Design ladder logic that uses a timer and counter to measure a time of 50.0 days. 

12. Develop the ladder logic that will turn on an output (light), 15 seconds after switch (A) has 

been turned on. 

13. Develop the ladder logic that will turn on a output (light), after a switch (A) has been closed 

10 times. Push button (B) will reset the counters. 

14. Develop a program that will latch on an output (B), 20 seconds after input (A) has been turned 

on. The timer will continue to cycle up to 20 seconds, and reset itself, until A has been turned 

off. After the third time the timer has timed to 20 seconds, B will be unlatched. 

15. A motor will be connected to a PLC and controlled by two switches. The GO switch will start 

the motor, and the STOP switch will stop it. If the motor is going, and the GO switch is thrown, 

this will also stop the motor. If the STOP switch was used to stop the motor, the GO switch 

must be thrown twice to start the motor. When the motor is running, a light should be turned on 

(a small lamp will be provided). 

16. In dangerous processes it is common to use two palm buttons that require a operator to use 

both hands to start a process (this keeps hands out of presses, etc.). To develop this there are 

two inputs that must be turned on within 0.25s of each other before a machine cycle may begin. 



17. Design a conveyor control system that follows the design guidelines below. 

- The conveyor has an optical sensor S1 that detects boxes entering a workcell 

- There is also an optical sensor S2 that detects boxes leaving the workcell 

- The boxes enter the workcell on a conveyor controlled by output C1 

- The boxes exit the workcell on a conveyor controlled by output C2 

- The controller must keep a running count of boxes using the entry and exit sensors 

- If there are more than five boxes in the workcell the entry conveyor will stop 

- If there are no boxes in the workcell the exit conveyor will be turned off 

- If the entry conveyor has been stopped for more than 30 seconds the count will be 

reset to zero, assuming that the boxes in the workcell were scrapped. 

18. Write a ladder logic program that does what is described below. 

- When button A is pushed, a light will flash for 5 seconds. 

- The flashing light will be on for 0.25 sec and off for 0.75 sec. 

- If button A has been pushed 5 times the light will not flash until the system is 

reset. 

- The system can be reset by pressing button B 

19. Write a program that will turn on a flashing light for the first 15 seconds after a PLC is turned 

on. The light should flash for half a second on and half a second off. 

20. A buffer can hold up to 10 parts. Parts enter the buffer on a conveyor controller by output conveyor. 

As parts arrive they trigger an input sensor enter. When a part is removed from the 

buffer they trigger the exit sensor. Write a program to stop the conveyor when the buffer is full, 

and restart it when there are fewer than 10 parts in the buffer. As normal the system should also 

include a start and stop button. 

21. What is wrong with the following ladder logic? What will happen if it is used? 

A 

L 

X 

B 

U 

Y 

X 

Y 

22. We are using a pneumatic cylinder in a process. The cylinder can become stuck, and we need 

to detect this. Proximity sensors are added to both endpoints of the cylinder’s travel to indicate 

when it has reached the end of motion. If the cylinder takes more than 2 seconds to complete a 

motion this will indicate a problem. When this occurs the machine should be shut down and a 

light turned on. Develop ladder logic that will cycle the cylinder in and out repeatedly, and 

watch for failure. 




1. edge triggered means the event when a logic signal goes from false to true (positive edge) or 

from true to false (negative edge). 

2. no, but they are essential for retentive timers, and very important for counters. 

3. Timers on PLC-5s and Micrologix are 16 bit, so they are limited to a range of -32768 to 

+32767. ControlLogix timers are 32 bit and have a range of -2,147,483,648 to 2,147,483,647. 

4. the un underflow bit. This may result in a fault in some PLCs. 

5. 

first pass 

stop 

U 

motor 

start 

L 

motor 

start 

motor 

stop 

motor 

6. 

input 

TON 

delays turning on 

TOF 

delays turning off 



7. 

A 

RTF 

Timer t 

Preset 3.5s 

Accum. 0 

(EN) 

(DN) 

A 

t.EN 

t.DN 

t.TT 

t.ACC 

0 3 6 10 16 18 20 



8. 

A 

RTO 

Timer t 

(EN) 

Preset 10s 

Accum. 1 

(DN) 

t.EN 

t.TT 

t.DN 

A 

t.ACC 

0 3 6 9 14 17 19 20 

A 

TOF 

Timer t 

Preset 0.5s 

Accum. 0 

(EN) 

(DN) 

A 

t.EN 

t.TT 

t.DN 

t.ACC 

0 15 45 150 200 225 



9. 

input 

TON 

RTO 

TOF 

RTF 

0 1 2 3 4 5 6 7 sec 

10. 

A 

RTO 

Timer t 

Preset 2s 

A 

RES 

t 

11. 

A 

tick.DN 

wait.DN 

tick.DN 

TON 

Timer tick 

Base 1.0 

Preset 3600 

CTU 

Counter wait 

Preset 1200 

Light 



12. 

A 

seal_in 

seal_in 

seal_in 

TON 

timer delay 

delay 15 sec 

delay.DN 

light 

13. 

B 

cnt 

RES 

A 

CTU 

counter cnt 

presetR 10 

cnt.DN 

light 



14. 

A 

delay.DN 

TON 

timer delay 

delay 20 s 

delay.DN 

TON 

timer A_held 

delay 20 s 

delay.DN 

B 

L 

A_held.DN 

CTU 

counter cnt 

preset 3 

cnt.DN 

B 

U 



15. 

go 

stop 

c_0.DN 

c_1.DN 

motor 

motor 

go 

CTU 

Counter c_0 

Preset 2 

Accumulator 1 

CTU 

Counter c_1 

Preset 3 

Accumulator 1 

c_1.DN 

RES 

c_0 

RES 

c_1 

stop 

c_0.DN 

CTD 

Counter c_0 

Preset 2 

Accumulator 1 

CTD 

Counter c_1 

Preset 3 

Accumulator 1 



16. 

left_button 

TON 

Timer left 

Preset 0.25s 

right_button 

TON 

Timer right 

Preset 0.25s 

left.TT 

right.TT 

stop 

on 

on 



17. 

S1 

CTU 

Counter C_0 

Preset 6 

CTU 

Counter C_1 

Preset 1 

S2 

CTD 

Counter C_0 

Preset 6 

CTD 

Counter C_1 

Preset 1 

C_0/DN 

C_1/DN 

C1 

C2 

C_0/DN 

T_0/DN 

TON 

Timer T_0 

Preset 30s 

RES 

C_0 

RES 

C_1 



18. 

A 

T4:0/TT 

C5:0/DN 

T4:0/TT 

T4:2/DN 

TON 

timer T4:0 

delay 5s 

TON 

timer T4:1 

delay 0.25s 

T4:1/DN 

TON 

timer T4:2 

delay 0.75s 

CTU 

counter C5:0 

preset 5 

T4:1/TT 

light 

B 

RES 



19. 

First scan 

T4:0/TT 

T4:2/TT 

T4:2/DN 

T4:1/DN 

TON 

T4:0 

delay 15s 

TON 

T4:1 

delay 0.5s 

TON 

T4:2 

delay 0.5s 

light 

20. 

start 

active 

stop 

active 

enter 

exit 

active 

C5:0/DN 

CTU 

counter C5:0 

preset 10 

CTD 

counter C5:0 

preset 10 

active 

21. The normal output ‘Y’ is repeated twice. In this example the value of ‘Y’ would always match 

‘B’, and the earlier rung with ‘A’ would have no effect on ‘Y’. 



22. 

GIVE SOLUTION 


1. Draw the timer and counter done bits for the ladder logic below. Assume that the accumulators 



of all the timers and counters are reset to begin with. 

A 

TON 

Timer T_0 

Preset 2s 

RTO 

Timer T_1 

Preset 2s 

TOF 

Timer T_2 

Preset 2s 

CTU 

Counter C_0 

Preset 2 

Acc. 0 

CTD 

Counter C_1 

Preset 2 

Acc. 0 

A 

T_0/DN 

T_1/DN 

T_2/DN 

C_0/DN 

C_1/DN 

0 5 10 15 20 

t(sec) 

2. Write a ladder logic program that will count the number of parts in a buffer. As parts arrive they 

activate input A. As parts leave they will activate input B. If the number of parts is less than 8 

then a conveyor motor, output C, will be turned on. 



3. Explain what would happen in the following program when A is on or off. 

A 

MCR 

TON 

t 

5s 

MCR 

4. Write a simple program that will use one timer to flash a light. The light should be on for 1.0 

seconds and off for 0.5 seconds. Do not include start or stop buttons. 

5. We are developing a safety system (using a PLC-5) for a large industrial press. The press is 

activated by turning on the compressor power relay (R, connected to O:013/05). After R has 

been on for 30 seconds the press can be activated to move (P connected to O:013/06). The 

delay is needed for pressure to build up. After the press has been activated (with P) the system 

must be shut down (R and P off), and then the cycle may begin again. For safety, there is a sensor 

that detects when a worker is inside the press (S, connected to I:011/02), which must be off 

before the press can be activated. There is also a button that must be pushed 5 times (B, connected 

to I:011/01) before the press cycle can begin. If at any time the worker enters the press 

(and S becomes active) the press will be shut down (P and R turned off). Develop the ladder 

logic. State all assumptions, and show all work. 

6. Write a program that only uses one timer. When an input A is turned on a light will be on for 10 

seconds. After that it will be off for two seconds, and then again on for 5 seconds. After that 

the light will not turn on again until the input A is turned off. 

7. A new printing station will add a logo to parts as they travel along an assembly line. When a 

part arrives a ‘part’ sensor will detect it. After this the ‘clamp’ output is turned on for 10 seconds 

to hold the part during the operation. For the first 2 seconds the part is being held a 

‘spray’ output will be turned on to apply the thermoset ink. For the last 8 seconds a ‘heat’ output 

will be turned on to cure the ink. After this the part is released and allowed to continue 

along the line. Write the ladder logic for this process. 

8. Write a ladder logic program. that will turn on an output Q five seconds after an input A is 

turned on. If input B is on the delay will be eight seconds. YOU MAY ONLY USE ONE 

TIMER. 


plc design - 10.1 

10. STRUCTURED LOGIC DESIGN 

Topics: 

• Timing diagrams 


• Designing ladder logic with process sequence bits and timing diagrams 

Objectives: 

• Know examples of applications to industrial problems. 

• Know how to design time base control programs. 


Traditionally ladder logic programs have been written by thinking about the process 

and then beginning to write the program. This always leads to programs that require 

debugging. And, the final program is always the subject of some doubt. Structured design 

techniques, such as Boolean algebra, lead to programs that are predictable and reliable. 

The structured design techniques in this and the following chapters are provided to make 

ladder logic design routine and predictable for simple sequential systems. 

Note: Structured design is very important in engineering, but many engineers will write 

software without taking the time or effort to design it. This often comes from previous 

experience with programming where a program was written, and then debugged. This 

approach is not acceptable for mission critical systems such as industrial controls. The 

time required for a poorly designed program is 10% on design, 30% on writing, 40% 

debugging and testing, 10% documentation. The time required for a high quality program 

design is 30% design, 10% writing software, 10% debugging and testing, 10% 

documentation. Yes, a well designed program requires less time! Most beginners perceive 

the writing and debugging as more challenging and productive, and so they will 

rush through the design stage. If you are spending time debugging ladder logic programs 

you are doing something wrong. Structured design also allows others to verify 

and modify your programs. 

Axiom: Spend as much time on the design of the program as possible. Resist the temptation 

to implement an incomplete design. 



Most control systems are sequential in nature. Sequential systems are often 

described with words such as mode and behavior. During normal operation these systems 

will have multiple steps or states of operation. In each operational state the system will 

behave differently. Typical states include start-up, shut-down, and normal operation. Consider 

a set of traffic lights - each light pattern constitutes a state. Lights may be green or 

yellow in one direction and red in the other. The lights change in a predictable sequence. 

Sometimes traffic lights are equipped with special features such as cross walk buttons that 

alter the behavior of the lights to give pedestrians time to cross busy roads. 

Sequential systems are complex and difficult to design. In the previous chapter 

timing charts and process sequence bits were discussed as basic design techniques. But, 

more complex systems require more mature techniques, such as those shown in Figure 

10.1. For simpler controllers we can use limited design techniques such as process 

sequence bits and flow charts. More complex processes, such as traffic lights, will have 

many states of operation and controllers can be designed using state diagrams. If the control 

problem involves multiple states of operation, such as one controller for two independent 

traffic lights, then Petri net or SFC based designs are preferred. 

simple/small 

A typical machine will use a sequence of repetitive steps that can be clearly identisequential 

problem 

complex/large 

single process 

very clear steps 

STATE DIAGRAM 

steps with SEQUENCE BITS 

some deviations 

performance 

shorter is important 

FLOW CHART development 

time 

multiple 

processes 

buffered (waiting) 

state triggers 

PETRI NET 

no waiting with 

single states 

BLOCK LOGIC 

EQUATIONS 

SFC/GRAFSET 

Figure 10.1 

Sequential Design Techniques 

10.2 PROCESS SEQUENCE BITS 



fied. Ladder logic can be written that follows this sequence. The steps for this design 

method are; 

1. Understand the process. 

2. Write the steps of operation in sequence and give each step a number. 

3. For each step assign a bit. 

4. Write the ladder logic to turn the bits on/off as the process moves through its 

states. 

5. Write the ladder logic to perform machine functions for each step. 

6. If the process is repetitive, have the last step go back to the first. 

Consider the example of a flag raising controller in Figure 10.2 and Figure 10.3. 

The problem begins with a written description of the process. This is then turned into a set 

of numbered steps. Each of the numbered steps is then converted to ladder logic. 



Description: 

Steps: 

A flag raiser that will go up when an up button is pushed, and down when a 

down button is pushed, both push buttons are momentary. There are 

limit switches at the top and bottom to stop the flag pole. When turned 

on at first the flag should be lowered until it is at the bottom of the pole. 

1. The flag is moving down the pole waiting for the bottom limit switch. 

2. The flag is idle at the bottom of the pole waiting for the up button. 

3. The flag moves up, waiting for the top limit switch. 

4. The flag is idle at the top of the pole waiting for the down button. 

Ladder Logic: 

first scan 

This section of ladder logic forces the flag raiser 

to start with only one state on, in this case it 

should be the first one, step 1. 

L 

U 

U 

U 

step 1 

step 2 

step 3 

step 4 

step 1 

step 1 

bottom limit switch 

L 

down 

motor 

step 2 

The ladder logic for step 1 turns on the motor to 

lower the flag and when the bottom limit 

switch is hit it goes to step 2. 

U 

step 1 

step 2 

flag up button 

L 

step 3 

The ladder logic for step 2 only waits for the 

push button to raise the flag. 

U 

step 2 

Figure 10.2 

A Process Sequence Bit Design Example 



step 3 

step 3 

top limit switch 

L 

up 

motor 

step 4 

The ladder logic for step 3 turns on the motor to 

raise the flag and when the top limit switch is 

hit it goes to step 4. 

U 

step 3 

step 4 

flag down button 

L 

step 1 

The ladder logic for step 4 only waits for the 

push button to lower the flag. 

U 

step 4 

Figure 10.3 

A Process Sequence Bit Design Example (continued) 

The previous method uses latched bits, but the use of latches is sometimes discouraged. 

A more common method of implementation, without latches, is shown in Figure 

10.4. 



step4 

bottom LS 

step2 

step1 

step1 

FS 

step1 

flag up button 

step3 

step2 

step2 

step2 

top LS 

step4 

step3 

step3 

step3 

flag down button 

step1 

step4 

step4 

step 1 

step 3 

Timing diagrams can be valuable when designing ladder logic for processes that 

are only dependant on time. The timing diagram is drawn with clear start and stop times. 

Ladder logic is constructed with timers that are used to turn outputs on and off at appropridown 

motor 

up 

motor 

Figure 10.4 

Process Sequence Bits Without Latches 

Similar methods are explored in further detail in the book Cascading Logic 

(Kirckof, 2003). 

10.3 TIMING DIAGRAMS 



ate times. The basic method is; 


2. Identify the outputs that are time dependant. 

3. Draw a timing diagram for the outputs. 

4. Assign a timer for each time when an output turns on or off. 

5. Write the ladder logic to examine the timer values and turn outputs on or off. 

Consider the handicap door opener design in Figure 10.5 that begins with a verbal 

description. The verbal description is converted to a timing diagram, with t=0 being when 

the door open button is pushed. On the timing diagram the critical times are 2s, 10s, 14s. 

The ladder logic is constructed in a careful order. The first item is the latch to seal-in the 

open button, but shut off after the last door closes. auto is used to turn on the three timers 

for the critical times. The logic for opening the doors is then written to use the timers. 



Description: A handicap door opener has a button that will open two doors. When the button 

is pushed (momentarily) the first door will start to open immediately, the second 

door will start to open 2 seconds later. The first door power will stay open for a total of 

10 seconds, and the second door power will stay on for 14 seconds. Use a timing diagram 

to design the ladder logic. 

Timing Diagram: 

door 1 

door 2 

Ladder Logic: 

2s 10s 14s 

open button 

auto 

t_14.DN 

auto 

auto 

TON 

Timer t_2 

Delay 2s 

TON 

Timer t_10 

Delay 10s 

t_10.TT 

t_2.TT 

t_2.DN 

TON 

Timer t_14 

Delay 14s 

door 1 

door 2 

Figure 10.5 

Design With a Timing Diagram 




10.5 SUMMARY 

• Timing diagrams can show how a system changes over time. 

• Process sequence bits can be used to design a process that changes over time. 

• Timing diagrams can be used for systems with a time driven performance. 


1. Write ladder logic that will give the following timing diagram for B after input A is pushed. 

After A is pushed any changes in the state of A will be ignored. 

true 

false 

0 2 5 6 8 9 

t(sec) 

2. Design ladder logic for the timing diagram below. When an input A becomes active the 

sequence should start. 

X 

Y 

Z 

100 300 500 700 900 1100 1900 

t (ms) 

3. A wrapping process is to be controlled with a PLC. The general sequence of operations is 

described below. Develop the ladder logic using process sequence bits. 

1. The folder is idle until a part arrives. 

2. When a part arrives it triggers the part sensor and the part is held in place by 

actuating the hold actuator. 



3. The first wrap is done by turning on output paper for 1 second. 

4. The paper is then folded by turning on the crease output for 0.5 seconds. 

5. An adhesive is applied by turning on output tape for 0.75 seconds. 

6. The part is release by turning off output hold. 

7. The process pauses until the part sensors goes off, and then the machine returns 

to idle. 


1. 

on 

t_a.DN 

t_b.DN 

t_c.DN 

t_d.DN 

t_a.TT 

t_c.TT 

TON 

Timer t_a 

Base 1s 

Preset 2 

TON 

Timer t_b 

Base 1s 

Preset 3 

TON 

Timer t_c 

Base 1s 

Preset 1 

TON 

Timer t_d 

Base 1s 

Preset 2 

TON 

Timer t_e 

Base 1s 

Preset 1 

output 

t_e.TT 



2. 

A 

t_1.EN 

stop 

TON 

t_1 

0.100 s 

TON 

t_3 

0.300 s 

TON 

t_5 

0.500 s 

TON 

t_7 

0.700 s 

TON 

t_9 

0.900 s 

TON 

t_11 

1.100 s 

t_1.TT 

TON 

t_19 

1.900 s 

X 

t_5.DN 

t_19.DN 

t_1.DN 

t_5.DN 

t_3.DN 

t_7.DN 

Y 

t_9.DN 

t_11.DN 

t_11.TT 

Z 



3. 

(for both solutions 

step2 

step3 

hold 

step4 

step5 

step2 

step3 

step4 

paper 

crease 

tape 



(without latches 

first pass 

step1 

part 

step1 

part 

stop 

part 

paper_delay.DN 

stop 

step2 

step2 

step2 


crease_delay.DN 

stop 

TON 

paper_delay 

delay 1 s 

step3 

step3 

step3 


tape_delay.DN 

stop 

TON 

crease_delay 

delay 0.5 s 

step4 

step4 

step4 

tape_delay.DN 

part 

stop 

TON 

tape_delay 

delay 0.75 s 

step5 

step5 



(with latches 

first pass 

step1 

stop 

L step1 

Ustep2 

Ustep3 

Ustep4 

Ustep5 

part 

step2 


step3 


step4 

tape_delay.DN 

step5 part 

L step2 

U step1 

TON 

paper_delay 

delay 1 s 

L step3 

U step2 

TON 

crease_delay 

delay 0.5 s 

L step4 

U step3 

TON 

tape_delay 

delay 0.75 s 

L step5 

U step4 

L step1 

U step5 


1. Convert the following timing diagram to ladder logic. It should begin when input ‘A’ becomes 



true. 

X 

t(sec) 

0 0.2 0.5 1.2 1.3 1.4 1.6 2.0 

2. Use the timing diagram below to design ladder logic. The sequence should start when input X 

turns on. X may only be on momentarily, but the sequence should continue to execute until it 

ends at 26 seconds. 

A 

B 

0 

3 5 11 22 26 t (sec) 

3. Use the timing diagram below to design ladder logic. The sequence should start when input X 

turns on. X may only be on momentarily, but the sequence should execute anyway. 

A 

B 

2 3 5 7 11 16 22 26 t (sec) 

4. Write a program that will execute the following steps. When in steps b) or d), output C will be 

true. Output X will be true when in step c). 

a) Start in an idle state. If input G becomes true go to b) 

b) Wait until P becomes true before going to step c). 

c) Wait for 3 seconds then go to step d). 

d) Wait for P to become false, and then go to step b). 

5. Write a program that will execute the following steps. When in steps b) or d), output C will be 

true. Output X will be true when in step c). 



a) Start in an idle state. If input G becomes true go to b) 

b) Wait until P becomes true before going to step c). If input S becomes true then go to step a). 

c) Wait for 3 seconds then go to step d). 

d) Wait for P to become false, and then go to step b). 

6. A PLC is to control an amusement park water ride. The ride will fill a tank of water and splash 

a tour group. 10 seconds later a water jet will be ejected at another point. Develop ladder logic 

for the process that follows the steps listed below. 

1. The process starts in ‘idle’. 

2. The ‘cart_detect’ opens the ‘filling’ valve. 

3. After a delay of 30 seconds from the start of the filling of the tank the tank ‘outlet’ 

valve opens. When the tank is ‘full’ the ‘filling’ valve closes. 

4. When the tank is empty the ‘outlet’ valve is closed. 

5. After a 10 second delay, from the tank outlet valve opening, a water ‘jet’ is 

opened. 

6. After ‘2’ seconds the water ‘jet’ is closed and the process returns to the ‘idle 

state. 

7. Write a ladder logic program to extend and retract a cylinder after a start button is pushed. 

There are limit switches at the ends of travel. If the cylinder is extending if more than 5 seconds 

the machine should shut down and turn on a fault light. If it is retracting for more than 3 

seconds it should also shut down and turn on the fault light. It can be reset with a reset button. 

8. Design a program with sequence bits for a hydraulic press that will advance when two palm 

buttons are pushed. Top and bottom limit switches are used to reverse the advance and stop 

after a retract. At any time the hands removed from the palm button will stop an advance and 

retract the press. Include start and stop buttons to put the press in and out of an active mode. 

9. A machine has been built for filling barrels. Use process sequence bits to design ladder logic 

for the sequential process as described below. 

1. The process begins in an idle state. 

2. If the ‘fluid_pressure’ and ‘barrel_present’ inputs are on, the system will open a flow valve 

for 2 seconds with output ‘flow’. 

3. The ‘flow’ valve will then be turned off for 10 seconds. 

4. The ‘flow’ valve will then be turned on until the ‘full’ sensor indicates the barrel is full. 

5. The system will wait until the ‘barrel_present’ sensor goes off before going to the idle state. 

10. Design ladder logic for an oven using process sequence bits. (Note: the solution will only be 

graded if the process sequence bit method is used.) The operations are as listed below. 

1. The oven begins in an IDLE state. 

2. An operator presses a start button and an ALARM output is turned on for 1 minute. 

3. The ALARM output is turned off and the HEAT is turned on for 3 minutes to allow the temperature 

to rise to the acceptable range. 

4. The CONVEYOR output is turned on. 

5. If the STOP input is activated (turned off) the HEAT will be turned off, but the CON- 

VEYOR output will be kept on for two minutes. After this the oven returns to IDLE. 



11. We are developing a safety system (using a PLC-5) for a large industrial press. The press is 

activated by turning on the compressor power relay (R, connected to O:013/05). After R has 

been on for 30 seconds the press can be activated to move (P connected to O:013/06). The 

delay is needed for pressure to build up. After the press has been activated (with P for 1.0 seconds) 

the system must be shut down (R and P off), and then the cycle may begin again. For 

safety, there is a sensor that detects when a worker is inside the press (S, connected to I:011/ 

02), which must be off before the press can be activated. There is also a button that must be 

pushed 5 times (B, connected to I:011/01) before the press cycle can begin. If at any time the 

worker enters the press (and S becomes active) the press will be shut down (P and R turned 

off). Develop the process sequence and sequence bits, and then ladder logic for the states. State 

all assumptions, and show all work. 

12. A machine is being designed to wrap boxes of chocolate. The boxes arrive at the machine on a 

conveyor belt. The list below shows the process steps in sequence. 

1. The box arrives and is detected by an optical sensor (P), after this the conveyor 

is stopped (C) and the box is clamped in place (H). 

2. A wrapping mechanism (W) is turned on for 2 seconds. 

3. A sticker cylinder (S) is turned on for 1 second to put consumer labelling on the 

box. 

4. The clamp (H) is turned off and the conveyor (C) is turned on. 

5. After the box leaves the system returns to an idle state. 

Develop ladder logic programs for the system using the following methods. Don’t forget to 

include regular start and stop inputs. 

i) a timing diagram 

ii) process sequence bits 


plc flowchart - 11.1 

11. FLOWCHART BASED DESIGN 

Topics: 

• Describing process control using flowcharts 

• Conversion of flowcharts to ladder logic 

Objectives: 

• Ba able to describe a process with a flowchart. 

• Be able to convert a flowchart to ladder logic. 


A flowchart is ideal for a process that has sequential process steps. The steps will 

be executed in a simple order that may change as the result of some simple decisions. The 

symbols used for flowcharts are shown in Figure 11.1. These blocks are connected using 

arrows to indicate the sequence of the steps. The different blocks imply different types of 

program actions. Programs always need a start block, but PLC programs rarely stop so the 

stop block is rarely used. Other important blocks include operations and decisions. The 

other functions may be used but are not necessary for most PLC applications. 

Start/Stop 

Operation 

Decision 

I/O 

Disk/Storage 

Subroutine 

Figure 11.1 

Flowchart Symbols 



A flowchart is shown in Figure 11.2 for a control system for a large water tank. 

When a start button is pushed the tank will start to fill, and the flow out will be stopped. 

When full, or the stop button is pushed the outlet will open up, and the flow in will be 

stopped. In the flowchart the general flow of execution starts at the top. The first operation 

is to open the outlet valve and close the inlet valve. Next, a single decision block is used to 

wait for a button to be pushed. when the button is pushed the yes branch is followed and 

the inlet valve is opened, and the outlet valve is closed. Then the flow chart goes into a 

loop that uses two decision blocks to wait until the tank is full, or the stop button is 

pushed. If either case occurs the inlet valve is closed and the outlet valve is opened. The 

system then goes back to wait for the start button to be pushed again. When the controller 

is on the program should always be running, so only a start block is needed. Many beginners 

will neglect to put in checks for stop buttons. 



START 

Open outlet valve 

Close inlet valve 

start button pushed? 

no 

yes 

Open inlet valve 

Close outlet valve 

Is tank full? 

yes 



no 

stop button pushed? 

no 

yes 

Figure 11.2 

A Flowchart for a Tank Filler 

The general method for constructing flowcharts is: 


2. Determine the major actions, these are drawn as blocks. 

3. Determine the sequences of operations, these are drawn with arrows. 



4. When the sequence may change use decision blocks for branching. 

Once a flowchart has been created ladder logic can be written. There are two basic 

techniques that can be used, the first presented uses blocks of ladder logic code. The second 

uses normal ladder logic. 

11.2 BLOCK LOGIC 

The first step is to name each block in the flowchart, as shown in Figure 11.3. Each 

of the numbered steps will then be converted to ladder logic 



STEP 1: Add labels to each block in the flowchart 

START 

F1 



F2 


no 

F3 

yes 



F4 

Is tank full? 

yes 

F6 



no 

F5 


yes 

no 

Figure 11.3 

Labeling Blocks in the Flowchart 

Each block in the flowchart will be converted to a block of ladder logic. To do this 

we will use the MCR (Master Control Relay) instruction (it will be discussed in more 

detail later.) The instruction is shown in Figure 11.4, and will appear as a matched pair of 

outputs labelled MCR. If the first MCR line is true then the ladder logic on the following 

lines will be scanned as normal to the second MCR. If the first line is false the lines to the 



next MCR block will all be forced off. If a normal output is used inside an MCR block, it 

may be forced off. Therefore latches will be used in this method. 

Note: We will use MCR instructions to implement some of the state based programs. 

This allows us to switch off part of the ladder logic. The one significant note to 

remember is that any normal outputs (not latches and timers) will be FORCED 

OFF. Unless this is what you want, put the normal outputs outside MCR blocks. 

A 

MCR 

If A is true then the MCR will cause the ladder in between 

to be executed. If A is false the outputs are forced off. 

MCR 

Figure 11.4 

The MCR Function 

The first part of the ladder logic required will reset the logic to an initial condition, 

as shown in Figure 11.5. The line will only be true for the first scan of the PLC, and at that 

time it will turn on the flowchart block F1 which is the reset all values off operation. All 

other operations will be turned off. 



STEP 2: Write ladder logic to force the PLC into the first state 

first scan 

L 

F1 

U 

F2 

U 

F3 

U 

F4 

U 

F5 

U 

F6 

Figure 11.5 

Initial Reset of States 

The ladder logic for the first state is shown in Figure 11.6. When F1 is true the 

logic between the MCR lines will be scanned, if F1 is false the logic will be ignored. This 

logic turns on the outlet valve and turns off the inlet valve. It then turns off operation F1, 

and turns on the next operation F2. 



STEP 3: Write ladder logic for each function in the flowchart 

F1 

MCR 

L 

outlet 

U 

inlet 

U 

L 

F1 

F2 

MCR 

Figure 11.6 

Ladder Logic for the Operation F1 

The ladder logic for operation F2 is simple, and when the start button is pushed, it 

will turn off F2 and turn on F3. The ladder logic for operation F3 opens the inlet valve and 

moves to operation F4. 



F2 

start 

MCR 

U 

F2 

L 

F3 

F3 

MCR 

MCR 

U 

outlet 

L 

inlet 

U 

F3 

L 

F4 

MCR 

Figure 11.7 

Ladder Logic for Flowchart Operations F2 and F3 

The ladder logic for operation F4 turns off F4, and if the tank is full it turns on F6, 

otherwise F5 is turned on. The ladder logic for operation F5 is very similar. 



F4 

MCR 

tank full 

tank full 

U 

L 

L 

F4 

F6 

F5 

MCR 

F5 

MCR 

stop 

stop 

U 

L 

L 

F5 

F6 

F4 

MCR 

Figure 11.8 Ladder Logic for Operations F4 and F5 

The ladder logic for operation F6 turns the outlet valve on and turns off the inlet 

valve. It then ends operation F6 and returns to operation F2. 



F6 

MCR 

L 

outlet 

U 

inlet 

U 

L 

F6 

F2 

MCR 

Figure 11.9 

Ladder Logic for Operation F6 

11.3 SEQUENCE BITS 

In general there is a preference for methods that do not use MCR statements or 

latches. The flowchart used in the previous example can be implemented without these 

instructions using the following method. The first step to this process is shown in Figure 

11.10. As before each of the blocks in the flowchart are labelled, but now the connecting 

arrows (transitions) in the diagram must also be labelled. These transitions indicate when 

another function block will be activated. 



START 

F1 

T1 



T2 

F2 

is the NO 


no 

F3 

yes 

T3 



F4 

T4 

Is tank full? 

yes 

T6 

F6 



F5 

T5 

no 

is the NC 


yes 

no 

Figure 11.10 

Label the Flowchart Blocks and Arrows 

The first section of ladder logic is shown in Figure 11.11. This indicates when the 

transitions between functions should occur. All of the logic for the transitions should be 

kept together, and appear before the state logic that follows in Figure 11.12. 



FS 

F1 

F6 

T1 

T2 

F2 

F2 

F3 

F5 

F4 

F4 

F5 

start 

start 

stop 

full 

full 

stop 

T3 

T4 

T5 

T6 

Figure 11.11 

The Transition Logic 

The logic shown in Figure 11.12 will keep a function on, or switch to the next 

function. Consider the first ladder rung for F1, it will be turned on by transition T1 and 

once function F1 is on it will keep itself on, unless T2 occurs shutting it off. If T2 has 

occurred the next line of ladder logic will turn on F2. The function logic is followed by 

output logic that relates output values to the active functions. 



F1 

T1 

T2 

F1 

F2 

T2 

T3 

F2 

F3 

T3 

T4 

F3 

F4 

T4 

T5 

T6 

F4 

F5 

T5 

T4 

T6 

F5 

F6 

T6 

T2 

F6 

F1 

F2 

outlet 

F6 

F3 

F4 

inlet 

F5 

Figure 11.12 

The Function Logic and Outputs 



11.4 SUMMARY 

• Flowcharts are suited to processes with a single flow of execution. 

• Flowcharts are suited to processes with clear sequences of operation. 


1. Convert the following flow chart to ladder logic. 

start 

A on 

is B on? 

yes 

no 

A off 

no 

is C on? 

yes 

2. Draw a flow chart for cutting the grass, then develop ladder logic for three of the actions/decisions. 

3. Design a garage door controller using a flowchart. The behavior of the garage door controller is 

as follows, 

- there is a single button in the garage, and a single button remote control. 

- when the button is pushed the door will move up or down. 

- if the button is pushed once while moving, the door will stop, a second push will 

start motion again in the opposite direction. 

- there are top/bottom limit switches to stop the motion of the door. 

- there is a light beam across the bottom of the door. If the beam is cut while the 

door is closing the door will stop and reverse. 

- there is a garage light that will be on for 5 minutes after the door opens or closes. 




1. 

first scan 

L 

F1 

start 

U 

U 

F2 

F3 

F1 

A on 

F1 

U F4 

MCR 

F2 

is B on? 

no 

yes 

L 

U 

A 

F1 

F3 

A off 

F2 

B 

L F2 

MCR 

MCR 

U F2 

no 

F4 

is C on? 

yes 

F3 

L F3 

MCR 

MCR 

F4 

C 

MCR 

U F4 

U 

U 

A 

F3 

C 

L 

U 

F1 

F4 

L F4 

MCR 

L F2 

MCR 



2. 

Start 

Get mower and 

gas can 

F1 

F2 

Is gas can 

empty? 

yes 

get gas 

F3 

F4 

F5 

no 

Fill mower 

Pull cord 

F6 

Is Mower on? 

no 

F7 

yes 

Push Mower 

F8 

Is all lawn cut? 

no 

yes 

F9 

Stop mower 

F10 

Put gas and 

mower away 



FS 

F1 

F2 

F3 

F4 

F5 

F6 

F7 

F8 

F9 

F10 

F1 

MCR 

L 

L 

U 

L 

mower 

gas can 

F1 

F2 

MCR 

F2 

gas can empty 

gas can empty 

MCR 

L 

U 

L 

U 

F3 

F2 

F4 

F2 

MCR 



F3 

gas can full 

MCR 

fill gas tank 

L 

U 

F4 

F3 

F4 

MCR 

MCR 

TON 

Timer t_0 

Delay 5s 

t_0.DN 

t_0.DN 

L 

U 

F5 

F4 

pour gas 

F5 

cord pulled 

cord pulled 

F6 

mower on 

mower on 

MCR 

MCR 

pull cord 

L 

U 

F6 

F5 

MCR 

MCR 

L F7 

L F5 

U F6 

MCR 

ETC..................... 



3. 

start 

ST1 

is 

remote or 

button pushed? 

no 

yes 

ST2 

turn on door close 

ST3 

is 

remote or 

button or bottom 

limit pushed? 

no 

ST4 

is 

light beam 

on? 

yes 

ST5 

yes 

turn off door close 

no 

ST6 

is 

remote or 

button pushed? 

ST7 

yes 

turn on door open 

ST8 

ST9 

is 

remote or 

button or top 

limit pushed? 

yes 

turn off door open 

no 



first scan 

L 

ST1 

U 

ST2 

U 

ST3 

U 

ST4 

U 

ST5 

U 

ST6 

U 

ST7 

U 

ST8 

U 

ST9 

U 

door open 

U 

door close 

ST2 

ST7 

t_st2.DN 

TOF 

t_st2 

preset 300s 

garage light 



ST1 

button 

remote 

MCR 

U 

L 

ST1 

ST2 

ST2 

MCR 

MCR 

U 

ST2 

L 

ST3 

L 

door close 

MCR 



ST3 

button 

remote 

MCR 

U 

L 

ST3 

ST5 

bottom limit 

ST3 

U 

ST3 

L 

ST4 

ST4 

light beam 

MCR 

MCR 

U 

ST4 

light beam 

L 

U 

ST7 

ST4 

L 

ST3 

MCR 



ST5 

MCR 

U 

ST5 

L 

ST6 

U 

door close 

MCR 

ST6 

button 

remote 

MCR 

U 

L 

ST6 

ST7 

ST7 

MCR 

MCR 

U 

ST7 

L 

ST8 

L 

door open 

MCR 



ST8 

button 

remote 

MCR 

U 

L 

ST8 

ST9 

top limit 

ST9 

MCR 

MCR 

U 

ST9 

L 

ST1 

U 

door open 

MCR 




1. Develop ladder logic for the flowchart below. 

Start 

Turn A on 

Is B 

on? 

no 

yes 

Turn A off 

Is C 

on? 

no 

yes 

2. Use a flow chart to design a parking gate controller. 

keycard entry 

cars enter/leave 

gate 

light 

car detector 

- the gate will be raised by one output 

and lowered by another. If the gate 

gets stuck an over current detector 

will make a PLC input true. If this 

is the case the gate should reverse 

and the light should be turned on 

indefinitely. 

- if a valid keycard is entered a PLC 

input will be true. The gate is to 

rise and stay open for 10 seconds. 

- when a car is over the car detector a 

PLC input will go true. The gate is 

to open while this detector is 

active. If it is active for more that 

30 seconds the light should also 

turn on until the gate closes. 



3. A welding station is controlled by a PLC. On the outside is a safety cage that must be closed 

while the cell is active. A belt moves the parts into the welding station and back out. An inductive 

proximity sensor detects when a part is in place for welding, and the belt is stopped. To 

weld, an actuator is turned on for 3 seconds. As normal the cell has start and stop push buttons. 

a) Draw a flow chart 

b) Implement the chart in ladder logic 

Inputs 

DOOR OPEN (NC) 

START (NO) 

STOP (NC) 

PART PRESENT 

Outputs 

CONVEYOR ON 

WELD 

4. Convert the following flowchart to ladder logic. 

Start 

Turn off motor 

start 

pushed 

no 

yes 

Turn on motor 

stop 

pushed 

no 

yes 

5. A machine is being designed to wrap boxes of chocolate. The boxes arrive at the machine on a 

conveyor belt. The list below shows the process steps in sequence. 

1. The box arrives and is detected by an optical sensor (P), after this the conveyor 

is stopped (C) and the box is clamped in place (H). 

2. A wrapping mechanism (W) is turned on for 2 seconds. 

3. A sticker cylinder (S) is turned on for 1 second to put consumer labelling on the 



box. 

4. The clamp (H) is turned off and the conveyor (C) is turned on. 

5. After the box leaves the system returns to an idle state. 

Develop ladder logic for the system using a flowchart. Don’t forget to include regular start and 

stop inputs. 


plc states - 12.1 

12. STATE BASED DESIGN 

Topics: 

• Describing process control using state diagrams 

• Conversion of state diagrams to ladder logic 

• MCR blocks 

Objectives: 

• Be able to construct state diagrams for a process. 

• Be able to convert a state diagram to ladder logic directly. 

• Be able to convert state diagrams to ladder logic using equations. 


A system state is a mode of operation. Consider a bank machine that will go 

through very carefully selected states. The general sequence of states might be idle, scan 

card, get secret number, select transaction type, ask for amount of cash, count cash, deliver 

cash/return card, then idle. 

A State based system can be described with system states, and the transitions 

between those states. A state diagram is shown in Figure 12.1. The diagram has two states, 

State 1 and State 2. If the system is in state 1 and A happens the system will then go into 

state 2, otherwise it will remain in State 1. Likewise if the system is in state 2, and B happens 

the system will return to state 1. As shown in the figure this state diagram could be 

used for an automatic light controller. When the power is turned on the system will go into 

the lights off state. If motion is detected or an on push button is pushed the system will go 

to the lights on state. If the system is in the lights on state and 1 hour has passed, or an off 

push button is pushed then the system will go to the lights off state. The else statements 

are omitted on the second diagram, but they are implied. 



B 

else 

State 1 State 2 

A 

else 

This diagram could describe the operation of energy efficient lights in a room operated 

by two push buttons. State 1 might be lights off and state 2 might be lights on. The 

arrows between the states are called transitions and will be followed when the conditions 

are true. In this case if we were in state 1 and A occurred we would move to 

state 2. The else loop indicate that a state will stay active if a transition are is not followed. 

These are so obvious they are often omitted from state diagrams. 

power on 

off_pushbutton OR 1 hour timer 

Lights off 

on_pushbutton 

OR motion detector 

Lights on 

Figure 12.1 

A State Diagram 

The most essential part of creating state diagrams is identifying states. Some key 

questions to ask are, 

1. Consider the system, 

What does the system do normally? 

Does the system behavior change? 

Can something change how the system behaves? 

Is there a sequence to actions? 

2. List modes of operation where the system is doing one identifiable activity that 

will start and stop. Keep in mind that some activities may just be to wait. 

Consider the design of a coffee vending machine. The first step requires the identification 

of vending machine states as shown in Figure 12.2. The main state is the idle state. 

There is an inserting coins state where the total can be displayed. When enough coins have 

been inserted the user may select their drink of choice. After this the make coffee state will 



be active while coffee is being brewed. If an error is detected the service needed state will 

be activated. 

STATES 

idle - the machine has no coins and is doing nothing 

inserting coins - coins have been entered and the total is displayed 

user choose - enough money has been entered and the user is making coffee selection 

make coffee - the selected type is being made 

service needed - the machine is out of coffee, cups, or another error has occurred 

Notes: 

1. These states can be subjective, and different designers might pick others. 

2. The states are highly specific to the machine. 

3. The previous/next states are not part of the states. 

4. There is a clean difference between states. 

Figure 12.2 

Definition of Vending Machine States 

The states are then drawn in a state diagram as shown in Figure 12.3. Transitions 

are added as needed between the states. Here we can see that when powered up the 

machine will start in an idle state. The transitions here are based on the inputs and sensors 

in the vending machine. The state diagram is quite subjective, and complex diagrams will 

differ from design to design. These diagrams also expose the controller behavior. Consider 

that if the machine needs maintenance, and it is unplugged and plugged back in, the service 

needed statement would not be reentered until the next customer paid for but did not 

receive their coffee. In a commercial design we would want to fix this oversight. 



power up 

service 

needed 

reset button 

idle 

coin inserted 

coin return 

inserting 

coins 

no cups 

OR no coffee 

OR jam sensor 

cup removed 

coin return 

right amount 

entered 

make 

coffee 

button pushed 

user 

choose 

Figure 12.3 

State Diagram for a Coffee Machine 

12.1.1 State Diagram Example 

Consider the traffic lights in Figure 12.4. The normal sequences for traffic lights 

are a green light in one direction for a long period of time, typically 10 or more seconds. 

This is followed by a brief yellow light, typically 4 seconds. This is then followed by a 

similar light pattern in the other direction. It is understood that a green or yellow light in 

one direction implies a red light in the other direction. Pedestrian buttons are provided so 

that when pedestrians are present a cross walk light can be turned on and the duration of 

the green light increased. 



Red 

Yellow 

Green 

North/South 

L1 

L2 

L3 

Walk Button - S1 

Red 

Yellow 

Green 

East/West 

L4 

L5 

L6 

Walk Button - S2 

Figure 12.4 

Traffic Lights 

The first step for developing a controller is to define the inputs and outputs of the 

system as shown in Figure 12.5. First we will describe the system variables. These will 

vary as the system moves from state to state. Please note that some of these together can 

define a state (alone they are not the states). The inputs are used when defining the transitions. 

The outputs can be used to define the system state. 

We have eight items that are ON or OFF 

L1 

L2 

L3 

L4 

L5 

L6 

S1 

S2 

OUTPUTS 

INPUTS 

Note that each state will lead 

to a different set of outputs. 

The inputs are often 

part, or all of the transitions. 

A simple diagram can be drawn to show sequences for the lights 

Figure 12.5 

Inputs and Outputs for Traffic Light Controller 



Previously state diagrams were used to define the system, it is possible to use a 

state table as shown in Figure 12.6. Here the light sequences are listed in order. Each state 

is given a name to ease interpretation, but the corresponding output pattern is also given. 

The system state is defined as the bit pattern of the 6 lights. Note that there are only 4 patterns, 

but 6 binary bits could give as many as 64. 

Step 1: Define the System States and put them (roughly) in sequence 

State Description 

Green East/West 

Yellow East/West 

Green North/South 

Yellow North/South 

System State 

L1 L2 L3 L4 L5 L6 

State Table 

# L1 L2 L3 L4 L5 L6 

1 

2 

3 

4 

1 

1 

0 

0 

0 

0 

0 

1 

0 

0 

1 

0 

0 

0 

1 

1 

0 

1 

0 

0 

1 

0 

0 

0 

A binary number 

0 = light off 

1 = light on 

Here the four states 

determine how the 6 

outputs are switched 

on/off. 

Figure 12.6 

System State Table for Traffic Lights 

Transitions can be added to the state table to clarify the operation, as shown in Figure 

12.7. Here the transition from Green E/W to Yellow E/W is S1. What this means is 

that a cross walk button must be pushed to end the green light. This is not normal, normally 

the lights would use a delay. The transition from Yellow E/W to Green N/S is 

caused by a 4 second delay (this is normal.) The next transition is also abnormal, requiring 

that the cross walk button be pushed to end the Green N/S state. The last state has a 4 second 

delay before returning to the first state in the table. In this state table the sequence will 

always be the same, but the times will vary for the green lights. 



Step 2: Define State Transition Triggers, and add them to the list of states 

Description # L1 L2 L3 L4 L5 L6 transition 

Green East/West 1 

1 0 0 0 0 1 S1 

Yellow East/West 2 1 0 0 0 1 0 delay 

0 0 1 1 0 0 

4sec 

Green North/South 3 

S2 

Yellow North/South 4 0 1 0 1 0 0 

delay 4 sec 

Figure 12.7 

State Table with Transitions 

A state diagram for the system is shown in Figure 12.8. This diagram is equivalent 

to the state table in Figure 12.7, but it can be valuable for doing visual inspection. 

Step 3: Draw the State Transition Diagram 

delay 4sec 

grn. EW 

pushbutton NS (i.e., S1,S2 = 10) 

yel. NS 

first scan 

delay 4sec 

yel. EW 

pushbutton EW (i.e. 01) 

grn. NS 

Figure 12.8 

A Traffic Light State Diagram 

12.1.2 Conversion to Ladder Logic 

12.1.2.1 - Block Logic Conversion 



State diagrams can be converted directly to ladder logic using block logic. This 

technique will produce larger programs, but it is a simple method to understand, and easy 

to debug. The previous traffic light example is to be implemented in ladder logic. The 

inputs and outputs are defined in Figure 12.9, assuming it will be implemented on an 

Allen Bradley Micrologix. first scan is the address of the first scan in the PLC. The locations 

state_1 to state_4 are internal memory locations that will be used to track which 

states are on. The behave like outputs, but are not available for connection outside the 

PLC. The input and output values are determined by the PLC layout. 

STATES 

state_1 - green E/W 

state_2 - yellow E/W 

state_3 - green N/S 

state_4 - yellow N/S 

OUTPUTS 

L1 - red N/S 

L2 - yellow N/S 

L3 - green N/S 

L4 - red E/W 

L5 - yellow E/W 

L6 - green E/W 

INPUTS 

S1 - cross 

S2 - cross 

S:FS - first scan 

Figure 12.9 

Inputs and Outputs for Traffic Light Controller 

The initial ladder logic block shown in Figure 12.10 will initialize the states of the 

PLC, so that only state 1 is on. The first scan indicator first scan will execute the MCR 

block when the PLC is first turned on, and the latches will turn on the value for state_1 and 

turn off the others. 



RESET THE STATES 

S:FS 

MCR 

state_1 

L 

state_2 

U 

state_3 

U 

state_4 

U 

MCR 

Figure 12.10 

Ladder Logic to Initialize Traffic Light Controller 

Note: We will use MCR instructions to implement some of the state based programs. 

This allows us to switch off part of the ladder logic. The one significant note to 

remember is that any normal outputs (not latches and timers) will be FORCED 

OFF. Unless this is what you want, put the normal outputs outside MCR blocks. 

A 

MCR 

If A is true then the MCR will cause the ladder in between 

to be executed. If A is false the outputs are forced off. 

MCR 

The next section of ladder logic only deals with outputs. For example the output O/ 

1 is the N/S red light, which will be on for states 1 and 2, or B3/1 and B3/2 respectively. 

Putting normal outputs outside the MCR blocks is important. If they were inside the 



blocks they could only be on when the MCR block was active, otherwise they would be 

forced off. Note: Many beginners will make the careless mistake of repeating outputs in 

this section of the program. 

TURN ON LIGHTS AS REQUIRED 

state_1 

L1 

state_2 

state_4 

L2 

state_3 

L3 

state_3 

L4 

state_4 

state_2 

L5 

state_1 

L6 

Figure 12.11 

General Output Control Logic 

The first state is implemented in Figure 12.10. If state_1 is active this will be 

active. The transition is S1 which will end state_1 and start state_2. 



FIRST STATE WAIT FOR TRANSITIONS 

state_1 

MCR 

S1 

S1 

L1 

L2 

MCR 

U 

L 

Figure 12.12 

Ladder Logic for First State 

The second state is more complex because it involves a time delay, as shown in 

Figure 12.13. When the state is active the TON timer will be timing. When the timer is 

done state 2 will be unlatched, and state 3 will be latched on. The timer is nonretentive, so 

if state_2 if off the MCR block will force all of the outputs off, including the timer, causing 

it to reset. 



SECOND STATE WAIT FOR TRANSITIONS 

state_2 

MCR 

TON 

t_st2 

delay 4 s 

t_st2.DN 

t_st2.DN 

state_2 

U 

state_3 

L 

MCR 

Figure 12.13 

Ladder Logic for Second State 

The third and fourth states are shown in Figure 12.14 and Figure 12.15. Their layout 

is very similar to that of the first two states. 

THIRD STATE WAIT FOR TRANSITIONS 

state_3 

MCR 

S2 

S2 

state_3 

U 

state_4 

L 

MCR 

Figure 12.14 

Ladder Logic for State Three 



FOURTH STATE WAIT FOR TRANSITIONS 

state_4 

MCR 

t_st4 

RTO 

delay 4s 

t_st4.DN 

t_st4.DN 

t_st4.DN 

state_4 

U 

state_1 

L 

t_st4 

RST 

MCR 

Figure 12.15 

Ladder Logic for State Four 

The previous example only had one path through the state tables, so there was 

never a choice between states. The state diagram in Figure 12.16 could potentially have 

problems if two transitions occur simultaneously. For example if state STB is active and A 

and C occur simultaneously, the system could go to either STA or STC (or both in a poorly 

written program.) To resolve this problem we should choose one of the two transitions as 

having a higher priority, meaning that it should be chosen over the other transition. This 

decision will normally be clear, but if not an arbitrary decision is still needed. 



STA 

B 

D 

STC 

A 

C 

STB 

first scan 

Figure 12.16 

A State Diagram with Priority Problems 

The state diagram in Figure 12.16 is implemented with ladder logic in Figure 

12.17 and Figure 12.18. The implementation is the same as described before, but for state 

STB additional ladder logic is added to disable transition A if transition C is active, therefore 

giving priority to C. 



first scan 

L 

STB 

U 

STA 

U 

STC 

STA 

MCR 

B 

U 

STA 

L 

STB 

MCR 

STB 

MCR 

C 

Note: if A and C are true at the same time then C 

will have priority. PRIORITIZATION is important 

when simultaneous branches are possible. 

A 

C 

U 

L 

U 

STB 

STC 

STB 

L 

STA 

MCR 



Figure 12.17 

State Diagram for Prioritization Problem 

STC 

MCR 

D 

U 

STC 

L 

STB 

MCR 

Figure 12.18 

State Diagram for Prioritization Problem 

The Block Logic technique described does not require any special knowledge and 

the programs can be written directly from the state diagram. The final programs can be 

easily modified, and finding problems is easier. But, these programs are much larger and 

less efficient. 

12.1.2.2 - State Equations 

State diagrams can be converted to Boolean equations and then to Ladder Logic. 

The first technique that will be described is state equations. These equations contain three 

main parts, as shown below in Figure 12.19. To describe them simply - a state will be on if 

it is already on, or if it has been turned on by a transition from another state, but it will be 

turned off if there was a transition to another state. An equation is required for each state 

in the state diagram. 



Informally, 

State X = (State X + just arrived from another state) and has not left for another state 

Formally, 

⎛ 

⎞ 

STATE i 

= ⎜STATE i 

+ ∑ ( T j, i 

• STATE j 

) ⎟ 

⎝ 

⎠ 

n 

j = 1 

m 

• 

∏ 

k = 1 

T i k 

( , 

• STATE i 

) 

where, STATE i = A variable that will reflect if state i is on 

n 

m 

= 

= 

the number of transitions to state i 

the number of transitions out of state i 

T ji , = The logical condition of a transition from state j to i 

T ik , 

= The logical condition of a transition out of state i to k 

Figure 12.19 

State Equations 

The state equation method can be applied to the traffic light example in Figure 

12.8. The first step in the process is to define variable names (or PLC memory locations) 

to keep track of which states are on or off. Next, the state diagram is examined, one state at 

a time. The first equation if for ST1, or state 1 - green NS. The start of the equation can be 

read as ST1 will be on if it is on, or if ST4 is on, and it has been on for 4s, or if it is the first 

scan of the PLC. The end of the equation can be read as ST1 will be turned off if it is on, 

but S1 has been pushed and S2 is off. As discussed before, the first half of the equation 

will turn the state on, but the second half will turn it off. The first scan is also used to turn 

on ST1 when the PLC starts. It is put outside the terms to force ST1 on, even if the exit 

conditions are true. 



Defined state variables: 

ST1 = state 1 - green NS 

ST2 

ST3 

ST4 

= 

= 

= 

state 2 - yellow NS 

state 3 - green EW 

state 4 - yellow EW 

The state entrance and exit condition equations: 

ST1 = ( ST1 + ST4 ⋅ TON 2 ( ST4, 

4s) 

) ⋅ ST1 ⋅ S1 ⋅S2 

+ FS 

ST2 = ( ST2 + ST1 ⋅ S1 ⋅ S2) ⋅ ST2 ⋅ TON 1 

( ST2, 

4s) 

ST3 = ( ST3 + ST2 ⋅ TON 1 

( ST2, 

4s) 

) ⋅ ST3 ⋅S1 ⋅S2 

ST4 = ( ST4 + ST3 ⋅ S1 ⋅ S2) ⋅ ST4 ⋅ TON 2 

( ST4, 

4s) 

Note: Timers are represented in these equations in the form TONi(A, delay). TON indicates 

that it is an on-delay timer, A is the input to the timer, and delay is the timer 

delay value. The subscript i is used to differentiate timers. 

Figure 12.20 

State Equations for the Traffic Light Example 

The equations in Figure 12.20 cannot be implemented in ladder logic because of 

the NOT over the last terms. The equations are simplified in Figure 12.21 so that all NOT 

operators are only over a single variable. 



Now, simplify these for implementation in ladder logic. 

ST1 = ( ST1 + ST4 ⋅ TON 2 

( ST4, 

4) 

) ⋅ ( ST1 + S1 + S2) 

+ FS 

ST2 = ( ST2 + ST1 ⋅S1 ⋅S2) ⋅ ( ST2 + TON 1 

( ST2, 

4) 

) 

ST3 = ( ST3 + ST2 ⋅ TON 1 

( ST2, 

4) 

) ⋅ ( ST3 + S1 + S2) 

ST4 = ( ST4 + ST3 ⋅S1 ⋅S2) ⋅ ( ST4 + TON 2 ( ST4, 

4) 

) 

Figure 12.21 

Simplified Boolean Equations 

These equations are then converted to the ladder logic shown in Figure 12.22 and 

Figure 12.23. At the top of the program the two timers are defined. (Note: it is tempting to 

combine the timers, but it is better to keep them separate.) Next, the Boolean state equations 

are implemented in ladder logic. After this we use the states to turn specific lights on. 



DEFINE THE TIMERS 

ST4 

timer on 

t_st4 

delay 4 sec 

ST2 

THE STATE EQUATIONS 

ST1 

ST1 

timer on 

t_st2 

delay 4 sec 

ST1X 

ST4 

t_st2.DN 

S1 

first scan 

S2 

ST2 

ST2 

ST2X 

ST1 S1 S2 

t_st4.DN 

ST3 

ST2 

t_st4.DN 

ST3 

S1 

ST3X 

S2 

ST4 

ST4 

ST4X 

ST3 S1 S2 

t_st2.DN 

Figure 12.22 

Ladder Logic for the State Equations 



OUTPUT LOGIC FOR THE LIGHTS 

ST1 

L1 

ST2 

ST4 

L2 

ST3 

L3 

ST3 

L4 

ST4 

ST2 

L5 

ST1 

L6 

Figure 12.23 

Ladder Logic for the State Equations 

This method will provide the most compact code of all techniques, but there are 

potential problems. Consider the example in Figure 12.23. If push button S1 has been 

pushed the line for ST1 should turn off, and the line for ST2 should turn on. But, the line 

for ST2 depends upon the value for ST1 that has just been turned off. This will cause a 

problem if the value of ST1 goes off immediately after the line of ladder logic has been 

scanned. In effect the PLC will get lost and none of the states will be on. This problem 

arises because the equations are normally calculated in parallel, and then all values are 

updated simultaneously. To overcome this problem the ladder logic could be modified to 

the form shown in Figure 12.24. Here some temporary variables are used to hold the new 

state values. After all the equations are solved the states are updated to their new values. 



THE STATE EQUATIONS 

ST1 

ST1 

ST1X 

ST4 

t_st4.DN 

S1 

first scan 

S2 

ST2 

ST2 

ST2X 

ST1 S1 S2 

t_st2.DN 

ST3 

ST2 

t_st2.DN 

ST3 

S1 

ST3X 

S2 

ST4 

ST4 

ST4X 

ST3 S1 S2 

t_st4.DN 

ST1X 

ST2X 

ST3X 

ST4X 

ST1 

ST2 

ST3 

ST4 

Figure 12.24 

Delayed State Updating 

When multiple transitions out of a state exist we must take care to add priorities. 



Each of the alternate transitions out of a state should be give a priority, from highest to 

lowest. The state equations can then be written to suppress transitions of lower priority 

when one or more occur simultaneously. The state diagram in Figure 12.25 has two transitions 

A and C that could occur simultaneously. The equations have been written to give A 

a higher priority. When A occurs, it will block C in the equation for STC. These equations 

have been converted to ladder logic in Figure 12.26. 

STA 

B 

D 

STC 

A 

C 

STB 

first scan 

STA = ( STA + STB ⋅ A) ⋅ STA ⋅ B 

STB = ( STB + STA ⋅ B + STC ⋅ D) ⋅STB ⋅ A ⋅STB ⋅ C + FS 

STC = ( STC + STB ⋅ C ⋅ A) ⋅ STC ⋅ D 

Figure 12.25 

State Equations with Prioritization 



STA 

STA 

STAX 

STB 

A 

B 

STB 

STB 

STB 

STBX 

STA 

B 

A 

C 

STC 

D 

FS 

STC 

STB C A 

STC 

D 

STCX 

STAX 

STBX 

STCX 

STA 

STB 

STC 

Figure 12.26 

Ladder Logic with Prioritization 

12.1.2.3 - State-Transition Equations 



A state diagram may be converted to equations by writing an equation for each 

state and each transition. A sample set of equations is seen in Figure 12.27 for the traffic 

light example of Figure 12.8. Each state and transition needs to be assigned a unique variable 

name. (Note: It is a good idea to note these on the diagram) These are then used to 

write the equations for the diagram. The transition equations are written by looking at the 

each state, and then determining which transitions will end that state. For example, if ST1 

is true, and crosswalk button S1 is pushed, and S2 is not, then transition T1 will be true. 

The state equations are similar to the state equations in the previous State Equation 

method, except they now only refer to the transitions. Recall, the basic form of these equations 

is that the state will be on if it is already on, or it has been turned on by a transition. 

The state will be turned off if an exiting transition occurs. In this example the first scan 

was given it’s own transition, but it could have also been put into the equation for T4. 

defined state and transition variables: 

ST1 = state 1 - green NS 

ST2 = state 2 - yellow NS 

T1 = transition from ST1 to ST2 


ST3 

= 

state 3 - green EW 


ST4 

= 

state 4 - yellow EW 


T5 = transition to ST1 for first scan 

state and transition equations: 

T4 = ST4 ⋅ TON 2 ( ST4, 

4) 

ST1 = ( ST1 + T4 + T5) ⋅ T1 

T1 

= 

ST1 ⋅ S1 ⋅ S2 

ST2 = ( ST2 + T1) ⋅ T2 

T2 = ST2 ⋅ TON 1 

( ST2, 

4) 

ST3 = ( ST3 + T2) ⋅ T3 

T3 

= 

ST3 ⋅ S1 ⋅ S2 

ST4 = ( ST4 + T3) ⋅ T4 

T5 

= 

FS 

Figure 12.27 

State-Transition Equations 

These equations can be converted directly to the ladder logic in Figure 12.28, Figure 

12.29 and Figure 12.30. It is very important that the transition equations all occur 

before the state equations. By updating the transition equations first and then updating the 

state equations the problem of state variable values changing is negated - recall this problem 

was discussed in the State Equations section. 



UPDATE TIMERS 

ST4 

timer on 

t_st4 

delay 4 sec 

ST2 

CALCULATE TRANSITION EQUATIONS 

ST4 t_st4.DN 

timer on 

t_st2 

delay 4 sec 

T4 

ST1 S1 S2 T1 

ST2 

t_st2.DN 

T2 

ST3 S1 S2 T3 

FS 

T5 

Figure 12.28 

Ladder Logic for the State-Transition Equations 



CALCULATE STATE EQUATIONS 

ST1 

T1 

ST1 

T4 

T5 

ST2 

T2 

ST2 

T1 

ST3 

T3 

ST3 

T2 

ST4 

T4 

ST4 

T3 

Figure 12.29 




UPDATE OUTPUTS 

ST1 

L1 

ST2 

ST4 

L2 

ST3 

L3 

ST3 

L4 

ST4 

ST2 

L5 

ST1 

L6 

Figure 12.30 


The problem of prioritization also occurs with the State-Transition equations. 

Equations were written for the State Diagram in Figure 12.31. The problem will occur if 

transitions A and C occur simultaneously. In the example transition T2 is given a higher 

priority, and if it is true, then the transition T3 will be suppressed when calculating STC. In 

this example the transitions have been considered in the state update equations, but they 

can also be used in the transition equations. 



STA 

T5 

B 

T4 

D 

STC 

A 

T2 

STB 

C 

T3 

T1 

first scan (FS) 

T1 

= 

FS 

STA = ( STA + T2) ⋅ T5 

T2 

= 

STB ⋅ A 

STB = ( STB + T5 + T4 + T1) ⋅T2 ⋅T3 

T3 

= 

STB ⋅ C 

STC = ( STC + T3 ⋅ T2) ⋅ T4 

T4 

= 

STC ⋅ D 

T5 

= 

STA ⋅ B 

Figure 12.31 

Prioritization for State Transition Equations 

12.2 SUMMARY 

• State diagrams are suited to processes with a single flow of execution. 

• State diagrams are suited to problems that has clearly defines modes of execution. 

• Controller diagrams can be converted to ladder logic using MCR blocks 

• State diagrams can also be converted to ladder logic using equations 

• The sequence of operations is important when converting state diagrams to ladder 

logic. 


1. Draw a state diagram for a microwave oven. 



2. Convert the following state diagram to equations. 

Inputs 

A 

B 

C 

D 

E 

F 

Outputs 

P 

Q 

R 

AC ( + D) 

F + E 

S1 

FS 

state 

P Q R 

S0 

BA 

S0 

S1 

S2 

0 

1 

1 

1 

0 

1 

1 

1 

0 

EC ( + D+ 

F) 

S2 

3. Implement the following state diagram with equations. 

ST3 

C 

D 

FS 

ST2 

B 

E 

ST4 

A 

ST1 

F 



4. Given the following state diagram, use equations to implement ladder logic. 

state 1 

A 

C * B 

state 3 

B 

state 2 

C + B 

5. Convert the following state diagram to logic using equations. 

A 

state 1 state 2 

B 

C 

D 

E 

F 

state 3 

6. You have been asked to program a PLC that is controlling a handicapped access door opener. 

The client has provided the electrical wiring diagram below to show how the PLC inputs and 

outputs have been wired. Button A is located inside and button B is located outside. When 

either button is pushed the motor will be turned on to open the door. The motor is to be kept on 

for a total of 15 seconds to allow the person to enter. After the motor is turned off the door will 

fall closed. In the event that somebody gets caught in the door the thermal relay will go off, and 

the motor should be turned off. After 20,000 cycles the door should stop working and the light 



should go on to indicate that maintenance is required. 

24 V DC 

Output Card 

00 

01 

02 

03 

04 

Relay 

120 V AC 

Power 

Supply 

COM. 

Motor 

05 

06 

24 V lamp 

07 

COM 

rack ’machine’ 

slot 0 

+24 V DC 

Power 

Supply 

GND 



24 V AC 

Power 

Supply 

button A 

button B 

thermal relay 


24V AC 

00 

01 

02 

03 

04 

05 

06 

07 

COM 

rack ’machine’ 

slot 1 

a) Develop a state diagram for the control of the door. 

b) Convert the state diagram to ladder logic. (list the input and the output addresses 

first) 

c) Convert the state diagram to Boolean equations. 

7. Design a garage door controller using a) block logic, and b) state-transition equations. The 

behavior of the garage door controller is as follows, 












1. 

Timer Done + Cancel Button + Door Open 

IDLE 

Time Button 

COOK 

Time Button 

Cancel Button 

Power Button 

CLOCK 

SET 

Start Button 

COOK 

TIME SET 

2. 

T1 

T2 

= 

= 

FS 

S1( BA) 

T3 = S2( EC ( + D+ 

F) 

) 

T4 = S1( F+ 

E) 

T5 = S0( AC ( + D) 

) 

S1 = ( S1 + T1 + T3 + T5)T2T4 

S2 = ( S2 + T2)T3 

S0 = ( S0 + T4T2)T5 

P = S1 + S2 

Q = S0 + S2 

R = S0 + S1 



3. 

T1 

T2 

= ST1 • A 

= ST2 • B 

T3 = ST1 • C 

T4 = ST3 • D 

T5 = ST1 • E 

T6 = ST4 • F 

ST1 = ( ST1 + T2 + T4 + T6) ⋅T1 ⋅T3 ⋅T5 

ST2 = ( ST2 + T1 ⋅T3 ⋅T5) ⋅ T2 

ST3 = ( ST3 + T3 ⋅ T5) ⋅ T4 

ST4 = ( ST4 + T5 + FS) ⋅ T6 

ST1 A T1 

ST2 B T2 

ST1 C T3 

ST3 D T4 

ST1 E T5 

ST4 F T6 

ST1 T1 T3 T5 

ST1 

T2 

T4 

T6 

ST2 T2 ST2 

T1 T3 T5 

ST3 T4 ST3 

T3 

T5 

ST4 T6 ST4 

T5 

FS 



4. 

ST1 

B 

T2 

A 

T1 

ST2 

C * B 

T3 

T4 

C + B 

ST3 


T1 = ST2 ⋅ A 

T2 

= 

ST1 ⋅ B 

T3 = ST3 ⋅ ( C⋅ 

B) 

T4 = ST2 ⋅ ( C+ 

B) 

ST1 = ( ST1 + T1) ⋅ T2 + FS 

ST2 = ( ST2 + T2 + T3) ⋅T1 ⋅T4 

ST3 = ( ST3 + T4 ⋅ T1) ⋅ T3 

ST2 

ST1 

A 

B 

T1 

T2 

ST3 C B 

T3 

ST2 

T2 

C 

B 

ST1 

T1 

first scan 

T4 

ST1 

T1 

T4 

ST2 

ST2 

T2 

T3 

T3 

ST3 

ST3 

T4 

T1 



5. 

TA 

TB 

TC 

TD 

TE 

TF 

= 

= 

= 

= 

= 

= 

ST2 ⋅ A 

ST1 ⋅ B 

ST3 ⋅ C 

ST1 ⋅ D ⋅B 

ST2 ⋅ E⋅ 

A 

ST3 ⋅ F ⋅C 

ST1 = ( ST1 + TA + TC) ⋅ TB ⋅TD 

ST2 = ( ST2 + TB + TF) ⋅ TA ⋅TE 

ST3 = ( ST3 + TD + TE) ⋅ TC ⋅TF 

ST2 A 

ST1 B 

ST3 C 

ST1 D B 

ST2 E A 

ST3 F C 

ST1 TB TD 

TA 

TA 

TB 

TC 

TD 

TE 

TF 

ST1 

TC 

ST2 TA TE 

TB 

ST2 

TF 

ST3 TC TF 

TD 

ST3 

TE 



6. 

a) 

button A + button B 

door idle 

motor on 

door opening 

thermal relay + 15 sec delay 

counter > 20,000 

reset button - assumed 

service mode 

b) 

Legend 

button A 

button B 

motor 

thermal relay 

reset button 

state 1 

state 2 

state 3 

lamp 

Machine:0.I.Data.1 


Machine:1.O.Data.3 


Machine:0.I.Data.4 - assumed 

Machine:1.O.Data.7 



first scan 

MCR 

L 

state 1 

U 

state 2 

U 

state 3 

MCR 

state 2 

motor 

state 3 

light 

state 1 

MCR 

button A 

L 

state 2 

button B 

U 

state 1 

MCR 



state 2 

MCR 

TON 

t_st2 

preset 15s 

t_st2.DN 

L 

state 1 

thermal relay 

U 

state 2 

CTU 

maintain 

preset 20000 

maintain.DN 

L 

state 3 

U 

state 2 

U 

state 1 

MCR 



state 3 

MCR 

reset button ?? 

L 

state 1 

U 

state 3 

RES 

counter 

MCR 

c) 

S0 = ( S0 + S1( delay( 15) + thermal) 

)S0( buttonA + buttonB) 

S1 = ( S1 + S0( buttonA + buttonB) 

)S1( delay( 15) + thermal)S3( counter) 

S3 = ( S3 + S2( counter) 

)S3( reset) 

motor 

= 

S1 

light 

= 

S3 



7. 

a) block logic method 

door 

closed 

(state 3) 

remote OR button OR bottom limit 

remote OR button 

door 

closing 

(state 2) 

light sensor 

door 

opening 

(state 4) 


door 

opened 

(state 1) 

remote OR button OR top limit 



FS 

L 

state_1 

U 

state_2 

U 

state_3 

U 

state_4 

state_2 

close_door 

state_4 

open_door 

state_2 

state_4 

TOF 

light_on 

preset 300s 

light_on.DN 

garage_light 

state_1 

MCR 

remote 

U 

state_1 

button 

L 

state_2 

MCR 



state 2 

MCR 

remote 

U 

state_2 

button 

bottom_limit 

L 

state_3 

light_beam 

U 

state_2 

L 

state_4 

MCR 

state_3 

MCR 

remote 

U 

state_3 

button 

L 

state_4 

MCR 



state_4 

MCR 

remote 

U 

state_4 

button 

top_limit 

L 

state_1 

MCR 



b) state-transition equations 

door 

closed 

(state 3) 

remote OR button OR bottom limit 


door 

closing 

(state 2) 

light sensor 

door 

opening 

(state 4) 


door 

opened 

(state 1) 

remote OR button OR top limit 

using the previous state diagram. 

ST1 = state 1 

ST2 = state 2 

ST3 = state 3 

ST4 = state 4 


ST1 = ( ST1 + T5) ⋅ T1 

ST2 = ( ST2 + T1) ⋅T2 ⋅T3 

ST3 = ( ST3 + T2) ⋅ T4 

ST4 = ( ST4 + T3 + T4) ⋅ T5 

T1 = state 1 to state 2 





T1 = ST1 ⋅ ( remote + button) 

T2 = ST2 ⋅ ( remote + button + bottomlimit) 

T3 = ST2 ⋅ ( remote + button) 

T4 = ST3 ⋅ ( lighbeam) 

T5 = ST4 ⋅ ( remote + button + toplimit) + FS 



ST1 

remote 

T1 

button 

ST2 

remote 

T2 

button 

bottom limit 

ST3 

remote 

T3 

button 

ST3 

light_beam 

T4 

ST4 

remote 

T5 

button 

top_limit 

first_scan 



T1 

ST1 

ST1 

T5 

T2 

T3 

ST2 

ST2 

T1 

T4 

ST3 

ST3 

T2 

T5 

ST4 

ST4 

T3 

T4 

ST2 

close do 

ST4 

open doo 

ST2 

ST4 

TOF 

light_on 

preset 300s 

light_on.DN 

garage_light 




1. Describe the difference between the block logic, delayed update, and transition equation methods 

for converting state diagrams to ladder logic. 

2. Write the ladder logic for the state diagram below using the block logic method. 

FS 

ST1 

A 

B 

ST2 

D 

ST3 

C 

3. Convert the following state diagram to ladder logic using the block logic method. Give the stop 

button higher priority. 

ST0: idle 

A 

STOP 

ST1: X on 

B 

STOP 

D + STOP 

ST3: Z on 

C 

ST2: Y on 



4. Convert the following state diagram to ladder logic using the delayed update method. 

part 

FS 

idle 

part 

active 

reset 

fault 

jam 

5. Use equations to develop ladder logic for the state diagram below using the delayed update 

method. Be sure to deal with the priority problems. 

FS 

D + E 

STA 

A 

STD 

E 

E 

STB 

C 

STC 

B 



6. Implement the State-Transition equations.in the figure below with ladder logic. 

STA 

T5 

B 

T4 

D 

STC 

A 

T2 

STB 

C 

T3 

T1 

first scan (FS) 

T1 

= 

FS 

STA = ( STA + T2) ⋅ T5 

T2 

= 

STB ⋅ A 

STB = ( STB + T5 + T4 + T1) ⋅T2 ⋅T3 

T3 

= 

STB ⋅ C 

STC = ( STC + T3 ⋅ T2) ⋅ T4 

T4 

= 

STC ⋅ D 

T5 

= 

STA ⋅ B 

7. Write ladder logic to implement the state diagram below using state transition equations. 

FS 

A 

B 

STA STB STC 

C 

C 

8. Convert the following state diagram to ladder logic using a) an equation based method, b) a 



method that is not based on equations. 

FS 

START 

STB 

STA 

5s delay 

RESET 

DONE 

STOP 

STE 

FAULT 

STD 

LIMIT 

STC 

9. The state diagram below is for a simple elevator controller. a) Develop a ladder logic program 

that implements it with Boolean equations. b) Develop the ladder logic using the block logic 

technique. c) Develop the ladder logic using the delayed update method. 

up_request 

move 

up 

at_floor 

pause 

up 

FS 

idle 

up_request 

down_request 

door_closed 

door_closed 

down_request 

move 

down 

at_floor 

pause 

down 

10. Write ladder logic for the state diagram below a) using an equation based method. b) without 



using an equation based method. 

OFFHOOK 

IDLE 

OFFHOOK 

FS 

OFFHOOK 

CONNECTED 

OFFHOOK 

ANSWERED 

RINGING 

DIALED 

DIALING 

11. For the state diagram for the traffic light example, add a 15 second green light timer and speed 

up signal for an emergency vehicle. A strobe light mounted on fire trucks will cause the lights 

to change so that the truck doesn’t need to stop. Modify the state diagram to include this 

option. Implement the new state diagram with ladder logic. 

12. Design a program with a state diagram for a hydraulic press that will advance when two palm 

buttons are pushed. Top and bottom limit switches are used to reverse the advance and stop 

after a retract. At any time the hands removed from the palm button will stop an advance and 

retract the press. Include start and stop buttons to put the press in and out of an active mode. 

13. In dangerous processes it is common to use two palm buttons that require a operator to use 

both hands to start a process (this keeps hands out of presses, etc.). To develop this there are 

two inputs (P1 and P2) that must both be turned on within 0.25s of each other before a machine 

cycle may begin. 

Develop ladder logic with a state diagram to control a process that has a start (START) and stop 

(STOP) button for the power. After the power is on the palm buttons (P1 and P2) may be used 

as described above to start a cycle. The cycle will consist of turning on an output (MOVE) for 

2 seconds. After the press has been cycled 1000 times the press power should turn off and an 

output (LIGHT) should go on. 



14. Use a state diagram to design a parking gate controller. 

keycard entry 

cars enter/leave 

gate 

light 

car detector 

- the gate will be raised by one output 

and lowered by another. If the gate 

gets stuck an over current detector 

will make a PLC input true. If this 

is the case the gate should reverse 

and the light should be turned on 

indefinitely. 

- if a valid keycard is entered a PLC 

input will be true. The gate is to 

rise and stay open for 10 seconds. 

- when a car is over the car detector a 

PLC input will go true. The gate is 

to open while this detector is 

active. If it is active for more that 

30 seconds the light should also 

turn on until the gate closes. 

15. This morning you received a call from Mr. Ian M. Daasprate at the Old Fashioned Widget 

Company. In the past when they built a new machine they would used punched paper cards for 

control, but their supplier of punched paper readers went out of business in 1972 and they have 

decided to try using PLCs this time. He explains that the machine will dip wooden parts in varnish 

for 2 seconds, and then apply heat for 5 minutes to dry the coat, after this they are manually 

removed from the machine, and a new part is put in. They are also considering a premium 

line of parts that would call for a dip time of 30 seconds, and a drying time of 10 minutes. He 

then refers you to the project manager, Ann Nooyed. 

You call Ann and she explains how the machine should operate. There should be start and stop 

buttons. The start button will be pressed when the new part has been loaded, and is ready to be 

coated. A light should be mounted to indicate when the machine is in operation. The part is 

mounted on a wheel that is rotated by a motor. To dip the part, the motor is turned on until a 

switch is closed. To remove the part from the dipping bath the motor is turned on until a second 

switch is closed. If the motor to rotate the wheel is on for more that 10 seconds before hitting a 

switch, the machine should be turned off, and a fault light turned on. The fault condition will 

be cleared by manually setting the machine back to its initial state, and hitting the start button 

twice. If the part has been dipped and dried properly, then a done light should be lit. To select a 

premium product you will use an input switch that needs to be pushed before the start button is 

pushed. She closes by saying she will be going on vacation and you need to have it done before 

she returns. 

You hang up the phone and, after a bit of thought, decide to use the following outputs and inputs, 



INPUTS 

I/1 - start push button 

I/2 - stop button 

I/3 - premium part push button 

I/4 - switch - part is in bath on wheel 

I/5 - switch - part is out of bath on wheel 

OUTPUTS 

O/1 - start button 

O/2 - in operation 

O/3 - fault light 

O/4 - part done light 

O/5 - motor on 

O/6 - heater power supply 

a) Draw a state diagram for the process. 

b) List the variables needed to indicate when each state is on, and list any timers 

and counters used. 

c) Write a Boolean expression for each transition in the state diagram. 

d) Do a simple wiring diagram for the PLC. 

e) Write the ladder logic for the state that involves moving the part into the dipping 

bath. 

16. Design ladder logic with a state diagram for the following process description. 

a) A toggle start switch (TS1) and a limit switch on a safety gate (LS1) must both 

be on before a solenoid (SOL1) can be energized to extend a stamping cylinder 

to the top of a part. Should a part detect sensor (PS1) also be considered? 

Explain your answer. 

b) While the stamping solenoid is energized, it must remain energized until a limit 

switch (LS2) is activated. This second limit switch indicates the end of a stroke. 

At this point the solenoid should be de-energized, thus retracting the cylinder. 

c) When the cylinder is fully retracted a limit switch (LS3) is activated. The cycle 

may not begin again until this limit switch is active. This is one way to ensure 

that a new part is present, is there another? 

d) A cycle counter should also be included to allow counts of parts produced. 

When this value exceeds some variable amount (from 1 to 5000) the machine 

should shut down, and a job done light lit up. 

e) A safety check should be included. If the cylinder solenoid has been on for more 

than 5 seconds, it suggests that the cylinder is jammed, or the machine has a 

fault. If this is the case the machine should be shut down, and a maintenance 

light turned on. 

f) Implement the ladder diagram on a PLC in the laboratory. 

g) Fully document the ladder logic and prepare a short report - This should be of 

use to another engineer that will be maintaining the system. 


plc numbers - 13.1 

13. NUMBERS AND DATA 

Topics: 

• Number bases; binary, octal, decimal, hexadecimal 

• Binary calculations; 2s compliments, addition, subtraction and Boolean operations 

• Encoded values; BCD and ASCII 

• Error detection; parity, gray code and checksums 

Objectives: 

• To be familiar with binary, octal and hexadecimal numbering systems. 

• To be able to convert between different numbering systems. 

• To understand 2s compliment negative numbers. 

• To be able to convert ASCII and BCD values. 

• To be aware of basic error detection techniques. 


Base 10 (decimal) numbers developed naturally because the original developers 

(probably) had ten fingers, or 10 digits. Now consider logical systems that only have wires 

that can be on or off. When counting with a wire the only digits are 0 and 1, giving a base 

2 numbering system. Numbering systems for computers are often based on base 2 numbers, 

but base 4, 8, 16 and 32 are commonly used. A list of numbering systems is give in 

Figure 13.1. An example of counting in these different numbering systems is shown in 

Figure 13.2. 

Base 

2 

8 

10 

16 

Name 

Binary 

Octal 

Decimal 

Hexadecimal 

Data Unit 

Bit 

Nibble 

Digit 

Byte 

Figure 13.1 

Numbering Systems 



decimal 

binary 

octal 

hexadecimal 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

0 

1 

10 

11 

100 

101 

110 

111 

1000 

1001 

1010 

1011 

1100 

1101 

1110 

1111 

10000 

10001 

10010 

10011 

10100 

0 

1 

2 

3 

4 

5 

6 

7 

10 

11 

12 

13 

14 

15 

16 

17 

20 

21 

22 

23 

24 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

a 

b 

c 

d 

ef 

10 

11 

12 

13 

14 

Note: As with all numbering systems 

most significant digits are at left, 

least significant digits are at right. 

Figure 13.2 

Numbers in Decimal, Binary, Octal and Hexadecimal 

The effect of changing the base of a number does not change the actual value, only 

how it is written. The basic rules of mathematics still apply, but many beginners will feel 

disoriented. This chapter will cover basic topics that are needed to use more complex programming 

instructions later in the book. These will include the basic number systems, 

conversion between different number bases, and some data oriented topics. 

13.2 NUMERICAL VALUES 

13.2.1 Binary 

Binary numbers are the most fundamental numbering system in all computers. A 

single binary digit (a bit) corresponds to the condition of a single wire. If the voltage on 

the wire is true the bit value is 1. If the voltage is off the bit value is 0. If two or more wires 

are used then each new wire adds another significant digit. Each binary number will have 

an equivalent digital value. Figure 13.3 shows how to convert a binary number to a decimal 

equivalent. Consider the digits, starting at the right. The least significant digit is 1, and 



is in the 0th position. To convert this to a decimal equivalent the number base (2) is raised 

to the position of the digit, and multiplied by the digit. In this case the least significant 

digit is a trivial conversion. Consider the most significant digit, with a value of 1 in the 6th 

position. This is converted by the number base to the exponent 6 and multiplying by the 

digit value of 1. This method can also be used for converting the other number system to 

decimal. 

2 6 = 64 

2 5 = 32 

2 4 = 16 

2 3 = 8 

2 2 = 4 

2 1 = 2 

2 0 = 1 

1 1 1 0 0 0 1 

1(2 6 ) = 

1(2 5 ) = 

1(2 4 ) = 

0(2 3 ) = 

0(2 2 ) = 

0(2 1 ) = 

1(2 0 ) = 

64 

32 

16 

0 

0 

0 

1 

113 

Figure 13.3 

Conversion of a Binary Number to a Decimal Number 

Decimal numbers can be converted to binary numbers using division, as shown in 

Figure 13.4. This technique begins by dividing the decimal number by the base of the new 

number. The fraction after the decimal gives the least significant digit of the new number 

when it is multiplied by the number base. The whole part of the number is now divided 

again. This process continues until the whole number is zero. This method will also work 

for conversion to other number bases. 



start with decimal number 932 

for binary 

(base 2) 

932 

-------- = 466.0 

2(0.0) = 0 

2 

466 

-------- = 233.0 

2(0.0) = 0 

2 

233 

-------- = 116.5 

2(0.5) = 1 

2 

116 

-------- = 58.0 

2(0.0) = 0 

2 

58 

----- = 29.0 

2(0.0) = 0 

2 

29 

----- = 14.5 

2(0.5) = 1 

2 

done 

14 

----- = 7.0 

2(0.0) = 0 

2 

7 

-- = 3.5 

2(0.5) = 1 

2 

3 

-- = 1.5 

2(0.5) = 1 

2 

1 

-- = 0.5 

2(0.5) = 1 

2 

1110100100 

multiply places after decimal by division 

base, in this case it is 2 because of the binary. 

* This method works for other number bases also, the divisor and multipliers 

should be changed to the new number bases. 

Figure 13.4 

Conversion from Decimal to Binary 

Most scientific calculators will convert between number bases. But, it is important 

to understand the conversions between number bases. And, when used frequently enough 

the conversions can be done in your head. 

Binary numbers come in three basic forms - a bit, a byte and a word. A bit is a single 

binary digit, a byte is eight binary digits, and a word is 16 digits. Words and bytes are 



shown in Figure 13.5. Notice that on both numbers the least significant digit is on the right 

hand side of the numbers. And, in the word there are two bytes, and the right hand one is 

the least significant byte. 

BYTE 

WORD 

MSB 

LSB 

MSB 

LSB 

0110 1011 

0110 1011 0100 0010 

most 

significant 

byte 

least 

significant 

byte 

Figure 13.5 

Bytes and Words 

Binary numbers can also represent fractions, as shown in Figure 13.6. The conversion 

to and from binary is identical to the previous techniques, except that for values to the 

right of the decimal the equivalents are fractions. 

binary: 

101.011 

12 ( 2 ) = 4 0( 2 1 ) = 0 1( 2 0 ) = 1 0( 2 – 1 ) = 0 12 ( – 2 ) 

1 

= -- 1( 2 – 3 ) 

4 

= 

1 

-- 

8 

= 4+ 0 + 1 + 0 + 

1 

-- + 

1 

-- = 5.375 

4 8 

decimal 

Figure 13.6 

A Binary Decimal Number 

13.2.1.1 - Boolean Operations 

In the next chapter you will learn that entire blocks of inputs and outputs can be 

used as a single binary number (typically a word). Each bit of the number would correspond 

to an output or input as shown in Figure 13.7. 



There are three motors M 1 , M 2 and M 3 represented with three bits in a binary 

number. When any bit is on the corresponding motor is on. 

100 = Motor 1 is the only one on 

111 = All three motors are on 

in total there are 2 n or 2 3 possible combinations of motors on. 

Figure 13.7 

Motor Outputs Represented with a Binary Number 

We can then manipulate the inputs or outputs using Boolean operations. Boolean 

algebra has been discussed before for variables with single values, but it is the same for 

multiple bits. Common operations that use multiple bits in numbers are shown in Figure 

13.8. These operations compare only one bit at a time in the number, except the shift 

instructions that move all the bits one place left or right. 

Name 

Example 

Result 

AND 

OR 

NOT 

EOR 

NAND 

shift left 

shift right 

etc. 

0010 * 1010 

0010 + 1010 

0010 

0010 eor 1010 

0010 * 1010 

111000 

111000 

0010 

1010 

1101 

1000 

1101 

110001 

011100 

(other results are possible) 

(other results are possible) 

Figure 13.8 

Boolean Operations on Binary Numbers 

13.2.1.2 - Binary Mathematics 

Negative numbers are a particular problem with binary numbers. As a result there 

are three common numbering systems used as shown in Figure 13.9. Unsigned binary 

numbers are common, but they can only be used for positive values. Both signed and 2s 

compliment numbers allow positive and negative values, but the maximum positive values 

is reduced by half. 2s compliment numbers are very popular because the hardware and 

software to add and subtract is simpler and faster. All three types of numbers will be found 

in PLCs. 



Type 

unsigned 

signed 

2s compliment 

Description 

binary numbers can only have positive values. 

the most significant bit (MSB) of the binary number 

is used to indicate positive/negative. 

negative numbers are represented by complimenting 

the binary number and then adding 1. 

Range for Byte 

0 to 255 

-127 to 127 

-128 to 127 

Figure 13.9 

Binary (Integer) Number Types 

Examples of signed binary numbers are shown in Figure 13.10. These numbers use 

the most significant bit to indicate when a number is negative. 

decimal 

binary byte 

2 

1 

0 

-0 

-1 

00000010 

00000001 

00000000 

10000000 

10000001 

-2 10000010 

Note: there are two zeros 

Figure 13.10 

Signed Binary Numbers 

An example of 2s compliment numbers are shown in Figure 13.11. Basically, if the 

number is positive, it will be a regular binary number. If the number is to be negative, we 

start the positive number, compliment it (reverse all the bits), then add 1. Basically when 

these numbers are negative, then the most significant bit is set. To convert from a negative 

2s compliment number, subtract 1, and then invert the number. 



decimal binary byte METHOD FOR MAKING A NEGATIVE NUMBER 

2 

1 

0 

-1 

-2 

00000010 

00000001 

00000000 

11111111 

11111110 

1. write the binary number for the positive 

for -30 we write 30 = 00011110 

2. Invert (compliment) the number 

00011110 becomes 11100001 

3. Add 1 

11100001 + 00000001 = 11100010 

Figure 13.11 

2s Compliment Numbers 

Using 2s compliments for negative numbers eliminates the redundant zeros of 

signed binaries, and makes the hardware and software easier to implement. As a result 

most of the integer operations in a PLC will do addition and subtraction using 2s compliment 

numbers. When adding 2s compliment numbers, we don’t need to pay special attention 

to negative values. And, if we want to subtract one number from another, we apply 

the twos compliment to the value to be subtracted, and then apply it to the other value. 

Figure 13.12 shows the addition of numbers using 2s compliment numbers. The 

three operations result in zero, positive and negative values. Notice that in all three operation 

the top number is positive, while the bottom operation is negative (this is easy to see 

because the MSB of the numbers is set). All three of the additions are using bytes, this is 

important for considering the results of the calculations. In the left and right hand calculations 

the additions result in a 9th bit - when dealing with 8 bit numbers we call this bit the 

carry C. If the calculation started with a positive and negative value, and ended up with a 

carry bit, there is no problem, and the carry bit should be ignored. If doing the calculation 

on a calculator you will see the carry bit, but when using a PLC you must look elsewhere 

to find it. 



+ 

00000001 = 1 

11111111 = -1 

+ 

00000001 = 1 

11111110 = -2 

+ 

00000010 = 2 

11111111 = -1 

C+00000000 = 0 

11111111 = -1 

C+00000001 = 1 

ignore the carry bits 

Note: Normally the carry bit is ignored during the operation, 

but some additional logic is required to make 

sure that the number has not overflowed and moved 

outside of the range of the numbers. Here the 2s compliment 

byte can have values from -128 to 127. 

Figure 13.12 

Adding 2s Compliment Numbers 

The integers have limited value ranges, for example a 16 bit word ranges from - 

32,768 to 32,767 whereas a 32 bit word ranges from -2,147,483,648 to 2,147,483,647. In 

some cases calculations will give results outside this range, and the Overflow O bit will be 

set. (Note: an overflow condition is a major error, and the PLC will probably halt when 

this happens.) For an addition operation the Overflow bit will be set when the sign of both 

numbers is the same, but the sign of the result is opposite. When the signs of the numbers 

are opposite an overflow cannot occur. This can be seen in Figure 13.13 where the numbers 

two of the three calculations are outside the range. When this happens the result goes 

from positive to negative, or the other way. 

+ 

01111111 = 127 

00000011 = 3 

+ 

10000001 = -127 

11111111 = -1 

+ 

10000001 = -127 

11111110 = -2 

10000010 = -126 

C = 0 

O = 1 (error) 

10000000 = -128 

C = 1 

O = 0 (no error) 

01111111 = 127 

C = 1 

O = 1 (error) 

Note: If an overflow bit is set this indicates that a calculation is outside and 

acceptable range. When this error occurs the PLC will halt. Do not ignore the 

limitations of the numbers. 

Figure 13.13 

Carry and Overflow Bits 

These bits also apply to multiplication and division operations. In addition the PLC 

will also have bits to indicate when the result of an operation is zero Z and negative N. 



13.2.2 Other Base Number Systems 

Other number bases are typically converted to and from binary for storage and 

mathematical operations. Hexadecimal numbers are popular for representing binary values 

because they are quite compact compared to binary. (Note: large binary numbers with 

a long string of 1s and 0s are next to impossible to read.) Octal numbers are also popular 

for inputs and outputs because they work in counts of eight; inputs and outputs are in 

counts of eight. 

An example of conversion to, and from, hexadecimal is shown in Figure 13.14 and 

Figure 13.15. Note that both of these conversions are identical to the methods used for 

binary numbers, and the same techniques extend to octal numbers also. 

16 3 = 4096 

16 2 = 256 

16 1 = 16 

16 0 = 1 

f 8 a 3 

15(16 3 ) = 

8(16 2 ) = 

10(16 1 ) = 

3(16 0 ) = 

61440 

2048 

160 

3 

63651 

Figure 13.14 

Conversion of a Hexadecimal Number to a Decimal Number 

5724 

----------- = 357.75 

16(0.75) = 12 ’c’ 

16 

357 

-------- = 22.3125 

16(0.3125) = 5 

16 

22 

----- = 1.375 

16(0.375) = 6 

16 

----- 

1 

= 0.0625 

16(0.0625) = 1 

16 

1 6 5 c 

Figure 13.15 

Conversion from Decimal to Hexadecimal 



13.2.3 BCD (Binary Coded Decimal) 

Binary Coded Decimal (BCD) numbers use four binary bits (a nibble) for each 

digit. (Note: this is not a base number system, but it only represents decimal digits.) This 

means that one byte can hold two digits from 00 to 99, whereas in binary it could hold 

from 0 to 255. A separate bit must be assigned for negative numbers. This method is very 

popular when numbers are to be output or input to the computer. An example of a BCD 

number is shown in Figure 13.16. In the example there are four digits, therefore 16 bits are 

required. Note that the most significant digit and bits are both on the left hand side. The 

BCD number is the binary equivalent of each digit. 

1263 

decimal 

0001 0010 0110 0011 BCD 

Note: this example shows four digits 

in two bytes. The hex values 

would also be 1263. 

Figure 13.16 

A BCD Encoded Number 

Most PLCs store BCD numbers in words, allowing values between 0000 and 9999. 

They also provide functions to convert to and from BCD. It is also possible to calculations 

with BCD numbers, but this is uncommon, and when necessary most PLCs have functions 

to do the calculations. But, when doing calculations you should probably avoid BCD and 

use integer mathematics instead. Try to be aware when your numbers are BCD values and 

convert them to integer or binary value before doing any calculations. 

13.3 DATA CHARACTERIZATION 

13.3.1 ASCII (American Standard Code for Information Interchange) 

When dealing with non-numerical values or data we can use plain text characters 

and strings. Each character is given a unique identifier and we can use these to store and 

interpret data. The ASCII (American Standard Code for Information Interchange) is a very 

common character encryption system is shown in Figure 13.17 and Figure 13.18. The 

table includes the basic written characters, as well as some special characters, and some 

control codes. Each one is given a unique number. Consider the letter A, it is readily recognized 

by most computers world-wide when they see the number 65. 



Figure 13.17 

ASCII Character Table 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

A 

B 

C 

D 

E 

F 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

1A 

1B 

1C 

1D 

1E 

1F 

00000000 

00000001 

00000010 

00000011 

00000100 

00000101 

00000110 

00000111 

00001000 

00001001 

00001010 

00001011 

00001100 

00001101 

00001110 

00001111 

00010000 

00010001 

00010010 

00010011 

00010100 

00010101 

00010110 

00010111 

00011000 

00011001 

00011010 

00011011 

00011100 

00011101 

00011110 

00011111 

NUL 

SOH 

STX 

ETX 

EOT 

ENQ 

ACK 

BEL 

BS 

HT 

LF 

VT 

FF 

CR 

S0 

S1 

DLE 

DC1 

DC2 

DC3 

DC4 

NAK 

SYN 

ETB 

CAN 

EM 

SUB 

ESC 

FS 

GS 

RS 

US 

decimal 

hexadecimal 

binary 

ASCII 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

62 

63 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

2A 

2B 

2C 

2D 

2E 

2F 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

3A 

3B 

3C 

3D 

3E 

3F 

00100000 

00100001 

00100010 

00100011 

00100100 

00100101 

00100110 

00100111 

00101000 

00101001 

00101010 

00101011 

00101100 

00101101 

00101110 

00101111 

00110000 

00110001 

00110010 

00110011 

00110100 

00110101 

00110110 

00110111 

00111000 

00111001 

00111010 

00111011 

00111100 

00111101 

00111110 

00111111 

space 

! 

“ 

# 

$ 

% 

& 

‘ 

( 

) 

* 

+ 

, 

- 

. 

/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

: 

; 

< 

= 

> 

? 

decimal 

hexadecimal 

binary 

ASCII 



decimal 

hexadecimal 

binary 

ASCII 

decimal 

hexadecimal 

binary 

ASCII 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

92 

93 

94 

95 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

4A 

4B 

4C 

4D 

4E 

4F 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

5A 

5B 

5C 

5D 

5E 

5F 

01000000 

01000001 

01000010 

01000011 

01000100 

01000101 

01000110 

01000111 

01001000 

01001001 

01001010 

01001011 

01001100 

01001101 

01001110 

01001111 

01010000 

01010001 

01010010 

01010011 

01010100 

01010101 

01010110 

01010111 

01011000 

01011001 

01011010 

01011011 

01011100 

01011101 

01011110 

01011111 

@ 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

L 

M 

N 

O 

P 

Q 

R 

S 

T 

U 

V 

W 

X 

Y 

Z 

[ 

yen 

] 

^ 

_ 

96 

97 

98 

99 

100 

101 

102 

103 

104 

105 

106 

107 

108 

109 

110 

111 

112 

113 

114 

115 

116 

117 

118 

119 

120 

121 

122 

123 

124 

125 

126 

127 

60 

61 

62 

63 

64 

65 

66 

67 

68 

69 

6A 

6B 

6C 

6D 

6E 

6F 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

7A 

7B 

7C 

7D 

7E 

7F 

01100000 

01100001 

01100010 

01100011 

01100100 

01100101 

01100110 

01100111 

01101000 

01101001 

01101010 

01101011 

01101100 

01101101 

01101110 

01101111 

01110000 

01110001 

01110010 

01110011 

01110100 

01110101 

01110110 

01110111 

01111000 

01111001 

01111010 

01111011 

01111100 

01111101 

01111110 

01111111 

‘ 

a 

b 

c 

d 

e 

f 

g 

h 

i 

j 

k 

l 

m 

n 

o 

p 

q 

r 

s 

t 

u 

v 

w 

x 

y 

z 

{ 

| 

} 

r arr. 

l arr. 

Figure 13.18 

ASCII Character Table 

This table has the codes from 0 to 127, but there are more extensive tables that 

contain special graphics symbols, international characters, etc. It is best to use the basic 

codes, as they are supported widely, and should suffice for all controls tasks. 



An example of a string of characters encoded in ASCII is shown in Figure 13.19. 

e.g. The sequence of numbers below will convert to 

A W e e T e s t 

A 

space 

W 

e 

e 

space 

T 

e 

s 

t 

65 

32 

87 

101 

101 

32 

84 

101 

115 

116 

Figure 13.19 

A String of Characters Encoded in ASCII 

When the characters are organized into a string to be transmitted and LF and/or CR 

code are often put at the end to indicate the end of a line. When stored in a computer an 

ASCII value of zero is used to end the string. 

13.3.2 Parity 

Errors often occur when data is transmitted or stored. This is very important when 

transmitting data in noisy factories, over phone lines, etc. Parity bits can be added to data 

as a simple check of transmitted data for errors. If the data contains error it can be retransmitted, 

or ignored. 

A parity bit is normally a 9th bit added onto an 8 bit byte. When the data is 

encoded the number of true bits are counted. The parity bit is then set to indicate if there 

are an even or odd number of true bits. When the byte is decoded the parity bit is checked 

to make sure it that there are an even or odd number of data bits true. If the parity bit is not 

satisfied, then the byte is judged to be in error. There are two types of parity, even or odd. 

These are both based upon an even or odd number of data bits being true. The odd parity 

bit is true if there are an odd number of bits on in a binary number. On the other hand the 

Even parity is set if there are an even number of true bits. This is illustrated in Figure 

13.20. 



Odd Parity 

Even Parity 

data 

bits 

10101110 

10111000 

00101010 

10111101 

parity 

bit 

1 

0 

0 

1 

Figure 13.20 

Parity Bits on a Byte 

Parity bits are normally suitable for single bytes, but are not reliable for data with a 

number of bits. 

Note: Control systems perform important tasks that can be dangerous in certain circumstances. 

If an error occurs there could be serious consequences. As a result error 

detection methods are very important for control system. When error detection occurs 

the system should either be robust enough to recover from the error, or the system 

should fail-safe. If you ignore these design concepts you will eventually cause an 

accident. 

13.3.3 Checksums 

Parity bits are suitable for a few bits of data, but checksums are better for larger 

data transmissions. These are simply an algebraic sum of all of the data transmitted. 

Before data is transmitted the numeric values of all of the bytes are added. This sum is 

then transmitted with the data. At the receiving end the data values are summed again, and 

the total is compared to the checksum. If they match the data is accepted as good. An 

example of this method is shown in Figure 13.21. 



DATA 

124 

43 

255 

9 

27 

47 

CHECKSUM 

505 

Figure 13.21 

A Simplistic Checksum 

Checksums are very common in data transmission, but these are also hidden from 

the average user. If you plan to transmit data to or from a PLC you will need to consider 

parity and checksum values to verify the data. Small errors in data can have major consequences 

in received data. Consider an oven temperature transmitted as a binary integer 

(1023d = 0000 0100 0000 0000b). If a single bit were to be changed, and was not detected 

the temperature might become (0000 0110 0000 0000b = 1535d) This small change would 

dramatically change the process. 

13.3.4 Gray Code 

Parity bits and checksums are for checking data that may have any value. Gray 

code is used for checking data that must follow a binary sequence. This is common for 

devices such as angular encoders. The concept is that as the binary number counts up or 

down, only one bit changes at a time. Thus making it easier to detect erroneous bit 

changes. An example of a gray code sequence is shown in Figure 13.22. Notice that only 

one bit changes from one number to the next. If more than a single bit changes between 

numbers, then an error can be detected. 

ASIDE: When the signal level in a wire rises or drops, it induces a magnetic pulse that 

excites a signal in other nearby lines. This phenomenon is known as cross-talk. This 

signal is often too small to be noticed, but several simultaneous changes, coupled with 

background noise could result in erroneous values. 



decimal 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

gray code 

0000 

0001 

0011 

0010 

0110 

0111 

0101 

0100 

1100 

1101 

1111 

1110 

1010 

1011 

1001 

1000 

Figure 13.22 

Gray Code for a Nibble 

13.4 SUMMARY 

• Binary, octal, decimal and hexadecimal numbers were all discussed. 

• 2s compliments allow negative binary numbers. 

• BCD numbers encode digits in nibbles. 

• ASCII values are numerical equivalents for common alphanumeric characters. 

• Gray code, parity bits and checksums can be used for error detection. 


1. Why are binary, octal and hexadecimal used for computer applications? 

2. Is a word is 3 nibbles? 

3. What are the specific purpose for Gray code and parity? 

4. Convert the following numbers to/from binary 



a) from base 10: 54,321 b) from base 2: 110000101101 

5. Convert the BCD number below to a decimal number, 

0110 0010 0111 1001 

6. Convert the following binary number to a BCD number, 

0100 1011 

7. Convert the following binary number to a Hexadecimal value, 

0100 1011 

8. Convert the following binary number to a octal, 

0100 1011 

9. Convert the decimal value below to a binary byte, and then determine the odd parity bit, 

97 

10. Convert the following from binary to decimal, hexadecimal, BCD and octal. 

a) 101101 

b) 11011011 

c) 10000000001 

d) 0010110110101 



11. Convert the following from decimal to binary, hexadecimal, BCD and octal. 

a) 1 

b) 17 

c) 20456 

d) -10 

12. Convert the following from hexadecimal to binary, decimal, BCD and octal. 

a) 1 

b) 17 

c) ABC 

d) -A 

13. Convert the following from BCD to binary, decimal, hexadecimal and octal. 

a) 1001 

b) 1001 0011 

c) 0011 0110 0001 

d) 0000 0101 0111 0100 

14. Convert the following from octal to binary, decimal, hexadecimal and BCD. 

a) 7 

b) 17 

c) 777 

d) 32634 

15. 

a) Represent the decimal value thumb wheel input, 3532, as a Binary Coded Decimal 

(BCD) and a Hexadecimal Value (without using a calculator). 

i) BCD 

ii) Hexadecimal 

b) What is the corresponding decimal value of the BCD value, 

1001111010011011? 

16. Add/subtract/multiply/divide the following numbers. 

a) binary 101101101 + 01010101111011 

b) hexadecimal 101 + ABC 

c) octal 123 + 777 

d) binary 110110111 - 0101111 

e) hexadecimal ABC - 123 

f) octal 777 - 123 

g) binary 0101111 - 110110111 

h) hexadecimal 123-ABC 

i) octal 123 - 777 

j) 2s complement bytes 10111011 + 00000011 

k) 2s complement bytes 00111011 + 00000011 

l) binary 101101101 * 10101 

m) octal 123 * 777 

n) octal 777 / 123 

o) binary 101101101 / 10101 

p) hexadecimal ABC / 123 



17. Do the following operations with 8 bit bytes, and indicate the condition of the overflow and 

carry bits. 

a) 10111011 + 00000011 

d) 110110111 - 01011111 

b) 00111011 + 00000011 

e) 01101011 + 01111011 

c) 11011011 + 11011111 

f) 10110110 - 11101110 

18. Consider the three BCD numbers listed below. 

1001 0110 0101 0001 

0010 0100 0011 1000 

0100 0011 0101 0001 

a) Convert these numbers to their decimal values. 

b) Convert the decimal values to binary. 

c) Calculate a checksum for all three binary numbers. 

d) What would the even parity bits be for the binary words found in b). 

19. Is the 2nd bit set in the hexadecimal value F49? 

20. Explain where grey code occurs when creating Karnaugh maps. 

21. Convert the decimal number 1000 to a binary number, and then to hexadecimal. 


1. base 2, 4, 8, and 16 numbers translate more naturally to the numbers stored in the computer. 

2. no, it is four nibbles 

3. Both of these are coding schemes designed to increase immunity to noise. A parity bit can be 

used to check for a changed bit in a byte. Gray code can be used to check for a value error in a 

stream of continuous values. 

4. a) 1101 0100 0011 0001, b) 3117 

5. 6279 

6. 0111 0101 

7. 4B 

8. 113 



9. 1100001 odd parity bit = 1 

10. 

binary 

BCD 

decimal 

hex 

octal 

101101 11011011 10000000001 0010110110101 

0100 0101 0010 0001 1001 0001 0000 0010 0101 0001 0100 0110 0001 

45 219 1025 1461 

2D DB 401 5B5 

55 333 2001 2665 

11. 

decimal 

BCD 

binary 

hex 

octal 

1 17 20456 -10 

0001 0001 0111 0010 0000 0100 0101 0110 -0001 0000 

1 10001 0100 1111 1110 1000 1111 1111 1111 0110 

1 11 4FE8 FFF6 

1 21 47750 177766 

12. 

hex 

BCD 

binary 

decimal 

octal 

1 17 ABC -A 

0001 0010 0011 0010 0111 0100 1000 -0001 0000 

1 10111 0000 1010 1011 1100 1111 1111 1111 0110 

1 23 2748 -10 

1 27 5274 177766 

13. 

BCD 

binary 

decimal 

hex 

octal 

1001 1001 0011 0011 0110 0001 0000 0101 0111 0100 

1001 101 1101 1 0110 1001 10 0011 1110 

9 93 361 0574 

9 5D 169 23E 

11 135 551 1076 



14. 

octal 

binary 

decimal 

hex 

BCD 

7 17 777 32634 

111 1111 1 1111 1111 0011 0101 1001 1100 

7 15 511 13724 

7 F 1FF 359C 

0111 0001 0101 0101 0001 0001 0001 0011 0111 0010 0100 

15. a) 3532 = 0011 0101 0011 0010 = DCC, b0 the number is not a valid BCD 

16. 

a) 0001 0110 1110 1000 

b) BBD 

c) 1122 

d) 0000 0001 1000 1000 

e) 999 

f) 654 

g) 1111 1110 0111 1000 

h) -999 

i) -654 

j) 0000 0001 0111 1010 

k) 0000 0000 0011 1110 

l) 0001 1101 1111 0001 

m) 122655 

n) 6 

o) 0000 0000 0001 0001 

p) 9 

17. 

a) 10111011 + 00000011=1011 1110 

b) 00111011 + 00000011=0011 1110 

c) 11011011 + 11011111=1011 1010+C+O 

d) 110110111 - 01011111=0101 1000+C+O 

e) 01101011 + 01111011=1110 0110 

f) 10110110 - 11101110=1100 1000 

18. a) 9651, 2438, 4351, b) 0010 0101 1011 0011, 0000 1001 1000 0110, 0001 0000 1111 1111, c) 

16440, d) 1, 0, 0 

19. The binary value is 1111 0100 1001, so the second bit is 0 

20. when selecting the sequence of bit changes for Karnaugh maps, only one bit is changed at a 

time. This is the same method used for grey code number sequences. By using the code the bits 

in the map are naturally grouped. 



21. 

1000 10 = 1111101000 2 = 3e8 16 


1. Why are hexadecimal numbers useful when working with PLCs? 


plc memory - 14.1 

14. PLC MEMORY 

Topics: 

• ControlLogix memory types; program and data 

• Data types; output, input, status, bit, timer, counter, integer, floating point, etc. 

• Memory addresses; words, bits, data files, expressions, literal values and indirect. 

Objectives: 

• To know the basic memory types available 

• To be able to use addresses for locations in memory 


Advanced ladder logic functions such as timers and counters allow controllers to 

perform calculations, make decisions and do other complex tasks. They are more complex 

than basic input contacts and output coils and they rely upon data stored in the memory of 

the PLC. The memory of the PLC is organized to hold different types of programs and 

data. This chapter will discuss these memory types. Functions that use them will be discussed 

in following chapters. 

14.2 PROGRAM VS VARIABLE MEMORY 

The memory in a PLC is divided into program and variable memory. The program 

memory contains the instructions to be executed and cannot be changed while the PLC is 

running. (Note: some PLCs allow on-line editing to make minor program changes while a 

program is running.) The variable memory is changed while the PLC is running. In ControlLogix 

the memory is defined using variable names (also called tags and aliases). 



ASIDE: In older Allen Bradley PLCs the memory was often organized as files. There 

are two fundamental types of memory used in Allen-Bradley PLCs - Program and 

Data memory. Memory is organized into blocks of up to 1000 elements in an array 

called a file. The Program file holds programs, such as ladder logic. There are eight 

Data files defined by default, but additional data files can be added if they are needed. 

Program Files 

Data Files 

2 

3 

999 

O0 

I1 

S2 

B3 

T4 

C5 

R6 

N7 

Outputs 

Inputs 

Status 

Bits 

Timers 

Counters 

Control 

Integer 

These are a collection of up to 1000 

slots to store up to 1000 programs. 

The main program will 

be stored in program file 2. SFC 

programs must be in file 1, and 

file 0 is used for program and 

password information. All other 

program files from 3 to 999 can 

be used for subroutines. 

F8 

Float 

This is where the variable data is 

stored that the PLC programs 

operate on. This is quite complicated, 

so a detailed explanation 

follows. 



14.3 PROGRAMS 

The PLC has a list of ’Main Tasks’ that contain the main program(s) run each scan 

of the PLC. Additional programs can be created that are called as subroutines. Valid program 

types include Ladder Logic, Structured Text, Sequential Function Charts, and Function 

Block Diagrams. 

Program files can also be created for ’Power-Up Handling’ and ’Controller 

Faults’. The power-up programs are used to initialize the controller on the first scan. In 

previous chapters this was done in the main program using the ’S:FS’ bit. Fault programs 

are used to respond to specific failures or issues that may lead to failure of the control system. 

Normally these programs are used to recover from minor failures, or shut down a system 

safely. 

14.4 VARIABLES (TAGS) 

Allen Bradley uses the terminology ’tags’ to describe variables, status, and input/ 

output (I/O) values for the controller. ’Controller Tags’ include status values and I/O definitions. 

These are scoped, meaning that they can be global and used by all programs on the 

PLC. These can also be local, limiting their use to a program that owns it. 

Variable tags can be an alias for another tags, or be given a data type. Some of the 

common tag types are listed below. 

Type 

BOOL 

CONTROL 

COUNTER 

DINT 

INT 

MESSAGE 

PID 

REAL 

SINT 

STRING 

TIMER 

Description 

Holds TRUE or FALSE values 

General purpose memory for complex instructions 

Counter memory 

32 bit 2s compliment integer -2,147,483,648 to 2,147,483,647 

16 bit 2s compliment integer -32,768 to 32,767 

Used for communication with remote devices 

Used for PID control functions 

32 bit floating point value +/-1.1754944e-38 to +/-3.4028237e38 

8 bit 2s compliment integer -128 to 127 

An ASCII string 

Timer memory 

Figure 14.1 

Selected ControlLogic Data Types 



For older Allen Bradley PLCs data files are used for storing different information 

types, as shown below. These locations are numbered from 0 to 999. 

The letter in front of the number indicates the data type. For example, F8: is 

read as floating point numbers in data file 8. Numbers are not given for O: 

and I:, but they are implied to be O0: and I1:. The number that follows the : 

is the location number. Each file may contain from 0 to 999 locations that 

may store values. For the input I: and output O: files the locations are converted 

to physical locations on the PLC using rack and slot numbers. The 

addresses that can be used will depend upon the hardware configuration. 

The status S2: file is more complex and is discussed later. The other memory 

locations are simply slots to store data in. For example, F8:35 would 

indicate the 36th value in the 8th data file which is floating point numbers. 

Rack 

I/O slot number in rack 

Interface to 

outside world 

Fixed types of 

Data files 

O:000 

I:nnn 

S2:nnn 

B3:nnn 

T4:nnn 

C5:nnn 

R6:nnn 

N7:nnn 

F8:nnn 

outputs 

inputs 

processor status 

bits in words 

timers 

counters 

control words 

integer numbers 

floating point numbers 

Other files 9-999 can be created and used. 

The user defined data files can have different 

data types. 

Data values do not always need to be stored in memory, they can be define literally. 

Figure 14.2 shows an example of two different data values. The first is an integer, the 

second is a real number. Hexadecimal numbers can be indicated by following the number 

with H, a leading zero is also needed when the first digit is A, B, C, D, E or F. A binary 

number is indicated by adding a B to the end of the number. 



8 - an integer 

8.5 - a floating point number 

08FH - a hexadecimal value 8F 

01101101B - a binary number 01101101 

Figure 14.2 

Literal Data Values 

Data types can be created in variable size 1D, 2D, or 3D arrays. 

Sometimes we will want to refer to an array of values, as shown in Figure 14.3. 

This data type is indicated by beginning the number with a pound or hash sign ’#’. The 

first example describes an array of floating point numbers staring in file 8 at location 5. 

The second example is for an array of integers in file 7 starting at location 0. The length of 

the array is determined elsewhere. 

test[1, 4] - returns the value in the 2nd row and 5th column of array test 

Figure 14.3 

Arrays 

Expressions allow addresses and functions to be typed in and interpreted when the 

program is run. The example in Figure 14.4 will get a floating point number from ’test’, 

perform a sine transformation, and then add 1.3. The text string is not interpreted until the 

PLC is running, and if there is an error, it may not occur until the program is running - so 

use this function cautiously. 

expression - a text string that describes a complex operation. 

“sin(test) + 1.3” - a simple calculation 

Figure 14.4 

Expressions 

These data types and addressing modes will be discussed more as applicable functions 

are presented later in this chapter and book. 



Figure 14.5 shows a simple example ladder logic with functions. The basic operation 

is such that while input A is true the functions will be performed. The first statement 

will move (MOV) the literal value of 130 into integer memory X. The next move function 

will copy the value from X to Y. The third statement will add integers value in X and Y and 

store the results in Z. 

A 

MOV 

source 130 

destination X 

MOV 

source X 

destination Y 

ADD 

sourceA X 

sourceB Y 

destination Z 

Figure 14.5 

An Example of Ladder Logic Functions 

14.4.1 Timer and Counter Memory 

Previous chapters have discussed the basic operation of timers and counters. The 

ability to address their memory directly allows some powerful tools. The bits and words 

for timers are; 

EN - timer enabled bit 

TT - timer timing bit 

DN - timer done bit 

FS - timer first scan 

LS - timer last scan 

OV - timer value overflowed 

ER - timer error 

PRE - preset word 

ACC - accumulated time word 

Counter have the following bits and words. 



CU - count up bit 

CD - count down bit 

DN - counter done bit 

OV - overflow bit 

UN - underflow bit 

PRE - preset word 

ACC - accumulated count word 

As discussed before we can access timer and counter bits and words. Examples of 

these are shown in Figure 14.6. The bit values can only be read, and should not be 

changed. The presets and accumulators can be read and overwritten. 

Words 

timer.PRE - the preset value for timer T4:0 

timer.ACC - the accumulated value for timer T4:0 

counter.PRE - the preset value for counter C5:0 

counter.ACC - the accumulated value for counter C5:0 

Bits 

timer.EN - indicates when the input to timer T4:0 is true 

timer.TT - indicates when the timer T4:0 is counting 

timer.DN - indicates when timer T4:0 has reached the maximum 

counter.CU - indicates when the count up instruction is true for C5:0 

counter.CD - indicates when the count down instruction is true for C5:0 

counter.DN - indicates when the counter C5:0 has reached the preset 

counter.OV - indicates when the counter C5:0 passes the maximum value (2,147,483,647) 

counter.UN - indicates when the counter C5:0 passes the minimum value (-2,147,483,648) 

Figure 14.6 

Examples of Timer and Counter Addresses 

Consider the simple ladder logic example in Figure 14.7. It shows the use of a 

timer timing TT bit to seal on the timer when a door input has gone true. While the timer is 

counting, the bit will stay true and keep the timer counting. When it reaches the 10 second 

delay the TT bit will turn off. The next line of ladder logic will turn on a light while the 

timer is counting for the first 10 seconds. 



DOOR 

example.TT 

TON 

example 

delay 10s 

example.TT 

LIGHT 

Figure 14.7 

Door Light Example 

14.4.2 PLC Status Bits 

Status memory allows a program to check the PLC operation, and also make some 

changes. A selected list of status bits is shown in Figure 14.8 for Allen-Bradley Control- 

Logix PLCs. More complete lists are available in the manuals. The first six bits are commonly 

used and are given simple designations for use with simple ladder logic. More 

advanced instructions require the use of Get System Value (GSV) and Set System Value 

(SSV) functions. These functions can get/set different values depending upon the type of 

data object is being used. In the sample list given one data object is the ’WALLCLOCK- 

TIME’. One of the attributes of the class is the DateTime that contains the current time. It 

is also possible to use the ’PROGRAM’ object instance ’MainProgram’ attribute 

’LastScanTime’ to determine how long the program took to run in the previous scan. 



Immediately accessible status values 

S:FS - First Scan Flag 

S:N - The last calculation resulted in a negative value 

S:Z - The last calculation resulted in a zero 

S:V - The last calculation resulted in an overflow 

S:C - The last calculation resulted in a carry 

S:MINOR - A minor (non-critical/recoverable) error has occurred 

Examples of SOME values available using the GSV and SSV functions 

CONTROLLERDEVICE - information about the PLC 

PROGRAM - information about the program running 

LastScanTime 

MaxScanTime 

TASK 

EnableTimeout 

LastScanTime 

MaxScanTime 

Priority 

StartTime 

Watchdog 

WALLCLOCKTIME - the current time 

DateTime 

DINT[0] - year 

DINT[1] - month 1=january 

DINT[2] - day 1 to 31 

DINT[3] - hour 0 to 24 

DINT[4] - minute 0 to 59 

DINT[5] - second 0 to 59 

DINT[6] - microseconds 0 to 999,999 

Figure 14.8 

Status Bits and Words for ControlLogix 

An example of getting and setting system status values is shown in Figure 14.9. 

The first line of ladder logic will get the current time from the class ’WALLCLOCK- 

TIME’. In this case the class does not have an instance so it is blank. The attribute being 

recalled is the DateTime that will be written to the DINT array time[0..6]. For example 

’time[3]’ should give the current hour. In the second line the Watchdog time for the Main- 

Program is set to 200 ms. If the program MainProgram takes longer than 200ms to execute 



a fault will be generated. 

GSV 

Class Name: WALLCLOCKTIME 

Instance Name: 

Attribute Name: DateTime 

Dest: time[0] 

SSV 

Class Name: TASK 

Instance Name: MainProgram 

Attribute Name: Watchdog 

Source: 200 

Figure 14.9 

Reading and Setting Status bits with GSV and SSV 

As always, additional classes and attributes for the status values can be found in 

the manuals for the processors and instructions being used. 



A selected list of status bits is shown below for Allen-Bradley Micrologic and PLC- 

5 PLCs. More complete lists are available in the manuals. For example the first 

four bits S2:0/x indicate the results of calculations, including carry, overflow, zero 

and negative/sign. The S2:1/15 will be true once when the PLC is turned on - this 

is the first scan bit. The time for the last scan will be stored in S2:8. The date and 

clock can be stored and read from locations S2:18 to S2:23. 

S2:0/0 carry in math operation 

S2:0/1 overflow in math operation 

S2:0/2 zero in math operation 

S2:0/3 sign in math operation 

S2:1/15 first scan of program file 

S2:8 the scan time (ms) 

S2:18 year 

S2:19 month 

S2:20 day 

S2:21 hour 

S2:22 minute 

S2:23 second 

S2:28 watchdog setpoint 

S2:29 fault routine file number 

S2:30 STI (selectable timed interrupt) setpoint 

S2:31 STI file number 

S2:46-S2:54,S2:55-S2:56 PII (Programmable Input Interrupt) settings 

S2:55 STI last scan time (ms) 

S2:77 communication scan time (ms) 

14.4.3 User Function Control Memory 

Simple ladder logic functions can complete operations in a single scan of ladder 

logic. Other functions such as timers and counters will require multiple ladder logic scans 

to finish. While timers and counters have their own memory for control, a generic type of 

control memory is defined for other function. This memory contains the bits and words in 

Figure 14.10. Any given function will only use some of the values. The meaning of particular 

bits and words will be described later when discussing specific functions. 



EN - enable bit 

EU - enable unload 

DN - done bit 

EM - empty bit 

ER - error bit 

UL - unload bit 

IN - inhibit bit 

FD - found bit 

LEN - length word 

POS - position word 

Figure 14.10 

Bits and Words for Control Memory 

14.5 SUMMARY 

• Program are given unique names and can be for power-up, regular scans, and 

faults. 

• Tags and aliases are used for naming variables and I/O. 

• Files are like arrays and are indicated with []. 

• Expressions allow equations to be typed in. 

• Literal values for binary and hexadecimal values are followed by B and H. 


1. How are timer and counter memory similar? 

2. What types of memory cannot be changed? 

3. Develop Ladder Logic for a car door/seat belt safety system. When the car door is open, or the 

seatbelt is not done up, a buzzer will sound for 5 seconds if the key has been switched on. A 

cabin light will be switched on when the door is open and stay on for 10 seconds after it is 

closed, unless a key has started the ignition power. 

4. Write ladder logic for the following problem description. When button A is pressed a value of 

1001 will be stored in X. When button B is pressed a value of -345 will be stored in Y, when it 

is not pressed a value of 99 will be stored in Y. When button C is pressed X and Y will be added, 

and the result will be stored in Z. 

5. Using the status memory locations, write a program that will flash a light for the first 15 sec- 



onds after it has been turned on. The light should flash once a second. 

6. How many words are required for timer and counter memory? 


1. both are similar. The timer and counter memories both use double words for the accumulator 

and presets, and they use bits to track the status of the functions. These bits are somewhat different, 

but parallel in function. 

2. Inputs cannot be changed by the program, and some of the status bits/words cannot be changed 

by the user. 

3. 

door open 

seat belt connected 

Inputs 

door open 

seat belt connected 

key on 

key on 

Outputs 

buzzer 

light 

TON 

Timer t_remind 

Delay 5s 

t_remind.TT 

door open 

buzzer 

TOF 

Timer t_light 

Delay 10s 

t_light.DN 

key on 

light 



4. 

A 

B 

B 

C 

MOV 

Source 1001 

Dest X 

MOV 

Source -345 

Dest Y 

MOV 

Source 99 

Dest Y 

ADD 

Source A X 

Source B Y 

Dest Z 



10. 

first scan 

RTF 

t_initial 

delay 15 s 

t_initial.DN 

RTO 

t_off 

delay 0.5 s 

t_off.DN 

RTO 

t_on 

delay 0.5 s 

t_on.DN 

t_off 

RES 

t_on.DN 

t_on 

RES 

t_initial.DN 

t_off.DN 

O/1 

11. three long words (3 * 32 bits) are used for a timer or a counter. 


1. Could timer ‘T’ and counter ‘C’ memory types be replaced with control ‘R’ memory types? 

Explain your answer. 


plc basic functions - 15.1 

15. LADDER LOGIC FUNCTIONS 

Topics: 

• Functions for data handling, mathematics, conversions, array operations, statistics, 

comparison and Boolean operations. 


Objectives: 

• To understand basic functions that allow calculations and comparisons 

• To understand array functions using memory files 


Ladder logic input contacts and output coils allow simple logical decisions. Functions 

extend basic ladder logic to allow other types of control. For example, the addition of 

timers and counters allowed event based control. A longer list of functions is shown in 

Figure 15.1. Combinatorial Logic and Event functions have already been covered. This 

chapter will discuss Data Handling and Numerical Logic. The next chapter will cover 

Lists and Program Control and some of the Input and Output functions. Remaining functions 

will be discussed in later chapters. 



Combinatorial Logic 

- relay contacts and coils 

Events 

- timer instructions 

- counter instructions 

Data Handling 

- moves 

- mathematics 

- conversions 

Numerical Logic 

- boolean operations 

- comparisons 

Lists 

- shift registers/stacks 

- sequencers 

Program Control 

- branching/looping 

- immediate inputs/outputs 

- fault/interrupt detection 

Input and Output 

- PID 

- communications 

- high speed counters 

- ASCII string functions 

Figure 15.1 

Basic PLC Function Categories 

Most of the functions will use PLC memory locations to get values, store values 

and track function status. Most function will normally become active when the input is 

true. But, some functions, such as TOF timers, can remain active when the input is off. 

Other functions will only operate when the input goes from false to true, this is known as 

positive edge triggered. Consider a counter that only counts when the input goes from 

false to true, the length of time the input is true does not change the function behavior. A 

negative edge triggered function would be triggered when the input goes from true to 

false. Most functions are not edge triggered: unless stated assume functions are not edge 

triggered. 



NOTE: I do not draw functions exactly as they appear in manuals and programming software. 

This helps save space and makes the instructions somewhat easier to read. All of 

the necessary information is given. 

15.2 DATA HANDLING 

15.2.1 Move Functions 

There are two basic types of move functions; 

MOV(value,destination) - moves a value to a memory location 

MVM(value,mask,destination) - moves a value to a memory location, but with a 

mask to select specific bits. 

The simple MOV will take a value from one location in memory and place it in 

another memory location. Examples of the basic MOV are given in Figure 15.2. When A 

is true the MOV function moves a floating point number from the source to the destination 

address. The data in the source address is left unchanged. When B is true the floating point 

number in the source will be converted to an integer and stored in the destination address 

in integer memory. The floating point number will be rounded up or down to the nearest 

integer. When C is true the integer value of 123 will be placed in the integer file test_int. 



A 

MOV 

Source test_real_1 

Destination test_real_2 

B 

MOV 

Source test_real_1 

Destination test_int 

C 

MOV 

Source 123 

Destination test_int 

NOTE: when a function changes a value, except for inputs and outputs, the value is 

changed immediately. Consider Figure 15.2, if A, B and C are all true, then the 

value in test_real_2 will change before the next instruction starts. This is different 

than the input and output scans that only happen before and after the logic scan. 

Figure 15.2 

Examples of the MOV Function 

A more complex example of move functions is given in Figure 15.3. When A 

becomes true the first move statement will move the value of 130 into int_0. And, the second 

move statement will move the value of -9385 from int_1 to int_2. (Note: The number 

is shown as negative because we are using 2s compliment.) For the simple MOVs the 

binary values are not needed, but for the MVM statement the binary values are essential. 

The statement moves the binary bits from int_3 to int_5, but only those bits that are also 

on in the mask int_4, other bits in the destination will be left untouched. Notice that the 

first bit int_5.0 is true in the destination address before and after, but it is not true in the 

mask. The MVM function is very useful for applications where individual binary bits are 

to be manipulated, but they are less useful when dealing with actual number values. 



A 

MOV 

source 130 

dest int_0 

MOV 

source int_1 

dest int_2 

MVM 

source int_3 

mask int_4 

dest int_5 

MVM 

source int_3 

mask int_4 

dest int_6 

binary 

before 

decimal 

binary 

after 

decimal 

int_0 

int_1 

int_2 

int_3 

int_4 

int_5 

int_6 

0000000000000000 

1101101101010111 

1000000000000000 

0101100010111011 

0010101010101010 

0000000000000001 

1101110111111111 

0 

-9385 

-32768 

22715 

10922 

1 

becomes 

0000000010000010 

1101101101010111 

1101101101010111 

0101100010111011 

0010101010101010 

0000100010101011 

1101110111111111 

130 

-9385 

-9385 

22715 

10922 

2219 

NOTE: the concept of a mask is very useful, and it will be used in other functions. 

Masks allow instructions to change a couple of bits in a binary number without having 

to change the entire number. You might want to do this when you are using bits in 

a number to represent states, modes, status, etc. 

Figure 15.3 

Example of the MOV and MVM Statement with Binary Values 

15.2.2 Mathematical Functions 

Mathematical functions will retrieve one or more values, perform an operation and 



store the result in memory. Figure 15.4 shows an ADD function that will retrieve values 

from int_1 and real_1, convert them both to the type of the destination address, add the 

floating point numbers, and store the result in real_2. The function has two sources 

labelled source A and source B. In the case of ADD functions the sequence can change, 

but this is not true for other operations such as subtraction and division. A list of other 

simple arithmetic function follows. Some of the functions, such as the negative function 

are unary, so there is only one source. 

A 

ADD 

source A int_1 

source B real_1 

destination real_2 

ADD(value,value,destination) - add two values 

SUB(value,value,destination) - subtract 

MUL(value,value,destination) - multiply 

DIV(value,value,destination) - divide 

NEG(value,destination) - reverse sign from positive/negative 

CLR(value) - clear the memory location 

NOTE: To save space the function types are shown in the shortened notation above. 

For example the function ADD(value, value, destination) requires two source values 

and will store it in a destination. It will use this notation in a few places to 

reduce the bulk of the function descriptions. 

Figure 15.4 

Arithmetic Functions 

An application of the arithmetic function is shown in Figure 15.5. Most of the 

operations provide the results we would expect. The second ADD function retrieves a 

value from int_3, adds 1 and overwrites the source - this is normally known as an increment 

operation. The first DIV statement divides the integer 25 by 10, the result is rounded 

to the nearest integer, in this case 3, and the result is stored in int_6. The NEG instruction 

takes the new value of -10, not the original value of 0, from int_4 inverts the sign and 

stores it in int_7. 



ADD 


source B int_1 

dest. int_2 

ADD 

source A 1 


dest. int_3 

SUB 



dest. int_4 

MULT 



dest. int_5 

DIV 



dest. int_6 

NEG 


dest. int_7 

CLR 

dest. int_8 

DIV 

source A flt_1 

source B flt_0 

dest. flt_2 

addr. before after 

int_0 

int_1 

int_2 

int_3 

int_4 

int_5 

int_6 

int_7 

int_8 

flt_0 

flt_1 

flt_2 

flt_3 

10 

25 

0 

0 

0 

0 

0 

0 

100 

10.0 

25.0 

0 

0 

10 

25 

35 

1 

-10 

250 

3 

10 

0 

10.0 

25.0 

2.5 

2.5 

Note: recall, integer 

values are limited 

to ranges between - 

32768 and 32767, 

and there are no 

fractions. 

DIV 



dest. flt_3 

Figure 15.5 

Arithmetic Function Example 

A list of more advanced functions are given in Figure 15.6. This list includes basic 

trigonometry functions, exponents, logarithms and a square root function. The last function 

CPT will accept an expression and perform a complex calculation. 



ACS(value,destination) - inverse cosine 

COS(value,destination) - cosine 

ASN(value,destination) - inverse sine 

SIN(value,destination) - sine 

ATN(value,destination) - inverse tangent 

TAN(value,destination) - tangent 

XPY(value,value,destination) - X to the power of Y 

LN(value,destination) - natural log 

LOG(value,destination) - base 10 log 

SQR(value,destination) - square root 

CPT(destination,expression) - does a calculation 

Figure 15.6 

Advanced Mathematical Functions 

Figure 15.7 shows an example where an equation has been converted to ladder 

logic. The first step in the conversion is to convert the variables in the equation to unused 

memory locations in the PLC. The equation can then be converted using the most nested 

calculations in the equation, such as the LN function. In this case the results of the LN 

function are stored in another memory location, to be recalled later. The other operations 

are implemented in a similar manner. (Note: This equation could have been implemented 

in other forms, using fewer memory locations.) 



given 

A 

= 

lnB+ 

e C acos( D) 

LN 

Source B 

Dest. temp_1 

XPY 

SourceA 2.718 

SourceB C 

Dest temp_2 

ACS 

SourceA D 

Dest. temp_3 

MUL 

SourceA temp_2 

SourceB temp_3 

Dest temp_4 

ADD 


SourceB temp_4 

Dest temp_5 

SQR 


Dest. A 

Figure 15.7 

An Equation in Ladder Logic 

The same equation in Figure 15.7 could have been implemented with a CPT function 

as shown in Figure 15.8. The equation uses the same memory locations chosen in Figure 

15.7. The expression is typed directly into the PLC programming software. 



go 

CPT 

Dest. A 

Expression 

SQR(LN(B)+XPY(2.718,C)*ACS(D)) 

Figure 15.8 

Calculations with a Compute Function 

Math functions can result in status flags such as overflow, carry, etc. care must be 

taken to avoid problems such as overflows. These problems are less common when using 

floating point numbers. Integers are more prone to these problems because they are limited 

to the range. 

15.2.3 Conversions 

Ladder logic conversion functions are listed in Figure 15.9. The example function 

will retrieve a BCD number from the D type (BCD) memory and convert it to a floating 

point number that will be stored in F8:2. The other function will convert from 2s compliment 

binary to BCD, and between radians and degrees. 

A 

FRD 

Source A D10:5 

Dest. F8:2 

TOD(value,destination) - convert from BCD to 2s compliment 

FRD(value,destination) - convert from 2s compliment to BCD 

DEG(value,destination) - convert from radians to degrees 

RAD(value,destination) - convert from degrees to radians 

Figure 15.9 

Conversion Functions 

Examples of the conversion functions are given in Figure 15.10. The functions 

load in a source value, do the conversion, and store the results. The TOD conversion to 

BCD could result in an overflow error. 



FRD 

Source bcd_1 

Dest. int_0 

TOD 

Source int_1 

Dest. bcd_0 

DEG 

Source real_0 

Dest. real_2 

Addr. 

Before 

after 

RAD 

Source real_1 

Dest. real_3 

int_0 

int_1 

real_0 

real_1 

real_2 

real_3 

bcd_0 

bcd_1 

0 

548 

3.141 

45 

0 

0 

0000 0000 0000 0000 

0001 0111 1001 0011 

1793 

548 

3.141 

45 

180 

0.785 

0000 0101 0100 1000 

0001 0111 1001 0011 

these are shown in 

binary BCD form 

Figure 15.10 

Conversion Example 

15.2.4 Array Data Functions 

Arrays allow us to store multiple data values. In a PLC this will be a sequential 

series of numbers in integer, floating point, or other memory. For example, assume we are 

measuring and storing the weight of a bag of chips in floating point memory starting at 

weight[0]. We could read a weight value every 10 minutes, and once every hour find the 

average of the six weights. This section will focus on techniques that manipulate groups of 

data organized in arrays, also called blocks in the manuals. 



15.2.4.1 - Statistics 

Functions are available that allow statistical calculations. These functions are 

listed in Figure 15.11. When A becomes true the average (AVE) conversion will start at 

memory location weight[0] and average a total of 4 values. The control word 

weight_control is used to keep track of the progress of the operation, and to determine 

when the operation is complete. This operation, and the others, are edge triggered. The 

operation may require multiple scans to be completed. When the operation is done the 

average will be stored in weight_avg and the weight_control.DN bit will be turned on. 

A 

AVE 

File weight[0] 

Dest weight_avg 

Control weight_control 

length 4 

position 0 

AVE(start value,destination,control,length) - average of values 

STD(start value,destination,control,length) - standard deviation of values 

SRT(start value,control,length) - sort a list of values 

Figure 15.11 

Statistic Functions 

Examples of the statistical functions are given in Figure 15.12 for an array of data 

that starts at weight[0] and is 4 values long. When done the average will be stored in 

weight_avg, and the standard deviation will be stored in weight_std. The set of values will 

also be sorted in ascending order from weight[0] to weight[3]. Each of the function should 

have their own control memory to prevent overlap. It is not a good idea to activate the sort 

and the other calculations at the same time, as the sort may move values during the calculation, 

resulting in incorrect calculations. 



A 

AVE 


Dest weight_avg 

Control c_1 

length 4 

position 0 

B 

STD 


Dest weight_std 


length 4 

position 0 

Addr. 

C 

before 

after A 

after B 

after C 

SRT 



length 4 

position 0 

weight[0] 

weight[1] 

weight[2] 

weight[3] 

weight_avg 

weight_std 

3 

1 

2 

4 

0 

0 

3 

1 

2 

4 

2.5 

0 

3 

1 

2 

4 

2.5 

1.29 

1 

2 

3 

4 

2.5 

1.29 

Figure 15.12 

Statistical Calculations 

ASIDE: These function will allow a real-time calculation of SPC data for control 

limits, etc. The only PLC function missing is a random function that 

would allow random sample times. 

15.2.4.2 - Block Operations 

A basic block function is shown in Figure 15.13. This COP (copy) function will 



copy an array of 10 values starting at n[50] to n[40]. The FAL function will perform mathematical 

operations using an expression string, and the FSC function will allow two arrays 

to be compared using an expression. The FLL function will fill a block of memory with a 

single value. 

A 

COP 

Source n[50] 

Dest n[40] 

Length 10 

COP(start value,destination,length) - copies a block of values 

FAL(control,length,mode,destination,expression) - will perform basic math 

operations to multiple values. 

FSC(control,length,mode,expression) - will do a comparison to multiple values 

FLL(value,destination,length) - copies a single value to a block of memory 

Figure 15.13 

Block Operation Functions 

Figure 15.14 shows an example of the FAL function with different addressing 

modes. The first FAL function will do the following calculations n[5]=n[0]+5, 

n[6]=n[1]+5, n[7]=n[2]+5, n[7]=n[3]+5, n[9]=n[4]+5. The second FAL statement will 

be n[5]=n[0]+5, n[6]=n[0]+5, n[7]=n[0]+5, n[7]=n[0]+5, n[9]=n[0]+5. With a mode 

of 2 the instruction will do two of the calculations when there is a positive edge from B 

(i.e., a transition from false to true). The result of the last FAL statement will be 

n[5]=n[0]+5, n[5]=n[1]+5, n[5]=n[2]+5, n[5]=n[3]+5, n[5]=n[4]+5. The last operation 

would seem to be useless, but notice that the mode is incremental. This mode will do 

one calculation for each positive transition of C. The all mode will perform all five calculations 

in a single scan whenever there is a positive edge on the input. It is also possible to 

put in a number that will indicate the number of calculations per scan. The calculation 

time can be long for large arrays and trying to do all of the calculations in one scan may 

lead to a watchdog time-out fault. 



A 

FAL 


length 5 

position 0 

Mode all 

Destination n[c_0.POS + 5] 

Expression n[c_0.POS] + 5 

array to array 

B 

FAL 

Control R6:1 

length 5 

position 0 

Mode 2 

Destination n[c_0.POS + 5] 

Expression n[0] + 5 

element to array 

array to element 

C 

FAL 


length 5 

position 0 

Mode incremental 

Destination n[5] 

Expression n[c_0.POS] + 5 

array to element 

Figure 15.14 

File Algebra Example 

15.3 LOGICAL FUNCTIONS 

15.3.1 Comparison of Values 

Comparison functions are shown in Figure 15.15. Previous function blocks were 

outputs, these replace input contacts. The example shows an EQU (equal) function that 

compares two floating point numbers. If the numbers are equal, the output bit light is true, 

otherwise it is false. Other types of equality functions are also listed. 



EQU 

A 

B 

light 

EQU(value,value) - equal 

NEQ(value,value) - not equal 

LES(value,value) - less than 

LEQ(value,value) - less than or equal 

GRT(value,value) - greater than 

GEQ(value,value) - greater than or equal 

CMP(expression) - compares two values for equality 

MEQ(value,mask,threshold) - compare for equality using a mask 

LIM(low limit,value,high limit) - check for a value between limits 

Figure 15.15 

Comparison Functions 

The example in Figure 15.16 shows the six basic comparison functions. To the 

right of the figure are examples of the comparison operations. 



EQU 

A int_3 

B int_2 

NEQ 

A int_3 

B int_2 

LES 

A int_3 

B int_2 

LEQ 

A int_3 

B int_2 

GRT 

A int_3 

B int_2 

GEQ 

A int_3 

B int_2 

O_0 

O_1 

O_2 

O_3 

O_4 

O_5 

int_3=5 

int_2=3 

int_3=3 

int_2=3 

int_3=1 

int_2=3 

O_0=0 

O_1=1 

O_2=0 

O_3=0 

O_4=1 

O_5=1 

O_0=1 

O_1=0 

O_2=0 

O_3=1 

O_4=0 

O_5=1 

O_0=0 

O_1=1 

O_2=1 

O_3=1 

O_4=0 

O_5=0 

Figure 15.16 

Comparison Function Examples 

The ladder logic in Figure 15.16 is recreated in Figure 15.17 with the CMP function 

that allows text expressions. 



CMP 

expression 

int_3 = int_2 

CMP 

expression 

int_3 int_2 

CMP 

expression 

int_3 < int_2 

CMP 

expression 

int_3 int_2 

CMP 

expression 

int_3 >= int_2 

O_0 

O_1 

O_2 

O_3 

O_4 

O_5 

Figure 15.17 

Equivalent Statements Using CMP Statements 

Expressions can also be used to do more complex comparisons, as shown in Figure 

15.18. The expression will determine if B is between A and C. 

CMP 

expression 

(B > A) & (B < C) 

X 

Figure 15.18 

A More Complex Comparison Expression 

The LIM and MEQ functions are shown in Figure 15.19. The first three functions 

will compare a test value to high and low limits. If the high limit is above the low limit and 

the test value is between or equal to one limit, then it will be true. If the low limit is above 



the high limit then the function is only true for test values outside the range. The masked 

equal will compare the bits of two numbers, but only those bits that are true in the mask. 

LIM 

low limit int_0 

test value int_1 

high limit int_2 

int_5.0 

LIM 




int_5.1 

LIM 




int_5.2 

MEQ 

source int_0 

mask int_1 

compare int_2 

int_5.3 

MEQ 

source int_0 

mask int_1 

compare int_4 

int_5.4 

Addr. 

before (decimal) 

before (binary) 

after (binary) 

int_0 

int_1 

int_2 

int_3 

int_4 

int_5 

1 

5 

11 

15 

0 

0000000000000001 

0000000000000101 

0000000000001011 

0000000000001111 

0000000000001000 

0000000000000000 

0000000000000001 

0000000000000101 

0000000000001011 

0000000000001111 

0000000000001000 

0000000000001101 

Figure 15.19 

Complex Comparison Functions 



Figure 15.20 shows a numberline that helps determine when the LIM function will 

be true. 

high limit 

low limit 

low limit 

high limit 

Figure 15.20 

A Number Line for the LIM Function 

File to file comparisons are also permitted using the FSC instruction shown in Figure 

15.21. The instruction uses the control word c_0. It will interpret the expression 10 

times, doing two comparisons per logic scan (the Mode is 2). The comparisons will be 

f[10]


15.3.2 Boolean Functions 

Figure 15.22 shows Boolean algebra functions. The function shown will obtain 

data words from bit memory, perform an and operation, and store the results in a new location 

in bit memory. These functions are all oriented to word level operations. The ability to 

perform Boolean operations allows logical operations on more than a single bit. 

A 

AND(value,value,destination) - Binary and function 

OR(value,value,destination) - Binary or function 

NOT(value,value,destination) - Binary not function 

XOR(value,value,destination) - Binary exclusive or function 

AND 

source int_A 

source int_B 

dest. int_X 

Figure 15.22 

Boolean Functions 

The use of the Boolean functions is shown in Figure 15.23. The first three functions 

require two arguments, while the last function only requires one. The AND function 

will only turn on bits in the result that are true in both of the source words. The OR function 

will turn on a bit in the result word if either of the source word bits is on. The XOR 

function will only turn on a bit in the result word if the bit is on in only one of the source 

words. The NOT function reverses all of the bits in the source word. 



after 

addr. 

n[0] 

n[1] 

n[2] 

n[3] 

n[4] 

n[5] 

data (binary) 

0011010111011011 

1010010011101010 

0010010011001010 

1011010111111011 

1001000100110001 

1100101000100100 

AND 

source A n[0] 

source B n[1] 

dest. n[2] 

OR 

source A n[0] 

source B n[1] 

dest. n[3] 

XOR 

source A n[0] 

source B n[1] 

dest. n[4] 

NOT 

source A n[0] 

dest. n[5] 

Figure 15.23 

Boolean Function Example 


15.4.1 Simple Calculation 

Problem: A switch will increment a counter on when engaged. This counter can be 

reset by a second switch. The value in the counter should be multiplied by 2, and then displayed 

as a BCD output using (O:0.0/0 - O:0.0/7) 



Solution: 

SW1 

CTU 

Counter cnt 

Preset 0 

MUL 

SourceA cnt.ACC 

SourceB 2 

Dest. dbl 

SW2 

MVM 

Source dbl 

Mask 00FFh 

Dest. output_word 

RES 

cnt 

Figure 15.24 

A Simple Calculation Example 

15.4.2 For-Next 

Problem: Design a for-next loop that is similar to ones found in traditional programming 

languages. When A is true the ladder logic should be active for 10 scans, and 

the scan number from 1 to 10 should be stored in n0. 

Solution: 

A 

GRT 

SourceA n0 

SourceB 10 

MOV 

Source 0 

Dest n0 

LEQ 

SourceA n0 

SourceB 10 

ADD 

SourceA n0 

SourceB 1 

Dest. n0 

Figure 15.25 

A Simple Comparison Example 



As designed the program differs from traditional loops because it will only complete 

one ’loop’ each time the logic is scanned. 

15.4.3 Series Calculation 

Problem: Create a ladder logic program that will start when input A is turned on 

and calculate the series below. The value of n will start at 1 and with each scan of the ladder 

logic n will increase until n=100. While the sequence is being incremented, any 

change in A will be ignored. 

x = 2( n – 1) 

Solution: 

go 

A 

A 

go 

LEQ 

Source A n 

Source B 100 

MOV 

Source A 1 

Dest. n 

go 

go 

CPT 

Dest. x 

Expression 

2 * (n - 1) 

go 

ADD 

Source A 1 

Source B n 

Dest. n 

Figure 15.26 

A Series Calculation Example 



15.4.4 Flashing Lights 

Problem: We are designing a movie theater marquee, and they want the traditional 

flashing lights. The lights have been connected to the outputs of the PLC from O[0] to 

O[17] - an INT. When the PLC is turned, every second light should be on. Every half second 

the lights should reverse. The result will be that in one second two lights side-by-side 

will be on half a second each. 

Solution: 

t_b.DN 

TON 

timer t_a 

Delay 0.5s 

t_a.DN 

TON 

timer t_b 

Delay 0.5s 

t_a.TT 

MOV 

Source pattern 

Dest O 

t_a.TT 

NOT 

Source pattern 

Dest O 

pattern = 0101 0101 0101 0101 

Figure 15.27 

A Flashing Light Example 

15.5 SUMMARY 

• Functions can get values from memory, do simple operations, and return the 

results to memory. 

• Scientific and statistics math functions are available. 

• Masked function allow operations that only change a few bits. 

• Expressions can be used to perform more complex operations. 

• Conversions are available for angles and BCD numbers. 

• Array oriented file commands allow multiple operations in one scan. 



• Values can be compared to make decisions. 

• Boolean functions allow bit level operations. 

• Function change value in data memory immediately. 


1. Do the calculation below with ladder logic, 

n_2 = -(5 - n_0 / n_1) 

2. Implement the following function, 

x = atan y⎛------------------------ 

y+ log( y) 

⎞ 

⎝ 

⎛ ⎝ y + 1 ⎠⎠ 

⎞ 

3. A switch will increment a counter on when engaged. This counter can be reset by a second 

switch. The value in the counter should be multiplied by 5, and then displayed as a binary output 

using output integer ’O_lights’. 

4. Create a ladder logic program that will start when input A is turned on and calculate the series 

below. The value of n will start at 0 and with each scan of the ladder logic n will increase by 2 

until n=20. While the sequence is being incremented, any change in A will be ignored. 

x = 2( log( n) 

– 1) 

5. The following program uses indirect addressing. Indicate what the new values in memory will 

be when button A is pushed after the first and second instructions. 

A 

ADD 

Source A 1 

Source B n[0] 

Dest. n[n[1]] 

A 

addr before after 1st 

n[0] 

n[1] 

n[2] 

1 

2 

3 

after 2nd 

ADD 

Source A n[n[0]] 

Source B n[n[1]] 

Dest. n[n[0]] 

6. A thumbwheel input card acquires a four digit BCD count. A sensor detects parts dropping 



down a chute. When the count matches the BCD value the chute is closed, and a light is turned 

on until a reset button is pushed. A start button must be pushed to start the part feeding. 

Develop the ladder logic for this controller. Use a structured design technique such as a state 

diagram. 

Inputs 

Outputs 

bcd_in - BCD input card 

part_detect 

start_button 

reset_button 

chute_open 

light 

7. Describe the difference between incremental, all and a number for file oriented instruction, 

such as FAL. 

8. What is the maximum number of elements that moved with a file instruction? What might happen 

if too many are transferred in one scan? 

9. Write a ladder logic program to do the following calculation. If the result is greater than 20.0, 

then the output ’solenoid’ will be turned on. 

A = D– 

Be 

–--- 

T 

C 

10. Write ladder logic to reset an RTO counter (timer) without using the RES instruction. 

11. Write a program that will use Boolean operations and comparison functions to determine if 

bits 9, 4 and 2 are set in the input word input_card. If they are set, turn on output bit match. 

12. Explain how the mask works in the following MVM function. Develop a Boolean equation. 

MVM 

Source S 

Mask M 

Dest D 




1. 

DIV 

Source A n_0 

Source B n_1 

Dest N7:2 

SUB 

Source A 5 

Source B n_2 

Dest N7:2 

NEG 

Source n_2 

Dest n_2 

2. 

LOG 

Source y 

Dest temp_1 

ADD 

Source A y 

Source B temp_1 

Dest temp_2 

ADD 

Source A y 

Source B 1 

Dest temp_3 

DIV 

Source A temp_2 


Dest temp_4 

MUL 

Source A y 


Dest temp_5 

ATN 

Source temp_5 

Dest x 



3. 

count 

reset 

CTU 

Counter cnt 

Preset 1234 

RES cnt 

MUL 

Source A 5 

Source B cnt.ACC 

Dest O_lights 

4. 

A 

A 

active 

active 

EQ 

Source A 20 

Source B n 

LEQ 

Source A n 

Source B 20 

MOV 

Source -2 

Dest n 

active 

active 

ADD 

Source A n 

Source B 2 

Dest n 

LOG 

Source n 

Dest x 

SUB 

Source A x 

Source B 1 

Dest x 

MUL 

Source A x 

Source B 2 

Dest x 



5. 

addr before after 1st after 2nd 

n[0] 1 1 1 

n[1] 

n[2] 

2 

3 

2 

2 

4 

2 

6. 

first scan 

S1 

waiting 

start 

S2 

parts 

counting 

(chute open) 

reset 

S3 

bin 

full 

(light on) 

count 

exceeded 



first scan 

L 

S1 

U 

S2 

S2 

S3 

S1 

start 

U 

MCR 

L 

S3 

chute 

light 

S2 

U 

S1 

FRD 

Source A bcd_in 

Dest. cnt.ACC 

MCR 



S2 

part detect 

C5:0/DN 

MCR 

CTD 

counter cnt 

preset 0 

L 

S3 

U 

S2 

MCR 

S3 

reset 

MCR 

L 

S1 

U 

S3 

MCR 

7. an incremental mode will do one calculation when the input to the function is a positive edge - 

goes from false to true. The all mode will attempt to complete the calculation in a single scan. 

If a number is used, the function will do that many calculations per scan while the input is true. 

8. The maximum number is 1000. If the instruction takes too long the instruction may be paused 

and continued the next scan, or it may lead to a PLC fault because the scan takes too long. 



9. 

NEG 

Source T 

Dest A 

DIV 

Source A 

Source C 

Dest A 

XPY 

Source A 2.718 

Source A 

Dest A 

MUL 

Source B 

Source A 

Dest A 

SUB 

Source D 

Source A 

Dest A 

GRT 

Source A 

Source 20.0 

solenoid 

10. 

reset 

MOV 

Source 0 

Dest timer.ACC 



11. 

AND 

Source A input_card 

Source B 0000 0010 0001 0100 (binary) 

Dest temp 

EQU 

Source A 0000 0010 0001 0100 (binary) 

Source B temp 

match 

12. 

The data in the source location will be moved bit by bit to the destination for every bit 

that is set in the mask. Every other bit in the destination will be retain the previous 

value. The source address is not changed. 

D = (S & M) + (D & M) 


1. Write a ladder logic program that will implement the function below, and if the result is greater 

than 100.5 then the output ’too_hot’ will be turned on. 

X = 6 + Ae B cos( C + 5) 

2. Use an FAL instruction to average the values in n[0] to n[20] and store them in ’n_avg’. 

3. Write some simple ladder logic to change the preset value of a counter. When the input ‘A’ is 

active the preset should be 13, otherwise it will be 9. 

4. The 16 input bits from ’input_card_A’ are to be read and XORed with the inputs from 

’input_card_B’. The result is to be written to the output card ’output_card’. If the binary pattern 

of the outputs is 1010 0101 0111 0110 then the output ’match_bell’ will be set. Write the 

ladder logic. 

5. A machine ejects parts into three chutes. Three optical sensors (A, B and C) are positioned in 

each of the slots to count the parts. The count should start when the reset (R) button is pushed. 

The count will stop, and an indicator light (L) turned on when the average number of parts 

counted as 100 or greater. 

6. Write ladder logic to calculate the average of the values from thickness[0] to thickness[99]. The 

operation should start after a momentary contact push button A is pushed. The result should be 



stored in ’thickness_avg’. If button B is pushed, all operations should be complete in a single 

scan. Otherwise, only ten values will be calculated each scan. (Note: this means that it will take 

10 scans to complete the calculation if A is pushed.) 

7. Write and simplify a Boolean equation that implements the masked move (MVM) instruction. 

The source is S, the mask is M and the destination is D. 

8. a) Write ladder logic to calculate and store the binary sequence in 32 bit integer (DINT) memory 

starting at n[0] up to n[200] so that n[0] = 1, n[1] = 2, n[2] = 4, n[3] = 8, n[4] = 16, etc. b) 

Will the program operate as expected? 


plc advanced functions - 16.1 

16. ADVANCED LADDER LOGIC FUNCTIONS 

Topics: 

• Shift registers, stacks and sequencers 

• Program control; branching, looping, subroutines, temporary ends and one shots 

• Interrupts; timed, fault and input driven 

• Immediate inputs and outputs 

• Block transfer 

• Conversion of State diagrams using program subroutines 


Objectives: 

• To understand shift registers, stacks and sequencers. 

• To understand program control statements. 

• To understand the use of interrupts. 

• To understand the operation of immediate input and output instructions. 

• To be prepared to use the block transfer instruction later. 

• Be able to apply the advanced function in ladder logic design. 


This chapter covers advanced functions, but this definition is somewhat arbitrary. 

The array functions in the last chapter could be classified as advanced functions. The functions 

in this section tend to do things that are not oriented to simple data values. The list 

functions will allow storage and recovery of bits and words. These functions are useful 

when implementing buffered and queued systems. The program control functions will do 

things that don’t follow the simple model of ladder logic execution - these functions recognize 

the program is executed left-to-right top-to-bottom. Finally, the input output functions 

will be discussed, and how they allow us to work around the normal input and output 

scans. 

16.2 LIST FUNCTIONS 

16.2.1 Shift Registers 

Shift registers are oriented to single data bits. A shift register can only hold so 

many bits, so when a new bit is put in, one must be removed. An example of a shift regis- 



ter is given in Figure 16.1. The shift register is the word ’example’, and it is 5 bits long. 

When A becomes true the bits all shift right to the least significant bit. When they shift a 

new bit is needed, and it is taken from new_bit. The bit that is shifted out, on the right 

hand side, is moved to the control word UL (unload) bit c.UL. This function will not complete 

in a single ladder logic scan, so the control word c is used. The function is edge triggered, 

so A would have to turn on 5 more times before the bit just loaded from new_bit 

would emerge to the unload bit. When A has a positive edge the 5 bits in example will be 

shifted in memory. In this case it is taking the value of bit example.0 and putting it in the 

control word bit c.UL. It then shifts the bits once to the right, example.0 = example.1 then 

example.1 = example.2 then example.2 = example.3 then example.3 = example.4. Then 

the input bit is put into the most significant bit example.4 = new_bit. The bits in the shift 

register would be shifted to the left with the BSR function. 

example 

31 

bits shift right 

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

LSB 

00 

new_bit 

5 

c.UL 

A 

BSR 

File example 

Control c 

Bit address new_bit 

Length 5 

BSL - shifts left from the LSB to the MSB. The LSB must be supplied 

BSR - similar to the BSL, except the bit is input to the MSB and shifted to the LSB 

Figure 16.1 

Shift Register Functions 

There are other types of shift registers not implemented in the ControlLogix processors. 

These are shown in Figure 16.2. The primary difference is that the arithmetic 

shifts will put a zero into the shift register, instead of allowing an arbitrary bit. The rotate 

functions shift bits around in an endless circle. These functions can also be implemented 

using the BSR and BSL instructions when needed. 



Arithmetic Shift Left (ASL) 

carry msb 

lsb 

0 0 0 0 0 0 0 0 0 0 

Arithmetic Shift Right (ASR) 

0 

carry 

0 0 0 0 0 0 0 0 0 

Rotate Left (ROL) 

Rotate Right (ROR) 

0 0 0 0 0 0 0 0 

carry 

0 

0 0 0 0 0 0 0 0 

carry 

0 

Figure 16.2 

Shift Register Variations 

16.2.2 Stacks 

Stacks store integer words in a two ended buffer. There are two basic types of 

stacks; first-on-first-out (FIFO) and last-in-first-out (LIFO). As words are pushed on the 

stack it gets larger, when words are pulled off it gets smaller. When you retrieve a word 

from a LIFO stack you get the word that is the entry end of the stack. But, when you get a 

word from a FIFO stack you get the word from the exit end of the stack (it has also been 

there the longest). A useful analogy is a pile of work on your desk. As new work arrives 

you drop it on the top of the stack. If your stack is LIFO, you pick your next job from the 

top of the pile. If your stack is FIFO, you pick your work from the bottom of the pile. 

Stacks are very helpful when dealing with practical situations such as buffers in production 

lines. If the buffer is only a delay then a FIFO stack will keep the data in order. If 

product is buffered by piling it up then a LIFO stack works better, as shown in Figure 16.3. 

In a FIFO stack the parts pass through an entry gate, but are stopped by the exit gate. In the 

LIFO stack the parts enter the stack and lower the plate, when more parts are needed the 

plate is raised. In this arrangement the order of the parts in the stack will be reversed. 



entry gate 

exit gate 

FIFO 

LIFO 

Figure 16.3 

Buffers and Stack Types 

The ladder logic functions are FFL to load the stack, and FFU to unload it. The 

example in Figure 16.4 shows two instructions to load and unload a FIFO stack. The first 

time this FFL is activated (edge triggered) it will grab the word (16 bits) from the input 

card word_in and store them on the stack, at stack[0]. The next value would be stored at 

stack[1], and so on until the stack length is reached at stack[4]. When the FFU is activated 

the word at stack[0] will be moved to the output card word_out. The values on the stack 

will be shifted up so that the value previously in stack[1] moves to stack[0], stack[2] 

moves to stack[1], etc. If the stack is full or empty, an a load or unload occurs the error bit 

will be set c.ER. 



A 

FFL 

source word_in 

FIFO stack[0] 


length 5 

position 0 

B 

FFU 

FIFO stack[0] 

destination word_out 


length 5 

position 0 

Figure 16.4 

FIFO Stack Instructions 

The LIFO stack commands are shown in Figure 16.5. As values are loaded on the 

stack the will be added sequentially stack[0], stack[1], stack[2], stack[3] then stack[4]. 

When values are unloaded they will be taken from the last loaded position, so if the stack 

is full the value of stack[4] will be removed first. 

A 

B 

LFL 

source word_in 

LIFO stack[0] 


length 5 

position 0 

LFU 

LIFO stack[0] 

destination word_out 


length 5 

position 0 

Figure 16.5 

LIFO Stack Commands 



16.2.3 Sequencers 

A mechanical music box is a simple example of a sequencer. As the drum in the 

music box turns it has small pins that will sound different notes. The song sequence is 

fixed, and it always follows the same pattern. Traffic light controllers are now controlled 

with electronics, but previously they used sequencers that were based on a rotating drum 

with cams that would open and close relay terminals. One of these cams is shown in Figure 

16.6. The cam rotates slowly, and the surfaces under the contacts will rise and fall to 

open and close contacts. For a traffic light controllers the speed of rotation would set the 

total cycle time for the traffic lights. Each cam will control one light, and by adjusting the 

circumferential length of rises and drops the on and off times can be adjusted. 

As the cam rotates it makes contact 

with none, one, or two terminals, as 

determined by the depressions and 

rises in the rotating cam. 

Figure 16.6 

A Single Cam in a Drum Sequencer 

A PLC sequencer uses a list of words in memory. It recalls the words one at a time 

and moves the words to another memory location or to outputs. When the end of the list is 

reached the sequencer will return to the first word and the process begins again. A 

sequencer is shown in Figure 16.7. The SQO instruction will retrieve words from bit 

memory starting at sequence[0]. The length is 4 so the end of the list will be at 

sequence[0]+4 or sequence[4] (the total length of ’sequence’ is actually 5). The sequencer 

is edge triggered, and each time A becomes true the retrieve a word from the list and move 

it to output_lights. When the sequencer reaches the end of the list the sequencer will return 

to the second position in the list sequence[1]. The first item in the list is sequence[0], and 

it will only be sent to the output if the SQO instruction is active on the first scan of the 

PLC, otherwise the first word sent to the output is sequence[1]. The mask value is 000Fh, 

or 0000000000001111b so only the four least significant bits will be transferred to the output, 

the other output bits will not be changed. The other instructions allow words to be 

added or removed from the sequencer list. 



A 

SQO 

File sequence[0] 

Mask 000F 

Destination output_lights 


Length 4 

Position 0 

SQO(start,mask,destination,control,length) - sequencer output from table to memory 

SQI(start,mask,source,control,length) - sequencer input from memory address to table 

SQL(start,source,control,length) - sequencer load to set up the sequencer parameters 

Figure 16.7 

The Basic Sequencer Instruction 

An example of a sequencer is given in Figure 16.8 for traffic light control. The 

light patterns are stored in memory (entered manually by the programmer). These are then 

moved out to the output card as the function is activated. The mask (003Fh = 

0000000000111111b) is used so that only the 6 least significant bits are changed. 



advance 

SQO 

File light_pattern 

Mask 003Fh 

Destination lights_output 


Length 4 

Position 0 

light_pattern[0] 

light_pattern[1] 

0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 

0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 

0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 

0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 

0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 

NS - red 

NS - yellow 

NS - green 

EW - red 

EW - yellow 

EW - green 

Figure 16.8 

A Sequencer For Traffic Light Control 

Figure 16.9 shows examples of the other sequencer functions. When A goes from 

false to true, the SQL function will move to the next position in the sequencer list, for 

example sequence_rem[1], and load a value from input_word. If A then remains true the 

value in sequence_rem[1] will be overwritten each scan. When the end of the sequencer 

list is encountered, the position will reset to 1. 

The sequencer input (SQI) function will compare values in the sequence list to the 

source compare_word while B is true. If the two values match match_output will stay on 

while B remains true. The mask value is 0005h or 0000000000000101b, so only the first 

and third bits will be compared. This instruction does not automatically change the position, 

so logic is shown that will increment the position every scan while C is true. 



A 

B 

C 

SQI 

File sequence_rem[0] 

Mask 0005 

Source compare_word 


Length 9 

Position 0 

GT 

SourceA c_2.POS 

SourceB 9 

SQL 

File sequence_rem[0] 

Source input_word 


Length 9 

Position 0 

ADD 

SourceA c_2.POS 

SourceB 1 

Dest c_2.POS 

MOV 

Source 1 

Dest c_2.POS 

match_output 

Figure 16.9 

Sequencer Instruction Examples 

These instructions are well suited to processes with a single flow of execution, 

such as traffic lights. 

16.3 PROGRAM CONTROL 

16.3.1 Branching and Looping 

These functions allow parts of ladder logic programs to be included or excluded 

from each program scan. These functions are similar to functions in other programming 

languages such as C, C++, Java, Pascal, etc. 

Entire sections of programs can be bypassed using the JMP instruction in Figure 



16.10. If A is true the program will jump over the next three lines to the line with the LBL 

Label_01. If A is false the JMP statement will be ignored, and the program scan will continue 

normally. If A is false X will have the same value as B, and Y can be turned on by C 

and off by D. If A is true then X and Y will keep their previous values, unlike the MCR 

statement. Any instructions that follow the LBL statement will not be affected by the JMP 

so Z will always be equal to E. If a jump statement is true the program will run faster. 

A 

B 

JMP 

Label_01 

X 

If A is true, the program 

will jump to LBL:01. 

If A is false the program 

goes to the next 

line. 

C 

L 

Y 

D 

U 

Y 

Label_01 

LBL 

E 

Z 

Figure 16.10 

A JMP Instruction 

Subroutines jump to other programs, as is shown in Figure 16.11. When A is true 

the JSR function will jump to the subroutine program in file 3. The JSR instruction two 

arguments are passed, A and B. The subroutine (SBR) function receives these two arguments 

and puts them in X and Y. When B is true the subroutine will end and return to program 

file 2 where it was called (Note: a subroutine can have multiple returns). The RET 

function returns the value Z to the calling program where it is put in location C. By passing 

arguments (instead of having the subroutine use global memory locations) the subroutine 

can be used for more than one operation. For example, a subroutine could be given an 

angle in degrees and return a value in radians. A subroutine can be called more than once 

in a program, but if not called, it will be ignored. 



MainProgram 

A 

JSR (Jump subroutine) 

Routine Name: TestSubroutine 

Input par A 

Input par B 

Return par C 

A separate ladder logic program is stored in program file 3. This feature 

allows users to create their own functions. In this case if A is 

true, then the program below will be executed and then when done 

the ladder scan will continue after the subroutine instruction. The 

number of data values passed and returned is variable. 

SBR (subroutine arguments) 

Input par X 

Input par Y 

TestSubroutine 

If ’test’ is true the subroutine will return and the values listed will 

be returned to the return par. For this example the value that is in 

’Z’ will be placed in ’C’. 

test 

RET 

Return par Z 

Figure 16.11 

Subroutines 

The ’FOR’ function in Figure 16.12 will (within the same logic scan) call a subroutine 

5 times (from 0 to 9 in steps of 2) when A is true. In this example the subroutine 

contains an ADD function that will add 1 to the value of i. So when this ’FOR’ statement 

is complete the value of j will 5 larger. For-next loops can be put inside other for-next 

loops, this is called nesting. If A was false the program not call the subroutine. When A is 

true, all 5 loops will be completed in a single program scan. If B is true the NXT statement 

will return to the FOR instruction, and stop looping, even if the loop is not complete. Care 

must be used for this instruction so that the ladder logic does not get caught in an infinite, 

or long loop - if this happens the PLC will experience a fault and halt. 



A 

FOR 

Routine Name: LoopRoutine 

index i 

initial value 0 

terminal value 9 

step size 2 

LoopRoutine 

SBR 

ADD 

Source 1 

Source i 

Dest j 

B 

BRK 

Note: if A is true then the loop will repeat 10 times, and the value of i will be increased 

by 10. If A is not true, then the subroutine will never be called. 

Figure 16.12 

A For-Next Loop 

Ladder logic programs always have an end statement, as shown in Figure 16.13. 

Most modern software automatically inserts this. PLCs will experience faults if this is not 

present. The temporary end (TND) statement will skip the remaining portion of a program. 

If C is true then the program will end, and the next line with D and Y will be 

ignored. If C is false then the TND will have no effect and Y will be equal to D. 



A 

B 

X 

C 

TND 

D 

Y 

END 

When the end (or End Of File) is encountered the PLC will stop scanning the 

ladder, and start updating the outputs. This will not be true if it is a subroutine 

or a step in an SFC. 

Figure 16.13 

End Statements 

The one shot contact in Figure 16.14 can be used to turn on a ladder run for a single 

scan. When A has a positive edge the oneshot will turn on the run for a single scan. Bit 

last_bit_value is used here to track to rung status. 

A 

last_bit_value 

ONS 

B 

A 

B 

Figure 16.14 

One Shot Instruction 



16.3.2 Fault Handling 

A fault condition can stop a PLC. If the PLC is controlling a dangerous process 

this could lead to significant damage to personnel and equipment. There are two types of 

faults that occur; terminal (major) and warnings (minor). A minor fault will normally set 

an error bit, but not stop the PLC. A major failure will normally stop the PLC, but an interrupt 

can be used to run a program that can reset the fault bit in memory and continue operation 

(or shut down safely). Not all major faults are recoverable. A complete list of these 

faults is available in PLC processor manuals. 

The PLC can be set up to run a program when a fault occurs, such as a divide by 

zero. These routines are program files under ’Control Fault Handler’. These routines will 

be called when a fault occurs. Values are set in status memory to indicate the source of the 

faults. 

Figure 16.15 shows two example programs. The default program ’MainProgram’ 

will generate a fault, and the interrupt program called ’Recover’ will detect the fault and 

fix it. When A is true a compute function will interpret the expression, using indirect 

addressing. If B becomes true then the value in n[0] will become negative. If A becomes 

true after this then the expression will become n[10] +10. The negative value for the 

address will cause a fault, and program file ’Recover’ will be run. 

In the fault program the fault values are read with an GSV function and the fault 

code is checked. In this case the error will result in a status error of 0x2104. When this is 

the case the n[0] is set back to zero, and the fault code in fault_data[2] is cleared. This 

value is then written back to the status memory using an SSV function. If the fault was not 

cleared the PLC would enter a fault state and stop (the fault light on the front of the PLC 

will turn on). 



MainProgram 

A 

B 

CPT 

Dest n[1] 

Expression 

n[n[0]] + 10 

MOV 

Source -10 

Dest n[0] 

Recover 

GSV 

Object: PROGRAM 

Instance: THIS 

Attribute: MAJORFAULTRECORD 

Dest: fault_data (Note: DINT[11]) 

EQU 

SourceA fault_data[2] 

SourceB 0x2104 

MOV 

Source 0 

Dest N7:0 

CLR 

Dest. fault_data[2] 

SSV 

Object: PROGRAM 

Instance: THIS 

Attribute: MAJORFAULTRECORD 

Dest: fault_data 

Figure 16.15 

A Fault Recovery Program 

16.3.3 Interrupts 

The PLC can be set up to run programs automatically using interrupts. This is routinely 

done for a few reasons; 

• to run a program at a regular timed interval (e.g. SPC calculations) 



• to respond when a long instruction is complete (e.g. analog input) 

• when a certain input changed (e.g. panic button) 

Allen Bradley allows interrupts, but they are called periodic/event tasks. By 

default the main program is defined as a ’continuous’ task, meaning that it runs as often as 

possible, typically 10-100 times per second. Only one continuos task is allowed. A ’periodic’ 

task can be created that has a given update time. ’Event’ tasks can be triggered by a 

variety of actions, including input changes, tag changes, EVENT instructions, and servo 

control changes. 

A timed interrupt will run a program at regular intervals. To set a timed interrupt 

the program in file number should be put in S2:31. The program will be run every S2:30 

times 1 milliseconds. In Figure 16.16 program 2 will set up an interrupt that will run program 

3 every 5 seconds. Program 3 will add the value of I:000 to N7:10. This type of 

timed interrupt is very useful when controlling processes where a constant time interval is 

important. The timed interrupts are enabled by setting bit S2:2/1 in PLC-5s. 

When activated, interrupt routines will stop the PLC, and the ladder logic is interpreted 

immediately. If multiple interrupts occur at the same time the ones with the higher 

priority will occur first. If the PLC is in the middle of a program scan when interrupted 

this can cause problems. To overcome this a program can disable interrupts temporarily 

using the UID and UIE functions. Figure 16.16 shows an example where the interrupts are 

disabled for a FAL instruction. Only the ladder logic between the UID and UIE will be 

disabled, the first line of ladder logic could be interrupted. This would be important if an 

interrupt routine could change a value between n[0] and n[4]. For example, an interrupt 

could occur while the FAL instruction was at n[7]=n[2]+5. The interrupt could change 

the values of n[1] and n[4], and then end. The FAL instruction would then complete the 

calculations. But, the results would be based on the old value for n[1] and the new value 

for n[4]. 



A 

X 

UID 

B 

FAL 


length 5 

position 0 

Mode all 

Destination n[5 + c.POS] 

Expression n[c.POS] + 5 

UIE 

Figure 16.16 

Disabling Interrupts 

16.4 INPUT AND OUTPUT FUNCTIONS 

16.4.1 Immediate I/O Instructions 

The input scan normally records the inputs before the program scan, and the output 

scan normally updates the outputs after the program scan, as shown in Figure 16.17. 

Immediate input and output instructions can be used to update some of the inputs or outputs 

during the program scan. 



• The normal operation of the PLC is 

fast [input scan] 

Input values scanned 

slow [ladder logic is checked] 

Outputs are updated in 

memory only, as the 

ladder logic is scanned 

fast [outputs updated] 

Output values are 

updated to match 

values in memory 

Figure 16.17 

Input, Program and Output Scan 

Figure 16.18 shows a segment within a program that will update the input word 

input_value, determine a new value for output_value.1, and update the output word 

output_value immediately. The process can be repeated many times during the program 

scan allowing faster than normal response times. These instructions are less useful on 

newer PLCs with networked hardware and software, so Allen Bradley does not support 

IIN for newer PLCs such as ControlLogix, even though the IOT is supported. 



e.g. Check for nuclear reactor overheat 

input_value.03 overheat sensor 

output_value.01 reactor shutdown 

IIN 

input_value 

input_value.3 

output_value.1 

IOT 

output_value 

These added statements can allow the ladder logic to examine a critical 

input, and adjust a critical output many times during the execution of 

ladder logic that might take too long for safety. 

Note: When these instructions are used the normal assumption that all inputs and 

outputs are updated before and after the program scan is no longer valid. 

Figure 16.18 

Immediate Inputs and Outputs 

16.5 DESIGN TECHNIQUES 

16.5.1 State Diagrams 

The block logic method was introduced in chapter 8 to implement state diagrams 

using MCR blocks. A better implementation of this method is possible using subroutines 

in program files. The ladder logic for each state will be put in separate subroutines. 

Consider the state diagram in Figure 16.19. This state diagram shows three states 

with four transitions. There is a potential conflict between transitions A and C. 



STA 

B 

D 

STC 

A 

C 

STB 

light_0 = STA 

light_1 = STB 

light_2 = STC 

first scan 

Figure 16.19 

A State Diagram 

The main program for the state diagram is shown in Figure 16.20. This program is 

stored in the MainProgram so that it is run by default. The first rung in the program resets 

the states so that the first scan state is on, while the other states are turned off. The following 

logic will call the subroutine for each state. The logic that uses the current state is 

placed in the main program. It is also possible to put this logic in the state subroutines. 



S:FS 

L 

STB 

U 

STA 

STA 

STB 

STC 

STA 

STB 

STC 

U 

JSR 

sta_transitions 

JSR 

stb_transitions 

JSR 

stc_transitions 

L 

L 

L 

STC 

light_0 

light_1 

light_2 

Figure 16.20 The Main Program for the State Diagram (Program File 2) 

The ladder logic for each of the state subroutines is shown in Figure 16.21. These 

blocks of logic examine the transitions and change states as required. Note that state STB 

includes logic to give state C higher priority, by blocking A when C is active. 



sta_transitions 

B 

U 

STA 

L 

STB 

stb_transitions 

C 

U 

STB 

A 

C 

L 

U 

STC 

STB 

stc_transitions 

D 

L 

U 

STA 

STC 

L 

STB 

Figure 16.21 

Subroutines for the States 

The arrangement of the subroutines in Figure 16.20 and Figure 16.21 could experience 

problems with racing conditions. For example, if STA is active, and both B and C are 

true at the same time the main program would jump to subroutine 3 where STB would be 

turned on. then the main program would jump to subroutine 4 where STC would be turned 

on. For the output logic STB would never have been on. If this problem might occur, the 

state diagram can be modified to slow down these race conditions. Figure 16.22 shows a 

technique that blocks race conditions by blocking a transition out of a state until the transition 

into a state is finished. The solution may not always be appropriate. 



STA 

B*A 

D*C 

STC 

A*(B + D) 

C*(B + D) 

STB 

first scan 

Figure 16.22 

A Modified State Diagram to Prevent Racing 

Another solution is to force the transition to wait for one scan as shown in Figure 

16.23 for state STA. A wait bit is used to indicate when a delay of at least one scan has 

occurred since the transition out of the state B became true. The wait bit is set by having 

the exit transition B true. The B3/0-STA will turn off the wait B3/10-wait when the transition 

to state B3/1-STB has occurred. If the wait was not turned off, it would still be on the 

next time we return to this state. 

Program 3 for STA 

sta_wait 

U 

STA 

L 

STB 

B 

STA 

sta_wait 

Figure 16.23 

Subroutines for State STA to Prevent Racing 




16.6.1 If-Then 

Problem: Convert the following C/Java program to ladder logic. 

void main(){ 

int A; 

for(A = 1; A < 10 ; A++){ 

if (A >= 5) then A = add(A); 

} 

} 

int add(int x){ 

x = x + 1; 

return x; 

} 

Solution: 

MainProgram 

S:FS 

FOR 

function name: increment 

index A 

initial value 1 

terminal value 10 

step size 2 

SBR 

Increment 

GEQ 

A 

5 

ADD 

A 

1 

Dest A 

RET 

Figure 16.24 

C Program Implementation 



16.6.2 Traffic Light 

Problem: Design and write ladder logic for a simple traffic light controller that has 

a single fixed sequence of 16 seconds for both green lights and 4 second for both yellow 

lights. Use either stacks or sequencers. 

Solution: The sequencer is the best solution to this problem. 

t.DN 

t.DN 

SQO 

File n[0] 

mask 0x003F 

Dest. O 


Length 10 

TON 

t 

preset 4.0 sec 

OUTPUTS 

O.0 NSG - north south green 

O.1 NSY - north south yellow 

O.2 NSR - north south red 

O.3 EWG - east west green 

O.4 EWY - east west yellow 

O.5 EWR - east west red 

Addr. 

n[0] 

n[1] 

n[2] 

n[3] 

n[4] 

n[5] 

n[6] 

n[7] 

n[8] 

n[9] 

n[10] 

Contents (in binary) 

0000000000001001 

0000000000100001 

0000000000100001 

0000000000100001 

0000000000100001 

0000000000100010 

0000000000001100 

0000000000001100 

0000000000001100 

0000000000001100 

0000000000010100 

Figure 16.25 

An Example Traffic Light Controller 

16.7 SUMMARY 

• Shift registers move bits through a queue. 

• Stacks will create a variable length list of words. 

• Sequencers allow a list of words to be stepped through. 

• Parts of programs can be skipped with jump and MCR statements, but MCR 

statements shut off outputs. 



• Subroutines can be called in other program files, and arguments can be passed. 

• For-next loops allow parts of the ladder logic to be repeated. 

• Interrupts allow parts to run automatically at fixed times, or when some event 

happens. 

• Immediate inputs and outputs update I/O without waiting for the normal scans. 


1. Design and write ladder logic for a simple traffic light controller that has a single fixed 

sequence of 16 seconds for both green lights and 4 seconds for both yellow lights. Use shift 

registers to implement it. 

2. A PLC is to be used to control a carillon (a bell tower). Each bell corresponds to a musical note 

and each has a pneumatic actuator that will ring it. The table below defines the tune to be programmed. 

Write a program that will run the tune once each time a start button is pushed. A 

stop button will stop the song. 

time sequence in seconds 

O:000/00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 

O:000/00 

O:000/01 

O:000/02 

O:000/03 

O:000/04 

O:000/05 

O:000/06 

O:000/07 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

1 

1 

0 

3. Consider a conveyor where parts enter on one end. they will be checked to be in a left or right 

orientation with a vision system. If neither left nor right is found, the part will be placed in a 

reject bin. The conveyor layout is shown below. 

vision 

left right reject 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

1 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

part movement 

along conveyor 

part sensor 



4. Why are MCR blocks different than JMP statements? 

5. What is a suitable reason to use interrupts? 

6. When would immediate inputs and outputs be used? 

7. Explain the significant differences between shift registers, stacks and sequencers. 

8. Design a ladder logic program that will run once every 30 seconds using interrupts. It will 

check to see if a water tank is full with input tank_full. If it is full, then a shutdown value 

(’shutdown’) will be latched on. 

9. At MOdern Manufacturing (MOMs), pancakes are made by multiple machines in three flavors; 

chocolate, blueberry and plain. When the pancakes are complete they travel along a single belt, 

in no specific order. They are buffered by putting them on the top of a stack. When they arrive 

at the stack the input ’detected’ becomes true, and the stack is loaded by making output ’stack’ 

high for one second. As the pancakes are put on the stack, a color detector is used to determine 

the pancakes type. A value is put in ’color_stack’ (1=chocolate, 2=blueberry, 3=plain) and bit 

’unload’ is made true. A pancake can be requested by pushing a button (’chocolate’, ’blueberry’, 

’plain’). Pancakes are then unloaded from the stack, by making ’unload’ high for 1 second, 

until the desired flavor is removed. Any pancakes removed aren’t returned to the stack. 

Design a ladder logic program to control this stack. 

10. a) What are the two fundamental types of interrupts? 

b) What are the advantages of interrupts in control programs? 

c) What potential problems can they create? 

d) Which instructions can prevent this problem? 

11. Write a ladder logic program to drive a set of flashing lights. In total there are 10 lights connected 

to ’lights[0]’ to ’lights[9]’. At any time every one out of three lights should be on. Every 

second the pattern on the lights should shift towards ’lights[9]’. 

12. Implement the following state diagram using subroutines. 

FS 

B 

A 

ST0 ST1 ST2 

C 

D 




1. 

t.DN 

t.DN 

b[0] = 0000 0000 0000 1111 (grn EW) 

b[1] = 0000 0000 0001 0000 (yel EW) 

b[2] = 0000 0011 1110 0000 (red EW) 

b[3] = 0000 0011 1100 0000 (grn NS) 

b[4] = 0000 0000 0010 0000 (yel NS) 

b[5] = 0000 0000 0001 1111 (red NS) 

TON 

Timer t 

Delay 4s 

BSR 

File b[0] 

Control c0 

Bit address c0.UL 

Length 10 

BSR 

File b[1] 



Length 10 

BSR 

File b[2] 



Length 10 

BSR 

File b[3] 



Length 10 

BSR 

File b[4] 



Length 10 

BSR 

File b[5] 



Length 10 



b[0].0 

b[1].0 

b[2].0 

b[3].0 

b[4].0 

b[5].0 

grn_EW 

yel_EW 

red_EW 

grn_NS 

yel_NS 

red_NS 



2. 

n[0] = 0000 0000 0000 0000 

n[1] = 0000 0000 0000 0110 

n[2] = 0000 0000 0001 0000 

n[3] = 0000 0000 0001 0000 

n[4] = 0000 0000 0000 0100 

n[5] = 0000 0000 0000 1000 

n[6] = 0000 0000 0100 0000 

n[7] = 0000 0000 0110 0000 

n[8] = 0000 0000 0000 0001 

n[9] = 0000 0000 1000 0000 

n[10] = 0000 0000 0000 0100 

n[11] = 0000 0000 0000 1100 

n[12] = 0000 0000 0000 0000 

n[13] = 0000 0000 0100 1000 

n[14] = 0000 0000 0000 0010 

n[15] = 0000 0000 0000 0100 

n[16] = 0000 0000 0000 1000 

n[17] = 0000 0000 0000 0001 

start 

stop 

play 

play 

NEQ 

Source A c.POS 

Source B 17 

t.DN 

TON 

Timer t 

Delay 4s 

t.DN 

SQO 

File n[0] 

Mask 0x00FF 

Destination lights 


Length 17 

Position 0 



3. 

assume: 

sensors.3 

sensors.0 = left orientation 

sensors.1 = right orientation 

sensors.2 = reject 

sensors.3 = part sensor 

b[0].2 

b[1].1 

b[2].0 

BSR 

File b[0] 


Bit address sensors.0 

Length 4 

BSR 

File b[1] 



Length 4 

BSR 

File b[2] 



Length 4 

left 

right 

reject 

4. In MCR blocks the outputs will all be forced off. This is not a problem for outputs such as 

retentive timers and latches, but it will force off normal outputs. JMP statements will skip over 

logic and not examine it or force it off. 

5. Timed interrupts are useful for processes that must happen at regular time intervals. Polled 

interrupts are useful to monitor inputs that must be checked more frequently than the ladder 

scan time will permit. Fault interrupts are important for processes where the complete failure 

of the PLC could be dangerous. 

6. These can be used to update inputs and outputs more frequently than the normal scan time permits. 

7. The main differences are: Shift registers focus on bits, stacks and sequencers on words Shift 

registers and sequencers are fixed length, stacks are variable lengths 



8. 

Checker 

configuration 

periodic task 

update 30000ms 

tank_full 

L 

shutdown 

9. 

S2 

Unloading 

pancakes 

pancake 

doesn’t match 

(not B3/2) 

T3 

S1 

Idle/ 

waiting 

pancake 

requested T1 

(B3/1) pancakes 

match 

(B3/2) 

T2 

1 second 

delay (T4:0) 

T4 

S3 

Unloading 

T6 

T5 

pancake arrives 

(I:000/3) 

S4 

Wait for 

type detect 

Test Done (B3/0) 

T7 

S5 Stacking 

1 second pancakes 

delay (T4:1) 

T1 = S1 • B3/1 

T2 = S2 • B3/2 

T3 = S2 • B3/2 

T4 = S3 • T4:0/DN 

T5 = S5 • T4:1/DN 

T6 = S1 • I:000/3 

T7 = S4 • B3/0 

S1 = ( S1 + T2 + T5 + FS) • T1 • T6 

S2 = ( S2 + T1 • T6 + T4) • T2 • T3 

S3 = ( S3 + T3) • T4 

S4 = ( S4 + T6) • T7 

S5 = ( S5 + T7) • T5 



S3 

S5 

TON 

timer t_s3 

delay 1s 

O:001/0 

TON 

timer t_s5 

delay 1s 

B3/0 

S2 

chocolate 

blueberry 

plain 

EQU 

SourceA waiting_color 

SourceB req_color 

stack 

LFL 

source color_detect 

LIFO n[0] 


length 10 

position 0 

LFU 

LIFO n[0] 

destination waiting_color 


length 10 

position 0 

pancakes_match 

pancake_requested 

chocolate 

blueberry 

plain 

MOV 

Source 1 

Dest req_color 

MOV 

Source 2 


MOV 

Source 3 




S1 

pancake_requested 

T1 

S2 


T2 

S2 


T3 

S3 

t_s3.DN 

T4 

S5 

t_s5.DN 

T5 

S1 

detected 

T6 

S4 

unload 

T7 

S1 

T1 

S1 

T2 

FS 

T6 

S2 

T2 

S2 

T1 

T4 

T3 

T6 

T5 

S3 

T4 

S3 

T3 

S4 

T7 

S4 

T6 

S5 

T5 

S5 

T7 



10. a) Timed, polled and fault, b) They remove the need to check for times or scan for memory 

changes, and they allow events to occur more often than the ladder logic is scanned. c) A few 

rungs of ladder logic might count on a value remaining constant, but an interrupt might change 

the memory, thereby corrupting the logic. d) The UID and UIE 

11. 

t.DN 

t.DN 

S:FS 

MOV 

source 1001001001 B 

dest. B 

TON 

t 

1 s 

BSR 

File B 


Bit c.UL 

Length 10 

MVM 

source B 

mask 0x03FF 

dest lights 



12. 

file 2 

FS 

L 

U 

ST0 

ST1 

file 3 

ST0 

ST1 

ST2 

A 

U 

JSR 

File 3 

JSR 

File 4 

JSR 

File 5 

L 

ST2 

ST1 

U 

ST0 

RET 

file 4 

C 

L 

ST0 

B 

C 

U 

L 

ST1 

ST2 

U 

ST1 

RET 

file 5 

D 

L 

ST1 

U 

ST2 

RET 




1. Using 3 different methods write a program that will continuously cycle a pattern of 12 lights 

connected to a PLC output card. The pattern should have one out of every three lights set. The 

light patterns should appear to move endlessly in one direction. 

2. Look at the manuals for the status memory in your PLC. 

a) Describe how to run program ’GetBetter’ when a divide by zero error occurs. 

b) Write the ladder logic needed to clear a PLC fault. 

c) Describe how to set up a timed interrupt to run ’Slowly’ every 2 seconds. 

3. Write an interrupt driven program that will run once every 5 seconds and calculate the average 

of the numbers from ’f[0]’ to ’f[19]’, and store the result in ’f_avg’. It will also determine the 

median and store it in ’f_med’. 

4. Write a program for SPC (Statistical Process Control) that will run once every 20 minutes using 

timed interrupts. When the program runs it will calculate the average of the data values in 

memory locations ’f[0]’ to ’f[39]’ (Note: these values are written into the PLC memory by 

another PLC using networking). The program will also find the range of the values by subtracting 

the maximum from the minimum value. The average will be compared to upper (f_ucl_x) 

and lower (f_lcl_x) limits. The range will also be compared to upper (f_ucl_r) and lower 

(f_lcl_r) limits. If the average, or range values are outside the limits, the process will stop, and 

an ‘out of control’ light will be turned on. The process will use start and stop buttons, and 

when running it will set memory bit ’in_control’. 

5. Develop a ladder logic program to control a light display outside a theater. The display consists 

of a row of 8 lights. When a patron walks past an optical sensor the lights will turn on in 

sequence, moving in the same direction. Initially all lights are off. Once triggered the lights 

turn on sequentially until all eight lights are on 1.6 seconds latter. After a delay of another 0.4 

seconds the lights start to turn off until all are off, again moving in the same direction as the 

patron. The effect is a moving light pattern that follows the patron as they walk into the theater. 

6. Write the ladder logic diagram that would be required to execute the following data manipulation 

for a preventative maintenance program. 

i) Keep track of the number of times a motor was started with toggle switch #1. 

ii) After 2000 motor starts turn on an indicator light on the operator panel. 

iii) Provide the capability to change the number of motor starts being tracked, prior 

to triggering of the indicator light. HINT: This capability will only require the 

change of a value in a compare statement rather than the addition of new lines 

of logic. 

iv) Keep track of the number of minutes that the motor has run. 

v) After 9000 minutes of operation turn the motor off automatically and also turn 

on an indicator light on the operator panel. 

7. Parts arrive at an oven on a conveyor belt and pass a barcode scanner. When the barcode scanner 

reads a valid barcode it outputs the numeric code as 32 bits to ’scanner_value’ and sets 



input ’scanner_value_valid’. The PLC must store this code until the parts pass through the 

oven. When the parts leave the oven they are detected by a proximity sensor connected to 

’part_leaving’. The barcode value read before must be output to ’barcode_output’. Write the 

ladder logic for the process. There can be up to ten parts inside the oven at any time. 

8. Write the ladder logic for the state diagram below using subroutines for the states. 

FS 

ST1 

A 

B 

ST2 

D 

ST3 

C 

9. Convert the following state diagram to ladder logic using subroutines. 

C 

FS A B 

X Y Z 

D 

E 


plc iec61131 - 17.1 

17. OPEN CONTROLLERS 

Topics: 

• Open systems 

• IEC 61131 standards 

• Open architecture controllers 

Objectives: 

• To understand the decision between choosing proprietary and public standards. 

• To understand the basic concepts behind the IEC 61131 standards. 


In previous decades (and now) PLC manufacturers favored “proprietary” or 

“closed” designs. This gave them control over the technology and customers. Essentially, 

a proprietary architecture kept some of the details of a system secret. This tended to limit 

customer choices and options. It was quite common to spend great sums of money to 

install a control system, and then be unable to perform some simple task because the manufacturer 

did not sell that type of solution. In these situations customers often had two 

choices; wait for the next release of the hardware/software and hope for a solution, or pay 

exorbitant fees to have custom work done by the manufacturer. 

“Open” systems have been around for decades, but only recently has their value 

been recognized. The most significant step occurred in 1981 when IBM broke from it’s 

corporate tradition and released a personal computer that could use hardware and software 

from other companies. Since that time IBM lost control of it’s child, but it has now 

adopted the open system philosophy as a core business strategy. All of the details of an 

open system are available for users and developers to use and modify. This has produced 

very stable, flexible and inexpensive solutions. Controls manufacturers are also moving 

toward open systems. One such effort involves Devicenet, which is discussed in a later 

chapter. 

A troubling trend that you should be aware of is that many manufacturers are mislabeling 

closed and semi-closed systems as open. An easy acid test for this type of system 

is the question “does the system allow me to choose alternate suppliers for all of the components?” 

If even one component can only be purchased from a single source, the system 

is not open. When you have a choice you should avoid “not-so-open” solutions. 


plc iec61131 - 17.2 

17.2 IEC 61131 

The IEC 1131 standards were developed to be a common and open framework for 

PLC architecture, agreed to by many standards groups and manufacturers. They were initially 

approved in 1992, and since then they have been reviewed as the IEC-61131 standards. 

The main components of the standard are; 

IEC 61131-1 Overview 

IEC 61131-2 Requirements and Test Procedures 

IEC 61131-3 Data types and programming 

IEC 61131-4 User Guidelines 

IEC 61131-5 Communications 

IEC 61131-7 Fuzzy control 

This standard is defined loosely enough so that each manufacturer will be able to 

keep their own look-and-feel, but the core data representations should become similar. 

The programming models (IEC 61131-3) have the greatest impact on the user. 

IL (Instruction List) - This is effectively mnemonic programming 

ST (Structured Text) - A BASIC like programming language 

LD (Ladder Diagram) - Relay logic diagram based programming 

FBD (Function Block Diagram) - A graphical dataflow programming method 

SFC (Sequential Function Charts) - A graphical method for structuring programs 

Most manufacturers already support most of these models, except Function Block 

programming. The programming model also describes standard functions and models. 

Most of the functions in the models are similar to the functions described in this book. The 

standard data types are shown in Figure 17.1. 


plc iec61131 - 17.3 

Name 

Type 

Bits 

Range 

BOOL 

SINT 

INT 

DINT 

LINT 

USINT 

UINT 

UDINT 

ULINT 

REAL 

LREAL 

TIME 

DATE 

TIME_OF_DAY, TOD 

DATE_AND_TIME, DT 

STRING 

BYTE 

WORD 

DWORD 

LWORD 

boolean 

short integer 

integer 

double integer 

long integer 

unsigned short integer 

unsigned integer 

unsigned double integer 

unsigned long integer 

real numbers 

long reals 

duration 

date 

time 

date and time 

string 

8 bits 

16 bits 

32 bits 

64 bits 

1 

8 

16 

32 

64 

8 

16 

32 

64 

32 

64 

not fixed 

not fixed 

not fixed 

not fixed 

variable 

8 

16 

32 

64 

0 to 1 

-128 to 127 

-32768 to 32767 

-2.1e-9 to 2.1e9 

-9.2e19 to 9.2e19 

0 to 255 

0 to 65536 

0 to 4.3e9 

0 to 1.8e20 

not fixed 

not fixed 

not fixed 

not fixed 

variable 

NA 

NA 

NA 

NA 

Figure 17.1 

IEC 61131-3 Data Types 

Previous chapters have described Ladder Logic (LD) programming in detail, and 

Sequential Function Chart (SFC) programming briefly. Following chapters will discuss 

Instruction List (IL), Structured Test (ST) and Function Block Diagram (FBD) programming 

in greater detail. 

17.3 OPEN ARCHITECTURE CONTROLLERS 

Personal computers have been driving the open architecture revolution. A personal 

computer is capable of replacing a PLC, given the right input and output components. As a 

result there have been many companies developing products to do control using the personal 

computer architecture. Most of these devices use two basic variations; 

• a standard personal computer with a normal operating system, such as Windows 

NT, runs a virtual PLC. 


plc iec61131 - 17.4 

- the computer is connected to a normal PLC rack 

- I/O cards are used in the computer to control input/output functions 

- the computer is networked to various sensors 

• a miniaturized personal computer is put into a PLC rack running a virtual PLC. 

In all cases the system is running a standard operating system, with some connection 

to rugged input and output cards. The PLC functions are performed by a virtual PLC 

that interprets the ladder logic and simulates a PLC. These can be fast, and more capable 

than a stand alone PLC, but also prone to the reliability problems of normal computers. 

For example, if an employee installs and runs a game on the control computer, the controller 

may act erratically, or stop working completely. Solutions to these problems are being 

developed, and the stability problem should be solved in the near future. 

17.4 SUMMARY 

• Open systems can be replaced with software or hardware from a third party. 

• Some companies call products open incorrectly. 

• The IEC 61131 standard encourages interchangeable systems. 

• Open architecture controllers replace a PLC with a computer. 


1. Describe why traditional PLC racks are not ’open’. 

2. Discuss why the IEC 61131 standards should lead to open architecture control systems. 


1. The hardware and software are only sold by Allen Bradley, and users are not given details to 

modify or change the hardware and software. 

2. The IEC standards are a first step to make programming methods between PLCs the same. The 

standard does not make programming uniform across all programming platforms, so it is not 

yet ready to develop completely portable controller programs and hardware. 


1. Write a ladder logic program to perform the function outlined below. (Hint: use a structured 


plc iec61131 - 17.5 

technique.) 

i) when the input ‘part’ turns on, the value ‘weight’ should be added to an array in 

memory. 

ii) if any ‘weight’ value is greater than 15, and output ‘halt’ should be turned on, 

and the process should stop. A ‘reset’ input will be turned on to clear the array 

and start the process again. 

iii) when ‘part’ has been activated 10 times the median of the part weights should 

be found. If it is greater that 14 the process should be stopped as described in 

step ii). 

iv) if the median is less than or equal to 14, then a ‘dump’ output should be turned 

on for 2 seconds. After that the matrix should be reset and the process should 

begin again. 


plc il - 18.1 

18. INSTRUCTION LIST PROGRAMMING 

Topics: 

• Instruction list (IL) opcodes and operations 

• Converting from ladder logic to IL 

• Stack oriented instruction delay 

• The Allen Bradley version of IL 

Objectives: 

• To learn the fundamentals of IL programming. 

• To understand the relationship between ladder logic and IL programs 

Note: Allen Bradley does not offer IL programming as a standard option so this 

chapter may be considered optional. 


Instruction list (IL) programming is defined as part of the IEC 61131 standard. It 

uses very simple instructions similar to the original mnemonic programming languages 

developed for PLCs. (Note: some readers will recognize the similarity to assembly language 

programming.) It is the most fundamental level of programming language - all other 

programming languages can be converted to IL programs. Most programmers do not use 

IL programming on a daily basis, unless they are using hand held programmers. 

18.2 THE IEC 61131 VERSION 

To ease understanding, this chapter will focus on the process of converting ladder 

logic to IL programs. A simple example is shown in Figure 18.1 using the definitions 

found in the IEC standard. The rung of ladder logic contains four inputs, and one output. It 

can be expressed in a Boolean equation using parentheses. The equation can then be 

directly converted to instructions. The beginning of the program begins at the START: 

label. At this point the first value is loaded, and the rest of the expression is broken up into 

small segments. The only significant change is that AND NOT becomes ANDN. 


plc il - 18.2 

I:000/00 

I:000/01 

O:001/00 

I:000/02 

I:000/03 

read as O:001/00 = I:000/00 AND ( I:000/01 OR ( I:000/02 AND NOT I:000/03) ) 

Label Opcode Operand Comment 

START: 

LD 

AND( 

OR( 

ANDN 

) 

) 

ST 

%I:000/00 

%I:000/01 

%I:000/02 

%I:000/03 

%O:001/00 

(* Load input bit 00 *) 

(* Start a branch and load input bit 01 *) 

(* Load input bit 02 *) 

(* Load input bit 03 and invert *) 

(* SET the output bit 00 *) 

Figure 18.1 

An Instruction List Example 

An important concept in this programming language is the stack. (Note: if you use 

a calculator with RPN you are already familiar with this.) You can think of it as a do later 

list. With the equation in Figure 18.1 the first term in the expression is LD I:000/00, but 

the first calculation should be ( I:000/02 AND NOT I:000/03). The instruction values are 

pushed on the stack until the most deeply nested term is found. Figure 18.2 illustrates how 

the expression is pushed on the stack. The LD instruction pushes the first value on the 

stack. The next instruction is an AND, but it is followed by a ’(’ so the stack must drop 

down. The OR( that follows also has the same effect. The ANDN instruction does not need 

to wait, so the calculation is done immediately and a result_1 remains. The next two ’)’ 

instructions remove the blocking ’(’ instruction from the stack, and allow the remaining 

OR I:000/1 and AND I:000/0 instructions to be done. The final result should be a single bit 

result_3. Two examples follow given different input conditions. If the final result in the 

stack is 0, then the output ST O:001/0 will set the output, otherwise it will turn it off. 


plc il - 18.3 

LD I:000/0 

AND( I:000/1 

OR( I:000/2 

ANDN I:000/3 

) 

) 

I:000/0 

I:000/1 

( 

AND I:000/0 

I:000/2 

( 

OR I:000/1 

( 

AND I:000/0 

result_1 

( 

OR I:000/1 

( 

AND I:000/0 

result_2 

( 

AND I:000/0 

result_3 

Given: 

I:000/0 = 1 

I:000/1 = 0 

I:000/2 = 1 

I:000/3 = 0 

1 

0 

( 

AND 1 

1 

( 

OR 0 

( 

AND 1 

1 

( 

OR 0 

( 

AND 1 

1 

( 

AND 1 

1 

AND 1 

1 

Given: 

I:000/0 = 0 

I:000/1 = 1 

I:000/2 = 0 

I:000/3 = 1 

0 

1 

( 

AND 0 

0 

( 

OR 1 

( 

AND 0 

0 

( 

OR 1 

( 

AND 0 

0 

( 

AND 1 

0 

AND 1 

0 

Figure 18.2 

Using a Stack for Instruction Lists 

A list of operations is given in Figure 18.3. The modifiers are; 

N - negates an input or output 

( - nests an operation and puts it on a stack to be pulled off by ’)’ 

C - forces a check for the currently evaluated results at the top of the stack 

These operators can use multiple data types, as indicated in the data types column. 

This list should be supported by all vendors, but additional functions can be called using 

the CAL function. 


plc il - 18.4 

Operator 

Modifiers 

Data Types 

Description 

LD 

ST 

S, R 

AND, & 

OR 

XOR 

ADD 

SUB 

MUL 

DIV 

GT 

GE 

EQ 

NE 

LE 

LT 

JMP 

CAL 

RET 

) 

N 

N 

N, ( 

N, ( 

N, ( 

( 

( 

( 

( 

( 

( 

( 

( 

( 

( 

C, N 

C, N 

C, N 

many 

many 

BOOL 

BOOL 

BOOL 

BOOL 

many 

many 

many 

many 

many 

many 

many 

many 

many 

many 

LABEL 

NAME 

set current result to value 

store current result to location 

set or reset a value (latches or flip-flops) 

boolean and 

boolean or 

boolean exclusive or 

mathematical add 

mathematical subtraction 

mathematical multiplication 

mathematical division 

comparison greater than > 

comparison greater than or equal >= 

comparison equals = 

comparison not equal 

comparison less than or equals

plc il - 18.5 

Ladder 

A 

X 

Instruction List (IL) 

LD A 

ST X 

A X LDN A 

ST X 

A B 

X LD A 

LD B 

ANB 

ST X 

A B 

X LD A 

LDN B 

ANB 

ST X 

A C X LD A 

LD B 

ORB 

B 

LD C 

ANB 

ST X 

A B 

X LD A 

LD B 

LD C 

C 

ORB 

ANB 

ST X 

A C 

X LD A 

LD B 

B D 

ORB 

LD C 

LD D 

ORB 

ANB 

ST X 

LD A 

AND B 

ST X 

LD A 

ANDN B 

ST X 

LD A 

OR B 

AND C 

ST X 

LD A 

LD B 

OR C 

ANB 

ST X 

LD A 

OR B 

LD C 

OR D 

ANB 

ST X 

Figure 18.4 

IL Equivalents for Ladder Logic 

Figure 18.5 shows the IL programs that are generated when there are multiple outputs. 

This often requires that the stack be used to preserve values that would be lost nor- 


plc il - 18.6 

mally using the MPS, MPP and MRD functions. The MPS instruction will store the current 

value of the top of the stack. Consider the first example with two outputs, the value of A is 

loaded on the stack with LD A. The instruction ST X examines the top of the stack, but 

does not remove the value, so it is still available for ST Y. In the third example the value of 

the top of the stack would not be correct when the second output rung was examined. So, 

when the output branch occurs the value at the top of the stack is copied using MPS, and 

pushed on the top of the stack. The copy is then ANDed with B and used to set X. After 

this the value at the top is pulled off with the MPP instruction, leaving the value at the top 

what is was before the first output rung. The last example shows multiple output rungs. 

Before the first rung the value is copied on the stack using MPS. Before the last rung the 

value at the top of the stack is discarded with the MPP instruction. But, the two center 

instructions use MRD to copy the right value to the top of the stack - it could be replaced 

with MPP then MPS. 


plc il - 18.7 

Ladder 

A 

X 

Y 

Instruction List (IL) 

LD A 

ST X 

ST Y 

A X LD A 

B 

Y 

ST X 

LD B 

ANB 

ST Y 

A B X LD A 

C 

Y 

MPS 

LD B 

ANB 

ST X 

MPP 

LD C 

ANB 

ST Y 

A B W LD A 

C 

X 

MPS 

LD B 

ANB 

Y ST W 

E 

MRD 

Z LD C 

ANB 

ST X 

MRD 

STY 

MPP 

LD E 

ANB 

ST Z 

LD A 

ST X 

AND B 

ST Y 

LD A 

MPS 

AND B 

ST X 

MPP 

AND C 

ST Y 

LD A 

MPS 

AND B 

ST W 

MRD 

AND C 

ST X 

MRD 

ST Y 

MPP 

AND E 

ST Z 

Figure 18.5 

IL Programs for Multiple Outputs 

Complex instructions can be represented in IL, as shown in Figure 18.6. Here the 

function are listed by their mnemonics, and this is followed by the arguments for the functions. 

The second line does not have any input contacts, so the stack is loaded with a true 


plc il - 18.8 

value. 

I:001/0 

TON 

Timer T4:0 

Delay 5s 

ADD 

SourceA 3 

SourceB T4:0.ACC 

Dest N7:0 

START:LD I:001/0 

TON(T4:0, 1.0, 5, 0) 

LD 1 

ADD (3, T4:0.ACC, N7:0) 

END 

Figure 18.6 

A Complex Ladder Rung and Equivalent IL 

An example of an instruction language subroutine is shown in Figure 18.7. This 

program will examine a BCD input on card I:000, and if it becomes higher than 100 then 2 

seconds later output O:001/00 will turn on. 


plc il - 18.9 

Program File 2: 

Label 

Opcode 

Operand 

Comment 

START: 

CAL 

3 

(* Jump to program file 3 *) 

Program File 3: 

Label 

Opcode 

Operand 

Comment 

TEST: 

ON: 

LD 

BCD_TO_INT 

ST 

GT 

JMPC 

CAL 

LD 

ST 

CAL 

LD 

ST 

RET 

%I:000 

%N7:0 

100 

ON 

RES(C5:0) 

2 

%C5:0.PR 

TON(C5:0) 

%C5:0.DN 

%O:001/00 

(* Load the word from input card 000 *) 

(* Convert the BCD value to an integer *) 

(* Store the value in N7:0 *) 

(* Check for the stored value (N7:0) > 100 *) 

(* If true jump to ON *) 

(* Reset the timer *) 

(* Load a value of 2 - for the preset *) 

(* Store 2 in the preset value *) 

(* Update the timer *) 

(* Get the timer done condition bit *) 

(* Set the output bit *) 

(* Return from the subroutine *) 

Figure 18.7 

An Example of an IL Program 

18.4 SUMMARY 

• Ladder logic can be converted to IL programs, but IL programs cannot always be 

converted to ladder logic. 

• IL programs use a stack to delay operations indicated by parentheses. 


plc il - 18.10 

• The Allen Bradley version is similar, but not identical to the IEC 61131 version 

of IL. 




1. Explain the operation of the stack. 

2. Convert the following ladder logic to IL programs. 

A C X 

B C D 

Y 

B 

C 

3. Write the ladder diagram programs that correspond to the following Boolean programs. 

LD 001 

OR 003 

LD 002 

OR 004 

AND LD 

LD 005 

OR 007 

AND 006 

OR LD 

OUT 204 

LD 001 

AND 002 

LD 004 

AND 005 

OR LD 

OR 007 

LD 003 

OR NOT 006 

AND LD 

LD NOT 001 

AND 002 

LD 004 

OR 007 

AND 005 

OR LD 

LD 003 

OR NOT 006 

AND LD 

OR NOT 008 

OUT 204 

AND 009 

OUT 206 

AND NOT 010 

OUT 201 


plc st - 19.1 

19. STRUCTURED TEXT PROGRAMMING 

Topics: 

• Basic language structure and syntax 

• Variables, functions, values 

• Program flow commands and structures 

• Function names 

• Program Example 

Objectives: 

• To be able to write functions in Structured Text programs 

• To understand the parallels between Ladder Logic and Structured Text 

• To understand differences between Allen Bradley and the standard 


If you know how to program in any high level language, such as Basic or C, you 

will be comfortable with Structured Text (ST) programming. ST programming is part of 

the IEC 61131 standard. An example program is shown in Figure 19.1. The program is 

called main and is defined between the statements PROGRAM and END_PROGRAM. 

Every program begins with statements the define the variables. In this case the variable i is 

defined to be an integer. The program follows the variable declarations. This program 

counts from 0 to 10 with a loop. When the example program starts the value of integer 

memory i will be set to zero. The REPEAT and END_REPEAT statements define the loop. 

The UNTIL statement defines when the loop must end. A line is present to increment the 

value of i for each loop. 


plc st - 19.2 

PROGRAM main 

VAR 

i : INT; 

END_VAR 

i := 0; 

REPEAT 

i := i + 1; 

UNTIL i >= 10; 

END_REPEAT; 

END_PROGRAM 

Note: Allen Bradley does not implement 

the standard so that the programs can be 

written with text only. When programming 

in RSLogix, only the section indicated 

to the left would be entered. The 

variable ’i’ would be defined as a tag, 

and the program would be defined as a 

task. 

Figure 19.1 

A Structured Text Example Program 

One important difference between ST and traditional programming languages is 

the nature of program flow control. A ST program will be run from beginning to end many 

times each second. A traditional program should not reach the end until it is completely 

finished. In the previous example the loop could lead to a program that (with some modification) 

might go into an infinite loop. If this were to happen during a control application 

the controller would stop responding, the process might become dangerous, and the controller 

watchdog timer would force a fault. 

ST has been designed to work with the other PLC programming languages. For 

example, a ladder logic program can call a structured text subroutine. 

19.2 THE LANGUAGE 

The language is composed of written statements separated by semicolons. The 

statements use predefined statements and program subroutines to change variables. The 

variables can be explicitly defined values, internally stored variables, or inputs and outputs. 

Spaces can be used to separate statements and variables, although they are not often 

necessary. Structured text is not case sensitive, but it can be useful to make variables lower 

case, and make statements upper case. Indenting and comments should also be used to 

increase readability and documents the program. Consider the example shown in Figure 

19.2. 


plc st - 19.3 

GOOD 

BAD 

*) 

FUNCTION sample 

INPUT_VAR 

END_VAR 

OUTPUT_VAR 

start : BOOL; (* a NO start input *) 

stop : BOOL; (* a NC stop input *) 

motor : BOOL;(* a motor control relay 

END_VAR 

motor := (motor + start) * stop;(* get the motor output *) 

END_FUNCTION 

FUNCTION sample 

INPUT_VAR 

START:BOOL;STOP:BOOL; 

END_VAR 

OUTPUT_VAR 

MOTOR:BOOL; 

END_VAR 

MOTOR:=(MOTOR+START)*STOP;END_FUNCTION 

Figure 19.2 

A Syntax and Structured Programming Example 

19.2.1 Elements of the Language 

ST programs allow named variables to be defined. This is similar to the use of 

symbols when programming in ladder logic. When selecting variable names they must 

begin with a letter, but after that they can include combinations of letters, numbers, and 

some symbols such as ’_’. Variable names are not case sensitive and can include any combination 

of upper and lower case letters. Variable names must also be the same as other 

key words in the system as shown in Figure 19.3. In addition, these variable must not have 

the same name as predefined functions, or user defined functions. 

Invalid variable names: START, DATA, PROJECT, SFC, SFC2, LADDER, I/O, ASCII, 

CAR, FORCE, PLC2, CONFIG, INC, ALL, YES, NO, STRUCTURED TEXT 

Valid memory/variable name examples: TESTER, I, I:000, I:000/00, T4:0, T4:0/DN, 

T4:0.ACC 

Figure 19.3 

Acceptable Variable Names 


plc st - 19.4 

When defining variables one of the declarations in Figure 19.4 can be used. These 

define the scope of the variables. The VAR_INPUT, VAR_OUTPUT and VAR_IN_OUT 

declarations are used for variables that are passed as arguments to the program or function. 

The RETAIN declaration is used to retain a variable value, even when the PLC power has 

been cycled. This is similar to a latch application. As mentioned before these are not used 

when writing Allen Bradley programs, but they are used when defining tags to be used by 

the structured programs. 

Declaration 

VAR 

VAR_INPUT 

VAR_OUTPUT 

VAR_IN_OUT 

VAR_EXTERNAL 

VAR_GLOBAL 

VAR_ACCESS 

RETAIN 

CONSTANT 

AT 

END_VAR 

Description 

the general variable declaration 

defines a variable list for a function 

defines output variables from a function 

defines variable that are both inputs and outputs from a function 

a global variable 

a value will be retained when the power is cycled 

a value that cannot be changed 

can tie a variable to a specific location in memory (without this variable 

locations are chosen by the compiler 

marks the end of a variable declaration 

Figure 19.4 

Variable Declarations 

Examples of variable declarations are given in Figure 19.5. 


plc st - 19.5 

Text Program Line 

VAR AT %B3:0 : WORD; END_VAR 

VAR AT %N7:0 : INT; END_VAR 

VAR RETAIN AT %O:000 : WORD ; END_VAR 

VAR_GLOBAL A AT %I:000/00 : BOOL ; END_VAR 

VAR_GLOBAL A AT %N7:0 : INT ; END_VAR 

VAR A AT %F8:0 : ARRAY [0..14] OF REAL; END_VAR 

VAR A : BOOL; END_VAR 

VAR A, B, C : INT ; END_VAR 

VAR A : STRING[10] ; END_VAR 

VAR A : ARRAY[1..5,1..6,1..7] OF INT; END_VAR 

VAR RETAIN RTBT A : ARRAY[1..5,1..6] OF INT; 

END_VAR 

VAR A : B; END_VAR 

VAR CONSTANT A : REAL := 5.12345 ; END_VAR 

VAR A AT %N7:0 : INT := 55; END_VAR 

VAR A : ARRAY[1..5] OF INT := [5(3)]; END_VAR 

VAR A : STRING[10] := ‘test’; END_VAR 

VAR A : ARRAY[0..2] OF BOOL := [1,0,1]; END_VAR 

VAR A : ARRAY[0..1,1..5] OF INT := [5(1),5(2)]; 

END_VAR 

Description 

a word in bit memory 

an integer in integer memory 

makes output bits retentive 

variable ‘A’ as input bit 

variable ‘A’ as an integer 

an array ‘A’ of 15 real values 

a boolean variable ‘A’ 

integers variables ‘A’, ‘B’, ‘C’ 

a string ‘A’ of length 10 

a 5x6x7 array ‘A’ of integers 

a 5x6 array of integers, filled 

with zeros after power off 

‘A’ is data type ‘B’ 

a constant value ‘A’ 

‘A’ starts with 55 

‘A’ starts with 3 in all 5 spots 

‘A’ contains ‘test’ initially 

an array of bits 

an array of integers filled with 1 

for [0,x] and 2 for [1,x] 

Figure 19.5 

Variable Declaration Examples 

Basic numbers are shown in Figure 19.6. Note the underline ‘_’ can be ignored, it 

can be used to break up long numbers, ie. 10_000 = 10000. These are the literal values discussed 

for Ladder Logic. 

number type 

integers 

real numbers 

real with exponents 

binary numbers 

octal numbers 

hexadecimal numbers 

boolean 

examples 

-100, 0, 100, 10_000 

-100.0, 0.0, 100.0, 10_000.0 

-1.0E-2, -1.0e-2, 0.0e0, 1.0E2 

2#111111111, 2#1111_1111, 2#1111_1101_0110_0101 

8#123, 8#777, 8#14 

16#FF, 16#ff, 16#9a, 16#01 

0, FALSE, 1, TRUE 

Figure 19.6 

Literal Number Examples 


plc st - 19.6 

Character strings defined as shown in Figure 19.7. 

example 

‘’ 

‘ ‘, ‘a’, ‘$’’, ‘$$’ 

‘$R$L’, ‘$r$l’,‘$0D$0A’ 

‘$P’, ‘$p’ 

‘$T’, ‘4t’ 

‘this%Tis a test$R$L’ 

description 

a zero length string 

a single character, a space, or ‘a’, or a single quote, or a dollar 

sign $ 

produces ASCII CR, LF combination - end of line characters 

form feed, will go to the top of the next page 

tab 

a string that results in ‘thisis a test’ 

Figure 19.7 

Character String Data 

Basic time and date values are described in Figure 19.8 and Figure 19.9. Although 

it should be noted that for ControlLogix the GSV function is used to get the values. 

Time Value 

25ms 

5.5hours 

3days, 5hours, 6min, 36sec 

Examples 

T#25ms, T#25.0ms, TIME#25.0ms, T#-25ms, t#25ms 

TIME#5.3h, T#5.3h, T#5h_30m, T#5h30m 

TIME#3d5h6m36s, T#3d_5h_6m_36s 

Figure 19.8 

Time Duration Examples 

description 

date values 

time of day 

date and time 

examples 

DATE#1996-12-25, D#1996-12-25 

TIME_OF_DAY#12:42:50.92, TOD#12:42:50.92 

DATE_AND_TIME#1996-12-25-12:42:50.92, DT#1996-12-25-12:42:50.92 

Figure 19.9 

Time and Date Examples 

The math functions available for structured text programs are listed in Figure 

19.10. It is worth noting that these functions match the structure of those available for ladder 

logic. Other, more advanced, functions are also available - a general rule of thumb is if 

a function is available in one language, it is often available for others. 


plc st - 19.7 

:= 

+ 

- 

/ 

* 

MOD(A,B) 

SQR(A) 

FRD(A) 

TOD(A) 

NEG(A) 

LN(A) 

LOG(A) 

DEG(A) 

RAD(A) 

SIN(A) 

COS(A) 

TAN(A) 

ASN(A) 

ACS(A) 

ATN(A) 

XPY(A,B) 

A**B 

assigns a value to a variable 

addition 

subtraction 

division 

multiplication 

modulo - this provides the remainder for an integer divide A/B 

square root of A 

from BCD to decimal 

to BCD from decimal 

reverse sign +/- 

natural logarithm 

base 10 logarithm 

from radians to degrees 

to radians from degrees 

sine 

cosine 

tangent 

arcsine, inverse sine 

arccosine - inverse cosine 

arctan - inverse tangent 

A to the power of B 

A to the power of B 

Figure 19.10 

Math Functions 

Functions for logical comparison are given in Figure 19.11. These will be used in 

expressions such as IF-THEN statements. 

> 

>= 

= 

plc st - 19.8 

AND(A,B) 

OR(A,B) 

XOR(A,B) 

NOT(A) 

! 

logical and 

logical or 

exclusive or 

logical not 

logical not (note: not implemented on AB controllers) 

Figure 19.12 

Boolean Functions 

The precedence of operations are listed in Figure 19.13 from highest to lowest. As 

normal expressions that are the most deeply nested between brackets will be solved first. 

(Note: when in doubt use brackets to ensure you get the sequence you expect.) 

highest priority 

! - (Note: not available on AB controllers) 

() 

functions 

XPY, ** 

negation 

SQR, TOD, FRD, NOT, NEG, LN, LOG, DEG, RAD, SIN, COS, TAN, ASN, ACS, ATN 

*, /, MOD 

+, - 

>, >=, =,

plc st - 19.9 

Special instructions include those shown in Figure 19.15. 

RETAIN(); 

IIN(); 

EXIT; 

EMPTY 

causes a bit to be retentive 

immediate input update 

will quit a FOR or WHILE loop 

Figure 19.15 

Special Instructions 

19.2.2 Putting Things Together in a Program 

Consider the program in Figure 19.16 to find the average of five values in a real 

array ’f[]’. The FOR loop in the example will loop five times adding the array values. 

After that the sum is divided to get the average. 

avg := 0; 

FOR (i := 0 TO 4) DO 

avg := avg + f[i]; 

END_FOR; 

avg := avg / 5; 

Figure 19.16 

A Program To Average Five Values In Memory With A For-Loop 

The previous example is implemented with a WHILE loop in Figure 19.17. The 

main differences is that the initial value and update for ’i’ must be done manually. 

avg := 0; 

i := 0; 

WHILE (i < 5) DO 

avg := avg + f[i]; 

i := i + 1; 

END_WHILE; 

avg := avg / 5; 

Figure 19.17 

A Program To Average Five Values In Memory With A While-Loop 


plc st - 19.10 

The example in Figure 19.18 shows the use of an IF statement. The example 

begins with a timer. These are handled slightly differently in ST programs. In this case if 

’b’ is true the timer will be active, if it is false the timer will reset. The second instruction 

calls ’TONR’ to update the timer. (Note: ST programs use the FBD_TIMER type, instead 

of the TIMER type.) The IF statement works as normal, only one of the three cases will 

occur with the ELSE defining the default if the other two fail. 

t.TimerEnable := b; 

TONR(t); 

IF (a = 1) THEN 

x := 1; 

ELSIF (b = 1 AND t.DN = 1) THEN 

y := 1; 

IF (I:000/02 = 0) THEN 

z := 1; 

END_IF; 

ELSE 

x := 0; 

y := 0; 

z := 0; 

END_IF; 

Figure 19.18 

Example With An If Statement 

Figure 19.19 shows the use of a CASE statement to set bits 0 to 3 of ’a’ based upon 

the value of ’test’. In the event none of the values are matched, ’a’ will be set to zero, turning 

off all bits. 

CASE test OF 

0: 

a.0 := 1; 

1: 

a.1 := 1; 

2: 

a.2 := 1; 

3: 

a.3 := 1; 

ELSE 

a := 0; 

END_CASE; 


plc st - 19.11 

Figure 19.19 

Use of a Case Statement 

The example in Figure 19.20 accepts a BCD input from ’bcd_input’ and uses it to 

change the delay time for TON delay time. When the input ’test_input’ is true the time 

will count. When the timer is done ’set’ will become true. 

FRD (bcd_input, delay_time); 

t.PRE := delay_time; 

IF (test_input) THEN 

t.EnableTimer := 1; 

ELSE 

t.EnableTimer := 0; 

END_IF; 

TONR(t); 

set := t.DN; 

Figure 19.20 

Function Data Conversions 

Most of the IEC61131-3 defined functions with arguments are given in Figure 

19.21. Some of the functions can be overloaded, for example ADD could have more than 

two values to add, and others have optional arguments. In most cases the optional arguments 

are things like preset values for timers. When arguments are left out they default to 

values, typically 0. ControlLogix uses many of the standard function names and arguments 

but does not support the overloading part of the standard. 


plc st - 19.12 

Function 

ABS(A); 

ACOS(A); 

ADD(A,B,...); 

AND(A,B,...); 

ASIN(A); 

ATAN(A); 

BCD_TO_INT(A); 

CONCAT(A,B,...); 

COS(A); 

CTD(CD:=A,LD:=B,PV:=C); 

CTU(CU:=A,R:=B,PV:=C); 

CTUD(CU:=A,CD:=B,R:=C,LD: 

=D,PV:=E); 

DELETE(IN:=A,L:=B,P:=C); 

DIV(A,B); 

EQ(A,B,C,...); 

EXP(A); 

EXPT(A,B); 

FIND(IN1:=A,IN2:=B); 

F_TRIG(A); 

GE(A,B,C,...); 

GT(A,B,C,...); 

INSERT(IN1:=A,IN2:=B,P:=C); 

INT_TO_BCD(A); 

INT_TO_REAL(A); 

LE(A,B,C,...); 

LEFT(IN:=A,L:=B); 

LEN(A); 

LIMIT(MN:=A,IN:=B,MX:=C); 

LN(A); 

LOG(A); 

LT(A,B,C,...); 

MAX(A,B,...); 

MID(IN:=A,L:=B,P:=C); 

MIN(A,B,...); 

MOD(A,B); 

MOVE(A); 

MUL(A,B,...); 

MUX(A,B,C,...); 

NE(A,B); 

NOT(A); 

OR(A,B,...); 

Description 

absolute value of A 

the inverse cosine of A 

add A+B+... 

logical and of inputs A,B,... 

the inverse sine of A 

the inverse tangent of A 

converts a BCD to an integer 

will return strings A,B,... joined together 

finds the cosine of A 

down counter active =C, A decreases, B resets 

up/down counter combined functions of the up and 

down counters 

will delete B characters at position C in string A 

A/B 

will compare A=B=C=... 

finds e**A where e is the natural number 

A**B 

will find the start of string B in string A 

a falling edge trigger 

will compare A>=B, B>=C, C>=... 

will compare A>B, B>C, C>... 

will insert string B into A at position C 

converts an integer to BCD 

converts A from integer to real 

will compare A

plc st - 19.13 

Function 

REAL_TO_INT(A); 

REPLACE(IN1:=A,IN2:=B,L:= 

C,P:=D); 

RIGHT(IN:=A,L:=B); 

ROL(IN:=A,N:=B); 

ROR(IN:=A,N:=B); 

RS(A,B); 

RTC(IN:=A,PDT:=B); 

R_TRIG(A); 

SEL(A,B,C); 

SHL(IN:=A,N:=B); 

SHR(IN:=A,N:=B); 

SIN(A); 

SQRT(A); 

SR(S1:=A,R:=B); 

SUB(A,B); 

TAN(A); 

TOF(IN:=A,PT:=B); 

TON(IN:=A,PT:=B); 

TP(IN:=A,PT:=B); 

TRUNC(A); 

XOR(A,B,...); 

Description 

converts A from real to integer 

will replace C characters at position D in string A with 

string B 

will return the right A characters of string B 

rolls left value A of length B bits 

rolls right value A of length B bits 

RS flip flop with input A and B 

will set and/or return current system time 

a rising edge trigger 

if a=0 output B if A=1 output C 

shift left value A of length B bits 

shift right value A of length B bits 

finds the sine of A 

square root of A 

SR flipflop with inputs A and B 

A-B 

finds the tangent of A 

off delay timer 

on delay timer 

pulse timer - a rising edge fires a fixed period pulse 

converts a real to an integer, no rounding 

logical exclusive or of inputs A,B,... 

Figure 19.21 

Structured Text Functions 

Control programs can become very large. When written in a single program these 

become confusing, and hard to write/debug. The best way to avoid the endless main program 

is to use subroutines to divide the main program. The IEC61131 standard allows the 

definition of subroutines/functions as shown in Figure 19.22. The function will accept up 

to three inputs and perform a simple calculation. It then returns one value. As mentioned 

before ControlLogix does not support overloading, so the function would not be able to 

have a variable size argument list. 


plc st - 19.14 

.... 

D := TEST(1.3, 3.4); (* sample calling program, here C will default to 3.14 *) 

E := TEST(1.3, 3.4, 6.28); (* here C will be given a new value *) 

.... 

FUNCTION TEST : REAL 

VAR_INPUT A, B : REAL; C : REAL := 3.14159; END VAR 

TEST := (A + B) / C; 

END_FUNCTION 

Figure 19.22 

Declaration of a Function 

19.3 AN EXAMPLE 

The example beginning in Figure 19.24 shows a subroutine implementing traffic 

lights in ST for the ControlLogix processor. The variable ’state’ is used to keep track of 

the current state of the lights. Timer enable bits are used to determine which transition 

should be checked. Finally the value of ’state’ is used to set the outputs. (Note: this is possible 

because ’=’ and ’:=’ are not the same.) This subroutine would be stored under a name 

such as ’TrafficLights’. It would then be called from the main program as shown in Figure 

19.23. 

JSR 

Function Name: TrafficLights 

Figure 19.23 

The Main Traffic Light Program 


plc st - 19.15 

SBR(); 

IF S:FS THEN 

state := 0; 

green_EW.TimerEnable := 1; 

yellow_EW.TimerEnable := 0; 

green_NS.TimerEnable := 0; 

yellow_NS.TimerEnable := 0; 

END_IF; 

TONR(green_EW); TONR(yellow_EW); 

TONR(green_NS); TONR(yellow_NS); 

CASE state OF 

0: IF green_EW.DN THEN 

state :=1; 



END_IF 

1: IF yellow_EW.DN THEN 

state :=2; 



END_IF 

2: IF green_NS.DN THEN 

state :=3; 



END_IF 

3: IF yellow_NS.DN THEN 

state :=0; 



END_IF 

Note: This example is for the AB 

ControlLogix platform, so it 

does not show the normal 

function and tag definitions. 

These are done separately in 

the tag editor. 

state : DINT 

green_EW : FBD_TIMER 

yellow_EW : FBD_TIMER 

green_NS : FBD_TIMER 

yellow_NS : FBD_TIMER 

light_EW_green : BOOL alias = 

rack:1:O.Data.0 

light_EW_yellow : BOOL alias = 


light_EW_red : BOOL alias = 


light_NS_green : BOOL alias = 


light_NS_yellow : BOOL alias = 


light_NS_red : BOOL alias = 


light_EW_green := (state = 0); 

light_EW_yellow := (state = 1); 

light_EW_red := (state = 2) OR (state = 3); 

light_NS_green := (state = 2); 

light_NS_yellow := (state = 3); 

light_NS_red := (state = 0) OR (state = 1); 

RET(); 

Figure 19.24 

Traffic Light Subroutine 


plc st - 19.16 

19.4 SUMMARY 

• Structured text programming variables, functions, syntax were discussed. 

• The differences between the standard and the Allen Bradley implementation 

were indicated as appropriate. 

• A traffic light example was used to illustrate a ControlLogix application 


1. 


1. 


1. Implement the following Boolean equations in a Structured Text program. If the program was 

for a state machine what changes would be required to make it work? 

light = ( light + dark • switch) • switch • light 

dark = ( dark + light • switch) • switch • dark 

2. Convert the following state diagram to ladder logic using Structured Text programming. 

C 

FS A B 

X Y Z 

D 

E 

3. Write logic for a traffic light controller using structured text. 

4. A temperature value is stored in F8:0. When it rises above 40 the following sequence should 

occur once. Write a ladder logic program that implement this function with a Structured Text 


plc st - 19.17 

program. 

horn 

2 5 11 15 t (s) 

5. Write a structured text program to control a press that has an advance and retract with limit 

switches. The press is started and stopped with start and stop buttons. 

6. Write a structured text program to sort a set of ten integer numbers and then find the median 

value. 


plc sfc - 20.1 

20. SEQUENTIAL FUNCTION CHARTS 

Topics: 

• Describing process control SFCs 

• Conversion of SFCs to ladder logic 

Objectives: 

• Learn to recognize parallel control problems. 

• Be able to develop SFCs for a process. 

• Be able to convert SFCs to ladder logic. 


All of the previous methods are well suited to processes that have a single state 

active at any one time. This is adequate for simpler machines and processes, but more 

complex machines are designed perform simultaneous operations. This requires a controller 

that is capable of concurrent processing - this means more than one state will be active 

at any one time. This could be achieved with multiple state diagrams, or with more mature 

techniques such as Sequential Function Charts. 

Sequential Function Charts (SFCs) are a graphical technique for writing concurrent 

control programs. (Note: They are also known as Grafcet or IEC 848.) SFCs are a 

subset of the more complex Petri net techniques that are discussed in another chapter. The 

basic elements of an SFC diagram are shown in Figure 20.1 and Figure 20.2. 



flowlines - connects steps and transitions (these basically indicate sequence) 

transition - causes a shift between steps, acts as a point of coordination 

Allows control to move to the next step when conditions 

met (basically an if or wait instruction) 

initial step - the first step 

step - basically a state of operation. A state often has an associated action 

step 

action 

macrostep - a collection of steps (basically a subroutine 

Figure 20.1 

Basic Elements in SFCs 



selection branch - an OR - only one path is followed 

simultaneous branch - an AND - both (or more) paths are followed 

Figure 20.2 

Basic Elements in SFCs 

The example in Figure 20.3 shows a SFC for control of a two door security system. 

One door requires a two digit entry code, the second door requires a three digit entry code. 

The execution of the system starts at the top of the diagram at the Start block when the 

power is turned on. There is an action associated with the Start block that locks the doors. 

(Note: in practice the SFC uses ladder logic for inputs and outputs, but this is not shown 

on the diagram.) After the start block the diagram immediately splits the execution into 

two processes and both steps 1 and 6 are active. Steps are quite similar to states in state 

diagrams. The transitions are similar to transitions in state diagrams, but they are drawn 

with thick lines that cross the normal transition path. When the right logical conditions are 

satisfied the transition will stop one step and start the next. While step 1 is active there are 

two possible transitions that could occur. If the first combination digit is correct then step 

1 will become inactive and step 2 will become active. If the digit is incorrect then the transition 

will then go on to wait for the later transition for the 5 second delay, and after that 

step 5 will be active. Step 1 does not have an action associated, so nothing should be done 

while waiting for either of the transitions. The logic for both of the doors will repeat once 

the cycle of combination-unlock-delay-lock has completed. 



Start 

lock doors 

1st digit 

OK 

1 

1st digit 

wrong 

1st digit 

OK 

6 

1st digit 

wrong 

2 

7 

2st digit 

OK 

2nd digit 

wrong 

2st digit 

OK 

2nd digit 

wrong 

3rd digit 

OK 

5 sec. 

delay 

3 

4 

unlock#1 

3rd digit 

wrong 

5 sec. 

delay 

8 

unlock#2 

9 relock#2 

5 relock#1 

Parallel/Concurrent because things happen separately, but at same time 

(this can also be done with state transition diagrams) 

Figure 20.3 

SFC for Control of Two Doors with Security Codes 

A simple SFC for controlling a stamping press is shown in Figure 20.4. (Note: this 

controller only has a single thread of execution, so it could also be implemented with state 

diagrams, flowcharts, or other methods.) In the diagram the press starts in an idle state. 

when an automatic button is pushed the press will turn on the press power and lights. 

When a part is detected the press ram will advance down to the bottom limit switch. The 



press will then retract the ram until the top limit switch is contacted, and the ram will be 

stopped. A stop button can stop the press only when it is advancing. (Note: normal designs 

require that stops work all the time.) When the press is stopped a reset button must be 

pushed before the automatic button can be pushed again. After step 6 the press will wait 

until the part is not present before waiting for the next part. Without this logic the press 

would cycle continuously. 

7 

reset 

button 

automatic 

button 

1 

1 

6 

2 power on 

light on 

part not 

detected 

part detect 

2 

3 advance on 

part hold on 

4 

5 

stop 

button 

light off 

advance off 

power off 

3 

5 

bottom 

limit 

4 advance off 

retract on 

top 

limit 

6 retract off 

part hold off 

Figure 20.4 

SFC for Controlling a Stamping Press 



The SFC can be converted directly to ladder logic with methods very similar to 

those used for state diagrams as shown in Figure 20.5 to Figure 20.9. The method shown is 

patterned after the block logic method. One significant difference is that the transitions 

must now be considered separately. The ladder logic begins with a section to initialize the 

states and transitions to a single value. The next section of the ladder logic considers the 

transitions and then checks for transition conditions. If satisfied the following step or transition 

can be turned on, and the transition turned off. This is followed by ladder logic to 

turn on outputs as requires by the steps. This section of ladder logic corresponds to the 

actions for each step. After that the steps are considered, and the logic moves to the following 

transitions or steps. The sequence examine transitions, do actions then do steps is 

very important. If other sequences are used outputs may not be actuated, or steps missed 

entirely. 



first scan 

INITIALIZE STEPS AND TRANSITIONS 

L 

step 1 

U 

step 2 

U 

step 3 

U 

step 4 

U 

step 5 

U 

step 6 

U 

transition 1 

U 

transition 2 

U 

transition 3 

U 

transition 4 

U 

transition 5 

U 

transition 6 

U 

transition 7 

Figure 20.5 

SFC Implemented in Ladder Logic 



CHECK TRANSITIONS 

transition 1 

automatic on 

L 

step 2 

U 

transition 1 

transition 7 

reset button 

L 

step 1 

U 

transition 7 

transition 2 

part detect 

L 

step 3 

U 

transition 2 

transition 3 

bottom limit 

L 

step 4 

U 

transition 3 

U 

transition 4 

transition 4 

stop button 

L 

step 5 

U 

transition 3 

U 

transition 4 

Figure 20.6 




transition 5 

top limit 

L 

step 6 

U 

transition 5 

transition 6 

part detected 

L 

step 2 

PERFORM ACTIVITIES FOR STEPS 

step 2 

U 

L 

transition 6 

power 

step 3 

L 

L 

light 

advance 

step 4 

L 

L 

part hold 

retract 

step 5 

U 

U 

advance 

light 

U 

advance 

U 

power 

Figure 20.7 



plc sfc - 20.10 

step 6 

U 

retract 

ENABLE TRANSITIONS 

step 1 

U 

U 

part hold 

step 1 

step 2 

L 

U 

transition 1 

step 2 

step 3 

L 

U 

transition 2 

step 3 

L 

transition 3 

step 4 

L 

U 

transition 4 

step 4 

step 5 

L 

U 

transition 5 

step 5 

L 

transition 7 

Figure 20.8 



plc sfc - 20.11 

step 6 

U 

step 6 

L 

transition 6 

Figure 20.9 


Many PLCs also allow SFCs to entered be as graphic diagrams. Small segments of 

ladder logic must then be entered for each transition and action. Each segment of ladder 

logic is kept in a separate program. If we consider the previous example the SFC diagram 

would be numbered as shown in Figure 20.10. The numbers are sequential and are for 

both transitions and steps. 


plc sfc - 20.12 

13 

reset 

button 

automatic 

button 

8 

2 

15 

3 power on 

light on 

part not 

detected 

part detect 

10 

4 advance on 

part hold on 

12 stop 

button 

7 light off 

advance off 

power off 

11 

14 

bottom 

limit 

5 advance off 

retract on 

top 

limit 

6 retract off 

part hold off 

Figure 20.10 

SFC Renumbered 

Some of the ladder logic for the SFC is shown in Figure 20.11. Each program corresponds 

to the number on the diagram. The ladder logic includes a new instruction, EOT, 

that will tell the PLC when a transition has completed. When the rung of ladder logic with 

the EOT output becomes true the SFC will move to the next step or transition. when developing 

graphical SFCs the ladder logic becomes very simple, and the PLC deals with turning 

states on and off properly. 


plc sfc - 20.13 

Program 3 (for step #3) 

L 

power 

L 

light 

Program 10 (for transition #10) 

part detect 

EOT step 2 

Program 4 (for step #3) 

L 

advance 

L 

part hold 

Program 11 (for transition #10) 

bottom limit 

EOT step 2 

Figure 20.11 

Sample Ladder Logic for a Graphical SFC Program 

SFCs can also be implemented using ladder logic that is not based on latches, or 

built in SFC capabilities. The previous SFC example is implemented below. The first segment 

of ladder logic in Figure 20.12 is for the transitions. The logic for the steps is shown 



plc sfc - 20.14 

ST7 

reset button 

TR13 

ST2 

automatic button 

TR8 

ST6 

part not detected 

TR15 

ST3 

part detect 

TR10 

ST4 

bottom limit 

TR11 

ST4 

stop button 

TR12 

ST5 

top limit 

TR14 

Figure 20.12 

Ladder logic for transitions 


plc sfc - 20.15 

ST2 

TR8 

ST2 

TR13 

FS 

ST3 

TR10 

ST3 

TR8 

TR15 

ST4 

TR11 

TR12 

ST4 

TR10 

ST5 

TR14 

ST5 

TR11 

TR12 

ST6 

TR13 

ST6 

TR14 

ST7 

TR13 

ST7 

TR12 

Figure 20.13 

Step logic 


plc sfc - 20.16 

Aside: The SFC approach can also be implemented with traditional programming languages. 

The example below shows the previous example implemented for a Basic 

Stamp II microcontroller. 

autoon = 1; detect=2; bottom=3; top=4; stop=5;reset=6 ‘define input pins 

input autoon; input detect; input button; input top; input stop; input reset 

s1=1; s2=0; s3=0; s4=0; s5=0; s6=0 ‘set to initial step 

advan=7;onlite=8; hold=9;retrac=10 ‘define outputs 

output advan; output onlite; output hold; output retrac 

step1: if s11 then step2; s1=2 





step6: if s61 then trans1; s6=2 

trans1: if (in11 or s12) then trans2;s1=0;s2=1 

trans2: (if in21 or s22) then trans3;s2=0;s3=1 

trans3: ................... 

stepa1: if (st21) then goto stepa2: high onlite 

................. 

goto step1 

Figure 20.14 

Implementing SFCs with High Level Languages 

20.2 A COMPARISON OF METHODS 

These methods are suited to different controller designs. The most basic controllers 

can be developed using process sequence bits and flowcharts. More complex control 

problems should be solved with state diagrams. If the controller needs to control concurrent 

processes the SFC methods could be used. It is also possible to mix methods together. 

For example, it is quite common to mix state based approaches with normal conditional 

logic. It is also possible to make a concurrent system using two or more state diagrams. 

20.3 SUMMARY 

• Sequential function charts are suited to processes with parallel operations 

• Controller diagrams can be converted to ladder logic using MCR blocks 

• The sequence of operations is important when converting SFCs to ladder logic. 


plc sfc - 20.17 


1. Develop an SFC for a two person assembly station. The station has two presses that may be 

used at the same time. Each press has a cycle button that will start the advance of the press. A 

bottom limit switch will stop the advance, and the cylinder must then be retracted until a top 

limit switch is hit. 

2. Create an SFC for traffic light control. The lights should have cross walk buttons for both directions 

of traffic lights. A normal light sequence for both directions will be green 16 seconds and 

yellow 4 seconds. If the cross walk button has been pushed, a walk light will be on for 10 seconds, 

and the green light will be extended to 24 seconds. 

3. Draw an SFC for a stamping press that can advance and retract when a cycle button is pushed, 

and then stop until the button is pushed again. 

4. Design a garage door controller using an SFC. The behavior of the garage door controller is as 

follows, 










plc sfc - 20.18 


1. 

start 

start button #1 

start button #2 

press #1 adv. 

press #2 adv. 

bottom limit switch #1 

bottom limit switch #2 

press #1 retract 

press #2 retract 

top limit switch #1 

top limit switch #2 

press #1 off 

press #2 off 


plc sfc - 20.19 

2. 

Start 

EW crosswalk button 

NO EW crosswalk button 

red NS, green EW 

walk light on for 10s 

24s delay 

16s delay 


red NS, yellow EW 

4s delay 

EW crosswalk button 

NO EW crosswalk button 


walk light on for 10s 

24s delay 

16s delay 


red NS, yellow EW 

4s delay 


plc sfc - 20.20 

3. 

start 

idle 

cycle button 

advance 

advance limit switch 

retract 

retract limit switch 


plc sfc - 20.21 

4. 

step 1 

step 2 

T1 

button + remote 

step 3 

close door 

T3 

light beam 

T2 

step 4 

button + remote + bottom limit 

T4 

button + remote 

step 5 

T5 

open door 

button + remote + top limit 


plc sfc - 20.22 

first scan 

L 

U 

U 

U 

U 

step 1 

step 2 

step 3 

step 4 

step 5 

U 

T1 

U 

T2 

U 

T3 

U 

U 

T4 

T5 


plc sfc - 20.23 

T1 

remote 

L 

step 3 

button 

U 

T1 

T2 

remote 

L 

step 4 

button 

U 

T2 

bottom limit 

U 

T3 

T3 

light beam 

L 

step 5 

U 

T2 

U 

T3 

T4 

remote 

L 

step 5 

button 

U 

T4 

T5 

remote 

L 

step 2 

button 

U 

T5 

top limit 


plc sfc - 20.24 

step 2 

step 4 

step 3 

step 5 

U 

U 

L 

L 

door open 

door close 

door close 

door open 

step 3 

step 5 

TOF 

T4:0 

preset 300s 

T4:0/DN 

garage light 


plc sfc - 20.25 

step 1 

step 2 

step 3 

step 4 

step 5 

U 

L 

U 

L 

U 

L 

L 

U 

L 

U 

L 

step 1 

step 2 

step 2 

T1 

step 3 

T2 

T3 

step 4 

T4 

step 5 

T5 


1. Develop an SFC for a vending machine and expand it into ladder logic. 


plc fb - 21.1 

21. FUNCTION BLOCK PROGRAMMING 

Topics: 

• The basic construction of FBDs 

• The relationship between ST and FBDs 

• Constructing function blocks with structured text 

• Design case 

Objectives: 

• To be able to write simple FBD programs 


Function Block Diagrams (FBDs) are another part of the IEC 61131-3 standard. 

The primary concept behind a FBD is data flow. In these types of programs the values 

flow from the inputs to the outputs, through function blocks. A sample FBD is shown in 

Figure 21.1. In this program the inputs N7:0 and N7:1 are used to calculate a value 

sin(N7:0) * ln(N7:1). The result of this calculation is compared to N7:2. If the calculated 

value is less than N7:2 then the output O:000/01 is turned on, otherwise it is turned off. 

Many readers will note the similarity of the program to block diagrams for control systems. 

N7:0 

N7:1 

N7:2 

SIN 

LN 

A 

* A 

B 

Figure 21.1 

A Simple Comparison Program 


plc fb - 21.2 

A FBD program is constructed using function blocks that are connected together to 

define the data exchange. The connecting lines will have a data type that must be compatible 

on both ends. The inputs and outputs of function blocks can be inverted. This is normally 

shown with a small circle at the point where the line touches the function block, as 


input output input output 

inverted input 

inverted output 

Figure 21.2 

Inverting Inputs and Outputs on Function Blocks 

The basic functions used in FBD programs are equivalent to the basic set used in 

Structured Text (ST) programs. Consider the basic addition function shown in Figure 21.3. 

The ST function on the left adds A and B, and stores the result in O. The function block on 

the right is equivalent. By convention the inputs are on the left of the function blocks, and 

the outputs on the right. 

Structural Text Function 

Function Block Equivalent 

O := ADD(A, B); 

A 

B 

ADD 

O 

Figure 21.3 

A Simple Function Block 

Some functions allow a variable number of arguments. In Figure 21.4 there is a 

third value input to the ADD block. This is known as overloading. 


plc fb - 21.3 



O := ADD(A, B, C); 

A 

B 

ADD 

O 

C 

Figure 21.4 

A Function with A Variable Argument List 

The ADD function in the previous example will add all of the arguments in any 

order and get the same result, but other functions are more particular. Consider the circular 

limit function shown in Figure 21.5. In the first ST function the maximum MX, minimum 

MN and test IN values are all used. In the second function the MX value is not defined and 

will default to 0. Both of the ST functions relate directly to the function blocks on the right 

side of the figure. 



O := LIM(MN := A, IN := B, MX := C); 

A 

B 

C 

MN 

IN 

MX 

LIM 

O 

O := LIM(MN := A, IN := B); 

A 

MN 

LIM 

O 

B 

IN 

Figure 21.5 

Function Argument Lists 

21.2 CREATING FUNCTION BLOCKS 

When developing a complex system it is desirable to create additional function 

blocks. This can be done with other FBDs, or using other IEC 61131-3 program types. 


plc fb - 21.4 

Figure 21.6 shows a divide function block created using ST. In this example the first statement 

declares it as a FUNCTION_BLOCK called divide. The input variables a and b, and 

the output variable c are declared. In the function the denominator is checked to make sure 

it is not 0. If not, the division will be performed, otherwise the output will be zero. 

divide 

a 

b 

c 

FUNCTION_BLOCK divide 

VAR_INPUT 

a: INT; 

b: INT; 

END_VAR 

VAR_OUTPUT 

c: INT; 

END_VAR 

IF b 0 THEN 

c := a / b; 

ELSE 

c := 0; 

END_IF; 

END_FUNCTION_BLOCK 

Figure 21.6 

Function Block Equivalencies 

21.3 DESIGN CASE 

21.4 SUMMARY 

• FBDs use data flow from left to right through function blocks 

• Inputs and outputs can be inverted 

• Function blocks can have variable argument list sizes 

• When arguments are left off default values are used 

• Function blocks can be created with ST 


plc fb - 21.5 




1. Develop a FBD for a system that will monitor a high temperature salt bath. The systems has 

start and stop buttons as normal. The temperature for the salt bath is available in temp. If the 

bath is above 250 C then the heater should be turned off. If the temperature is below 220 C 

then the heater should be turned on. Once the system has been in the acceptable range for 10 

minutes the system should shut off. 

2. Write a Function Block Diagram program to implement the following timing diagram. The 

sequence should begin when a variable ‘temp’ rises above 80. 

horn 

2 5 11 15 t (s) 

3. Convert the following state diagram to ladder logic using Function Block Diagrams. 

C 

FS A B 

X Y Z 

D 

E 


plc analog - 22.1 

22. ANALOG INPUTS AND OUTPUTS 

Topics: 

• Analog inputs and outputs 

• Sampling issues; aliasing, quantization error, resolution 

• Analog I/O with a PLC 

Objectives: 

• To understand the basics of conversion to and from analog values. 

• Be able to use analog I/O on a PLC. 


An analog value is continuous, not discrete, as shown in Figure 22.1. In the previous 

chapters, techniques were discussed for designing logical control systems that had 

inputs and outputs that could only be on or off. These systems are less common than the 

logical control systems, but they are very important. In this chapter we will examine analog 

inputs and outputs so that we may design continuous control systems in a later chapter. 

Voltage 

logical 

continuous 

t 

Figure 22.1 

Logical and Continuous Values 

Typical analog inputs and outputs for PLCs are listed below. Actuators and sensors 

that can be used with analog inputs and outputs will be discussed in later chapters. 

Inputs: 

• oven temperature 

• fluid pressure 

• fluid flow rate 



Outputs: 

• fluid valve position 

• motor position 

• motor velocity 

This chapter will focus on the general principles behind digital-to-analog (D/A) 

and analog-to-digital (A/D) conversion. The chapter will show how to output and input 

analog values with a PLC. 

22.2 ANALOG INPUTS 

To input an analog voltage (into a PLC or any other computer) the continuous voltage 

value must be sampled and then converted to a numerical value by an A/D converter. 

Figure 22.2 shows a continuous voltage changing over time. There are three samples 

shown on the figure. The process of sampling the data is not instantaneous, so each sample 

has a start and stop time. The time required to acquire the sample is called the sampling 

time. A/D converters can only acquire a limited number of samples per second. The time 

between samples is called the sampling period T, and the inverse of the sampling period is 

the sampling frequency (also called sampling rate). The sampling time is often much 

smaller than the sampling period. The sampling frequency is specified when buying hardware, 

but for a PLC a maximum sampling rate might be 20Hz. 

Voltage is sampled during these time periods 

voltage 

time 

T = (Sampling Frequency) -1 

Sampling time 

Figure 22.2 

Sampling an Analog Voltage 



A more realistic drawing of sampled data is shown in Figure 22.3. This data is 

noisier, and even between the start and end of the data sample there is a significant change 

in the voltage value. The data value sampled will be somewhere between the voltage at the 

start and end of the sample. The maximum (Vmax) and minimum (Vmin) voltages are a 

function of the control hardware. These are often specified when purchasing hardware, but 

reasonable ranges are; 

0V to 5V 

0V to 10V 

-5V to 5V 

-10V to 10V 

The number of bits of the A/D converter is the number of bits in the result word. If 

the A/D converter is 8 bit then the result can read up to 256 different voltage levels. Most 

A/D converters have 12 bits, 16 bit converters are used for precision measurements. 



Vt () 

V max 

Vt ( 2 ) 

Vt ( 1 ) 

V min 

τ 

t 

where, 

Vt () = the actual voltage over time 

τ 

= 

t 1 

t 2 

sample interval for A/D converter 

t = time 

t 1 , t 2 = time at start,end of sample 

Vt ( 1 

), Vt ( 2 

) = voltage at start, end of sample 

V min , V max = input voltage range of A/D converter 

N 

= 

number of bits in the A/D converter 

Figure 22.3 

Parameters for an A/D Conversion 

The parameters defined in Figure 22.3 can be used to calculate values for A/D converters. 

These equations are summarized in Figure 22.4. Equation 1 relates the number of 

bits of an A/D converter to the resolution. In a normal A/D converter the minimum range 

value, Rmin, is zero, however some devices will provide 2’s compliment negative numbers 

for negative voltages. Equation 2 gives the error that can be expected with an A/D 

converter given the range between the minimum and maximum voltages, and the resolution 

(this is commonly called the quantization error). Equation 3 relates the voltage range 

and resolution to the voltage input to estimate the integer that the A/D converter will 

record. Finally, equation 4 allows a conversion between the integer value from the A/D 

converter, and a voltage in the computer. 



R = 2 N = R max – R min 

V 

V max 

– V min 

ERROR 

= ⎛---------------------------- 

⎞ 

⎝ 2R ⎠ 

(1) 

(2) 

V I 

= 

INT 

V in 

⎛ – 

⎝ 

---------------------------- ⎞ 

– ⎠ ( R – 1) 

+ Rmin 

V max 

V min 

V min 

(3) 

V 

V I 

– R min 

C = ⎛--------------------- 

⎞( Vmax – V 

⎝ ( R – 1) 

⎠ 

min ) + V min 

(4) 

where, 

RR , min , R max = absolute and relative resolution of A/D converter 

V I 

V C 

= the integer value representing the input voltage 

= the voltage calculated from the integer value 

V ERROR 

= 

the maximum quantization error 

Figure 22.4 

A/D Converter Equations 

Consider a simple example, a 10 bit A/D converter can read voltages between - 

10V and 10V. This gives a resolution of 1024, where 0 is -10V and 1023 is +10V. Because 

there are only 1024 steps there is a maximum error of ±9.8mV. If a voltage of 4.564V is 

input into the PLC, the A/D converter converts the voltage to an integer value of 745. 

When we convert this back to a voltage the result is 4.565V. The resulting quantization 

error is 4.565V-4.564V=+0.001V. This error can be reduced by selecting an A/D converter 

with more bits. Each bit halves the quantization error. 



Given, 

N = 10, R min 

= 0 

= 10V 

V max 

V min 

= 

– 10V 

V in 

= 4.564V 

Calculate, 

R = R max = 2 N = 1024 

V 

V max – V min 

ERROR = ⎛---------------------------- 

⎞ = 0.0098V 

⎝ 2R ⎠ 

V I 

V 

INT in 

– V = ⎛---------------------------- 

min ⎞ ( R – 1) 

+ 0 = 745 

⎝ – ⎠ 

V max 

V min 

V 

V I 

– 0 

C = ⎛-------------⎞( Vmax – V 

⎝R – 1 ⎠ 

min ) + V min = 4.565V 

Figure 22.5 

Sample Calculation of A/D Values 

If the voltage being sampled is changing too fast we may get false readings, as 

shown in Figure 22.6. In the upper graph the waveform completes seven cycles, and 9 

samples are taken. The bottom graph plots out the values read. The sampling frequency 

was too low, so the signal read appears to be different that it actually is, this is called aliasing. 



Figure 22.6 

Low Sampling Frequencies Cause Aliasing 

The Nyquist criterion specifies that sampling frequencies should be at least twice 

the frequency of the signal being measured, otherwise aliasing will occur. The example in 

Figure 22.6 violated this principle, so the signal was aliased. If this happens in real applications 

the process will appear to operate erratically. In practice the sample frequency 

should be 4 or more times faster than the system frequency. 

f AD 

> 2f signal where, 

f AD 

f signal 

= sampling frequency 

= maximum frequency of the input 

There are other practical details that should be considered when designing applications 

with analog inputs; 

• Noise - Since the sampling window for a signal is short, noise will have added 

effect on the signal read. For example, a momentary voltage spike might result 

in a higher than normal reading. Shielded data cables are commonly used to 

reduce the noise levels. 

• Delay - When the sample is requested, a short period of time passes before the 

final sample value is obtained. 

• Multiplexing - Most analog input cards allow multiple inputs. These may share 

the A/D converter using a technique called multiplexing. If there are 4 channels 



using an A/D converter with a maximum sampling rate of 100Hz, the maximum 

sampling rate per channel is 25Hz. 

• Signal Conditioners - Signal conditioners are used to amplify, or filter signals 

coming from transducers, before they are read by the A/D converter. 

• Resistance - A/D converters normally have high input impedance (resistance), so 

they affect circuits they are measuring. 

• Single Ended Inputs - Voltage inputs to a PLC can use a single common for multiple 

inputs, these types of inputs are called single ended inputs. These tend to 

be more prone to noise. 

• Double Ended Inputs - Each double ended input has its own common. This 

reduces problems with electrical noise, but also tends to reduce the number of 

inputs by half. 



ASIDE: This device is an 8 bit A/D converter. The main concept behind this is the successive 

approximation logic. Once the reset is toggled the converter will start by setting 

the most significant bit of the 8 bit number. This will be converted to a voltage Ve that 

is a function of the +/-Vref values. The value of Ve is compared to Vin and a simple 

logic check determines which is larger. If the value of Ve is larger the bit is turned off. 

The logic then repeats similar steps from the most to least significant bits. Once the last 

bit has been set on/off and checked the conversion will be complete, and a done bit can 

be set to indicate a valid conversion value. 

Vin above (+ve) or below (-ve) Ve 

Vin 

+Vref 

+ 

- 

clock 

successive 

approximation 

logic 

8 

D to A 

converter 

Ve 

reset 

done 

-Vref 

8 

data out 

Quite often an A/D converter will multiplex between various inputs. As it switches the 

voltage will be sampled by a sample and hold circuit. This will then be converted to a 

digital value. The sample and hold circuits can be used before the multiplexer to collect 

data values at the same instant in time. 

Figure 22.7 

A Successive Approximation A/D Converter 

22.2.1 Analog Inputs With a PLC-5 

The PLC 5 ladder logic in Figure 22.8 will control an analog input card. The Block 

Transfer Write (BTW) statement will send configuration data from integer memory to the 

analog card in rack 0, slot 0. The data from N7:30 to N7:66 describes the configuration for 

different input channels. Once the analog input card receives this it will start doing analog 



conversions. The instruction is edge triggered, so it is run with the first scan, but the input 

is turned off while it is active, BT10:0/EN. This instruction will require multiple scans 

before all of the data has been written to the card. The update input is only needed if the 

configuration for the input changes, but this would be unusual. The Block Transfer Read 

(BTR) will retrieve data from the card and store it in memory N7:10 to N7:29. This data 

will contain the analog input values. The function is edge triggered, so the enable bits prevent 

it from trying to read data before the card is configured BT10:0/EN. The BT10:1/EN 

bit will prevent if from starting another read until the previous one is complete. Without 

these the instructions experience continuous errors. The MOV instruction will move the 

data value from one analog input to another memory location when the BTR instruction is 

done. 

update 

S2:1/15 

BT10:0/EN 

BTW 

Rack: 0 

Group: 0 

Module: 0 

BT Array: BT10:0 

Data File: N7:30 

Length: 37 

Continuous: no 

BT10:0/EN 

BT10:1/EN 

BTR 

Rack: 0 

Group: 0 

Module: 0 



Length: 20 


BT10:1/DN 

MOV 

Source N7:15 

Dest N7:0 

note: 

analog 

channel #2 

Note: The basic operation is that the BTW will send the control block to the input 

card. The inputs are used because the BTR and BTW commands may take longer 

than one scan. 

Figure 22.8 

Ladder Logic to Control an Analog Input Card 

The data to configure a 1771-IFE Analog Input Card is shown in Figure 22.9. 



(Note: each type of card will be different, and you need to refer to the manuals for this 

information.) The 1771-IFE is a 12 bit card, so the range will have up to 2**12 = 4096 

values. The card can have 8 double ended inputs, or 16 single ended inputs (these are set 

with jumpers on the board). To configure the card a total of 37 data words are needed. The 

voltage range of different inputs are set using the bits in word 0 (N7:30) and 1 (N7:31). 

For example, to set the voltage range on channel 10 to -5V to 5V we would need to set the 

bits, N7:31/3 = 1 and N7:31/2 = 0. Bits in data word 2 (N7:32) are set to determine the 

general configuration of the card. For example, if word 2 was 0001 0100 0000 0000b the 

card would be set for; a delay of 00010 between samples, to return 2s compliment results, 

using single ended inputs, and no filtering. The remaining data words, from 3 to 36, allow 

data values to be scaled to a new range. Words 3 and 4 are for channel 1, words 5 and 6 are 

for channels 2 and so on. To scale the data, the new minimum value is put in the first word 

(word 3 for channel 1), and the maximum value is put in the second word (word 4 for 

channel 1). The card then automatically converts the actual data reading between 0 and 

4095 to the new data range indicated in word 3 and 4. One oddity of this card is that the 

data values for scaling must always be BCD, regardless of the data type setting. The manual 

for this card claims that putting zeros in the scaling values will cause the card to leave 

the data unscaled, but in practice it is better to enter values of 0 for the minimum and 4095 

for the maximum. 



N7:30 

0 

1 

2 

3 

4 

5 

6 

R8 R8 R7 R7 R6 R6 R5 R5 R4 R4 R3 R3 R2 R2 R1 R1 

R16 R16 R15 R15 R14 R14 R13 R13 R12 R12 R11 R11 R10 R10 R9 R9 

S S S S S N N T F F F F F F F F 

L1 

U1 

L2 

U2 

33 

34 

35 

36 

L15 

U15 

L16 

U16 

R1,R2,...R16 - range values 00 

01 

10 

11 

1 to 5V 

0 to 5V 

-5 to 5V 

-10 to 10V 

T - input type - (0) gives single ended, (1) gives double ended 

N - data format - 

00 

01 

10 

11 

BCD 

not used 

2’s complement binary 

signed magnitude binary 

F - filter function - a value of (0) will result in no filtering, up to a value of (99BCD) 

S - real time sampling mode - (0) samples always, (11111binary) gives long delays. 

L1,L2,...L16 - lower input scaling word values 

U1,U2,...,U16 - upper input scaling word values 

Figure 22.9 

Configuration Data for an 1771-IFE Analog Input Card 

The block of data returned by the BTR statement is shown in Figure 22.10. Bits 0- 

2 in word 0 (N7:10) will indicate the status of the card, such as error conditions. Words 1 

to 4 will reflect status values for each channel. Words 1 and 2 indicate if the input voltage 

is outside the set range (e.g., -5V to 5V). Word 3 gives the sign of the data, which is 



important if the data is not in 2s compliment form. Word 4 indicates when data has been 

read from a channel. The data values for the analog inputs are stored in words from 5 to 

19. In this example, the status for channel 9 are N7:11/8 (under range), N7:12/8 (over 

range), N7:13/8 (sign) and N7:14/8 (data read). The data value for channel 9 is in N7:13. 

N7:10 

0 

1 

2 

3 

4 

D D D 

u16 u15 u14 u13 u12 u11 u10 u9 u8 u7 u6 u5 u4 u3 u2 u1 

v16 v15 v14 v13 v12 v11 v10 v9 v8 v7 v6 v5 v4 v3 v2 v1 

s16 s15 s14 s13 s12 s11 s10 s9 s8 s7 s6 s5 s4 s3 s2 s1 

d1 d1 d1 d1 d1 d1 d1 d1 d1 d1 d1 d1 d1 d1 d1 d1 

19 

d16 d16 d16 d16 d16 d16 d16 d16 d16 d16 d16 d16 d16 d16 d16 d16 

D - diagnostics 

u - under range for input channels 

v - over range for input channels 

s - sign of data 

d - data values read from inputs 

Figure 22.10 

Data Returned by the 1771-IFE Analog Input Card 

Most new PLC programming software provides tools, such as dialog boxes to help 

set up the data parameters for the card. If these aids are not available, the values can be set 

manually in the PLC memory. 

22.3 ANALOG OUTPUTS 

Analog outputs are much simpler than analog inputs. To set an analog output an 

integer is converted to a voltage. This process is very fast, and does not experience the 

timing problems with analog inputs. But, analog outputs are subject to quantization errors. 

Figure 22.11 gives a summary of the important relationships. These relationships are 

almost identical to those of the A/D converter. 



R = 2 N = R max – R min 

V 

V max 

– V min 

ERROR 

= ⎛---------------------------- 

⎞ 

⎝ 2R ⎠ 

V I 

INT V desired 

– V 

= ⎛----------------------------------- 

min ⎞ 

⎝ – ⎠ ( R – 1) 

+ Rmin 

V max 

V min 

V 

V I 

– R min 

output = ⎛--------------------- 

⎞( Vmax – V 

⎝ ( R – 1) 

⎠ 

min ) + V min 

(5) 

(6) 

(7) 

(8) 

where, 

RR , min , R max = absolute and relative resolution of A/D converter 

= the maximum quantization error 

V ERROR 

V I 

= 

V output 

V desired 

the integer value representing the desired voltage 

= the voltage output using the integer value 

= the desired analog output value 

Figure 22.11 

Analog Output Relationships 

Assume we are using an 8 bit D/A converter that outputs values between 0V and 

10V. We have a resolution of 256, where 0 results in an output of 0V and 255 results in 

10V. The quantization error will be 20mV. If we want to output a voltage of 6.234V, we 

would specify an output integer of 159, this would result in an output voltage of 6.235V. 

The quantization error would be 6.235V-6.234V=0.001V. 



Given, 

N = 8, R min 

= 0 

= 10V 

V max 

V min 

Calculate, 

= 

0V 

V desired 

= 6.234V 

R = R max 

= 2 N = 256 

V 

V max 

– V min 

ERROR = ⎛---------------------------- 

⎞ = 0.020V 

⎝ 2R ⎠ 

V I 

V in 

– V = INT ⎛---------------------------- 

min ⎞ ( R – 1) 

+ 0 = 159 

⎝ – ⎠ 

V max 

V min 

V 

V I 

– 0 

C 

= ⎛-------------⎞( Vmax – V 

⎝R – 1 ⎠ 

min 

) + V min 

= 6.235V 

The current output from a D/A converter is normally limited to a small value, typically 

less than 20mA. This is enough for instrumentation, but for high current loads, such 

as motors, a current amplifier is needed. This type of interface will be discussed later. If 

the current limit is exceeded for 5V output, the voltage will decrease (so don’t exceed the 

rated voltage). If the current limit is exceeded for long periods of time the D/A output may 

be damaged. 



ASIDE: 

5KΩ 

MSB bit 3 

10KΩ 

V – 

- 

V ss 

Computer 

bit 2 

bit 1 

20KΩ 

40KΩ 

V + 

+ 

0 

V o 

+ 

- 

LSB 

bit 0 

80KΩ 

First we write the obvious, 

V + 

= 0 = V – 

Next, sum the currents into the inverting input as a function of the output voltage and the 

input voltages from the computer, 

V b3 

V b2 

V b1 

V b0 

-------------- + -------------- + -------------- + -------------- 

10KΩ 20KΩ 40KΩ 80KΩ 

= 

V 

----------- o 

5KΩ 

∴V 

o 

= 0.5V b3 

+ 0.25V b2 

+ 0.125V b1 

+ 0.0625V b0 

Consider an example where the binary output is 1110, with 5V for on, 

∴V 

o 

= 0.5( 5V) + 0.25( 5V) + 0.125( 5V) + 0.625( 0V) 

= 4.375V 

Figure 22.12 

A Digital-To-Analog Converter 

22.3.1 Analog Outputs With A PLC-5 

The PLC-5 ladder logic in Figure 22.13 can be used to set analog output voltages 

with a 1771-OFE Analog Output Card. The BTW instruction will write configuration 

memory to the card (the contents are described later). Values can also be read back from 

the card using a BTR, but this is only valuable when checking the status of the card and 

detecting errors. The BTW is edge triggered, so the BT10:0/EN input prevents the BTW 

from restarting the instruction until the previous block has been sent. The MOV instruc- 



tion will change the output value for channel 1 on the card. 

BT10:0/EN 

update 

Figure 22.13 

Controlling a 1771-OFE Analog Output Card 

Block Transfer Write 

Module Type Generic Block Transfer 

Rack 000 

Group 3 

Module 0 

Control Block BT10:0 

Data File N9:0 

Length 13 

Continuous No 

MOV 

Source 300 

Dest N9:0 

The configuration memory structure for the 1771-OFE Analog Output Card is 

shown in Figure 22.14. The card has four 12 bit output channels. The first four words set 

the output values for the card. Word 0 (N9:0) sets the value for channel 1, word 1 (N9:1) 

sets the value for channel 2, etc. Word 4 configures the card. Bit 16 (N9:4/15) will set the 

data format, bits 5 to 12 (/4 to /11) will enable scaling factors for channels, and bits 1 to 4 

(/0 to /3) will provide signs for the data in words 0 to 3. The words from 5 to 13 allow 

scaling factors, so that the values in words 0 to 3 can be provided in another range of values, 

and then converted to the appropriate values. Good default values for the scaling factors 

are 0 for the lower limit and 4095 for the upper limit. 



N9:0 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

D1 

D2 

D3 

D4 

f s s s s s s s s p4 p3 p2 p1 

L1 

U1 

L2 

U2 

L3 

U3 

L4 

U4 

D - data value words for channels 1, 2, 3 or 4 

f - data format bit (1) binary, (0) BCD 

s - scaling factor bits 

p - data sign bits for the four output channels 

L - lower scaling limit words for output channels 1, 2, 3 or 4 

U - upper scaling limit words for output channels 1, 2, 3 or 4 

Figure 22.14 

Configuration Data for a 1771-OFE Output Card 

22.3.2 Pulse Width Modulation (PWM) Outputs 

An equivalent analog output voltage can be generated using pulse width modulation, 

as shown in Figure 22.15. In this method the output circuitry is only capable of outputing 

a fixed voltage (in the figure ’A’) or 0V. To obtain an analog voltage between the 

maximum and minimum the voltage is turned on and off quickly to reduce the effective 

voltage. The output is a square wave voltage at a high frequency, typically over 20Khz, 

above the hearing range. The duty cycle of the wave determines the effective voltage of 

the output. It is the percentage of time the output is on relative to the time it is off. If the 

duty cycle is 100% the output is always on. If the wave is on for the same time it is off the 

duty cycle is 50%. If the wave is always off, the duty cycle is 0%. 



A 

t 

V eff 

= 

A 

A 

t 

V eff 

= 

------ 

3A 

4 

A 

t 

V eff 

= 

A 

-- 

2 

A 

t 

V eff 

= 

A 

-- 

4 

A 

t 

V eff 

= 0 

Figure 22.15 

Pulse Width Modulated (PWM) Signals 

PWM is commonly used in power electronics, such as servo motor control systems. 

In this case the response time of the motor is slow enough that the motor effectively 

filters the high frequency of the signal. The PWM signal can also be put through a low 

pass filter to produce an analog DC voltage. 



Aside: A basic low pass RC filter is shown below. This circuit is suitable for an analog 

output that does not draw much current. (drawing too much current will result in large 

losses across the resistor.) The corner frequency can be easily found by looking at the 

circuit as a voltage divider. 

V PWM 

R 

C 

V analog 

⎛ 

--------- 

1 ⎞ 

⎜ jωC ⎟ 

1 

V analog = V PWM ⎜-------------------- 

⎟ = V ⎛ 

⎜ 1 PWM ----------------------- ⎞ 

R + --------- ⎟ 

⎝jωCR + 1⎠ 

⎝ jωC⎠ 

V analog 

--------------- 

V PWM 

ω 

= 

------- 

1 

CR 

= ----------------------- 

1 

jωCR + 1 

corner frequency 

As an example consider that the PWM signal is used at a frequency of 100KHz, an it is to 

be used with a system that has a response time (time constant) of 0.1seconds. Therefore 

the corner frequency should be between 10Hz (1/0.1s) and 100KHz. This can be put at 

the mid point of 1000Hz, or 6.2Krad/s. This system also requires the arbitrary selection 

of a resistor or capacitor value. We will pick the capacitor value to be 0.1uF so that we 

don’t need an electrolytic. 

R 

1 1 10 4 

= ------- = ------------------------- = ------- = 1.59KΩ 

Cω 10 – 7 2π10 3 2π 

Figure 22.16 

Converting a PWM Signal to an Analog Voltage 

In some cases the frequency of the output is not fixed, but the duty cycle of the output 

is maintained. 

22.3.3 Shielding 

When a changing magnetic field cuts across a conductor, it will induce a current 



flow. The resistance in the circuits will convert this to a voltage. These unwanted voltages 

result in erroneous readings from sensors, and signal to outputs. Shielding will reduce the 

effects of the interference. When shielding and grounding are done properly, the effects of 

electrical noise will be negligible. Shielding is normally used for; all logical signals in 

noisy environments, high speed counters or high speed circuitry, and all analog signals. 

There are two major approaches to reducing noise; shielding and twisted pairs. 

Shielding involves encasing conductors and electrical equipment with metal. As a result 

electrical equipment is normally housed in metal cases. Wires are normally put in cables 

with a metal sheath surrounding both wires. The metal sheath may be a thin film, or a 

woven metal mesh. Shielded wires are connected at one end to "drain" the unwanted signals 

into the cases of the instruments. Figure 22.17 shows a thermocouple connected with 

a thermocouple. The cross section of the wire contains two insulated conductors. Both of 

the wires are covered with a metal foil, and final covering of insulation finishes the cable. 

The wires are connected to the thermocouple as expected, but the shield is only connected 

on the amplifier end to the case. The case is then connected to the shielding ground, shown 

here as three diagonal lines. 

Two conductor 

shielded cable 

cross section 

Insulated wires 

Metal sheath 

Insulating cover 

Figure 22.17 

Shielding for a Thermocouple 

A twisted pair is shown in Figure 22.18. The two wires are twisted at regular intervals, 

effectively forming small loops. In this case the small loops reverse every twist, so 

any induced currents are cancel out for every two twists. 



1" or less typical 

Figure 22.18 

A Twisted Pair 

When designing shielding, the following design points will reduce the effects of 

electromagnetic interference. 

• Avoid “noisy” equipment when possible. 

• Choose a metal cabinet that will shield the control electronics. 

• Use shielded cables and twisted pair wires. 

• Separate high current, and AC/DC wires from each other when possible. 

• Use current oriented methods such as sourcing and sinking for logical I/O. 

• Use high frequency filters to eliminate high frequency noise. 

• Use power line filters to eliminate noise from the power supply. 


22.4.1 Process Monitor 

the 

Problem: Design ladder logic that will monitor the dimension of a part in a die. If 

Solution: 

22.5 SUMMARY 

• A/D conversion will convert a continuous value to an integer value. 

• D/A conversion is easier and faster and will convert a digital value to an analog 

value. 

• Resolution limits the accuracy of A/D and D/A converters. 

• Sampling too slowly will alias the real signal. 

• Analog inputs are sensitive to noise. 

• The analog I/O cards are configured with a few words of memory. 

• BTW and BTR functions are needed to communicate with the analog I/O cards. 



• Analog shielding should be used to improve the quality of electrical signals. 


1. Analog inputs require: 

a) A Digital to Analog conversion at the PLC input interface module 

b) Analog to Digital conversion at the PLC input interface module 

c) No conversion is required 

d) None of the above 

2. You need to read an analog voltage that has a range of -10V to 10V to a precision of +/-0.05V. 

What resolution of A/D converter is needed? 

3. We are given a 12 bit analog input with a range of -10V to 10V. If we put in 2.735V, what will 

the integer value be after the A/D conversion? What is the error? What voltage can we calculate? 

4. Use manuals on the web for an analog input card, and describe the process that would be 

needed to set up the card to read an input voltage between -2V and 7V. This description should 

include jumper settings, configuration memory and ladder logic. 

5. We need to select a digital to analog converter for an application. The output will vary from -5V 

to 10V DC, and we need to be able to specify the voltage to within 50mV. What resolution will 

be required? How many bits will this D/A converter need? What will the accuracy be? 

6. Write a program that will input an analog voltage, do the calculation below, and output an analog 

voltage. 

V out 

= 

ln( V in 

) 

7. The following calculation will be made when input A is true. If the result x is between 1 and 10 

then the output B will be turned on. The value of x will be output as an analog voltage. Create a 

ladder logic program to perform these tasks. 

x = 5 y 1 + siny 

A = I:000/00 

B = O:001/00 

x = F8:0 

y = F8:1 

8. You are developing a controller for a game that measures hand strength. To do this a START 

button is pushed, 3 seconds later a LIGHT is turned on for one second to let the user know 

when to start squeezing. The analog value is read at 0.3s after the light is on. The value is converted 

to a force F with the equation below. The force is displayed by converting it to BCD and 



writing it to an output card (O:001). If the value exceeds 100 then a BIG_LIGHT and SIREN 

are turned on for 5sec. Use a structured design technique to develop ladder logic.. 

F 

= 

V 

------ in 

6 


1. b) 

2. 

R 

10V – (– 

10V) 

= --------------------------------- = 200 7 bits = 128 

0.1V 

8 bits = 256 

The minimum number of bits is 8. 

3. 

N = 12 R = 4096 V min 

= – 10V V max 

= 10V 

V 

V I 

INT in 

– V = ⎛---------------------------- 

min ⎞ 

⎝ – ⎠ R = 2608 

V max 

V min 

V in 

= 2.735V 

V C 

V I 

= ⎛ 

⎝ 

----⎞ R ⎠ 

( Vmax – V min ) + V min = 2.734V 

4. for the 1771-IFE card you would put keying in the back of the card, because voltage is being 

measured, jumpers inside the card are already in the default position. Calibration might be 

required, this can be done using jumper settings and suppling known voltages, then adjusting 

trim potentiometers on the card. The card can then be installed in the rack - it is recommended 

that they be as close to the CPU as possible. After the programming software is running the 

card is added to the IO configuration, and automatic settings can be used - these change the 

memory values to set values in integer memory. 



5. 

A card with a voltage range from -10V to +10V will be selected to cover the 

entire range. 

R = --------------------------------- 

10V – (– 

10V) 

= 400 minimum resolution 

0.050V 

8 bits = 256 

9 bits = 512 

10 bits = 1024 

The A/D converter needs a minimum of 9 bits, but this number of bits is not 

commonly available, but 10 bits is, so that will be selected. 

V 

V max 

– V min 

ERROR 

= ⎛---------------------------- 

⎞ = 

10V – (– 

10V) 

⎝ 2R ⎠ 

--------------------------------- = ± 

2( 1024) 

0.00976V 



6. 

FS 

BT9:1/EN 

BT9:1/EN 

BT9:1/DN 

BT9:0/EN 

BTW 

Rack 0 

Group 0 

Module 0 


Data N7:0 

Length 37 

Continuous No 

BTR 

Rack 0 

Group 0 

Module 0 


Data N7:37 

Length 20 

Continuous No 

BTW 

Rack 0 

Group 1 

Module 0 


Data N7:57 

Length 13 

Continuous No 

CPT 

Dest N7:57 

Expression 

"LN (N7:41)" 



7. 

A 

SIN 

Source A F8:1 

Dest. F8:0 

ADD 

Source A 1 

Source B F8:0 

Dest. F8:0 

SQR 

Source A F8:0 

Dest. F8:0 

XPY 

Source A 5 

Source B F8:1 

Dest. F8:2 

MUL 

Source A F8:0 

Source B F8:2 

Dest. F8:0 

LIM 

lower lim. 1 

value F8:0 

upper lim. 10 

B 

A 

A 

BT9:0/EN 

MOV 

Source A F8:0 

Dest. N7:0 

BTW 

Rack 0 

Group 0 

Module 0 


Data N7:0 

Length 13 

Continuous No 



8. 

FS 

S1 TON(S1,START) S2 F>100 S3 

waiting sampling winner 

TON(S2, 1sec) 

FS 

ST2 

ST3 

L 

U 

U 

ST1 

ST2 

ST3 

BTW 

Device Analog Input 

location 000 

Control BT10:0 

Data N9:0 

Length 37 

LIGHT 

BIG_LIGHT 

TON(S3, 5sec) 

T4:0/DN 

BT10:1/DN 

T4:1/DN 

T4:1/DN 

TON 

T4:1 

preset 1s 

BTR 

Device Analog Input 

location 000 

Control BT10:1 

Data N9:40 

Length 20 

DIV 

Source A N9:40 

Source B 6 

Dest. N7:0 

U ST2 

ST1 

START 

T4:0/TT 

T4:0/DN 

MCR 

U 

SIREN 

TON 

T4:0 

preset 3s 

ST1 

T4:1/DN 

L 

ST1 

TOD 

Source A N7:0 

Dest. O:001 

GRT 

Source A N7:0 

U 

Source B 100 

L 

ST1 

ST3 

ST2 

L 

MOV 

Source 0.0 

Dest F8:0 

MCR 

MCR 

ST2 

ST3 

T4:2/DN 

TON 

T4:2 

preset 5s 

MCR 

MCR 

U 

ST3 

TON 

T4:0 

preset 0.3s 

L 

MCR 

ST1 




1 In detail, describe the process of setting up analog inputs and outputs for a range of -10V to 10V 

in 2s compliment in realtime sampling mode. 

2. A machine is connected to a load cell that outputs a voltage proportional to the mass on a platform. 

When unloaded the cell outputs a voltage of 1V. A mass of 500Kg results in a 6V output. 

Write a program that will measure the mass when an input sensor (M) becomes true. If the 

mass is not between 300Kg and 400Kg and alarm output (A) will be turned on. Write ladder 

logic and indicate the general settings for the analog IO. 

3. Develop a program to sample analog data values and calculate the average, standard deviation, 

and the control limits. The general steps are listed below. 

1. Read ’m’ sampled inputs. 

2. Randomly select values and calculate the average and store in memory. Calculate 

the standard deviation of the ’n’ stored values. 

3. Compare the inputs to the standard deviation. If it is larger than 3 deviations 

from the mean, halt the process. 

4. If it is larger than 2 then increase a counter A, or if it is larger than 1 increase a 

second counter B. If it is less than 1 reset the counters. 

5. If counter A is =3 or B is =5 then shut down. 

6. Goto 1. 

X j 

= 

m 

∑ 

i = 1 

X i 

------------- 

n 

X 

= 

n 

∑ 

j = 1 

X j 

m 

∑ 

( X i 

– X j ) 

σ 

i = 1 

X 

= ------------------------------ 

n – 1 

UCL = X + 3σ X 

LCL = X – 3σ X 


continuous sensors - 23.1 

23. CONTINUOUS SENSORS 

Topics: 

• Continuous sensor issues; accuracy, resolution, etc. 

• Angular measurement; potentiometers, encoders and tachometers 

• Linear measurement; potentiometers, LVDTs, Moire fringes and accelerometers 

• Force measurement; strain gages and piezoelectric 

• Liquid and fluid measurement; pressure and flow 

• Temperature measurement; RTDs, thermocouples and thermistors 

• Other sensors 

• Continuous signal inputs and wiring 

• Glossary 

Objectives: 

• To understand the common continuous sensor types. 

• To understand interfacing issues. 


Continuous sensors convert physical phenomena to measurable signals, typically 

voltages or currents. Consider a simple temperature measuring device, there will be an 

increase in output voltage proportional to a temperature rise. A computer could measure 

the voltage, and convert it to a temperature. The basic physical phenomena typically measured 

with sensors include; 

- angular or linear position 

- acceleration 

- temperature 

- pressure or flow rates 

- stress, strain or force 

- light intensity 

- sound 

Most of these sensors are based on subtle electrical properties of materials and 

devices. As a result the signals often require signal conditioners. These are often amplifiers 

that boost currents and voltages to larger voltages. 

Sensors are also called transducers. This is because they convert an input phenomena 

to an output in a different form. This transformation relies upon a manufactured 

device with limitations and imperfection. As a result sensor limitations are often charac- 



terized with; 

Accuracy - This is the maximum difference between the indicated and actual reading. 

For example, if a sensor reads a force of 100N with a ±1% accuracy, then 

the force could be anywhere from 99N to 101N. 

Resolution - Used for systems that step through readings. This is the smallest 

increment that the sensor can detect, this may also be incorporated into the 

accuracy value. For example if a sensor measures up to 10 inches of linear displacements, 

and it outputs a number between 0 and 100, then the resolution of 

the device is 0.1 inches. 

Repeatability - When a single sensor condition is made and repeated, there will be 

a small variation for that particular reading. If we take a statistical range for 

repeated readings (e.g., ±3 standard deviations) this will be the repeatability. 

For example, if a flow rate sensor has a repeatability of 0.5cfm, readings for an 

actual flow of 100cfm should rarely be outside 99.5cfm to 100.5cfm. 

Linearity - In a linear sensor the input phenomenon has a linear relationship with 

the output signal. In most sensors this is a desirable feature. When the relationship 

is not linear, the conversion from the sensor output (e.g., voltage) to a calculated 

quantity (e.g., force) becomes more complex. 

Precision - This considers accuracy, resolution and repeatability or one device relative 

to another. 

Range - Natural limits for the sensor. For example, a sensor for reading angular 

rotation may only rotate 200 degrees. 

Dynamic Response - The frequency range for regular operation of the sensor. Typically 

sensors will have an upper operation frequency, occasionally there will be 

lower frequency limits. For example, our ears hear best between 10Hz and 

16KHz. 

Environmental - Sensors all have some limitations over factors such as temperature, 

humidity, dirt/oil, corrosives and pressures. For example many sensors 

will work in relative humidities (RH) from 10% to 80%. 

Calibration - When manufactured or installed, many sensors will need some calibration 

to determine or set the relationship between the input phenomena, and 

output. For example, a temperature reading sensor may need to be zeroed or 

adjusted so that the measured temperature matches the actual temperature. This 

may require special equipment, and need to be performed frequently. 

Cost - Generally more precision costs more. Some sensors are very inexpensive, 

but the signal conditioning equipment costs are significant. 

23.2 INDUSTRIAL SENSORS 

This section describes sensors that will be of use for industrial measurements. The 

sections have been divided by the phenomena to be measured. Where possible details are 

provided. 



23.2.1 Angular Displacement 

23.2.1.1 - Potentiometers 

Potentiometers measure the angular position of a shaft using a variable resistor. A 

potentiometer is shown in Figure 23.1. The potentiometer is resistor, normally made with 

a thin film of resistive material. A wiper can be moved along the surface of the resistive 

film. As the wiper moves toward one end there will be a change in resistance proportional 

to the distance moved. If a voltage is applied across the resistor, the voltage at the wiper 

interpolate the voltages at the ends of the resistor. 

V 1 

V 1 

V 2 

resistive 

film 

physical 

V w 

V 2 

V w 

wiper 

schematic 

Figure 23.1 

A Potentiometer 

The potentiometer in Figure 23.2 is being used as a voltage divider. As the wiper 

rotates the output voltage will be proportional to the angle of rotation. 



θ max θ w 

www.PAControl.com 

V 2 

V 1 

θ w 

V out = ( V 2 – V 1 ) ⎛----------⎞ + V 

⎝θ ⎠ 1 

max 

V out 

Figure 23.2 

A Potentiometer as a Voltage Divider 

Potentiometers are popular because they are inexpensive, and don’t require special 

signal conditioners. But, they have limited accuracy, normally in the range of 1% and they 

are subject to mechanical wear. 

Potentiometers measure absolute position, and they are calibrated by rotating them 

in their mounting brackets, and then tightening them in place. The range of rotation is normally 

limited to less than 360 degrees or multiples of 360 degrees. Some potentiometers 

can rotate without limits, and the wiper will jump from one end of the resistor to the other. 

Faults in potentiometers can be detected by designing the potentiometer to never 

reach the ends of the range of motion. If an output voltage from the potentiometer ever 

reaches either end of the range, then a problem has occurred, and the machine can be shut 

down. Two examples of problems that might cause this are wires that fall off, or the potentiometer 

rotates in its mounting. 

23.2.2 Encoders 

Encoders use rotating disks with optical windows, as shown in Figure 23.3. The 

encoder contains an optical disk with fine windows etched into it. Light from emitters 

passes through the openings in the disk to detectors. As the encoder shaft is rotated, the 

light beams are broken. The encoder shown here is a quadrature encode, and it will be discussed 

later.


light 

emitters 

light 

detectors 

Shaft rotates 

Note: this type of encoder is 

commonly used in computer 

mice with a roller 

ball. 

Figure 23.3 

An Encoder Disk 

There are two fundamental types of encoders; absolute and incremental. An absolute 

encoder will measure the position of the shaft for a single rotation. The same shaft 

angle will always produce the same reading. The output is normally a binary or grey code 

number. An incremental (or relative) encoder will output two pulses that can be used to 

determine displacement. Logic circuits or software is used to determine the direction of 

rotation, and count pulses to determine the displacement. The velocity can be determined 

by measuring the time between pulses. 

Encoder disks are shown in Figure 23.4. The absolute encoder has two rings, the 

outer ring is the most significant digit of the encoder, the inner ring is the least significant 

digit. The relative encoder has two rings, with one ring rotated a few degrees ahead of the 

other, but otherwise the same. Both rings detect position to a quarter of the disk. To add 

accuracy to the absolute encoder more rings must be added to the disk, and more emitters 

and detectors. To add accuracy to the relative encoder we only need to add more windows 

to the existing two rings. Typical encoders will have from 2 to thousands of windows per 

ring. 



sensors read across 

a single radial line 

relative encoder 

(quadrature) 

absolute encoder 

Figure 23.4 

Encoder Disks 

When using absolute encoders, the position during a single rotation is measured 

directly. If the encoder rotates multiple times then the total number of rotations must be 

counted separately. 

When using a relative encoder, the distance of rotation is determined by counting 

the pulses from one of the rings. If the encoder only rotates in one direction then a simple 

count of pulses from one ring will determine the total distance. If the encoder can rotate 

both directions a second ring must be used to determine when to subtract pulses. The 

quadrature scheme, using two rings, is shown in Figure 23.5. The signals are set up so that 

one is out of phase with the other. Notice that for different directions of rotation, input B 

either leads or lags A. 



Quad input A 

clockwise rotation 

Quad Input B 

Note the change 

as direction 

is reversed 

total displacement can be determined 

by adding/subtracting pulse counts 

(direction determines add/subtract) 

Quad input A 

counterclockwise rotation 

Quad Input B 

Note: To determine direction we can do a simple check. If both are off or on, the first to 

change state determines direction. Consider a point in the graphs above where both 

A and B are off. If A is the first input to turn on the encoder is rotating clockwise. If 

B is the first to turn on the rotation is counterclockwise. 

Aside: A circuit (or program) can be built for this circuit using an up/down counter. If 

the positive edge of input A is used to trigger the clock, and input B is used to drive 

the up/down count, the counter will keep track of the encoder position. 

Figure 23.5 

Quadrature Encoders 

Interfaces for encoders are commonly available for PLCs and as purchased units. 

Newer PLCs will also allow two normal inputs to be used to decode encoder inputs. 



Normally absolute and relative encoders require a calibration phase when a controller 

is turned on. This normally involves moving an axis until it reaches a logical sensor 

that marks the end of the range. The end of range is then used as the zero position. 

Machines using encoders, and other relative sensors, are noticeable in that they normally 

move to some extreme position before use. 

23.2.2.1 - Tachometers 

Tachometers measure the velocity of a rotating shaft. A common technique is to 

mount a magnet to a rotating shaft. When the magnetic moves past a stationary pick-up 

coil, current is induced. For each rotation of the shaft there is a pulse in the coil, as shown 

in Figure 23.6. When the time between the pulses is measured the period for one rotation 

can be found, and the frequency calculated. This technique often requires some signal 

conditioning circuitry. 

rotating 

shaft 

pickup 

coil 

Vout 

Vout 

t 

magnet 

1/f 

Figure 23.6 

A Magnetic Tachometer 

Another common technique uses a simple permanent magnet DC generator (note: 

you can also use a small DC motor). The generator is hooked to the rotating shaft. The 

rotation of a shaft will induce a voltage proportional to the angular velocity. This technique 

will introduce some drag into the system, and is used where efficiency is not an 

issue. 

Both of these techniques are common, and inexpensive. 

23.2.3 Linear Position 

23.2.3.1 - Potentiometers 



Rotational potentiometers were discussed before, but potentiometers are also 

available in linear/sliding form. These are capable of measuring linear displacement over 

long distances. Figure 23.7 shows the output voltage when using the potentiometer as a 

voltage divider. 

V 2 

V out 

V out 

V 1 

V 2 

V 1 

= 

+ ( – ) ⎛ 

⎝ a L -- ⎞ 

⎠ 

L a 

V 1 

Figure 23.7 

Linear Potentiometer 

Linear/sliding potentiometers have the same general advantages and disadvantages 

of rotating potentiometers. 

23.2.3.2 - Linear Variable Differential Transformers (LVDT) 

Linear Variable Differential Transformers (LVDTs) measure linear displacements 

over a limited range. The basic device is shown in Figure 23.8. It consists of outer coils 

with an inner moving magnetic core. High frequency alternating current (AC) is applied to 

the center coil. This generates a magnetic field that induces a current in the two outside 

coils. The core will pull the magnetic field towards it, so in the figure more current will be 

induced in the left hand coil. The outside coils are wound in opposite directions so that 

when the core is in the center the induced currents cancel, and the signal out is zero 

(0Vac). The magnitude of the signal out voltage on either line indicates the position of the 

core. Near the center of motion the change in voltage is proportional to the displacement. 

But, further from the center the relationship becomes nonlinear. 



A rod drives 

the sliding core 

∆x 

∆V = K∆x 

where, 

∆V = output voltage 

K = constant for device 

∆x = core displacement 

AC input 

signal out 

Figure 23.8 

An LVDT 

Aside: The circuit below can be used to produce a voltage that is proportional to position. 

The two diodes convert the AC wave to a half wave DC wave. The capacitor and resistor 

values can be selected to act as a low pass filter. The final capacitor should be large 

enough to smooth out the voltage ripple on the output. 

Vac in 

LVDT 

Vac out 

Vdc out 

Figure 23.9 

A Simple Signal Conditioner for an LVDT 

These devices are more accurate than linear potentiometers, and have less friction. 

Typical applications for these devices include measuring dimensions on parts for quality 



control. They are often used for pressure measurements with Bourdon tubes and bellows/ 

diaphragms. A major disadvantage of these sensors is the high cost, often in the thousands. 

23.2.3.3 - Moire Fringes 

High precision linear displacement measurements can be made with Moire 

Fringes, as shown in Figure 23.10. Both of the strips are transparent (or reflective), with 

black lines at measured intervals. The spacing of the lines determines the accuracy of the 

position measurements. The stationary strip is offset at an angle so that the strips interfere 

to give irregular patterns. As the moving strip travels by a stationary strip the patterns will 

move up, or down, depending upon the speed and direction of motion. 

Moving 

Stationary 

Note: you can recreate this effect with the strips below. Photocopy the pattern twice, 

overlay the sheets and hold them up to the light. You will notice that shifting one sheet 

will cause the stripes to move up or down. 

Figure 23.10 

The Moire Fringe Effect 

A device to measure the motion of the moire fringes is shown in Figure 23.11. A 

light source is collimated by passing it through a narrow slit to make it one slit width. This 

is then passed through the fringes to be detected by light sensors. At least two light sensors 

are needed to detect the bright and dark locations. Two sensors, close enough, can act as a 

quadrature pair, and the same method used for quadrature encoders can be used to determine 

direction and distance of motion. 



on 

off 

on 

off 

Figure 23.11 

Measuring Motion with Moire Fringes 

These are used in high precision applications over long distances, often meters. 

They can be purchased from a number of suppliers, but the cost will be high. Typical 

applications include Coordinate Measuring Machines (CMMs). 

23.2.3.4 - Accelerometers 

Accelerometers measure acceleration using a mass suspended on a force sensor, as 

shown in Figure 23.12. When the sensor accelerates, the inertial resistance of the mass 

will cause the force sensor to deflect. By measuring the deflection the acceleration can be 

determined. In this case the mass is cantilevered on the force sensor. A base and housing 

enclose the sensor. A small mounting stud (a threaded shaft) is used to mount the accelerometer. 

Base 

Mounting 

Stud 

Force 

Sensor 

Mass 

Housing 

Figure 23.12 

A Cross Section of an Accelerometer 

Accelerometers are dynamic sensors, typically used for measuring vibrations 



between 10Hz to 10KHz. Temperature variations will affect the accuracy of the sensors. 

Standard accelerometers can be linear up to 100,000 m/s**2: high shock designs can be 

used up to 1,000,000 m/s**2. There is often a trade-off between a wide frequency range 

and device sensitivity (note: higher sensitivity requires a larger mass). Figure 23.13 shows 

the sensitivity of two accelerometers with different resonant frequencies. A smaller resonant 

frequency limits the maximum frequency for the reading. The smaller frequency 

results in a smaller sensitivity. The units for sensitivity is charge per m/s**2. 

resonant freq. (Hz) 

22 KHz 

180KHz 

sensitivity 

4.5 pC/(m/s**2) 

.004 

Figure 23.13 

Piezoelectric Accelerometer Sensitivities 

The force sensor is often a small piece of piezoelectric material (discussed later in 

this chapter). The piezoelectic material can be used to measure the force in shear or compression. 

Piezoelectric based accelerometers typically have parameters such as, 

-100 to 250°C operating range 

1mV/g to 30V/g sensitivity 

operate well below one forth of the natural frequency 

The accelerometer is mounted on the vibration source as shown in Figure 23.14. 

The accelerometer is electrically isolated from the vibration source so that the sensor may 

be grounded at the amplifier (to reduce electrical noise). Cables are fixed to the surface of 

the vibration source, close to the accelerometer, and are fixed to the surface as often as 

possible to prevent noise from the cable striking the surface. Background vibrations can be 

detected by attaching control electrodes to non-vibrating surfaces. Each accelerometer is 

different, but some general application guidelines are; 

• The control vibrations should be less than 1/3 of the signal for the error to be less 

than 12%). 

• Mass of the accelerometers should be less than a tenth of the measurement mass. 

• These devices can be calibrated with shakers, for example a 1g shaker will hit a 

peak velocity of 9.81 m/s**2. 



Sealant to prevent moisture 

hookup wire 

isolated 

stud 

accelerometer 

isolated 

wafer 

surface 

Figure 23.14 

Mounting an Accelerometer 

Equipment normally used when doing vibration testing is shown in Figure 23.15. 

The sensor needs to be mounted on the equipment to be tested. A pre-amplifier normally 

converts the charge generated by the accelerometer to a voltage. The voltage can then be 

analyzed to determine the vibration frequencies. 

preamp 

Sensor 

Source of vibrations, 

or site for vibration 

measurement 

signal processor/ 

recorder 

control system 

Figure 23.15 

Typical Connection for Accelerometers 

Accelerometers are commonly used for control systems that adjust speeds to 

reduce vibration and noise. Computer Controlled Milling machines now use these sensors 

to actively eliminate chatter, and detect tool failure. The signal from accelerometers can be 



integrated to find velocity and acceleration. 

Currently accelerometers cost hundreds or thousands per channel. But, advances in 

micromachining are already beginning to provide integrated circuit accelerometers at a 

low cost. Their current use is for airbag deployment systems in automobiles. 

23.2.4 Forces and Moments 

23.2.4.1 - Strain Gages 

Strain gages measure strain in materials using the change in resistance of a wire. 

The wire is glued to the surface of a part, so that it undergoes the same strain as the part (at 

the mount point). Figure 23.16 shows the basic properties of the undeformed wire. Basically, 

the resistance of the wire is a function of the resistivity, length, and cross sectional 

area. 

w 

L 

- 

t 

I 

+ 

V 

R 

= 

V 

-- = ρ L I Ā - = ρ ----- 

L wt 

where, 

R = resistance of wire 

VI , = voltage and current 

L 

= 

length of wire 

wt , = width and thickness 

A 

= 

cross sectional area of conductor 

ρ = resistivity of material 

Figure 23.16 

The Electrical Properties of a Wire 



After the wire in Figure 23.16 has been deformed it will take on the new dimensions 

and resistance shown in Figure 23.17. If a force is applied as shown, the wire will 

become longer, as predicted by Young’s modulus. But, the cross sectional area will 

decrease, as predicted by Poison’s ratio. The new length and cross sectional area can then 

be used to find a new resistance. 

w’ 

L’ 

t’ 

σ 

= 

F 

-- = ----- 

F 

= Eε 

A wt 

∴ε 

= 

--------- 

F 

Ewt 

F 

R' = ρ------- L' = ρ⎛--------------------------------------------- 

L( 1 + ε) 

⎞ 

w't' ⎝w( 1 – νε)t( 1 – νε) 

⎠ 

∴∆R 

= R' – R = R 

( 1 + ε) 

( --------------------------------------- – 

1 – νε) ( 1 – νε) 

1 

where, 

ν = poissons ratio for the material 

F = applied force 

E 

= 

Youngs modulus for the material 

σε , = stress and strain of material 

Aside: Gauge factor, as defined below, is a commonly used measure of stain gauge 

sensitivity. 

GF 

= 

⎛------ 

∆R⎞ 

⎝ R ⎠ 

------------ 

ε 

Figure 23.17 

The Electrical and Mechanical Properties of the Deformed Wire 



Aside: Changes in strain gauge resistance are typically small (large values would require 

strains that would cause the gauges to plastically deform). As a result, Wheatstone 

bridges are used to amplify the small change. In this circuit the variable resistor R2 

would be tuned until Vo = 0V. Then the resistance of the strain gage can be calculated 

using the given equation. 

V+ 

R 

R 2 

R 1 

strain 

= ------------- when Vo = 0V 

R 3 

R2 

R1 

R4 

- 

+ 

Vo 

Rstrain 

R3 

R5 

Figure 23.18 

Measuring Strain with a Wheatstone Bridge 

A strain gage must be small for accurate readings, so the wire is actually wound in 

a uniaxial or rosette pattern, as shown in Figure 23.19. When using uniaxial gages the 

direction is important, it must be placed in the direction of the normal stress. (Note: the 

gages cannot read shear stress.) Rosette gages are less sensitive to direction, and if a shear 

force is present the gage will measure the resulting normal force at 45 degrees. These 

gauges are sold on thin films that are glued to the surface of a part. The process of mounting 

strain gages involves surface cleaning. application of adhesives, and soldering leads to 

the strain gages. 



stress 

direction 

uniaxial 

rosette 

Figure 23.19 

Wire Arrangements in Strain Gages 

A design techniques using strain gages is to design a part with a narrowed neck to 

mount the strain gage on, as shown in Figure 23.20. In the narrow neck the strain is proportional 

to the load on the member, so it may be used to measure force. These parts are 

often called load cells. 

mounted in narrow section 

to increase strain effect 

F 

F 

Figure 23.20 

Using a Narrow to Increase Strain 

Strain gauges are inexpensive, and can be used to measure a wide range of stresses 

with accuracies under 1%. Gages require calibration before each use. This often involves 

making a reading with no load, or a known load applied. An example application includes 

using strain gages to measure die forces during stamping to estimate when maintenance is 

needed. 

23.2.4.2 - Piezoelectric 

When a crystal undergoes strain it displaces a small amount of charge. In other 

words, when the distance between atoms in the crystal lattice changes some electrons are 

forced out or drawn in. This also changes the capacitance of the crystal. This is known as 



the Piezoelectric effect. Figure 23.21 shows the relationships for a crystal undergoing a 

linear deformation. The charge generated is a function of the force applied, the strain in 

the material, and a constant specific to the material. The change in capacitance is proportional 

to the change in the thickness. 

F 

b 

+ 

q 

- 

c 

a 

F 

C = 

εab 

-------- i = εg----F 

d c 

dt 

where, 

C = capacitance change 

abc , , = geometry of material 

ε = dielectric constant (quartz typ. 4.06*10**-11 F/m) 

i = current generated 

F = force applied 

g = constant for material (quartz typ. 50*10**-3 Vm/N) 

E 

= 

Youngs modulus (quartz typ. 8.6*10**10 N/m**2) 

Figure 23.21 

The Piezoelectric Effect 

These crystals are used for force sensors, but they are also used for applications 

such as microphones and pressure sensors. Applying an electrical charge can induce 

strain, allowing them to be used as actuators, such as audio speakers. 

When using piezoelectric sensors charge amplifiers are needed to convert the small 

amount of charge to a larger voltage. These sensors are best suited to dynamic measurements, 

when used for static measurements they tend to drift or slowly lose charge, and the 

signal value will change. 



23.2.5 Liquids and Gases 

There are a number of factors to be considered when examining liquids and gasses. 

• Flow velocity 

• Density 

• Viscosity 

• Pressure 

There are a number of differences factors to be considered when dealing with fluids 

and gases. Normally a fluid is considered incompressible, while a gas normally follows 

the ideal gas law. Also, given sufficiently high enough temperatures, or low enough 

pressures a fluid can be come a gas. 

PV 

= 

nRT 

where, 

P = the gas pressure 

V = the volume of the gas 

n = the number of moles of the gas 

R = the ideal gas constant = 

T = the gas temperature 

When flowing, the flow may be smooth, or laminar. In case of high flow rates or 

unrestricted flow, turbulence may result. The Reynold’s number is used to determine the 

transition to turbulence. The equation below is for calculation the Reynold’s number for 

fluid flow in a pipe. A value below 2000 will result in laminar flow. At a value of about 

3000 the fluid flow will become uneven. At a value between 7000 and 8000 the flow will 

become turbulent. 



R = 

VDρ 

----------- 

u 

where, 

R 

= 

Reynolds number 

V = 

D 

= 

ρ = 

u = 

velocity 

pipe diameter 

fluid density 

viscosity 

23.2.5.1 - Pressure 

Figure 23.22 shows different two mechanisms for pressure measurement. The 

Bourdon tube uses a circular pressure tube. When the pressure inside is higher than the 

surrounding air pressure (14.7psi approx.) the tube will straighten. A position sensor, connected 

to the end of the tube, will be elongated when the pressure increases. 

pressure 

increase 

pressure 

increase 

position sensor 

position sensor 

pressure 

pressure 

a) Bourdon Tube 

b) Baffle 

Figure 23.22 

Pressure Transducers 



These sensors are very common and have typical accuracies of 0.5%. 

23.2.5.2 - Venturi Valves 

When a flowing fluid or gas passes through a narrow pipe section (neck) the pressure 

drops. If there is no flow the pressure before and after the neck will be the same. The 

faster the fluid flow, the greater the pressure difference before and after the neck. This is 

known as a Venturi valve. Figure 23.23 shows a Venturi valve being used to measure a 

fluid flow rate. The fluid flow rate will be proportional to the pressure difference before 

and at the neck (or after the neck) of the valve. 

differential 

pressure 

transducer 

fluid flow 

Figure 23.23 

A Venturi Valve 



Aside: Bernoulli’s equation can be used to relate the pressure drop in a venturi valve. 

-- 

p 

ρ 

v 2 

+ ---- + gz = C 

2 

where, 

p 

= 

pressure 

ρ = density 

v 

g 

z 

= 

= 

= 

velocity 

gravitational constant 

height above a reference 

C = constant 

Consider the centerline of the fluid flow through the valve. Assume the fluid is incompressible, 

so the density does not change. And, assume that the center line of the valve does 

not change. This gives us a simpler equation, as shown below, that relates the velocity 

and pressure before and after it is compressed. 

p 

--------------- before 

ρ 

v before 

2 

+ ----------------- + gz = C = 

2 

p 

--------------- before 

+ ----------------- = 

ρ 2 

p before 

v before 

2 

p 

------------ after 

ρ 

p 

------------ after 

ρ 

v after 

2 

+ -------------- 

2 

⎛ 

– p after 

ρ v after 

⎞ 

= ⎜-------------- 

– ----------------- ⎟ 

⎝ 2 2 ⎠ 

2 

v before 

2 

v after 

2 

+ -------------- + gz 

2 

The flow velocity v in the valve will be larger than the velocity in the larger pipe section 

before. So, the right hand side of the expression will be positive. This will mean 

that the pressure before will always be higher than the pressure after, and the difference 

will be proportional to the velocity squared. 

Figure 23.24 

The Pressure Relationship for a Venturi Valve 

Venturi valves allow pressures to be read without moving parts, which makes them 

very reliable and durable. They work well for both fluids and gases. It is also common to 

use Venturi valves to generate vacuums for actuators, such as suction cups. 

23.2.5.3 - Coriolis Flow Meter 

Fluid passes through thin tubes, causing them to vibrate. As the fluid approaches 

the point of maximum vibration it accelerates. When leaving the point it decelerates. The 



result is a distributed force that causes a bending moment, and hence twisting of the pipe. 

The amount of bending is proportional to the velocity of the fluid flow. These devices typically 

have a large constriction on the flow, and result is significant loses. Some of the 

devices also use bent tubes to increase the sensitivity, but this also increases the flow resistance. 

The typical accuracy for a Coriolis flowmeter is 0.1%. 

23.2.5.4 - Magnetic Flow Meter 

A magnetic sensor applies a magnetic field perpendicular to the flow of a conductive 

fluid. As the fluid moves, the electrons in the fluid experience an electromotive force. 

The result is that a potential (voltage) can be measured perpendicular to the direction of 

the flow and the magnetic field. The higher the flow rate, the greater the voltage. The typical 

accuracy for these sensors is 0.5%. 

drops. 

These flowmeters don’t oppose fluid flow, and so they don’t result in pressure 

23.2.5.5 - Ultrasonic Flow Meter 

A transmitter emits a high frequency sound at point on a tube. The signal must then 

pass through the fluid to a detector where it is picked up. If the fluid is flowing in the same 

direction as the sound it will arrive sooner. If the sound is against the flow it will take 

longer to arrive. In a transit time flow meter two sounds are used, one traveling forward, 

and the other in the opposite direction. The difference in travel time for the sounds is used 

to determine the flow velocity. 

A doppler flowmeter bounces a soundwave off particle in a flow. If the particle is 

moving away from the emitter and detector pair, then the detected frequency will be lowered, 

if it is moving towards them the frequency will be higher. 

The transmitter and receiver have a minimal impact on the fluid flow, and therefore 

don’t result in pressure drops. 

23.2.5.6 - Vortex Flow Meter 

Fluid flowing past a large (typically flat) obstacle will shed vortices. The frequency 

of the vortices will be proportional to the flow rate. Measuring the frequency 

allows an estimate of the flow rate. These sensors tend be low cost and are popular for low 

accuracy applications. 



23.2.5.7 - Positive Displacement Meters 

In some cases more precise readings of flow rates and volumes may be required. 

These can be obtained by using a positive displacement meter. In effect these meters are 

like pumps run in reverse. As the fluid is pushed through the meter it produces a measurable 

output, normally on a rotating shaft. 

23.2.5.8 - Pitot Tubes 

Gas flow rates can be measured using Pitot tubes, as shown in Figure 23.25. These 

are small tubes that project into a flow. The diameter of the tube is small (typically less 

than 1/8") so that it doesn’t affect the flow. 

gas flow 

pitot 

tube 

connecting hose 

pressure 

sensor 

Figure 23.25 

Pitot Tubes for Measuring Gas Flow Rates 

23.2.6 Temperature 

Temperature measurements are very common with control systems. The temperature 

ranges are normally described with the following classifications. 

very low temperatures


very high temperatures > 2000 deg C - e.g. plasma systems 

23.2.6.1 - Resistive Temperature Detectors (RTDs) 

When a metal wire is heated the resistance increases. So, a temperature can be 

measured using the resistance of a wire. Resistive Temperature Detectors (RTDs) normally 

use a wire or film of platinum, nickel, copper or nickel-iron alloys. The metals are 

wound or wrapped over an insulator, and covered for protection. The resistances of these 

alloys are shown in Figure 23.26. 

Material 

Temperature 

Range C (F) 

Typical 

Resistance 

(ohms) 

Platinum -200 - 850 (-328 - 1562) 

Nickel -80 - 300 (-112 - 572) 

Copper -200 - 260 (-328 - 500) 

Figure 23.26 RTD Properties 

100 

120 

10 

These devices have positive temperature coefficients that cause resistance to 

increase linearly with temperature. A platinum RTD might have a resistance of 100 ohms 

at 0C, that will increase by 0.4 ohms/°C. The total resistance of an RTD might double over 

the temperature range. 

A current must be passed through the RTD to measure the resistance. (Note: a voltage 

divider can be used to convert the resistance to a voltage.) The current through the 

RTD should be kept to a minimum to prevent self heating. These devices are more linear 

than thermocouples, and can have accuracies of 0.05%. But, they can be expensive 

23.2.6.2 - Thermocouples 

Each metal has a natural potential level, and when two different metals touch there 

is a small potential difference, a voltage. (Note: when designing assemblies, dissimilar 

metals should not touch, this will lead to corrosion.) Thermocouples use a junction of dissimilar 

metals to generate a voltage proportional to temperature. This principle was discovered 

by T.J. Seebeck. 

The basic calculations for thermocouples are shown in Figure 23.27. This calculation 

provides the measured voltage using a reference temperature and a constant specific 



to the device. The equation can also be rearranged to provide a temperature given a voltage. 

measuring 

device 

+ 

- V out 

V out = α( T– 

T ref ) 

V 

∴T = --------- out 

+ T 

α ref 

where, 

α = constant (V/C) 50 ------ µV (typical) 

°C 

TT , ref 

= current and reference temperatures 

Figure 23.27 

Thermocouple Calculations 

The list in Table 1 shows different junction types, and the normal temperature 

ranges. Both thermocouples, and signal conditioners are commonly available, and relatively 

inexpensive. For example, most PLC vendors sell thermocouple input cards that 

will allow multiple inputs into the PLC. 

Table 1: Thermocouple Types 

ANSI 

Type 

Materials 

Temperature 

Range 

(°F) 

Voltage Range 

(mV) 

T copper/constantan -200 to 400 -5.60 to 17.82 

J iron/constantan 0 to 870 0 to 42.28 

E chromel/constantan -200 to 900 -8.82 to 68.78 

K chromel/aluminum -200 to 1250 -5.97 to 50.63 

R platinum-13%rhodium/platinum 0 to 1450 0 to 16.74 

S platinum-10%rhodium/platinum 0 to 1450 0 to 14.97 

C tungsten-5%rhenium/tungsten-26%rhenium 0 to 2760 0 to 37.07 



mV 

80 

E 

60 

K 

40 

J 

C 

20 

T 

R 

S 

0 

0 500 1000 1500 2000 2500 

( °F) 

Figure 23.28 

Thermocouple Temperature Voltage Relationships (Approximate) 

The junction where the thermocouple is connected to the measurement instrument 

is normally cooled to reduce the thermocouple effects at those junctions. When using a 

thermocouple for precision measurement, a second thermocouple can be kept at a known 

temperature for reference. A series of thermocouples connected together in series produces 

a higher voltage and is called a thermopile. Readings can approach an accuracy of 

0.5%. 

23.2.6.3 - Thermistors 

Thermistors are non-linear devices, their resistance will decrease with an increase 

in temperature. (Note: this is because the extra heat reduces electron mobility in the semiconductor.) 

The resistance can change by more than 1000 times. The basic calculation is 


often metal oxide semiconductors The calculation uses a reference temperature 

and resistance, with a constant for the device, to predict the resistance at another temperature. 

The expression can be rearranged to calculate the temperature given the resistance. 



R t 

= 

R o e 

β⎛ 

1 T -- – ---- 

1 ⎞ 

⎝ ⎠ 

T o 

∴T 

where, 

βT 

= -------------------------------- o 

R 

T t 

o 

ln⎛----- 

⎞ + β 

⎝ ⎠ 

R o 

R o 

, R t 

= resistances at reference and measured temps. 

T o 

, T = reference and actual temperatures 

β = constant for device 

Figure 23.29 

Thermistor Calculations 

Aside: The circuit below can be used to convert the resistance of the thermistor to a voltage 

using a Wheatstone bridge and an inverting amplifier. 

+V 

R1 

R3 

R5 

R2 

R4 

- 

+ 

Vout 

Figure 23.30 

Thermistor Signal Conditioning Circuit 



Thermistors are small, inexpensive devices that are often made as beads, or metallized 

surfaces. The devices respond quickly to temperature changes, and they have a 

higher resistance, so junction effects are not an issue. Typical accuracies are 1%, but the 

devices are not linear, have a limited temperature/resistance range and can be self heating. 

23.2.6.4 - Other Sensors 

IC sensors are becoming more popular. They output a digital reading and can have 

accuracies better than 0.01%. But, they have limited temperature ranges, and require some 

knowledge of interfacing methods for serial or parallel data. 

Pyrometers are non-contact temperature measuring devices that use radiated heat. 

These are normally used for high temperature applications, or for production lines where it 

is not possible to mount other sensors to the material. 

23.2.7 Light 

23.2.7.1 - Light Dependant Resistors (LDR) 

Light dependant resistors (LDRs) change from high resistance (>Mohms) in bright 

light to low resistance (


Aside: an LDR can be used in a voltage divider to convert the change in resistance to a 

measurable voltage. 

V high 

These are common in low 

cost night lights. 

V out 

V low 

Figure 23.31 

A Light Level Detector Circuit 

23.2.8 Chemical 

23.2.8.1 - pH 

The pH of an ionic fluid can be measured over the range from a strong base (alkaline) 

with pH=14, to a neutral value, pH=7, to a strong acid, pH=0. These measurements 

are normally made with electrodes that are in direct contact with the fluids. 

23.2.8.2 - Conductivity 

Conductivity of a material, often a liquid is often used to detect impurities. This 

can be measured directly be applying a voltage across two plates submerged in the liquid 

and measuring the current. High frequency inductive fields is another alternative. 



23.2.9 Others 

A number of other detectors/sensors are listed below, 

Combustion - gases such as CO2 can be an indicator of combustion 

Humidity - normally in gases 

Dew Point - to determine when condensation will form 

23.3 INPUT ISSUES 

Signals from transducers are typically too small to be read by a normal analog 

input card. Amplifiers are used to increase the magnitude of these signals. An example of 

a single ended signal amplifier is shown in Figure 23.32. The amplifier is in an inverting 

configuration, so the output will have an opposite sign from the input. Adjustments are 

provided for gain and offset adjustments. 

Note: op-amps are used in this section to implement the amplifiers because they are 

inexpensive, common, and well suited to simple design and construction projects. 

When purchasing a commercial signal conditioner, the circuitry will be more complex, 

and include other circuitry for other factors such as temperature compensation. 



+V 

Ro 

offset 

Rf 

Rg 

-V 

gain 

Vin 

Ri 

- 

+ 

Vout 

R 

V f + R g 

out 

= ⎛ 

⎝ 

---------------- ⎞ 

⎠ Vin + offset 

R i 

Figure 23.32 

A Single Ended Signal Amplifier 

A differential amplifier with a current input is shown in Figure 23.33. Note that Rc 

converts a current to a voltage. The voltage is then amplified to a larger voltage. 

Iin 

Rc 

R1 

R2 

- 

+ 

Rf 

Vout 

R3 

R4 

Figure 23.33 

A Current Amplifier 



The circuit in Figure 23.34 will convert a differential (double ended) signal to a 

single ended signal. The two input op-amps are used as unity gain followers, to create a 

high input impedance. The following amplifier amplifies the voltage difference. 

- 

+ 

Vin 

- 

+ 

Vout 

- 

+ 

CMRR 

adjust 

Figure 23.34 

A Differential Input to Single Ended Output Amplifier 

The Wheatstone bridge can be used to convert a resistance to a voltage output, as 

shown in Figure 23.35. If the resistor values are all made the same (and close to the value 

of R3) then the equation can be simplified. 



+V 

R1 

R3 

R5 

R2 

R4 

- 

+ 

Vout 

R 2 

V out VR ( 5 ) ⎛----------------- 

⎞ 1 

----- ----- 

1 1 

= ⎛ ⎛ + + ----- ⎞ – ----- 

1 ⎞ 

⎝⎝R 1 + R ⎠⎝ 

2 R 3 R 4 R ⎠ 5 R ⎠ 3 

or if R = R 1 

= R 2 

= R 4 

= R 5 

V out = V⎛-------- 

R ⎞ 

⎝2R ⎠ 3 

Figure 23.35 

A Resistance to Voltage Amplifier 

23.4 SENSOR GLOSSARY 

Ammeter - A meter to indicate electrical current. It is normally part of a DMM 

Bellows - This is a flexible volumed that will expand or contract with a pressure 

change. This often looks like a cylinder with a large radius (typ. 2") but it is 

very thin (type 1/4"). It can be set up so that when pressure changes, the displacement 

of one side can be measured to determine pressure. 

Bourdon tube - Widely used industrial gage to measure pressure and vacuum. It 

resembles a crescent moon. When the pressure inside changes the moon shape 

will tend to straighten out. By measuring the displacement of the tip the pressure 

can be measured. 

Chromatographic instruments - laboratory-type instruments used to analyze chemical 

compounds and gases. 

Inductance-coil pulse generator - transducer used to measure rotational speed. Out- 



put is pulse train. 

Interferometers - These use the interference of light waves 180 degrees out of 

phase to determine distances. Typical sources of the monochromatic light 

required are lasers. 

Linear-Variable-Differential transformer (LVDT) electromechanical transducer 

used to measure angular or linear displacement. Output is Voltage 

Manometer - liquid column gage used widely in industry to measure pressure. 

Ohmmeter - meter to indicate electrical resistance 

Optical Pyrometer - device to measure temperature of an object at high temperatures 

by sensing the brightness of an objects surface. 

Orifice Plate - widely used flowmeter to indicate fluid flow rates 

Photometric Transducers - a class of transducers used to sense light, including 

phototubes, photodiodes, phototransistors, and photoconductors. 

Piezoelectric Accelerometer - Transducer used to measure vibration. Output is 

emf. 

Pitot Tube - Laboratory device used to measure flow. 

Positive displacement Flowmeter - Variety of transducers used to measure flow. 

Typical output is pulse train. 

Potentiometer - instrument used to measure voltage 

Pressure Transducers - A class of transducers used to measure pressure. Typical 

output is voltage. Operation of the transducer can be based on strain gages or 

other devices. 

Radiation pyrometer - device to measure temperature by sensing the thermal radiation 

emitted from the object. 

Resolver - this device is similar to an incremental encoder, except that it uses coils 

to generate magnetic fields. This is like a rotary transformer. 

Strain Gage - Widely used to indicate torque, force, pressure, and other variables. 

Output is change in resistance due to strain, which can be converted into voltage. 

Thermistor - Also called a resistance thermometer; an instrument used to measure 

temperature. Operation is based on change in resistance as a function of temperature. 

Thermocouple - widely used temperature transducer based on the Seebeck effect, 

in which a junction of two dissimilar metals emits emf related to temperature. 

Turbine Flowmeter - transducer to measure flow rate. Output is pulse train. 

Venturi Tube - device used to measure flow rates. 

23.5 SUMMARY 

• Selection of continuous sensors must include issues such as accuracy and resolution. 

• Angular positions can be measured with potentiometers and encoders (more 

accurate). 

• Tachometers are useful for measuring angular velocity. 



• Linear positions can be measured with potentiometers (limited accuracy), LVDTs 

(limited range), moire fringes (high accuracy). 

• Accelerometers measure acceleration of masses. 

• Strain gauges and piezoelectric elements measure force. 

• Pressure can be measured indirectly with bellows and Bourdon tubes. 

• Flow rates can be measured with Venturi valves and pitot tubes. 

• Temperatures can be measured with RTDs, thermocouples, and thermistors. 

• Input signals can be single ended for more inputs or double ended for more accuracy. 

23.6 REFERENCES 

Bryan, L.A. and Bryan, E.A., Programmable Controllers; Theory and Implementation, Industrial 

Text Co., 1988. 

Swainston, F., A Systems Approach to Programmable Controllers, Delmar Publishers Inc., 1992. 


1. Name two types of inputs that would be analog input values (versus a digital value). 

2. Search the web for common sensor manufacturers for 5 different types of continuous sensors. If 

possible identify prices for the units. Sensor manufacturers include (hyde park, banner, allen 

bradley, omron, etc.) 

3. What is the resolution of an absolute optical encoder that has six binary tracks? nine tracks? 

twelve tracks? 

4. Suggest a couple of methods for collecting data on the factory floor 

5. If a thermocouple generates a voltage of 30mV at 800F and 40mV at 1000F, what voltage will 

be generated at 1200F? 

6. A potentiometer is to be used to measure the position of a rotating robot link (as a voltage 

divider). The power supply connected across the potentiometer is 5.0 V, and the total wiper 

travel is 300 degrees. The wiper arm is directly connected to the rotational joint so that a given 

rotation of the joint corresponds to an equal rotation of the wiper arm. 

a) If the joint is at 42 degrees, what voltage will be output from the potentiometer? 

b) If the joint has been moved, and the potentiometer output is 2.765V, what is the 

position of the potentiometer? 

7. A motor has an encoder mounted on it. The motor is driving a reducing gear box with a 50:1 



ratio. If the position of the geared down shaft needs to be positioned to 0.1 degrees, what is the 

minimum resolution of the incremental encoder? 

8. What is the difference between a strain gauge and an accelerometer? How do they work? 

9. Use the equations for a permanent magnet DC motor to explain how it can be used as a tachometer. 

10. What are the trade-offs between encoders and potentiometers? 

11. A potentiometer is connected to a PLC analog input card. The potentiometer can rotate 300 

degrees, and the voltage supply for the potentiometer is +/-10V. Write a ladder logic program 

to read the voltage from the potentiometer and convert it to an angle in radians stored in F8:0. 


1. Temperature and displacement 

2. Sensors can be found at www.ab.com, www.omron.com, etc 

3. 360°/64steps, 360°/512steps, 360°/4096steps 

4. data bucket, smart machines, PLCs with analog inputs and network connections 

5. 

V out 

= α( T– 

T ref 

) 0.030 = α( 800 – T ref 

) 0.040 = α( 1000 – T ref 

) 

-- 

1 

α 

800 – T ref 

1000 – T 

= ----------------------- = -------------------------- ref 

0.030 0.040 

800 – T ref 

= 750 – 0.75T ref 

50 = 0.25T ref T ref = 200F α = -------------------------- 

0.040 

= 

1000 – 200 

V out 

= 0.00005( 1200 – 200) = 0.050V 

------------- 

50µV 

F 



6. 

θ w 

a) V out = ( V 2 – V 1 ) ⎛----------⎞ + V 

⎝ ⎠ 1 = ( 5V – 0V) 

⎛----------------- 

42deg ⎞ + 0V = 0.7V 

⎝300deg⎠ 

θ max 

θ w 

b) 2.765V = ( 5V – 0V) 

⎛----------------- 

⎞ + 0V 

⎝300deg⎠ 

θ w 

2.765V = ( 5V – 0V) 

⎛----------------- 

⎞ + 0V 

⎝300deg⎠ 

= 165.9deg 

θ w 

7. 

θ output 

= 

0.1------------- 

deg 

count 

θ input 

--------------- 

θ output 

50 

= ----- θ 

1 input = 50⎛0.1------------- 

deg ⎞ = 5------------- 

deg 

⎝ count⎠ 

count 

R 

360 deg -------- 

= ------------------ 

rot 

5------------- 

deg = 72 count ------------- 

rot 

count 

8. 

strain gauge measures strain in a material using a stretching wire that increases resistance 

- accelerometers measure acceleration with a cantilevered mass on a piezoelectric 

element. 

9. 

R 

DMM V = K s ω 

ω· + ω⎛----- 

K2 ⎞ = V ⎛ K 

⎝JR⎠ 

s ----- ⎞ 

⎝JR⎠ 

V s 

= ω( K) + ω· ⎛JR 

⎝ 

----- ⎞ 

K ⎠ 

+ 

- 

When the motor shaft is turned by 

another torque source a voltage is generated 

that is proportional to the angular 

velocity. This is the reverse emf. A dmm, 

or other high impedance instrument can 

be used to measure this, thus minizing 

the loses in resistor R. 



10. 

encoders cost more but can have higher resolutions. Potentiometers have limited 

ranges of motion 

11. 

FS 

BT9:0/EN 

BT9:1/DN 

BT9:1/EN 

BTW 

Rack: 0 

Group: 0 

Module: 0 



Length: 37 


BTR 

Rack: 0 

Group: 0 

Module: 0 



Length: 20 


CPT 

Dest F8:0 

Expression 

"20.0 * N7:41 / 4095.0 - 10" 

CPT 

Dest F8:0 

Expression 

"300.0 * (F8:0 + 10) / 20" 

RAD 

Source F8:0 

Dest F8:1 


1. Write a simple C program to read incremental encoder inputs (A and B) to determine the current 

position of the encoder. Note: use the quadrature encoding to determine the position of the 

motor. 



2. A high precision potentiometer has an accuracy of +/- 0.1% and can rotate 300degrees and is 

used as a voltage divider with a of 0V and 5V. The output voltage is being read by an A/D converter 

with a 0V to 10V input range. How many bits does the A/D converter need to accommodate 

the accuracy of the potentiometer? 

3. The table of position and voltage values below were measured for an inexpensive potentiometer. 

Write a C subroutine that will accept a voltage value and interpolate the position value. 

theta (deg) V 

0 

67 

145 

195 

213 

296 

315 

0.1 

0.6 

1.6 

2.4 

3.4 

4.2 

5.0 


continuous actuators - 24.1 

24. CONTINUOUS ACTUATORS 

Topics: 

• Servo Motors; AC and DC 

• Stepper motors 

• Single axis motion control 

• Hydraulic actuators 

Objectives: 

• To understand the main differences between continuous actuators 

• Be able to select a continuous actuator 

• To be able to plan a motion for a single servo actuator 


Continuous actuators allow a system to position or adjust outputs over a wide 

range of values. Even in their simplest form, continuous actuators tend to be mechanically 

complex devices. For example, a linear slide system might be composed of a motor with 

an electronic controller driving a mechanical slide with a ball screw. The cost for such 

actuators can easily be higher than for the control system itself. These actuators also 

require sophisticated control techniques that will be discussed in later chapters. In general, 

when there is a choice, it is better to use discrete actuators to reduce costs and complexity. 

24.2 ELECTRIC MOTORS 

An electric motor is composed of a rotating center, called the rotor, and a stationary 

outside, called the stator. These motors use the attraction and repulsion of magnetic 

fields to induce forces, and hence motion. Typical electric motors use at least one electromagnetic 

coil, and sometimes permanent magnets to set up opposing fields. When a voltage 

is applied to these coils the result is a torque and rotation of an output shaft. There are 

a variety of motor configuration the yields motors suitable for different applications. Most 

notably, as the voltages supplied to the motors will vary the speeds and torques that they 

will provide. 



• Motor Categories 

• AC motors - rotate with relatively constant speeds proportional to the frequency 

of the supply power 

induction motors - squirrel cage, wound rotor - inexpensive, efficient. 

synchronous - fixed speed, efficient 

• DC motors - have large torque and speed ranges 

permanent magnet - variable speed 

wound rotor and stator - series, shunt and compound (universal) 

• Hybrid 

brushless permanent magnet - 

stepper motors 

• Contactors are used to switch motor power on/off 

• Drives can be used to vary motor speeds electrically. This can also be done with 

mechanical or hydraulic machines. 

• Popular drive categories 

• Variable Frequency Drives (VFD) - vary the frequency of the power 

delivered to the motor to vary speed. 

• DC motor controllers - variable voltage or current to vary the motor speed 

• Eddy Current Clutches for AC motors - low efficiency, uses a moving 

iron drum and windings 

• Wound rotor AC motor controllers - low efficiency, uses variable resistors 

to adjust the winding currents 

A control system is required when a motor is used for an application that requires 

continuous position or velocity. A typical controller is shown in Figure 24.1. In any controlled 

system a command generator is required to specify a desired position. The controller 

will compare the feedback from the encoder to the desired position or velocity to 

determine the system error. The controller will then generate an output, based on the system 

error. The output is then passed through a power amplifier, which in turn drives the 

motor. The encoder is connected directly to the motor shaft to provide feedback of position. 



command 

generator 

(e.g., PLC) 

desired position 

or velocity 

controller 

voltage/ 

current 

power 

amp 

amplified 

voltage/ 

current 

motor 

encoder 

Figure 24.1 

A Typical Feedback Motor Controller 

24.2.1 Basic Brushed DC Motors 

In a DC motor there is normally a set of coils on the rotor that turn inside a stator 

populated with permanent magnets. Figure 24.2 shows a simplified model of a motor. The 

magnets provide a permanent magnetic field for the rotor to push against. When current is 

run through the wire loop it creates a magnetic field. 

I 

I 

magnetic 

field 

axis of 

rotation ω 



Figure 24.2 

A Simplified Rotor 

The power is delivered to the rotor using a commutator and brushes, as shown in 

Figure 24.3. In the figure the power is supplied to the rotor through graphite brushes rubbing 

against the commutator. The commutator is split so that every half revolution the 

polarity of the voltage on the rotor, and the induced magnetic field reverses to push against 

the permanent magnets. 

motor 

shaft 

brushes 

Top 

Front 

split commutator 

split commutator 

motor 

shaft 

brushes 

V+ power V- 

supply 

Figure 24.3 

A Split Ring Commutator 

The direction of rotation will be determined by the polarity of the applied voltage, 

and the speed is proportional to the voltage. A feedback controller is used with these 

motors to provide motor positioning and velocity control. 

These motors are losing popularity to brushless motors. The brushes are subject to 



wear, which increases maintenance costs. In addition, the use of brushes increases resistance, 

and lowers the motors efficiency. 

ASIDE: The controller to drive a servo motor normally uses a Pulse Width Modulated 

(PWM) signal. As shown below the signal produces an effective voltage that is relative 

to the time that the signal is on. The percentage of time that the signal is on is 

called the duty cycle. When the voltage is on all the time the effective voltage delivered 

is the maximum voltage. So, if the voltage is only on half the time, the effective 

voltage is half the maximum voltage. This method is popular because it can produce 

a variable effective voltage efficiently. The frequency of these waves is normally 

above 20KHz, above the range of human hearing. 

V max 

0 

V max 

0 

V max 

0 

V max 

0 

50% duty cycle 



0% duty cycle 

V eff 

= --------V 

50 

100 max 

t 

V eff 

= --------V 

20 

100 max 

t 

V eff 

= 

100 

--------V 

100 max 

t 

V eff 

= --------V 

0 

100 max 

t 

Figure 24.4 

Pulse Width Modulation (PWM) For Control 



ASIDE: A PWM signal can be used to drive a motor with the circuit shown below. The 

PWM signal switches the NPN transistor, thus switching power to the motor. In this 

case the voltage polarity on the motor will always be the same direction, so the 

motor may only turn in one direction. 

signal 

source 

V+ 

DC motor 

V+ 

V- 

power 

supply 

com 

Figure 24.5 

PWM Unidirectional Motor Control Circuit 



ASIDE: When a motor is to be controlled 

with PWM in two directions 

the H-bridge circuit (shown below) 

is a popular choice. These can be 

built with individual components, or 

purchased as integrated circuits for 

smaller motors. To turn the motor in 

one direction the PWM signal is 

applied to the Va inputs, while the 

Vb inputs are held low. In this 

arrangement the positive voltage is 

at the left side of the motor. To 

reverse the direction the PWM signal 

is applied to the Vb inputs, while 

the Va inputs are held low. This 

applies the positive voltage to the 

right side of the motor. 

Va 

Vb 

+Vs 

-Vs 

Vb 

Va 

Figure 24.6 

PWM Bidirectional Motor Control Circuit 

24.2.2 AC Motors 

• Power is normally generated as 3-phase AC, so using this increases the efficiency 

of electrical drives. 

• In AC motors the AC current is used to create changing fields in the motor. 

• Typically AC motors have windings on the stator with multiple poles. Each pole 

is a pair of windings. As the AC current reverses, the magnetic field in the rotor appears to 

rotate. 



L1 

stator windings 

rotor 

Neut. 

Figure 24.7 

A 2 Pole Single Phase AC Motor 



L2 

L1 

L3 

Neut. 

Neut. 

Neut. 

Figure 24.8 

A 6 Pole 3-Phase AC Motor 

• The number of windings (poles) can be an integer multiple of the number of 

phases of power. More poles results in a lower rotational speed of the motor. 

• Rotor types for induction motors are listed below. Their function is to intersect 

changing magnetic fields from the stator. The changing field induces currents in the rotor. 

These currents in turn set up magnetic fields that oppose fields from the stator, generating 

a torque. 

Squirrel cage - has the shape of a wheel with end caps and bars 

Wound Rotor - the rotor has coils wound. These may be connected to external 

contacts via commutator 

• Induction motors require slip. If the motor turns at the precise speed of the stator 

field, it will not see a changing magnetic field. The result would be a collapse of the rotor 

magnetic field. As a result an induction motor always turns slightly slower than the stator 

field. The difference is called the slip. This is typically a few percent. As the motor is 

loaded the slip will increase until the motor stalls. 



An induction motor has the windings on the stator. The rotor is normally a squirrel 

cage design. The squirrel cage is a cast aluminum core that when exposed to a changing 

magnetic field will set up an opposing field. When an AC voltage is applied to the stator 

coils an AC magnetic field is created, the squirrel cage sets up an opposing magnetic field 

and the resulting torque causes the motor to turn. 

The motor will turn at a frequency close to that of the applied voltage, but there is 

always some slip. It is possible to control the speed of the motor by controlling the frequency 

of the AC voltage. Synchronous motor drives control the speed of the motors by 

synthesizing a variable frequency AC waveform, as shown in Figure 24.9. 

Controller 

Figure 24.9 

AC Motor Speed Control 

These drives should be used for applications that only require a single rotational 

direction. The torque speed curve for a typical induction motor is shown in Figure 24.10. 

When the motor is used with a fixed frequency AC source the synchronous speed of the 

motor will be the frequency of AC voltage divided by the number of poles in the motor. 

The motor actually has the maximum torque below the synchronous speed. For example a 

2 pole motor might have a synchronous speed of (2*60*60/2) 3600 RPM, but be rated for 

3520 RPM. When a feedback controller is used the issue of slip becomes insignificant. 



torque 

operating range 

synchronous speed 

speed 

Figure 24.10 

Torque Speed Curve for an Induction Motor 

Class A 

torque 

speed 

Class B 

torque 

speed 

Class C 

torque 

speed 

Class D 

torque 

speed 

Figure 24.11 

NEMA Squirrel Cage Torque Speed Curves 



• Wound rotor induction motors use external resistors. varying the resistance 

allows the motors torque speed curve to vary. As the resistance value is increased the 

motor torque speed curve shifts from the Class A to Class D shapes. 

• The figure below shows the relationship between the motor speed and applied 

power, slip, and number of poles. An ideal motor with no load would have a slip of 0%. 

RPM 

where, 

= 

f120 ---------- ⎛ 

p ⎝ 

1 

f 

= 

– ------------- 

S ⎞ 

100% ⎠ 

power frequency (60Hz typ.) 

p 

= 

number of poles (2, 4, 6, etc...) 

RPM 

= 

motor speed in rotations per minute 

S 

= 

motor slip 

• Single phase AC motors can run in either direction. To compensate for this a 

shading pole is used on the stator windings. It basically acts as an inductor to one side of 

the field which slows the filed buildup and collapse. The result is that the field strength 

seems to naturally rotate. 

• Thermal protection is normally used in motors to prevent overheating. 

• Universal motors were presented earlier for DC applications, but they can also be 

used for AC power sources. This is because the field polarity in the rotor and stator both 

reverse as the AC current reverses. 

• Synchronous motors are different from induction motors in that they are designed 

to rotate at the frequency of the fields, in other words there is no slip. 

• Synchronous motors use generated fields in the rotor to oppose the stators field. 

• Starting AC motors can be hard because of the low torque at low speeds. To deal 

with this a switching arrangement is often used. At low speeds other coils or capacitors are 

connected into the circuits. At higher speeds centrifugal switches disconnect these and the 

motor behavior switches. 



• Single phase induction motors are typically used for loads under 1HP. Various 

types (based upon their starting and running modes) are, 

- split phase - there are two windings on the motor. A starting winding is 

used to provide torque at lower speeds. 

- capacitor run - 

- capacitor start 

- capacitor start and run 

- shaded pole - these motors use a small offset coil (such as a single copper 

winding) to encourage the field buildup to occur asymmetrically. These 

motors are for low torque applications much less than 1HP. 

- universal motors (also used with DC) have a wound rotor and stator that 

are connected in series. 



Split Winding 

Vin 

running 

winding 

squirrel cage 

rotor 

starting winding 

starting capacitor 

Capacitor Start 

Vin 

running 

winding 

squirrel cage 

rotor 


capacitor 

Capacitor Run 

Vin 

running 

winding 

squirrel cage 

rotor 

capacitor winding 

Figure 24.12 

Single Phase Motor Configurations 



running capacitor 

Capacitor Start and Capacitor Run Motor 

starting capacitor 

Vin 

running 

winding 

squirrel cage 

rotor 


Figure 24.13 

Single Phase Motor Configurations 

24.2.3 Brushless DC Motors 

Brushless motors use a permanent magnet on the rotor, and use windings on the 

stator. Therefore there is no need to use brushes and a commutator to switch the polarity of 

the voltage on the coil. The lack of brushes means that these motors require less maintenance 

than the brushed DC motors. 

A typical Brushless DC motor could have three poles, each corresponding to one 

power input, as shown in Figure 24.14. Each of coils is separately controlled. The coils are 

switched on to attract or repel the permanent magnet rotor. 



V1 

V2 

N 

S 

V3 

Figure 24.14 

A Brushless DC Motor 

To continuously rotate these motors the current in the stator coils must alternate 

continuously. If the power supplied to the coils was a 3-phase AC sinusoidal waveform, 

the motor will rotate continuously. The applied voltage can also be trapezoidal, which will 

give a similar effect. The changing waveforms are controller using position feedback from 

the motor to select switching times. The speed of the motor is proportional to the frequency 

of the signal. 

A typical torque speed curve for a brushless motor is shown in Figure 24.15. 



torque 

speed 

Figure 24.15 

Torque Speed Curve for a Brushless DC Motor 

24.2.4 Stepper Motors 

Stepper motors are designed for positioning. They move one step at a time with a 

typical step size of 1.8 degrees giving 200 steps per revolution. Other motors are designed 

for step sizes of 1.8, 2.0, 2.5, 5, 15 and 30 degrees. 

There are two basic types of stepper motors, unipolar and bipolar, as shown in Figure 

24.16. The unipolar uses center tapped windings and can use a single power supply. 

The bipolar motor is simpler but requires a positive and negative supply and more complex 

switching circuitry. 

1 

a 

b 

1a 

1b 

a 

b 

2a 

2b 

unipolar 

2 

bipolar 



Figure 24.16 

Unipolar and Bipolar Stepper Motor Windings 

The motors are turned by applying different voltages at the motor terminals. The 

voltage change patterns for a unipolar motor are shown in Figure 24.17. For example, 

when the motor is turned on we might apply the voltages as shown in line 1. To rotate the 

motor we would then output the voltages on line 2, then 3, then 4, then 1, etc. Reversing 

the sequence causes the motor to turn in the opposite direction. The dynamics of the motor 

and load limit the maximum speed of switching, this is normally a few thousand steps per 

second. When not turning the output voltages are held to keep the motor in position. 

1a 

2a 

1b 

2b 

Step 

1a 

2a 

1b 

2b 

controller 

stepper 

motor 

1 

2 

3 

4 

1 

0 

0 

1 

0 

1 

1 

0 

1 

1 

0 

0 

0 

0 

1 

1 

To turn the motor the phases are stepped through 1, 2, 3, 4, and then back to 1. 

To reverse the direction of the motor the sequence of steps can be reversed, 

eg. 4, 3, 2, 1, 4, ..... If a set of outputs is kept on constantly the motor will be 

held in position. 

Figure 24.17 

Stepper Motor Control Sequence for a Unipolar Motor 

Stepper motors do not require feedback except when used in high reliability applications 

and when the dynamic conditions could lead to slip. A stepper motor slips when 

the holding torque is overcome, or it is accelerated too fast. When the motor slips it will 

move a number of degrees from the current position. The slip cannot be detected without 

position feedback. 

Stepper motors are relatively weak compared to other motor types. The torque 

speed curve for the motors is shown in Figure 24.18. In addition they have different static 

and dynamic holding torques. These motors are also prone to resonant conditions because 

of the stepped motion control. 



torque 

speed 

Figure 24.18 

Stepper Motor Torque Speed Curve 

The motors are used with controllers that perform many of the basic control functions. 

At the minimum a translator controller will take care of switching the coil voltages. 

A more sophisticated indexing controller will accept motion parameters, such as distance, 

and convert them to individual steps. Other types of controllers also provide finer step resolutions 

with a process known as microstepping. This effectively divides the logical steps 

described in Figure 24.17 and converts them to sinusoidal steps. 

translators - the user indicates maximum velocity and acceleration and a distance 

to move 

indexer - the user indicates direction and number of steps to take 

microstepping - each step is subdivided into smaller steps to give more resolution 

24.2.5 Wound Field Motors 

• Uses DC power on the rotor and stator to generate the magnetic field (i.e., no permanent 

magnets) 

• Shunt motors 

- have the rotor and stator coils connected in parallel. 

- when the load on these motors is reduced the current flow increases 

slightly, increasing the field, and slowing the motor. 

- these motors have a relatively small variation in speed as they are varied, 

and are considered to have a relatively constant speed. 

- the speed of the motor can be controlled by changing the supply voltage, 

or by putting a rheostat/resistor in series with the stator windings. 



I a 

V a 

= ----- 

R a 

T = K t I a φ 

where, 

I a 

, V a 

, R a 

= Armature current, voltage and resistance 

T 

K t 

= 

= 

Torque on motor shaft 

Motor speed constant 

φ = 

motor field flux 

ω 

operating 

range 

T 

• Series motors\ 

- have the rotor and stator coils connected in series. 

- as the motor speed increases the current increases, the motor can theoreti- 



cally accelerate to infinite speeds if unloaded. This makes the dangerous 

when used in applications where they are potentially unloaded. 

- these motors typically have greater starting torques that shunt motors 

I a 

= 

V 

---------------- a 

R a 

+ R f 

2 

T = K t 

I a 

φ = K t 

I a 

where, 

I a 

, V a 

= Armature current, voltage 

R a 

, R f 

= Armature and field coil resistance 

T 

K t 

= 

= 

Torque on motor shaft 

Motor speed constant 

φ = 

motor field flux 

ω 

stall torque 

T 



The XXXXXXX 

e f = r a i a + Dl a i a + e m 

e m 

T 

= 

= 

K e θD 

K T i a 

e a = ( r a + l a D)i a + K e Dθ 

e a 

= ( r a 

+ l a 

D) 

⎛----- 

T ⎞ 

⎝ ⎠ 

+ K e 

Dθ 

K T 

Figure 24.19 

Equations for an armature controlled DC motor 

• Compound motors\ 

- have the rotor and stator coils connected in series. 

- differential compound motors have the shunt and series winding field 

aligned so that they oppose each other. 

- cumulative compound motors have the shunt and series winding fields 

aligned so that they add 

ω 

cumulative 

differential 

T 



e f = r f i f + l f i f D 

T 

= 

K T i f 

T 

-- = JD 2 + BD 

θ 

-- 

θ 

T 

-- 

θ 

i f 

θ 

--- 

e f 

T 

--- 

e f 

= ----------------------- 

1 

JD 2 + BD 

-- 

θ T K 

= -- = ----------------------- T 

Ti f JD 2 + BD 

θ 

-- i f 

⎛ K 

--- 

T 

⎞ 1 

= = ⎜----------------------- 

i f e f 

T 

-- i JD 2 ⎟ 

⎛----------------- 

⎞ 

⎝ + BD⎠ 

⎝r f + l f D⎠ 

f 

= --- = K ⎛ 1 

T 

----------------- ⎞ 

⎝ + l f 

D⎠ 

i f 

e f 

r f 

Figure 24.20 

Equations for a controlled field motor 

24.3 HYDRAULICS 

Hydraulic systems are used in applications requiring a large amount of force and 

slow speeds. When used for continuous actuation they are mainly used with position feedback. 

An example system is shown in Figure 24.21. The controller examines the position 

of the hydraulic system, and drivers a servo valve. This controls the flow of fluid to the 

actuator. The remainder of the provides the hydraulic power to drive the system. 



controller 

valve 

hydraulic 

power 

supply 

position 

sensor 

position 

hydraulic 

actuator 

sump 

Figure 24.21 

Hydraulic Servo System 

The valve used in a hydraulic system is typically a solenoid controlled valve that is 

simply opened or closed. Newer, more expensive, valve designs use a scheme like pulse 

with modulation (PWM) which open/close the valve quickly to adjust the flow rate. 

24.4 OTHER SYSTEMS 

The continuous actuators discussed earlier in the chapter are the more common 

types. For the purposes of completeness additional actuators are listed and described 

briefly below. 

Heaters - to control a heater with a continuous temperature a PWM scheme can be 

used to limit a DC voltage, or an SCR can be used to supply part of an AC 

waveform. 

Pneumatics - air controlled systems can be used for positioning with suitable feedback. 

Velocities can also be controlled using fast acting valves. 

Linear Motors - a linear motor works on the same principles as a normal rotary 

motor. The primary difference is that they have a limited travel and their cost is 

typically much higher than other linear actuators. 

Ball Screws - rotation is converted to linear motion using balls screws. These are 

low friction screws that drive nuts filled with ball bearings. These are normally 

used with slides to bear mechanical loads. 



24.5 SUMMARY 

• AC motors work at higher speeds 

• DC motors work over a range of speeds 

• Motion control introduces velocity and acceleration limits to servo control 

• Hydraulics make positioning easy 


1. A stepping motor is to be used to drive each of the three linear axes of a cartesian coordinate 

robot. The motor output shaft will be connected to a screw thread with a screw pitch of 0.125”. 

It is desired that the control resolution of each of the axes be 0.025” 

a) to achieve this control resolution how many step angles are required on the stepper 

motor? 

b) What is the corresponding step angle? 

c) Determine the pulse rate that will be required to drive a given joint at a velocity 

of 3.0”/sec. 

2. For the stepper motor in the previous question, a pulse train is to be generated by the robot controller. 

a) How many pulses are required to rotate the motor through three complete revolutions? 

b) If it is desired to rotate the motor at a speed of 25 rev/min, what pulse rate must 

be generated by the robot controller? 

3. Explain the differences between stepper motors, variable frequency induction motors and DC 

motors using tables. 

4. 5. Short answer, 

a) Compare the various types of motors discussed in the class using a detailed table. 

b) When using a motor there are the static and kinetic friction limits. Will deadband correction 

allow the motor to move slower than both, one, or neither? Explain your answer. 

c) What is the purpose of a calibration curve? 




1. 

a) P = 0.125⎛------ 

in ⎞ R = 0.025--------- 

in 

⎝rot⎠ 

step 

0.025--------- 

in 

θ = 

R 

-- = -------------------------- 

step 

P 

0.125⎛ 

⎝ 

------ 

in 

= 0.2--------- 

rot Thus 

⎞ step 

rot⎠ 

b) θ = 0.2--------- rot = 72 --------- 

deg 

step step 

------------------ 

1 

0.2--------- 

rot = 5 step --------- 

rot 

step 

c) 

PPS 

3 in ---- 

= ------------------------ 

s 

0.025--------- 

in = 120 steps ------------ 

s 

step 

2. 

a) 

pulses 

= ( 3rot) ⎛5 step --------- ⎞ = 15steps 

⎝ rot ⎠ 

b) pulses 

--------------- = ⎛25 -------- 

rot ⎞⎛ 5 

step 

--------- ⎞ = 125 steps ------------ = 125⎛------------ 

1min ⎞steps 

------------ = 2.08 step --------- 

s ⎝ min⎠⎝ 

rot ⎠ min ⎝ 60s ⎠ min s 

3. 

4. 

stepper motor 

vfd 

dc motor 

speed 

very low speeds 

limited speed range 

wide range 

torque 

low torque 

good at rated speed 

decreases at higher speeds 



a) 

(ans. 

Motor Type 

Cost 

Torque 

Speed 

Applications 

AC/Inuction 

DC Brushed 

DC Brushless 

Stepper 

Shunt 

Series 

low 

low/med 

high 

low/med 

med 

med 

med 

med 

med 

low 

med 

high 

limited 

variable 

variable 

low 

varies 

varies 

consumer applications/large power 

short life 

high precision 

positioning 

large break away torques 

b) Deadband correction allows the motor to break free of the statis friction. Once moving freely 

the torque required to ‘stick’ the motor is determined by the lower kinetic friction. Generally this 

means that the motor can move slightly slower than the static friction minimum speed, but not the 

kinetic friction minimum speed. 

c) Calibration is a process where instrumentation outputs are related to inputs. These results are 

then used later to relate measurement equipment outputs with actual phenomenon. For example, 

in the laboratory, tachometers are calibrated by turning them at a steady speed. The speed is measured 

with a strobe tachometer and the voltage output is also recorded. These are then used to 

make a graph relating voltage and speed. Later the strobe tachometer is not used and the voltage 

output of the tach. is used to calculate the speed. 


1. A stepper motor is to be used to actuate one joint of a robot arm in a light duty pick and place 

application. The step angle of the motor is 10 degrees. For each pulse received from the pulse 

train source the motor rotates through a distance of one step angle. 

a) What is the resolution of the stepper motor? 

b) Relate this value to the definitions of control resolution, spatial resolution, and 

accuracy, as discussed in class. 

c) For the stepper motor, a pulse train is to be generated by a motion controller. 

How many pulses are required to rotate the motor through three complete revolutions? 

If it is desired to rotate the motor at a speed of 25 rev/min, what pulse 

rate must be generated by the robot controller? 

2. Describe the voltage ripple that would occur when using a permanent magnet DC motor as a 

tachometer. Hint: consider the use of the commutator to switch the polarity of the coil. 

3. Compare the advantages/disadvantages of DC permanent magnet motors and AC induction 

motors. 


plc pid - 25.1 

25. CONTINUOUS CONTROL 

Topics: 

• Feedback control of continuous systems 

• Control of systems with logical actuators 

• PID control with continuous actuators 

• Analysis of PID controlled systems 

• PID control with a PLC 


Objectives: 

• To understand the concepts behind continuous control 

• Be able to control a system with logical actuators 

• Be able to analyze and control system with a PID controller 


Continuous processes require continuous sensors and/or actuators. For example, 

an oven temperature can be measured with a thermocouple. Simple decision-based control 

schemes can use continuous sensor values to control logical outputs, such as a heating element. 

Linear control equations can be used to examine continuous sensor values and set 

outputs for continuous actuators, such as a variable position gas valve. 

Two continuous control systems are shown in Figure 25.1. The water tank can be 

controlled valves. In a simple control scheme, one of the valves is set by the process, but 

we control the other to maximize some control object. If the water tank was actually a city 

water tank, the outlet valve would be the domestic and industrial water users. The inlet 

valve would be set to keep the tank level at maximum. If the level drops there will be a 

reduced water pressure at the outlet, and if the tank becomes too full it could overflow. 

The conveyor will move boxes between stations. Two common choices are to have it 

move continuously, or to move the boxes between positions, and then stop. When starting 

and stopping the boxes should be accelerated quickly, but not so quickly that they slip. 

And, the conveyor should stop at precise positions. In both of these systems, a good control 

system design will result in better performance. 



valve 

a) Water Tank 

q 1 

q 2 

valve 

h 

motor 

controller 

Vin 

b) Motor Driven Conveyor 

Figure 25.1 

Continuous Systems 

A mechanical control system is pictured in Figure 25.2 that could be used for the 

water tank in Figure 25.1. This controller will adjust the valve position, therefore controlling 

the flow rate into the tank. The height of the fluid in the tank will change the hydrostatic 

pressure at the bottom of the tank. A pressure line is connected to a pressure cell. As 

the pressure inside the cell changes, the cell will expand and contract, opening and closing 

the valve. As the tank fills the pressure becomes higher, the cell expands, and the valve 

closes, reducing the flow in. The desired height of the tank can be adjusted by sliding the 

pressure cell up/down a distance x. In this example the height x is called the setpoint. The 

control variable is the position of the valve, and, the feedback variable is the water pressure 

from the tank. The controller is the pressure cell. 



q 1 

Main water 

supply 

q 2 

x 

For control add, 

feedback 

setpoint 

system error 

1. Feedback of hydrostatic pressure through a rubber tube. 

2. This input slider adjusts the position of the bellows (can 

be adjusted with a screwdriver). 

3. Bellows expand/contract as pressure increases/decreases, 

and move the rod that closes/opens the valve 

4. The valve changes the flow into the tank, thus changing 

the water height. 

1. Some means of measuring the water height (system state) 

2. Some input for desired control height 

3. Some error compensation 

4. An actuator to change the system input 

Figure 25.2 

A Feedback Controller 

Continuous control systems typically need a target value, this is called a setpoint. 

The controller should be designed with some objective in mind. Typical objectives are 

listed below. 

fastest response - reach the setpoint as fast as possible (e.g., hard drive speed) 

smooth response - reduce acceleration and jerks (e.g., elevators) 

energy efficient - minimize energy usage (e.g., industrial oven) 

noise immunity - ignores disturbances in the system (e.g., variable wind gusts) 

An engineer can design a controller mathematically when performance and stability 

are important issues. A common industrial practice is to purchase a PID unit, connect it 



to a process, and tune it through trial and error. This is suitable for simpler systems, but 

these systems are less efficient and prone to instability. In other words it is quick and easy, 

but these systems can go out-of-control. 

25.2 CONTROL OF LOGICAL ACTUATOR SYSTEMS 

Many continuous systems will be controlled with logical actuators. Common 

examples include building HVAC (Heating, Ventilation and Air Conditioning) systems. 

The system setpoint is entered on a thermostat. The controller will then attempt to keep 

the temperature within a few degrees as shown in Figure 25.3. If the temperature is below 

the bottom limit the heater is turned on. When it passes the upper limit it is turned off, and 

it will stay off until if passes the lower limit. If the gap between the upper and lower the 

boundaries is larger, the heater will turn on less often, but be on for longer, and the temperature 

will vary more. This technique is not exact, and time lags will often lead to overshoot 

above and below the temperature limits. 

upper 

temp. 

limit 

set temp. 

(nominal) 

lower 

temp. 

limit 

room 

temp. 

overshoot 

time 

heater on heater off heater on heater off heater on 

Note: This system turns on/off continuously. This behavior is known hunting. If the limits 

are set too close to the nominal value, the system will hunt at a faster rate. Therefore, to 

prevent wear and improve efficiency we normally try to set the limits as far away from 

nominal as possible. 

Figure 25.3 

Continuous Control with a Logical Actuator 

Figure 25.4 shows a controller that will keep the temperature between 72 and 74 



(degrees presumably). The temperature will be read and stored in temp, and the output to 

turn the heater on is connected to heater. 

GRT 

SourceA temp 

SourceB 74 

U 

heater 

LES 

SourceA temp 

SourceB 72 

L 

heater 

Figure 25.4 

A Ladder Logic Controller for a Logical Actuator 

25.3 CONTROL OF CONTINUOUS ACTUATOR SYSTEMS 

25.3.1 Block Diagrams 

Figure 25.5 shows a simple block diagram for controlling arm position. The system 

setpoint, or input, is the desired position for the arm. The arm position is expressed 

with the joint angles. The input enters a summation block, shown as a circle, where the 

actual joint angles are subtracted from the desired joint angles. The resulting difference is 

called the error. The error is transformed to joint torques by the first block labeled neural 

system and muscles. The next block, arm structure and dynamics, converts the torques to 

new arm positions. The new arm positions are converted back to joint angles by the eyes. 



θ neural 

desired + θ error τ applied 

system and 

muscles 

- 

θ actual 

arm structure 

and dynamics 

real world 

arm position 

eyes 

** This block diagram shows a system that has dynamics, actuators, 

feedback sensors, error determination, and objectives 

Figure 25.5 

A Block Diagram 

The blocks in block diagrams represent real systems that have inputs and outputs. 

The inputs and outputs can be real quantities, such as fluid flow rates, voltages, or pressures. 

The inputs and outputs can also be calculated as values in computer programs. In 

continuous systems the blocks can be described using differential equations. Laplace 

transforms and transfer functions are often used for linear systems. 

25.3.2 Feedback Control Systems 

As introduced in the previous section, feedback control systems compare the 

desired and actual outputs to find a system error. A controller can use the error to drive an 

actuator to minimize the error. When a system uses the output value for control, it is called 

a feedback control system. When the feedback is subtracted from the input, the system has 

negative feedback. A negative feedback system is desirable because it is generally more 

stable, and will reduce system errors. Systems without feedback are less accurate and may 

become unstable. 

A car is shown in Figure 25.6, without and with a velocity control system. First, 

consider the car by itself, the control variable is the gas pedal angle. The output is the 

velocity of the car. The negative feedback controller is shown inside the dashed line. Normally 

the driver will act as the control system, adjusting the speed to get a desired velocity. 

But, most automobile manufacturers offer cruise control systems that will 

automatically control the speed of the system. The driver will activate the system and set 



the desired velocity for the cruise controller with buttons. When running, the cruise control 

system will observe the velocity, determine the speed error, and then adjust the gas 

pedal angle to increase or decrease the velocity. 

INPUT 

(e.g. θgas) 


variable 

SYSTEM 

(e.g. a car) 

OUTPUT 

(e.g. velocity) 

v desired 

+ 

_ 

v error 

Driver or 

cruise control 

θgas 

car 

v actual 

Figure 25.6 

Addition of a Control System to a Car 

The control system must perform some type of calculation with Verror, to select a 

new θgas. This can be implemented with mechanical mechanisms, electronics, or software. 

Figure 25.7 lists a number of rules that a person would use when acting as the controller. 

The driver will have some target velocity (that will occasionally be based on speed 

limits). The driver will then compare the target velocity to the actual velocity, and determine 

the difference between the target and actual. This difference is then used to adjust the 

gas pedal angle. 

1. If v error is a little positive/negative, increase/decrease θ gas a little. 

2. If v error is very big/small, increase/decrease θ gas a lot. 

3. If v error is near zero, keep θ gas the same. 

4. If v error suddenly becomes bigger/smaller, then increase/decrease θ gas quickly. 

Figure 25.7 

Human Control Rules for Car Speed 

Mathematical rules are required when developing an automatic controller. The 



next two sections describe different approaches to controller design. 

25.3.3 Proportional Controllers 

Figure 25.8 shows a block diagram for a common servo motor controlled positioning 

system. The input is a numerical position for the motor, designated as C. (Note: The 

relationship between the motor shaft angle and C is determined by the encoder.) The difference 

between the desired and actual C values is the system error. The controller then 

converts the error to a control voltage V. The current amplifier keeps the voltage V the 

same, but increases the current (and power) to drive the servomotor. The servomotor will 

turn in response to a voltage, and drive an encoder and a ball screw. The encoder is part of 

the negative feedback loop. The ball screw converts the rotation into a linear displacement 

x. In this system, the position x is not measured directly, but it is estimated using the motor 

shaft angle. 

C desired 

+ e 

V 

V ωθ , actual x 

Controller Current DC 

Ball 

- 

Amplifier Servomotor 

Screw 

C actual 

Encoder 

Figure 25.8 

A Servomotor Feedback Controller 

The blocks for the system in Figure 25.8 could be described with the equations in 

Figure 25.9. The summation block becomes a simple subtraction. The control equation is 

the simplest type, called a proportional controller. It will simply multiply the error by a 

constant Kp. A larger value for Kp will give a faster response. The current amplifier keeps 

the voltage the same. The motor is assumed to be a permanent magnet DC servo motor, 

and the ideal equation for such a motor is given. In the equation J is the polar mass 

moment of inertia, R is the resistance of the motor coils, and Km is a constant for the 

motor. The velocity of the motor shaft must be integrated to get position. The ball screw 

will convert the rotation into a linear position if the angle is divided by the Threads Per 

Inch (TPI) on the screw. The encoder will count a fixed number of Pulses Per Revolution 

(PPR). 



Summation Block: 

e = C desired 

– C actual 

(1) 

Controller: 

V c 

= 

K p e 

(2) 

Current Amplifier: 

Servomotor: 

Ball Screw: 

Encoder: 

V m 

= V c 

---- 

d 

⎝ 

⎛ dt⎠ 

⎞ ⎛ K 2 ⎞ K ω + ⎜--------- 

m ⎟ ω = ⎛------ 

m 

⎝ JR ⎠ 

⎝JR⎠ 

ω = ----θ 

d 

dt actual 

x 

= 

C actual 

θ 

------------- actual 

TPI 

= PPR( θ actual ) 

⎞ Vm 

(3) 

(4) 

(5) 

(6) 

(7) 

Figure 25.9 

A Servomotor Feedback Controller 

The system equations can be combined algebraically to give a single equation for 

the entire system as shown in Figure 25.10. The resulting equation (12) is a second order 

non-homogeneous differential equation that can be solved to model the performance of the 

system. 

---- 

d 

⎝ 

⎛ dt⎠ 

⎞ 2 θ ⎛ K 2 ⎞ 

--------- m actual ⎜ ⎟ 

⎛---- 

d ⎞ K 

(21.4), (21.5) + θactual = ⎛------ 

m ⎞ Vm 

(21.8) 

⎝ JR ⎠ 

⎝dt⎠ 

⎝JR⎠ 

(21.2), (21.3) = K p e 

(21.9) 

V m 

(21.1), (21.9) V m = K p ( C desired – C actual ) 

(21.10) 

d 

⎝ 

⎛ ---- 

dt⎠ 

⎞ 2 θ ⎛ K 2 ⎞ 

--------- m actual ⎜ ⎟ 

⎛---- 

d ⎞ K 

(21.8), (21.10) + 

m 

⎝ JR ⎠ 

⎝dt⎠ 

θactual = ⎛ 

⎝ 

------⎞ JR⎠ 

Kp ( C desired 

– C actual 

) (21.11) 

(21.7), (21.11) 

d 

⎝ 

⎛ ---- 

dt⎠ 

⎞ 2 θ ⎛ K 2 ⎞ 

--------- m d 

+ actual ⎜ ⎟ 

⎛---- 

⎝ JR ⎠ 

⎝dt⎠ 

⎞ θactual 

K m 

= ⎛ 

⎝ 

------⎞ JR⎠ 

Kp ( C desired 

– PPRθ actual 

) 

d 

⎝ 

⎛ ---- 

dt⎠ 

⎞ 2 θ K 2 

+ ⎛ ⎞ 

--------- m actual ⎜ ⎟ 

⎛---- 

d ⎞ K m ( PPR)K p 

⎝ JR ⎠ 

⎝dt⎠ 

θactual + ⎝ 

⎛ ------------------------------ 

JR ⎠ 

⎞ θactual = 

(21.12) 

⎛K p K 

------------- m ⎞ 

⎝ JR ⎠ Cdesired 


plc pid - 25.10 

Figure 25.10 

A Combined System Model 

A proportional control system can be implemented with the ladder logic shown in 

Figure 25.11 and Figure 25.12. The first ladder logic sections setup and read the analog 

input value, this is the feedback value. 

S2:1/15 - first scan 

MOV 

Source 0000 0000 0000 0001 

Dest N7:0 

BT9:0/EN 

BT9:1/EN 

MOV 

Source 0000 0101 0000 0000 

Dest N7:2 

BTW 

Rack: 0 

Group: 0 

Module: 0 



Length: 37 


BTR 

Rack: 0 

Group: 0 

Module: 0 



Length: 20 


Figure 25.11 

Implementing a Proportional Controller with PLC-5 Ladder Logic 

The control system has a start/stop button. When the system is active B3/0 will be 

on, and the proportional controller calculation will be performed with the SUB and MUL 

functions. When the system is inactive the MOV function will set the output to zero. The 

last BTW function will continually output the calculated controller voltage. 


plc pid - 25.11 

I:001/1 - START 

B3/0 

I:001/0 - ESTOP 

B3/0 - ON 

B3/0 - ON MOV 

Source 0 

Dest N9:60 

B3/0 - ON 

BT9:2/EN 

BT9:1/DN 

SUB 

SourceA N7:80 

SourceB N7:42 

Dest N7:81 

MUL 

SourceA N7:81 

SourceB 2 

Dest N9:60 



Rack 000 

Group 1 

Module 0 



Length 13 

Continuous No 

Figure 25.12 

Implementing a Proportional Controller with PLC-5 Ladder Logic 

This controller may be able to update a few times per second. This is an important 

design consideration - recall that the Nyquist Criterion requires that the actual system 

response be much slower than the controller. This controller will only be suitable for systems 

that don’t change faster than once per second. (Note: The speed limitation is a practical 

limitation for a PLC-5 processor based upon the update times for analog inputs and 

outputs.) This must also be considered if you choose to do a numerical analysis of the control 

system. 


plc pid - 25.12 

25.3.4 PID Control Systems 

Proportional-Integral-Derivative (PID) controllers are the most common controller 

choice. The basic controller equation is shown in Figure 25.13. The equation uses the system 

error e, to calculate a control variable u. The equation uses three terms. The proportional 

term, Kp, will push the system in the right direction. The derivative term, Kd will 

respond quickly to changes. The integral term, Ki will respond to long-term errors. The 

values of Kc, Ki and Kp can be selected, or tuned, to get a desired system response. 

u = K c e+ K i ∫edt 

+ K ⎛de 

d ----- ⎞ Kc 

⎝dt⎠ 

Ki 

Kd 

Relative weights of components 

Figure 25.13 

PID Equation 

Figure 25.14 shows a (partial) block diagram for a system that includes a PID controller. 

The desired setpoint for the system is a potentiometer set up as a voltage divider. A 

summer block will subtract the input and feedback voltages. The error then passes through 

terms for the proportional, integral and derivative terms; the results are summed together. 

An amplifier increases the power of the control variable u, to drive a motor. The motor 

then turns the shaft of another potentiometer, which will produce a feedback voltage proportional 

to shaft position. 

proportional 

PID Controller 

V 

+ 

- 

K p 

( e) 

integral 

e 

K i 

( 

∫e) 

derivative 

K ⎛ d 

d ⎝ 

----e ⎞ 

dt ⎠ 

+ 

+ 

+ 

u 

+V 

amp 

-V 

motor 

V 

Figure 25.14 

A PID Control System 


plc pid - 25.13 

Recall the cruise control system for a car. Figure 25.15 shows various equations 

that could be used as the controller. 

PID Controller 

dv 

θ gas 

= K p 

v error 

+ K i ∫v error 

dt + K ⎛ error 

d 

---------------- ⎞ 

⎝ dt ⎠ 

PI Controller 

θ gas = K p v error + K i v error dt 

PD Controller 

dv 

θ gas 

= K p v error 

+ K ⎛ error 

d 

---------------- ⎞ 

⎝ dt ⎠ 

∫ 

P Controller 

θ gas 

= 

K p v error 

Figure 25.15 

Different Controllers 

When implementing these equations in a computer program the equations can be 

rewritten as shown in Figure 25.16. To do this calculation, previous error and control values 

must be stored. The calculation also require the scan time T between updates. 

u n 

u n – 1 

e ⎛ 

n 

K p 

K i 

T K d 

+ + -----⎞ e ⎛ 

⎝ 

T ⎠ n – 1 

– K p 

2 K d 

– -----⎞ K 

= + + + e ⎛ d 

⎝ T ⎠ n – 2 

-----⎞ 

⎝ T ⎠ 

Figure 25.16 

A PID Calculation 

The PID calculation is available as a ladder logic function, as shown in Figure 

25.17. This can be used in place of the SUB and MUL functions in Figure 25.12. In this 

example the calculation uses the feedback variable stored in Proc Location (as read from 

the analog input). The result is stored in N7:2 (to be an analog output). The control block 

uses the parameters stored in PD12:0 to perform the calculations. Most PLC programming 

software will provide dialogues to set these value. 


plc pid - 25.14 

PID 

Control Block: PD12:0 

Proc Variable: N7:0 

Tieback: N7:1 

Control Output: N7:2 

Note: When entering the ladder logic program into the computer you will be able to 

enter the PID parameters on a popup screen. 

Figure 25.17 

PLC-5 PID Control Block 

PID controllers can also be purchased as cards or stand-alone modules that will 

perform the PID calculations in hardware. These are useful when the response time must 

be faster than is possible with a PLC and ladder logic. 


25.4.1 Oven Temperature Control 

Problem: Design an analog controller that will read an oven temperature between 

1200F and 1500F. When it passes 1500 degrees the oven will be turned off, when it falls 

below 1200F it will be turned on again. The voltage from the thermocouple is passed 

through a signal conditioner that gives 1V at 500F and 3V at 1500F. The controller should 

have a start button and E-stop. 

Solution: 


plc pid - 25.15 

Select a 12 bit 1771-IFE card and use the 0V to 5V range on channel 1 with 

double ended inputs. 

V 

V 1V INT in – V = ⎛---------------------------- 

min ⎞ R = 819 

⎝V R = 2 N max 

– V ⎠ min 

= 4096 

V 

V 3V INT in 

– V = ⎛---------------------------- 

min ⎞ 

⎝V max 

– V ⎠ R = 2458 

min 

Cards: I:000 - Analog Input 

I:001 - DC Inputs 

I:002 - DC Outputs 


plc pid - 25.16 


MOV 

Source 0000 0000 0000 0001 

Dest N7:0 

MOV 

Source 0000 0101 0000 0000 

Dest N7:2 

BTW 

Rack: 0 

Group: 0 

Module: 0 



Length: 37 


BT9:0/EN 

BT9:1/EN 

BTR 

Rack: 0 

Group: 0 

Module: 0 



Length: 20 


I:001/1 - START 

I:001/0 - ESTOP 

B3/0 - ON 

B3/0 - ON 

BT9:0/DN 

BT9:1/DN 

GRT 

SourceA N7:42 

SourceB 2458 

U 

B3/1 - HEAT 

LES 

SourceA N7:42 

SourceB 819 

L 

B3/1 - HEAT 

B3/0 - ON B3/1 - HEAT O:002/0 

HEATER 

Figure 25.18 

Oven Control Program with PLC-5 


plc pid - 25.17 

25.4.2 Water Tank Level Control 

Problem: The system in Figure 25.19 will control the height of the water in a tank. 

The input from the pressure transducer, Vp, will vary between 0V (empty tank) and 5V 

(full tank). A voltage output, Vo, will position a valve to change the tank fill rate. Vo varies 

between 0V (no water flow) and 5V (maximum flow). The system will always be on: the 

emergency stop is connected electrically. The desired height of a tank is specified by 

another voltage, Vd. The output voltage is calculated using Vo = 0.5 (Vd - Vp). If the output 

voltage is greater than 5V is will be made 5V, and below 0V is will be made 0V. 

Digital 

to Analog 

Converter 

Amp 

PLC 

Running 


Program 

Water 

Supply 

Analog 

to Digital 

Converter 

Amp 

Water Tank 

pressure 

transducer 

Figure 25.19 

Water Tank Level Controller 


plc pid - 25.18 

SOLUTION 

Analog Input: 

Analog Output: 

Select a 12 bit 1771-IFE card and use the 0V to 5V range 

on channel 1 with double ended inputs. 

R = 2 N = 4096 

Select a 12 bit 1771-OFE card and use the 0V to 5V range 

on channel 1. 

R = 2 N = 4096 

Cards: 

Memory: 

I:000 - Analog Input 

I:001 - Analog Output 

N7:80 - Vd 


plc pid - 25.19 


MOV 

Source 0000 0000 0000 0001 

Dest N7:0 

BT9:0/EN 

BT9:1/EN 

MOV 

Source 0000 0101 0000 0000 

Dest N7:2 

MOV 

Source 1000 0000 0000 0000 

Dest N7:64 

BTW 

Rack: 0 

Group: 0 

Module: 0 



Length: 37 


BTR 

Rack: 0 

Group: 0 

Module: 0 



Length: 20 


Figure 25.20 

A Water Tank Level Control Program 


plc pid - 25.20 

BT9:0/DN 

BT9:2/EN 

BT9:1/DN 

SUB 

SourceA N7:80 

SourceB N7:42 

Dest N7:81 

DIV 

SourceA N7:81 

SourceB 2 

Dest N7:60 



Rack 000 

Group 1 

Module 0 



Length 13 

Continuous No 

Figure 25.21 

A Water Tank Level Control Program 

25.4.3 Position Measurement 

- A touch sensor combined with a servo mechanism to measure a dimension 

- the sensor must be compliant. The servo axis speed must be slow enough so that 

the motion can stop within the compliance of the sensor 

- move until the sensor touches then stop and backup slowly until it releases 

- used for CMMs 

25.5 SUMMARY 

• Negative feedback controllers make a continuous system stable. 

• When controlling a continuous system with a logical actuator set points can be 

used. 


plc pid - 25.21 

• Block diagrams can be used to describe controlled systems. 

• Block diagrams can be converted to equations for analysis. 

• Continuous actuator systems can use P, PI, PD, PID controllers. 


1. What is the advantage of feedback in a control system? 

2. Can PID control solve problems of inaccuracy in a machine? 

3. If a control system should respond to long term errors, but not respond to sudden changes, what 

type of control equation should be used? 

4. Develop a ladder logic program that implements a PID controller using the discrete equation. 

5. Why is logical control so popular when continuous control allows more precision? 

6. Design the complete ladder logic for a control system that implements the control equation 

below for motor speed control. Assume that the motor speed is read from a tachometer, into an 

analog input card in rack 0, slot 0, input 1. The tachometer voltage will be between 0 and 

8Vdc, for speeds between 0 and 1000rpm. The voltage output to drive the motor controller is 

output from an analog output card in rack 0, slot 1, output 1. Assume the desired RPM is stored 

in N7:0. 

V motor = ( rpm moter – rpm desired )0.02154 

where, 

V motor 

= 

rpm moter 

rpm desired 

The voltage output to the motor 

= The RPM of the motor 

= The desired RPM of the motor 

7. Write a ladder logic control program to keep a water tank at a given height. The control system 

will be active after the Start button is pushed, but it can be stopped by a Stop button. The water 

height in the tank is measured with an ultrasonic sensor that will output 10V at 1m depth, and 

1V at 10cm depth. A solenoid controlled valve will open and close to allow water to enter. The 

water height setpoint is put in N7:0, in centimeters, and the actual height should be +/-5cm. 

8. Implement a program that will input (from I:000) an analog voltage Vi and output (to O:001) 

half that voltage, Vi/2. If the input voltage is between 3V and 5V the output O:002/0 will be 

turned on. Include start and stop buttons that will force the output voltage to zero when not 

running. Do not show the bits that would be set in memory, but list the settings that should be 

made for the cards (e.g. voltage range). 


plc pid - 25.22 


1. Feedback control, more specifically negative feedback, can improve the stability and accuracy 

of a control system. 

2. A PID controller will compare a setpoint and output variable. If there is a persistent error, the 

integral part of the controller will adjust the output to reduce long term errors. 

3. A PI controller 

4. 

Assume the values: 

update 

N7:0 = Analog input value 

N7:1 = Analog output value 

N7:2 = Setpoint 

MOV 

Source F8:4 

Dest F8:5 

MOV 

Source F8:3 

Dest F8:4 

SUB 

Source A N7:2 

Source B N7:0 

Dest F8:3 

F8:0 = Kp 

F8:1 = Kd 

F8:2 = Ki 

F8:3 = ei 

F8:4 = ei-1 

F8:5 = ei-2 

F8:6 = T (Scan Time) 

CPT 

Dest F8:10 

Expression 

CPT 

Dest F8:11 

Expression 

CPT 

Dest F8:12 

Expression 

"F8:0 + F8:2 * F8:6 + F8:1 | F8:6" 

"-F8:0 - 2 * F8:1 | F8:6" 

"F8:1 | F8:6" 

CPT 

Dest N7:1 

Expression 

"N7:1+F8:3*F8:10+F8:4*F8:11+F8:5*F8:12" 


plc pid - 25.23 

5. Logical control is more popular because the system is more controllable. This means either 

happen, or they don’t happen. If a system requires a continuous control system then it will tend 

to be unstable, and even when controlled a precise values can be hard to obtain. The need for 

control also implies that the system requires some accuracy, thus the process will tend to vary, 

and be a source of quality control problems. 

6. 

FS 

BT9:1/EN 

BT9:2/EN 

BT9:1/DN 

BT9:0/EN 

BTW 

Rack 0 

Group 0 

Module 0 


Data N7:0 

Length 37 

Continuous No 

BTR 

Rack 0 

Group 0 

Module 0 


Data N7:37 

Length 20 

Continuous No 

BTW 

Rack 0 

Group 1 

Module 0 


Data N7:57 

Length 13 

Continuous No 

CPT 

Dest N7:57 

Expression 

"0.02154*(N7:41-F8:0)" 


plc pid - 25.24 

7. 


BTW 

Rack: 0 

Group: 0 

Module: 0 



Length: 37 


BT9:0/EN 

START 

BT9:1/EN 

ESTOP 

BTR 

Rack: 0 

Group: 0 

Module: 0 



Length: 20 


B3/0 - ON 

B3/0 - ON 

Note: Assume that a 12 bit analog 

input card is set for 

0 to 10V input. Thus 

giving a range of 0V(0) 

BT9:0/DN 

BT9:1/DN 

GRT 

SourceA F8:2 

SourceB F8:1 

ADD 

Source A N7:0 

Source B 5 

Dest F8:0 

SUB 

Source A N7:0 

Source B 5 

Dest F8:1 

DIV 

Source A N7:43 

Source B 409.5 

Dest F8:2 

U 

B3/1 - VALVE 

LES 

SourceA F8:2 

SourceB F8:0 

L 

B3/1 - VALVE 

B3/0 - ON B3/1 - VALVE O:002/0 

VALVE 


plc pid - 25.25 

8. 

FS 

active 

start 

stop 

BTW 

Rack 0 

Group 0 

Module 0 


Data N7:0 

Length 37 

Continuous No 

active 

BT9:1/EN 

BT9:1/EN 

BT9:0/EN 

BTR 

Rack 0 

Group 0 

Module 0 


Data N7:37 

Length 20 

Continuous No 

BTW 

Rack 0 

Group 1 

Module 0 


Data N7:57 

Length 13 

Continuous No 

active 

BT9:1/DN 

LIM 

upper 2048 

lower 1229 

test N7:41 

active 

DIV 

sourceA N7:41 

sourceB 2 

dest N7:57 

MOV 

source 0 

dest N7:57 

O:002/0 

assume: 

12 bit input and output 

2s complement values 

-10V to 10V range 

constant update 

no filtering 

scale from -4095 to 4095 

3V → -----4095 

3 

= 1229 

10 

5V → -----4095 

5 

= 2048 

10 


plc pid - 25.26 


1. Design a basic feedback control system for temperature control of an oven. Indicate major 

components, and where they are used. 

2. Develop ladder logic for a system that adjusts the height of a box of plastic pellets. An ultrasonic 

sensor detects the top surface of the plastic pellets. The ultrasonic sensor has been calibrated 

so that when the output is above 5V the box is in the right height range. When it is less 

than 5V, a motor should be turned on until the box height results in an input of 6V. 

3. Write a program that implements a simple proportional controller. The analog input card is in 

slot 0 of the PLC rack, and the analog output card is in slot 1. The setpoint for the controller is 

stored in N7:0. The gain constant is stored in F8:0. 

4. A conveyor line is to be controlled with either a variable frequency drive, or a brushless servo 

motor. Workers will place boxes on the inlet side of the conveyor, these will be detected with a 

‘box present’ sensor. The box position is also detected with an ultrasonic sensor with a range 

from 10cm to 1m . When present, boxes on the conveyor will be moved until they are 55cm 

from the sensor. Once in place, the system will stop until the box is removed. After this, the 

process can begin again when a new box is detected. Design all of the required ladder logic for 

the process. 

5. A temperature control system is being developed to control the water flow rate for cooling a 

mold set. Unfortunately the sensor in the dies doesn’t allow us to measure the temperature. But 

it does provide a set of bimetallic contacts that close when the die is above 110C. Luckily a 

Variable Frequency Drive (VFD) is available for controlling the flow rate of the water. The 

control scheme will increase the water flow rate when the die temperature input, HOT, is 

active. When the HOT input if off the flow rate will be decreased, until the flow rate is zero. In 

other words, when the HOT input is on, a timer will start. The time accumulated, DELAY, will 

be proportional to a voltage output to control the VFD. If the HOT sensors turns off the 

DELAY value will be decreased until it has a value of zero. Write the ladder logic for this controller. 

6. Implement the system in the block diagram below in ladder logic. Indicate all of the settings 

required for the analog IO cards. The calculations are to be done with voltage values, therefore 


plc pid - 25.27 

input values must be converted from their integer values. 

F8:0 

+ 

5.0 

D/A 

output 

- 

0.2 

A/D 

input 


plc fuzzy - 26.1 

26. FUZZY LOGIC 

 

Topics: 

• Fuzzy logic theory; sets, rules and solving 

• 

Objectives: 

• To understand fuzzy logic control. 

• Be able to implement a fuzzy logic controller. 


Fuzzy logic is well suited to implementing control rules that can only be expressed 

verbally, or systems that cannot be modelled with linear differential equations. Rules and 

membership sets are used to make a decision. A simple verbal rule set is shown in Figure 

26.1. These rules concern how fast to fill a bucket, based upon how full it is. 

1. If (bucket is full) then (stop filling) 

2. If (bucket is half full) then (fill slowly) 

3. If (bucket is empty) then (fill quickly) 

Figure 26.1 

A Fuzzy Logic Rule Set 

The outstanding question is "What does it mean when the bucket is empty, half 

full, or full?" And, what is meant by filling the bucket slowly or quickly. We can define 

sets that indicate when something is true (1), false (0), or a bit of both (0-1), as shown in 

Figure 26.2. Consider the bucket is full set. When the height is 0, the set membership is 0, 

so nobody would think the bucket is full. As the height increases more people think the 

bucket is full until they all think it is full. There is no definite line stating that the bucket is 

full. The other bucket states have similar functions. Notice that the angle function relates 

the valve angle to the fill rate. The sets are shifted to the right. In reality this would probably 

mean that the valve would have to be turned a large angle before flow begins, but after 

that it increases quickly. 



1 

0 

bucket is full 

1 

0 

stop filling 

1 

0 

bucket is half full 

1 

0 

fill slowly 

1 

0 

bucket is empty 

height 

1 

0 

fill quickly 

angle 

Figure 26.2 

Fuzzy Sets 

Now, if we are given a height we can examine the rules, and find output values, as 

shown in Figure 26.3. This begins be comparing the bucket height to find the membership 

for bucket is full at 0.75, bucket is half full at 1.0 and bucket is empty at 0. Rule 3 is 

ignored because the membership was 0. The result for rule 1 is 0.75, so the 0.75 membership 

value is found on the stop filling and a value of a1 is found for the valve angle. For 

rule 2 the result was 1.0, so the fill slowly set is examined to find a value. In this case there 

is a range where fill slowly is 1.0, so the center point is chosen to get angle a2. These two 

results can then be combined with a weighted average to get 

angle = --------------------------------------------- 

0.75( a1) + 1.0( a2) 

. 

0.75 + 1.0 



1. If (bucket is full) then (stop filling) 

1 

bucket is full 

0 

height 

1 

0 

stop filling 

a1 

angle 

2. If (bucket is half full) then (fill slowly) 

1 

0 

bucket is half full 

1 

0 

fill slowly 

height 

a2 

angle 

3. If (bucket is empty) then (fill quickly) 

1 

0 

bucket is empty 

height 

1 

0 

fill quickly 

angle 

Figure 26.3 

Fuzzy Rule Solving 

An example of a fuzzy logic controller for controlling a servomotor is shown in 

Figure 26.4 [Lee and Lau, 1988]. This controller rules examines the system error, and the 

rate of error change to select a motor voltage. In this example the set memberships are 

defined with straight lines, but this will have a minimal effect on the controller performance. 



v desired v error 

Fuzzy V 

v actual 

motor 

Motor I motor 

Logic 

Power 

Servo 

+ 

- Controller Amplifier Motor 

The rules for the fuzzy logic controller are; 

1. If v error is LP and d / dt v error is any then V motor is LP. 

2. If v error is SP and d / dt v error is SP or ZE then V motor is SP. 

3. If v error is ZE and d / dt v error is SP then V motor is ZE. 

4. If v error is ZE and d / dt v error is SN then V motor is SN. 

5. If v error is SN and d / dt v error is SN then V motor is SN. 

6. If v error is LN and d / dt v error is any then V motor is LN. 

The sets for v error , d / dt v error , and V motor are; 

v error 

d / dt v error 

V motor 

1 

1 

1 

LN 

0 

-100 -50 0 50 100 

rps 

0 

-6 -3 0 3 6 

rps/s 

0 

0 6 12 18 24 

V 

1 

1 

1 

SN 

0 

-100 -50 0 50 100 

rps 

0 

-6 -3 0 3 6 

rps/s 

0 

0 6 12 18 24 

V 

1 

1 

1 

ZE 

0 

-100 -50 0 50 100 

rps 

0 

-6 -3 0 3 6 

rps/s 

0 

0 6 12 18 24 

V 

SP 

1 

0 

-100 -50 0 50 100 

rps 

1 

0 

-6 -3 0 3 6 

rps/s 

1 

0 

0 6 12 18 24 

V 

LP 

1 

0 

-100 -50 0 50 100 

1 

rps 0 

-6 -3 0 3 6 

1 

rps/s 0 

0 6 12 18 24 

V 

Figure 26.4 

A Fuzzy Logic Servo Motor Controller 

Consider the case where v error = 30 rps and d / dt v error = 1 rps / s . Rule 1to 6 are calculated 




1. If v error is LP and d / dt v error is any then V motor is LP. 

1 

1 

1 

0 

rps 0 

rps/s 0 

-100 -50 0 50 100 

-6 -3 0 3 6 

ANY VALUE 

30rps 

(so ignore) 

This has about 0.6 (out of 1) membership 

0 6 12 18 24 

V 

17V 

(could also 

have chosen 

some value 

above 17V) 

2. If v error is SP and d / dt v error is SP or ZE then V motor is SP. 

the OR means take the 

highest of the two 

memberships 

the AND means take the 

lowest of the two 

memberships 

1 

0 

rps 

-100-50 0 50 100 

30rps 

1 

0 

-6 -3 0 3 6 

1rps/s 

rps/s 

1 

0 

-6 -3 0 3 6 

1rps/s 

rps/s 

1 

0 

0 6 12 18 24 

14V 

V 


3. If v error is ZE and d / dt v error is SP then V motor is ZE. 

1 

0 

-100 -50 0 50 100 

30rps 

1 

1 

rps 0 

rps/s 

-6 -3 0 3 6 

0 

1rps/s 


0 6 12 18 24 

the lowest results in 0 set 

membership 

V 



4. If v error is ZE and d / dt v error is SN then V motor is SN. 

1 

1 

1 

0 

-100 -50 0 50 100 

30rps 

rps 0 

-6 -3 0 3 6 

1rps/s 


rps/s 0 

0 6 12 18 24 

the lowest results in 0 set 

membership 

V 

5. If v error is SN and d / dt v error is SN then V motor is SN. 

1 

1 

1 

0 

-100 -50 0 50 100 

rps 0 

-6 -3 0 3 6 

rps/s 0 

0 6 12 18 24 

V 

30rps 

1rps 


6. If v error is LN and d / dt v error is any then V motor is LN. 

1 

1 

1 

0 

-100 -50 0 50 100 

rps 

0 

-6 -3 0 3 6 

rps/s 

0 

0 6 12 18 24 

V 

30rps 

ANY VALUE 

This has about 0 (out of 1) membership 

Figure 26.5 

Rule Calculation 

The results from the individual rules can be combined using the calculation in Figure 

26.6. In this case only two of the rules matched, so only two terms are used, to give a 



final motor control voltage of 15.8V. 

V motor 

= 

n 

∑ 

( V motori )( membership i ) 

i--------------------------------------------------------------------- 

= 1 

n 

∑ 

i = 1 

( membership i 

) 

V motor 

= --------------------------------------------------- 0.6( 17V) + 0.4( 14V) 

= 

0.6 + 0.4 

15.8V 

Figure 26.6 

Rule Results Calculation 

26.2 COMMERCIAL CONTROLLERS 

At the time of writing Allen Bradley did not offer any Fuzzy Logic systems for 

their PLCs. But, other vendors such as Omron offer commercial controllers. Their controller 

has 8 inputs and 2 outputs. It will accept up to 128 rules that operate on sets defined 

with polygons with up to 7 points. 

It is also possible to implement a fuzzy logic controller manually, possible in structured 

text. 


Li, Y.F., and Lau, C.C., “Application of Fuzzy Control for Servo Systems”, IEEE International 

Conference on Robotics and Automation, Philadelphia, 1988, pp. 1511-1519. 

26.4 SUMMARY 

• Fuzzy rules can be developed verbally to describe a controller. 

• Fuzzy sets can be developed statistically or by opinion. 

• Solving fuzzy logic involves finding fuzzy set values and then calculating a value 

for each rule. These values for each rule are combined with a weighted average. 






1. Find products that include fuzzy logic controllers in their designs. 

2. Suggest 5 control problems that might be suitable for fuzzy logic control. 

3. Two fuzzy rules, and the sets they use are given below. If v error = 30rps, and d / dt v error = 3 rps / s , 

find V motor . 

1. If (v error is ZE) and ( d / dt v error is ZE) then (V motor is ZE). 

2. If (v error is SP) or ( d / dt v error is SP) then (V motor is SP). 

v error 

d / dt v error 

V motor 

1 

1 

1 

SN 

0 

-100 -50 0 50 100 

rps 

0 

-6 -3 0 3 6 

rps/s 

0 

0 6 12 18 24 

V 

1 

1 

1 

ZE 

0 

-100 -50 0 50 100 

rps 

0 

-6 -3 0 3 6 

rps/s 

0 

0 6 12 18 24 

V 

SP 

1 

0 

-100 -50 0 50 100 

rps 

1 

0 

-6 -3 0 3 6 

rps/s 

1 

0 

0 6 12 18 24 

V 

4. Develop a set of fuzzy control rules adjusting the water temperature in a sink. 

5. Develop a fuzzy logic control algorithm and implement it in structured text. The fuzzy rule set 

below is to be used to control the speed of a motor. When the error (difference between desired 

and actual speeds) is large the system will respond faster. When the difference is smaller the 



response will be smaller. Calculate the outputs for the system given errors of 5, 20 and 40. 

Big Error 

100% 

0% 

100% 

Small Error 

0% 

20 

10 30 

10 30 

error 

error 

Big Output 

error 

50 

Small Output 

5 

if (big error) then (big output) 

if (small error) then (small output) 

50 

error 


plc serial - 27.1 

27. SERIAL COMMUNICATION 

Topics: 

• Serial communication and RS-232c 

• ASCII ladder logic functions 


Objectives: 

• To understand serial communications with RS-232 

• Be able to use serial communications with a PLC 


Multiple control systems will be used for complex processes. These control systems 

may be PLCs, but other controllers include robots, data terminals and computers. For 

these controllers to work together, they must communicate. This chapter will discuss communication 

techniques between computers, and how these apply to PLCs. 

The simplest form of communication is a direct connection between two computers. 

A network will simultaneously connect a large number of computers on a network. 

Data can be transmitted one bit at a time in series, this is called serial communication. 

Data bits can also be sent in parallel. The transmission rate will often be limited to some 

maximum value, from a few bits per second, to billions of bits per second. The communications 

often have limited distances, from a few feet to thousands of miles/kilometers. 

Data communications have evolved from the 1800’s when telegraph machines 

were used to transmit simple messages using Morse code. This process was automated 

with teletype machines that allowed a user to type a message at one terminal, and the 

results would be printed on a remote terminal. Meanwhile, the telephone system began to 

emerge as a large network for interconnecting users. In the late 1950s Bell Telephone 

introduced data communication networks, and Texaco began to use remote monitoring 

and control to automate a polymerization plant. By the 1960s data communications and 

the phone system were being used together. In the late 1960s and 1970s modern data communications 

techniques were developed. This included the early version of the Internet, 

called ARPAnet. Before the 1980s the most common computer configuration was a centralized 

mainframe computer with remote data terminals, connected with serial data line. 

In the 1980s the personal computer began to displace the central computer. As a result, 

high speed networks are now displacing the dedicated serial connections. Serial communications 

and networks are both very important in modern control applications. 



An example of a networked control system is shown in Figure 27.1. The computer 

and PLC are connected with an RS-232 (serial data) connection. This connection can only 

connect two devices. Devicenet is used by the Computer to communicate with various 

actuators and sensors. Devicenet can support up to 63 actuators and sensors. The PLC 

inputs and outputs are connected as normal to the process. 

Computer 

Devicenet 

RS-232 

Process 

Actuators 



Sensors 

PLC 


Actuators 

Normal I/O on PLC 


Sensors 

Figure 27.1 

A Communication Example 

27.2 SERIAL COMMUNICATIONS 

Serial communications send a single bit at a time between computers. This only 

requires a single communication channel, as opposed to 8 channels to send a byte. With 

only one channel the costs are lower, but the communication rates are slower. The communication 

channels are often wire based, but they may also be can be optical and radio. Figure 

27.2 shows some of the standard electrical connections. RS-232c is the most common 

standard that is based on a voltage change levels. At the sending computer an input will 

either be true or false. The line driver will convert a false value in to a Txd voltage 

between +3V to +15V, true will be between -3V to -15V. A cable connects the Txd and 

com on the sending computer to the Rxd and com inputs on the receiving computer. The 

receiver converts the positive and negative voltages back to logic voltage levels in the 

receiving computer. The cable length is limited to 50 feet to reduce the effects of electrical 

noise. When RS-232 is used on the factory floor, care is required to reduce the effects of 

electrical noise - careful grounding and shielded cables are often used. 



50 ft 

In 

RS-232c 

Txd 

com 

Rxd 

Out 

3000 ft 

RS-422a 

In 

Out 

3000 ft 

RS-423a 

In 

Out 

Figure 27.2 

Serial Data Standards 

The RS-422a cable uses a 20 mA current loop instead of voltage levels. This 

makes the systems more immune to electrical noise, so the cable can be up to 3000 feet 

long. The RS-423a standard uses a differential voltage level across two lines, also making 

the system more immune to electrical noise, thus allowing longer cables. To provide serial 

communication in two directions these circuits must be connected in both directions. 

To transmit data, the sequence of bits follows a pattern, like that shown in Figure 

27.3. The transmission starts at the left hand side. Each bit will be true or false for a fixed 

period of time, determined by the transmission speed. 



A typical data byte looks like the one below. The voltage/current on the line is 

made true or false. The width of the bits determines the possible bits per second (bps). The 

value shown before is used to transmit a single byte. Between bytes, and when the line is 

idle, the Txd is kept true, this helps the receiver detect when a sender is present. A single 

start bit is sent by making the Txd false. In this example the next eight bits are the transmitted 

data, a byte with the value 17. The data is followed by a parity bit that can be used 

to check the byte. In this example there are two data bits set, and even parity is being used, 

so the parity bit is set. The parity bit is followed by two stop bits to help separate this byte 

from the next one. 

true 

false 

before start data parity stop idle 

Descriptions: 

before - this is a period where no bit is being sent and the line is true. 

start - a single bit to help get the systems synchronized. 

data - this could be 7 or 8 bits, but is almost always 8 now. The value shown here is a 

byte with the binary value 00010010 (the least significant bit is sent first). 

parity - this lets us check to see if the byte was sent properly. The most common 

choices here are no parity bit, an even parity bit, or an odd parity bit. In this case 

there are two bits set in the data byte. If we are using even parity the bit would be 

true. If we are using odd parity the bit would be false. 

stop - the stop bits allow a pause at the end of the data. One or two stop bits can be 

used. 

idle - a period of time where the line is true before the next byte. 

Figure 27.3 

A Serial Data Byte 

Some of the byte settings are optional, such as the number of data bits (7 or 8), the 

parity bit (none, even or odd) and the number of stop bits (1 or 2). The sending and receiving 

computers must know what these settings are to properly receive and decode the data. 

Most computers send the data asynchronously, meaning that the data could be sent at any 

time, without warning. This makes the bit settings more important. 

Another method used to detect data errors is half-duplex and full-duplex transmission. 

In half-duplex transmission the data is only sent in one direction. But, in full-duplex 



transmission a copy of any byte received is sent back to the sender to verify that it was 

sent and received correctly. (Note: if you type and nothing shows up on a screen, or characters 

show up twice you may have to change the half/full duplex setting.) 

The transmission speed is the maximum number of bits that can be sent per second. 

The units for this is baud. The baud rate includes the start, parity and stop bits. For 

example a 9600 baud transmission of the data in Figure 27.3 would transfer up to 

9600 

bytes each second. Lower baud rates are 120, 300, 1.2K, 2.4K and 

( ----------------------------------- = 

1 + 8+ 1+ 

2) 

800 

9.6K. Higher speeds are 19.2K, 28.8K and 33.3K. (Note: When this is set improperly you 

will get many transmission errors, or garbage on your screen.) 

Serial lines have become one of the most common methods for transmitting data to 

instruments: most personal computers have two serial ports. The previous discussion of 

serial communications techniques also applies to devices such as modems. 

27.2.1 RS-232 

The RS-232c standard is based on a low/false voltage between +3 to +15V, and an 

high/true voltage between -3 to -15V (+/-12V is commonly used). Figure 27.4 shows 

some of the common connection schemes. In all methods the txd and rxd lines are crossed 

so that the sending txd outputs are into the listening rxd inputs when communicating 

between computers. When communicating with a communication device (modem), these 

lines are not crossed. In the modem connection the dsr and dtr lines are used to control the 

flow of data. In the computer the cts and rts lines are connected. These lines are all used 

for handshaking, to control the flow of data from sender to receiver. The null-modem configuration 

simplifies the handshaking between computers. The three wire configuration is 

a crude way to connect to devices, and data can be lost. 



Modem 

Computer 

com 

txd 

rxd 

dsr 

dtr 

com 

txd 

rxd 

dsr 

dtr 

Modem 

Computer 

Computer 

A 

com 

txd 

rxd 

cts 

rts 

com 

txd 

rxd 

cts 

rts 

Computer 

B 

Null-Modem 

Computer 

A 

com 

txd 

rxd 

dsr 

dtr 

cts 

rts 

com 

txd 

rxd 

dsr 

dtr 

cts 

rts 

Computer 

B 

Three wire 

Computer 

A 

com 

txd 

rxd 

cts 

rts 

com 

txd 

rxd 

cts 

rts 

Computer 

B 

Figure 27.4 

Common RS-232 Connection Schemes 

Common connectors for serial communications are shown in Figure 27.5. These 

connectors are either male (with pins) or female (with holes), and often use the assigned 

pins shown. The DB-9 connector is more common now, but the DB-25 connector is still in 

use. In any connection the RXD and TXD pins must be used to transmit and receive data. 

The COM must be connected to give a common voltage reference. All of the remaining 

pins are used for handshaking. 



DB-25 

1 2 3 4 5 6 7 8 9 10 11 12 13 

14 15 16 17 18 19 20 21 22 23 24 25 

DB-9 

1 2 3 4 5 

6 7 8 9 

Commonly used pins 

1 - GND (chassis ground) 

2 - TXD (transmit data) 

3 - RXD (receive data) 

4 - RTS (request to send) 

5 - CTS (clear to send) 

6 - DSR (data set ready) 

7 - COM (common) 

8 - DCD (Data Carrier Detect) 

20 - DTR (data terminal ready) 

Other pins 

9 - Positive Voltage 

10 - Negative Voltage 

11 - not used 

12 - Secondary Received Line Signal 

Detector 

13 - Secondary Clear to Send 

14 - Secondary Transmitted Data 

15 - Transmission Signal Element Timing 

(DCE) 

16 - Secondary Received Data 

17 - Receiver Signal Element Timing 

(DCE) 

18 - not used 

19 - Secondary Request to Send 

21 - Signal Quality Detector 

22 - Ring Indicator (RI) 

1 - DCD 

2 - RXD 

3 - TXD 

4 - DTR 

5 - COM 

6 - DSR 

7 - RTS 

8 - CTS 

9 - RI 

Note: these connectors 

often have 

very small numbers 

printed on 

them to help you 

identify the pins. 

Figure 27.5 

Typical RS-232 Pin Assignments and Names 

The handshaking lines are to be used to detect the status of the sender and receiver, 

and to regulate the flow of data. It would be unusual for most of these pins to be connected 

in any one application. The most common pins are provided on the DB-9 connector, and 

are also described below. 

TXD/RXD - (transmit data, receive data) - data lines 

DCD - (data carrier detect) - this indicates when a remote device is present 



RI - (ring indicator) - this is used by modems to indicate when a connection is 

about to be made. 

CTS/RTS - (clear to send, ready to send) 

DSR/DTR - (data set ready, data terminal ready) these handshaking lines indicate 

when the remote machine is ready to receive data. 

COM - a common ground to provide a common reference voltage for the TXD and 

RXD. 

When a computer is ready to receive data it will set the CTS bit, the remote 

machine will notice this on the RTS pin. The DSR pin is similar in that it indicates the 

modem is ready to transmit data. XON and XOFF characters are used for a software only 

flow control scheme. 

Many PLC processors have an RS-232 port that is normally used for programming 

the PLC. Figure 27.6 shows a PLC-5 processor connected to a personal computer with a 

Null-Modem line. It is connected to the channel 0 serial connector on the PLC-5 processor, 

and to the com 1 port on the computer. In this example the terminal could be a personal 

computer running a terminal emulation program. The ladder logic below will send a 

string to the serial port channel 0 when A goes true. In this case the string is stored is string 

memory ST9:0 and has a length of 4 characters. If the string stored in ST9:0 is HALFLIFE, 

the terminal program will display the string HALF. 

PLC5 

channel 0 

RS-232 Cable 

com 1 

Terminal 

Emulator 

A 

AWT 

Channel 0 

String Location ST9:0 

Length 4 

Figure 27.6 

Serial Output Using Ladder Logic 

The AWT (Ascii WriTe) function below will write to serial ports on the CPU only. 



To write to other serial ports the message function in Figure 27.7 must be used. In this 

example the message block will become active when A goes true. It will use the message 

parameters stored in message memory MG9:0. The parameters set indicate that the message 

is to Write data stored at N7:50, N7:51 and N7:52. This will write the ASCII string 

ABC to the serial port. 

A 

MSG 

Control Block MG9:0 

Memory Values: 

setup stored 

in MG9:0 

Data Stored in memory 

Read/Write 

Data Table 

Size 

Local/Remote 

Remote Station 

Link ID 

Remote Link type 

Local Node Addr. 

Processor Type 

Dest. Addr. 

N7:50 

N7:51 

N7:52 

Write 

N7:50 

3 

Local 

N/A 

N/A 

N/A 

20 

ASCII 

N/A 

65 

66 

67 

Figure 27.7 

Message Function for Serial Communication 

27.2.1.1 - ASCII Functions 

ASCII functions allow programs to manipulate strings in the memory of the PLC. 

The basic functions are listed in Figure 27.8. 



ABL(channel, control)- reports the number of ASCII characters including line endings 

ACB(channel, control) - reports the numbers of ASCII characters in buffer 

ACI(string, dest) - convert ASCII string to integer 

ACN(string, string,dest) - concatenate strings 

AEX(string, start, length, dest) - this will cut a segment of a string out of a larger string 

AIC(integer, string) - convert an integer to a string 

AHL(channel, mask, mask, control) - does data handshaking 

ARD(channel, dest, control, length) - will get characters from the ASCII buffer 

ARL(channel, dest, control, length) - will get characters from an ASCII buffer 

ASC(string, start, string, result) - this will look for one string inside another 

ASR(string, string) - compares two strings 

AWT(channel, string, control, length) - will write characters to an ASCII output 

Figure 27.8 

PLC-5 ASCII Functions 

In the example in Figure 27.9, the characters "Hi " are placed into string memory 

ST10:1. The ACB function checks to see how many characters have been received, and 

are waiting in channel 0. When the number of characters equals 2, the ARD (Ascii ReaD) 

function will then copy those characters into memory ST10:0, and bit R6:0/DN will be set. 

This done bit will cause the two characters to be concatenated to the "Hi ", and the result 

written back to the serial port. So, if I typed in my initial "HJ", I would get the response 

"HI HJ". 



R6:1/EN 

GEQ 

Source A R6:1.POS 

Source B 2 

R6:0/DN 

ACB 

Channel 0 


ARL 

Channel 0 

Dest ST10:0 


Length 2 

ACN 

StringA ST10:1 

StringB ST10:0 

Dest ST10:2 

ST10:1 = "HI " 

AWT 

Channel 0 

String ST10:2 

Length 7 

Figure 27.9 

An ASCII String Example 

The ASCII functions can also be used to support simple number conversions. The 

example in Figure 27.10 will convert the strings in ST9:10 and ST9:11 to integers, add the 

numbers, and store the result as a string in ST9:12. 



ACI 

String ST9:10 

Dest N7:0 

ACI 

String ST9:11 

Dest N7:1 

ADD 

SourceA N7:0 

SourceB N7:1 

Dest N7:2 

AIC 

Source N7:2 

String ST9:12 

Figure 27.10 

A String to Integer Conversion Example 

Many of the remaining string functions are illustrated in Figure 27.11. When A is 

true the ABL and ACB functions will check for characters that have arrived on channel 1, 

but have not been retrieved with an ARD function. If the characters "ABC" have 

arrived ( is an ASCII carriage return) the ACB would count the three characters, and 

store the value in R6:0.POS. The ABL function would also count the and store a 

value of four in R6:1.POS. If B is true, and the string in ST9:0 is "ABCDEFGHIJKL", 

then "EF" will be stored in ST9:1. The last function will compare the strings in ST9:2 and 

ST9:3, and if they are equal, output O:001/2 will be turned on. 



A 

ACB 

Channel 1 


ABL 

Channel 1 


B 

AEX 

Source ST9:0 

Index 5 

Length 2 

Dest ST9:1 

ASR 

StringA ST9:2 

StringB ST9:3 

O:001/2 

Figure 27.11 

String Manipulation Functions 

The AHL function can be used to do handshaking with a remote serial device. 

27.3 PARALLEL COMMUNICATIONS 

Parallel data transmission will transmit multiple bits at the same time over multiple 

wires. This does allow faster data transmission rates, but the connectors and cables 

become much larger, more expensive and less flexible. These interfaces still use handshaking 

to control data flow. 

These interfaces are common for computer printer cables and short interface 

cables, but they are uncommon on PLCs. A list of common interfaces follows. 

Centronics printer interface - These are the common printer interface used on most 

personal computers. It was made popular by the now defunct Centronics printer 

company. 

GPIB/IEEE-488 - (General Purpose Instruments Bus) This bus was developed by 

Hewlett Packard Inc. for connecting instruments. It is still available as an option 



on many new instruments. 


27.4.1 PLC Interface To a Robot 

Problem: A robot will be loading parts into a box until the box reaches a prescribed 

weight. A PLC will feed parts into a pickup fixture when it is empty. The PLC will tell the 

robot when to pick up a part and load it into the box by passing it an ASCII string, 

"pickup". 

PLC 

RS-232 

"pickup" = pickup part 

Robot 

feed part part waiting box full 

Parts 

Feeder 

Parts Pickup 

Fixture 

Box and 

Weigh Scale 

Figure 27.12 

Box Loading System 

Solution: The following ladder logic will implement part of the control system for 

the system in Figure 27.12. 



part waiting 

box full 

feed part 

part waiting 

ST10:0 = "pickup" 

ONS 

Bit B3:0 

AWT 

Channel 0 

String ST10:0 

Length 6 

Figure 27.13 

A Box Loading System 

27.5 SUMMARY 

• Serial communications pass data one bit at a time. 

• RS-232 communications use voltage levels for short distances. A variety of communications 

cables and settings were discussed. 

• ASCII functions are available of PLCs making serial communications possible. 


1. Describe what the bits would be when an A (ASCII 65) is transmitted in an RS-232 interface 

with 8 data bits, even parity and 1 stop bit. 

2. Divide the string in ST10:0 by the string in ST10:1 and store the results in ST10:2. Check for a 

divide by zero error. 

ST10:0 “100” 

ST10:1 “10” 

ST10:2 

3. How long would it take to transmit an ASCII file over a serial line with 8 data bits, no parity, 1 

stop bit? What if the data were 7 bits long? 

4. Write a number guessing program that will allow a user to enter a number on a terminal that 

transmits it to a PLC where it is compared to a value in N7:0. If the guess is above "Hi" will be 

returned. If below "Lo" will be returned. When it matches "ON" will be returned. 



5. Write a program that will convert a numerical value stored in F8:0 and write it out the RS-232 

output on a PLC-5 processor. 


1. 

before start data parity stop 

2. 

ACI 

Source ST10:0 

Dest N7:0 

ACI 

Source ST10:1 

Dest N7:1 

NEQ 

Source A 0 

Source B N7:1 

DIV 

Source A N7:0 

Source B N7:1 

Dest N7:2 

AIC 

Source N7:2 

Dest ST10:2 

3. If we assume 9600 baud, for (1start+8data+0parity+1stop)=10 bits/byte we get 960 bytes per 

second. If there are only 7 data bits per byte this becomes 9600/9 = 1067 bytes per second. 



4. 

R6:0/DN 

R6:4/EN 

EQU 

SourceA R6:4.POS 

Source B 2 

ACB 

Channel 0 


ARL 

Channel 0 

Dest ST9:0 


Length 3 

ACI 

Source ST9:0 

Dest N7:1 

ST9:1="Lo" 

ST9:2="ON" 

ST9:3="Hi" 

LES 

Source A N7:1 

Source B N7:0 

EQ 

Source A N7:1 

Source B N7:0 

GRT 

Source A N7:1 

Source B N7:0 

AWT 

Channel 0 

Source ST9:1 


Length 2 

AWT 

Channel 0 

Source ST9:2 


Length 2 

AWT 

Channel 0 

Source ST9:3 


Length 2 



5. 

MOV 

Source F8:0 

Dest N7:0 

AIC 

Source N7:0 

Dest ST9:0 

R6:0/EN 

AWT 

ASCII WRITE 

Channel 

Source 


String Length 

Characters Sent 

0 

ST9:0 

R6:0 

5 


1. Describe an application of ASCII communications. 

2. Write a ladder logic program to output an ASCII warning message on channel 1 when the value 

in N7:0 is less than 10, or greater than 20. The message should be "out of temp range". 

3. Write a program that will send an ASCII message every minute. The message should begin 

with the word ‘count’, followed by a number. The number will be 1 on the first scan of the 

PLC, and increment once each minute. 

4. A PLC will be controlled by ASCII commands received through the RS-232C communications 

port. The commands will cause the PLC to move between the states shown in the state dia- 



gram. Implement the ladder logic. 

FS 

“start” 

IDLE 

“estop” 

ACTIVE 

“reset” 

FAULT 

“error” 

5. A program is to be written to control a robot through an RS-232c interface. The robot has 

already been programmed to respond to two ASCII strings. When the robot receives the string 

‘start’ it will move a part from a feeder to a screw machine. When the robot receives an ‘idle’ 

command it will become inactive (safe). The PLC has ‘start’ and ‘end’ inputs to control the 

process. The PLC also has two other inputs that indicate when the parts feeder has parts available 

(‘part present’) and when the screw machine is done (‘machine idle’). The ‘start’ button 

will start a cycle where the robot repeatedly loads parts into the screw machine whenever the 

‘machine idle’ input is true. If the ‘part present’ sensor is off (i.e., no parts), or the ‘end’ input 

is off (a stop requested), the screw machine will be allowed to finish, but then the process will 

stop and the robot will be sent the idle command. Use a structured design method (e.g., state 

diagrams) to develop a complete ladder logic program to perform the task. 

6. A PLC-5 is connected to a scale that measures weights and then sends an ASCII string. The 

string format is ‘XXXX.XX’. So a weight of 29.9 grams would result in a string of ‘0029.90’. 

The PLC is to read the string and then check to see if the weight is between 18.23 and 18.95 

grams. If it is not then an error output light should be set until a reset button is pushed. 


plc network - 28.1 

28. NETWORKING 

 

 

Topics: 

• Networks; topology, OSI model, hardware and design issues 

• Network types; Devicenet, CANbus, Controlnet, Ethernet, and DH+ 


Objectives: 

• To understand network types and related issues 

• Be able to network using Devicenet, Ethernet and DH+ 


A computer with a single network interface can communicate with many other 

computers. This economy and flexibility has made networks the interface of choice, 

eclipsing point-to-point methods such as RS-232. Typical advantages of networks include 

resource sharing and ease of communication. But, networks do require more knowledge 

and understanding. 

Small networks are often called Local Area Networks (LANs). These may connect 

a few hundred computers within a distance of hundreds of meters. These networks are 

inexpensive, often costing $100 or less per network node. Data can be transmitted at rates 

of millions of bits per second. Many controls system are using networks to communicate 

with other controllers and computers. Typical applications include; 

• taking quality readings with a PLC and sending the data to a database computer. 

• distributing recipes or special orders to batch processing equipment. 

• remote monitoring of equipment. 

Larger Wide Area Networks (WANs) are used for communicating over long distances 

between LANs. These are not common in controls applications, but might be 

needed for a very large scale process. An example might be an oil pipeline control system 

that is spread over thousands of miles. 



28.1.1 Topology 

The structure of a network is called the topology. Figure 28.1 shows the basic network 

topologies. The Bus and Ring topologies both share the same network wire. In the 

Star configuration each computer has a single wire that connects it to a central hub. 

LAN 

A Wire Loop 

Central Connection 

... 

Bus 

Ring 

Star 

Figure 28.1 

Network Topologies 

In the Ring and Bus topologies the network control is distributed between all of the 

computers on the network. The wiring only uses a single loop or run of wire. But, because 

there is only one wire, the network will slow down significantly as traffic increases. This 

also requires more sophisticated network interfaces that can determine when a computer is 

allowed to transmit messages. It is also possible for a problem on the network wires to halt 

the entire network. 

The Star topology requires more wire overall to connect each computer to an intelligent 

hub. But, the network interfaces in the computer become simpler, and the network 

becomes more reliable. Another term commonly used is that it is deterministic, this means 

that performance can be predicted. This can be important in critical applications. 

For a factory environment the bus topology is popular. The large number of wires 

required for a star configuration can be expensive and confusing. The loop of wire 

required for a ring topology is also difficult to connect, and it can lead to ground loop 

problems. Figure 28.2 shows a tree topology that is constructed out of smaller bus networks. 

Repeaters are used to boost the signal strength and allow the network to be larger. 



... 

R 

Repeater 

R 

R 

R 

Figure 28.2 

The Tree Topology 

28.1.2 OSI Network Model 

The Open System Interconnection (OSI) model in Figure 28.3 was developed as a 

tool to describe the various hardware and software parts found in a network system. It is 

most useful for educational purposes, and explaining the things that should happen for a 

successful network application. The model contains seven layers, with the hardware at the 

bottom, and the software at the top. The darkened arrow shows that a message originating 

in an application program in computer #1 must travel through all of the layers in both 

computers to arrive at the application in computer #2. This could be part of the process of 

reading email. 



Layer Computer #1 Unit of Transmission 

Computer #2 

7 

Application 

Message 

Application 

6 

Presentation 

Message 

Presentation 

5 

Session 

Message 

Session 

4 

Transport 

Message 

Transport 

3 

Network 

Packet 

Network 

2 

Data Link 

Frame 

Data Link 

1 

Physical 

Bit 

Physical 

Interconnecting Medium 

Application - This is high level software on the computer. 

Presentation - Translates application requests into network operations. 

Session - This deals with multiple interactions between computers. 

Transport - Breaks up and recombines data to small packets. 

Network - Network addresses and routing added to make frame. 

Data Link - The encryption for many bits, including error correction added to a 

frame. 

Physical - The voltage and timing for a single bit in a frame. 

Interconnecting Medium - (not part of the standard) The wires or transmission 

medium of the network. 

Figure 28.3 

The OSI Network Model 

The Physical layer describes items such as voltage levels and timing for the transmission 

of single bits. The Data Link layer deals with sending a small amount of data, 

such as a byte, and error correction. Together, these two layers would describe the serial 

byte shown in the previous chapter. The Network layer determines how to move the message 

through the network. If this were for an internet connection this layer would be 

responsible for adding the correct network address. The Transport layer will divide small 

amounts of data into smaller packets, or recombine them into one larger piece. This layer 

also checks for data integrity, often with a checksum. The Session layer will deal with 

issues that go beyond a single block of data. In particular it will deal with resuming transmission 

if it is interrupted or corrupted. The Session layer will often make long term connections 

to the remote machine. The Presentation layer acts as an application interface so 



that syntax, formats and codes are consistent between the two networked machines. For 

example this might convert ’\’ to ’/’ in HTML files. This layer also provides subroutines 

that the user may call to access network functions, and perform functions such as encryption 

and compression. The Application layer is where the user program resides. On a computer 

this might be a web browser, or a ladder logic program on a PLC. 

Most products can be described with only a couple of layers. Some networking 

products may omit layers in the model. 

28.1.3 Networking Hardware 

The following is a description of most of the hardware that will be needed in the 

design of networks. 

• Computer (or network enabled equipment) 

• Network Interface Hardware - The network interface may already be built into 

the computer/PLC/sensor/etc. These may cost $15 to over $1000. 

• The Media - The physical network connection between network nodes. 

10baseT (twisted pair) is the most popular. It is a pair of twisted copper 

wires terminated with an RJ-45 connector. 

10base2 (thin wire) is thin shielded coaxial cable with BNC connectors 

10baseF (fiber optic) is costly, but signal transmission and noise properties 

are very good. 

• Repeaters (Physical Layer) - These accept signals and retransmit them so that 

longer networks can be built. 

• Hub/Concentrator - A central connection point that network wires will be connected 

to. It will pass network packets to local computers, or to remote networks 

if they are available. 

• Router (Network Layer) - Will isolate different networks, but redirect traffic to 

other LANs. 

• Bridges (Data link layer) - These are intelligent devices that can convert data on 

one type of network, to data on another type of network. These can also be used 

to isolate two networks. 

• Gateway (Application Layer) - A Gateway is a full computer that will direct traffic 

to different networks, and possibly screen packets. These are often used to 

create firewalls for security. 

Figure 28.4 shows the basic OSI model equivalents for some of the networking 

hardware described before. 



7 - application 

6 - presentation 

gateway 

5 - session 

4 - transport 

3 - network 

2 - data link 

1 - physical 

repeater 

bridge/ 

switch 

router 

Figure 28.4 

Network Devices and the OSI Model 

Layer Computer #1 

Computer #2 

7 

Application 

Application 

6 

Presentation 

Presentation 

5 

Session 

Session 

4 

Transport 

Router 

Transport 

3 

Network 

Network 

Network 

2 

Data Link 

Data Link 

Data Link 

1 

Physical 

Physical 

Physical 

Interconnecting Medium 

Figure 28.5 

The OSI Network Model with a Router 



28.1.4 Control Network Issues 

A wide variety of networks are commercially available, and each has particular 

strengths and weaknesses. The differences arise from their basic designs. One simple issue 

is the use of the network to deliver power to the nodes. Some control networks will also 

supply enough power to drive some sensors and simple devices. This can eliminate separate 

power supplies, but it can reduce the data transmission rates on the network. The use 

of network taps or tees to connect to the network cable is also important. Some taps or tees 

are simple passive electrical connections, but others involve sophisticated active tees that 

are more costly, but allow longer networks. 

The transmission type determines the communication speed and noise immunity. 

The simplest transmission method is baseband, where voltages are switched off and on to 

signal bit states. This method is subject to noise, and must operate at lower speeds. RS-232 

is an example of baseband transmission. Carrierband transmission uses FSK (Frequency 

Shift Keying) that will switch a signal between two frequencies to indicate a true or false 

bit. This technique is very similar to FM (Frequency Modulation) radio where the frequency 

of the audio wave is transmitted by changing the frequency of a carrier frequency 

about 100MHz. This method allows higher transmission speeds, with reduced noise 

effects. Broadband networks transmit data over more than one channel by using multiple 

carrier frequencies on the same wire. This is similar to sending many cable television 

channels over the same wire. These networks can achieve very large transmission speeds, 

and can also be used to guarantee real time network access. 

The bus network topology only uses a single transmission wire for all nodes. If all 

of the nodes decide to send messages simultaneously, the messages would be corrupted (a 

collision occurs). There are a variety of methods for dealing with network collisions, and 

arbitration. 

CSMA/CD (Collision Sense Multiple Access/Collision Detection) - if two nodes 

start talking and detect a collision then they will stop, wait a random time, and 

then start again. 

CSMA/BA (Collision Sense Multiple Access/Bitwise Arbitration) - if two nodes 

start talking at the same time the will stop and use their node addresses to determine 

which one goes first. 

Master-Slave - one device one the network is the master and is the only one that 

may start communication. slave devices will only respond to requests from the 

master. 

Token Passing - A token, or permission to talk, is passed sequentially around a network 

so that only one station may talk at a time. 

The token passing method is deterministic, but it may require that a node with an 

urgent message wait to receive the token. The master-slave method will put a single 



machine in charge of sending and receiving. This can be restrictive if multiple controllers 

are to exist on the same network. The CSMA/CD and CSMA/BA methods will both allow 

nodes to talk when needed. But, as the number of collisions increase the network performance 

degrades quickly. 

28.2 NETWORK STANDARDS 

Bus types are listed below. 

Low level busses - these are low level protocols that other networks are built upon. 

RS-485, Bitbus, CAN bus, Lonworks, Arcnet 

General open buses - these are complete network types with fully published standards. 

ASI, Devicenet, Interbus-S, Profibus, Smart Distributed System (SDS), 

Seriplex 

Specialty buses - these are buses that are proprietary. 

Genius I/O, Sensoplex 

28.2.1 Devicenet 

Devicenet has become one of the most widely supported control networks. It is an 

open standard, so components from a variety of manufacturers can be used together in the 

same control system. It is supported and promoted by the Open Devicenet Vendors Association 

(ODVA) (see http://www.odva.org). This group includes members from all of the 

major controls manufacturers. 

This network has been designed to be noise resistant and robust. One major change 

for the control engineer is that the PLC chassis can be eliminated and the network can be 

connected directly to the sensors and actuators. This will reduce the total amount of wiring 

by moving I/O points closer to the application point. This can also simplify the connection 

of complex devices, such as HMIs. Two way communications inputs and outputs allow 

diagnosis of network problems from the main controller. 

Devicenet covers all seven layers of the OSI standard. The protocol has a limited 

number of network address, with very small data packets. But this also helps limit network 

traffic and ensure responsiveness. The length of the network cables will limit the maximum 

speed of the network. The basic features of are listed below. 

• A single bus cable that delivers data and power. 

• Up to 64 nodes on the network. 



• Data packet size of 0-8 bytes. 

• Lengths of 500m/250m/100m for speeds of 125kbps/250kbps/500kbps respectively. 

• Devices can be added/removed while power is on. 

• Based on the CANbus (Controller Area Network) protocol for OSI levels 1 and 

2. 

• Addressing includes peer-to-peer, multicast, master/slave, polling or change of 

state. 

An example of a Devicenet network is shown in Figure 28.6. The dark black lines 

are the network cable. Terminators are required at the ends of the network cable to reduce 

electrical noise. In this case the PC would probably be running some sort of software 

based PLC program. The computer would have a card that can communicate with 

Devicenet devices. The FlexIO rack is a miniature rack that can hold various types of 

input and output modules. Power taps (or tees) split the signal to small side branches. In 

this case one of the taps connects a power supply, to provide the 24Vdc supply to the network. 

Another two taps are used to connect a smart sensor and another FlexIO rack. The 

Smart sensor uses power from the network, and contains enough logic so that it is one 

node on the network. The network uses thin trunk line and thick trunk line which may 

limit network performance. 

thin 

trunk tap 

line 

thin 

trunk 

line 

power tap 

thick trunk line 

terminator 

tap 

drop 

line 

drop 

line 

FlexIO 

rack 

PC 

terminator 

Smart 

sensor 

FlexIO 

rack 

power 

supply 

Figure 28.6 

A Devicenet Network 

The network cable is important for delivering power and data. Figure 28.7 shows a 

basic cable with two wires for data and two wires for the power. The cable is also shielded 

to reduce the effects of electrical noise. The two basic types are thick and thin trunk line. 

The cables may come with a variety of connections to devices. 



• bare wires 

• unsealed screw connector 

• sealed mini connector 

• sealed micro connector 

• vampire taps 

power (24Vdc) 

data 

drain/shield 

Thick trunk - carries up to 8A for power up to 500m 

Thin trunk - up to 3A for power up to 100m 

Figure 28.7 

Shielded Network Cable 

Some of the design issues for this network include; 

• Power supplies are directly connected to the network power lines. 

• Length to speed is 156m/78m/39m to 125Kbps/250Kbps/500Kbps respectively. 

• A single drop is limited to 6m. 

• Each node on the network will have its own address between 0 and 63. 

If a PLC-5 was to be connected to Devicenet a scanner card would need to be 

placed in the rack. The ladder logic in Figure 28.8 would communicate with the sensors 

through a scanner card in slot 3. The read and write blocks would read and write the 

Devicenet input values to integer memory from N7:40 to N7:59. The outputs would be 

copied from the integer memory between N7:20 to N7:39. The ladder logic to process 

inputs and outputs would need to examine and set bits in integer memory. 



MG9:0/EN 

MSG 

Send/Rec Message 


(EN) 

(DN) 

(ER) 

MG9:1/EN 

MSG 



(EN) 

(DN) 

(ER) 

MG9:0 

MG9:1 

Read/Write 

Data Table 

Size 

Local/Remote 


Link ID 




Dest. Addr. 

Write 

N7:20 

20 

Remote 

?? 

?? 

?? 

N/A 

???? 

???? 

Read/Write 

Data Table 

Size 

Local/Remote 


Link ID 




Dest. Addr. 

Read 

N7:40 

20 

Remote 

?? 

?? 

?? 

N/A 

???? 

???? 

Note: Get exact settings for these parametersXXXXXXXXXXXXXXXXX 

Figure 28.8 

Communicating with Devicenet Inputs and Outputs 

On an Allen Bradley Softlogix PLC the I/O will be copied into blocks of integer 

memory. These blocks are selected by the user in setup software. The ladder logic would 

then using integer memory for inputs and outputs, as shown in Figure 28.9. Here the 

inputs are copied into N9 integer memory, and the outputs are set by copying the N10 

block of memory back to the outputs. 



N9:0 

N10:23 

Figure 28.9 

Devicenet Inputs and Outputs in Software Based PLCs 

28.2.2 CANbus 

The CANbus (Controller Area Network bus) standard is part of the Devicenet 

standard. Integrated circuits are now sold by many of the major vendors (Motorola, Intel, 

etc.) that support some, or all, of the standard on a single chip. This section will discuss 

many of the technical details of the standard. 

CANbus covers the first two layers of the OSI model. The network has a bus topology 

and uses bit wise resolution for collisions on the network (i.e., the lower the network 

identifier, the higher the priority for sending). A data frame is shown in Figure 28.10. The 

frame is like a long serial byte, like that seen in the previous chapter. The frame begins 

with a start bit. This is then followed with a message identifier. For Devicenet this is a 5 

bit address code (for up to 64 nodes) and a 6 bit command code. The ready to receive it bit 

will be set by the receiving machine. (Note: both the sender and listener share the same 

wire.) If the receiving machine does not set this bit the remainder of the message is 

aborted, and the message is resent later. While sending the first few bits, the sender monitors 

the bits to ensure that the bits send are heard the same way. If the bits do not agree, 

then another node on the network has tried to write a message at the same time - there was 

a collision. The two devices then wait a period of time, based on their identifier and then 

start to resend. The second node will then detect the message, and wait until it is done. The 

next 6 bits indicate the number of bytes to be sent, from 0 to 8. This is followed by two 

sets of bits for CRC (Cyclic Redundancy Check) error checking, this is a checksum of earlier 

bits. The next bit ACK slot is set by the receiving node if the data was received correctly. 

If there was a CRC error this bit would not be set, and the message would be resent. 

The remaining bits end the transmission. The end of frame bits are equivalent to stop bits. 

There must be a delay of at least 3 bits before the next message begins. 



1 bit 

11 bits 

1 bit 

start of frame 

identifier 

ready to receive it 

arbitration field 

6 bits 

0-8 bytes 

15 bits 

1 bit 

1 bit 

1 bit 

7 bits 

>= 3 bits 

control field - contains number of data bytes 

data - the information to be passed 

CRC sequence 

CRC delimiter 

ACK slot - other listeners turn this on to indicate frame received 

ACK delimiter 

end of frame 

delay before next frame 

Figure 28.10 

A CANbus Data Frame 

Because of the bitwise arbitration, the address with the lowest identifier will get 

the highest priority, and be able to send messages faster when there is a conflict. As a 

result the controller is normally put at address 0. And, lower priority devices are put near 

the end of the address range. 

28.2.3 Controlnet 

Controlnet is complimentary to Devicenet. It is also supported by a consortium of 

companies, (http://www.controlnet.org) and it conducts some projects in cooperation with 

the Devicenet group. The standard is designed for communication between controllers, 

and permits more complex messages than Devicenet. It is not suitable for communication 

with individual sensors and actuators, or with devices off the factory floor. 

Controlnet is more complicated method than Devicenet. Some of the key features 



of this network include, 

• Multiple controllers and I/O on one network 

• Deterministic 

• Data rates up to 5Mbps 

• Multiple topologies (bus, star, tree) 

• Multiple media (coax, fiber, etc.) 

• Up to 99 nodes with addresses, up to 48 without a repeater 

• Data packets up to 510 bytes 

• Unlimited I/O points 

• Maximum length examples 

1000m with coax at 5Mbps - 2 nodes 

250m with coax at 5Mbps - 48 nodes 

5000m with coax at 5Mbps with repeaters 

3000m with fiber at 5Mbps 

30Km with fiber at 5Mbps and repeaters 

• 5 repeaters in series, 48 segments in parallel 

• Devices powered individually (no network power) 

• Devices can be removed while network is active 

This control network is unique because it supports a real-time messaging scheme 

called Concurrent Time Domain Multiple Access (CTDMA). The network has a scheduled 

(high priority) and unscheduled (low priority) update. When collisions are detected, 

the system will wait a time of at least 2ms, for unscheduled messages. But, scheduled messages 

will be passed sooner, during a special time window. 

28.2.4 Ethernet 

Ethernet has become the predominate networking format. Version I was released in 

1980 by a consortium of companies. In the 1980s various versions of ethernet frames were 

released. These include Version II and Novell Networking (IEEE 802.3). Most modern 

ethernet cards will support different types of frames. 

The ethernet frame is shown in Figure 28.11. The first six bytes are the destination 

address for the message. If all of the bits in the bytes are set then any computer that 

receives the message will read it. The first three bytes of the address are specific to the 

card manufacturer, and the remaining bytes specify the remote address. The address is 

common for all versions of ethernet. The source address specifies the message sender. The 

first three bytes are specific to the card manufacturer. The remaining bytes include the 

source address. This is also identical in all versions of ethernet. The ethernet type identifies 

the frame as a Version II ethernet packet if the value is greater than 05DChex. The 

other ethernet types use these to bytes to indicate the datalength. The data can be between 



46 to 1500 bytes in length. The frame concludes with a checksum that will be used to verify 

that the data has been transmitted correctly. When the end of the transmission is 

detected, the last four bytes are then used to verify that the frame was received correctly. 

6 bytes destination address 

6 bytes source address 

2 bytes ethernet type 

46-1500 bytes data 

4 bytes checksum 

Figure 28.11 

Ethernet Version II Frame 

28.2.5 Profibus 

Another control network that is popular in europe, but also available world wide. It 

is also promoted by a consortium of companies (http://www.profibus.com). General features 

include; 

• A token passing between up to three masters 

• Maximum of 126 nodes 

• Straight bus topology 

• Length from 9600m/9.6Kbps with 7 repeaters to 500m/12Mbps with 4 repeaters 

• With fiber optic cable lengths can be over 80Km 

• 2 data lines and shield 

• Power needed at each station 

• Uses RS-485, ethernet, fiber optics, etc. 

• 2048 bits of I/O per network frame 

28.2.6 Sercos 

The SErial Real-time COmmunication System (SERCOS) is an open standard 

designed for multi-axis motion control systems. The motion controller and axes can be 



implemented separately and then connected using the SERCOS network. Many vendors 

offer cards that allow PLCs to act as clients and/or motion controllers. 

• Deterministic with response times as small as a few nanoseconds 

• Data rates of 2, 4, 8 and 16 Mbaud 

• Documented with IEC 61491 in 1995 and 2002 

• Uses a fiber optic rings, RS-485 and buses 

28.3 PROPRIETARY NETWORKS 

28.3.1 Data Highway 

Allen-Bradley has developed the Data Highway II (DH+) network for passing data 

and programs between PLCs and to computers. This bus network allows up to 64 PLCs to 

be connected with a single twisted pair in a shielded cable. Token passing is used to control 

traffic on the network. Computers can also be connected to the DH+ network, with a 

network card to download programs and monitor the PLC. The network will support data 

rates of 57.6Kbps and 230 Kbps 

The DH+ basic data frame is shown in Figure 28.12. The frame is byte oriented. 

The first byte is the DLE or delimiter byte, which is always $10. When this byte is 

received the PLC will interpret the next byte as a command. The SOH identifies the message 

as a DH+ message. The next byte indicates the destination station - each node one the 

network must have a unique number. This is followed by the DLE and STX bytes that identify 

the start of the data. The data follows, and its’ length is determined by the command 

type - this will be discussed later. This is then followed by a DLE and ETX pair that mark 

the end of the message. The last byte transmitted is a checksum to determine the correctness 

of the message. 



1 byte 

1 byte 

DLE = 10H 

SOH = 01H 

header fields 

1 byte 

STN - the destination number 

1 byte 

1 byte 

1 byte 

1 byte 

DLE = 10H 

STX = 02H 

data 

DLE = 10H 

ETX = 03H 

start fields 

termination fields 

1 byte 

block check - a 2s compliment checksum of the DATA and STN values 

Figure 28.12 

The Basic DH+ Data Frame 

The general structure for the data is shown in Figure 28.13. This packet will 

change for different commands. The first two bytes indicate the destination, DST, and 

source, SRC, for the message. The next byte is the command, CMD, which will determine 

the action to be taken. Sometimes, the function, FNC, will be needed to modify the command. 

The transaction, TNS, field is a unique message identifier. The two address, ADDR, 

bytes identify a target memory location. The DATA fields contain the information to be 

passed. Finally, the SIZE of the data field is transmitted. 



optional 

optional 

optional 

optional 

1 byte 

1 byte 

1 byte 

1 byte 

2 byte 

1 byte 

2 byte 

variable 

1 byte 

DST - destination node for the message 

SRC - the node that sent the message 

CMD - network command - sometime FNC is required 

STS - message send/receive status 

TNS - transaction field (a unique message ID) 

FNC may be required with some CMD values 

ADDR - a memory location 

DATA - a variable length set of data 

SIZE - size of a data field 

Figure 28.13 

Data Filed Values 

Examples of commands are shown in Figure 28.14. These focus on moving memory 

and status information between the PLC, and remote programming software, and other 

PLCs. More details can be found in the Allen-Bradley DH+ manuals. 



CMD 

00 

01 

02 

05 

06 

06 

06 

06 

06 

06 

06 

06 

08 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

0F 

FNC 

00 

01 

02 

03 

04 

05 

06 

07 

00 

01 

02 

11 

17 

18 

26 

29 

3A 

41 

50 

52 

53 

55 

57 

5E 

67 

68 

A2 

AA 

Description 

Protected write 

Unprotected read 

Protected bit write 

Unprotected bit write 

Echo 

Read diagnostic counters 

Set variables 

Diagnostic status 

Set timeout 

Set NAKs 

Set ENQs 

Read diagnostic counters 

Unprotected write 

Word range write 

Word range read 

Bit write 

Get edit resource 

Read bytes physical 

Write bits physical 

Read-modify-write 

Read section size 

Set CPU mode 

Disable forces 

Download all request 

Download completed 

Upload all request 

Upload completed 

Initialize memory 

Modify PLC-2 compatibility file 

typed write 

typed read 

Protected logical read - 3 address fields 

Protected logical write - 3 addr. fields 

Figure 28.14 

DH+ Commands for a PLC-5 (all numbers are hexadecimal) 

The ladder logic in Figure 28.15 can be used to copy data from the memory of one 

PLC to another. Unlike other networking schemes, there are no login procedures. In this 

example the first MSG instruction will write the message from the local memory N7:20 - 

N7:39 to the remote PLC-5 (node 2) into its memory from N7:40 to N7:59. The second 



MSG instruction will copy the memory from the remote PLC-5 memory N7:40 to N7:59 

to the remote PLC-5 memory N7:20 to N7:39. This transfer will require many scans of 

ladder logic, so the EN bits will prevent a read or write instruction from restarting until the 

previous MSG instruction is complete. 

MG9:0/EN 

MSG 



(EN) 

(DN) 

(ER) 

MG9:1/EN 

MSG 



(EN) 

(DN) 

(ER) 

MG9:0 

MG9:1 

Read/Write 

Data Table 

Size 

Local/Remote 


Link ID 




Dest. Addr. 

Write 

N7:20 

20 

Local 

N/A 

N/A 

N/A 

2 

PLC-5 

N7:40 

Read/Write 

Data Table 

Size 

Local/Remote 


Link ID 




Dest. Addr. 

Read 

N7:40 

20 

Local 

N/A 

N/A 

N/A 

2 

PLC-5 

N7:20 

Figure 28.15 

Ladder Logic for Reading and Writing to PLC Memory 

The DH+ data packets can be transmitted over other data links, including ethernet 

and RS-232. 

28.4 NETWORK COMPARISONS 



Table 1: Network Comparison 

Network topology addresses length speed packet size 

Bluetooth wireless 8 10 64Kbps continuous 

CANopen bus 127 25m-1000m 1Mbps- 

10Kbps 

8 bytes 

ControlNet bus or star 99 250m- 

1000m 

wire, 3- 

30km fiber 

5Mbps 

0-510 bytes 

Devicenet bus 64 500m 125- 

500Kbps 

8 bytes 

Ethernet bus, star 1024 85m coax, 

100m 

twisted pair, 

400m-50km 

fiber 

10- 

1000Gbps 

46- 

1500bytes 

Foundation 

Fieldbus 

star unlimited 100m 

twisted pair, 

2km fiber 

Interbus bus 512 12.8km 

with 400m 

segments 

Lonworks 

bus, ring, 

star 

100Mbps



28.5.1 Devicenet 

Problem: A robot will be loading parts into a box until the box reaches a prescribed 

weight. A PLC will feed parts into a pickup fixture when it is empty. The PLC will tell the 

robot when to pick up a part and load it using Devicenet. 

PLC 

RS-232 

"pickup" = pickup part 

Robot 

feed part part waiting box full 

Parts 

Feeder 

Parts Pickup 

Fixture 

Box and 

Weigh Scale 

Figure 28.16 

Box Loading System 

Solution: The following ladder logic will implement part of the control system for 

the system in Figure 28.16. 



Figure 28.17 

A Box Loading System 

28.6 SUMMARY 

• Networks come in a variety of topologies, but buses are most common on factory 

floors. 

• The OSI model can help when describing network related hardware and software. 

• Networks can be connected with a variety of routers, bridges, gateways, etc. 

• Devicenet is designed for interfacing to a few inputs and outputs. 

• Controlnet is designed for interfacing between controllers. 

• Controlnet and devicenet are based on CANbus. 

• Ethernet is common, and can be used for high speed communication. 

• Profibus is another control network. 


1. Explain why networks are important in manufacturing controls. 

2. We will use a PLC to control a cereal box filling machine. For single runs the quantities of 

cereal types are controlled using timers. There are 6 different timers that control flow, and 

these result in different ratios of product. The values for the timer presets will be downloaded 

from another PLC using the DH+ network. Write the ladder logic for the PLC. 

3. 

a) We are developing ladder logic for an oven to be used in a baking facility. A 

PLC is controlling the temperature of an oven using an analog voltage output. 

The oven must be started with a push button and can be stopped at any time 

with a stop push button. A recipe is used to control the times at each temperawww.PAControl.com


ture (this is written into the PLC memory by another PLC). When idle, the output 

voltage should be 0V, and during heating the output voltages, in sequence, 

are 5V, 7.5V, 9V. The timer preset values, in sequence, are in N7:0, N7:1, N7:2. 

When the oven is on, a value of 1 should be stored in N7:3, and when the oven 

is off, a value of 0 should be stored in N7:3. Draw a state diagram and write the 

ladder logic for this station. 

b) We are using a PLC as a master controller in a baking facility. It will update recipes 

in remote PLCs using DH+. The master station is #1, the remote stations 

are #2 and #3. When an operator pushes one of three buttons, it will change the 

recipes in two remote PLCs if both of the remote PLCs are idle. While the 

remote PLCs are running they will change words in their internal memories 

(N7:3=0 means idle and N7:3=1 means active). The new recipe values will be 

written to the remote PLCs using DH+. The table below shows the values for 

each PLC. Write the ladder logic for the master controller. 

button A 

button B 

button C 

PLC #2 

13 

690 

45 

17 

235 

75 

14 

745 

34 

PLC #3 

76 

345 

987 

345 

764 

87 

72 

234 

12 

34 

456 

67 

56 

645 

23 

456 

568 

8 

4. A controls network is to be 1500m long. Suggest three different types of networks that would 

meet the specifications. 

5 How many data bytes (maximum) could be transferred in one second with DH+? 

6. Is the OSI model able to describe all networked systems? 

7. What are the different methods for resolving collisions on a bus network? 


1. These networks allow us to pass data between devices so that individually controlled systems 

can be integrated into a more complex manufacturing facility. An example might be a serial 

connection to a PLC so that SPC data can be collected as product is made, or recipes downloaded 

as they are needed. 



2. 

MG9:0/EN 

MG9:0/DN 

on 

on 

MSG 

MG9:0 

FAL 

DEST. #T4:0.PRE 

EXPR. #N7:0 

Read Message 

Remote station #1 

Remote Addr. N7:0 

Length 6 

Destination N7:0 

start 

on 

stop 

on 

box present 

on 

TON 

T4:0 

TON 

T4:1 

TON 

T4:2 

TON 

T4:3 

TON 

T4:4 

TON 

T4:5 

T4:0/TT 

fill hearts 

T4:1/TT 

fill moons 

ETC... 



3. 

a) start stop 

on N7:3/0 

T4:2/DN 

on N7:3/0 

MOV 

Source N7:0 

Dest T4:0.PRE 

MOV 

Source N7:1 

Dest T4:1.PRE 

on 

T4:0/DN 

T4:1/DN 

BT10:0/EN 

T4:0/TT 

T4:1/TT 

T4:2/TT 

on 

MOV 

Source N7:2 

Dest T4:2.PRE 

TON 

Timer T4:0 

Delay 0s 

TON 

Timer T4:1 

Delay 0s 

TON 

Timer T4:2 

Delay 0s 



Rack 000 

Group 3 

Module 0 



Length 13 

Continuous No 

MOV 

Source 2095 

Dest N9:0 

MOV 

Source 3071 

Dest N9:0 

MOV 

Source 3686 

Dest N9:0 

MOV 

Source 0 

Dest N9:0 



b) MG9:0/EN 

MSG 

MG9:1/EN 

MG9:2/EN 

MG9:3/EN 

MG9:0 

Read/Write Write 

Data Table N7:40 

Size 3 

Local/Remote Local 

Remote N/A 

Link ID N/A 

Remote Link N/A 

Local Node 2 

Processor PLC-5 

Dest. Addr. N7:0 

MG9:1 

Read/Write 

Data Table 

Size 

Local/Remote 

Remote 

Link ID 

Remote Link 

Local Node 

Processor 

Dest. Addr. 

Write 

N7:43 

6 

Local 

N/A 

N/A 

N/A 

3 

PLC-5 

N7:0 

Read/Write 

Data Table 

Size 



MSG 



Local/Remote 

Remote 

Link ID 

Remote Link 

Local Node 


Dest. Addr. 

(EN) 

(DN) 

(ER) 

(EN) 

(DN) 

(ER) 

MSG 

(EN) 

Send/Rec Message (DN) 


(ER) 

MSG 

(EN) 

Send/Rec Message (DN) 


(ER) 

MG9:2 

MG9:3 

Read Read/Write 

N7:3 Data Table 

1 Size 1 

Local 

N/A 

N/A 

N/A 

2 

PLC-5 

N7:0 

Local/Remote 

Remote 

Link ID 

Remote Link 

Local Node 


Dest. Addr. 

Read 

N7:3 

Local 

N/A 

N/A 

N/A 

3 

PLC-5 

N7:1 

A 

N7:0/0 

N7:0/1 

COP 

Source N7:10 

Dest N7:40 

Length 9 

B 

N7:0/0 

N7:0/1 

COP 

Source N7:20 

Dest N7:40 

Length 9 

N7:10 

N7:20 

N7:30 

C 

13 

17 

14 

N7:0/0 

690 

235 

745 

45 

75 

34 

76 

72 

56 

N7:0/1 

345 

234 

645 

987 

12 

23 

345 

34 

456 

COP 

Source N7:30 

Dest N7:40 

Length 9 

764 

456 

568 

87 

67 

8 

0 

0 

0 



4. Controlnet, Profibus, Ethernet with multiple subnets 

5 the maximum transfer rate is 230 Kbps, with 11 bits per byte (1start+8data+2+stop) for 20909 

bytes per second. Each memory write packet contains 17 overhead bytes, and as many as 2000 

data bytes. Therefore as many as 20909*2000/(2000+17) = 20732 bytes could be transmitted 

per second. Note that this is ideal, the actual maximum rates would be actually be a fraction of 

this value. 

6. The OSI model is just a model, so it can be used to describe parts of systems, and what their 

functions are. When used to describe actual networking hardware and software, the parts may 

only apply to one or two layers. Some parts may implement all of the layers in the model. 

7. When more than one client tries to start talking simultaneously on a bus network they interfere, 

this is called a collision. When this occurs they both stop, and will wait a period of time before 

starting again. If they both wait different amounts of time the next one to start talking will get 

priority, and the other will have to wait. With CSMA/CD the clients wait a random amount of 

time. With CSMA/BA the clients wait based upon their network address, so their priority is 

related to their network address. Other networking methods prevent collisions by limiting 

communications. Master-slave networks require that client do not less talk, unless they are 

responding to a request from a master machine. Token passing only permits the holder of the 

token to talk. 


1. Describe an application for DH networking. 

2. The response times of hydraulic switches is being tested in a PLC controlled station. When the 

units arrive a ‘part present’ sensor turns on. The part is then clamped in place by turning on a 

‘clamp’ output. 1 seconds after clamping, a ‘flow’ output is turned on to start the test. The 

response time is the delay between when ‘flow’ is turned on, and the ‘engaged’ input turns on. 

When the unit has responded, up to 10 seconds later, the ‘flow’ output is turned off, and the 

system is allowed to sit for 5 seconds to discharge before unclamping. The result of the test is 

written to one of the memory locations from F8:0 to F8:39, for a total of 40 separate tests. 

When 40 tests have been done, the memory block from F8:0 to F8:39 is sent to another PLC 

using DH+, and the process starts again. Write the ladder logic to control the station. 

3. a) Controls are to be developed for a machine that packages golf tees. Each container will normally 

hold 1000 tees filled from three different hoppers, each containing a different color. For 

marketing purposes the ratio of colors is changed frequently. To make the controller easy to 

reconfigure, the number of tees from each hopper are stored in the memory locations N7:0, 

N7:1 and N7:2. The process is activated when an empty package arrives, activating a 

PRESENT input. When filling the package, the machine opens a single hopper with a solenoid, 

and counts the tees with an optical sensor, until the specified count has been surpassed. It then 

repeats the operation with the two other hoppers. When done, it activates a SEAL for 2 seconds 



to advance a heated ram that seals the package. After that, the DONE output is turned on until 

the PRESENT sensor turns off. Write the ladder logic for this process. 

b) Write a ladder logic program that will read and parse values from an RS-232 input. The format 

of the input will be an eleven character line with three integer numbers separated by commas. 

The integers will be padded to three characters by padding with zeros. The line will be terminated 

with a CR and a LF. The three integers are to be parsed and stored in the memory locations 

N7:0, N7:1 and N7:2 to be used in a golf tee packaging machine. 

4. A master PLC is located at the top of a mine shaft and controls an elevator system. A second 

PLC is located half a mile below to monitor the bottom of the elevator shaft. At the top of the 

mine shaft the PLC has inputs for the door (D), a top limit switch (T), and start (G) and stop (S) 

pushbuttons. The PLC has two outputs to apply power (P) to the motor, or reverse (R) the 

motor direction. The PLC at the bottom of the elevator shaft checks a bottom limit switch (B) 

and a door closed (C) sensor. The two PLCs are connected using DH+. Write ladder logic for 

both PLCs and indicate the communication settings. Use structured design techniques. 


plc internet - 29.1 

29. INTERNET 

 

Topics: 

• Internet; addressing, protocols, formats, etc. 


Objectives: 

• To understand the Internet topics related to shop floor monitoring and control 


• The Internet is just a lot of LANs and WANs connected together. If your computer 

is on one LAN that is connected to the Internet, you can reach computers on other 

LANs. 

• The information that networks typically communicate includes, 

email - text files, binary files (MIME encoded) 

programs - binary, or uuencoded 

web pages - (HTML) Hyper Text Markup Language 

• To transfer this information we count on access procedures that allow agreement 

about when computers talk and listen, and what they say. 

email - (SMTP) Simple Mail Transfer Protocol, POP3, IMAP 

programs - (FTP) File Transfer Protocol 

login sessions - Telnet 

web access - (HTTP) Hyper Text Transfer Protocol 



Aside: Open a Dos window and type ‘telnet river.it.gvsu.edu 25’. this will connect you to the 

main student computer. But instead of the normal main door, you are talking to a program 

that delivers mail. Type the following to send an email message. 

ehlo northpole.com 

mail from: santa 

rcpt to: jackh 

data 

Subject: Bogus mail 

this is mail that is not really from santa 

29.1.1 Computer Addresses 

• Computers are often given names, because names are easy to remember. 

• In truth the computers are given numbers. 

Machine Name: 

Alternate Name: 

IP Number: 

claymore.engineer.gvsu.edu 

www.eod.gvsu.edu 

148.61.104.215 

• When we ask for a computer by name, your computer must find the number. It does this using a 

DNS (Domain Name Server). On campus we have two ‘148.61.1.10’ and ‘148.61.1.15’. 

EXERCISE: In netscape go to the location above using the name, and using the IP number 

(148.61.104.215). 

• The number has four parts. The first two digits ‘148.61’ indicate to all of the internet that the 

computer is at ‘gvsu.edu’, or on campus here (we actually pay a yearly fee of about $50 to register 

this internationally). The third number indicates what LAN the computer is located on 

(Basically each hub has its own number). Finally the last digit is specific to a machine. 



EXERCISE: Run the program ‘winipcfg’. You will see numbers come up, including an IP 

number, and gateway. The IP number has been temporarily assigned to your computer. The 

gateway number is the IP address for the router. The router is a small computer that controls 

traffic between local computers (it is normally found in a locked cabinet/closet). 

• Netmask, name servers, gateway 

29.1.1.1 - IPV6 

29.1.2 Phone Lines 

• The merit dialup network is a good example. It is an extension of the internet that you can reach 

by phone. 

• The phone based connection is slower (about 5 MB/hour peak) 

• There are a few main types, 

SLIP - most common 

PPP - also common 

ISDN - an faster, more expensive connection, geared to permanent connections 

• You need a modem in your computer, and you must dial up to another computer that has a 

modem and is connected to the Internet. The slower of the two modems determines the speed 

of the connection. Typical modem speeds are, 

- 52.4 kbps - very fast 

- 28.8/33.3 kbps - moderate speed, inexpensive 

- 14.4 kbps - a bit slow for internet access 

- 2.4, 9.6 kpbs - ouch 

- 300 bps - just shoot me 

29.1.3 Mail Transfer Protocols 

• Popular email methods include, 



SMTP (Simple Mail Transfer Protocol) - for sending mail 

POP3 - for retrieving mail 

IMAP - for retrieving mail 

EXERCISE: In netscape go to the ‘edit-preferences’ selection. Choose the ‘mail and groups’ 

option. Notice how there is a choice for mail service type under ‘Mail Server’. It should be 

set for ‘POP3’ and refer to ‘mailhost.gvsu.edu’. This is where one of the campus mail servers 

lives. Set it up for your river account, and check to see if you have any mail. 

• Note that the campus mail system ‘ccmail’ is not standard. It will communicate with other mail 

programs using standard services, but internally special software must be used. Soon ccmail 

will be available using the POP3 standard, so that you will be able to view your ccmail using 

Netscape, but some of the features of ccmail will not be available. 

• Listservers allow you to send mail to a single address, and it will distribute it to many users (IT 

can set this up for you). 

29.1.4 FTP - File Transfer Protocol 

• This is a method for retrieving or sending files to remote computers. 

Aside: In Netscape ask for the location ‘ftp://sunsite.unc.edu’ This will connect you via ftp the 

same way as with the windows and the dos software. 

29.1.5 HTTP - Hypertext Transfer Protocol 

• This is the protocol used for talking to a web server. 

29.1.6 Novell 

• Allows us to share files stored on a server. 



29.1.7 Security 

• Security problems usually arise through protocols. For example it is common for a hacker to 

gain access through the mail system. 

• The system administrator is responsible for security, and if you are using the campus server, 

security problems will normally be limited to a single user. 

• Be careful with passwords, this is your own protection again hacking. General rules include, 

1. Don’t leave yourself logged in when somebody else has access to your computer. 

2. Don’t give your password to anybody (even the system administrator). 

3. Pick a password that is not, 

- in the dictionary 

- some variation of your name 

- all lower case letters 

- found in television 

- star trek, the bible 

- pet/children/spouse/nick names 

- swear words 

- colloquial phrases 

- birthdays 

- etc. 

4. Watch for unusual activity in you computer account. 

5. Don’t be afraid to call information technology and ask questions. 

6. Don’t run software that comes from suspect or unknown sources. 

7. Don’t write your password down or give it to others. 

29.1.7.1 - Firewall 

29.1.7.2 - IP Masquerading 

29.1.8 HTML - Hyper Text Markup Language 

• This is a format that is invisible to the user on the web. It allows documents to be formatted to fit 

the local screen. 



Aside: While looking at a home page in Netscape select ‘View - Page Source’. You will see a 

window that includes the actual HTML file - This file was interpreted by Netscape to make 

the page you saw previously. Look through the file to see if you can find any text that was 

on the original page. 

• Editors are available that allow users to update HTML documents the same way they use word 

processors. 

• Keep in mind that the website is just another computer. You have directories and files there too. 

To create a web site that has multiple files we need to create other files or directory names. 

• Note that some web servers do not observe upper/lower case and cut the ‘html’ extension to 

‘htm’. Microsoft based computers are notorious for this, and this will be the most common 

source of trouble. 

29.1.9 URLs 

• In HTML documents we need to refer to resources. To do this we use a label to identify the type 

of resource, followed by a location. 

• Universal Resource Locators (URLs) 

- http:WEB_SITE_NAME 

- ftp:FTP_SITE_NAME 

- mailto:USER@MAIL_SERVER 

- news:NEWSGROUP_NAME 

EXERCISE: In netscape type in ‘mailto:YOUR_NAME@river.it.gvsu.edu’. After you are 

done try ‘news:gvsu’. 

29.1.10 Encryption 

• Allows some degree of privacy, but this is not guaranteed. 



• Basically, if you have something you don’t want seen, don’t do it on the computer. 

29.1.11 Compression 

• We can make a file smaller by compressing it (unless it is already compressed, then it gets 

larger) 

• File compression can make files harder to use in Web documents, but the smaller size makes 

them faster to download. A good rule of thumb is that when the file is MB is size, compression 

will have a large impact. 

• Many file formats have compression built in, including, 

images - JPG, GIF 

video - MPEG, AVI 

programs - installation programs are normally compressed 

• Typical compression formats include, 

zip - zip, medium range compression 

gz - g-zip - good compression 

Z - unix compression 

Stuffit - A Mac compression format 

• Some files, such as text, will become 1/10 of their original size. 

29.1.12 Clients and Servers 

• Some computers are set up to serve others as centers of activity, sort of like a campus library. 

Other computers are set up only as users, like bookshelves in a closed office. The server is 

open to all, while the private bookshelf has very limited access. 

• A computer server will answer requests from other computers. These requests may be, 

- to get/put files with FTP 

- to send email 

- to provide web pages 



• A client does not answer requests. 

• Both clients and servers can generate requests. 

EXERCISE: Using Netscape try to access the IP number of the machine beside you. You will 

get a message that says the connection was refused. This is because the machine is a client. 

You have already been using servers to get web pages. 

• Any computer that is connected to the network Client or Server must be able to generate 

requests. You can see this as the Servers have more capabilities than the Clients. 

• Microsoft and Apple computers have limited server capabilities, while unix and other computer 

types generally have more. 

Windows 3.1 - No client or server support without special software 

Windows 95 - No server support without special software 

Windows NT - Limited server support with special versions 

MacOS - Some server support with special software 

Unix - Both client and server models built in 

• In general you are best advised to use the main campus servers. But in some cases the extra 

effort to set up and maintain your own server may also be useful. 

• To set up your own server machine you might, 

1. Purchase a computer and network card. A Pentium class machine will actually 

provide more than enough power for a small web site. 

2. Purchase of copy of Windows NT server version. 

3. Choose a name for your computer that is easy to remember. An example is ‘artsite’. 

4. Call the Information technology people on campus, and request an IP address. 

Also ask for the gateway number, netmask, and nameserver numbers. They will 

add your machine to the campus DNS so that others may find it by name (the 

number will always work if chosen properly). 

5. Connect the computer to the network, then turn it on. 

6. Install Windows NT, and when asked provide the network information. Indicate 

that web serving will be permitted. 

7. Modify web pages as required. 



29.1.13 Java 

• This is a programming language that is supported on most Internet based computers. 

• These programs will run on any computer - there is no need for a Mac, PC and Unix version. 

• Most users don’t need to program in Java, but the results can be used in your web pages 

EXERCISE: Go to ‘www.javasoft.com’ and look at some sample java programs. 

29.1.14 Javascript 

• Simple programs can be written as part of an html file that will add abilities to the HTML page. 

29.1.15 CGI 

• CGI (Common Gateway Interface) is a very popular technique to allow the html page on the client 

to run programs on the server. 

• Typical examples of these include, 

- counters 

- feedback forms 

- information requests 

29.1.16 ActiveX 

• This is a programming method proposed by Microsoft to reduce the success of Java - It has been 

part of the antitrust suit against Microsoft by the Justice Department. 

• It will only work on IBM PC computers running the ‘Internet Explorer’ browser from Microsoft. 

• One major advantage of ActiveX is that it allows users to take advantage of programs written for 



Windows machines. 

• Note: Unless there is no choice avoid this technique. If similar capabilities are needed, use Java 

instead. 

29.1.17 Graphics 

• Two good formats are, 

GIF - well suited to limited color images - no loss in compression. Use these for 

line images, technical drawings, etc 

JPG - well suited to photographs - image can be highly compressed with minimal 

distortion. Use these for photographs. 

• Digital cameras will permit image capture and storage - images in JPG format are best. 

• Scanners will capture images, but this is a poor alternative as the image sizes are larger and 

image quality is poorer 

- Photographs tend to become grainy when scanned. 

- Line drawings become blurred. 

• Screen captures are also possible, but do these with a lower color resolution on the screen (256 

color mode). 


29.2.1 Remote Monitoring System 

Problem: A system is to be designed to allow engineeers and managers to monitor 

the shop floor conditions in real time. A network system and architecture must be 

designed to allow this system to work effectively without creating the potential for 

secutiry breaches. 



Solution: 

29.3 SUMMARY 

• The internet can be use to monitor and control shop floor activities. 




1. 


plc hmi - 30.1 

30. HUMAN MACHINE INTERFACES (HMI) 

 

Topics: 

• 

• 

Objectives: 

• 

• 

• 


• These allow control systems to be much more interactive than before. 

• The basic purpose of an HMI is to allow easy graphical interface with a process. 

• These devices have been known by a number of names, 

- touch screens 

- displays 

- Man Machine Interface (MMI) 

- Human Machine Interface (HMI) 

• These allow an operator to use simple displays to determine machine condition 

and make simple settings. 

• The most common uses are, 

- display machine faults 

- display machine status 

- allow the operator to start and stop cycles 

- monitor part counts 



• These devices allow certain advantages such as, 

- color coding allows for easy identification (eg. red for trouble) 

- pictures/icons allow fast recognition 

- use of pictures eases problems of illiteracy 

- screen can be changed to allow different levels of information and access 

• The general implementation steps are, 

1. Layout screens on PC based software. 

2. Download the screens to the HMI unit. 

3. Connect the unit to a PLC. 

4. Read and write to the HMI using PLC memory locations to get input and update 

screens. 

• To control the HMI from a PLC the user inputs set bits in the PLC memory, and 

other bits in the PLC memory can be set to turn on/off items on the HMI screen. 

30.2 HMI/MMI DESIGN 

• The common trend is to adopt a user interface which often have, 

- Icons 

- A pointer device (such as a mouse) 

- Full color 

- Support for multiple windows, which run programs simultaneously 

- Popup menus 

- Windows can be moved, scaled, moved forward/back, etc. 

• The current demands on user interfaces are, 

- on-line help 

- adaptive dialog/response 

- feedback to the user 

- ability to interrupt processes 

- consistent modules 

- a logical display layout 

- deal with many processes simultaneously 

• To design an HMI interface, the first step is to identify, 



1. Who needs what information? 

2. How do they expect to see it presented? 

3. When does information need to be presented? 

4. Do the operators have any special needs? 

5. Is sound important? 

6. What choices should the operator have? 


• Design an HMI for a press controller. The two will be connected by a Devicenet 

network. 

Press and PLC 

HMI 

Figure 30.1 

A PLC With Connected HMI 

30.4 SUMMARY 






1. 


plc electrical - 31.1 

31. ELECTRICAL DESIGN AND CONSTRUCTION 

Topics: 

• Electrical wiring issues; cabinet wiring and layout, grounding, shielding and 

inductive loads 

• Enclosures 

Objectives: 

• To learn the major issues in designing controllers including; electrical schematics, 

panel layout, grounding, shielding, enclosures. 


It is uncommon for engineers to build their own controller designs. For example, 

once the electrical designs are complete, they must be built by an electrician. Therefore, it 

is your responsibility to effectively communicate your design intentions to the electricians 

through drawings. In some factories, the electricians also enter the ladder logic and do 

debugging. This chapter discusses the design issues in implementation that must be considered 

by the designer. 

31.2 ELECTRICAL WIRING DIAGRAMS 

In an industrial setting a PLC is not simply "plugged into a wall socket". The electrical 

design for each machine must include at least the following components. 

transformers - to step down AC supply voltages to lower levels 

power contacts - to manually enable/disable power to the machine with e-stop buttons 

terminals - to connect devices 

fuses or breakers - will cause power to fail if too much current is drawn 

grounding - to provide a path for current to flow when there is an electrical fault 

enclosure - to protect the equipment, and users from accidental contact 

A control system will normally use AC and DC power at different voltage levels. 

Control cabinets are often supplied with single phase AC at 220/440/550V, or two phase 

AC at 220/440Vac, or three phase AC at 330/550V. This power must be dropped down to a 



lower voltage level for the controls and DC power supplies. 110Vac is common in North 

America, and 220Vac is common in Europe and the Commonwealth countries. It is also 

common for a controls cabinet to supply a higher voltage to other equipment, such as 

motors. 

An example of a wiring diagram for a motor controller is shown in Figure 31.1 

(note: the symbols are discussed in detail later). Dashed lines indicate a single purchased 

component. This system uses 3 phase AC power (L1, L2 and L3) connected to the terminals. 

The three phases are then connected to a power interrupter. Next, all three phases are 

supplied to a motor starter that contains three contacts, M, and three thermal overload 

relays (breakers). The contacts, M, will be controlled by the coil, M. The output of the 

motor starter goes to a three phase AC motor. Power is supplied by connecting a step 

down transformer to the control electronics by connecting to phases L2 and L3. The lower 

voltage is then used to supply power to the left and right rails of the ladder below. The 

neutral rail is also grounded. The logic consists of two push buttons. The start push button 

is normally open, so that if something fails the motor cannot be started. The stop push button 

is normally closed, so that if a wire or connection fails the system halts safely. The system 

controls the motor starter coil M, and uses a spare contact on the starter, M, to seal in 

the motor stater. 



terminals power interrupter motor starter 

L1 

L2 

L3 

M 

M 

M 

motor 

3 phase 

AC 

step down transformer 

0010 

0020 

start 

stop 

M 

0030 

M 

Aside: The voltage for the step down transformer is connected between phases L2 and 

L3. This will increase the effective voltage by 50% of the magnitude of the voltage 

on a single phase. 

Figure 31.1 

A Motor Controller Schematic 

The diagram also shows numbering for the wires in the device. This is essential for 

industrial control systems that may contain hundreds or thousands of wires. These numbering 

schemes are often particular to each facility, but there are tools to help make wire 

labels that will appear in the final controls cabinet. 



Once the electrical design is complete, a layout for the controls cabinet is developed, 

as shown in Figure 31.2. The physical dimensions of the devices must be considered, 

and adequate space is needed to run wires between components. In the cabinet the 

AC power would enter at the terminal block, and be connected to the main breaker. It 

would then be connected to the contactors and overload relays that constitute the motor 

starter. Two of the phases are also connected to the transformer to power the logic. The 

start and stop buttons are at the left of the box (note: normally these are mounted elsewhere, 

and a separate layout drawing would be needed). 

Main 

Breaker 

Contactors 

Overload 

Start 

Transformer 

Stop 

Terminal Block 

Figure 31.2 

A Physical Layout for the Control Cabinet 

The final layout in the cabinet might look like the one shown in Figure 31.3. 



L1 

L2 

L3 

start 

stop 

3 phase AC 

motor 

3 phase 

AC 

Figure 31.3 

Final Panel Wiring 



When being built the system will follow certain standards that may be company 

policy, or legal requirements. This often includes items such as; 

hold downs - the will secure the wire so they don’t move 

labels - wire labels help troubleshooting 

strain reliefs - these will hold the wire so that it will not be pulled out of screw terminals 

grounding - grounding wires may be needed on each metal piece for safety 

A photograph of an industrial controls cabinet is shown in Figure 31.4. 

Get a photo of a controls cabinet with 

wire runs, terminal strip, buttons on panel front, etc 

Figure 31.4 

An Industrial Controls Cabinet 

When including a PLC in the ladder diagram still remains. But, it does tend to 

become more complex. Figure 31.5 shows a schematic diagram for a PLC based motor 

control system, similar to the previous motor control example. 

XXXXXXXXXXXXXX This figure shows the E-stop wired to cutoff power to all 

of the devices in the circuit, including the PLC. All critical safety functions should be 

hardwired this way. 



L1 

L2 

L3 

M 

M 

M 

PLC 

ADD TO DIAGRAM................. 

Figure 31.5 

An Electrical Schematic with a PLC 



31.2.1 Selecting Voltages 

When selecting voltage ranges and types for inputs and outputs of a PLC some 

care can save time, money and effort. Figure 31.6 that shows three different voltage levels 

being used, therefore requiring three different input cards. If the initial design had selected 

a standard supply voltage for the system, then only one power supply, and PLC input card 

would have been required. 

48Vdc 

24Vdc 

5Vdc 

+ 

- 

+ 

- 

+ 

- 

PLC Input Cards 

I0 

com 

I0 

com 

I0 

com 


+ 

24Vdc 

I0 

I1 

I2 

I3 

- 

com 

Figure 31.6 

Standardized Voltages 



31.2.2 Grounding 

The terms ground and common are often interchanged (I do this often), but they do 

mean different things. The term, ground, comes from the fact that most electrical systems 

find a local voltage level by placing some metal in the earth (ground). This is then connected 

to all of the electrical outlets in the building. If there is an electrical fault, the current 

will be drawn off to the ground. The term, common, refers to a reference voltage that 

components of a system will use as common zero voltage. Therefore the function of the 

ground is for safety, and the common is for voltage reference. Sometimes the common and 

ground are connected. 

The most important reason for grounding is human safety. Electrical current running 

through the human body can have devastating effects, especially near the heart. Figure 

31.7 shows some of the different current levels, and the probable physiological effects. 

The current is dependant upon the resistance of the body, and the contacts. A typical scenario 

is, a hand touches a high voltage source, and current travels through the body and 

out a foot to ground. If the person is wearing rubber gloves and boots, the resistance is 

high and very little current will flow. But, if the person has a sweaty hand (salty water is a 

good conductor), and is standing barefoot in a pool of water their resistance will be much 

lower. The voltages in the table are suggested as reasonable for a healthy adult in normal 

circumstances. But, during design, you should assume that no voltage is safe. 

current in body (mA) 

0-1 

1-5 

10-20 

20-50 

50-100 

100-300 

300+ 

effect 

negligible (normal circumstances, 5VDC) 

uncomfortable (normal circumstances, 24VDC) 

possibility for harm (normal circumstances, 120VAC) 

muscles contract (normal circumstances, 220VAC) 

pain, fainting, physical injuries 

heart fibrillates 

burns, breathing stops, etc. 

Figure 31.7 

Current Levels 



Aside: Step potential is another problem. Electron waves from a fault travel out in a radial 

direction through the ground. If a worker has two feet on the ground at different radial 

distances, there will be a potential difference between the feet that will cause a current 

to flow through the legs. The gist of this is - if there is a fault, don’t run/walk away/ 

towards. 

Figure 31.8 shows a grounded system with a metal enclosures. The left-hand 

enclosure contains a transformer, and the enclosure is connected directly to ground. The 

wires enter and exit the enclosure through insulated strain reliefs so that they don’t contact 

the enclosure. The second enclosure contains a load, and is connected in a similar manner 

to the first enclosure. In the event of a major fault, one of the "live" electrical conductors 

may come loose and touch the metal enclosure. If the enclosure were not grounded, anybody 

touching the enclosure would receive an electrical shock. When the enclosure is 

grounded, the path of resistance between the case and the ground would be very small 

(about 1 ohm). But, the resistance of the path through the body would be much higher 

(thousands of ohms or more). So if there were a fault, the current flow through the ground 

might "blow" a fuse. If a worker were touching the case their resistance would be so low 

that they might not even notice the fault. 

wire break off 

and touches case 

Current can flow two ways, but most will follow the path of least 

resistance, good grounding will keep the worker relatively safe 

in the case of faults. 

Figure 31.8 

Grounding for Safety 



Note: Always ground systems first before applying power. The first time a system is 

activated it will have a higher chance of failure. 

When improperly grounded a system can behave erratically or be destroyed. 

Ground loops are caused when too many separate connections to ground are made creating 

loops of wire. Figure 31.9 shows ground wires as darker lines. A ground loop caused 

because an extra ground was connected between device A and ground. The last connection 

creates a loop. If a current is induced, the loop may have different voltages at different 

points. The connection on the right is preferred, using a tree configuration. The grounds 

for devices A and B are connected back to the power supply, and then to the ground. 

extra ground 

creates a loop 

Preferred 

device A 

device A 

device B 

device B 

+V -V 

power 

supply 

gnd 

ground loop 

+V 

gnd 

-V 

power 

supply 

Figure 31.9 

Eliminating Ground Loops 

Problems often occur in large facilities because they may have multiple ground 

points at different end of large buildings, or in different buildings. This can cause current 

to flow through the ground wires. As the current flows it will create different voltages at 

different points along the wire. This problem can be eliminated by using electrical isolation 

systems, such as optocouplers. 



When designing and building electrical control systems, the following points 

should prove useful. 

• Avoid ground loops 

- Connect the enclosure to the ground bus. 

- Each PLC component should be grounded back to the main PLC chassis. 

The PLC chassis should be grounded to the backplate. 

- The ground wire should be separated from power wiring inside enclosures. 

- Connect the machine ground to the enclosure ground. 

• Ensure good electrical connection 

- Use star washers to ensure good electrical connection. 

- Mount ground wires on bare metal, remove paint if needed. 

- Use 12AWG stranded copper for PLC equipment grounds and 8AWG 

stranded copper for enclosure backplate grounds. 

- The ground connection should have little resistance (


31.2.4 Suppressors 

Most of us have seen a Vandegraaf generator, or some other inductive device that 

can generate large sparks using inductive coils. On the factory floor there are some massive 

inductive loads that make this a significant design problem. This includes devices 

such as large motors and inductive furnaces. The root of the problem is that coils of wire 

act as inductors and when current is applied they build up magnetic fields, requiring 

energy. When the applied voltage is removed and the fields collapse the energy is dumped 

back out into the electrical system. As a result, when an inductive load is turned on it 

draws an excess amount of current (and lights dim), and when it is turn it off there is a 

power surge. In practical terms this means that large inductive loads will create voltage 

spikes that will damage our equipment. 

Surge suppressors can be used to protect equipment from voltage spikes caused by 

inductive loads. Figure 31.11 shows the schematic equivalent of an uncompensated inductive 

load. For this to work reliably we would need to over design the system above the 

rated loads. The second schematic shows a technique for compensating for an AC inductive 

load using a resistor capacitor pair. It effectively acts as a high pass filter that allows a 

high frequency voltage spike to be short circuited. The final surge suppressor is common 

for DC loads. The diode allows current to flow from the negative to the positive. If a negative 

voltage spike is encountered it will short circuit through the diode. 



output 

common 

Control Relay (PLC) 

inductive load 

VDC+/VAC 

VDC-/COM. 

Power supply 

Uncompensated 

output 

common 

Relay or Triac 


L 

C R Vs 

- 

VAC 

COM. 

Power supply 

R = Vs*(.5 to 1) ohms 

C = (.5 to 1)/Adc (microfarads) 

Vcapacitor = 2(Vswitching) + (200 to 300) V 

where, 

Adc is the rated amperage of the load 

Vs is the voltage of the load/power supply 

Vswitching may be up to 10*Vs 

+ 

Compensating 

for AC loads 

output 


+ 

Compensating 

for DC loads 

common 

Relay or Transistor 

- 

Power supply 

Figure 31.11 

Surge Suppressors 

31.2.5 PLC Enclosures 

PLCs are well built and rugged, but they are still relatively easy to damage on the 

factory floor. As a result, enclosures are often used to protect them from the local environment. 

Some of the most important factors are listed below with short explanations. 



Dirt - Dust and grime can enter the PLC through air ventilation ducts. As dirt clogs 

internal circuitry, and external circuitry, it can effect operation. A storage cabinet 

such as Nema 4 or 12 can help protect the PLC. 

Humidity - Humidity is not a problem with many modern materials. But, if the 

humidity condenses, the water can cause corrosion, conduct current, etc. Condensation 

should be avoided at all costs. 

Temperature - The semiconductor chips in the PLC have operating ranges where 

they are operational. As the temperature is moved out of this range, they will 

not operate properly, and the PLC will shut down. Ambient heat generated in 

the PLC will help keep the PLC operational at lower temperatures (generally to 

0°C). The upper range for the devices is about 60°C, which is generally sufficient 

for sealed cabinets, but warm temperatures, or other heat sources (e.g. 

direct irradiation from the sun) can raise the temperature above acceptable limits. 

In extreme conditions heating, or cooling units may be required. (This 

includes “cold-starts” for PLCs before their semiconductors heat up). 

Shock and Vibration - The nature of most industrial equipment is to apply energy 

to change workpieces. As this energy is applied, shocks and vibrations are often 

produced. Both will travel through solid materials with ease. While PLCs are 

designed to withstand a great deal of shock and vibration, special elastomer/ 

spring or other mounting equipment may be required. Also note that careful 

consideration of vibration is also required when wiring. 

Interference - Electromagnetic fields from other sources can induce currents. 

Power - Power will fluctuate in the factory as large equipment is turned on and off. 

To avoid this, various options are available. Use an isolation transformer. A 

UPS (Uninterruptable Power Supply) is also becoming an inexpensive option, 

and are widely available for personal computers. 

A standard set of enclosures was developed by NEMA (National Electric Manufacturers 

Association). These enclosures are intended for voltage ratings below 1000Vac. 

Figure 31.12 shows some of the rated cabinets. Type 12 enclosures are a common choice 

for factory floor applications. 



Type 1 - General purpose - indoors 

Type 2 - Dirt and water resistant - indoors 

Type 3 - Dust-tight, rain-tight and sleet (ice) resistant - outdoors 

Type 3R- Rainproof and sleet (ice) resistant - outdoors 

Type 3S- Rainproof and sleet (ice) resistant - outdoors 

Type 4 - Water-tight and dust-tight - indoors and outdoors 

Type 4X - Water-tight and Dust-tight - indoors and outdoors 

Type 5 - Dust-tight and dirt resistant - indoors 

Type 6 - Waterproof - indoors and outdoors 

Type 6P - Waterproof submersible - indoors and outdoors 

Type 7 - Hazardous locations - class I 

Type 8 - Hazardous locations - class I 

Type 9 - Hazardous locations - class II 

Type 10 - Hazardous locations - class II 

Type 11 - Gas-tight, water-tight, oiltight - indoors 

Type 12 - Dust-tight and drip-tight - indoors 

Type 13 - Oil-tight and dust-tight - indoors 

Factor 

1 

2 

3 

3R 

3S 

4 

4X 

5 

6 

6P 

11 

12 

12K13 

Prevent human contact 

falling dirt 

liquid drop/light splash 

airborne dust/particles 

wind blown dust 

liquid heavy stream/splash 

oil/coolant seepage 

oil/coolant spray/splash 

corrosive environment 

temporarily submerged 

prolonged submersion 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

x 

Figure 31.12 

NEMA Enclosures 

31.2.6 Wire and Cable Grouping 

In a controls cabinet the conductors are passed through channels or bundled. When 

dissimilar conductors are run side-by-side problems can arise. The basic categories of conductors 

are shown in Figure 31.13. In general category 1 conductors should not be 

grouped with other conductor categories. Care should be used when running category 2 

and 3 conductors together. 



more sensitive 

category 1 

AC power lines 

high power AC/DC IO 

category 2 

analog IO signals 

low power AC/DC IO 

remote communications 

category 3 

low voltage dc power 

local communications 

NO (Normally open) - When wiring switches or sensors that start actions, use normore 

noisy 

Figure 31.13 

Wire and Cable Categories 

• Types of wire pathways - channels - raceways/trays - conduit 

• Conductor types enter and exit the controls cabinet separately 

angles 

• When conductors mst be near incompatible types, they should cross at right 

• 

31.3 FAIL-SAFE DESIGN 

All systems will fail eventually. A fail-safe design will minimize the damage to 

people and equipment. Consider the selection electrical connections. If wires are cut or 

connections fail, the equipment should still be safe. For example, if a normally closed stop 

button is used, and the connector is broken, it will cause the machine to stop as if the stop 

button has been pressed. 



mally open switches so that if there is a problem the process will not start. 

NC (Normally Closed) - When wiring switches that stop processes use normally 

closed so that if they fail the process will stop. E-Stops must always be NC, and 

they must cut off the master power, not just be another input to the PLC. 

Hardware 

• Use redundancy in hardware. 

• Directly connect emergency stops to the PLC, or the main power supply. 

• Use well controlled startup procedures that check for problems. 

• Shutdown buttons must be easily accessible from all points around the 

machine. 

31.4 SAFETY RULES SUMMARY 

A set of safety rules was developed by Jim Rowell (http://www.mrplc.com, 

"Industrial Control Safety; or How to Scare the Bejesus Out of Me"). These are summarized 

below. 

Grounding and Fuses 

• Always ground power supplies and transformers. 

• Ground all metal enclosures, casings, etc. 

• All ground connections should be made with dedicated wires that are 

exposed so that their presence is obvious. 

• Use fuses for all AC power lines, but not on the neutrals or grounds. 

• If ground fault interrupts are used they should respond faster than the control 

system. 

Hot vs. Neutral Wiring 

• Use PNP wiring schemes for systems, especially for inputs that can initiate 

actions. 

• Loads should be wired so that the ground/neutral is always connected, 

and the power is switched. 

• Sourcing and sinking are often confused, so check the diagrams or look 

for PNP/NPN markings. 

AC / DC 

• Use lower voltages when possible, preferably below 50V. 

• For distant switches and sensors use DC. 

Devices 

• Use properly rated isolation transformers and power supplies for control 

systems. Beware autotransformers. 

• Use Positive or Force-Guided Relays and contacts can fail safely and prevent 

operation in the event of a failure. 

• Some ’relay replacement’ devices do not adequately isolate the inputs and 

output and should not be used in safety critical applications. 

Starts 



• Use NO buttons and wiring for inputs that start processes. 

• Select palm-buttons, and other startup hardware carefully to ensure that 

they are safety rated and will ensure that an operator is clear of the 

machine. 

• When two-hand start buttons are used, use both the NO and NC outputs 

for each button. The ladder logic can then watch both for a completed 

actuation. 

Stops 

• E-stop buttons should completely halt all parts of a machine that are not 

needed for safety. 

• E-stops should be hard-wired to kill power to electrically actuated systems. 

• Use many red mushroom head E-stop buttons that are easy to reach. 

• Use red non-mushroom head buttons for regular stops. 

• A restart sequence should be required after a stop button is released. 

• E-stop buttons should release pressure in machines to allow easy 

’escape’. 

• An ’extraction procedure’ should be developed so that trapped workers 

can be freed. 

• If there are any power storage devices (such as a capacitor bank) make 

sure they are disabled by the E-stops. 

• Use NC buttons and wiring for inputs that stop processes. 

• Use guards that prevent operation when unsafe, such as door open detection. 

• If the failure of a stop input could cause a catastrophic failure, add a 

backup. 

Construction 

• Wire so that the power enters at the top of a device. 

• Take special care to review regulations when working with machines that 

are like presses or brakes. 

• Check breaker ratings for overload cases and supplemental protection. 

• A power disconnect should be located on or in a control cabinet. 

• Wires should be grouped by the power/voltage ratings. Run separate conduits 

or raceways for different voltages. 

• Wire insulation should be rated for the highest voltage in the cabinet. 

• Use colored lights to indicate operational states. Green indicates in operation 

safely, red indicates problems. 

• Construct cabinets to avoid contamination from materials such as oils. 

• Conduits should be sealed with removable compounds if they lead to 

spaces at different temperatures and humidity levels. 

• Position terminal strips and other components above 18" for ergonomic 

reasons. 

• Cabinets should be protected with suitably rated fuses. 

• Finger sized objects should not be able to reach any live voltages in a finished 

cabinet, however DMM probes should be able to measure voltages. 




31.6 SUMMARY 

• Electrical schematics used to layout and wire controls cabinets. 

• JIC wiring symbols can be used to describe electrical components. 

• Grounding and shielding can keep a system safe and running reliably. 

• Failsafe designs ensure that a controller will cause minimal damage in the event 

of a failure. 

• PLC enclosure are selected to protect a PLC from its environment. 


1. What steps are required to replace a defective PLC? 


1. in a rack the defective card is removed and replaced. If the card has wiring terminals these are 

removed first, and connected to the replacement card. 


1. Where is the best location for a PLC enclosure? 

2. What is a typical temperature and humidity range for a PLC? 

3. Draw the electrical schematic and panel layout for the relay logic below. The system will be 

connected to 3 phase power. Be sure to include a master power disconnect. 

A 

C 

B 

B 



4. Why are nodes and wires labelled on a schematic, and in the controls cabinet? 

5. Locate at least 10 JIC symbols for the sensors and actuators in earlier chapters. 

6. How are shielding and grounding alike? Are shields and grounds connected? 

7. What are significant grounding problems? 

8. Why should grounds be connected in a tree configuration? 


plc software - 32.1 

32. SOFTWARE ENGINEERING 

Topics: 

• Electrical wiring issues; cabinet wiring and layout, grounding, shielding and 

inductive loads 

• Controller design; failsafe, debugging, troubleshooting, forcing 

• Process modelling with the ANSI/ISA-S5.1-1984 standard 

• Programming large systems 

• Documentation 

Objectives: 

• To learn the major issues in program design. 

• Be able to document a process with a process diagram. 

• Be able to document a design project. 

• Be able to develop a project strategy for large programs. 


A careful, structured approach to designing software will cut the total development 

time, and result in a more reliable system. 

32.1.1 Fail Safe Design 

It is necessary to predict how systems will fail. Some of the common problems that 

will occur are listed below. 

Component jams - An actuator or part becomes jammed. This can be detected by 

adding sensors for actuator positions and part presence. 

Operator detected failure - Some unexpected failures will be detected by the operator. 

In those cases the operator must be able to shut down the machine easily. 

Erroneous input - An input could be triggered unintentionally. This could include 

something falling against a start button. 

Unsafe modes - Some systems need to be entered by the operators or maintenance 

crew. People detectors can be used to prevent operation while people are 

present. 

Programming errors - A large program that is poorly written can behave erratically 

when an unanticipated input is encountered. This is also a problem with 

assumed startup conditions. 



Sabotage - For various reasons, some individuals may try to damage a system. 

These problems can be minimized preventing access. 

Random failure - Each component is prone to random failure. It is worth considering 

what would happen if any of these components were to fail. 

Some design rules that will help improve the safety of a system are listed below. 

Programs 

• A fail-safe design - Programs should be designed so that they check for 

problems, and shut down in safe ways. Most PLC’s also have imminent 

power failure sensors, use these whenever danger is present to shut down 

the system safely. 

• Proper programming techniques and modular programming will help 

detect possible problems on paper instead of in operation. 

• Modular well designed programs. 

• Use predictable, non-configured programs. 

• Make the program inaccessible to unauthorized persons. 

• Check for system OK at start-up. 

• Use PLC built in functions for error and failure detection. 

People 

• Provide clear and current documentation for maintenance and operators. 

• Provide training for new users and engineers to reduce careless and uninformed 

mistakes. 

32.2 DEBUGGING 

Most engineers have taken a programming course where they learned to write a 

program and then debug it. Debugging involves running the program, testing it for errors, 

and then fixing them. Even for an experienced programmer it is common to spend more 

time debugging than writing software. For PLCs this is not acceptable! If you are running 

the program and it is operating irrationally it will often damage hardware. Also, if the 

error is not obvious, you should go back and reexamine the program design. When a program 

is debugged by trial and error, there are probably errors remaining in the logic, and 

the program is very hard to trust. Remember, a bug in a PLC program might kill somebody. 

Note: when running a program for the first time it can be a good idea to keep one hand 

on the E-stop button. 



32.2.1 Troubleshooting 

After a system is in operation it will eventually fail. When a failure occurs it is 

important to be able to identify and solve problems quickly. The following list of steps 

will help track down errors in a PLC system. 

1. Look at the process and see if it is in a normal state. i.e. no jammed actuators, 

broken parts, etc. If there are visible problems, fix them and restart the process. 

2. Look at the PLC to see which error lights are on. Each PLC vendor will provide 

documents that indicate which problems correspond to the error lights. Common 

error lights are given below. If any off the warning lights are on, look for 

electrical supply problems to the PLC. 

HALT - something has stopped the CPU 

RUN - the PLC thinks it is OK (and probably is) 

ERROR - a physical problem has occurred with the PLC 

3. Check indicator lights on I/O cards, see if they match the system. i.e., look at 

sensors that are on/off, and actuators on/off, check to see that the lights on the 

PLC I/O cards agree. If any of the light disagree with the physical reality, then 

interface electronics/mechanics need inspection. 

4. Consult the manuals, or use software if available. If no obvious problems exist 

the problem is not simple, and requires a technically skilled approach. 

5. If all else fails call the vendor (or the contractor) for help. 

32.2.2 Forcing 

Most PLCs will allow a user to force inputs and outputs. This means that they can 

be turned on, regardless of the physical inputs and program results. This can be convenient 

for debugging programs, and, it makes it easy to break and destroy things! When forces 

are used they can make the program perform erratically. They can also make outputs occur 

out of sequence. If there is a logic problem, then these don’t help a programmer identify 

these problems. 

Many companies will require extensive paperwork and permissions before forces 

can be used. I don’t recommend forcing inputs or outputs, except in the most extreme circumstances. 

32.3 PROCESS MODELLING 

There are many process modeling techniques, but only a few are suited to process 

control. The ANSI/ISA-S5.1-1984 Piping and Instrumentation Diagram (P&ID) standard 



provides good tools for documenting processes. A simple example is shown in Figure 

32.1. 

control valve 

FV 

11 

Figure 32.1 

A Process Model 

The symbols used on the diagrams are shown in the figure below 

XXXXXXXXXXXXX. Note that the modifier used for the instruments can be applied to 

other discrete devices. 



Discrete Device Symbols 

Instruments 

field mounted 

panel mounted 

unaccessible or embedded 

auxilliary location, operator accessible 

Controls 

Computer Function 

PLC 

Shared Display/Control 

Figure 32.2 

Symbols for Functions and Instruments 

The process model is carefully labeled to indicate the function of each of the function 

on the diagram. Table 2 shows a list of the different instrumentation letter codes. 

XXXXXXXXXXXXXXXXXXXXX 

Table 1: ANSI/ISA-S5.1-1984 Instrumentation Symbols and Identification 

LETTER FIRST LETTER SECOND LETTER 

A Analysis Alarm 

B Burner, Combustion User’s Choice 



Table 1: ANSI/ISA-S5.1-1984 Instrumentation Symbols and Identification 

LETTER FIRST LETTER SECOND LETTER 

C User’s Choice Control 

D 

User’s Choice 

E Voltage Sensor (Primary Element) 

F 

Flow Rate 

G User’s Choice Glass (Sight Tube) 

H 

Hand (Manually Initiated) 

I Current (Electric) Indicate 

J 

Power 

K Time or Time Schedule Control Station 

L Level Light (pilot) 

M 

User’s Choice 

N User’s Choice User’s Choice 

O User’s Choice Orifice, Restriction 

P Pressure, Vacuum Point (Test Connection) 

Q 

Quantity 

R Radiation Record or Print 

S Speed or Frequency Switch 

T Temperature Transmit 

U Multivariable Multifunction 

V Vibration, Mechanical Analysis Valve, Damper, Louver 

W Weight, Force Well 

X Unclassified Unclassified 

Y Event, State or Presence Relay, Compute 

Z Position, Dimension Driver, Actuator, Unclassified 

The line symbols also describe the type of flow. Figure 32.3 shows a few of the 

popular flow lines. 



Connection to process 

Instrument Supply 

Hydraulic 

Pneumatic 

Capillary Tube 

Electric Signal 

EM, Sonic, Radioactive 

Mechanical Connection 

Software Connection 

Figure 32.3 

Flow Line Symbols and Types 

Figure 32.4 shows some of the more popular sensor and actuator symbols. 



orifice plate 

magnetic 

control valve 

(pneumatic activated) 

rotameter 

venturi or nozzle 

Figure 32.4 

Sensor and Actuator Symbols and Types 

32.4 PROGRAMMING FOR LARGE SYSTEMS 

Previous chapters have explored design techniques to solve large problems using 

techniques such as state diagrams and SFCs. Large systems may contain hundreds of those 

types of problems. This section will attempt to lay a philosophical approach that will help 

you approach these designs. The most important concepts are clarity and simplicity. 

32.4.1 Developing a Program Structure 

Understanding the process will simplify the controller design. When the system is 

only partially understood, or vaguely defined the development process becomes iterative. 

Programs will be developed, and modified until they are acceptable. When information 

and events are clearly understood the program design will become obvious. Questions that 

can help clarify the system include; 

"What are the inputs?" 

"What are the outputs?" 

"What are the sequences of inputs and outputs?" 

"Can a diagram of the system operation be drawn?" 



"What information does the system need?" 

"What information does the system produce?" 

When possible a large controls problems should be broken down into smaller problems. 

This often happens when parts of the system operate independent of each other. This 

may also happen when operations occur in a fixed sequence. If this is the case the controls 

problem can be divided into the two smaller (and simpler) portions. The questions to ask 

are; 

"Will these operations ever occur at the same time?" 

"Will this operation happen regardless of other operations?" 

"Is there a clear sequence of operations?" 

"Is there a physical division in the process or machine?" 

After examining the system the controller should be broken into operations. This 

can be done with a tree structure as shown in Figure 32.5. This breaks control into smaller 

tasks that need to be executed. This technique is only used to divide the programming 

tasks into smaller sections that are distinct. 

Press 

Conveyor in Press Pickup bin 

part detected 

advance 

bin replaced 

full detect 

adv./retract 

idle 

part detect 

advancing 

retracting 

Figure 32.5 

Functional Diagram for Press Control 



Each block in the functional diagram can be written as a separate subroutine. A 

higher level executive program will call these subroutines as needed. The executive program 

can also be broken into smaller parts. This keeps the main program more compact, 

and reduces the overall execution time. And, because the subroutines only run when they 

should, the change of unexpected operation is reduced. This is the method promoted by 

methods such as SFCs and FBDs. 

Each functional program should be given its’ own block of memory so that there 

are no conflicts with shared memory. System wide data or status information can be kept 

in common areas. Typical examples include a flag to indicate a certain product type, or a 

recipe oriented system. 

Testing should be considered during software planning and writing. The best scenario 

is that the software is written in small pieces, and then each piece is tested. This is 

important in a large system. When a system is written as a single large piece of code, it 

becomes much more difficult to identify the source of errors. 

The most disregarded statement involves documentation. All documentation 

should be written when the software is written. If the documentation can be written first, 

the software is usually more reliable and easier to write. Comments should be entered 

when ladder logic is entered. This often helps to clarify thoughts and expose careless 

errors. Documentation is essential on large projects where others are likely to maintain the 

system. Even if you maintain it, you are likely to forget what your original design intention 

was. 

below. 

Some of the common pitfalls encountered by designers on large projects are listed 

• Amateur designers rush through design to start work early, but details they 

missed take much longer to fix when they are half way implemented. 

• Details are not planned out and the project becomes one huge complex task 

instead of groups of small simple tasks. 

• Designers write one huge program, instead of smaller programs. This makes 

proof reading much harder, and not very enjoyable. 

• Programmers sit at the keyboard and debug by trial and error. If a programmer is 

testing a program and an error occurs, there are two possible scenarios. First, 

the programmer knows what the problem is, and can fix it immediately. Second, 

the programmer only has a vague idea, and often makes no progress doing trialand-error 

debugging. If trial-and-error programming is going on the program is 

not understood, and it should be fixed through replanning. 

• Small details are left to be completed later. These are sometimes left undone, and 

lead to failures in operation. 

• The design is not frozen, and small refinements and add-ons take significant 



amounts of time, and often lead to major design changes. 

• The designers use unprofessional approaches. They tend to follow poor designs, 

against the advice of their colleagues. This is often because the design is their 

child 

• Designers get a good dose of the not invented here syndrome. Basically, if we 

didn’t develop it, it must not be any good. 

• Limited knowledge will cause problems. The saying goes “If the only tool you 

know how to use is a hammer every problem looks like a nail.” 

• Biting off more than you can chew. some projects are overly ambitious. Avoid 

adding wild extras, and just meet the needs of the project. Sometimes an unnecessary 

extra can take more time than the rest of the project. 

32.4.2 Program Verification and Simulation 

After a program has been written it is important to verify that it works as intended, 

before it is used in production. In a simple application this might involve running the program 

on the machine, and looking for improper operation. In a complex application this 

approach is not suitable. A good approach to software development involves the following 

steps in approximate order: 

1. Structured design - design and write the software to meet a clear set of objectives. 

2. Modular testing - small segments of the program can be written, and then tested 

individually. It is much easier to debug and verify the operation of a small program. 

3. Code review - review the code modules for compliance to the design. This 

should be done by others, but at least you should review your own code. 

4. Modular building - the software modules can then be added one at a time, and 

the system tested again. Any problems that arise can then be attributed to interactions 

with the new module. 

5. Design confirmation - verify that the system works as the design requires. 

6. Error proofing - the system can be tested by trying expected and unexpected 

failures. When doing this testing, irrational things should also be considered. 

This might include unplugging sensors, jamming actuators, operator errors, etc. 

7. Burn-in - a test that last a long period of time. Some errors won’t appear until a 

machine has run for a few thousand cycles, or over a period of days. 

Program testing can be done on machines, but this is not always possible or desireable. 

In these cases simulators allow the programs to be tested without the actual machine. 

The use of a simulator typically follows the basic steps below. 

1. The machine inputs and outputs are identified. 



2. A basic model of the system is developed in terms of the inputs and outputs. 

This might include items such as when sensor changes are expected, what 

effects actuators should have, and expected operator inputs. 

3. A system simulator is constructed with some combination of specialized software 

and hardware. 

4. The system is verified for the expect operation of the system. 

5. The system is then used for testing software and verifying the operation. 

A detailed description of simulator usage is available [Kinner, 1992]. 

32.5 DOCUMENTATION 

Poor documentation is a common complaint lodged against control system designers. 

Good documentation is developed as a project progresses. Many engineers will leave 

the documentation to the end of a project as an afterthought. But, by that point many of the 

details have been forgotten. So, it takes longer to recall the details of the work, and the 

report is always lacking. 

A set of PLC design forms are given in Figure 32.6 to Figure 32.12. These can be 

used before, during and after a controls project. These forms can then be kept in design or 

maintenance offices so that others can get easy access and make updates at the controller 

is changed. Figure 32.6 shows a design cover page. This should be completed with information 

such as a unique project name, contact person, and controller type. The list of 

changes below help to track design, redesign and maintenance that has been done to the 

machine. This cover sheet acts as a quick overview on the history of the machine. Figure 

32.7 to Figure 32.9 show sheets that allow free form planning of the design. Figure 32.10 

shows a sheet for planning the input and output memory locations. Figure 32.11 shows a 

sheet for planning internal memory locations, and finally Figure 32.12 shows a sheet for 

planning the ladder logic. The sheets should be used in the order they are given, but they 

do not all need to be used. When the system has been built and tested, a copy of the working 

ladder logic should be attached to the end of the bundle of pages. 



PLC Project Sheet 

Project ID: 

Start Date: 

Contact Person: 

PLC Model: 

Attached Materials/Revisions: 

Date Name # Sheets Reason 

Figure 32.6 

Design Cover Page 



Project Notes 

Project ID: 

System Description 

I/O Notes 

Power Notes 

Other Notes 

Date: 

Page 

Name: 

of 

Figure 32.7 

Project Note Page 



Design Notes 

Project ID: 

Date: 

State Diagram 

Flow Chart 

Sequential Function Chart 

Boolean Equations 

Truth Table 

Safety 

Communications 

Other Notes 

Page 

Name: 

of 

Figure 32.8 

Project Diagramming Page 



Application Notes 

Project ID: 

Test Plan 

Electrical I/O 

PLC Modules 

Other Notes 

Date: 

Page 

Name: 

of 

Figure 32.9 

Project Diagramming and Notes Page 



Input/Output Card 

Page 

of 

Project I.D. Name Date 

Card Type Rack # Slot # 

Notes: 

input/output JIC symbol Description 

Vin 

00 

01 

02 

03 

04 

05 

06 

07 

08/10 

09/11 

10/12 

11/13 

12/14 

13/15 

14/16 

15/17 

com 

Figure 32.10 

IO Planning Page 



Internal Locations Page of 

Project I.D. Name Date 

Register or Word 

Internal Word 

Description 

Figure 32.11 

Internal Memory Locations Page 



Program Listing 

Page 

of 

Project I.D. 

rung# 

Name 

Date 

comments 

Figure 32.12 

Ladder Logic Page 



These design sheets are provided as examples. PLC vendors often supply similar 

sheets. Many companies also have their own internal design documentation procedures. If 

you are in a company without standardized design formats, you should consider implementing 

such a system. 

32.6 COMMISIONING 

When a new machine is being prepared for production, or has been delivered by a 

supplier, it is normal to go through a set of commissioning procedures. Some typical steps 

are listed below. 

1. Visual inspection 

• verify that the machine meets internal and external safety codes 

- electrical codes 

- worker safety codes (e.g., OSHA) 

• determine if all components are present 

2. Mechanical installation 

• physically located the machine 

• connect to adjacent machines 

• connect water, air and other required services 

3. Electrical installation 

• connect grounds and power 

• high potential and ground fault tests 

• verify sensor inputs to the PLC 

4. Functional tests 

• start the machine and test the emergency stops 

• test for basic functionality 

5. Process verification 

• run the machine and make adjustments to produce product 

• collect process capability data 

• determine required maintenance procedures 

6. Contract/specification verification 

• review the contact requirements and check off individually on each one 

• review the specification requirements and check off each one individually 

• request that any non-compliant requirements are corrected 

7. Put into production 

• start the process in the production environment and begin normal use 

32.7 SAFETY 

- 



32.7.1 IEC 61508/61511 safety standards 

REF: McCrea-Steele, R., "Proven-in-Use: Making the right choices for process 

safety", Hotlinks, Invensys, Summer 2003. 

REF: Eberhard, A, "Safety in Programmable Applications", Automation World, 

Nov., 2004. 

- these standards cover electrical, electronic, and programmable electronic systems. 

- three categories of software languages covered by the standard 

- FPL (Fixed Programming Language) - a very limited approach to programming. 

For example the system is programmed by setting parameters. 

- LVL (Limited Variability Language) - a language with a strict programming 

model, such as ladder logic. 

- FVL (Full Variability Language) - a language that gives full access to a 

systems, such as C. 

- Safety Integrity Level (SIL) - the safety requirements for a function in a system 

Low demand: 

level 4: P = 10^-4 to 10^-5 

level 3: P = 10^-3 to 10^-4 

level 2: P = 10^-2 to 10^-3 

level 1: P = 10^-1 to 10^-2 

High Demand or continuous mode: 

level 4: P = 10^-8 to 10^-9 

level 3: P = 10^-7 to 10^-8 

level 2: P = 10^-6 to 10^-7 

level 1: P = 10^-5 to 10^-6 

- System safety levels are defined as, 

SIF (Safety Instrumented Function) - The SIL for each function is chosen 

to ensure an overall system functionality. 

SIS (Safety Instrumented System) - A combined system with one or more 

logic processors. 

SFF (Safe Failure Fraction) - the ratio of safe and dangerous detected failwww.PAControl.com


ures to the total failures. 

- To calculate the SFF 

- do an FMEA for each system component in the system 

- classify failure modes as safe or dangerous 

- calculate the probabilities of safe/dangerous failures (S/D [0, 1]) 

- estimate the fraction of the failures that can be detected (F [0, 1]) 

- SFF = .... 

- 

32.8 LEAN MANUFACTURING 

- lean manufacturing has received attention lately, but it embodies many common 

sense machine design concepts. 

- In simple terms lean manufacturing involves eliminating waste from a system. 

- Some general concepts to use when designing lean machines include, 

- setups should be minimized or eliminated 

- product changeovers should be minimized or eliminated 

- make the tool fit the job, not the other way. If necessary, design a new tool 

- design the machine be faster than the needed cycle time to allow flexibility 

and excess capacity - this does seem contradictory, but it allows better 

use of other resources. For example, if a worker takes a bathroom break, 

the production can continue with fewer workers. 

- allow batches with a minimum capacity of one. 

- people are part of the process and should integrate smoothly - the motions 

or workers are often described as dance like. 

- eliminate wasted steps, all should go into making the part 

- work should flow smoothly to avoid wasted motion 

- do not waste motion by spacing out machines 

- make-one, check-one 

- design "decouplers" to allow operations to happen independantly. 

- eliminate material waste that does not go into the product 

- pull work through the cell 



- design the product so that it is easy to manufacture 

- use methods that are obvious, so that anybody can understand - this 

makes workers portable and able to easily cover for others. 

- use poke-yoke 

- design tools to reduce the needs for guards. 


Kenner, R. H., “The Use of Simulation Within a PLC to Improve Program Development and Testing”, 

Proceedings of the First Automation Fair, Philadelphia, 1990. 

Paques, Joseph-Jean, “Basic Safety Rules for Using Programmable Controllers”, ISA Transactions, 

Vol. 29, No. 2, 1990. 

32.10 SUMMARY 

• Debugging and forcing are signs of a poorly written program. 

• Process models can be used to completely describe a process. 

• When programming large systems, it is important to subdivide the project into 

smaller parts. 

• Documentation should be done at all phases of the project. 


1. List 5 advantages of using structured design and documentation techniques. 


1. more reliable programs - less debugging time - more routine - others can pick up where you left 

off - reduces confusion 


1. What documentation is requires for a ladder logic based controller? Are comments important? 

Why? 



2. When should inputs and outputs be assigned when planning a control system? 

3. Discuss when I/O placement and wiring documentation should be updated? 

4. Should you use output forces? 

5. Find web addresses for 10 PLC vendors. Investigate their web sites to determine how they 

would be as suppliers. 


plc selection - 33.1 

33. SELECTING A PLC 

Topics: 

• The PLC selection process 

• Estimating program memory and time requirements 

• Selecting hardware 

Objectives: 

• Be able to select a hardware and software vendor. 

• Be able to size a PLC to an application 

• Be able to select needed hardware and software. 


After the planning phase of the design, the equipment can be ordered. This decision 

is usually based upon the required inputs, outputs and functions of the controller. The 

first decision is the type of controller; rack, mini, micro, or software based. This decision 

will depend upon the basic criteria listed below. 

• Number of logical inputs and outputs. 

• Memory - Often 1K and up. Need is dictated by size of ladder logic program. A 

ladder element will take only a few bytes, and will be specified in manufacturers 

documentation. 

• Number of special I/O modules - When doing some exotic applications, a large 

number of special add-on cards may be required. 

• Scan Time - Big programs or faster processes will require shorter scan times. 

And, the shorter the scan time, the higher the cost. Typical values for this are 1 

microsecond per simple ladder instruction 

• Communications - Serial and networked connections allow the PLC to be programmed 

and talk to other PLCs. The needs are determined by the application. 

• Software - Availability of programming software and other tools determines the 

programming and debugging ease. 

The process of selecting a PLC can be broken into the steps listed below. 

1. Understand the process to be controlled (Note: This is done using the design 

sheets in the previous chapter). 

• List the number and types of inputs and outputs. 

• Determine how the process is to be controlled. 



• Determine special needs such as distance between parts of the process. 

2. If not already specified, a single vendor should be selected. Factors that might 

be considered are, (Note: Vendor research may be needed here.) 

• Manuals and documentation 

• Support while developing programs 

• The range of products available 

• Support while troubleshooting 

• Shipping times for emergency replacements 

• Training 

• The track record for the company 

• Business practices (billing, upgrades/obsolete products, etc.) 

3. Plan the ladder logic for the controls. (Note: Use the standard design sheets.) 

4. Count the program instructions and enter the values into the sheets in Figure 

33.1 and Figure 33.2. Use the instruction times and memory requirements for 

each instruction to determine if the PLC has sufficient memory, and if the 

response time will be adequate for the process. Samples of scan times and 

memory are given in Figure 33.3 and Figure 33.4. 



PLC MEMORY TIME ESTIMATES - Part A 

Project ID: 

Name: 

Date: 

Instruction 

Type 

Time 

Max 

(us) 

Time 

Min. 

(us) 

Instruction 

Memory 

(words) 

Instruction 

Data 

(words) 

Instruction 

Count 

(number) 

Total 

Memory 

(words) 

Min. 

Time 

(us) 

Max. 

Time 

(us) 

contacts 

outputs 

timers 

counter 

Figure 33.1 

Memory and Time Tally Sheet 

Total 



PLC MEMORY TIME REQUIREMENTS - Part B 

Project ID: 

Name: 

Date: 

TIME 

Input Scan Time 

Output Scan Time 

Overhead Time 

Program Scan Time 

Communication Time 

Other Times 

TOTAL 

us 

us 

us 

us 

us 

us 

us 

MEMORY 

Total Memory 

Other Memory 

TOTAL 

words 

words 

words 

bytes 

Figure 33.2 

Memory and Timer Requirement Sheet 



Typical values for an Allen-Bradley micrologix controller are, 

input scan time 8us 

output scan times 8us 

housekeeping 180us 

overhead memory for controller 280 words 

Instruction 

Type 

Time 

Max 

(us) 

Time 

Min. 

(us) 

Instruction 

Memory 

(words) 

Instruction 

Data 

(words) 

CTD - count down 

CTU- count up 

XIC - normally open contact 

XIO - normally closed contact 

OSR - one shot relay 

OTE - output enable 

OTL - output latch 

OTU - output unlatch 

RES - reset 

RTO - retentive on time 

TOF - off timer 

TON - on timer 

27.22 

26.67 

1.72 

1.72 

11.48 

4.43 

3.16 

3.16 

4.25 

27.49 

31.65 

30.38 

32.19 

29.84 

1.54 

1.54 

13.02 

4.43 

4.97 

4.97 

15.19 

38.34 

39.42 

38.34 

1 

1 

.75 

.75 

1 

.75 

.75 

.75 

1 

1 

1 

1 

3 

3 

0 

0 

0 

0 

0 

0 

0 

3 

3 

3 

Figure 33.3 

Typical Instruction Times and Memory Usage for a Micrologix Controller 



Typical values for an Allen-Bradley PLC-5 controller are, 

input scan time ?us 

output scan times ?us 

housekeeping ?us 

overhead memory for controller ? words 

Instruction 

Type 

Time 

Max 

(us) 

Time 

Min. 

(us) 

Instruction 

Memory 

(words) 

Instruction 

Data 

(words) 

CTD - count down 

CTU- count up 

XIC - normally open contact 

XIO - normally closed contact 

OSR - one shot relay 

OTE - output enable 

OTL - output latch 

OTU - output unlatch 

RES - reset 

RTO - retentive on time 

TOF - off timer 

TON - on timer 

3.3 

3.4 

0.32 

0.32 

6.2 

0.48 

0.48 

0.48 

2.2 

4.1 

2.6 

4.1 

3.4 

3.4 

0.16 

0.16 

6.0 

0.48 

0.16 

0.16 

1.0 

2.4 

3.2 

2.6 

3 

3 

1 

1 

6 

1 

1 

1 

3 

3 

3 

3 

3 

3 

0 

0 

0 

0 

0 

0 

0 

3 

3 

3 

Figure 33.4 

Typical Instruction Times and Memory Usage for a PLC-5 Controller 

5. Look for special program needs and check the PLC model. (e.g. PID) 

6. Estimate the cost for suitable hardware, programming software, cables, manuals, 

training, etc., or ask for a quote from a vendor. 

33.2 SPECIAL I/O MODULES 

Many different special I/O modules are available. Some module types are listed 

below for illustration, but the commercial selection is very large. Generally most vendors 

offer competitive modules. Some modules, such as fuzzy logic and vision, are only 

offered by a few supplier, such as Omron. This may occasionally drive a decision to purchase 

a particular type of controller. 

PLC CPU’s 

• A wide variety of CPU’s are available, and can often be used interchangeably 

in the rack systems. the basic formula is price/performance. The 

table below compares a few CPU units in various criteria. 



FEATURE 

PLC 

Siemens Siemens Siemens 

S5-90U S5-100U S5-115U 

(CPU 944) 

Siemens 

CPU03 

AEG 

PC-A984-145 

RAM (KB) 

4 


ized programming units, but the software runs on a multi-use, 

user supplied computer. This approach is typically preferred. 

2. Hand held units (or integrated) - Allow programming of PLC 

using a calculator type interface. Often done using mnemonics. 

3. Specialized programming units - Effectively a portable computer 

that allows graphical editing of the ladder logic, and fast uploading/downloading/monitoring 

of the PLC. 

Ethernet/modem 

• For communication with remote computers. This is now an option on 

many CPUs. 

TTL input/outputs 

• When dealing with lower TTL voltages (0-5Vdc) most input cards will 

not recognize these. These cards allow switching of these voltages. 

Encoder counter module 

• Takes inputs from an encoder and tracks position. This allows encoder 

changes that are much faster than the PLC can scan. 

Human Machine Interface (HMI) 

• A-B/Siemens/Omron/Modicon/etc offer human interface systems. The 

user can use touch screens, screen and buttons, LCD/LED and a keypad. 

ASCII module 

• Adds an serial port for communicating with standard serial ports RS-232/ 

422. 

IBM PC computer cards 

• An IBM compatible computer card that plugs into a PLC bus, and allows 

use of common software. 

• For example, Siemens CP580 the Simatic AT; 

- serial ports: RS-232C, RS-422, TTY 

- RGB monitor driver (VGA) 

- keyboard and mouse interfaces 

- 3.5” disk 

Counters 

• Each card will have 1 to 16 counters at speeds up to 200KHz. 

• The counter can be set to zero, or up/down, or gating can occur with an 

external input. 

Thermocouple 

• Thermocouples can be used to measure temperature, but these low voltage 

devices require sensitive electronics to get accurate temperature 

readings. 

Analog Input/Output 

• These cards measure voltages in various ranges, and allow monitoring of 

continuous processes. These cards can also output analog voltages to 

help control external processes, etc. 

PID modules 

• There are 2 types of PID modules. In the first the CPU does the calculation, 

in the second, a second controller card does the calculation. 

- when the CPU does the calculation the PID loop is slower. 



- when a specialized card controls the PID loop, it is faster, but it 

costs less. 

• Typical applications - positioning workpieces. 

Stepper motor 

• Allows control of a stepper motor from a PLC rack. 

Servo control module 

• Has an encoder and amplifier pair built in to the card. 

Diagnostic Modules 

• Plug in and they monitor the CPU status. 

Specialty cards for IBM PC interface 

• Siemens/Allen-Bradley/etc. have cards that fit into IBM buses, and will 

communicate with PLC’s. 

Communications 

• This allows communications or networks protocols in addition to what is 

available on the PLC. This includes DH+, etc. 

Thumb Wheel Module 

• Numbers can be dialed in on wheels with digits from 0 to 9. 

BCD input/output module 

• Allows numbers to be output/input in BCD. 

BASIC module 

• Allows the user to write programs in the BASIC programming language. 

Short distance RF transmitters 

• e.g., Omron V600/V620 ID system 

• ID Tags - Special “tags” can be attached to products, and as they pass 

within range of pickup sensors, they transmit an ID number, or a packet 

of data. This data can then be used, updated, and rewritten to the tags by 

the PLC. Messages are stored as ASCII text. 

Voice Recognition/Speech 

• In some cases verbal I/O can be useful. Speech recognition methods are 

still very limited, the user must control their speech, and background 

noise causes problems. 

33.3 SUMMARY 

• Both suppliers and products should be evaluated. 

• A single supplier can be advantageous in simplifying maintenance. 

• The time and memory requirements for a program can be estimated using design 

work. 

• Special I/O modules can be selected to suit project needs. 






1. What is the most commonly used type of I/O interface? 

2. What is a large memory size for a PLC? 

3. What factors affect the selection of the size of a PLC. 


plc function ref - 34.1 

34. FUNCTION REFERENCE 

The function references that follow are meant to be an aid for programming. There 

are some notes that should be observed, especially because this list discusses instructions 

for more than one type of PLC. 

• The following function descriptions are for both the Micrologix and PLC-5 processor 

families. There are some differences between PLC models and families. 

- Floating point operations are not available on the micrologix. 

- Some instruction names, definition and terminologies have been changed 

from older to newer models. I attempt to point these out, or provide a 

general description that is true for all. 

- Details for specific instructions can be found in the manuals available at 

(http://www.ab.com) 

• Many flags in status memory can be used with functions, including; 

S2:0/0 carry in math operation 

S2:0/1 overflow in math operation 

S2:0/2 zero in math operation 

S2:0/3 sign in math operation 

34.1 FUNCTION DESCRIPTIONS 

34.1.1 General Functions 

AFI - Always False Instruction 

AFI 

Description: 

Status Bits: none 

Registers: none 

Available on: Micrologix, PLC-5 

Putting this instruction in a line will force the line to be false. This is primarily 

designed for debugging programs. 



IIN, IOT - Immediate INput, Immediate OuTput 

A 

IIN 

I:001 

B 

IOT 

O:002 

Description: 

These functions update a few inputs and outputs during a program scan, 

instead of the beginning and end. In this example the IIN function will 

update the input values on ’I:001’ if ’A’ is true. If ’B’ is true then the 

output values will be updated for ’O:002’. 




OTL, OTU - OutpuT Latch, OutpuT Unlatch 

A 

L 

X 

B 

U 

X 

Description: 

The OTL ’L’ will latch on an output or memory bit, and the ’OTL’ ’U’ will 

unlatch it. If a value has been changed with a latch its value will stay 

fixed even if the PLC has been restarted. 






XIC, XIO, OTE - eXamine If Closed, eXamine If Open, OuTput Enable 

A 

I:001/0 

B 

I:001/1 

Description: 




These are the three most basic and common instructions. The input ’A’ is a 

normally open contact (XIC), the input ’B’ is a normally closed contact 

(XIO). Both of the outputs are normally off (OTE). 

34.1.2 Program Control 

JMP, LBL - JuMP, LaBeL 

A 

Description: 

2 

LBL 




B 

JMP 

JUMP 

Label 2 

The JMP instruction will allow the PLC to bypass some ladder logic 

instructions. When ’A’ is true in this example the JMP will go to label 

’2’, after which the program scan will continue normally. If ’A’ is false 

the JMP will be ignored and program execution will continue normally. 

In either case, ’X’ will be equal to ’B’. 

X 



MCR - Master Control Relay 

A 

MCR 

Description: 




MCR 

MCR instructions need to be used in pairs. If the first MCR line is true the 

instructions up to the next MCR will be examined normally. If the first 

MCR line is not true the outputs on the lines after will be FORCED 

OFF. Be careful when using normal outputs in these blocks. 

ONS - ONe Shot 

A 

B3/10 

ONS 

X 

Description: 

This instruction will allow a line to be true for only one scan. If ’A’ 

becomes true then output of the ’ONS’ instruction will turn on for only 

one scan. ’A’ must be turned off for one scan before the ’ONS’ can be 

triggered again. The bit is used to track the previous input state, it is 

similar to an enabled bit. 






OSR, OSF - One Shot Rising, One Shot Falling 

A 

OSR 

ONE SHOT RISING 

Storage Bit B3:4/5 

Output Bit 2 

Output Word O:001 

Description: 

This instruction will convert a single positive edge and convert it to a bit 

that is on for only one scan. When ’A’ goes from false to true a positive 

(or rising) edge occurs, and bit ’O:001/2’ will be on for one scan. Bit 

’B3:4/5’ is used to track the state of the input to the function, and it can 

be considered equivalent to an enable bit. 

The OSF function is similar to the OSR function, except it is triggered on a 

negative edge where the input falls from true to false. 




TND - Temporary eND 

A 

TND 

Description: 

When ’A’ is true this statement will cause the PLC to stop examining the 

ladder logic program, as if it has encountered the normal end-of-program 

statement. 




34.1.3 Timers and Counters 

Counter memory instructions can share the same memory location, so some redundant 

bits are mentioned here. 



CTD - CounT Down 

A 

CTD 

COUNT DOWN 

Counter C5:0 

Preset 50 

Accum. 0 

Description: 

The counter accumulator will decrease once each time the input goes from 

false to true. If the accumulator value reaches the preset the done bit, 

DN, will be set. The accumulator value will still decrease even when the 

done bit is set 

Status Bits: 

Registers: 

CU 

CD 

DN 

OV 

UN 

ACC 

PRE 

Not used for this instruction 

Will be true when the input is true 

Will be set when ACC < PRE 


Will be set if the counter value has gone below -32,768 

The time that has passed since the input went true 

The maximum time delay before the timer goes on 




CTU - CounT Up 

A 

CTU 

COUNT UP 

Counter 

Preset 

Accum. 

C5:0 

50 

0 

Description: 

The counter accumulator will increase once each time the input goes from 

false to true. If the accumulator value reaches the preset the done bit, 

DN, will be set. The accumulator value will still increase even when the 

done bit is set 

Status Bits: 

Registers: 

CU 

CD 

DN 

OV 

UN 

ACC 

PRE 

Will be true when the input is true 


Will be set when ACC >= PRE 

Will be set if the counter value has gone above 32,767 


The total count 

The maximum count before the counter goes on 




TOF - Timer OFf 

A 

Description: 

Status Bits: 

Registers: 

TOF 

TIMER OFF DELAY 

Timer T4:0 

Time Base 1.0 

Preset 10 

Accum. 0 

This timer will delay turning off (the done bit, DN, will turn on immediately). 

Once the input turns off the accumulated value (ACC) will start 

to increase from zero. When the preset (PRE) value is reached the DN 

bit is turned off and the accumulator will reset to zero. If the input turns 

on before the off delay is complete the accumulator will reset to zero. 

EN 

TT 

DN 

ACC 

PRE 


This bit is true while the input to the timer is true 

This bit is true while the accumulator value is increasing 

This bit is true when the accumulator value is less than the preset 

value and the input is true, or the accumulator is changing 

The time that has passed since the input went false 

The maximum time delay before the timer goes off 



TON - Timer ON 

A 

Description: 

Status Bits: 

Registers: 

TON 

TIMER ON DELAY 

Timer T4:0 

Time Base 1.0 

Preset 10 

Accum. 0 

This timer will delay turning on, but will turn off immediately. Once the 

input turns on the accumulated value (ACC) will start to increase from 

zero. When the preset (PRE) value is reached the DN bit is set. The done 

bit will turn off and the accumulator will reset to zero if the input goes 

false. 

EN 

TT 

DN 

ACC 

PRE 




This bit is true when the accumulator value is equal to the preset 

value 





RTO - RetentiveTimer On 

A 

Description: 

Status Bits: 

Registers: 

RTO 

RETENTIVE TIMER ON 

Timer T4:0 

Time Base 1.0 

Preset 10 

Accum. 0 

This timer will delay turning on. When the input turns on the accumulated 

value (ACC) will start to increase from zero. When the preset (PRE) 

value is reached the DN bit is set. If the input goes false the accumulator 

value is not reset to zero. To reset the timer and turn off the timer the 

RES instruction should be used. 

EN 

TT 

DN 

ACC 

PRE 




This bit is true when the accumulator value is less than the preset 

value 



34.1.4 Compare 

CMP - CoMPare 

CMP 

COMPARE 

Expression 

“(N7:0 + 8) > N7:1” 

A 

Description: 

Status Bits: 

This function uses a free form expression to compare the two values. The 

comparison values that are allowed include =, >, >=, ,


DTR - Data TRansition 

DTR 

DATA TRANSITION 

Source N7:0 

Mask 00FF 

Reference N7:1 

Description: 

This function will examine the source value and mask out bits using the 

mask. The value will be compared to the Reference value, and if the 

values agree, then the function will be true for one scan, after that it 

will be false. 

A 

Status Bits: 

none 



EQU, GEQ, GRT, LEQ, LES, NEQ - EQUals, Greater than or EQuals, GReater Than, 

Less than or EQuals, LESs than, Not EQuals 

EQU 

EQUALS 

Source A 

Source B 

N7:0 

N7:1 

A 

Description: 

Status Bits: 

The basic compare has six variations. Each of these will look at the values 

in source A and B and check for the comparison case. If the comparison 

case is true, the output will be true. The types are, 

EQU - Equals 

GEQ - Greater than or equals 

GRT - Greater than 

LEQ - Less than or equals 

LES - Less than 

NEQ - Not equal 

none 





FBC, DDT - File Bit Compare, Diagnostic DetecT 

A 

CLR 

Dest S2:24 

Description: 

FBC 

FILE BIT COMPARE 

Source #B3:0 

Reference 

Result 

Cmp Control 

Length 

Position 

Result Control 

Length 

Position 

#B9:0 

#N10:0 

R6:0 

10 

0 

R6:1 

3 

0 

This instruction will compare the bits in two files and store the positions 

of differences in a result file. In this example the files compared when 

’A’ goes true. Both files start at ’B3:0’ and ’B9:0’ and 10 bits are to be 

compared. When differences are found the bit numbers will be stored 

in a list starting at ’N10:0’, the list can have up to three values (integer 

words). The ’Cmp Control’ word is for the bits being compared. The 

’Result Control’ word is for the list of differences. The manual recommends 

clearing ’S:24’ before running this instruction to avoid a possible 

processor fault. 

The DDT instruction is the same as the FBC instruction, except that 

when a different bit is found the source bit overwrites the reference 

bit. It is useful for storing a reference pattern for later use by a FBC. 

Status Bits: 

Registers: 

EN (Cmp) 

DN (Cmp) 

ER (Cmp) 

IN (Cmp) 

FD (Cmp) 

DN (Result) 

ER (Result) 

LEN (Cmp) 

POS (Cmp) 

LEN (Result) 

POS (Result) 

enable - enabled when the instruction input is active 

done - enabled when the operation is complete 

error - set if an error occurred during the operation 

inhibit - set when mismatch found, must be cleared to 

continue the comparison 

found - set when a mismatch is found 

done - set when the result list is full 

error - set if an error occurred with the results list 

length - the number of bits to be compared 

position - the position of the current bit being compared 

length - the number of result positions allowed 

position - the location of the last result added 




LIM - LIMit 

LIM 

LIMIT TEST (CIRC) 

Low limit N7:0 

Test 

N7:1 

High Limit N7:2 

A 

Description: 

Status Bits: 

Registers: 

This function will check to see if a value is between two limits. If the 

high limit is larger than the low limit and the test value is >= low limit 

or


34.1.5 Calculation and Conversion 

ACS, ASN, ATN, COS, LN, LOG, NEG, SIN, SQR, TAN - ArcCosine, ArcSiNe, 

ArcTaNgent, COSine, Logarythm Natural, LOGarythm, 

NEGative, SINe, SQuare Root, TANgent 

A 

ACS 

ARCCOSINE 

Source 

Dest 

N7:0 

N7:1 

Description: 

Status Bits: 

These are unary math functions that will load a value from the source, do 

the calculation indicated, and store the results in the destination. Functions 

possible include 

ACS - Arccosine (inverse cosine) in radians 

ASN - Arcsine (inverse sine) in radians 

ATN - Arctangent (inverse tangent) in radians 

COS - Cosine using radians 

LN - Natural Logarithm 

LOG - Base 10 logarithm 

NEG - Sign change from positive to negative, or reverse 

SIN - Sine using radians 

SQR - Square root 

TAN - Tangent using radians 

C 

V 

Z 

S 

Carry - set if a carry is generated 

Overflow - only set if value exceeds maximum for number type 

Zero - sets if the result is zero. 

Sign - set if result is negative 





ADD, DIV, MUL, SUB, XPY - ADDition, DIVision, MULtiplication, 

SUBtraction, X to the Power of Y 

Description: 

Status Bits: 

A 

ADD 

ADD 

Source A N7:0 

Source B N7:1 

Dest N7:2 

These are binary math functions that will load two values from sources A 

and B, do the calculation indicated, and store the results in the destination. 

Functions possible include 

ADD - Add two numbers 

DIV - Divide source A by source B 

MUL - Multiply A and B 

SUB - Subtract B from A 

XPY - Raise X to the power of Y 

C 

V 

Z 

S 



Carry - sets if a carry is generated 



Sign - sets if the result is negative 



AVE, STD - AVErage, STandard Deviation 

Description: 

A 

AVE 

AVERAGE FILE 

File 

#N7:0 

Dest 

N7:10 


Length 10 

Postion 0 

These functions do the basic statistical calculations, average (AVE) and 

standard deviation (STD). When the input goes from false to true the 

calculation is begun. The values to be used for the calculation are 

taken from the memory starting at the start of the file location, for the 

length indicated. The final result is stored in the Dest. The control file 

is used for the calculation to keep track of position, and indicate when 

the calculation is done (it may take more than one PLC scan). 

Status Bits: 

C 

V 

Z 

S 

EN 

DN 

ER 

Carry - always 0 




Enable - on when the instruction input is on 

Done - set when the calculation is complete 

Error - set if an error was encountered during calculation 





CLR - CLeaR 

A 

CLR 

CLR 

Dest N7:0 

Description: 

Status Bits: 

This value will clear a memory location by putting a zero in it when the 

input to the function is true. 

none 



CPT - ComPuTe 

A 

CPT 

COMPUTE 

Dest 

Expression 

“N7:1 - N7:3” 

N7:0 

Description: 

Status Bits: 

This expression allows free-form entry of equations. A maximum of 80 

characters is permitted. Operations allowed include +, -, | (divide), *, 

FRD, BCD, SQR, AND, OR, NOT, XOR, ** (x**y = x to power y), 

RAD, DEG, LOG, LN, SIN, COS, TAN, ASN, ACS, ATN 

none 


Available on: PLC-5 



FRD, TOD, DEG, RAD - FRom bcD to integer, TO bcD from integer, 

DEGrees from radians, RADians from degrees 

Description: 

Status Bits: 

A 

FRD 

FROM BCD 

Source N7:0 

Dest 

N7:1 

This function will convert the value in the source location and store the 

result in the Dest location. The functions possible include, 

FRD - From BCD to a 2s compliment integer number 

TOD - From 2s compliment integer number to BCD 

DEG - Convert from radians to degrees 

RAD - Convert from degrees to radians 

C 

V 

Z 

S 


Overflow - sets if an overflow as generated during conversion 


Sign - sets if the MSB of the result is set 





SRT - SoRT 

Description: 

A 

SRT 

SORT 

File 

#N7:0 


Length 10 

Position 0 

This functions sort the values in memory from lowest value in the first 

location to the highest value. When the input goes from false to true 

the calculation is begun. The values to be used for the calculation are 

sorted in the memory starting at the start of the file location, for the 

length indicated. The control file is used for the calculation to keep 

track of position, and indicate when the calculation is done (it may 

take more than one PLC scan). 

Status Bits: 

EN 

DN 

ER 

Enable - on when the instruction input is on 

Done - set when the calculation is complete 

Error - set if an error was encountered during calculation 





34.1.6 Logical 

AND, OR, XOR - AND, OR, eXclusive OR 

Description: 

Status Bits: 

A 

AND 

BITWISE AND 

Source A N7:0 

Source B N7:1 

Dest N7:2 

These functions do basic boolean operations to the numbers in locations 

A and B. The results of the operation are stored in Dest. These calculations 

will be perform whenever the input is true. The functions are, 

AND - Bitwise and 

OR - Bitwise or 

XOR - Bitwise exclusive or 

C 

V 

Z 

S 




Overflow - always 0 



NOT - NOT 

Description: 

A 

NOT 

NOT 

Source N7:0 

Dest 

N7:1 

This function will invert all of the bits in a word in memory whenever the 

input is true. 

Status Bits: 

C 

V 

Z 

S 









34.1.7 Move 

BTD - BiT Distribute 

A 

BTD 

BIT FIELD DISTRIB 

Source N7:0 

Source bit 0 

Dest N7:1 

Dest bit 4 

Length 5 

Description: 

Status Bits: 

This function will copy the bits starting at N7:0/0 to N7:1/4 for a length 

of 5 bits. 

none 



MOV - MOVe 

A 

MOV 

MOVE 

Source N7:0 

Dest 

N7:1 

Description: This instruction will move values from one location to another, and if 

necessary change value types, such as integer to a floating point. 

Status Bits: 

C 

V 

Z 

S 


Overflow - Sets if an overflow occurred during conversion 







MVM - MoVe Masked 

Description: 

Status Bits: 

A 

MVM 

MAKSED MOVE 

Source N7:0 

Mask N7:1 

Dest N7:2 

This function will retrieve the values from the source and mask memory 

and AND them together. Only the bits that are true in the mask will be 

copied to the new location. 

C 

V 

Z 

S 







34.1.8 File 

Most file instructions will contain Mode options. The user may choose these with 

the implications listed below. 

All - All of the operations will be completed in a single scan when the input to the 

function is edge triggered. Care must be used not to create an operation so long 

it causes a watchdog fault in the PLC 

Incremental - Each time there is a positive input edge the function will advance the 

file operation by one. 

’number’ - when a number is supplied the function will perform that many iterations 

while the input rung is true. 



COP - file COPy 

A 

COP 

COPY FILE 

Source 

Dest 

Length 

#N7:50 

#N7:20 

4 

Description: 

Status Bits: 

Registers: 

This instruction copies from one list to another. When ’A’ is true the 

instruction will copy the entire source list to the destination location in 

a single scan. In this example this would mean N7:20=N7:50, 

N7:21=N7:51, N7:22=N7:52 and N7:23=N7:53. The source values 

are not changed. This instruction will not convert data types. 

none 

none 




FAL - File Arithmetic and Logic 

A 

Description: 

FAL 

FILE ARITH/LOGICAL 


Length 10 

Position 0 

Mode ALL 

Dest 

Expression 

#N7:10 

#N7:0 - N7:21 

This function will evaluate the expression over a range of values. The 

length specifies the number of positions in the expression and destination 

files. The position value will be updated to indicate the current 

position in the calculation. See earlier in this section for a description 

of the Mode variable. This example would perform all of the calculations 

in a single scan. These calculations would be N7:10=N7:0- 

N7:21, N7:11=N7:1-N7:21, ......N7:19=N7:9-N7:21. More complex 

mathematical expressions can be used with the following operators; 

+, -, *, | - basic math 

BCD/FRD - BCD conversion 

SQR - square root 

AND, OR, NOT, XOR - Boolean operators 

Note: advanced math operators are also available 

Status Bits: 

Registers: 

EN 

DN 

ER 

POS 

LEN 

enable - this will be on while the function is active 

done - this will be on when a calculation has completed 

error - this will be set if there was an error during calculation 

position - tracks the current position in the list 

length - the length of the file 




FLL - file FiLL 

A 

FLL 

FILE FILL 

Source 

Destination 

Length 

F8:0 

#F8:30 

10 

Description: 

Status Bits: 

The contents of a single memory location are copied into a list. In this 

example the value in ’F8:0’ is copied into locations ’F8:30’ to ’F8:39’ 

each scan when ’A’ is true. The source value is not changed. This 

instruction will not convert data types. 

none 

Registers: 

none 




FSC - File Search and Compare 

A 

FSC 

FILE SEARCH/COMPARE 


Length 14 

Position 0 

Mode 3 

Expression #F8:5 > F8:0 

X 

Description: 

lists of numbers can be compared using the FSC command. When ’A’ 

becomes true the function will start to compare values as determined 

by the ’Mode’ (see the beginning of this section for details on the 

mode). The expression will be evaluated from the initial locations in 

the expression. The end of the list is determined by the Length. In this 

example 3 values will be evaluated for each scan. The comparison in 

the first scan will be F8:5>F8:0, F8:6>F8:0 and F8:7>F8:0. This 

instruction will continue until all 14 values have been compared, and 

all are true, at which time X will turn on and stay on while A is on. If 

any values are false the compare will stop, and the output will stay off. 

Status Bits: 

Registers: 

EN 

DN 

ER 

IN 

FD 

LEN 

POS 

enable - will be on while the instruction input is on 

done - will be on when the length is reached, or a false compare 

occurred 

error - will occur if there is an error in the expression or range 

inhibit - if a false statement is found the inhibit bit will be set. if 

this is turned off (i.e., R6:36/IN=0) the search will continue 

found - this bit will be set when a false condition is found 

length - the number of the comparison list 

position - the current position in the comparison list 




34.1.9 List 

BSL, BSR - Bit Shift Left, Bit Shift Right 

A 

Description: 

Status Bits: 

BSL 

BIT SHIFT LEFT 

File 


Bit Address 

Length 6 

#B3:0 

R6:0 

I:0.0/0 

These functions will shift bits through left or right through a string of bits 

starting at #B3:0 with a length of 6 in the example above. As the bits 

shift the bit shifted out will be put in the UL bit. A new bit will be 

shifted into the vacant spot from the Bit Address. When the bits are 

shifted they are moved in the memory locations starting at file #B3:0. 

The two options available are: 

BSR - Bit Shift Right 

BSL - Bit Shift Left 

EN 

DN 

ER 

UL 



Enable - is on when the input to the function is on 

Done - is on when the shift operation is complete 

Error - indicates when an error has occurred 

Unload - the unloaded value is stored in this bit 



FFL, FFU, LFL, LFU - FiFo Load, FiFo Unload, LiFo Load, LiFo Unload 

Description: 

Status Bits: 

A 

B 

FFL 

FIFO LOAD 

Source 

FIFO 


Length 

N7:0 

N7:10 

R6:0 

10 

Stack instructions will take integer words and store them, and then allow 

later retrieval. The load instructions will store a value on the stack on a 

false to true input change. The Unload instructions will remove a 

value from that stack and store it in the Dest location. A Last On First 

Off stack will return the last value pushed on. A First On First Off 

stack will give the oldest value on the stack. If an attempt to load more 

than the stack length, the values will be ignored. The instructions 

available are: 

FFL - FIFO stack load 

FFU - FIFO stack unload 

LFL - LIFO stack load 

LFU - LIFO stack unload 

EN 

DN 

ER 

UL 



Position 0 

FFU 

FIFO UNLOAD 

FIFO N7:10 

Dest 

N7:11 


Length 10 

Position 0 

Enable - is on when the input to the function is on 

Done - is on when the shift operation is complete 

Error - indicates when an error has occurred 

Unload - the unloaded value is stored in this bit 



SQI - SeQuencer Input 

A 

Description: 

Status Bits: 

Registers: 

SQI 

SEQUENCER INPUT 

File 

#N7:10 

Mask FF00 

Source N7:0 


This will compare a source value to a set of values in a sequencer table. 

In this example the 8 most significant bits of ’N7:0’ will be loaded 

each time ’A’ goes from false to true. The sequencer will load words 

from ’N7:10’ to ’N7:17’. 

EN 

DN 

ER 

POS 

LEN 


Length 

Position 

enable - true when the function is enabled 

done - set when the sequencer is full 

error - set if an error has occured 

position - the current location in the sequencer 

length - the total length of the sequencer 

7 

0 

SQL - SeQuencer Load 

A 

Description: 

Status Bits: 

SQL 

SEQUENCER LOAD 

File 

#N7:10 

Source N7:0 


Length 6 

Position 0 

When the input goes from false to true the value at the source will be 

loaded into the sequencer. After the position has reached the length the 

following values will be ignored, and the done bit will be set. 

EN 

DN 

ER 



Enable - will be true when the input to the function is true 

Done - will be set when the sequencer is fully loaded 

Error - will be set when there has been an error 



SQO - SeQuencer Output 

A 

SQO 

SEQUENCER OUTPUT 

File 

#N7:10 

Mask FF00 

Dest 

N7:0 


Length 6 

Position 0 

Description: 

Status Bits: 

When the input goes from false to true the sequencer will output a value 

from a new position in the sequencer table. After the position has 

reached the length the sequencer will reset to position 1. Note that the 

first entry in the sequencer table will only be output the first time the 

function is un, or if reset has been used. 

EN 

DN 

ER 

Enable - will be true when the input to the function is true 

Done - will be set when the sequencer is fully loaded 

Error - will be set when there has been an error 



34.1.10 Program Control 

EOT - End Of Transition 

A 

Description: 

EOT 

This function will cause a transition in an SFC. This will be in a program 

file for an SFC step. When ’A’ becomes true the transition will end 

and the SFC will move to the next step and transitions. 

Status Bits: 

Registers: 

none 

none 




FOR, NXT, BRK - For, Next, Break 

A 

FOR 

FOR 

Label Number 

Index 

Initial Value 

Terminal Value 

Step Size 2 

0 

N7:0 

0 

10 

B 

BRK 

C 

NXT 

NEXT 

Label Number 0 

Description: 

Status Bits: 

Registers: 

This instruction will create a loop like traditional programming languages 

with a start and end value with a step size for each loop. 

Instructions between the FOR and NXT will be repeated. If the line 

with the BRK statement becomes true, the NXT command will be 

ignored. 

none 

none 




JSR/SBR/RET - Jump Subroutine / Subroutine / Return 

A 

JSR 

JUMP TO SUBROUTINE 

Program File 3 

Input par N7:0 

Input par N7:1 

Return par N7:10 



B 

SBR 

SUBROUTINE 

Input par 

Input par 

N7:20 

N7:21 

Description: 

Status Bits: 

Registers: 

C 

RET 

RETURN() 




The JSR will jump to another program file and pass a list of arguments 

that can be a variable length. The first statement in the subroutine program 

file should be SBR to retrieve the arguments passed. The subroutine 

will end with the RET command that will go back to where the 

JSR function was encountered. The RET function can return a variable 

number of arguments. 

none 

none 




SFR - Sequential Function chart Reset 

A 

SFR 

SFC RESET 

Prog File Number 

Restart Step At 

3 

Description: 

Status Bits: 

Registers: 

This function will reset a SFC. In this example when ’A’ goes true the 

SFC main program stored in program file 3 will be examined. All sub 

programs will be examined, and then the SFC will be reset to the initial 

position. 

none 

none 


UID, UIE - User Interrupt Disable, User Interrupt Enable 

A 

B 

UID 

UIE 

Description: 

Status Bits: 

Registers: 

This instruction is used to turn of interrupts. If ’A’ is true, then the following 

ladder logic will be run without interrupts. If ’B’ is true the 

interrupts will be reenabled. These instructions will only be of concern 

when using user programmed interrupt functions. These are normally 

only used when a critical process may be completed within a given 

time, or when the ladder logic between the UID and UIE conflicts 

with one of the interrupt programs. 

none 

none 




34.1.11 Advanced Input/Output 

BTR, BTW - Block Transfer Read, Block Transfer Write 

A 

BTR 

BLOCK TRANSFER READ 

Rack 2 

Group 3 

Module 0 


Data File 

Length 

Continuous 

N9:10 

13 

N 

Description: 

These instructions communicate with complex input-output cards in a 

PLC rack. The instruction is needed when a card requires more than 

one word of input and/or output data. The rack and group indicate the 

location of the card as ’O:023’. The module number is needed when 

using two slot addressing for larger racks (this is not needed for racks 

with less than 8 cards). The control memory is ’BT’, although integer 

memory could also be used. The data file indicates the location of the 

data to be sent, in this case it is from ’N9:10’ to ’N9:22’. The length 

and contents of the data file are dependant upon the card type. If the 

instruction is continuous, it will send out the data as soon as the last 

transmission is complete. If it is not continuous ’A’ must go from false 

to true to trigger a transmission. 

Status Bits: 

Registers: 

EN 

ST 

DN 

ER 

CO 

EW 

NR 

TO 

RW 

RLEN 

DLEN 

FILE 

ELEM 

RGS 


enable - 

start - 

done - 

error - 

continuous - 

enable waiting - 

no response - 

time out - 

read write - 

requested data length - 

transmitted data length - 

file number - 

element number - 

rack, group, slot - card address 



MSG - MeSsaGe 

A 

MSG 

SEND/RECEIVE MESSAGE 


Description: 

This is a multipurpose instruction that deals with communications in general. 

The instruction is controlled by the contents of the control block, 

which is normally set up using the programming software. The 

instruction can send and receive data across most interfaces including 

DH, DH+, Ethernet, RS-232, RS-422 and RS-485. The message 

blocks ’MG’ are preferred for storing the configuration, but integer 

memory may also be used. The messages are segments of PLC memory. 

These can be read from, or written to a remote destination. 

Status Bits: 

EN 

ST 

DN 

ER 

CO 

EW 

NR 

TO 

enable - indicates when the instruction is active 

start - 

done - indicates when the instruction is complete 

error - an error occurred 

continuous - when set the instruction doesn’t need a true input 

enabled waiting - 

no response - the remote destination was not detected 

time out - the remote destination did not respond in time 

Registers: many refer to manuals 




PID - Proportional Integral Derivative controller 

A 

PID 

PID 

PID File PD9:0 

Process Variable N10:0 

Control Variable N10:30 

Description: 

This function calculates a value for a control output based on a feedback 

value. When ’A’ is true the instruction will do a PID calculation. In 

this example the PID calculation is based on the parameters stored in 

’PD9:0’. It will use the setpoint ’PD9:0.SP’, and the feedback value 

’N10:0’ to calculate a new control output ’N10:30’. The control variables 

are normally set using the programming software, although it is 

possible to set up this instruction using MOV instructions. 

Status Bits: 

Registers: 

EN 

DN 

KC 

TI 

TD 

MAXS 

MINS 

SP 

enable - indicates when the input is active 

done - this indicates when the instruction is done (not available 

when using the ’PD’ control block. 

controller gain - the overall gain for the controller 

reset time - this gives a relative time for integration 

rate time - this gives a relative time for the derivative 

maximum setpoint - the largest value for the setpoint 

minimum setpoint - the smallest value for the setpoint 

setpoint - the setpoint for the process 

Note: This is only a partial list, see the manuals for additional 

status bits and registers. 




34.1.12 String 

ABL, ACB - Ascii availaBle Line, Ascii Characters in Buffer 

A 

ABL 

ASCII TEST FOR LINE 

Channel 0 


Characters 

Description: 

Status Bits: 

The ABL instruction checks for available characters in the input buffer. 

In this example, when ’A’ goes true the function will check the input 

buffer for channel ’0’ and put characters in ’R6:0.POS’. The count 

will include end of line characters such as ’CR’ and ’LF’. 

The ACB instruction is the same, except that it does not include the end 

of line characters. 

none 

Registers: POS the number of characters waiting in the buffer. 




ACI, AIC - Ascii string Convert to Integer, Ascii Integer to string Conversion 

A 

ACI 

STRING TO INTEGER CONVERSION 

Source ST10:2 

Dest 

N9:5 

Description: 

The ACI instruction will convert a string to an integer value. In this 

example it retrieve the string in ’ST10:2’, convert it to an integer and 

store it in ’N9:5’. When converting to an integer it is possible to have 

an overflow error. 

The AIC function will convert an integer to a string. 

Status Bits: 

C 

V 

Z 

N 

Carry - sets if a carry is generated 




Registers: POS the number of characters waiting in the buffer. 


ACN - Ascii string CoNcatenate 

A 

ACN 

STRING CONCATENATE 

SourceA ST10:0 

SourceB ST10:1 

Dest 

ST10:2 

Description: 

Status Bits: 

Registers: 

This will concatenate two strings together into one combined string. In 

this example while ’A’ is true the strings in ’ST10:0’ and ’ST10:1’ 

will be added together and stored in ’ST10:2’. 

none 

none 




AEX - Ascii string EXtract 

A 

Description: 

AEX 

STRING EXTRACT 

Source ST9:4 

Index 11 

Number 3 

Dest 

ST9:0 

This function will remove part of a string. In this example the characters 

in the 12th, 13th and 14th positions (’3’ charaters starting at the 11th 

position), are copied to the location ST9:0. The original string is not 

changed. 

Status Bits: 

Registers: 

none 

none 


AHL - Ascii Handshake Line 

A 

AHL 

ASCII HANDSHAKE LINE 

Channel 1 

AND Mask 0000 

OR Mask 0003 


Channel Status 

Description: 

This instruction will check the serial interface using the DTR and RTS 

send bits. Bit 0 is DTR and bit 1 is the RTS. If a bit is set in the AND 

mask the bits will be turned off, otherwise they will be left alone. If a 

bit is set in the OR word a bit will be turned on, otherwise they will be 

left alone. In this example the DTR and RTS bits will be turned on for 

channel 1. 

Status Bits: 

EN 

DN 

ER 

enable - this is set when the instruction is active 

done - when the bits have been reset this bit is on 

error - this bit is set if an error has occurred 

Registers: 

none 




ARD, ARL - Ascii ReaD, Ascii Read Line 

Description: 

A 

ARD 

ASCII READ 

Channel 

Dest 


String Length 

Characters Read 

0 

ST10:0 

R6:10 

15 

The ARD instruction will read characters and write them to a string. In 

this example the characters are read from channel 0 and written to 

’ST10:0’. All of the characters in the buffer, up to 15 in total, will be 

removed and written to the string memory. The number of characters 

will be stored in ’R6:10.POS’. 

The ARL function is similar to the ARD function, except that the end-ofline 

values ’CR’ or ’LF’ will mark the end of a line. With the parameters 

above the string will be copied until 15 characters are reached, or 

there are fewer than 15 characters, or an end-of-line character is 

found. 

Status Bits: 

EN 

DN 

ER 

UL 

EM 

EU 

enable - will be set while the instruction is enabled 

done - will be set when then string has been read 

error - will be set if an error has occurred 

unload - 

empty - will be set if no characters were found 

queue - 

Registers: POS the number of characters copied 




ASC - Ascii string Search for Character 

A 

ASC 

STRING SEARCH 

Source ST9:0 

Index 20 

Search ST9:1 

Result 

Description: 

This function will search a string for a character. In this example the 

character will look for the character in string ’ST9:0’ in position 20 

(21st) in string ’ST9:1’. If a match is NOT found the bit ’S2:17/8’ will 

be turned on. 

Status Bits: 

Registers: 

S2:17/8 

none 

ascii minor fault bit - this bit will be set if there was no match 


ASR - Ascii StRing compare 

A 

ASR 

ASCII STRING COMPARE 

SourceA ST10:10 

SourceB ST10:11 

X 

Description: 

This instruction will compare two strings. In this example, if ’A’ is true 

then the strings ’ST10:10’ and ’ST10:11’ will be compared. If they are 

equal then ’X’ will be true, otherwise it will be false. If the strings are 

different lengths then the bit ’S2:17/8’ will be set. 

Status Bits: 

Registers: 

S2:17/8 

none 

ascii minor fault bit - this bit will be set if the string lengths 

don’t match. 




AWT, AWA - Ascii WriTe, Ascii Write Append 

A 

AWT 

ASCII WRITE 

Channel 

Source 


String Length 

Characters Sent 

0 

ST11:9 

R6:3 

14 

Description: 

The AWT instruction will send a character string. In this example, when 

’A’ goes from false to true, up to 14 characters will be sent from 

’ST11:9’ to channel 0. This does not append any end of line characters. 

The AWA function has a similar operation, except that the channel configuration 

characters are added - by default these are ’CR’ and ’LF’. 

Status Bits: 

EN 

DN 

ER 

UL 

EM 

EU 

enable - this will be set while the instruction is active 

done - this will be set after the string has been sent 

error bit - set when an error has occurred 

unload - 

empty - set if no string was found 

queue - 

Registers: POS the number of characters sent instructions 


34.2 DATA TYPES 

The following table describes the arguments and return values for functions. Some 

notes are; 

• ’immediate’ values are numerical, not memory addresses. 

• ’returns’ indicates that the function returns that data value. 

• numbers between ’[’ and ’]’ indicate a range of values. 

• values such as ’yes’ and ’no’ are typed in literally. 



Table 1: Instruction Data Types 

Function Argument Data Types Edge Triggered 

ABL 

channel 

control 

characters 

immediate int [0-4] 

R 

returns N 

yes 

ACB 

channel 

control 

characters 


R 

returns N 

yes 

ACI 

source 

destination 

ST 

N 

no 

ACN 

source A 

source B 

ST 

ST 

no 

ACS 

source 

destination 

N,F,immediate 

N,F 

no 

ADD 

source A 

source B 

destination 

N,F,immediate 

N,F,immediate 

N,F 

no 

AEX 

source 

index 

number 

destination 

ST 



ST 

no 

AFI 

no 

AHL 

channel 

AND mask 

OR mask 

control 


immediate hex [0000-ffff] 

immediate hex [0000-ffff] 

R 

yes 

AIC 

source 

destination 

N, immediate int 

ST 

no 

ARD 

channel 

destination 

control 

string length 

characters read 


ST 

R 


returns N 

yes 





ARL 

channel 

destination 

control 

string length 

characters read 


ST 

R 


returns N 

yes 

ASC 

source 

index 

search 

result 

ST 

N, immediate 

ST 

R 

no 

ASN 

source 

destination 

N,F,immediate 

N,F 

no 

ASR 

source A 

source B 

ST 

ST 

no 

ATN 

source 

destination 

N,F,immediate 

N,F 

no 

AVE 

file 

destination 

control 

length 

position 

#F,#N 

F,N 

R 

N,immediate int 

returns N 

yes 

AWA 

channel 

source 

control 

string length 

characters sent 


ST 

R 


returns N 

yes 

AWT 

channel 

source 

control 

length 

characters sent 

N, immediate int 

ST 

R 


returns N 

yes 

BSL 

file 

control 

bit address 

length 

#B,#N 

R 

any bit 


yes 



BSR 

BTD 

BTR 

BTW 

file 

control 

bit address 

length 

source 

source bit 

destination 

destination bit 

length 

rack 

group 

module 

control block 

data file 

length 

continuous 

rack 

group 

module 

control block 

data file 

length 

continuous 

#B,#N 

R 

any bit 


N,B,immediate 

N,immediate int [0-15] 

N 



immediate octal [000-277] 



BT,N 

N 


’yes’,’no’ 




BT,N 

N 


’yes’,’no’ 

CLR destination N,F no 

CMP expression expression no 

COP 

COS 

CPT 

CTD 

source 

destination 

length 

source 

destination 

destination 

expression 

counter 

preset 

accumulated 



#any 

#any 


F,immediate 

F 

N,F 

expression 

C 

returns N 

returns N 

yes 

no 

yes 

yes 

no 

no 

no 

yes 





CTU 

counter 

preset 

accumulated 

C 

returns N 

returns N 

yes 

DDT 

source 

reference 

result 

compare control 

length 

position 

result control 

length 

position 

binary 










plc glossary - 35.1 

35. COMBINED GLOSSARY OF TERMS 

35.1 A 

abort - the disrupption of normal operation. 

absolute pressure - a pressure measured relative to zero pressure. 

absorption loss - when sound or vibration energy is lost in a transmitting or reflecting medium. This is the 

result of generation of other forms of energy such as heat. 

absorbtive law - a special case of Boolean algebra where A(A+B) becomes A. 

AC (Alternating Current) - most commonly an electrical current and voltage that changes in a sinusoidal 

pattern as a function of time. It is also used for voltages and currents that are not steady (DC). 

Electrical power is normally distributed at 60Hz or 50Hz. 

AC contactor - a contactor designed for AC power. 

acceptance test - a test for evaluating a newly purchased system’s performance, capabilities, and conformity 

to specifications, before accepting, and paying the supplier. 

accumulator - a temporary data register in a computer CPU. 

accuracy - the difference between an ideal value and a physically realizable value. The companion to 

accuracy is repeatability. 

acidity - a solution that has an excessive number of hydrogen atoms. Acids are normally corrosive. 

acoustic - another term for sound. 

acknowledgement (ACK) - a response that indicates that data has been transmitted correctly. 

actuator - a device that when activated will result in a mechanical motion. For example a motor, a solenoid 

valve, etc. 

A/D - Analog to digital converter (see ADC). 

ADC (Analog to Digital Converter) - a circuit that will convert an analog voltage to a digital value, also 

refered to as A/D. 

ADCCP (Advanced Data Communications Procedure) - ANSI standard for synchronous communication 

links with primary and secondary functions. 

address - a code (often a number) that specifies a location in a computers memory. 

address register - a pointer to memory locations. 

adsorption - the ability of a material or apparatus to adsorb energy. 

agitator - causes fluids or gases to mix. 

AI (Artificial Intelligence) - the use of computer software to mimic some of the cognitive human processes. 

air dump valve - this valve will open to release system pressure when system power is removed. 

algorithms - a software procedure to solve a particular problem. 

aliasing - in digital systems there are natural limits to resolution and time that can be exceeded, thus aliasing 

the data. For example. an event may happen too fast to be noticed, or a point may be too small to 

be displayed on a monitor. 

alkaline - a solution that has an excess of HO pairs will be a base. This is the compliment to an acid. 

alpha rays - ions that are emitted as the result of atomic fission or fusion. 

alphanumeric - a sequence of characters that contains both numbers and letters. 

ALU (Arithmetic Logic Unit) - a part of a computer that is dedicated to mathematical operations. 

AM (Amplitude Modulation) - a fixed frequency carrier signal that is changed in amplitude to encode a 

change in a signal. 

ambient - normal or current environmental conditions. 

ambient noise - a sort of background noise that is difficult to isolate, and tends to be present throughout the 

volume of interest. 

ambient temperature - the normal temperature of the design environment. 

amplifier - increased (or possibly decreases) the magnitude or power of a signal. 

analog signal - a signal that has continuous values, typically voltage. 



analysis - the process of review to measure some quality. 

and - a Boolean operation that requires all arguments to be true before the result is true. 

annealing - heating of metal to relieve internal stresses. In many cases this may soften the material. 

annotation - a special note added to a design for explanatory purposes. 

ANSI (American National Standards Institute) - a developer of standards, and a member of ISO. 

APF (All Plastic Fibre cable) - fiber optic cable that is made of plastic, instead of glass. 

API (Application Program Interface) - a set of functions, and procedures that describes how a program will 

use another service/library/program/etc. 

APT (Automatically Programmed Tools) - a language used for directing computer controlled machine tools. 

application - the task which a tool is put to, This normally suggets some level of user or real world 

interaction. 

application layer - the top layer in the OSI model that includes programs the user would run, such as a mail 

reader. 

arc - when the electric field strength exceeds the dielectric breakdown voltage, electrons will flow. 

architecture - they general layout or design at a higher level. 

armature - the central rotating portion of a DC motor or generator, or a moving part of a relay. 

ARPA (Advanced Research Projects Agency) - now DARPA. Originally funded ARPANET. 

ARPANET - originally sponsored by ARPA. A packet switching network that was in service from the early 

1970s, until 1990. 

ASCII (American Standard Code for Information Interchange) - a set of numerical codes that correspond to 

numbers, letters, special characters, and control codes. The most popular standard 

ASIC (Application Specific Integrated Circuit) - a specially designed and programmed logic circuit. Used 

for medium to low level production of complex functions. 

aspirator - a device that moves materials with suction. 

assembler - converts assembly language into machine code. 

assembly language - a mnemonic set of commands that can be directly converted into commands for a CPU. 

associative dimensioning - a method for linking dimension elements to elements in a drawing. 

associative laws - Boolean algebra laws A+(B+C) = (A+B)+C or A(BC) = (AB)C 

asynchronous - events that happen on an irregular basis, and are not predictable. 

asynchronous communications (serial) - strings of characters (often ASCII) are broken down into a series of 

on/off bits. These are framed with start/stop bits, and parity checks for error detection, and then 

send out one character at a time. The use of start bits allows the characters to be sent out at 

irregular times. 

attenuation - to decrease the magnitude of a signal. 

attenuation - as the sound/vibration energy propagates, it will undergo losses. The losses are known as 

attenuation, and are often measured in dB. For general specifications, the attenuation may be tied 

to units of dB/ft. 

attribute - a nongraphical feature of a part, such as color. 

audible range - the range of frequencies that the human ear can normally detect from 16 to 20,000 Hz. 

automatic control - a feedback of a system state is compared to a desired value and the control value for the 

system is adjusted by electronics, mechanics and/or computer to compensate for differences. 

automated - a process that operates without human intervention. 

auxiliary power - secondary power supplies for remote or isolated systems. 

AWG (American Wire Gauge) - specifies conductor size. As the number gets larger, the conductors get 

smaller. 

35.2 B 

B-spline - a fitted curve/surface that is commonly used in CAD and graphic systems. 

backbone - a central network line that ties together distributed networks. 

background - in multitasking systems, processes may be running in the background while the user is 



working in the foreground, giving the user the impression that they are the only user of the 

machine (except when the background job is computationally intensive). 

background suppression - the ability of a sensing system to discriminate between the signal of interest, and 

background noise or signals. 

backplane - a circuit board located at the back of a circuit board cabinet. The backplane has connectors that 

boards are plugged into as they are added. 

backup - a redundant system to replace a system that has failed. 

backward chaining - an expert system looks at the results and looks at the rules to see logically how to get 

there. 

band pressure Level - when measuring the spectrum of a sound, it is generally done by looking at 

frequencies in a certain bandwidth. This bandwidth will have a certain pressure value that is an 

aggregate for whatever frequencies are in the bandwidth. 

base - 1. a substance that will have an excess of HO ions in solution form. This will react with an acid. 2. the 

base numbering system used. For example base 10 is decimal, base 2 is binary 

baseband - a network strategy in which there is a single carrier frequency, that all connected machines must 

watch continually, and participate in each transaction. 

BASIC (Beginner’s All-purpose Symbolic Instruction Code) - a computer language designed to allow easy 

use of the computer. 

batch processing - an outdated method involving running only one program on a computer at once, 

sequentially. The only practical use is for very intensive jobs on a supercomputer. 

battery backup - a battery based power supply that keeps a computer (or only memory) on when the master 

power is off. 

BAUD - The maximum number of bits that may be transmitted through a serial line in one second. This also 

includes some overhead bits. 

baudot code - an old code similar to ASCII for teleprinter machines. 

BCC (Block Check Character) - a character that can check the validity of the data in a block. 

BCD (Binary Coded Decimal) - numerical digits (0 to 9) are encoded using 4 bits. This allows two 

numerical digits to each byte. 

beam - a wave of energy waves such as light or sound. A beam implies that it is not radiating in all 

directions, and covers an arc or cone of a few degrees. 

bearing - a mechanical support between two moving surfaces. Common types are ball bearings (light 

weight) and roller bearings (heavy weight), journal bearings (rotating shafts). 

beats - if two different sound frequencies are mixed, they will generate other frequencies. if a 1000Hz and 

1001Hz sound are heard, a 1Hz (=1000-1001) sound will be perceived. 

benchmark - a figure to compare with. If talking about computers, these are often some numbers that can be 

use to do relative rankings of speeds, etc. If talking about design, we can benchmark our products 

against our competitors to determine our weaknesses. 

Bernoulli’s principle - a higher fluid flow rate will result in a lower pressure. 

beta ratio - a ratio of pipe diameter to orifice diameter. 

beta rays - electrons are emitted from a fission or fusion reaction. 

beta site - a software tester who is actually using the software for practical applications, while looking for 

bugs. After this stage, software will be released commercially. 

big-endian - a strategy for storing or transmitting the most significant byte first. 

BIOS (Basic Input Output System) - a set of basic system calls for accessing hardware, or software services 

in a computer. This is typically a level lower than the operating system. 

binary - a base 2 numbering system with the digits 0 and 1. 

bit - a single binary digit. Typically the symbols 0 and 1 are used to represent the bit value. 

bit/nibble/byte/word - binary numbers use a 2 value number system (as opposed to the decimal 0-9, binary 

uses 0-1). A bit refers to a single binary digit, and as we add digits we get larger numbers. A bit is 

1 digit, a nibble is 4 digits, a byte is 8 digits, and a word is 16 digits. 



decimal(base 10) 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

. 

. 

. 

binary(base 2) 

0 

1 

10 

11 

100 

101 

110 

111 

1000 

1001 

1010 

1011 

. 

. 

. 

octal(base 8) 

0 

1 

2 

3 

4 

5 

6 

7 

10 

11 

12 

13 

. 

. 

. 

e.g. differences 

decimal 

binary 

15 ... tens 

3,052 ... thousands 

1,000,365 ... millions 

1 ... bit 

0110 .... nibble (up to 16 values) 

10011101 ... byte (up to 256 values) 

0101000110101011 ... work (up to 64,256 values) 

Most significant bit 

least significant bit 

BITNET (Because It’s Time NET) - An academic network that has been merged with CSNET. 

blackboard - a computer architecture when different computers share a common memory area (each has its 

own private area) for sharing/passing information. 

block - a group of bytes or words. 

block diagrams - a special diagram for illustrating a control system design. 

binary - specifies a number system that has 2 digits, or two states. 

binary number - a collection of binary values that allows numbers to be constructed. A binary number is 

base 2, whereas normal numbering systems are base 10. 

blast furnace - a furnace that generates high temperatures by blowing air into the combustion. 

bleed nozzle - a valve or nozzle for releasing pressure from a system. 

block diagram - a symbolic diagram that illustrates a system layout and connection. This can be ued for 

analysis, planning and/or programming. 

BOC (Bell Operating Company) - there are a total of 7 regional telephone companies in the U.S.A. 

boiler - a device that will boil water into steam by burning fuel. 

BOM (Bills Of Materials) - list of materials needed in the production of parts, assemblies, etc. These lists are 

used to ensure all required materials are available before starting an operation. 

Boolean - a system of numbers based on logic, instead of real numbers. There are many similarities to 

normal mathematics and algebra, but a separate set of operators, axioms, etc. are used. 



bottom-up design - the opposite of top-down design. In this methodology the most simple/basic functions 

are designed first. These simple elements are then combined into more complex elements. This 

continues until all of the hierarchical design elements are complete. 

bounce - switch contacts may not make absolute contact when switching. They make and break contact a 

few times as they are coming into contact. 

Bourdon tube - a pressure tube that converts pressure to displacement. 

BPS (Bits Per Second) - the total number of bits that can be passed between a sender and listener in one 

second. This is also known as the BAUD rate. 

branch - a command in a program that can cause it to start running elsewhere. 

bread board - a term used to describe a temporary electronic mounting board. This is used to prototype a 

circuit before doing final construction. The main purpose is to verify the basic design. 

breadth first search - an AI search technique that examines all possible decisions before making the next 

move. 

breakaway torque - the start-up torque. The value is typically high, and is a function of friction, inertia, 

deflection, etc. 

breakdown torque - the maximum torque that an AC motor can produce at the rated voltage and frequency. 

bridge - 1. an arrangement of (typically 4) balanced resistors used for measurement. 2. A network device 

that connects two different networks, and sorts out packets to pass across. 

broadband networks - multiple frequencies are used with multiplexing to increase the transmission rates in 

networks. 

broad-band noise - the noise spectrum for a particular noise source is spread over a large range of 

frequencies. 

broadcast - a network term that describes a general broadcast that should be delivered to all clients on a 

network. For example this is how Ethernet sends all of its packets. 

brush - a sliding electrical conductor that conducts power to/from a rotor. 

BSC (Binary Synchronous Communication) - a byte oriented synchronous communication protocol 

developed by IBM. 

BSD (Berkeley Software Distribution) - one of the major versions of UNIX. 

buffer - a temporary area in which data is stored on its way from one place to another. Used for 

communication bottlenecks and asynchronous connections. 

bugs - hardware or software problems that prevent desired components operation. 

bumpless transfer - a smooth transition between manual and automatic modes. 

burn-in - a high temperature pre-operation to expose system problems. 

burner - a term often used for a device that programs EPROMs, PALs, etc. or a bad cook. 

bus - a computer has buses (collections of conductors) to move data, addresses, and control signals between 

components. For example to get a memory value, the address value provided the binary memory 

address, the control bus instructs all the devices to read/write, and to examine the address. If the 

address is valid for one part of the computer, it will put a value on the data bus that the CPU can 

then read. 

byte - an 8 bit binary number. The most common unit for modern computers. 

35.3 C 

C - A programming language that followed B (which followed A). It has been widely used in software 

development in the 80s and 90s. It has grown up to become C++ and Java. 

CAA (Computer Aided Analysis) - allows the user to input the definition of a part and calculate the 

performance variables. 

cable - a communication wire with electrical and mechanical shielding for harsh environments. 

CAD (Computer Aided Design) - is the creation and optimization of the design itself using the computer as 

a productivity tool. Components of CAD include computer graphics, a user interface, and 

geometric modelling. 



CAD (Computer Aided Drafting) - is one component of CAD which allows the user to input engineering 

drawings on the computer screen and print them out to a plotter or other device. 

CADD (Computer Aided Design Drafting) - the earliest forms of CAD systems were simple electronic 

versions of manual drafting, and thus are called CADD. 

CAE (Computer Aided Engineering) - the use of computers to assist in engineering. One example is the use 

of Finite Element Analysis (FEA) to verify the strength of a design. 

CAM (Computer Aided Manufacturing) - a family of methods that involves computer supported 

manufacturing on the factory floor. 

capacitor - a device for storing energy or mass. 

capacitance - referring to the ability of a device to store energy. This is used for electrical capacitors, thermal 

masses, gas cylinders, etc. 

capacity - the ability to absorb something else. 

carrier - a high/low frequency signal that is used to transmit another signal. 

carry flag - an indication when a mathematical operator has gone past the limitations of the hardware/ 

software. 

cascade - a method for connecting devices to increase their range, or connecting things so that they operate 

in sequence. This is also called chaining. 

CASE (Computer Aided Software Engineering) - software tools are used by the developer/programmer to 

generate code, track changes, perform testing, and a number of other possible functions. 

cassette - a holder for audio and data tapes. 

CCITT (Consultative Committee for International Telegraph and Telephone) - recommended X25. A 

member of the ITU of the United Nations. 

CD-ROM (Compact Disc Read Only Memory) - originally developed for home entertainment, these have 

turned out to be high density storage media available for all platforms at very low prices (< $100 

at the bottom end). The storage of these drives is well over 500 MB. 

CE (Concurrent Engineering) - an engineering method that involves people from all stages of a product 

design, from marketing to shipping. 

CE - a mark placed on products to indicate that they conform to the standards set by the European Common 

Union. 

Celsius - a temperature scale the uses 0 as the freezing point of water and 100 as the boiling point. 

centrifugal force - the force on an orbiting object the would cause it to accelerate outwards. 

centripetal force - the force that must be applied to an orbiting object so that it will not fly outwards. 

channel - an independent signal pathway. 

character - a single byte, that when displayed is some recognizable form, such as a letter in the alphabet, or a 

punctuation mark. 

checksum - when many bytes of data are transmitted, a checksum can be used to check the validity of the 

data. It is commonly the numerical sum of all of the bytes transmitted. 

chip - a loose term for an integrated circuit. 

chromatography - gases or liquids can be analyzed by how far their constituent parts can migrate through a 

porous material. 

CIM (Computer Integrated Manufacturing) - computers can be used at a higher level to track and guide 

products as they move through the facility. CIM may or may not include CAD/CAM. 

CL (Cutter Location) - an APT program is converted into a set of x-y-z locations stored in a CL file. In turn 

these are sent to the NC machine via tapes, etc. 

clear - a signal or operation to reset data and status values. 

client-server - a networking model that describes network services, and user programs. 

clipping - the automatic cutting of lines that project outside the viewing area on a computer screen. 

clock - a signal from a digital oscillator. This is used to make all of the devices in a digital system work 

synchronously. 

clock speed - the rate at which a computers main time clock works at. The CPU instruction speed is usually 

some multiple or fraction of this number, but true program execution speeds are loosely related at 

best. 

closed loop - a system that measures system performance and trims the operation. This is also known as 

feedback. If there is no feedback the system is called open loop. 



CMOS (Complimentary Metal Oxide Semi-conductor) - a low power microchip technology that has high 

noise immunity. 

CNC (Computer Numerical Control) - machine tools are equipped with a control computer, and will perform 

a task. The most popular is milling. 

coalescing - a process for filtering liquids suspended in air. The liquid condenses on glass fibers. 

coaxial cable - a central wire contains a signal conductor, and an outer shield provides noise immunity. This 

configuration is limited by its coaxial geometry, but it provides very high noise immunity. 

coax - see coaxial cable. 

cogging - a machine steps through motions in a jerking manner. The result may be low frequency vibration. 

coil - wire wound into a coil (tightly packed helix) used to create electromagnetic attraction. Used in relays, 

motors, solenoids, etc. These are also used alone as inductors. 

collisions - when more than one network client tries to send a packet at any one time, they will collide. Both 

of the packets will be corrupted, and as a result special algorithms and hardware are used to abort 

the write, wait for a random time, and retry the transmission. Collisions are a good measure of 

network overuse. 

colorimetry - a method for identifying chemicals using their colors. 

combustion - a burning process generating heat and light when certain chemicals are added. 

command - a computer term for a function that has an immediate effect, such as listing the files in a 

directory. 

commision - the typical name for getting equipment operational after delivery/installation. 

communication - the transfer of data between computing systems. 

commutative laws - Booleans algebra laws A+B = B+A and AB=BA. 

compare - a computer program element that examines one or more variables, determines equality/inequality, 

and then performs some action, sometimes a branch. 

compatibility - a measure of the similarity of a design to a standard. This is often expressed as a percentage 

for software. Anything less than 100% is not desirable. 

compiler - a tool to change a high level language such as C into assembler. 

compliment - to take the logical negative. TRUE becomes false and vice versa. 

component - an interchangeable part of a larger system. Components can be used to cut down manufacturing 

and maintenance difficulties. 

compressor - a device that will decrease the volume of a gas - and increase the pressure. 

computer - a device constructed about a central instruction processor. In general the computer can be 

reconfigured (software/firmware/hardware) to perform alternate tasks. 

Computer Graphics - is the use of the computer to draw pictures using an input device to specify geometry 

and other attributes and an output device to display a picture. It allows engineers to communicate 

with the computer through geometry. 

concentric - a shared center between two or more objects. 

concurrent - two or more activities occur at the same time, but are not necessarily the same. 

concurrent engineering - all phases of the products life are considered during design, and not later during 

design review stages. 

condenser - a system component that will convert steam to water. Typically used in power generators. 

conduction - the transfer of energy through some medium. 

configuration - a numbers of multifunction components can be connected in a variety of configurations. 

connection - a network term for communication that involves first establishing a connection, second data 

transmission, and third closing the connection. Connectionless networking does not require 

connection. 

constant - a number with a value that should not vary. 

constraints - are performance variables with limits. Constraints are used to specify when a design is feasible. 

If constraints are not met, the design is not feasible. 

contact - 1. metal pieces that when touched will allow current to pass, when separated will stop the flow of 

current. 2. in PLCs contacts are two vertical lines that represent an input, or internal memory 

location. 

contactor - a high current relay. 

continuous Noise - a noise that is ongoing, and present. This differentiates from instantaneous, or 



intermittent noise sources. 

continuous Spectrum - a noise has a set of components that are evenly distributed on a spectral graph. 

control relay - a relay that does not control any external devices directly. It is used like a variable in a high 

level programming language. 

control variable - a system parameter that we can set to change the system operation. 

controls - a system that is attached to a process. Its purpose is to direct the process to some set value. 

convection - the transfer of heat energy to liquid or gas that is moving past the surface of an object. 

cook’s constant - another name for the fudge factor. 

core memory - an outdated term describing memory made using small torii that could be polarized 

magnetically to store data bits. The term lives on when describing some concepts, for example a 

‘core dump’ in UNIX. Believe it or not this has not been used for decades but still appears in 

many new textbooks. 

coriolis force - a force that tends to cause spinning in moving frames of reference. Consider the direction of 

the water swirl down a drain pipe, it changes from the north to the south of the earth. 

correction factor - a formal version of the ‘fudge factor’. Typically a value used to multiply or add another 

value to account for hard to quantify values. This is the friend of the factor of safety. 

counter - a system to count events. This can be either software or hardware. 

cps (characters per second) - This can be a good measure of printing or data transmission speed, but it is not 

commonly used, instead the more confusing ‘baud’ is preferred. 

CPU (Central Processing Unit) - the main computer element that examines machine code instructions and 

executes results. 

CRC (Cyclic Redundancy Check) - used to check transmitted blocks of data for validity. 

criteria - are performance variables used to measure the quality of a design. Criteria are usually defined in 

terms of degree - for example, lowest cost or smallest volume or lowest stress. Criteria are used to 

optimize a design. 

crosstalk - signals in one conductor induce signals in other conductors, possibly creating false signals. 

CRT (Cathode Ray Tubes) - are the display device of choice today. A CRT consists of a phosphor-coated 

screen and one or more electron guns to draw the screen image. 

crucible - 1. a vessel for holding high temperature materials 2. 

CSA (Canadian Standards Association) - an association that develops standards and does some product 

testing. 

CSMA/CD (Carrier Sense Multiple Access with Collision Detection) - a protocol that causes computers to 

use the same communication line by waiting for turns. This is used in networks such as Ethernet. 

CSNET (Computer+Science NETwork) - a large network that was merged with BITNET. 

CTS (Clear To Send) - used to prevent collisions in asynchronous serial communications. 

current loop - communications that use a full electronic loop to reduce the effects of induced noise. RS-422 

uses this. 

current rating - this is typically the maximum current that a designer should expect from a system, or the 

maximum current that an input will draw. Although some devices will continue to work outside 

rated values, not all will, and thus this limit should be observed in a robust system. Note: 

exceeding these limits is unsafe, and should be done only under proper engineering conditions. 

current sink - a device that allow current to flow through to ground when activated. 

current source - a device that provides current from another source when activated. 

cursors - are movable trackers on a computer screen which indicate the currently addressed screen position, 

or the focus of user input. The cursor is usually represented by an arrow, a flashing character or 

cross-hair. 

customer requirements - the qualitative and quantitative minimums and maximums specified by a customer. 

These drive the product design process. 

cycle - one period of a periodic function. 

cylinder - a piston will be driven in a cylinder for a variety of purposes. The cylinder guides the piston, and 

provides a seal between the front and rear of the piston. 



35.4 D 

daisy chain - allows serial communication of devices to transfer data through each (and every) device 

between two points. 

darlington coupled - two transistors are ganged together by connecting collectors to bases to increase the 

gain. These increase the input impedance, and reduce the back propagation of noise from loads. 

DARPA (Defense Advanced Research Projects Agency) - replaced ARPA. This is a branch of the US 

department of defence that has participated in a large number of research projects. 

data acquisition - refers to the automated collection of information collected from a process or system. 

data highway - a term for a communication bus between two separated computers, or peripherals. This term 

is mainly used for PLC’s. 

data link layer - an OSI model layer 

data logger - a dedicated system for data acquisition. 

data register - stores data values temporarily in a CPU. 

database - a software program that stores and recalls data in an organized way. 

DARPA (Defense Advanced Research Projects Agency) - 

DC (Direct Current) - a current that flows only in one direction. The alternative is AC. 

DCA (Defense Communications Agency) - developed DDN. 

DCD (Data Carrier Detect) - used as a handshake in asynchronous communication. 

DCE (Data Communications Equipment) - A term used when describing unintelligent serial 

communications clients. An example of this equipment is a modem. The complement to this is 

DTE. 

DCE (Distributed Computing Environment) - applications can be distributed over a number of computers 

because of the use of standards interfaces, functions, and procedures. 

DDN (Defense Data Network) - a group of DoD networks, including MILNET. 

dead band - a region for a device when it no longer operates. 

dead time - a delay between an event occurring and the resulting action. 

debounce - a switch may not make sudden and complete contact as it is closes, circuitry can be added to 

remove a few on-off transitions as the switch mechanically bounces. 

debug - after a program has been written it undergoes a testing stage called debugging that involves trying to 

locate and eliminate logic and other errors. This is also a time when most engineers deeply regret 

not spending more time on the initial design. 

decibel (dB) - a logarithmic compression of values that makes them more suited to human perception (for 

both scaleability and reference) 

decision support - the use of on-line data, and decision analysis tools are used when making decisions. One 

example is the selection of electronic components based on specifications, projected costs, etc. 

DECnet (Digital Equipment Corporation net) - a proprietary network architecture developed by DEC. 

decrement - to decrease a numeric value. 

dedicated computer - a computer with only one task. 

default - a standard condition. 

demorgan’s laws - Boolean laws great for simplifying equations ~(AB) = ~A + ~B, or ~(A+B) = ~A~B. 

density - a mass per unit volume. 

depth first search - an artificial intelligence technique that follows a single line of reasoning first. 

derivative control - a control technique that uses changes in the system of setpoint to drive the system. This 

control approach gives fast response to change. 

design - creation of a new part/product based on perceived needs. Design implies a few steps that are ill 

defined, but generally include, rough conceptual design, detailed design, analysis, redesign, and 

testing. 

design capture - the process of formally describing a design, either through drafted drawings, schematic 

drawings, etc. 

design cycle - the steps of the design. The use of the word cycle implies that it never ends, although we must 

at some point decide to release a design. 

design Variables - are the parameters in the design that describe the part. Design variables usually include 



geometric dimensions, material type, tolerances, and engineering notes. 

detector - a device to determine when a certain condition has been met. 

device driver - controls a hardware device with a piece of modular software. 

DFA (Design For Assembly) - a method that guides product design/redesign to ease assembly times and 

difficulties. 

DFT (Design for Testability) - a set of design axioms that generally calls for the reduction of test steps, with 

the greatest coverage for failure modes in each test step. 

diagnostic - a system or set of procedures that may be followed to identify where systems may have failed. 

These are most often done for mission critical systems, or industrial machines where the user may 

not have the technical capability to evaluate the system. 

diaphragm - used to separate two materials, while allowing pressure to be transmitted. 

differential - refers to a relative difference between two values. Also used to describe a calculus derivative 

operator. 

differential amplifier - an amplifier that will subtract two or more input voltages. 

diffuse field - multiple reflections result in a uniform and high sound pressure level. 

digital - a system based on binary on-off values. 

DIN (the Deutsches Institut for Normung) - a German standards institute. 

diode - a semiconductor device that will allow current to flow in one direction. 

DIP switches - small banks of switches designed to have the same footprint as an integrated circuit. 

distributed - suggests that computer programs are split into parts or functions and run on different computers 

distributed system - a system can be split into parts. Typical components split are mechanical, computer, 

sensors, software, etc. 

DLE (Data Link Escape) - An RS-232 communications interface line. 

DMA (Direct Memory Access) - used as a method of transferring memory in and out of a computer without 

slowing down the CPU. 

DNS (Domain Name System) - an internet method for name and address tracking. 

documentation - (don’t buy equipment without it) - one or more documents that instruct in the use, 

installation, setup, maintenance, troubleshooting, etc. for software or machinery. A poor design 

supported by good documentation can often be more useful than a good design unsupported by 

poor documentation. 

domain - the basic name for a small or large network. For example (unc.edu) is the general extension for the 

University on North Carolina. 

doppler shift - as objects move relative to each other, a frequency generated by one will be perceived at 

another frequency by the other. 

DOS (Disk Operating System) - the portion of an operating system that handles basic I/O operations. The 

most common example is Microsoft MS-DOS for IBM PCs. 

dotted decimal notation - the method for addressing computers on the internet with IP numbers such as 

‘129.100.100.13’. 

double pole - a double pole switch will allow connection between two contacts. These are useful when 

making motor reversers. see also single pole. 

double precision - a real number is represented with 8 bytes (single precision is 4) to give more precision for 

calculations. 

double throw - a switch or relay that has two sets of contacts. 

download - to retrieve a program from a server or higher level computer. 

downtime - a system is removed from production for a given amount of downtime. 

drag - a force that is the result of a motion of an object in a viscous fluid. 

drop - a term describing a short connection to peripheral I/O. 

drum sequencer - a drum has raised/lowered sections and as it rotates it opens/closes contacts and will give 

sequential operation. 

dry contact - an isolated output, often a relay switched output. 

DSP (Digital Signal Processor) - a medium complexity microcontroller that has a build in floating point unit. 

These are very common in devices such as modems. 

DSR (Data Set Ready) - used as a data handshake in asynchronous communications. 



DTE (Data Terminal Equipment) - a serial communication line used in RS-232 

DTR (Data Terminal Ready) - used as a data handshake in asynchronous communications to indicate a 

listener is ready to receive data. 

dump - a large block of memory is moved at once (as a sort of system snapshot). 

duplex - serial communication that is in both directions between computers at the same time. 

dynamic braking - a motor is used as a brake by connecting the windings to resistors. In effect the motor 

becomes a generator, and the resistors dissipate the energy as heat. 

dynamic variable - a variable with a value that is constantly changing. 

dyne - a unit of force 

35.5 E 

EBCDIC (Extended Binary-Coded Decimal Information Code) - a code for representing keyboard and 

control characters. 

eccentric - two or more objects do not have a common center. 

echo - a reflected sound wave. 

ECMA (European Computer Manufacturer’s Associated) - 

eddy currents - small currents that circulate in metals as currents flow in nearby conductors. Generally 

unwanted. 

EDIF (Electronic Design Interchange Format) - a standard to allow the interchange of graphics and data 

between computers so that it may be changed, and modifications tracked. 

EEPROM (Electrically Erasable Programmable Read Only Memory) - 

effective sound pressure - the RMS pressure value gives the effective sound value for fluctuating pressure 

values. This value is some fraction of the peak pressure value. 

EIA (Electronic Industries Association) - A common industry standards group focusing on electrical 

standards. 

electro-optic isolator - uses optical emitter, and photo sensitive switches for electrical isolation. 

electromagnetic - a broad range term reering to magnetic waves. This goes from low frequenc signals such 

as AM radio, up to very high frequency waves such as light and X-rays. 

electrostatic - devices that used trapped charge to apply forces and caused distribution. An example is 

droplets of paint that have been electrically charged can be caused to disperse evenly over a 

surface that is oppositely charged. 

electrostatics discharge - a sudden release of static electric charge (in nongrounded systems). This can lead 

to uncomfortable electrical shocks, or destruction of circuitry. 

email (electronic mail) - refers to messages passed between computers on networks, that are sent from one 

user to another. Almost any modern computer will support some for of email. 

EMI (ElectroMagnetic Interference) - transient magnetic fields cause noise in other systems. 

emulsify - to mix two materials that would not normally mix. for example an emulsifier can cause oil and 

water to mix. 

enable - a digital signal that allows a device to work. 

encoding - a conversion between different data forms. 

energize - to apply power to a circuit or component. 

energy - the result of work. This concept underlies all of engineering. Energy is shaped, directed and focused 

to perform tasks. 

engineering work stations - are self contained computer graphics systems with a local CPU which can be 

networked to larger computers if necessary. The engineering work station is capable of 

performing engineering synthesis, analysis, and optimization operations locally. Work stations 

typically have more than 1 MByte of RAM, and a high resolution screen greater than 512 by 512 

pixels. 

EOH (End of Header) - A code in a message header that marks the end of the header block. 

EOT (End Of Transmission) - an ASCII code to indicate the end of a communications. 



EPROM (Erasable Programmable Read Only Memory) - a memory type that can be programmed with 

voltages, and erased with ultraviolet light. 

EPS (Encapsulated PostScript) - a high quality graphics description language understood by high end 

printers. Originally developed by Adobe Systems Limited. This standard is becoming very 

popular. 

error signal - a control signal that is the difference between a desired and actual position. 

ESD - see electrostatic discharge. 

esters - a chemical that was formed by a reaction between alcohol and an acid. 

ETX (End Of Text) - a marker to indicate the end of a text block in data transmission. 

even parity - a checksum bit used to verify data in other bits of a byte. 

execution - when a computer is under the control of a program, the program is said to be executing. 

expansion principle - when heat is applied a liquid will expand. 

expert systems - is a branch of artificial intelligence designed to emulate human expertise with software. 

Expert systems are in use in many arenas and are beginning to be seen in CAD systems. These 

systems use rules derived from human experts. 

35.6 F 

fail safe - a design concept where system failure will bring the system to an idle or safe state. 

false - a logical negative, or zero. 

Faraday’s electromagnetic induction law - if a conductor moves through a magnetic field a current will be 

induced. The angle between the motion and the magnetic field needs to be 90 deg for maximum 

current. 

Farenheit - a temperature system that has 180 degrees between the freezing and boiling point of water. 

fatal error - an error so significant that a software/hardware cannot continue to operate in a reliable manner. 

fault - a small error that may be recoverable, or may result in a fatal error. 

FAX (facsimile) - an image is scanned and transmitted over phone lines and reconstructed at the other end. 

FCS (Frame Check Sequence) - data check flag for communications. 

FDDI (Fibre Distributed Data Interface) - a fibre optic token ring network scheme in which the control 

tokens are counter rotating. 

FDX (Full Duplex) - all characters that are transmitted are reflected back to the sender. 

FEA (Finite Element Analysis) - is a numerical technique in which the analysis of a complex part is 

subdivided into the analysis of small simple subdivisions. 

feedback - a common engineering term for a system that examines the output of a system and uses is to tune 

the system. Common forms are negative feedback to make systems stable, and positive feedback 

to make systems unstable (e.g. oscillators). 

fetch - when the CPU gets a data value from memory. 

fiberoptics - data can be transmitted by switching light on/off, and transmitting the signal through an optical 

fiber. This is becoming the method of choice for most long distance data lines because of the low 

losses and immunity to EMI. 

FIFO (First In First Out) - items are pushed on a stack. The items can then be pulled back off last first. 

file - a concept of a serial sequence of bytes that the computer can store information in, normally on the disk. 

This is a ubiquitous concept, but file is also used by Allen Bradley to describe an array of data. 

filter - a device that will selectively pass matter or energy. 

firmware - software stored on ROM (or equivalent). 

flag - a single binary bit that indicates that an event has/has not happened. 

flag - a single bit variable that is true or not. The concept is that if a flag is set, then some event has 

happened, or completed, and the flag should trigger some other event. 

flame - an email, or netnews item that is overtly critical of another user, or an opinion. These are common 

because of the ad-hoc nature of the networks. 

flange - a thick junction for joining two pipes. 



floating point - uses integer math to represent real numbers. 

flow chart - a schematic diagram for representing program flow. This can be used during design of software, 

or afterwards to explain its operation. 

flow meter - a device for measuring the flow rate of fluid. 

flow rate - the volume of fluid moving through an area in a fixed unit of time. 

fluorescence - incoming UV light or X-ray strike a material and cause the emission of a different frequency 

light. 

FM (Frequency Modulation) - transmits a signal using a carrier of constant magnitude but changing 

frequency. The frequency shift is proportional to the signal strength. 

force - a PLC output or input value can be set on artificially to test programs or hardware. This method is not 

suggested. 

format - 1. a physical and/or data structure that makes data rereadable, 2. the process of putting a structure 

on a disk or other media. 

forward chaining - an expert system approach to examine a set of facts and reason about the probable 

outcome. 

fragmentation - the splitting of an network data packet into smaller fragments to ease transmission. 

frame buffers - store the raster image in memory locations for each pixel. The number of colors or shades of 

gray for each pixel is determined by the number of bits of information for each pixel in the frame 

buffer. 

free field - a sound field where none of the sound energy is reflected. Generally there aren’t any nearby 

walls, or they are covered with sound absorbing materials. 

frequency - the number of cycles per second for a sinusoidally oscillating vibration/sound. 

friction - the force resulting from the mechanical contact between two masses. 

FSK (Frequency Shift Keying) - uses two different frequencies, shifting back and forth to transmit bits 

serially. 

FTP (File Transfer Protocol) - a popular internet protocol for moving files between computers. 

fudge factor - a number that is used to multiply or add to other values to make the experimental and 

theoretical values agree. 

full duplex - a two way serial communication channel can carry information both ways, and each character 

that is sent is reflected back to the sender for verification. 

fuse - a device that will destruct when excessive current flows. It is used to protect the electrical device, 

humans, and other devices when abnormally high currents are drawn. Note: fuses are essential 

devices and should never be bypassed, or replaced with fuses having higher current rating. 

35.7 G 

galvonometer - a simple device used to measure currents. This device is similar to a simple DC motor. 

gamma rays - high energy electromagnetic waves resulting from atomic fission or fusion. 

gate - 1. a circuit that performs on of the Boolean algebra function (i.e., and, or, not, etc.) 2. a connection 

between a runner and a part, this can be seen on most injection molded parts as a small bump 

where the material entered the main mold cavity. 

gateway - translates and routes packets between dissimilar networks. 

Geiger-Mueller tube - a device that can detect ionizing particles (eg, atomic radiation) using a gas filled 

tube. 

global optimum - the absolute best solution to a problem. When found mathematically, the maximum or 

minimum cost/utility has been obtained. 

gpm (gallons per minute) - a flow rate. 

grafcet - a method for programming PLCs that is based on Petri nets. This is now known as SFCs and is part 

of the IEC 1131-3 standard. 

gray code - a modified binary code used for noisy environments. It is devised to only have one bit change at 

any time. Errors then become extremely obvious when counting up or down. 



ground - a buried conductor that acts to pull system neutral voltage values to a safe and common level. All 

electrical equipment should be connected to ground for safety purposes. 

GUI (Graphical User Interface) - the user interacts with a program through a graphical display, often using a 

mouse. This technology replaces the older systems that use menus to allow the user to select 

actions. 

35.8 H 

half cell - a probe that will generate a voltage proportional to the hydrogen content in a solution. 

half duplex - see HDX 

handshake - electrical lines used to establish and control communications. 

hard copy - a paper based printout. 

hardware - a mechanical or electrical system. The ‘functionality’ is ‘frozen’ in hardware, and often difficult 

to change. 

HDLC (High-level Data Link Control) - an ISO standard for communications. 

HDX (Half Duplex) - a two way serial connection between two computer. Unlike FDX, characters that are 

sent are not reflected back to the sender. 

head - pressure in a liquid that is the result of gravity. 

hermetic seal - an airtight seal. 

hertz - a measure of frequency in cycles per second. The unit is Hz. 

hex - see hexadecimal. 

hexadecimal - a base 16 number system where the digits are 0 to 9 then A to F, to give a total of 16 digits. 

This is commonly used when providing numbers to computers. 

high - another term used to describe a Boolean true, logical positive, or one. 

high level language - a language that uses very powerful commands to increase programming productivity. 

These days almost all applications use some form of high level language (i.e., basic, fortran, 

pascal, C, C++, etc.). 

horsepower - a unit for measuring power 

host - a networked (fully functional) computer. 

hot backup - a system on-line that can quickly replace a failed system. 

hydraulic - 1. a study of water 2. systems that use fluids to transmit power. 

hydrocarbon - a class of molecules that contain carbon and hydrogen. Examples are propane, octane. 

hysteresis - a sticking or lagging phenomenon that occurs in many systems. For example, in magnetic 

systems this is a small amount of magnetic repolarization in a reversing field, and in friction this 

is an effect based on coulomb friction that reverses sticking force. 

Hz - see hertz 

35.9 I 

IAB (internet Activities Board) - the developer of internet standards. 

IC (Integrated Circuit) - a microscopic circuit placed on a thin wafer of semiconductor. 

IEC (International Electrical Commission) - A Swiss electrical standards group. 

IEEE (Institute of Electrical and Electronics Engineers) - 

IEEE802 - a set of standards for LANs and MANs. 

IGES (Initial Graphics Exchange Specification) - a standard for moving data between various CAD systems. 

In particular the format can handle basic geometric entities, such as NURBS, but it is expected to 

be replaced by PDES/STEP in the near future. 

impact instrument - measurements are made based by striking an object. This generally creates an impulse 



function. 

impedance - In electrical systems this is both reactive and real resistance combined. This also applies to 

power transmission and flows in other types of systems. 

impulse Noise - a short duration, high intensity noise. This type of noise is often associated with explosions. 

increment - increase a numeric value. 

inductance - current flowing through a coil will store energy in a magnetic field. 

inductive heating - a metal part is placed inside a coil. A high frequency AC signal is passed through the coil 

and the resulting magnetic field melts the metal. 

infrared - light that has a frequency below the visible spectrum. 

inertia - a property where stored energy will keep something in motion unless there is energy added or 

released. 

inference - to make a decision using indirect logic. For example if you are wearing shoes, we can infer that 

you had to put them on. Deduction is the complementary concept. 

inference engine - the part of an expert system that processes rules and facts using forward or backward 

chaining. 

Insertion Loss - barriers, hoods, enclosures, etc. can be placed between a sound source, and listener, their 

presence increases reverberant sound levels and decreases direct sound energy. The increase in 

the reverberant sound is the insertion loss. 

instruction set - a list of all of the commands that available in a programmable system. This could be a list of 

PLC programming mnemonics, or a list of all of the commands in BASIC. 

instrument - a device that will read values from external sensors or probes, and might make control decision. 

intake stroke - in a piston cylinder arrangement this is the cycle where gas or liquid is drawn into the 

cylinder. 

integral control - a control method that looks at the system error over a long period of time. These controllers 

are relatively immune to noise and reduce the steady state error, but the do not respond quickly. 

integrate - to combine two components with clearly separable functions to obtain a new single component 

capable of more complex functions. 

intelligence - systems will often be able to do simple reasoning or adapt. This can mimic some aspects of 

human intelligence. These techiques are known as artificial intelligence. 

intelligent device - a device that contains some ability to control itself. This reduces the number of tasks that 

a main computer must perform. This is a form of distributed system. 

interface - a connection between a computer and another electrical device, or the real world. 

interlock - a device that will inhibit system operation until certain cnditions are met. These are often required 

for safety on industrial equipment to protect workers. 

intermittent noise - when sounds change level fluctuate significantly over a measurement time period. 

internet - an ad-hoc collection of networks that has evolved over a number of years to now include millions 

of computers in every continent, and by now every country. This network will continue to be the 

defacto standard for personal users. (commentary: The information revolution has begun already, 

and the internet has played a role previously unheard of by overcoming censorship and 

misinformation, such as that of Intel about the Pentium bug, a military coup in Russia failed 

because they were not able to cut off the flow of information via the internet, the Tianneman 

square massacre and related events were widely reported via internet, etc. The last stage to a 

popular acceptance of the internet will be the World Wide Web accessed via Mosiac/Netscape.) 

internet address - the unique identifier assigned to each machine on the internet. The address is a 32 bit 

binary identifier commonly described with the dotted decimal notation. 

interlacing - is a technique for saving memory and time in displaying a raster image. Each pass alternately 

displays the odd and then the even raster lines. In order to save memory, the odd and even lines 

may also contain the same information. 

interlock - a flag that ensures that concurrent streams of execution do not conflict, or that they cooperate. 

interpreter - programs that are not converted to machine language, but slowly examined one instruction at a 

time as they are executed. 

interrupt - a computer mechanism for temporarily stopping a program, and running another. 

inverter - a logic gate that will reverse logic levels from TRUE to/from FALSE. 

I/O (Input/Output) - a term describing anything that goes into or out of a computer. 



IOR (Inclusive OR) - a normal OR that will be true when any of the inputs are true in any combinations. also 

see Exclusive OR (EOR). 

ion - an atom, molecule or subatomic particle that has a positive or negative charge. 

IP (internet Protocol) - the network layer (OSI model) definitions that allow internet use. 

IP datagram - a standard unit of information on the internet. 

ISDN (Integrated Services Digital Network) - a combined protocol to carry voice, data and video over 56KB 

lines. 

ISO (International Standards Organization) - a group that develops international standards in a wide variety 

of areas. 

isolation - electrically isolated systems have no direct connection between two halves of the isolating device. 

Sound isolation uses barriers to physically separate rooms. 

isolation transformer - a transformer for isolating AC systems to reduce electrical noise. 

35.10 J 

JEC (Japanese Electrotechnical Committee) - A regional standards group. 

JIC (Joint International Congress) - an international standards group that focuses on electrical standards. 

They drafted the relay logic standards. 

JIT (Just in Time) - a philosophy when setting up and operating a manufacturing system such that materials 

required arrive at the worksite just in time to be used. This cuts work in process, storage space, 

and a number of other logistical problems, but requires very dependable supplies and methods. 

jog - a mode where a motor will be advanced while a button is held, but not latched on. It is often used for 

clearing jams, and loading new material. 

jump - a forced branch in a program 

jumper - a short wire, or connector to make a permanent setting of hardware parameters. 

35.11 K 

k, K - specifies magnitudes. 1K = 1024, 1k = 1000 for computers, otherwise 1K = 1k = 1000. Note - this is 

not universal, so double check the meanings when presented. 

Kelvin - temperature units that place 0 degrees at absolute zero. The magnitude of one degree is the same as 

the Celsius scale. 

KiloBaud, KBaud, KB, Baud - a transmission rate for serial communications (e.g. RS-232C, TTY, RS-422). 

A baud = 1bit/second, 1 Kilobaud = 1KBaud = 1KB = 1000 bits/second. In serial communication 

each byte typically requires 11 bits, so the transmission rate is about 1Kbaud/11 = 91 Bytes per 

second when using a 1KB transmission. 

Karnaugh maps - a method of graphically simplifying logic. 

kermit - a popular tool for transmitting binary and text files over text oriented connections, such as modems 

or telnet sessions. 

keying - small tabs, prongs, or fillers are used to stop connectors from mating when they are improperly 

oriented. 

kinematics/kinetics - is the measure of motion and forces of an object. This analysis is used to measure the 

performance of objects under load and/or in motion. 



35.12 L 

label - a name associated with some point in a program to be used by branch instructions. 

ladder diagram - a form of circuit diagram normally used for electrical control systems. 

ladder logic - a programming language for PLCs that has been developed to look like relay diagrams from 

the preceding technology of relay based controls. 

laminar flow - all of the particles of a fluid or gas are travelling in parallel. The complement to this is 

turbulent flow. 

laptop - a small computer that can be used on your lap. It contains a monitor ad keyboard. 

LAN (Local Area Network) - a network that is typically less than 1km in distance. Transmission rates tend 

to be high, and costs tend to be low. 

latch - an element that can have a certain input or output lock in. In PLCs these can hold an output on after 

an initial pulse, such as a stop button. 

LCD (Liquid Crystal Display) - a fluid between two sheets of light can be polarized to block light. These are 

commonly used in low power displays, but they require backlighting. 

leakage current - a small amount of current that will be present when a device is off. 

LED (Light Emitting Diode) - a semiconductor light that is based on a diode. 

LIFO (Last In First Out) - similar to FIFO, but the last item pushed onto the stack is the first pulled off. 

limit switch - a mechanical switch actuated by motion in a process. 

line printer - an old printer style that prints single lines of text. Most people will be familiar with dot matrix 

style of line printers. 

linear - describes a mathematical characteristic of a system where the differential equations are simple linear 

equations with coefficients. 

little-endian - transmission or storage of data when the least significant byte/bit comes first. 

load - In electrical system a load is an output that draws current and consumes power. In mechanical systems 

it is a mass, or a device that consumes power, such as a turbine. 

load cell - a device for measuring large forces. 

logic - 1. the ability to make decisions based on given values. 2. digital circuitry. 

loop - part of a program that is executed repeatedly, or a cable that connects back to itself. 

low - a logic negative, or zero. 

LRC (Linear Redundancy Check) - a block check character 

LSB (Least Significant Bit) - This is the bit with the smallest value in a binary number. for example if the 

number 10 is converted to binary the result is 1010. The most significant bit is on the left side, 

with a value of 8, and the least significant bit is on the right with a value of 1 - but it is not set in 

this example. 

LSD (Least Significant Digit) - This is the least significant digit in a number, found on the right side of a 

number when written out. For example, in the number $1,234,567 the digit 7 is the least 

significant. 

LSI (Large Scale Integration) - an integrated circuit that contains thousands of elements. 

LVDT (Linear Variable Differential Transformer) - a device that can detect linear displacement of a central 

sliding core in the transformer. 

35.13 M 

machine language - CPU instructions in numerical form. 

macro - a set of commands grouped for convenience. 

magnetic field - a field near flowing electrons that will induce other electrons nearby to flow in the opposite 

direction. 

MAN (Metropolitan Area Network) - a network designed for municipal scale connections. 

manifold - 1. a connectors that splits the flow of fluid or gas. These are used commonly in hydraulic and 



pneumatic systems. 2. a description for a geometry that does not have any infinitely small points 

or lines of contact or separation. Most solid modelers deal only with manifold geometry. 

MAP (Manufacturers Automation Protocol) - a network type designed for the factory floor that was widely 

promoted in the 1980s, but was never widely implemented due to high costs and complexity. 

mask - one binary word (or byte, etc) is used to block out, or add in digits to another binary number. 

mass flow rate - instead of measuring flow in terms of volume per unit of time we use mass per unit time. 

mass spectrometer - an instrument that identifies materials and relative proportions at the atomic level. This 

is done by observing their deflection as passed through a magnetic field. 

master/slave - a control scheme where one computer will control one or more slaves. This scheme is used in 

interfaces such as GPIB, but is increasingly being replaced with peer-to-peer and client/server 

networks. 

mathematical models - of an object or system predict the performance variable values based upon certain 

input conditions. Mathematical models are used during analysis and optimization procedures. 

matrix - an array of numbers 

MB MByte, KB, KByte - a unit of memory commonly used for computers. 1 KiloByte = 1 KByte = 1 KB = 

1024 bytes. 1 MegaByte = 1 MByte = 1MB = 1024*1024 bytes. 

MCR (Master Control Relay) - a relay that will shut down all power to a system. 

memory - binary numbers are often stored in memory for fast recall by computers. Inexpensive memory can 

be purchased in a wide variety of configurations, and is often directly connected to the CPU. 

memory - memory stores binary (0,1) patterns that a computer can read or write as program or data. Various 

types of memories can only be read, some memories lose their contents when power is off. 

RAM (Random Access Memory) - can be written to and read from quickly. 

It requires power to preserve the contents, and is often coupled with a 

battery or capacitor when long term storage is required. Storage available 

is over 1MByte 

ROM (Read Only Memory) - Programs and data are permanently written 

on this low cost ship. Storage available is over 1 MByte. 

EPROM (ELECTRICALLY Programmable Read Only Memory) - A program 

can be written to this memory using a special programmer, and 

erased with ultraviolet light. Storage available over 1MByte. After a program 

is written, it does not require power for storage. These chips have 

small windows for ultraviolet light. 

EEPROM/E2PROM (Electronically Erasable Programmable Read Only 

Memory) - These chips can be erased and programmed while in use with 

a computer, and store memory that is not sensitive to power. These can 

be slower, more expensive and with lower capacity (measured in Kbytes) 

than other memories. But, their permanent storage allows system configurations/data 

to be stored indefinitely after a computer is turned off. 

memory map - a listing of the addresses of different locations in a computer memory. Very useful when 

programming. 

menu - a multiple choice method of selecting program options. 

message - a short sequence of data passed between processes. 

microbar - a pressure unit (1 dyne per sq. cm) 

microphone - an audio transducer (sensor) used for sound measurements. 

microprocessor - the central control chip in a computer. This chip will execute program instructions to direct 

the computer. 

MILNET (MILitary NETwork) - began as part of ARPANET. 

MMI (Man Machine Interface) - a user interface terminal. 

mnemonic - a few characters that describe an operation. These allow a user to write programs in an intuitive 

manner, and have them easily converted to CPU instructions. 

MODEM (MOdulator/DEModulator) - a device for bidirectional serial communications over phone lines, 



etc. 

module - a part o a larger system that can be interchanged with others. 

monitor - an operation mode where the compuer can be watched in detail from step to step. This can also 

refer to a computer screen. 

motion detect flow meter - a fluid flow induces measurement. 

MRP (Material Requirements Planning) - a method for matching material required by jobs, to the equipment 

available in the factory. 

MSD (Most Significant Digit) - the larget valued digit in a number (eg. 6 is the MSD in 63422). This is often 

used for binary numbers. 

MTBF (Mean Time Between Failure) - the average time (hours usually) between the last repair of a product, 

and the next expected failure. 

MTTR (Mean Time To Repair) - The average time that a device will out of use after failure before it is 

repaired. This is related to the MTBF. 

multicast - a broadcast to some, but not necessarily all, hosts on a network. 

multiplexing - a way to efficiently use transmission media by having many signals run through one 

conductor, or one signal split to run through multiple conductors and rejoined at the receiving 

end. 

multiprocessor - a computer or system that uses more than one computer. Normally this term means a single 

computer with more than one CPU. This scheme can be used to increase processing speed, or 

increase reliability. 

multivibrator - a digital oscillator producing square or rectangular waveforms. 

35.14 N 

NAK (Negative AKnowledgement) - an ASCII control code. 

NAMUR - A european standards organization. 

NAND (Not AND) - a Boolean AND operation with the result inverted. 

narrowband - uses a small data transmission rate to reduce spectral requirements. 

NC - see normally opened/closed 

NC (Numerical Control) - a method for controlling machine tools, such as mills, using simple programs. 

negative logic - a 0 is a high voltage, and 1 is a low voltage. In Boolean terms it is a duality. 

NEMA (National Electrical Manufacturers Association) - this group publishes numerous standards for 

electrical equipment. 

nephelometry - a technique for determining the amount of solids suspended in water using light. 

nesting - a term that describes loops (such as FOR-NEXT loops) within loops in programs. 

network - a connection of typically more than two computers so that data, email, messages, resources and 

files may be shared. The term network implies, software, hardware, wires, etc. 

NFS (Network File System) - a protocol developed by Sun Microsystems to allow dissimilar computers to 

share files. The effect is that the various mounted remote disk drives act as a single local disk. 

NIC (Network Interace Card) - a computer card that allows a computer to communicate on a network, such 

as ethernet. 

NIH (Not Invented Here) - a short-lived and expensive corporate philosophy in which employees believe 

that if idea or technology was not developed in-house, it is somehow inferior. 

NIST (National Institute of Standards and Technology) - formerly NBS. 

NO - see normally opened 

node - one computer connected to a network. 

noise - 1. electrical noise is generated mainly by magnetic fields (also electric fields) that induce currents 

and voltages in other conductors, thereby decreasing the signals present. 2. a sound of high 

intensity that can be perceived by the human ear. 

non-fatal error - a minor error that might indicate a problem, but it does not seriously interfere with the 

program execution. 



nonpositive displacement pump - a pump that does not displace a fixed volume of fluid or gas. 

nonretentive - when power is lost values will be set back to 0. 

NOR (Not OR) - a Boolean function OR that has the results negated. 

normally opened/closed - refers to switch types. when in their normal states (not actuated) the normally open 

(NO) switch will not conduct current. When not actuated the normally closed (NC) switch will 

conduct current. 

NOT - a Boolean function that inverts values. A 1 will become a 0, and a 0 will become a 1. 

NOVRAM (NOn Volatile Random Access Memory) - memory that does not lose its contents when turned 

off. 

NPN - a bipolar junction transistor type. When referring to switching, these can be used to sink current to 

ground. 

NPSM - American national standard straight pipe thread for mechanical parts. 

NPT - American national standard taper pipe thread. 

NSF (National Science Foundation) - a large funder of science projects in USA. 

NSFNET (National Science Foundation NETwork) - funded a large network(s) in USA, including a high 

speed backbone, and connection to a number of super computers. 

NTSC (National Television Standards Committee) - a Red-Green-Blue based transmission standard for 

video, and audio signals. Very popular in North America, Competes with other standards 

internationally, such as PAL. 

null modem - a cable that connects two RS-232C devices. 

35.15 O 

OCR (Optical Character Recognition) - Images of text are scanned in, and the computer will try to interpret 

it, much as a human who is reading a page would. These systems are not perfect, and often rely 

on spell checkers, and other tricks to achieve reliabilities up to 99% 

octal - a base 8 numbering system that uses the digits 0 to 7. 

Octave - a doubling of frequency 

odd parity - a bit is set during communication to indicate when the data should have an odd number of bits. 

OEM (Original Equipment Manufacturer) - a term for a manufacturer that builds equipment for consumers, 

but uses major components from other manufacturers. 

off-line - two devices are connected, but not communicating. 

offset - a value is shifted away or towards some target value. 

one-shot - a switch that will turn on for one cycle. 

on-line - two devices are put into communications, and will stay in constant contact to pass information as 

required. 

opcode (operation code) - a single computer instruction. Typically followed by one or more operands. 

open collector - this refers to using transistors for current sourcing or sicking. 

open loop - a system that does monitor the result. open loop control systems are common when the process 

is well behaved. 

open-system - a computer architecture designed to encourage interconnection between various vendors 

hardware and software. 

operand - an operation has an argument (operand) with the mnemonic command. 

operating system - software that existing on a computer to allow a user to load/execute/develop their own 

programs, to interact with peripherals, etc. Good examples of this is UNIX, MS-DOS, OS/2. 

optimization - occurs after synthesis and after a satisfactory design is created. The design is optimized by 

iteratively proposing a design and using calculated design criteria to propose a better design. 

optoisolators - devices that use a light emitter to control a photoswitch. The effect is that inputs and outputs 

are electrically separate, but connected. These are of particular interest when an interface between 

very noisy environments are required. 

OR - the Boolean OR function. 



orifice - a small hole. Typically this is places in a fluid/gas flow to create a pressure difference and slow the 

flow. It will increase the flow resistance in the system. 

oscillator - a device that produces a sinusoidal output. 

oscilloscope - a device that can read and display voltages as a function for time. 

OSF (Open Software Foundation) - a consortium of large corporations (IBM, DEC, HP) that are promoting 

DCE. They have put forth a number of popular standards, such as the Motif Widget set for X- 

Windows programming. 

OSHA (Occupational safety and Health Act) - these direct what is safe in industrial and commercial 

operations. 

OSI (Open System Interconnect) - an international standards program to promote computer connectivity, 

regardless of computer type, or manufacturer. 

overshoot - the inertia of a controlled system will cause it to pass a target value and then return. 

overflow - the result of a mathematical operation passes by the numerical limitations of the hardware logic, 

or algorithm. 

35.16 P 

parallel communication - bits are passed in parallel conductors, thus increasing the transmission rates 

dramatically. 

parallel design process - evaluates all aspects of the design simultaneously in each iteration. The design 

itself is sent to all analysis modules including manufacturability, inspectibility, and engineering 

analysis modules; redesign decisions are based on all results at once. 

parallel programs - theoretically, these computer programs do more than one thing simultaneously. 

parity - a parity bit is often added to bytes for error detection purposes. The two typical parity methods are 

even and odd. Even parity bits are set when an even number of bits are present in the transmitted 

data (often 1 byte = 8 bits). 

particle velocity - the instantaneous velocity of a single molecule. 

Pascal - a basic unit of pressure 

Pascal’s law - any force applied to a fluid will be transmitted through the fluid and act on all enclosing 

surfaces. 

PC (Programmable Controller) - also called PLC. 

PCB (Printed Circuit Board) - alternate layers of insulating materials, with wire layout patterns are built up 

(sometimes with several layers). Holes thought the layers are used to connect the conductors to 

each other, and components inserted into the boards and soldered in place. 

PDES (Product Data Exchange using Step) - a new product design method that has attempted to include all 

needed information for all stages of a products life, including full solids modeling, tolerances, etc. 

peak level - the maximum pressure level for a cyclic variation 

peak-to-peak - the distance between the top and bottom of a sinusoidal variation. 

peer-to-peer - a communications form where connected devices to both read and write messages at any time. 

This is opposed to a master slave arrangement. 

performance variables - are parameters which define the operation of the part. Performance variables are 

used by the designer to measure whether the part will perform satisfactorily. 

period - the time for a repeating pattern to go from beginning to end. 

peripheral - devices added to computers for additional I/O. 

permanent magnet - a magnet that retains a magnetic field when the original magnetizing force is removed. 

petri-net - an enhanced state space diagram that allows concurrent execution flows. 

pH - a scale for determining is a solution is an acid or a base. 0-7 is acid, 7-4 is a base. 

photocell - a device that will convert photons to electrical energy. 

photoconductive cell - a device that has a resistance that will change as the number of incident photons 

changes. 

photoelectric cell - a device that will convert photons to electrical energy. 



photon - a single unit of light. Light is electromagnetic energy emitted as an electron orbit decays. 

physical layer - an OSI network model layer. 

PID (Proportional Integral Derivative) - a linear feedback control scheme that has gained popularity because 

of it’s relative simplicity. 

piezoelectric - a material (crystals/ceramics) that will generate a charge when a force is applied. A common 

transducer material. 

ping - an internet utility that makes a simple connection to a remote machine to see if it is reachable, and if it 

is operating. 

pink noise - noise that has the same amount of energy for each octave. 

piston - it will move inside a cylinder to convert a pressure to a mechanical motion or vice versa. 

pitch - a perceptual term for describing frequency. Low pitch means low frequency, high pitch means a 

higher frequency. 

pitot tube - a tube that is placed in a flow stream to measure flow pressure. 

pixels - are picture elements in a digitally generated and displayed picture. A pixel is the smallest 

addressable dot on the display device. 

PLA (Programmable Logic Array) - an integrated circuit that can be programmed to perform different logic 

functions. 

plane sound wave - the sound wave lies on a plane, not on a sphere. 

PLC (Programmable Logic Controller) - A rugged computer designs for control on the factory floor. 

pneumatics - a technique for control and actuation that uses air or gases. 

PNP - a bipolar junction transistor type. When referring to switching, these can be used to source current 

from a voltage source. 

poise - a unit of dynamic viscosity. 

polling - various inputs are checked in sequence for waiting inputs. 

port - 1. an undedicated connector that peripherals may be connected to. 2. a definable connection number 

for a machine, or a predefined value. 

positive displacement pump - a pump that displaces a fixed volume of fluid. 

positive logic - the normal method for logic implementation where 1 is a high voltage, and 0 is a low 

voltage. 

potentiometer - displacement or rotation is measured by a change in resistance. 

potting - a process where an area is filled with a material to seal it. An example is a sensor that is filled with 

epoxy to protect it from humidity. 

power level - the power of a sound, relative to a reference level 

power rating - this is generally the maximum power that a device can supply, or that it will require. Never 

exceed these values, as they may result in damaged equipment, fires, etc. 

power supply - a device that converts power to a usable form. A typical type uses 115Vac and outputs a DC 

voltage to be used by circuitry. 

PPP (Point-to-Point Protocol) - allows router to router or host to network connections over other 

synchronous and asynchronous connections. For example a modem connection can be used to 

connect to the internet using PPP. 

presentation layer - an OSI network model layer. 

pressure - a force that is distributed over some area. This can be applied to solids and gases. 

pressure based flow meter - uses difference in fluid pressures to measure speeds. 

pressure switch - activated above/below a preset pressure level. 

prioritized control - control operations are chosen on the basic of priorities. 

procedural language - a computer language where instructions happen one after the other in a clear 

sequence. 

process - a purposeful set of steps for some purpose. In engineering a process is often a machine, but not 

necessarily. 

processor - a loose term for the CPU. 

program - a sequential set of computer instructions designed to perform some task. 

programmable controller - another name for a PLC, it can also refer to a dedicated controller that uses a 

custom programming language. 

PROM (Programmable Read Only Memory) - 



protocol - conventions for communication to ensure compatibility between separated computers. 

proximity sensor - a sensor that will detect the presence of a mass nearby without contact. These use a 

variety of physical techniques including capacitance and inductance. 

pull-up resistor - this is used to normally pull a voltage on a line to a positive value. A switch/circuit can be 

used to pull it low. This is commonly needed in CMOS devices. 

pulse - a brief change in a digital signal. 

purge bubbling - a test to determine the pressure needed to force a gas into a liquid. 

PVC - poly vinyl chloride - a tough plastic commonly used in electrical and other applications. 

pyrometer - a device for measuring temperature 

35.17 Q 

QA (Quality Assurance) - a formal system that has been developed to improve the quality of a product. 

QFD (Quality Functional Deployment) - a matrix based method that focuses the designers on the significant 

design problems. 

quality - a measure of how well a product meets its specifications. Keep in mind that a product that exceeds 

its specifications may not be higher quality. 

quality circles - a team from all levels of a company that meets to discuss quality improvement. Each 

members is expected to bring their own perspective to the meeting. 

35.18 R 

rack - a housing for holding electronics modules/cards. 

rack fault - cards in racks often have error indicator lights that turn on when a fault has occurred. This allows 

fast replacement. 

radar () - radio waves are transmitted and reflected. The time between emission and detection determines the 

distance to an object. 

radiation - the transfer of energy or small particles (e.g., neutrons) directly through space. 

radiation pyrometry - a technique for measuring temperature by detecting radiated heat. 

radix - the base value of a numbering system. For example the radix of binary is 2. 

RAID (Redundant Array of Inexpensive Disks) - a method for robust disk storage that would allow removal 

of any disk drive without the interruption of service, or loss of data. 

RAM (Random Access Memory) - Computer memory that can be read from, and written to. This memory is 

the main memory type in computers. The most common types are volatile - they lose their 

contents when power is removed. 

random noise - there are no periodic waveforms, frequency and magnitude vary randomly. 

random-scan devices - draw an image by refreshing one line or vector at a time; hence they are also called 

vector-scan or calligraphic devices. The image is subjected to flicker if there are more lines in the 

scene that can be refreshed at the refresh rate. 

Rankine - A temperature system that uses absolute 0 as the base, and the scale is the same as the Fahrenheit 

scale. 

raster devices - process pictures in parallel line scans. The picture is created by determining parts of the 

scene on each scan line and painting the picture in scan-line order, usually from top to bottom. 

Raster devices are not subject to flicker because they always scan the complete display on each 

refresh, independent of the number of lines in the scene. 

rated - this will be used with other terms to indicate suggested target/maximum/minimum values for 

successful and safe operation. 

RBOC (Regional Bell Operating Company) - A regional telephone company. These were originally created 



after a US federal court split up the phone company into smaller units. 

Read/Write (R/W) - a digital device that can store and retrieve data, such as RAM. 

reagent - an chemical used in one or more chemical reactions. these are often used for identifying other 

chemicals. 

real-time - suggests a system must be able to respond to events that are occurring outside the computer in a 

reasonable amount of time. 

reciprocating - an oscillating linear motion. 

redundancy - 1. added data for checking accuracy. 2. extra system components or mechanisms added to 

decrease the chance of total system failure. 

refreshing - is required of a computer screen to maintain the screen image. Phosphors, which glow to show 

the image, decay at a fast rate, requiring the screen to be redrawn or refreshed several times a 

second to prevent the image from fading. 

regenerative braking - the motor windings are reverse, and in effect return power to the power source. This is 

highly efficient when done properly. 

register - a high speed storage area that can typically store a binary word for fast calculation. Registers are 

often part of the CPU. 

regulator - a device to maintain power output conditions (such as voltage) regardless of the load. 

relay - an electrical switch that comes in may different forms. The switch is activated by a magnetic coil that 

causes the switch to open or close. 

relay - a magnetic coil driven switch. The input goes to a coil. When power is applied, the coil generates a 

magnetic field, and pulls a metal contact, overcoming a spring, and making contact with a 

terminal. The contact and terminal are separately wired to provide an output that is isolated from 

the input. 

reliability - the probability of failure of a device. 

relief valve - designed to open when a pressure is exceeded. In a hydraulic system this will dump fluid back 

in the reservoir and keep the system pressure constant. 

repeatability - the ability of a system to return to the same value time after time. This can be measured with 

a standard deviation. 

repeater - added into networks to boost signals, or reduce noise problems. In effect one can be added to the 

end of one wire, and by repeating the signals into another network, the second network wire has a 

full strength signal. 

reset - a signal to computers that restarts the processor. 

resistance - this is a measurable resistance to energy or mass transfer. 

resistance heating - heat is generated by passing a current through a resistive material. 

resolution - the smallest division or feature size in a system. 

resonant frequency - the frequency at which the material will have the greatest response to an applied 

vibration or signal. This will often be the most likely frequency of self destruction. 

response time - the time required for a system to respond to a directed change. 

return - at the end of a subroutine, or interrupt, the program execution will return to where it branched. 

reverberation - when a sound wave hits a surface, part is reflected, and part is absorbed. The reflected part 

will add to the general (reverberant) sound levels in the room. 

Reynolds number - a dimensionless flow value based on fluid density and viscosity, flow rate and pipe 

diameter. 

RF (Radio Frequency) - the frequency at which a magnetic field oscillates when it is used to transmit a 

signal. Normally this range is from about 1MHz up to the GHz. 

RFI (Radio Frequency Interference) - radio and other changing magnetic fields can generate unwanted 

currents (and voltages) in wires. The resulting currents and voltages can interfere with the normal 

operation of an electrical device. Filters are often used to block these signals. 

RFS (Remote File System) - allows shared file systems (similar to NFS), and has been developed for System 

V UNIX. 

RGB (Red Green Blue) - three additive colors that can be used to simulate the other colors of the spectrum. 

This is the most popular scheme for specifying colors on computers. The alternate is to use Cyan- 

Magenta-Yellow for the subtractive color scheme. 

ripple voltage - when an AC voltage is converted to DC it is passed through diodes that rectify it, and then 



through capacitors that smooth it out. A small ripple still remains. 

RISC (Reduced Instruction Set Computer) - the more standard computer chips were CISC (Complete 

Instruction Set Computers) but these had architecture problems that limited speed. To overcome 

this the total number of instructions were reduced, allowing RISC computers to execute faster, 

but at the cost of larger programs. 

rlogin - allows a text based connection to a remote computer system in UNIX. 

robustness - the ability of a system to deal with and recover from unexpected input conditions. 

ROM (Read Only Memory) - a permanent form of computer memory with contents that cannot be 

overwritten. All computers contain some ROM to store the basic operating system - often called 

the BIOS in personal computers. 

rotameter - for measuring flow rate with a plug inside a tapered tube. 

router - as network packets travel through a network, a router will direct them towards their destinations 

using algorithms. 

RPC (Remote Procedure Call) - a connection to a specific port on a remote computer will request that a 

specific program be run. Typical examples are ping, mail, etc. 

RS-232C - a serial communication standard for low speed voltage based signals, this is very common on 

most computers. But, it has a low noise immunity that suggests other standards in harsh 

environments. 

RS-422 - a current loop based serial communication protocol that tends to perform well in noisy 

environments. 

RS-485 - uses two current loops for serial communications. 

RTC (Real-Time Clock) - A clock that can be used to generate interrupts to keep a computer process or 

operating system running at regular intervals. 

RTD (Resistance Temperature Detector) - as temperature is changed the resistance of many materials will 

also change. We can measure the resistance to determine the temperature. 

RTS (Request To Send) - A data handshaking line that is used to indicate when a signal is ready for 

transmission, and clearance is requested. 

rung - one level of logic in a ladder logic program or ladder diagram. 

R/W (Read/Write) - A digital line that is used to indicate if data on a bus is to be written to, or read from 

memory. 

35.19 S 

safety margin - a factor of safety between calculated maximums and rated maximums. 

SCADA (Supervisory Control And Data Acquisition) - computer remote monitoring and control of 

processes. 

scan-time - the time required for a PLC to perform one pass of the ladder logic. 

schematic - an abstract drawing showing components in a design as simple figures. The figures drawn are 

often the essential functional elements that must be considered in engineering calculations. 

scintillation - when some materials are high by high energy particles visible light or electromagnetic 

radiation is produced 

SCR (Silicon Controlled Rectifier) - a semiconductor that can switch AC loads. 

SDLC (Synchronous Data-Link Control) - IBM oriented data flow protocol with error checking. 

self-diagnosis - a self check sequence performed by many operation critical devices. 

sensitivity - the ability of a system to detect a change. 

sensor - a device that is externally connected to survey electrical or mechanical phenomena, and convert 

them to electrical or digital values for control or monitoring of systems. 

serial communication - elements are sent one after another. This method reduces cabling costs, but typically 

also reduces speed, etc. 

serial design - is the traditional design method. The steps in the design are performed in serial sequence. For 

example, first the geometry is specified, then the analysis is performed, and finally the 



manufacturability is evaluated. 

servo - a device that will take a desired operation input and amplify the power. 

session layer - an OSI network model layer. 

setpoint - a desired value for a controlled system. 

shield - a grounded conducting barrier that steps the propagation of electromagnetic waves. 

Siemens - a measure of electrical conductivity. 

signal conditioning - to prepare an input signal for use in a device through filtering, amplification, 

integration, differentiation, etc. 

simplex - single direction communication at any one time. 

simulation - a model of the product/process/etc is used to estimate the performance. This step comes before 

the more costly implementation steps that must follow. 

single-discipline team - a team assembled for a single purpose. 

single pole - a switch or relay that can only be opened or closed. See also single pole. 

single throw - a switch that will only switch one line. This is the simplest configuration. 

sinking - using a device that when active will allow current to flow through it to ground. This is 

complimented by sourcing. 

SLIP (Serial Line internet Protocol) - a method to run the internet Protocol (IP) over serial lines, such as 

modem connections. 

slip-ring - a connector that allows indefinite rotations, but maintains electrical contacts for passing power 

and electrical signals. 

slurry - a liquid with suspended particles. 

SMTP (Simple Mail Transfer Protocol) - the basic connection protocol for passing mail on the internet. 

snubber - a circuit that suppresses a sudden spike in voltage or current so that it will not damage other 

devices. 

software - a program, often stored on non-permanent media. 

solenoid - an actuator that uses a magnetic coil, and a lump of ferrous material. When the coil is energized a 

linear motion will occur. 

solid state - circuitry constructed entirely of semiconductors, and passive devices. (i.e., no gas as in tubes) 

sonar - sound waves are emitted and travel through gas/liquid. they are reflected by solid objects, and then 

detects back at the source. The travel time determines the distance to the object. 

sound - vibrations in the air travel as waves. As these waves strike the human ear, or other surfaces, the 

compression, and rarefaction of the air induces vibrations. In humans these vibrations induce 

perceived sound, in mechanical devices they manifest as distributed forces. 

sound absorption - as sound energy travels through, or reflects off a surface it must induce motion of the 

propagating medium. This induced motion will result in losses, largely heat, that will reduce the 

amplitude of the sound. 

sound analyzer - measurements can be made by setting the instrument for a certain bandwidth, and centre 

frequency. The measurement then encompasses the values over that range. 

sound level - a legally useful measure of sound, weighted for the human ear. Use dBA, dBB, dBC values. 

sound level meter - an instrument for measuring sound exposure values. 

source - an element in a system that supplies energy. 

sourcing - an output that when active will allow current to flow from a voltage source out to a device. It is 

complimented by sinking. 

specific gravity - the ratio between the density of a liquid/solid and water or a gas and air. 

spectrometer - determines the index of refraction of materials. 

spectrophotometer - measures the intensities of light at different points in the spectrum. 

spectrum - any periodic (and random) signal can be described as a collection of frequencies using a 

spectrum. The spectrum uses signal power, or intensity, plotted against frequency. 

spherical wave - a wave travels outward as if on the surface of an expanding sphere, starting from a point 

source. 

SQL (Structured Query Language) - a standard language for interrogating relational databases. 

standing wave - if a wave travels from a source, and is reflected back such that it arrives back at the source 

in phase, it can undergo superposition, and effectively amplify the sound from the source. 

static head - the hydrostatic pressure at the bottom of a water tank. 



steady state - describes a system response after a long period of time. In other words the transient effects 

have had time to dissipate. 

STEP (Standard for the Exchange of Product model data) - a standard that will allow transfer of solid model 

data (as well as others) between dissimilar CAD systems. 

step response - a typical test of system behavior that uses a sudden step input change with a measured 

response. 

stoichiometry - the general field that deals with balancing chemical equations. 

strain gauge - a wire mounted on a surface that will be stretched as the surface is strained. As the wire is 

stretched, the cross section is reduced, and the proportional change in resistance can be measured 

to estimate strain. 

strut - a two force structural member. 

subroutine - a reusable segment of a program that is called repeatedly. 

substrate - the base piece of a semiconductor that the layers are added to. 

switching - refers to devices that are purely on or off. Clearly this calls for discrete state devices. 

synchronous - two or more events happen at predictable times. 

synchronous motor - an AC motor. These motors tend to keep a near constant speed regardless of load. 

syntax error - an error that is fundamentally wrong in a language. 

synthesis - is the specification of values for the design variables. The engineer synthesizes a design and then 

evaluates its performance using analysis. 

system - a complex collection of components that performs a set of functions. 

35.20 T 

T1 - a 1.54 Mbps network data link. 

T3 - a 45 Mbps network data link. This can be done with parallel T1 lines and packet switching. 

tap - a connection to a power line. 

tare - the ratio between unloaded and loaded weights. 

TCP (Transmission Control Protocol) - a transport layer protocol that ensures reliable data communication 

when using IP communications. The protocol is connection oriented, with full duplex streams. 

tee - a tap into a larger line that does not add any special compensation, or conditioning. These connectors 

ofen have a T-shape. 

telnet - a standard method for logging into remote computers and having access if connect by a dumb 

terminal. 

temperature - the heat stored in an object. The relationship between temperature and energy content is 

specific to a material and is called the specific heat. 

temperature dependence - as temperature varies, so do physical properties of materials. This makes many 

devices sensitive to temperatures. 

thermal conductivity - the ability of a material to transfer heat energy. 

thermal gradient - the change in temperature as we move through a material. 

thermal lag - a delay between the time heat energy is applied and the time it arrives at the load. 

thermistor - a resistance based temperature measurement device. 

thermocouple - a device using joined metals that will generate a junction potential at different temperatures, 

used for temperature measurement. 

thermopiles - a series of thermocouples in series. 

thermoresistors - a category including RTDs and thermistors. 

throughput - the speed that actual data is transmitted/processed, etc. 

through beam - a beam is projected over an opening. If the beam is broken the sensor is activated. 

thumbwheel - a mechanical switch with multiple positions that allow digits to be entered directly. 

TIFF (Tagged Image File Format) - an image format best suited to scanned pictures, such as Fax 

transmissions. 

time-division multiplex - a circuit is switched between different devices for communication. 



time-proportional control - the amount of power delivered to an AC device is varied by changing the number 

of cycles delivered in a fixed period of time. 

timer - a device that can be set to have events happen at predetermined times. 

titration - a procedure for determining the strength of a solution using a reagent for detection. A chemical is 

added at a slow rate until the reagent detects a change. 

toggle switch - a switch with a large lever used for easy reviews of switch settings, and easy grasping. 

token - an indicator of control. Often when a process receives a token it can operate, when it is done it gives 

it up. 

TOP (Technical Office Protocol) - a network protocol designed for offices. It was promoted in conjunction 

with MAP in the 1980s, but never became widely used. 

top-down design - a design is done by first laying out the most abstract functions, and then filling in more of 

the details as they are required. 

topology - 1. The layout of a network. 2. a mathematical topic describing the connection of geometric 

entities. This is used for B-Rep models. 

torque - a moment or twisting action about an axis. 

torus - a donut shape 

toroidal core - a torus shaped magnetic core to increase magnetic conductivity. 

TPDDI (Twisted Pair Distributed Data Interface) - counter rotating token ring network connected with 

twisted pair medium. 

TQC (Total Quality Control) - a philosophical approach to developing quality methods that reach all levels 

and aspects of a company. 

transceiver (transmitter receiver) - a device to electrically interface between the computer network card, and 

the physical network medium. Packet collision hardware is present in these devices. 

transducer - a device that will convert energy from one form to another at proportional levels. 

transformations - include translation, rotation, and scaling of objects mathematically using matrix algebra. 

Transformations are used to move objects around in a scene. 

transformer - two separate coils wound about a common magnetic coil. Used for changing voltage, current 

and resistance levels. 

transient - a system response that occurs because of a change. These effects dissipate quickly and we are left 

with a steady state response. 

transmission path - a system component that is used for transmitting energy. 

transport layer - an OSI network model layer. 

TRIAC (TRIode Alternating Current) - a semiconductor switch suited to AC power. 

true - a logic positive, high, or 1. 

truth table - an exhaustive list of all possible logical input states, and the logical results. 

TTL (Transistor Transistor Logic) - a high speed for of transistor logic. 

TTY - a teletype terminal. 

turbine - a device that generates a rotational motion using gas or fluid pressure on fan blades or vanes. 

turbulent flow - fluids moving past an object, or changing direction will start to flow unevenly. This will 

occur when the Reynold’s number exceeds 4000. 

twisted pair - a sheme where wires are twisted to reduce the effects of EMI so that they may be used at 

higher frequencies. This is cassualy used to refer to 10b2 ethernet. 

TXD (Transmitted Data) - an output line for serial data transmission. It will be connected to an RXD input 

on a receiving station. 

35.21 U 

UART (Universal Asynchronous Receiver/Transmitter) - 

UDP (User Datagram Protocol) - a connectionless method for transmitting packets to other hosts on the 

network. It is seen as a counterpart to TCP. 

ultrasonic - sound or vibration at a frequency above that of the ear (> 16KHz typ.) 



ultraviolet - light with a frequency above the visible spectrum. 

UNIX - a very powerful operating system used on most high end and mid-range computers. The predecessor 

was Multics. This operating system was developed at AT & T, and grew up in the academic 

environment. As a result a wealth of public domain software has been developed, and the 

operating system is very well debugged. 

UPS (Uninterruptable Power Supply) - 

user friendly - a design scheme that similifies interaction so that no knowledge is needed to operae a device 

and errors are easy to recover from. It is also a marketing term that is badly misused. 

user interfaces - are the means of communicating with the computer. For CAD applications, a graphical 

interface is usually preferred. User friendliness is a measure of the ease of use of a program and 

implies a good user interface. 

UUCP (Unix to Unix Copy Program) - a common communication method between UNIX systems. 

35.22 V 

Vac - a voltage that is AC. 

vacuum - a pressure that is below another pressure. 

vane - a blade that can be extended to provide a good mechanical contact and/or seal. 

variable - a changeable location in memory. 

varistor - voltage applied changes resistance. 

valve - a system component for opening and closing mass/energy flow paths. An example is a water faucet 

or transistor. 

vapor - a gas. 

variable - it is typically a value that will change or can be changed. see also constant. 

VDT (Video Display Terminal) - also known as a dumb terminal 

velocity - a rate of change or speed. 

Venturi - an effect that uses an orifice in a flow to generate a differential pressure. These devices can 

generate small vacuums. 

viscosity - when moved a fluid will have some resistance proportional to internal friction. This determines 

how fast a liquid will flow. 

viscosity index - when heated fluid viscosity will decrease, this number is the relative rate of change with 

respect to temperature. 

VLSI (Very Large Scale Integration) - a measure of chip density. This indicates that there are over 

100,000(?) transistors on a single integrated circuit. Modern microprocessors commonly have 

millions of transistors. 

volt - a unit of electrical potential. 

voltage rating - the range or a maximum/minimum limit that is required to prevent damage, and ensure 

normal operation. Some devices will work outside these ranges, but not all will, so the limits 

should be observed for good designs. 

volume - the size of a region of space or quantity of fluid. 

volatile memory - most memory will lose its contents when power is removed, making it volatile. 

vortex - a swirling pattern in fluid flow. 

vortex shedding - a solid object in a flow stream might cause vortices. These vortices will travel with the 

flow and appear to be shed. 

35.23 W 

watchdog timer - a timer that expects to receive a pulse every fraction of a second. If a pulse is not received, 



it assumes the system is not operating normally, and a shutdown procedure is activated. 

watt - a unit of power that is commonly used for electrical systems, but applies to all. 

wavelength - the physical distance occupied by one cycle of a wave in a propagating medium. 

word - 1. a unit of 16 bits or two bytes. 2. a term used to describe a binary number in a computer (not limited 

to 16 bits). 

work - the transfer of energy. 

write - a digital value is stored in a memory location. 

WYSIWYG (What You See Is What You Get) - newer software allows users to review things on the screen 

before printing. In WYSIWYG mode, the layout on the screen matches the paper version exactly. 

35.24 X 

X.25- a packet switching standard by the CCITT. 

X.400 - a message handling system standard by the CCITT. 

X.500 - a directory services standard by the CCITT. 

X rays - very high frequency electromagnetic waves. 

X Windows - a window driven interface system that works over networks. The system was developed at 

MIT, and is quickly becoming the standard windowed interface. Personal computer 

manufacturers are slowly evolving their windowed operating systems towards X-Windows like 

standards. This standard only specifies low level details, higher level standards have been 

developed: Motif, and Openlook. 

XFER - transfer. 

XMIT - transmit. 

xmodem - a popular protocol for transmitting files over text based connections. compression and error 

checking are included. 

35.25 Y 

ymodem - a popular protocol for transmitting files over text based connections. compression and error 

checking are included. 

35.26 Z 

zmodem - a protocol for transmitting data over text based connections. 


plc references - 36.1 

36. PLC REFERENCES 

36.1 SUPPLIERS 

Asea Industrial Systems, 16250 West Glendale Dr., New Berlin, WI 53151, USA. 

Adaptek Inc., 1223 Michigan, Sandpoint, ID 83864, USA. 

Allen Bradley, 747 Alpha Drive, Highland Heights, OH 44143, USA. 

Automation Systems, 208 No. 12th Ave., Eldridge, IA 52748, USA. 

Bailey Controls Co., 29801 Euclid Ave., Wickliffe, OH 44092, USA. 

Cincinatti Milacron, Mason Rd. & Rte. 48, Lebanon, OH 45036, USA. 

Devilbiss Corp., 9776 Mt. Gilead Rd., Fredricktown, OH 43019, USA. 

Eagle Signal Controls, 8004 Cameron Rd., Austin, TX 78753, USA. 

Eaton Corp., 4201 North 27th St., Milwaukee, WI 53216, USA. 

Eaton Leonard Corp., 6305 ElCamino Real, Carlsbad, CA 92008, USA. 

Foxboro Co., Foxboro, MA 02035, USA. 

Furnas Electric, 1000 McKee St., Batavia, IL 60510, USA. 

GEC Automation Projects, 2870 Avondale Mill Rd., Macon, GA 31206, USA. 

General Electric, Automation Controls Dept., Box 8106, Charlottesville, VA 

22906, USA. 

General Numeric, 390 Kent Ave., Elk Grove Village, IL 60007, USA. 

Giddings & Lewis, Electrical Division, 666 South Military Rd., Fond du Lac, WI 

54935-7258, USA. 

Gould Inc., Programmable Control Division, PO Box 3083, Andover, MA 01810, 

USA. 

Guardian/Hitachi, 1550 W. Carroll Ave., Chicago, IL 60607, USA. 

Honeywell, IPC Division, 435 West Philadelphia St., York, PA 17404, USA. 

International Cybernetics Corp., 105 Delta Dr., Pittsburgh, Pennsylvania, 15238, 

USA, (412) 963-1444. 

Keyence Corp. of America, 3858 Carson St., Suite 203, Torrance, CA 90503, 

USA, (310) 540-2254. 

McGill Mfg. Co., Electrical Division, 1002 N. Campbell St., Valparaiso, IN 46383, 

USA. 

Mitsubishi Electric, 799 N. Bierman CircleMt. Prospect, IL 60056-2186, USA. 

Modicon (AEG), 6630 Campobello Rd., Mississauga, Ont., Canada L5N 2L8, 

(905) 821-8200. 

Modular Computer Systems Inc., 1650 W. McNabb Rd., Fort Lauderdale, FL 

33310, USA. 

Omron Electric, Control Division, One East Commerce Drive, Schaumburg, IL 

60195, USA. 

Reliance Electric, Centrl. Systems Division, 4900 Lewis Rd., Stone Mountain, GA 

30083, USA. 

Siemens, 10 Technology Drive, Peabody, MA 01960, USA. 

Square D Co., 4041 N. Richards St., Milwaukee, WI 53201, USA. 

Struthers-Dunn Systems Division, 4140 Utica Ridge Rd., Bettendorf, IA 52722, 



USA. 

Telemechanique, 901 Baltimore Blvd., Westminster, MD 21157, USA. 

Texas Instruments, Industrial Control Dept., PO Drawer 1255, Johnson City, IN 

37605-1255, USA. 

Toshiba, 13131 West Little York Rd., Houston, TX 77041, USA. 

Transduction Ltd., Airport Corporate Centre, 5155 Spectrum Way Bldg., No. 23, 

Mississauga, Ont., Canada, L4W 5A1, (905) 625-1907. 

Triconex, 16800 Aston St., Irvine, CA 92714, USA. 

Westinghouse Electric, 1512 Avis Drive, Madison Heights, MI 48071. 

36.2 PROFESSIONAL INTEREST GROUPS 

American National Standards Committee (ANSI), 1420 Broadway, Ney York, NY 

10018, USA. 

Electronic Industries Association (EIA), 2001 I Street NW, Washington, DC 

20006, USA. 

Institute of Electrical and Electronic Engineers (IEEE), 345 East 47th St., New 

York, NY 10017, USA. 

Instrument Society of America (ISA), 67 Alexander Drive, Research Triangle 

Park, NC 27709, USA. 

International Standards Organization (ISO), 1430 Broadway, New York, NY 

10018, USA. 

National Electrical Manufacturers Association (NEMA), 2101 L. Street NW, 

Washington, DC 20037, USA. 

Society of Manufacturing Engineers (SME), PO Box 930, One SME Drive, Dearborn, 

MI 48121, USA. 

36.3 PLC/DISCRETE CONTROL REFERENCES 

- The table below gives a topic-by-topic comparison of some PLC books. 

(H=Good coverage, M=Medium coverage, L=Low coverage, Blank=little/no coverage). 



Table 1: 

Author 

Introduction/Overview 

Wiring 

Discrete Sensors/Actuators 

Conditional Logic 

Numbering 

Timers/Counters/Latches 

Sequential Logic Design 

Advanced Functions 

Structured Text Programming 

Analog I/O 

Continuous Sensors/Actuators 

Continuous Control 

Fuzzy Control 

Data Interfacing/Networking 

Implementation/Selection 

Function Block Programming 

pages on PLC topics 

Filer... H M L H M H M H M M 303 

Chang... M L L L L M M L 80 

Petruzela H H M H H H L H L L L L 464 

Swainston H L L L L M H M M M M M 294 

Clements H M L L L L L L L L M H 197 

Asfahl L H L L L L 86 

Bollinger.. L M M M M M H H H 52 

Boucher M L M L M M H L L M M H 59 

Kirckof L L L M L M H L M 202 

Asfahl, C.R., “Robots and Manufacturing Automation”, second edition, Wiley, 

1992. 

Batten, G.L., Programmable Controllers: Hardware, Software, and Applications, 



Second Edition, McGraw-Hill, 1994. 

Batten, G.L., Batten, G.J., Programmable Controllers: Hardware, Software, and 

Applications, 

*Bertrand, R.M., “Programmable Controller Circuits”, Delmar, 1996. 

Bollinger, J.G., Duffie, N.A., “Computer Control of Machines and Processes”, 

Addison-Wesley, 1989. 

Bolton, w., Programmable Logic Controllers: An Introduction, Butterworth-Heinemann, 

1997. 

Bryan, L.A., Bryan, E.A., Programmable Controllers, Industrial Text and Video- 

Company, 1997. 

Boucher, T.O., “Computer Automation in Manufacturing; An Introduction”, Chapman 

and Hall, 1996. 

*Bryan, L.A., Bryan, E.A., Programmable Controllers, Industrial Text Company, 

19??. 

*Carrow, R.A., “Soft Logic: A Guide to Using a PC As a Programmable Logic 

Controller”, McGraw Hill, 1997. 

Chang, T-C, Wysk, R.A., Wang, H-P, “Computer-Aided Manufacturing”, second 

edition, Prentice Hall, 1998. 

Clements-Jewery, K., Jeffcoat, W., “The PLC Workbook; Programmable Logic 

Controllers made easy”, Prentice Hall, 1996. 

*Cox, R., Technician’s Guide to Programmable Controllers, Delmar Publishing, 

19??. 

?Crispin, A.J., “Programmable Logic Controllers and Their Engineering Applications”, 

Books Britain, 1996. 

*Dropka, E., Dropka, E., “Toshiba Medium PLC Primer”, Butterworth-Heinemann, 

1995. 

*Dunning, G., “Introduction to Programmable Logic Controllers”, Delmar, 1998. 

Filer, R., Leinonen, G., “Programmable Controllers and Designing Sequential 

Logic“, Saunders College Publishing, 1992. 

**Hughes, T.A., “Programmable Controllers (Resources for Measuremwnt and 

Control Series)”, Instrument Society of America, 1997. 

?Johnson, D.G., “Programmable Controllers for Factory Automation”, Marcel 

Dekker, 1987. 

Kirckof, G., Cascading Logic; A Machine Control Methodology for Programmable 

Logic Controllers, The Instrumentation, Systems, and Automation Society, 

2003. 

*Lewis, R.W., “Programming Industrial Control Systems using IES1131-3”, 

*Lewis, R.W., Antsaklis, P.J., “Programming Industrial Control Systems Using 

IEC 1131-3 (Iee Control Engineering, No. 59)”, Inspec/IEE, 1995. 

*Michel, G., Duncan, F., “Programmable Logic Controllers: Architecture and 

Application”, John Wiley & Sons, 1990. 

?Morriss, S.B., “Programmable Logic Controllers”, pub??, 2000. 

?Otter, J.D., “Programmable Logic Controllers: Operation, Interfacing and Programming”, 

??? 

Parr, E.A., Parr, A., Programmable Controllers: An Engineer’s Guide, Butterworth-Heinemann, 

1993. 



*Parr, E.A., “Programmable Controllers”, Butterworth-Heinemann, 1999. 

Petruzella, F., Programmable Logic Controllers, Second Edition, McGraw-Hill 

Publishing Co., 1998. 

*Ridley, J.E., “Introduction to Programmable Logic Controllers: The Mitsubishi 

Fx”, John Wiley & Sons, 1997. 

Rohner, P., PLC: Automation With Programmable Logic Controllers, International 

Specialized Book Service, 1996. 

*Rosandich, R.G., “Fundamentals of Programmable Logic Controllers”, EC&M 

Books, 1997. 

*Simpson, C.D., “Programmable Logic Controllers”, Regents/Prentice Hall, 1994. 

Sobh, M., Owen, J.C., Valvanis, K.P., Gracanin, S., “A Subject-Indexed Bibliography 

of Discrete Event Dynamic Systems”, IEEE Robotics and Applications 

Magazine, June 1994, pp. 14-20. 

**Stenerson, J., “Fundamentals of Programmable Logic Controllers, Sensors and 

Communications”, Prentice Hall, 1998. 

Sugiyama, H., Umehara, Y., Smith, E., “A Sequential Function Chart (SFC) Language 

for Batch Control”, ISA Transactions, Vol. 29, No. 2, 1990, pp. 63-69. 

Swainston, F., “A Systems Approach to Programmable Controllers”, Delmar, 

1992. 

Teng, S.H., Black, J. T., “Cellular Manufacturing Systems Modelling: The Petri 

Net Approach”, Journal of Manufacturing Systems, Vol. 9, No. 1, 1988, pp. 45- 

54. 

Warnock, I., Programmable Controllers: Operation and Application, Prentice Hall, 

19??. 

**Webb, J.W., Reis, R.A., “Programmable Logic Controllers, Principles and 

Applications”, Prentice Hall, 1995. 

Wright, C.P., Applied Measurement Engineering, Prentice-Hall, New Jersey, 1995. 


gfdl - 37.1 

37. GNU Free Documentation License 

Version 1.2, November 2002 

Copyright (C) 2000,2001,2002 Free Software Foundation, Inc. 

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37.1 PREAMBLE 

The purpose of this License is to make a manual, textbook, or other functional and useful document 

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gfdl - 37.3 

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and modification of the Modified Version to whoever possesses a copy of it. In addition, you 

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gfdl - 37.4 

* A. Use in the Title Page (and on the covers, if any) a title distinct from that of the 

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for authorship of the modifications in the Modified Version, together with at 

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it has fewer than five), unless they release you from this requirement. 

* C. State on the Title page the name of the publisher of the Modified Version, as 

the publisher. 

* D. Preserve all the copyright notices of the Document. 

* E. Add an appropriate copyright notice for your modifications adjacent to the 

other copyright notices. 

* F. Include, immediately after the copyright notices, a license notice giving the 

public permission to use the Modified Version under the terms of this License, 

in the form shown in the Addendum below. 

* G. Preserve in that license notice the full lists of Invariant Sections and required 

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* H. Include an unaltered copy of this License. 

* I. Preserve the section Entitled "History", Preserve its Title, and add to it an item 

stating at least the title, year, new authors, and publisher of the Modified Version 

as given on the Title Page. If there is no section Entitled "History" in the 

Document, create one stating the title, year, authors, and publisher of the Document 

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as stated in the previous sentence. 

* J. Preserve the network location, if any, given in the Document for public access 

to a Transparent copy of the Document, and likewise the network locations 

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that was published at least four years before the Document itself, or if the original 

publisher of the version it refers to gives permission. 

* K. For any section Entitled "Acknowledgements" or "Dedications", Preserve the 

Title of the section, and preserve in the section all the substance and tone of 

each of the contributor acknowledgements and/or dedications given therein. 

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in their titles. Section numbers or the equivalent are not considered part of the 

section titles. 

* M. Delete any section Entitled "Endorsements". Such a section may not be 

included in the Modified Version. 

* N. Do not retitle any existing section to be Entitled "Endorsements" or to conflict 

in title with any Invariant Section. 

* O. Preserve any Warranty Disclaimers. 

If the Modified Version includes new front-matter sections or appendices that qualify as Secondary 

Sections and contain no material copied from the Document, you may at your option designate 

some or all of these sections as invariant. To do this, add their titles to the list of Invariant 


gfdl - 37.5 

Sections in the Modified Version's license notice. These titles must be distinct from any other 

section titles. 

You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of 

your Modified Version by various parties--for example, statements of peer review or that the 

text has been approved by an organization as the authoritative definition of a standard. 

You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words 

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passage of Front-Cover Text and one of Back-Cover Text may be added by (or through 

arrangements made by) any one entity. If the Document already includes a cover text for the 

same cover, previously added by you or by arrangement made by the same entity you are acting 

on behalf of, you may not add another; but you may replace the old one, on explicit permission 

from the previous publisher that added the old one. 

The author(s) and publisher(s) of the Document do not by this License give permission to use 

their names for publicity for or to assert or imply endorsement of any Modified Version. 

37.6 COMBINING DOCUMENTS 

You may combine the Document with other documents released under this License, under the 

terms defined in section 4 above for modified versions, provided that you include in the combination 

all of the Invariant Sections of all of the original documents, unmodified, and list them 

all as Invariant Sections of your combined work in its license notice, and that you preserve all 

their Warranty Disclaimers. 

The combined work need only contain one copy of this License, and multiple identical Invariant 

Sections may be replaced with a single copy. If there are multiple Invariant Sections with the 

same name but different contents, make the title of each such section unique by adding at the 

end of it, in parentheses, the name of the original author or publisher of that section if known, 

or else a unique number. Make the same adjustment to the section titles in the list of Invariant 

Sections in the license notice of the combined work. 

In the combination, you must combine any sections Entitled "History" in the various original documents, 

forming one section Entitled "History"; likewise combine any sections Entitled 

"Acknowledgements", and any sections Entitled "Dedications". You must delete all sections 

Entitled "Endorsements." 

37.7 COLLECTIONS OF DOCUMENTS 

You may make a collection consisting of the Document and other documents released under this 

License, and replace the individual copies of this License in the various documents with a single 

copy that is included in the collection, provided that you follow the rules of this License for 

verbatim copying of each of the documents in all other respects. 

You may extract a single document from such a collection, and distribute it individually under this 

License, provided you insert a copy of this License into the extracted document, and follow 

this License in all other respects regarding verbatim copying of that document. 


gfdl - 37.6 

37.8 AGGREGATION WITH INDEPENDENT WORKS 

A compilation of the Document or its derivatives with other separate and independent documents 

or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the 

copyright resulting from the compilation is not used to limit the legal rights of the compilation's 

users beyond what the individual works permit. When the Document is included an 

aggregate, this License does not apply to the other works in the aggregate which are not themselves 

derivative works of the Document. 

If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if 

the Document is less than one half of the entire aggregate, the Document's Cover Texts may be 

placed on covers that bracket the Document within the aggregate, or the electronic equivalent 

of covers if the Document is in electronic form. Otherwise they must appear on printed covers 

that bracket the whole aggregate. 

37.9 TRANSLATION 

Translation is considered a kind of modification, so you may distribute translations of the Document 

under the terms of section 4. Replacing Invariant Sections with translations requires special 

permission from their copyright holders, but you may include translations of some or all 

Invariant Sections in addition to the original versions of these Invariant Sections. You may 

include a translation of this License, and all the license notices in the Document, and any Warrany 

Disclaimers, provided that you also include the original English version of this License 

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the translation and the original version of this License or a notice or disclaimer, the original 

version will prevail. 

If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the 

requirement (section 4) to Preserve its Title (section 1) will typically require changing the 

actual title. 

37.10 TERMINATION 

You may not copy, modify, sublicense, or distribute the Document except as expressly provided 

for under this License. Any other attempt to copy, modify, sublicense or distribute the Document 

is void, and will automatically terminate your rights under this License. However, parties 

who have received copies, or rights, from you under this License will not have their licenses 

terminated so long as such parties remain in full compliance. 

37.11 FUTURE REVISIONS OF THIS LICENSE 

The Free Software Foundation may publish new, revised versions of the GNU Free Documentawww.PAControl.com

gfdl - 37.7 

tion License from time to time. Such new versions will be similar in spirit to the present version, 

but may differ in detail to address new problems or concerns. See http://www.gnu.org/ 

copyleft/. 

Each version of the License is given a distinguishing version number. If the Document specifies 

that a particular numbered version of this License "or any later version" applies to it, you have 

the option of following the terms and conditions either of that specified version or of any later 

version that has been published (not as a draft) by the Free Software Foundation. If the Document 

does not specify a version number of this License, you may choose any version ever published 

(not as a draft) by the Free Software Foundation. 

37.12 How to use this License for your documents 

To use this License in a document you have written, include a copy of the License in the document 

and put the following copyright and license notices just after the title page: 

Copyright (c) YEAR YOUR NAME. 

Permission is granted to copy, distribute and/or modify this document 

under the terms of the GNU Free Documentation License, Version 1.2 

or any later version published by the Free Software Foundation; 

with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. 

A copy of the license is included in the section entitled "GNU 

Free Documentation License". 

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the 

"with...Texts." line with this: 

with the Invariant Sections being LIST THEIR TITLES, with the 

Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. 

If you have Invariant Sections without Cover Texts, or some other combination of the three, 

merge those two alternatives to suit the situation. 

If your document contains nontrivial examples of program code, we recommend releasing these 

examples in parallel under your choice of free software license, such as the GNU General Public 

License, to permit their use in free software.

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