APPLIED INTELLIGENT CONTROL OF INDUCTION MOTOR DRIVES

Hadi Junedi

—The induction motor plays very important role in industrial sectors, primarily due to its robustness and lowcost. When the mechanical load is applied to induction motor which requires speed control, some of the drive and controlstrategies are based on the estimated axis speed of the motor. The speed measurement directly reduces its stability and increases the cost of drive implementation. This paper proposes an alternative methodology for estimating the speed of a three phase induction motor driven by a voltage source inverter, using space vector modulation under the scalar control strategy and based on artificial intelligent controller such as fuzzy, neural and adaptive neuro fuzzy system. To validate the performance of the proposed method under motor load torque and speedreference set point variations, simulation results are presented.The simulation results validates under no load, constant load as well as variable load of the proposed methodand confirms ability to use induction motor speed control inpractice.The dynamic modeling, simulation and analysis of induction motor using Conventional, PI, Fuzzy Controller, ANN and Adaptive neuro fuzzy controller in open loop and closed loop have been presented. Keywords-Volatge Frequncy Control (V/F), Space Vector PWM (SPWM), Propotional Integral (PI) Controller, Fuzzy Logic Controller(FLC),Artificial Neural Network(ANN), Adaptive Neuro-Fuzzy controller(ANFIS)

https://www.ijert.org/control-techniques-employed-in-low-costvariable-speed-induction-motor-drives https://www.ijert.org/research/control-techniques-employed-in-low-costvariable-speed-induction-motor-drives-IJERTV3IS042271.pdf The wide application of induction motor drives is due to its peculiar features such as economically low cost, rugged construction,extreme reliability,and its robustness.The inherent incapability of variable speed operation in earlier era suppressed its application and thereby DC motors got evolved in drive applications.Rapid and regulated technologies and developments paved induction motor also into its control strategies in variable speed operation.The feasibility and effectiveness by these uncomplicated techniques led to enhancement of performance output and harmonic reductions.This paper deals with the control techniques such as Pulse Width Modulation(PWM),Space Vector Modulation(SVM) that are mainly incorporated and thus made IM more suited to drive applications.

APPLIED INTELLIGENT CONTROL OF INDUCTION MOTOR DRIVES Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 APPLIED INTELLIGENT CONTROL OF INDUCTION MOTOR DRIVES Tze-Fun Chan The Hong Kong Polytechnic University, Hong Kong, China Keli Shi Netpower Technologies, Inc., Texas, USA This edition first published 2011 Ó 2011 John Wiley & Sons (Asia) Pte Ltd Registered office John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop, #02-01, Singapore 129809 For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. All Rights Reserved. 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The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. MATLABÒ is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLABÒ software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLABÒ software. Library of Congress Cataloging-in-Publication Data Chan, Tze Fun. Applied intelligent control of induction motor drives / Tze-Fun Chan, Keli Shi. p. cm. Includes bibliographical references and index. ISBN 978-0-470-82556-3 (cloth) 1. Intelligent control systems. 2. Electric motors, Induction. I. Shi, Keli. II. Title. TJ217.5.C43 2011 621.46–dc22 2010035690 Print ISBN: 978-0-470-82556-3 ePDF ISBN: 978-0-470-82557-0 oBook ISBN: 978-0-470-82558-7 ePub ISBN: 978-0-470-82828-1 Typeset in 10/12pt Times by Thomson Digital, Noida, India. Contents Preface xiii Acknowledgments xvii About the Authors xxi List of Symbols 1 2 Introduction 1.1 Induction Motor 1.2 Induction Motor Control 1.3 Review of Previous Work 1.3.1 Scalar Control 1.3.2 Vector Control 1.3.3 Speed Sensorless Control 1.3.4 Intelligent Control of Induction Motor 1.3.5 Application Status and Research Trends of Induction Motor Control 1.4 Present Study References Philosophy of Induction Motor Control 2.1 Introduction 2.2 Induction Motor Control Theory 2.2.1 Nonlinear Feedback Control 2.2.2 Induction Motor Models 2.2.3 Field-Oriented Control 2.2.4 Direct Self Control 2.2.5 Acceleration Control Proposed 2.2.6 Need for Intelligent Control 2.2.7 Intelligent Induction Motor Control Schemes 2.3 Induction Motor Control Algorithms 2.4 Speed Estimation Algorithms 2.5 Hardware References xxiii 1 1 2 2 3 3 4 4 4 4 7 9 9 10 10 11 13 14 15 16 17 19 23 25 29 vi 3 4 5 Contents Modeling and Simulation of Induction Motor 3.1 Introduction 3.2 Modeling of Induction Motor 3.3 Current-Input Model of Induction Motor 3.3.1 Current (3/2) Rotating Transformation Sub-Model 3.3.2 Electrical Sub-Model 3.3.3 Mechanical Sub-Model 3.3.4 Simulation of Current-Input Model of Induction Motor 3.4 Voltage-Input Model of Induction Motor 3.4.1 Simulation Results of ‘Motor 1’ 3.4.2 Simulation Results of ‘Motor 2’ 3.4.3 Simulation Results of ‘Motor 3’ 3.5 Discrete-State Model of Induction Motor 3.6 Modeling and Simulation of Sinusoidal PWM 3.7 Modeling and Simulation of Encoder 3.8 Modeling of Decoder 3.9 Simulation of Induction Motor with PWM Inverter and Encoder/Decoder 3.10 MATLABÒ/Simulink Programming Examples 3.11 Summary References 31 31 32 34 35 35 37 37 40 43 43 44 45 49 51 54 Fundamentals of Intelligent Control Simulation 4.1 Introduction 4.2 Getting Started with Fuzzy Logical Simulation 4.2.1 Fuzzy Logic Control 4.2.2 Example: Fuzzy PI Controller 4.3 Getting Started with Neural-Network Simulation 4.3.1 Artificial Neural Network 4.3.2 Example: Implementing Park’s Transformation Using ANN 4.4 Getting Started with Kalman Filter Simulation 4.4.1 Kalman Filter 4.4.2 Example: Signal Estimation in the Presence of Noise by Kalman Filter 4.5 Getting Started with Genetic Algorithm Simulation 4.5.1 Genetic Algorithm 4.5.2 Example: Optimizing a Simulink Model by Genetic Algorithm 4.6 Summary References 75 75 75 75 77 83 83 Expert-System-based Acceleration Control 5.1 Introduction 5.2 Relationship between the Stator Voltage Vector and Rotor Acceleration 5.3 Analysis of Motor Acceleration of the Rotor 54 55 73 74 85 90 92 94 98 98 100 107 108 109 109 110 113 Contents Control Strategy of Voltage Vector Comparison and Voltage Vector Retaining 5.5 Expert-System Control for Induction Motor 5.6 Computer Simulation and Comparison 5.6.1 The First Simulation Example 5.6.2 The Second Simulation Example 5.6.3 The Third Simulation Example 5.6.4 The Fourth Simulation Example 5.6.5 The Fifth Simulation Example 5.7 Summary References vii 5.4 6 7 114 118 122 123 125 126 127 129 131 131 Hybrid Fuzzy/PI Two-Stage Control 6.1 Introduction 6.2 Two-Stage Control Strategy for an Induction Motor 6.3 Fuzzy Frequency Control 6.3.1 Fuzzy Database 6.3.2 Fuzzy Rulebase 6.3.3 Fuzzy Inference 6.3.4 Defuzzification 6.3.5 Fuzzy Frequency Controller 6.4 Current Magnitude PI Control 6.5 Hybrid Fuzzy/PI Two-Stage Controller for an Induction Motor 6.6 Simulation Study on a 7.5 kW Induction Motor 6.6.1 Comparison with Field-Oriented Control 6.6.2 Effects of Parameter Variation 6.6.3 Effects of Noise in the Measured Speed and Input Current 6.6.4 Effects of Magnetic Saturation 6.6.5 Effects of Load Torque Variation 6.7 Simulation Study on a 0.147 kW Induction Motor 6.8 MATLABÒ/Simulink Programming Examples 6.8.1 Programming Example 1: Voltage-Input Model of an Induction Motor 6.8.2 Programming Example 2: Fuzzy/PI Two-Stage Controller 6.9 Summary References 133 133 135 136 138 139 141 142 142 143 145 145 146 148 149 149 150 152 158 Neural-Network-based Direct Self Control 7.1 Introduction 7.2 Neural Networks 7.3 Neural-Network Controller of DSC 7.3.1 Flux Estimation Sub-Net 7.3.2 Torque Calculation Sub-Net 7.3.3 Flux Angle Encoder and Flux Magnitude Calculation Sub-Net 7.3.4 Hysteresis Comparator Sub-Net 167 167 168 170 170 171 158 163 165 166 173 178 viii 8 9 Contents 7.3.5 Optimum Switching Table Sub-Net 7.3.6 Linking of Neural Networks 7.4 Simulation of Neural-Network-based DSC 7.5 MATLABÒ/Simulink Programming Examples 7.5.1 Programming Example 1: Direct Self Controller 7.5.2 Programming Example 2: Neural-Network-based Optimum Switching Table 7.6 Summary References 180 183 184 187 187 Parameter Estimation Using Neural Networks 8.1 Introduction 8.2 Integral Equations Based on the ‘T’ Equivalent Circuit 8.3 Integral Equations based on the ‘G’ Equivalent Circuit 8.4 Parameter Estimation of Induction Motor Using ANN 8.4.1 Estimation of Electrical Parameters 8.4.2 ANN-based Mechanical Model 8.4.3 Simulation Studies 8.5 ANN-based Induction Motor Models 8.6 Effect of Noise in Training Data on Estimated Parameters 8.7 Estimation of Load, Flux and Speed 8.7.1 Estimation of Load 8.7.2 Estimation of Stator Flux 8.7.3 Estimation of Rotor Speed 8.8 MATLABÒ/Simulink Programming Examples 8.8.1 Programming Example 1: Field-Oriented Control (FOC) System 8.8.2 Programming Example 2: Sensorless Control of Induction Motor 8.9 Summary References 199 199 200 203 205 206 208 210 214 217 218 218 222 226 231 GA-Optimized Extended Kalman Filter for Speed Estimation 9.1 Introduction 9.2 Extended State Model of Induction Motor 9.3 Extended Kalman Filter Algorithm for Rotor Speed Estimation 9.3.1 Prediction of State 9.3.2 Estimation of Error Covariance Matrix 9.3.3 Computation of Kalman Filter Gain 9.3.4 State Estimation 9.3.5 Update of the Error Covariance Matrix 9.4 Optimized Extended Kalman Filter 9.5 Optimizing the Noise Matrices of EKF Using GA 9.6 Speed Estimation for a Sensorless Direct Self Controller 9.7 Speed Estimation for a Field-Oriented Controller 9.8 MATLABÒ/Simulink Programming Examples 243 243 244 245 245 245 245 246 246 247 250 253 255 260 192 196 197 231 234 240 241 ix Contents 9.8.1 Programming Example 1: Voltage-Frequency Controlled (VFC) Drive 9.8.2 Programming Example 2: GA-Optimized EKF for Speed Estimation 9.8.3 Programming Example 3: GA-based EKF Sensorless Voltage-Frequency Controlled Drive 9.8.4 Programming Example 4: GA-based EKF Sensorless FOC Induction Motor Drive 9.9 Summary References 10 Optimized Random PWM Strategies Based On Genetic Algorithms 10.1 Introduction 10.2 PWM Performance Evaluation 10.2.1 Fourier Analysis of PWM Waveform 10.2.2 Harmonic Evaluation of Typical Waveforms 10.3 Random PWM Methods 10.3.1 Random Carrier-Frequency PWM 10.3.2 Random Pulse-Position PWM 10.3.3 Random Pulse-Width PWM 10.3.4 Hybrid Random Pulse-Position and Pulse-Width PWM 10.3.5 Harmonic Evaluation Results 10.4 Optimized Random PWM Based on Genetic Algorithm 10.4.1 GA-Optimized Random Carrier-Frequency PWM 10.4.2 GA-Optimized Random-Pulse-Position PWM 10.4.3 GA-Optimized Random-Pulse-Width PWM 10.4.4 GA-Optimized Hybrid Random Pulse-Position and Pulse-Width PWM 10.4.5 Evaluation of Various GA-Optimized Random PWM Inverters 10.4.6 Switching Loss of GA-Optimized Random Single-Phase PWM Inverters 10.4.7 Linear Modulation Range of GA-Optimized Random Single-Phase PWM Inverters 10.4.8 Implementation of GA-Optimized Random Single-Phase PWM Inverter 10.4.9 Limitations of Reference Sinusoidal Frequency of GA-Optimized Random PWM Inverters 10.5 MATLABÒ/Simulink Programming Examples 10.5.1 Programming Example 1: A Single-Phase Sinusoidal PWM 10.5.2 Programming Example 2: Evaluation of a Four-Pulse Wave 10.5.3 Programming Example 3: Random Carrier-Frequency PWM 260 264 268 269 270 270 273 273 274 276 277 283 283 285 285 286 287 288 289 290 292 293 295 296 297 298 298 299 299 302 303 x Contents 10.6 Experiments on Various PWM Strategies 10.6.1 Implementation of PWM Methods Using DSP 10.6.2 Experimental Results 10.7 Summary References 11 12 305 305 307 310 310 Experimental Investigations 11.1 Introduction 11.2 Experimental Hardware Design for Induction Motor Control 11.2.1 Hardware Description 11.3 Software Development Method 11.4 Experiment 1: Determination of Motor Parameters 11.5 Experiment 2: Induction Motor Run Up 11.5.1 Program Design 11.5.2 Program Debug 11.5.3 Experimental Investigations 11.6 Experiment 3: Implementation of Fuzzy/PI Two-Stage Controller 11.6.1 Program Design 11.6.2 Program Debug 11.6.3 Performance Tests 11.7 Experiment 4: Speed Estimation Using a GA-Optimized Extended Kalman Filter 11.7.1 Program Design 11.7.2 GA-EKF Experimental Method 11.7.3 GA-EKF Experiments 11.7.4 Limitations of GA-EKF 11.8 DSP Programming Examples 11.8.1 Generation of 3-Phase Sinusoidal PWM 11.8.2 RTDX Programming 11.8.3 ADC Programming 11.8.4 CAP Programming 11.9 Summary References 313 313 314 314 320 321 321 322 324 327 330 330 338 339 Conclusions and Future Developments 12.1 Main Contributions of the Book 12.2 Industrial Applications of New Induction Motor Drives 12.3 Future Developments 12.3.1 Expert-System-based Acceleration Control 12.3.2 Hybrid Fuzzy/PI Two-Stage Control 12.3.3 Neural-Network-based Direct Self Control 12.3.4 Genetic Algorithm for an Extended Kalman Filter 12.3.5 Parameter Estimation Using Neural Networks 12.3.6 Optimized Random PWM Strategies Based on Genetic Algorithms 12.3.7 AI-Integrated Algorithm and Hardware Reference 373 374 375 377 378 378 378 378 378 344 345 345 346 349 352 354 359 361 364 370 370 378 379 379 Contents xi Appendix A Equivalent Circuits of an Induction Motor 381 Appendix B Parameters of Induction Motors 383 Appendix C M-File of Discrete-State Induction Motor Model 385 Appendix D Expert-System Acceleration Control Algorithm 387 Appendix E Activation Functions of Neural Network 391 Appendix F M-File of Extended Kalman Filter 393 Appendix G ADMC331-based Experimental System 395 Appendix H Experiment 1: Measuring the Electrical Parameters of Motor 3 397 Appendix I DSP Source Code for the Main Program of Experiment 2 403 Appendix J DSP Source Code for the Main Program of Experiment 3 407 Index 417 Preface Induction motors are the most important workhorses in industry and they are manufactured in large numbers. About half of the electrical energy generated in a developed country is ultimately consumed by electric motors, of which over 90 % are induction motors. For a relatively long period, induction motors have mainly been deployed in constant-speed motor drives for general purpose applications. The rapid development of power electronic devices and converter technologies in the past few decades, however, has made possible efficient speed control by varying the supply frequency, giving rise to various forms of adjustable-speed induction motor drives. In about the same period, there were also advances in control methods and artificial intelligence (AI) techniques, including expert system, fuzzy logic, neural networks and genetic algorithm. Researchers soon realized that the performance of induction motor drives can be enhanced by adopting artificial-intelligence-based methods. Since the 1990s, AI-based induction motor drives have received greater attention and numerous technical papers have been published. Speed-sensorless induction drives have also emerged as an important branch of induction motor research. A few good reference books on intelligent control and power electronic drives were written. Some electric drive manufacturers began to incorporate AI-control in their commercial products. This book aims to explore possible areas of induction motor control that require further investigation and development and focuses on the application of intelligent control principles and algorithms in order to make the controller independent of, or less sensitive to, motor parameter changes. Intelligent control is becoming an important and necessary method to solve difficult problems in control of induction motor drives. Based on classical electrical machine and control theory, the authors have investigated the applications of expert-system control, fuzzy-logic control, neural-network control, and genetic algorithm to various forms of induction motor drive. This book is the result of over fifteen years of research on intelligent control of induction motors undertaken by the authors at the Department of Electrical Engineering, the Hong Kong Polytechnic University and the United States. The methods are original and most of the work has been published in IEEE Transactions and international conferences. In the past few years, our publications have been increasingly cited by Science Citation Index journal papers, showing that our work is being rigorously followed up by the induction motor drives research community. We believe that the publication of a book or monograph summarizing our latest research findings on intelligent control will benefit the research community. This book will complement xiv Preface some of the fine references written by eminent electric drives and power electronic experts (such as Peter Vas, Bimal Bose, and Dote and Hoft, to name just a few), and at the same time the presentation will enable researchers to explore new research directions. Numerous examples, block diagrams, and simulation programs are provided for interested readers to conduct related investigations. This book adopts a practical simulation approach that enables interested readers to embark on research in intelligent control of electric drives with the minimum effort and time. Intelligent control techniques have to be used in practical applications where controller designs involve noise distribution (Kalman filter), pseudo-random data (random PWM), inference similar to human, system identification, and lookup table identification. Artificial intelligence techniques are presented in the context of the drive applications being considered and a strong link between AI and the induction motor drive is established throughout the chapters. The numerous simulation examples and results presented will shed new light on possible future induction motor drives research. There are twelve chapters in this book. Chapter 1 gives an overview of induction motor drives and reviews previous work in this important technical area. Chapter 2 presents the philosophy of induction motor control. From the classical induction motor model, the differential equations are formulated that fit in a generic control framework. Various control schemes are then discussed, followed by the development of general control algorithms. Modeling and simulation of induction motors are discussed in Chapter 3 with the aid of detailed MATLAB/Simulink block diagrams. Chapter 4 is a primer for simulation of intelligent control systems using MATLAB/ Simulink. Programming examples of fuzzy-logic, neural network, Kalman filter, and genetic algorithm are provided to familiarize readers with simulation programming involving intelligent techniques. The exercises will fast guide them into the intelligent control area. These models and simulation techniques form the basis of the intelligent control applications discussed in Chapters 5–10 which cover, in this order, expert-system-based acceleration control, hybrid fuzzy/PI two-stage control, neural-network-based direct self control, parameter estimation using neural networks, GA-optimized extended Kalman filter for speed estimation, and optimized random PWM strategy based on genetic algorithms. In Chapter 5, an expert-system-based acceleration controller is developed to overcome the three drawbacks (sensitivity to parameter variations, error accumulation, and the needs for continuous control with initial state) of the vector controller. In every time interval of the control process, the acceleration increments produced by two different voltage vectors are compared, yielding one optimum stator voltage vector which is selected and retained. The online inference control is built using an expert system with heuristic knowledge about the relationship between the motor voltage and acceleration. Because integral calculation and motor parameters are not involved, the new controller has no accumulation error of integral as in the conventional vector control schemes and the same controller can be used for different induction motors without modification. Simulation results obtained on the expert-systembased controller show that the performance is comparable with that of a conventional direct self controller, hence proving the feasibility of expert-system-based control. In Chapter 6, a hybrid fuzzy/PI two-stage control method is developed to optimize the dynamic performance of a current and slip frequency controller. Based on two features (current magnitude feature and slip frequency feature) of the field orientation principle, the authors apply different strategies to control the rotor speed during the acceleration stage and the steady- Preface xv state stage. The performance of the two-stage controller approximates that of a field-oriented controller. Besides, the new controller has the advantages of simplicity and insensitivity to motor parameter changes. Very encouraging results are obtained from a computer simulation using MATLAB/Simulink software and a DSP-based experiment. In Chapter 7, implementation of direct self control for an induction motor drive using artificial neural network (ANN) is discussed. ANN has the advantages of parallel computation and simple hardware, hence it is superior to a DSP-based controller in execution time and structure. In order to improve the performance of a direct self controller, an ANN-based DSC with seven layers of neurons is proposed at algorithm level. The execution time is decreased from 250 ms (for a DSP-based controller) to 21 ms (for the ANN-based controller), hence the torque and flux errors caused by long execution times are almost eliminated. A detailed simulation study is performed using MATLAB/Simulink and Neural-network Toolbox. Machine parameter estimation is important for field-oriented control (FOC) and sensorless control. Most parameter estimation methods are based on differential equations of the induction motor. Differential operators, however, will cause noise and greatly reduce the estimation precision. Nondifferentiable points will also exist in the motor currents due to rapid turn-on or turn-off of the ideal power electronic switches. Chapter 8 addresses the issue of parameter uncertainties of induction motors and presents a neural-network-based parameter estimation method using an integral model. By using the proposed ANN-based integral models, almost all the machine parameters can be derived directly from the measured data, namely the stator currents, stator voltages and rotor speed. With the estimated parameters, load, stator flux, and rotor speed may be estimated. Addressing the current research trend, a speed-sensorless controller using an extended Kalman filter (EKF) is investigated in Chapter 9. To improve the performance of the speedsensorless controller, noise covariance and weight matrices of the EKF are optimized by using a real-coded genetic algorithm (GA). MATLAB/Simulink based simulation and DSP-based experimental results are presented to confirm the efficacy of the GA-optimized EKF for speed estimation in an induction motor drive. Chapter 10 is devoted to optimized random pulse-width modulation (PWM) strategies. The optimized PWM inverter can spread harmonic energy and reduce total harmonic distortion, weighted total harmonic distortion, or distortion factor. Without incurring extra hardware cost and programming complexity, the optimized PWM is implemented by writing an optimized carrier sequence into the PWM controller in place of the conventional carrier generator. Comparison between simulation and experimental results verifies that output voltage of the optimized PWM technique is superior to that based on the standard triangular PWM and random PWM methods. A real-valued genetic algorithm is employed for implementing the optimization strategy. Chapter 11 describes the details of the experimental system and presents the experiments and experimental results. At the hardware level, an experimental system for the intelligent control of induction motor drive is proposed. The system is configured by a DSP (ADMC331), a power module (IRPT1058A), a three-phase Hall-effect current sensor, an encoder (Model GBZ02), a data acquisition card (PCL818HG), a PC host and a data-acquisition PC, as well as a 147 W three-phase induction motor. With the experimental hardware, the MATLAB/Simulink models, hybrid fuzzy/PI two-stage control algorithm, and GA-EKF method proposed in this book have been verified. It is proposed to use DSP TMS320F28335 for intelligent control with a real time data exchange (RTDX) technique. Many intelligent algorithms are complex and with xvi Preface larger data block (such as GA and Neural Network) which cannot be written into a DSP chip. With the RTDX technique, hardware-in-the-loop training and simulation may be implemented in the laboratory environment. The RTDX examples of DSP target C programming and PC host MATLAB programming are provided. Chapter 12 gives some conclusions and explores possible new developments of AI applications to induction motor drives. This book will be useful to academics and students (senior undergraduate, postgraduate, and PhD) who specialize in electric motor drives in general and induction motor drives in particular. The readers are assumed to have a good foundation on electrical machines (including reference frame theory and transformation techniques), control theory, and basics of artificial intelligence (such as expert systems, fuzzy logic theory, neural networks, and genetic algorithms). The book is at an advanced level, but senior undergraduate students specializing on electric motor drives projects should also find it a good reference. It also provides a practical guide to research students to get started with hardware implementation of intelligent control of induction motor drives. Tze-Fun Chan and Keli Shi March 2010 Acknowledgments The authors wish to thank John Wiley & Sons (Asia) Pte Ltd in supporting this project. The authors also wish to thank the Department of Electrical Engineering, the Hong Kong Polytechnic University, Hong Kong, China for the research facilities and support provided. In particular, they would like to offer their appreciation towards Dr Y.K. Wong and Prof. S.L. Ho of the same department for their stimulating ideas on intelligent control and induction motor drives. In the course of research on intelligent control of induction motor drives, the authors published a number of papers in different journals. These works report the authors’ original research results at various stages of development. The authors would like to express their gratitude to these journals for permitting the authors to reuse some of these published materials. In the writing of the book, the original materials are expanded and new results are included. Thanks are due to IEEE for permission to reproduce materials from the following published papers in IEEE Transactions and IEEE sponsored conferences: Transactions papers . . . . K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘Speed estimation of an induction motor drive using an optimized extended Kalman filter,’ IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. (Reproduced Figures 9.1–9.2, 9.4, 9.10 and Tables 9.1–9.2; Figures 10.16, 10.30, 10.31(c), 10.32(c) and 10.33(c); Figures 11.1, 11.24, 11.26, 11.28–11.29 and Table 11.12.) K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘A rule-based acceleration control scheme for an induction motor,’ IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. (Reproduced Figures 5.1–5.2, 5.4–5.5, 5.8–5.12 and Tables 5.1–5.2.) K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘Direct self control of induction motor based on neural network,’ IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. (Reproduced Figures 7.1–7.22 and Table 7.1.) K.L. Shi and Hui Li, ‘Optimized PWM strategy based on genetic algorithms,’ IEEE Transaction on Industrial Electronics, 52(5), 2005: 1458–1461. IEEE conference papers . K.L. Shi, T.F. Chan and Y.K. Wong, ‘A novel two-stage speed controller for an induction motor,’ The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper MD2-4, May 18–21, 1997, Milwaukee, Wisconsin, USA. xviii . . . . . . . . . Acknowledgments K.L. Shi, T.F. Chan and Y.K. Wong, ‘Modeling of the three-phase induction motor using SIMULINK,’ The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, May 18–21, 1997, Milwaukee, Wisconsin USA. (Reproduced Figures 3.2–3.4 and 3.7–3.12.) K.L. Shi, T.F. Chan and Y.K. Wong, ‘Hybrid fuzzy two-stage controller for an induction motor,’ 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp.1898–1903, October 11–14, 1998, San Diego, USA. (Reproduced Figures 6.1–6.5, 6.7–6.11 and Tables 6.1–6.4.) K.L. Shi, T.F. Chan and Y.K. Wong, ‘Direct self control of induction motor using artificial neural network,’ 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1696–1701, October 11–14, 1998, San Diego, USA October. K.L. Shi, T.F. Chan and Y.K. Wong and S.L. Ho, ‘An improved two-stage control scheme for an induction motor.’ Proceedings of the IEEE 1999 International Conference on Power Electronics and Drive Systems, pp. 405–410, July 27–29, 1999, Hong Kong. K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘A rule-based acceleration control scheme for an induction motor,’ Proceedings of IEEE International Electric Machines and Drives Conference (IEMDC ’99), Seattle, Washington, USA, pp. 613–615. K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘Speed estimation of induction motor using extended Kalman filter,’ IEEE 2000 Winter Meeting, vol. 1, pp. 243–248, January 23–27, 2000, Singapore. K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘Direct self control of induction motor based on neural network,’ IEEE Industry Applications Society (IEEE-IAS) 2000 Meeting, October 8–12, 2000, Vol. 3, pp. 1380–1387, Rome, Italy. K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘A novel hybrid fuzzy/PI two-stage controller for an induction motor drive,’ IEEE International Electric Machines and Drives Conference (IEMDC ’2001), pp.415–421, June 17–20, 2001, Cambridge, MA, USA. (Reproduced Figures 6.31 and 11.16.) K.L. Shi and Hui Li, ‘An optimized PWM method using genetic algorithms,’ in Proc. IEEE IECON 2003, Nov 2–6, 2003, Roanoke, VA, pp. 7–11. Thanks are due to Taylor & Francis Ltd for permission to reuse the contents of the following article in Chapter 5: . K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘A new acceleration control scheme for an inverter-fed induction motor,’ Electric Power Components and Systems, 27(5), 1999: 527–554. Thanks are due to ACTA Press for permission to reuse the contents of the following article in Chapters 3 and 6: . K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, ‘Modeling and simulation of a novel twostage controller for an induction motor,’ International Association of Science and Technology for Development (IASTED) Journal on Power and Energy Systems, 19(3), 1999: 257–264. Acknowledgments xix Thanks are also due to International Journal on Electrical Engineering Education for permission to reuse the contents of the following article in Chapter 3: . K.L. Shi, T.F. Chan and Y.K. Wong; ‘Modeling and simulation of the three-phase induction motor,’ International Journal on Electrical Engineering Education, 36(2), 1999: 163–172. Last but not least, the authors thank the production staff of John Wiley & Sons (Asia) Pte Ltd for their strong support and smooth cooperation. About the Authors Tze-Fun Chan received his B.Sc. (Eng.) and M.Phil. degrees in electrical engineering from the University of Hong Kong, Hong Kong, China, in 1974 and 1980, respectively. He received his PhD degree in electrical engineering from City University London, UK, in 2005. Since 1978, he has been with the Department of Electrical Engineering, the Hong Kong Polytechnic University, Hong Kong, China, where he is now Associate Professor and Associate Head of Department. Dr Chan’s research interests are self-excited induction generators, brushless a.c. generators, permanent-magnet machines, finite element analysis of electric machines, and electric motor drives control. In 2006, he was awarded a Prize Paper by IEEE Power Engineering Society Power Generation and Energy Development Committee. In 2007, he co-authored (with Prof. Loi Lei Lai) a book entitled Distributed Generation – Induction and Permanent Magnet Generators published by Wiley (ISBN: 978-0470-06208-1). In 2009, he was awarded another Prize Paper by IEEE Power Engineering Society Power Generation and Power Committee. Dr Chan is a Chartered Engineer, a member of Institution of Engineering and Technology, UK, a member of Hong Kong Institution of Engineers, Hong Kong, and a member of the Institute of Electrical and Electronic Engineers, USA. Keli Shi received his BS degree in electronics and electrical engineering from Chengdu University of Science and Technology and MS degree in electrical engineering from Harbin Institute of Technology in 1983 and 1989, respectively. He received his PhD in electrical engineering from the Hong Kong Polytechnic University in 2001. From 2001 to 2002, he was a Postdoctoral Scholar in the Electrical and Computer Engineering Department of Ryerson University, Canada. From 2003 to 2004, he was a Postdoctoral Scholar of Florida State University, Florida, USA. Currently, Dr Shi is a Director of Test Engineering in Netpower Technologies Inc., Texas, USA, where he has been since 2004. His research interests are DSP applications and intelligent control of induction and permanent-magnet motors. List of Symbols A, B, C An, Bn, Cn b cf G(t) H ire e e idr ; iqr ise e e ; iqs ids iss s s idr ; iqr s s ids ; iqs JM JL k kT Kn Ls LS LM Lm Lr Llr LR M p P Pn q(x) Q R Rr input and output matrices of a continuous system input and output matrices of a discrete system bias vector of neural network friction coefficient weighting matrix of noise matrix of output prediction in Kalman filter algorithm vector of rotor current in the excitation reference frame, A components of the vector of rotor current in the excitation reference frame, A vector of stator current in the excitation reference frame, A components the stator current vector in the excitation reference frame, A stator current vector in the stator reference frame, A components of the rotor current vector in the stator reference frame, A components of the stator current vector in the stator reference frame, A moment of inertia of the rotor, kg m2 moment of inertia of the load, kg m2 coefficient to calculate slip increment torque constant, N.m/Wb/A Kalman filter gain stator inductance in the ‘T’ equivalent circuit, H/ph stator inductance in the ‘G’ equivalent circuit, H/ph mutual inductance in the ‘T’ equivalent circuit, H/ph stator inductance in the ‘G’ equivalent circuit, H/ph rotor inductance in the ‘T’ equivalent circuit, H/ph rotor leakage inductance in the ‘T’ equivalent circuit, H/ph rotor inductance in the ‘G‘ equivalent circuit, H/ph sampling period, s differentiation operator (d/dt), s 1 number of poles error covariance matrix of Kalman filter algorithm feedback signal covariance matrix of system noise covariance matrix of measurement noise rotor resistance in the ‘T’ equivalent circuit, O/ph xxiv RR Rs RS T Tsteady TL u Vre e e Vdr ; Vqr Vse e e ; Vqs Vds Vss s s Vds ; Vqs v(t) w(t) w x y o or oo Doo oo * or * lm lm ldm, lqm ler ler * ledr ; leqr lsr lsdr ; lsqr lsM yr List of Symbols rotor resistance in the ‘G’ equivalent circuit, O/ph stator resistance in the ‘T’ equivalent circuit, O/ph stator resistance in the ‘G’ equivalent circuit, O/ph developed torque, N.m steady-state torque, N.m load torque, N.m control function, vector vector of the rotor voltage in the excitation reference frame, V components of the vector of rotor voltage in the excitation reference frame, V vector of the stator voltage in the excitation reference frame, V components of the vector of stator voltage in the excitation reference frame, V vector of stator voltage in the stator reference frame, V components of the vector of stator voltage in the stator reference frame, V noise matrix of output model (measurement noise) noise matrix of state model (system noise) weight vector of neural network system state system output supply angular frequency, synchronous speed of a 2-pole motor, rad/s slip speed of a 2-pole motor, rad/s rotor speed, rad/s speed error, rad/s speed command, rad/s instantaneous slip speed command, rad/s vector of stator flux of the ‘G’ equivalent circuit in the stator reference-frame, Wb command of stator flux vector of the ‘G’ equivalent circuit in the stator reference-frame, Wb components of stator flux vector of the ‘G’ equivalent circuit in the stator reference-frame, Wb vector of the rotor flux of the ‘T’ equivalent circuit in the excitation reference frame, Wb command of the rotor flux vector of the ‘T’ equivalent circuit in the excitation reference frame, Wb components of the rotor flux vector of the ‘T’ equivalent circuit in the excitation reference frame, Wb vector of the rotor flux of the ‘T’ equivalent circuit in the stator reference frame, Wb components of the rotor flux vector of the ‘T’ equivalent circuit in the stator reference frame, Wb vector of the airgap flux of the ‘G’ equivalent circuit in the stator reference frame, Wb angular position (phase) of the rotor flux vector in the stator reference frame, rad List of Symbols ym y(is) g F angular position (phase) of the stator flux vector in the stator reference frame, rad angular position (phase) of the stator current vector in the stator reference frame, rad normalized mechanical time constant kg.m matrix of state prediction in Kalman filter algorithm xxv 1 Introduction 1.1 Induction Motor Conversion from electrical energy to mechanical energy is an important process in modern industrial civilization. About half of the electricity generated in a developed country is eventually converted to mechanical energy, usually by means of electrical machines (Leonhard, 1996; Sen, 1997). Typical applications of electrical machine drives are: 1. 2. 3. 4. Appliances (washing machines, blowers, compressors, pumps); Heating/ventilation/air conditioning (HVAC); Industrial servo drives (motion control, robotics); Automotive control (electric vehicles). Since its invention in 1888, the induction motor has become the most widely used motor in industry. Compared with d.c. motors, the cage induction motor has distinct advantages (Novotny and Lipo, 1996) as listed below: 1. 2. 3. 4. 5. 6. No commutator and brushes, Ruggedness, Lower rotor inertia, Maintenance free, simpler protection, Smaller size and weight, Lower price. Consequently, most industrial drive applications employ induction motors. Unfortunately, the speed of an induction motor cannot be continuously varied without additional expensive equipment. High-performance control of an induction motor is more difficult than d.c. motors, because the induction motor is inherently a dynamic, recurrent, and nonlinear system. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 2 1.2 Applied Intelligent Control of Induction Motor Drives Induction Motor Control Induction motor control problems have attracted the attention of researchers for many years. Most of the earlier researches are based on classical control theory and electric machine theory, using precise mathematical models of the induction motor. As shown in Figure 1.1, an induction motor control system consists of the controller, sensors, inverter, and the induction motor. It can be seen that a study of induction motor control involves three main electrical engineering areas: control, power electronics, and electrical machines (Bose, 1981). Power supply Commands Controller Inverter Voltage and current sensors IM Speed or position sensors Load Figure 1.1 An induction motor control system. The induction motor can be described by a fifth order nonlinear differential equation with two inputs and only three state variables are available for measurement (Marino and Tomei, 1995). The control task is further complicated by the fact that the induction motor is subject to unpredictable disturbances (such as noise and load changes) and there are uncertainties in machine parameters. Induction motor control has constituted a theoretically interesting and practically important class of nonlinear systems, and is evolving into a benchmark example for nonlinear control (Ortega and Asher, 1998). Intelligent control, which includes expert-system control, fuzzy-logic control, neuralnetwork control, and genetic algorithm, is not only based on artificial intelligence (AI) theory, but also based on conventional control theory. Consequently, new control methods can be developed by the application of artificial intelligence (Bose, 1993). 1.3 Review of Previous Work Scientists and experts have devoted a lot of efforts to induction motor control in the past decades. Developing new control principle, algorithm, and hardware for induction motor control has become a challenge that industry must face today. The development of induction motor control may be summarized as follows. In 1946, Weygandt and Charp investigated the transient performance of induction motor by using an analog computer (Weygandt and Charp, 1946). In 1956, Bell Laboratories invented the thyristor (or silicon-controlled rectifier) (Bose, 1989). In 1959, Kovacs and Racz applied rotating reference frames and space vectors to the study of induction motor transients (Kovacs and Racz, 1959). Since 1960, various scalar control strategies of constant voltage/frequency (V/Hz) control of induction motor had been proposed (Bose, 1981). In 1961, McMurray and Shattuck proposed the inverter circuit with pulse width modulation (PWM) (McMurray and Slattuck, 1961). Introduction 3 In 1968 and in 1970, field orientation principle was first formulated by Hasse and Blaschke (Hasse, 1969; Blashke, 1972). In 1985, direct self control was proposed by M. Depenbrock, I. Takahashi, and T. Noguchi (Depenbrock, 1985; Takahashi and Noguchi, 1986). In the 1990s, intelligent control of induction motor received wide attention (Bose, 1992). Recently, revolutionary advances in computer technology, power electronics, modern control, and artificial intelligence have led to a new generation of induction motor control that may provide significant economic benefits. The voltage or current supplied to an induction motor can be expressed as a sinusoidal function of magnitude and frequency or magnitude and phase. Accordingly, induction motor control methods are classified into two categories: scalar control in which the voltage magnitude and frequency are adjusted, and vector control in which the voltage magnitude and phase are adjusted. 1.3.1 Scalar Control The scalar controllers are usually used in low-cost and low-performance drives. They control the magnitude/frequency of voltage or current. Typical studies of scalar control include openloop voltage/frequency (V/Hz) control, closed-loop V/Hz control, and stator current and slipfrequency control (Bose, 1981). When the load torque is constant and there are no stringent requirements on speed regulation, it suffices to use a variable-frequency induction motor drive with open-loop V/Hz control. Applications which require only a gradual change in speed are being replaced by open-loop controllers, often referred to as general purpose AC drives (Rajashekara, Kawamura, and Matsuse, 1996). When the drive requirements include faster dynamic response and more accurate speed or torque control, it is necessary to operate the motor in the closed-loop mode. Closed-loop scalar control includes closed-loop V/Hz control and stator current and slip frequency control. 1.3.2 Vector Control (Rajashekara, Kawamura, and Matsuse, 1996) The vector controllers are expensive and high-performance drives, which aim to control the magnitude and phase of voltage or current vectors. Vector control methods include fieldoriented control (FOC) and direct self control (DSC). Both methods attempt to reduce the complex nonlinear control structure into a linear one, a process that involves the evaluation of definite integrals. FOC uses the definite integral to obtain the rotor flux angle, whereas DSC uses the definite integral to obtain the stator flux space vector. Although the implementation of both methods has largely been successful, they suffer from the following drawbacks: 1. Sensitivity to parameter variations; 2. Error accumulation when evaluating the definite integrals; if the control time is long, degradation in the steady-state and transient responses will result due to drift in parameter values and excessive error accumulation; 3. In both methods, the control must be continuous and the calculation must begin from an initial state. 4 1.3.3 Applied Intelligent Control of Induction Motor Drives Speed Sensorless Control Speed sensorless control of induction motors is a new and promising research trend. To eliminate the speed and position sensors, many speed and position estimation algorithms have been proposed recently. These algorithms are generally based on complex calculations which involve the machine parameters and the measurement of terminal voltages and currents of the induction motor. Speed sensorless control can be regarded as open-loop control because the measurement is included in the controller (Rajashekara, Kawamura, and Matsuse, 1996). 1.3.4 Intelligent Control of Induction Motor Despite the great efforts devoted to induction motor control, many of the theoretical results cannot be directly applied to practical systems. The difficulties that arise in induction motor control are complex computations, model nonlinearity, and uncertainties in machine parameters. Recently, intelligent techniques are introduced in order to overcome these difficulties. Intelligent control methodology uses human motivated techniques and procedures (for example, forms of knowledge representation or decision making) for system control (Bose, 1997; Narendra and Mukhopadhyay, 1996). 1.3.5 Application Status and Research Trends of Induction Motor Control Among the above control techniques, market evidence shows that up to the present only two have found general acceptance. They are the open-loop constant V/Hz control for lowperformance applications and the indirect vector control for high-performance applications (Bose, 1993). Vector control principle, intelligent-based algorithm, and DSP-based hardware represent recent research trends of induction motor control. 1.4 Present Study The present research status of induction motor control suggests the areas that require further investigation and development. The objective of this book is to investigate intelligent control principles and algorithms in order to make the performance of the controller independent of, or less sensitive to, motor parameter changes. Based on theories of the induction motor and control principles, expert-system control, fuzzy-logic control, neural-network control, and genetic algorithm for induction motor drive will be investigated and developed. The scope of the present book is summarized as follows: 1. Computer modeling of induction motor The induction motor model typically consists of an electrical model and a mechanical model, which is a fifth-order nonlinear system. Using MATLAB/Simulink software, three induction motor models (current-input model, voltage-input model, discrete-state model) are constructed for the simulation studies of the induction motor drive. The three models can be used to simulate the actual induction motor effectively. In addition, a PWM model, an encoder model, and a decoder model are also proposed. Introduction 5 2. Expert-system based acceleration control An expert-system based acceleration controller is developed to overcome the drawbacks (sensitivity to parameter variations, error accumulation, and the needs for continuous control with initial state) of the vector controller. In every time interval of the control process, the acceleration increments produced by two different voltage vectors are compared, yielding one optimum stator voltage vector which is selected and retained. The on-line inference control is built using an expert system with heuristic knowledge about the relationship between the motor voltage and acceleration. Because integral calculation and motor parameters are not involved, the new controller has no accumulation error of integral as in the conventional vector control schemes and the same controller can be used for different induction motors without modification. Simulation results obtained on the expert-system based controller show that the performance is comparable with that of a conventional direct self controller, hence proving the feasibility of expert-system based control. 3. Hybrid fuzzy/PI two-stage control A hybrid fuzzy/PI two-stage control method is developed to optimize the dynamic performance of a current and slip frequency controller. Based on two features (current magnitude feature and slip frequency feature) of the field orientation principle, different strategies are proposed to control the rotor speed during the acceleration stage and the steady-state stage. The performance of the two-stage controller approximates that of a fieldoriented controller. Besides, the new controller has the advantages of simplicity and insensitivity to motor parameter changes. Very encouraging results are obtained from a computer simulation using MATLAB/Simulink software and experimental verification using a DSP-based drive. 4. Neural-network-based direct self control (DSC) Artificial neural network (ANN) has the advantages of parallel computation and simple hardware, hence it is superior to a DSP-based controller in execution time and structure. In order to improve the performance of a direct self controller, an ANN-based DSC with seven layers of neurons is proposed at algorithm level. The execution time is decreased from 250 ms (for a DSP-based controller) to 21 ms (for the ANN-based controller), hence the torque and flux errors caused by long execution times are almost eliminated. A detailed simulation study is performed using MATLAB/Simulink and Neural-network Toolbox. 5. Genetic algorithm based extended Kalman filter for rotor speed estimation of induction motor Addressing the current research trend, speed-sensorless controller with the extended Kalman filter is investigated. To improve the performance of the speed-sensorless controller, noise covariance and weight matrices of the extended Kalman filter are optimized by using a real-coded genetic algorithm (GA). MATLAB/Simulink-based simulation and DSP-based experimental results are presented to confirm the efficacy of the GA-optimized EKF for speed estimation in induction motor drives. 6. Parameter estimation using neural networks Integral models of an induction motor are described and implemented by using an artificial neural network (ANN) approach. By using the proposed ANN-based integral models, almost all the machine parameters can be derived directly from the measured data, namely the stator currents, stator voltages and rotor speed. With the estimated parameters, load, stator flux, and rotor speed may be estimated for induction motor control. 6 Applied Intelligent Control of Induction Motor Drives 7. Optimized random PWM strategies based on genetic algorithm Random carrier-frequency PWM, random pulse-position PWM, random pulse-width PWM, and hybrid random pulse-position and pulse-width PWM are optimized by genetic algorithm (GA). A single-phase inverter is employed for the optimization study, and the resulting waveforms are evaluated based on Fourier analysis. The validity of the GA-optimized random carrier-frequency PWM is verified by experimental studies on a DSP-based voltage controlled inverter. The GA-optimized PWM proposed may be applied to single-phase ac induction motor drives for low performance applications, such as pumps, fans and mixers, as well as uninterruptible power supply (UPS). 8. Hardware experiments At the hardware level, an experimental system for intelligent control of an induction motor is proposed and implemented. The system is configured by a DSP (ADMC331), a power module (IRPT1058A), a three-phase Hall-effect current sensor, an encoder (Model GBZ02), a data acquisition card (PCL818HG), a PC host and a data-acquisition PC, as well as a 147-W 3-phase induction motor. With the experimental hardware, the MATLAB/Simulink models, hybrid fuzzy/PI two-stage control algorithm, and GA-EKF method described in this book are verified. Using a TMS320F2812 DSP board and an IRAMX16UP60A inverter module, a GA-optimized single-phase randomcarrier-frequency PWM inverter is implemented. Besides, programming examples are presented to demonstrate RTDX (Real Time Data exchange) technique to exchange real-time data between a TMS320F28335 DSP and MATLAB software. With the RTDX technique, real-time DSP applications can be supported by a complex MATLAB AI program running simultaneously on a PC. 9. Programming examples Using MATLAB/Simulink software and CCStudio_v3.3 software, a large number of programming examples are described in the book and the source codes can be found on the book companion website as supplementary materials. The programming examples may be classified into the following categories. a. Modeling and simulation of induction motor (Chapter 3) b. Fundamentals of intelligent control simulation (Chapter 4) c. Induction motor control Expert-system based acceleration control (Chapter 5) Hybrid fuzzy/PI two-stage control (Chapter 6) Direct self control of induction motor (Chapter 7) Neural-network based direct self control (Chapter 7) Field-oriented control of induction motor (Chapter 8) Voltage-frequency controlled induction motor drive (Chapter 9). d. Estimations for induction motor drives Parameter estimation using neural networks (Chapter 8) Load estimation based on integral model of induction motor (Chapter 8) Flux estimation based on integral model of induction motor (Chapter 8) Rotor speed estimation based on integral model of induction motor (Chapter 8) GA-optimized extended Kalman filter for speed estimation (Chapter 9). e. Sensorless control of induction motor Integral-model-based sensorless control of induction motor (Chapter 8) Introduction 7 EKF-based sensorless V/Hz control of induction motor (Chapter 9) EKF-based sensorless field-oriented control (FOC) of induction motor (Chapter 9). f. PWM strategies Space vector PWM Simulink model (in the folder ‘Chapter 8.4’ of the book companion website) Optimized random PWM strategy based on genetic algorithms (Chapter 10). g. DSP TMS320F28335 programming examples 3-phase PWM programming example (Chapter 11) RTDX programming example (Chapter 11) ADC programming example (Chapter 11) CAP programming example (Chapter 11). References Blashke, F. (1972) The principle of field-orientation as applied to the new ‘Transvektor’ closed-loop control system for rotating-field machines. Simians Review, 34(5), 21–220. Bose, B.K. (1981) Adjustable Speed AC Drive Systems, IEEE Press, New York. Bose, B.K. (1989) Power electronics – an emerging technology. IEEE Transactions on Industrial Electronics, 36, 403–411. Bose, B.K. (1992) Recent advances in power electronics. IEEE Transactions on Power Electronics, 7(1), 2–16. Bose, B.K. (1993) Power electronics and motion control-technology status and recent trends. IEEE Transactions on Industry Applications, 29, 902–909. Bose, B.K. (1997) Expert system, fuzzy logic, and neural networks in power electronics and drives, in Power Electronics and Variable Frequency Drives: Technology and Applications (ed. B.K. Bose), IEEE Press, New Jersey. Depenbrock, M. (Inventor) (18, Oct. 1985) ‘Direct Self-control of the Flux and Rotary Moment of a Rotary-field Machine,’ United States Patent 4,678,248. Hasse, K. (1969) ‘About the Dynamics of Adjustable-speed Drives with Converter-fed Squirrel-cage Induction Motors’ (in German), Dissertation, Darmstadt Technische Hochschule. Kovacs, K.P. and Racz, J. (1959) Transiente Vorgane in Wechse Istrommaschinen, Verlag der Ungarischen Akademie der Wissenschaften, Budapest. Leonhard, W. (1996) Control of Electrical Drives, Springer-Verlag Berlin, Heidelberg. Marino, R. and Tomei, P. (1995) Nonlinear Control Design, Prentice Hall Europe, Hemel Hempstead. McMurray, W. and Slattuck, D.D. (1961) A silicon-controlled rectifier inverter with improved commutation. AIEE Transactions on Communications and Electronics, 80, 531–542. Narendra, K.S. and Mukhopadhyay, S. (1996) Intelligent Control Using Neural Networks, in Intelligent Control Systems: Theory and Applications (eds M.M. Gupta and N.K. Sinha), IEEE Press, New York. Novotny, D.W. and Lipo, T.A. (1996) Vector Control and Dynamics of AC Drives, Oxford University Press, Oxford. Ortega, R. and Asher, G. (1998) Joint special issue on nonlinear control of induction motor. IEEE Transactions on Industrial Electronics, 45(2), 367. Rajashekara, K., Kawamura, A., and Matsuse, K. (1996) Speed sensorless control of induction motor, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura,and K. Matsuse), IEEE Press, New Jersey. Sen, P.C. (1997) Principles of Electric Machines and Power Electronics, John Wiley & Sons, Inc., New York. Takahashi, I. and Noguchi, T. (1986) A new quick-response and high-efficiency control strategy of an induction motor. IEEE Transactions on Industry Applications, 22(5), 820–827. Weygandt, C.N. and Charp, S. (1946) Electromechanical transient performance of induction motors. AIEE Transactions, 64(Pt. III), 1000. 2 Philosophy of Induction Motor Control 2.1 Introduction Strong demands for high-performance motor drives in industry have stimulated the research on induction motor control. Despite the great effort devoted to this research area for many years, the desired performance in induction motor drives has not been achieved satisfactorily. In the 1970s, nonlinear controllability and observability began to be studied using differential geometric tools (Marino and Tomei, 1995), while the field-oriented controller was introduced in 1968 and 1970 on the basis of the mathematical model of the induction motor (Hasse, 1969; Blashke, 1972). Field-oriented control has the innovative feature that, based on the reference frame theory (proposed by R.H. Park in the late 1920s) (Krause, Wasynczuk, and Sudhoff, 1995), it makes use of nonlinear transformation of stator coordinates and of nonlinear state feedback (which aims at nonlinearity cancellation) to make the closed-loop system linear in the new coordinates. A theory of nonlinear feedback control design was developed during the 1980s (Marino and Tomei, 1995) and in 1985 direct self control was proposed (Depenbrock, 1985). In the direct self control scheme, the errors in the torque and flux are directly used to choose the inverter switching state with the hysteresis (or bang-bang) control strategy. Recently, induction motor control has involved more and more subject areas, such as modern nonlinear control, electrical machine, artificial intelligence, power electronics, signal processing, and computer science (Bose, 1993). Many research papers in this area have been published, and it is clear that the development of a new controller cannot be implemented briefly and in a single step. Consequently, the understanding and design of the controller should be made at theory, algorithm, and hardware levels to facilitate analysis and system realization. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 10 Applied Intelligent Control of Induction Motor Drives 2.2 Induction Motor Control Theory 2.2.1 Nonlinear Feedback Control Modern control design is fundamentally a time-domain technique. A state-space model of the system to be controlled, or plant, is required (Marino and Tomei, 1995). A commonly used model for a nonlinear system is (Vidyasagar, 1993): _ xðtÞ ¼ f ðt; xðtÞ; uðtÞÞ; xð0Þ ¼ x0 yðtÞ ¼ hðt; xðtÞÞ ð2:1Þ ð2:2Þ where t denotes time, x0 is the initial condition, x(t) denotes the value of the function x(.) at time t and is an n-dimensional vector, u(t) is similarly defined and is an m-dimensional vector, and the function f associates, with each value of t, x(t), and u(t), a corresponding n-dimensional vector. Following common convention, this is denoted as: t2Rþ , x(t)2Rn, u(t)2Rm, and f: R þ Rn Rm ! sRn. The quantity x(t), which is a vector of internal variables, is referred to as the state of the system at time t, while u(t) is called the control function. yðtÞ 2 Rs is a vector of measured outputs. When m ¼ s ¼ 1, we speak of single-input single-output (SISO) systems; we speak of multiple-input multiple-output (MIMO) systems when either m > 1 and s > 1. If we define vðtÞ ¼ qðxðtÞÞ þ sðxðtÞÞuðtÞ ð2:3Þ then the resulting variables y(t) and v(t) satisfy a linear differential equation of the form: y_ ðtÞ ¼ E1 yðtÞ þ E2 vðtÞ ð2:4Þ where the pair (E1, E2) is controllable. If this is the case, then the system represented by Equation (2.1) is said to be feedback linearizable. Note that since sðxðtÞÞ 6¼ 0 in some neighborhood of zero, Equation (2.3) can be rewritten as: uðtÞ ¼ qðxðtÞÞ 1 þ vðtÞ sðxðtÞÞ sðxðtÞÞ ð2:5Þ where q(x(t))/s(x(t)) and 1/s(x(t)) are smooth functions. Hence, if we think of v(t) as the external reference input applied to the system, then Equation (2.3) or Equation (2.5) represents nonlinear state feedback, and a nonlinear statedependent pre-filter, applied to the system Equation (2.1). Similarly, Equation (2.2) represents a nonlinear state-variable transformation. Feedback signals are a function of system state variables. Hence, a state feedback control system with the overall effects Equations (2.2) and (2.3) can be represented by Figure 2.1. 11 Philosophy of Induction Motor Control Reference input v PLANT Control function u 1 s(x(t)) + feedback signal State Output y x . x = f(t,x(t),u(t)) h(t,x(t)) q(x) Figure 2.1 A state feedback control system. In induction motor drives, the relationship between the rotor speed and the power input is not linear. In a vector control scheme, only three state variables (speed and currents in two phases) and two inputs (voltages) are available for measurement, hence the other two state variables (fluxes) have to be estimated. Using the state variables measured or estimated, feedback signals can be calculated by the vector controller. Consequently, the complex nonlinear control structure can be transformed into a linear one. 2.2.2 Induction Motor Models An induction motor model based on a ‘G’ equivalent circuit (Appendix A) in the stator reference frame may be expressed as a fifth-order nonlinear equation (Trzynadlowski, 1994): 8 doo > > > > dt > > > > > > dls > > > dm > > dt > > > > < s dlqm > dt > > > > > s > dids > > > > > dt > > > > > dis > > : qs dt ¼ 2P s s TL ðl i ls is Þ 3 2J dm qs qm ds J ¼ s s Rs ids þ Vds ¼ s s Rs iqs þ Vqs ¼ s kG ðLm RR þ LR Rs Þids þ ¼ s kG ðLm RR þ LR Rs Þiqs where kG ¼ L2 m 1 Lm LR , ð2:6Þ P P s s oo iqs þ kG RR lsdm þ kG oo lsqm þ kG LR Vds 2 2 P P s s oo ids kG oo lsdm þ kG LR Vqs þ kG RR lsqm 2 2 and electromagnetic torque T ¼ 23 P 2 s s lsdm iqs lsqm ids . s s ; iqs Þ are the In Equation (2.6), rotor speed oo, stator fluxes ðlsdm ; lsqm Þ, and stator currents ðids states, while rotor inertia J, stator and rotor inductances (Lm, LR), stator and rotor resistances s s (Rs, RR), and the number of poles P are the parameters. The voltages ðVds ; Vqs Þ are inputs, and TL is the load torque. 12 Applied Intelligent Control of Induction Motor Drives s s s s Let lsm ¼ lsdm þ jlsqm , lsR ¼ lsdR þ jlsqR , iss ¼ ids þ jiqR . The flux equations þ jiqs , and iRs ¼ idR can be written as: lsm ¼ Lm iss þ Lm iRs ð2:7Þ lsR ¼ lsm þ LR iRs : ð2:8Þ From Equations (2.7) and (2.8), the following equations can be derived. iss ð2:10Þ Lm Lm LR s lsR þ i LR þ Lm LR þ Lm s ð2:11Þ lsm ¼ lsR LR iRs iss ð2:9Þ LR þ Lm s 1 s l l Lm LR m LR R iss ¼ lsm ¼ lsm s ¼ i Lm R ls ¼ R Lm LR s 1þ i Lm R ð2:12Þ ð2:13Þ For convenience, Equation (2.6) is referred to as the 1st fifth-order equation. Substituting Equation (2.7) into Equation (2.6), the 2nd fifth-order equation is obtained. Substituting Equation (2.9) into Equation (2.6), the 3rd fifth-order equation is obtained. Substituting Equation (2.10) into Equation (2.6), the 4th fifth-order equation is obtained. Substituting Equation (2.11) into Equation (2.6), the 5th fifth-order equation is obtained. Substituting Equations (2.12) and (2.13) into Equation (2.6), the 6th fifth-order equation is obtained. The six fifth-order equations are listed as follows: 1st equation: s s with state variables flsdm ; lsqm ; ids ; iqs ; oo g. 2nd equation: s s s s with state variables fids ; iqs ; idR ; iqR ; oo g. 3rd equation: s s with state variables flsdm ; lsqm ; idR ; iqR ; oo g. 4th equation: with state variables flsdR ; lsqR ; lsdm ; lsqm ; oo g. 5th equation: s s with state variables flsdR ; lsqR ; ids ; iqs ; oo g. 6th equation: s s with state variables flsdR ; lsqR ; idR ; iqR ; oo g. Philosophy of Induction Motor Control 13 An induction motor ‘T’ equivalent circuit model (Appendix A) can be expressed as another fifth-order nonlinear equation in the stator reference frame (Trzynadlowski, 1994): 8 T doo 2 PLM s s L > s s > ¼ l i l i > dr qr qs ds > 3 dt 2JL J > r > > > > > s > dldr Rr s P Rr LM s > > oo lsqr þ ¼ ldr i > > > 2 dt L Lr ds r > > > > > < dlsqr Rr s P Rr LM s lqr þ oo lsdr þ i ¼ ð2:14Þ 2 L Lr qs dt > r > > > > > s > dids LM Rr PLM L2M Rr þ L2r Rs s Lr > s > ¼ lsdr þ i þ oo lsqr Vds > > 2 2 2 2 ÞL ds > dt L L L 2 L L L L L ð ÞL ð Þ ð L L L ð r s r s r s LM Þ r r s r > M M M > > > > s > > diqs LM Rr PLM LM 2 Rr þ L2r Rs s Lr > > ¼ lsqr i þ oo lsdr Vs : 2 2 dt 2ðLr Ls LM Þ ðLr Ls LM ÞLr ðLr Ls L2M ÞLr qs ðLr Ls L2M Þ qs s s In Equation (2.14), rotor speed oo, rotor fluxes ðlsdr ; lsqr Þ, and stator currents ðids ; iqs Þ are the states, while rotor inertia J, stator and rotor inductances (Ls, Lr), mutual inductance LM, stator and rotor resistances (Rs, Rr), and the number of poles P are the parameters. The voltages s s ðVds ; Vqs Þ are inputs, and TL is the load torque. From the ‘T’ equivalent circuit, another six fifth-order equations with different state variables can be obtained: 7th equation: s s with state variables flsdM ; lsqM ; ids ; iqs ; oo g. 8th equation: s s s s with state variables fids ; iqs ; idr ; iqr ; oo g. 9th equation: 10th equation: s s with state variables flsdM ; lsqM ; idr ; iqr ; oo g. s s s with state variables fldr ; lqr ; ldM ; lsqM ; oo g. 11th equation: 12th equation: s s ; iqs ; oo g. with state variables flsdr ; lsqr ; ids s s s s with state variables fldr ; lqr ; idr ; iqr ; oo g. The twelve fifth-order equations illustrate the major difficulty encountered in the control of induction motors. For example, in Equations (2.6) and (2.14), the multiplier operators of states render the induction motor becoming a nonlinear system (Trzynadlowski, 1994), while the differential operations give rise to a dynamic system (Delgado, Kambhampati, and Warwick, 1995). The system output speed oo is used to calculate the system variables, which makes the motor a recurrent system (Kung, 1993). In addition, local recurrent calculations are e involved in Equation (2.6). For example, the term ids appears on both sides of the current equation. Consequently, the induction motor can be referred to as a dynamic, recurrent, and nonlinear system. 2.2.3 Field-Oriented Control When the stator currents are controlled, the last two equations in Equation (2.14) (the 11th fifthorder equation) are neglected. Using the substitution or ¼ o (P/2)oo, the reduced-order 14 Applied Intelligent Control of Induction Motor Drives equation in the excitation reference-frame can be expressed as (Trzynadlowski, 1994): 8 T doo 2 PLM e e L e > > ¼ ldr iqs leqr ids > > dt 3 2JL J > r > > > > < dle Rr e Rr e dr ¼ ldr þ or leqr þ LM ids > L Lr dt r > > > > > > dle > > e : qr ¼ Rr leqr or ledr þ Rr LM iqs dt Lr Lr ð2:15Þ Based on Equation (2.15), the classical field-oriented control and the recent nonlinear inputoutput decoupled control have been proposed (Chan, Leung, and Ng, 1990). The field-orientation conditions can be expressed as (Trzynadlowski, 1994): leqr ¼ 0 ledr ¼ constant Replacing T and ledr with T and ledr respectively and substituting the field orientation M e e conditions into Equation (2.15) with T ¼ PL 3Lr ldr iqs , an indirect FOC scheme for an induction motor can be derived as follows: e ids ¼ dledr * Lr 1 e þ l * dt LM Rr LM dr ð2:16Þ 3Lr T* PLM ledr * ð2:17Þ 3Rr T* Pledr *2 ð2:18Þ e iqs ¼ or ¼ e e iss ¼ ids þ jiqs ejðor þ oo Þt : ð2:19Þ s T and ledr are the control commands, while oo is the feedback signal. The current vectors ids s and iqs and slip or are obtained from Equations (2.16)–(2.18), and then substituted into Equation (2.19) to give the vector iss for induction motor control. 2.2.4 Direct Self Control Equation (2.6) (the 1st fifth-order equation) is used to realize direct self control. Using the first three equations in Equation (2.6), we can obtain the stator flux lsm and torque T from the measured stator currents and voltages. Figure 2.2 shows that the direct self control system has the same architecture as the state feedback control system in modern control theory as shown in Figure 2.1. 15 Philosophy of Induction Motor Control Flux command Torque Flux Flux and torque calculations based on the first three equations of (2.6) Inverter Torque and flux controller Torque command IM Voltages Currents Figure 2.2 Direct self control system. Using one of the last two equations in Equation (2.6), we can estimate the rotor speed by measurements of voltage and current together with the flux. A control scheme of DSC with speed estimation is shown in Figure 2.3. Torque* Flux* Flux and torque calculations based on the first three equations of (2.6) Torque Flux Speed estimation based on the last two equations of (2.6) Figure 2.3 2.2.5 Inverter Estimated speed Speed controller Torque and flux controller Speed command Voltages IM Currents Direct self control system with speed estimation. Acceleration Control Proposed From the first three equations of Equation (2.6), torque T may be expressed as a function of stator current iss and stator flux lsm while the lsm is a function of iss and stator voltage Vss . The two functions may be expressed as: T ¼ f1 iss ; lsm ð2:20Þ lsm ¼ f2 iss ; Vss : ð2:21Þ 16 Applied Intelligent Control of Induction Motor Drives Equations (2.20) and (2.21) can be rewritten as: lsm ¼ f3 iss ; T Vss ¼ f4 lsm ; iss : doo þ TL into Equation (2.23), dt doo s ; is : Vss ¼ f5 dt ð2:22Þ ð2:23Þ Substituting Equation (2.22) and T ¼ J ð2:24Þ In acceleration control, Equation (2.24) is used as a control function while the acceleration doo/dt and iss are obtained or derived from the measured signals. Although the concept of acceleration control can be explained using the above theory, the details of the control scheme need to be developed at the algorithm level (Shi, Chan, and Wong, 1997). 2.2.6 Need for Intelligent Control The difficulties that arise in induction motor control can be classified under three categories: (a) complex computation, (b) nonlinearity, (c) uncertainty (Narendra and Mukhopadhyay, 1996). a. Complex computation – In induction motor control, application of conventional control theory and control algorithm often results in complex computations. The vector controls (especially direct self control) are seldom used in practical drive systems due to these complex computations and the associated control time delays. In state estimation control schemes (for example, speed sensorless control) and parameter identification, the computations will be even more complex. b. Nonlinearity – The presence of nonlinearites in an induction motor drive makes the control problem complicated. Current research efforts in nonlinear control theory focus on differential geometric methods and attempt to extend well-known results in linear control theory to the nonlinear domain. Despite the great interest in this area, many fundamental theoretical issues related to nonlinear control are currently still not well-understood. Consequently, many of the well-established theoretical results cannot be directly used for practical control. c. Uncertainty – Certain essential information required in the mathematical model of the induction motor drive system, such as load, exact values of machine parameters, and noise, is unknown. Although some parameter identification and state estimation algorithms have been proposed to resolve the problem at the expense of more complex computations, the uncertainty problem has not been completely solved in practical applications. Based on the nonlinear control theory as well as the human ability to comprehend, reason, and learn, intelligent techniques may be used to overcome the above difficulties. 17 Philosophy of Induction Motor Control 2.2.7 Intelligent Induction Motor Control Schemes Intelligence is defined as the ability to comprehend, reason, and learn. The definition of intelligent control from Astr€ om and McAvoy has been used widely: ‘An intelligent control system has the ability to comprehend, reason, and learn about processes, disturbances and operating conditions in order to optimize the performance of the process under consideration’ (Astr€ om and Bj€ orn, 1995). Intelligent control techniques are generally classified as expertsystem control, fuzzy-logic control, neural-network control, and genetic algorithm (Bose, 1993). Intelligent induction motor control thus refers to the control of an induction motor drive using the above artificial intelligence techniques. The applications of expertsystem, fuzzy-logic, neural-network, and genetic algorithm in induction motor drive system have been proposed in the literature (Bose, 1997b). 2.2.7.1 Expert-System Control Scheme (Bose, 1997a; Astr€om and Arzen, 1993) Expert system is the forerunner among all the AI techniques, and from the beginning (1960s) to 1980s, both terms (expert system and artificial intelligence) have been used synonymously in the literature. Expert systems have been considered as a powerful method to solve control problems without having strict knowledge of mathematical description, particularly to deal with qualitative knowledge and reasoning with symbolic operation in a complex system. Expert systems have been used for choice of a.c. drive products, monitoring and diagnostics, design and simulation for a drive system. However, their applications in induction motor control are relatively few. In this book, an expert-system based acceleration control scheme is proposed. The acceleration control knowledge and human comparison strategies are employed so that the cumulative error due to evaluation of integrals and machine parameters effects of the classical vector controller can be eliminated. 2.2.7.2 Fuzzy-Logic Control Scheme (Bose, 1997b) Fuzzy logic is another form of artificial intelligence, but its history and applications are more recent than expert systems. It is argued that human thinking does not always follow crisp ‘yes-no’ logic, but is often vague, uncertain, indecisive, or fuzzy. Based on this, Lofty Zadeh, a computer scientist, introduced the ‘fuzzy logic’ or fuzzy set theory in 1965 (Zadeh, 1965) that gradually emerged as a discipline in AI. The main characteristic of the fuzzy logic technique is to use the fuzzy rule sets and the linguistic representation of a human’s knowledge to describe the controlled plant or to construct the fuzzy controller. A fuzzylogic controller consists of fuzzification, fuzzy inference with rulebase and database, and defuzzification. Some fuzzy-logic controllers have already been designed for induction motor control, such as FOC with fuzzy efficiency optimizer and fuzzy-logic based DSC (Sousa, Bose, and Cleland, 1995; Mir, Zinger, and Elbuluk, 1994). In this book, a hybrid fuzzy/PI two-stage control scheme is proposed. In the scheme, the fuzzy-logic frequency controller and the PI current controller produce almost the same frequency and current magnitude control characteristics as a field-oriented controller. Effects of parameter variation, effects of noise in measured speed and input current, and effects of magnetic saturation are investigated. 18 Applied Intelligent Control of Induction Motor Drives 2.2.7.3 Neural-Network Control Scheme (Bose, 1997b; Simoes and Bose, 1995) Neural network is the most generic form of AI for emulation of human thinking compared to expert systems and fuzzy logic. In 1943, McCulloch and Pitts first proposed a network composed of binary-valued artificial neurons that were capable of performing simple threshold logic computations. The modern era of neural network with rejuvenated research practically started in 1982 when Hopfield presented his invention. Since then, many network models and learning rules have been introduced. The neural network is famous for its learning ability and arbitrary approximation to any continuous function. Research of the neural-network nonlinear dynamical control has been in progress since 1988 (Narendra and Mukhopadhyay, 1996). Recently, neural networks have been used for the parameter identification and state estimation of induction motor drive systems. Hybrid fuzzy and neural controller (also called a neuro-fuzzy controller) has been designed to control a 100 kW induction motor (Bose, Patel, and Rajashekara, 1997). Neural network with the advantage of parallel computation can be used to decrease the controller time-delay caused by complex computation. In this book, a neural-networkbased DSC scheme is proposed to decrease the controller time delay so that the torque and flux errors of a DSC can almost be eliminated. The proposed neural-network controller employs the individual training strategy with the fixed-weight and the supervised methods (Kung, 1993). 2.2.7.4 Genetic Algorithm (Fogel, 1994) Over the past 30 years, genetic algorithms were mainly developed in the USA by J. H. Holland, while evolutionary strategies were developed in Germany by I. Rechenberg and H.-P. Schwefel. Each of these constitutes a different approach, but they are both inspired by the principles of natural evolution. The GA is a stochastic global search method that mimics the metaphor of natural biological evolution. GA operates on a population of potential solutions applying the principle of survival of the fittest to produce (hopefully) better approximations to a solution. The most commonly used representation in GA is the binary alphabet {0, 1}, while there is an increasing interest in alternative encoding strategies, such as integer and real-coded representations (Wright, 1991). The GA differs substantially from the more traditional search and optimization methods, and the followings are the most significant: 1. GA searches a population of points in parallel instead of a single point. 2. GA does not require derivative information or other auxiliary knowledge; only the objective function and the corresponding fitness levels will influence the directions of search. 3. GA uses probabilistic transition rules instead of deterministic ones. In this book, a real-coded genetic algorithm is proposed to optimize the extended Kalman filter (EKF) for estimating the rotor speed of an induction motor. It is shown that the real-coded GA is effective for optimizing the EKF performance of three different controllers, namely the closedloop V/Hz controller, DSC, and FOC. The GA-EKF computer simulations for speed estimation show good noise rejection and they are less sensitive to machine parameter variations. Experiments are performed on a DSP-based FOC induction motor drive in order to verify the feasibility of the GA-EKF approach. 19 Philosophy of Induction Motor Control 2.3 Induction Motor Control Algorithms Different control algorithms are designed based on the control theory, principle, and hardware. Control algorithms of induction motor can be classified into three main categories (Rajashekara, Kawamura, and Matsuse, 1996; Bose, 1997b). (I) Scalar control: 1. Open-loop voltage/frequency (V/Hz) control 2. Slip frequency and voltage control 3. Slip frequency and current control (II) Vector control: 4. Direct FOC 5. Indirect FOC 6. Direct self control (DSC) 7. Acceleration control (III) Intelligent control: 8. Fuzzy control 9. Neural-network control 10. Expert-system control 11. Genetic algorithm A fictitious control system is shown in Figure 2.4 for explaining different induction motor control algorithms. Controller Command Reference commands Feedback Signals Voltage Current Subcontrollers Inverter State estimation and feedback signal calculation Speed estimation or measurement Figure 2.4 Speed IM Rotor speed A fictitious control system at the algorithm level. Figure 2.4 shows that a control algorithm can be characterized by the choice of feedback signals with the appropriate control function and control strategy. Various control algorithms are represented as follows: 1. Open-loop V/F control algorithm (Bose, 1981): a. Feedback signal F ¼ ½0 The open loop V/Hz control scheme has no feedback signal. const: o* j Vs j ¼ b. Control function u¼ o o* where |Vs| is stator voltage magnitude, o is supply frequency, and o is supply frequency command. The ratio |Vs|/o is maintained constant. c. Control strategy: constant V/Hz control to maintain constant stator flux. 20 Applied Intelligent Control of Induction Motor Drives 2. Slip frequency and voltage control algorithm (Trzynadlowski, 1994): a. Feedback signal F ¼ ½oo const: o j Vs j b. Control function u ¼ ¼ and or ¼ f ðoo * oo Þ o oo þ or where oo is rotor speed command and or is slip frequency. c. Control strategy: slip frequency control and constant V/Hz control. Setting the limit on the slip speed in the vicinity of the peak torque point provides fast response of the drive system according to the speed command. 3. Slip frequency and current control algorithm (Rajashekara, Kawamura, and Matsuse, 1996): oo a. Feedback signal F¼ jis j f1 ðoo * oo Þ jis j ¼ and or ¼ f2 ðoo * oo Þ b. Control function u¼ o oo þ or c. Control strategies: slip frequency control and current control. Setting the limit on the slip speed in vicinity of the peak torque point provides fast speed response of the drive system according to the reference speed. 4. Direct FOC algorithm (Trzynadlowski, 1994): The field orientation control algorithms can be divided into two types: direct FOC and indirect FOC. In the direct FOC scheme, the rotor flux ler , torque T, and rotor flux angle yr are feedback signals which are obtained from the air-gap flux (or stator voltage) and stator current signals. In the indirect FOC scheme, the rotor flux ler and torque T are control commands, while the rotor flux angle yr is the feedback signal which is obtained by summation of the rotor speed and reference slip frequency. In direct field-oriented control, 3 2 2 s 3 2 s 3 yr ids ids 7 7 6 is 7 6 6 6 ds 7 6 is 7 6 is 7 6 s 7 6 qs 7 6 qs 7 7 7 7 6 6 a. Feedback signal F ¼ 6 6 iqs 7 ¼ qðxÞ; where x ¼ 6 s 7 or x ¼ 6 s 7 6 s 7 6 ldr 7 6 Vds 7 5 5 4 ldr 5 4 4 s s l V qs qr TL " # ids ðT* T; lsdr * lsdr ; yr Þ b. Control function u ¼ iqs ðT* T; lsdr * lsdr ; yr Þ with the field-orientation conditions: leqr ¼ 0 and ledr ¼ const: c. Control strategies: coordinate transformations, current controlled and field-orientation conditions. 5. Indirect FOC algorithm (Trzynadlowski, 1994): a. Feedback signal F ¼ ½ yr " s # ids ðT* T; lsdr * lsdr ; yr Þ b. Control function u¼ s iqs ðT* T; lsdr * lsdr ; yr Þ 21 Philosophy of Induction Motor Control with the field-orientation conditions: leqr ¼ 0 and ledr ¼ const: Control strategies: coordinate transformations, current controlled and field orientation conditions. 6. DSC control algorithm (Baader, 1992): 2 s 3 ids 2 3 7 6 s l 6 is 7 6 qs 7 6 m 7 7 6 7 a. Feedback signal F¼6 4 ym 5 ¼ qðxÞ; where x ¼ 6 s 7 6 Vds 7 5 4 T s Vqs 2 3 s s s s Sa Vds ; T*; lm * ; Vqs ; ids ; iqs 7 6 6 7 7 6 s s s s b. Control function u ¼ 6 Sb Vds ; Vqs ; ids ; iqs ; T*; lm * 7 7 6 5 4 s s s s Sc Vds ; Vqs ; ids ; iqs ; T*; lm * Sa, Sb, and Sc are the status of inverter switches. c. Control strategy: hysteresis (bang-bang) control and optimum switching table. The principle of direct self control for the torque and the flux is based on hysteresis control with an optimum switching table. In this system, the instantaneous values of the flux and torque are calculated from the stator voltage and current. The flux and torque can then be controlled directly and independently by selecting the optimum inverter switching modes. The selection is made so as to restrict the errors of the flux and torque within the hysteresis bands and to obtain fast torque response with a low inverter switching frequency and low harmonic losses. 7. Acceleration control algorithm (Shi, 1997): 2 3 oo a 4 i a. Feedback signal F¼ ¼ qðxÞ where x ¼ ds 5 yðis Þ iqs 3 2 Sa ðyðis Þ; a*; aÞ 7 6 b. Control function u ¼ 4 Sb ðyðis Þ; a*; aÞ 5 Sc ðyðis Þ; a*; aÞ Sa, Sb, and Sc are the status of inverter switches, a is rotor acceleration and a is acceleration command. c. Control strategy: flux angle reasoning, acceleration comparison and expert system principle. In the acceleration control scheme, the approximate flux angles are obtained by an inference system from the stator current angles and acceleration states. The inverter switching modes are determined by comparing two accelerations produced by different voltage vectors with respect to the stator current angle. The acceleration and stator current angle are used as feedback signals. 22 Applied Intelligent Control of Induction Motor Drives 8. Fuzzy control algorithm (Sousa and Bose, 1994; Tang and Xu, 1994): 2 3 R a. Fuzzy controller input Finput ¼ 4 E 5 DE where R is the feedback signal, E is the error signal, and DE is the change in error signal. Flinguistic b. Fuzzification ¼ f ðFinput Þ minput where Flinguistic denotes the input fuzzy linguistic value and minput denotes the degree of membership of the input. u Flinguistic c. Fuzzy inference ¼K minput moutput where u denotes the crisp value of output fuzzy linguistic value and moutput denotes the fuzzy degree of membership of the output. u d. Defuzzification y¼g moutput where y denotes the output crisp value required by the plant. The control algorithm is based on the fuzzy set theory. A fuzzy control algorithm consists of fuzzification with a database, a fuzzy logic inference based on a rulebase, and defuzzification. The fuzzification operation implements the process of converting the crisp input values to fuzzy sets. The fuzzy set consists of elements each having a degree of membership and associated with linguistic values. The defuzzification operation is the process of determining the best numerical value to represent a given fuzzy set. The database stores memberships of fuzzy variables. The rulebase provides the necessary linguistic control rules for the fuzzy inference. 9. Neural-network control algorithm"(Bose, 1997a): # gðtÞ x a. Input-output pair ¼ z IMðxÞ where x is the input samples, z is the outputs, g(t) denotes the generation function of input samples, and IM denotes the plant outputs. w x b. Training ¼ Re f b z where w is the weight of network, b is the bias of network, f denotes the activation function, and Re denotes the training algorithm. c. Implementation z0 ¼ f ðwx0 þ bÞ 0 where z denotes the output of neural-network and x0 denotes the practical inputs. A neural model is mathematically represented by a basis function [w, b] and an activation function f(.). The selection of these functions often depends on the applications of neural network. Neural network is used to approximate the control function of induction motor through training procedures. 10. Expert system control algorithm (Astr€ om and Arzen, 1993; Lu, 1996; Bose, 1997a): a. Knowledge acquisition Kbase ¼ f ðExpert Þ where Kbase denotes the knowledge base, Expert denotes the expert knowledge, and f is the knowledge acquisition procedure. Philosophy of Induction Motor Control 23 b. Input and output interfaces x0 ¼ gðxÞ; and x ¼ hðz0 Þ 0 where x is the electrical signal. x and z0 denote the numerical and linguistic codes. G(.) implements the electrical signal encoding and h(.) implements the numerical and linguistic decoding. " #! Kbase 0 c. Inference engine z ¼ Inference x0 where Inference denotes the inference procedure. d. User interface L ¼ eðExecution Þ 0 ¼ f 0 ðUser ; Kbase Þ Kbase where Execution is the execution of the rules, L is natural language, User denotes a user, e(.) is an explanation function, and f0 denotes the modification procedure of the knowledge base. Based on the knowledge acquired from control experts in encoded form, the control function is derived by the on-line inference engine. The humanlike knowledge-inference system may be applied to cope with complex induction motor drive systems, or those with parameter uncertainties. 11. Genetic algorithm in control: gðtÞ x a. Input-output pair ¼ IMðxÞ z b. c. d. e. 2.4 where x denotes the input samples, z denotes the outputs, g(t) denotes the generation function of input samples, and IM denotes the plant outputs. Coding parameters S ¼ MðPÞ where P is controller parameters, M is coding method, and S is a genetic string. Reproduction with fitness evaluation Sn þ 1 ¼ RðSn Þ where Sn þ 1 is the new reproduction and R denotes the reproduction algorithm with fitness evaluation. Crossover and Mutation Sn þ 2 ¼ CMðSn þ 1 Þ where CM is the crossover and mutation method. Decoding parameters PL ¼ NðSL Þ where N is decoding method, SL is an optimum string, and PL is optimum controller parameters. Genetic algorithm is a search algorithm based on the mechanics of natural selection and natural genetics. GA has the properties that make it a powerful technique for optimizing controller parameters for an induction motor drive. Speed Estimation Algorithms The speed sensorless strategies have aroused great interest among induction motor control researchers. In these strategies, the motor speed is estimated and used as a feedback signal for closed-loop speed control. These algorithms may be classified into the following categories (Rajashekara, Kawamura, and Matsuse, 1996; Holtz, 1996; Ilas et al., 1996): 24 Applied Intelligent Control of Induction Motor Drives 1. Open loop with slip compensation algorithm (Rajashekara, Kawamura, and Matsuse, 1996). The rotor speed is obtained from summation of synchronous speed and slip speed which is estimated from the load. This algorithm can only be used in the steadystate case. Model: Speed estimation function: Steady-state torque-speed relationship. oo ¼ o þ or ðTL Þ 2. Slip frequency algorithm (Abbondanti and Brennen, 1975). The slip speed is calculated based on a steady-state model of the motor. Model: Speed estimation function: Steady-state ‘T’ equivalent circuit oo ¼ ðo; iss ; Vss Þ 3. Speed estimation algorithm using state equations (Joetten and Maeder, 1983). The rotor speed can be calculated from the state equation Equation (2.14), which can be expressed as Model: Speed estimation function: the 11th fifth-order model with ‘T’ equivalent circuit s s s s oo ¼ f ðVds ; Vqs ; ids ; iqs ; lsdr ; lsqr Þ 4. Flux estimation and flux vector control algorithm (Xu and Doncker, 1988). The rotor speed is obtained by estimating the synchronous speed and slip speed. The synchronous speed is replaced by stator flux speed and the slip speed is estimated based on machine parameters of the motor. Model: Speed estimation function: the first fifth-order equation with ‘G’ equivalent circuit s s s s oo ¼ f ðVds ; Vqs ; ids ; iqs ; lsdm ; lsqm Þ 5. Observer algorithm (Cuzner, 1990; Jansen, 1996). The fluxes are calculated by a voltage model and a current model, separately. The speed is estimated based on the difference between two fluxes. Model: Speed estimation function: Voltage model and current model oo ¼ f ðVds ; Vqs ; ids ; iqs ; ldr ; lqr ; kp ; kI Þ where Kp and KI are the adaptation mechanism gains. 6. Model reference adaptive algorithm (Trzynadlowski, 1994). A comparison is made between the outputs of two estimators. The first estimator, which does not involve the estimated rotor speed, is considered as a reference model of the induction motor. The second estimator, which involves the estimated rotor speed, is regarded as an adjustable model. The error between the outputs of the two estimators is used to derive a suitable adaptation mechanism that generates the estimated rotor speed to modify the adjustable model. 25 Philosophy of Induction Motor Control Model: Speed estimation function: Reference model of induction motor and adjustable model oo ¼ f ðea ; eb ; ~ea ; ~eb ; kp ; kI Þ where Kp and KI are the adaptation mechanism gains, ea and eb are outputs of the reference model of induction motor, and ~ea and ~eb are outputs of the adjustable model. The outputs may be flux, counter emf, reactive power, and so on. 7. Extended Kalman filter estimation algorithm (Salvatore, Stasi, and Tarchioni, 1993; Kim, Sul, and Park, 1996). Extended Kalman filter is employed to estimate the rotor speed, based on the measured stator currents and voltages. Kalman filter algorithm is based on complete electrical model of induction motor for determination of the system state. The rotor speed can be determined based on the measured voltages and currents. Using the state equations and Kalman filter, the rotor speed (an extended state) is estimated. Model: Speed estimation function: Complete electrical model of induction motor with an extended state, rotor speed. oo ¼ f ðVds ; Vqs ; ids ; iqs ; oo Þ 8. Neural network algorithm (Simoes and Bose, 1995). Neural network algorithm is based on a learning process. Neural networks have the advantages of extremely fast parallel computation and fault tolerance characteristics due to distributed network intelligence, which would be ideal for speed estimation of an induction motor. Model: Speed estimation function: Neural network oo ¼ f ðids ; iqs ; lds ; lqs Þ All speed sensorless algorithms depend on the mathematical model of the induction motor. 2.5 Hardware Hardware implementation of induction motor control involves three essential components, and hence three important technical areas: 1. Induction motor (involving electrical machine techniques) 2. Power inverter (involving power electronics techniques) 3. Controller (involving computer and control techniques). A scalar controller is usually implemented with analog electronic components, and a vector controller is implemented with a digital device DSP or a microcontroller. The fuzzy control algorithm may be implemented with a special fuzzy microcontroller or a DSP, while the expert system algorithm may be implemented with DSP. The DSP based controller is the current trend of induction motor control. With the ability of implementing complex computations, a DSP such as ADMC331 is a suitable solution to implement high-performance algorithms and intelligent algorithms for induction motor drives. Based on an understanding of the induction motor control system, a taxonomy of induction motor control is given in Table 2.1. 26 Table 2.1 Taxonomy of induction motor control. Algorithm Feedback signal Open-loop V/Hz control F ¼ {} Hardware Vss ; og Fuzzy slip and current control F ¼ {current, speed} u ¼ iss ; o Fuzzy-logic Constant V/Hz control Slip control based on static torquespeed characteristic Slip control based on static torque-speed characteristic Open-loop control Constant V/Hz control PI current magnitude control Slip control based on features of FOC Closed-loop control Closed-loop control PI current magnitude control Closed-loop control Slow response Medium-slow response Medium response Medium-fast response Robustness Robustness Robustness Robustness Electronic components Fuzzy device PWM current-controlled inverter PWM current-controlled inverter Electronic components PWM inverter Applied Intelligent Control of Induction Motor Drives Characteristics Slip and current control F ¼ {speed} u¼f Control function Control strategies Slip and voltage control Feedback signal Direct FOC Indirect FOC F ¼ {flux, voltage, current, speed} F ¼ {speed} DSC ANN-DSC Fuzz-logic DSC F ¼ {voltage, current, speed} u ¼ {iqs, ids} Control function Control strategies ANN-FOC Fuzzy-logic FOC u ¼ {Sa, Sb, Sc} Expert-system based Acceleration control F ¼ {current, speed} Philosophy of Induction Motor Control Algorithm u ¼ {Sa, Sb, Sc} Coordinate transformation Implementation of neural network Bang-bang control Implementation of neural network Acceleration comparison PI control Controller is partly implemented by fuzzy logic Optimum switch table Controller is partly implemented by fuzzy logic Flux angle estimation Flux and torque estimation Flux and torque estimation Bang-bang control Speed estimation Speed estimation Production system Parameter identification Parameter identification (continued) 27 28 Table 2.1 (Continued) Algorithm Characteristics Direct FOC Indirect FOC Fast response ANN-FOC Fuzzy-logic FOC Fast response Sensitive to motor parameter changes DSC ANN-DSC Fuzz-logic DSC Expert-system based Acceleration control Fast response Fast response Fast response Integral drift Integral drift Sensitive to speed sensor noise Discontinuous control Hardware DSP ANN and fuzzy devices DSP ANN and fuzzy devices DSP PWM PWM, Currentcontrolled inverter Inverter Inverter Inverter Current-controlled inverter Speed sensor Applied Intelligent Control of Induction Motor Drives Robustness against parameter changes and current noise Philosophy of Induction Motor Control 29 References Abbondanti, A. and Brennen, M.B. (1975) Variable speed induction motor drives use electronic slip calculator based on motor voltage and currents. IEEE Transactions on Industry Applications, IA-11(5), 483–488. Astr€ om, K.J. and Arzen, K.E. (1993) Expert control, in An Introduction to Intelligent and Autonomous Control (eds P.J. Antsaklis, K.M. Passino, and MA. Norwell) Kluwer Academic Publishers, pp. 163–168. Astr€ om, K.J. and Bj€ orn, W. (1995) Adaptive Control, Addison Wesley Publishing Company, Reading, MA. Baader, U., Depenbrock, M. and Gierse, G. (1992) Direct Self Control (DSC) of inverter-fed induction machine: a basis for speed control without speed measurement. IEEE Transactions on Industry Applications, 28(3), 581–589. Blashke, F. (1972) The principle of field-orientation as applied to the new ‘transvektor’ closed-loop control system for rotating-field machines. Simians Review, 34(5), 21–220. Bose, B.K. (1981) Adjustable Speed AC Drive Systems, IEEE Press, New York. Bose, B.K. (1993) Power electronics and motion control-technology status and recent trends. IEEE Transactions on Industry Applications, 29, 902–909. Bose, B.K. (1997a) Expert system, fuzzy logic, and neural networks in power electronics and drives, in Power Electronics and Variable Frequency Drives: Technology and Applications (ed. B.K. Bose), IEEE Press, New Jersey. Bose, B.K. (1997b) Intelligent control and estimation in power electronics and drives. The 1997 IEEE International Electric Machines and Drives Conference, USA, May. Bose, B.K., Patel, N.R., and Rajashekara, K. (1997) A neuro-fuzzy based on-line efficiency optimization control of a stator flux oriented direct vector controlled induction motor drive. IEEE Transactions on Industrial Electronics, 44, 270–273. Chan, C.C., Leung, W.S., and Ng, C.W. (1990) Adaptive decoupling control of induction motor drives. IEEE Transactions on Industrial Electronics, 37(1), 41–47. Cuzner, R.M., Lorenz, R.D., and Novotny, D.W. (1990) Application of nonlinear observers for rotor position detection on an induction motor using machine voltages and currents. IEEE Industry Applications Society, 416–421. Delgado, A., Kambhampati, C., and Warwick, K. (1995) Dynamic recurrent neural network for system identification and control. IEE Proceedings – Control Theory and Applications, 142(4), 307–314. Depenbrock, M. (Inventor) (18, Oct. 1985) Direct Self-control of the Flux and Rotary Moment of a Rotary-field Machine, United States Patent 4,678,248. Fogel, D.B. (1994) An introduction to simulated evolutionary optimization. IEEE Transactions on Neural Networks, 5(1), 3–14. Hasse, K. (1969) ‘About the Dynamics of Adjustable-speed Drives with Converter-fed Squirrel-cage Induction Motors’ (in German), Dissertation, Darmstadt Technische Hochschule. Holtz, J. (1996) Methods for speed sensorless control of AC drives, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura, and K. Matsuse), IEEE Press, New Jersey. Ilas, C., Bettini, A., Ferraris, L. et al. (1996) Comparison of different schemes without shaft sensors for field oriented control drives, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura, and K. Matsuse) IEEE Press, New Jersey. Jansen, P.L., Lorenz, R.D., and Novotny, D.W. (1996) Observer-based direct field orientation: analysis and comparison of alternative methods, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura, and K. Matsuse) IEEE Press, New Jersey. Joetten, R. and Maeder, G. (1983) Control methods for good dynamic performance induction motor drives based on current and voltage as measured quantities. IEEE Transactions on Industry Applications, IA-19(3), 356–363. Kim, Y.R., Sul, S.K., and Park, M.H. (1996) Speed sensorless vector control of induction motor using extended kalman filter, in Sensorless Control of AC Motor Drives, IEEE Press, New Jersey, pp. 215–223. Krause, P.C., Wasynczuk, O., and Sudhoff, S.D. (1995) Analysis of Electric Machinery, IEEE Press, New Jersey Kung, S.Y. (1993) Digital Neural Networks, PTR Prentice-Hall, Inc., New Jersey. Lu, Y.Z. (1996) Industrial Intelligent Control: Fundamentals and Applications, John Wiley & Sons Ltd, Chichester. Marino, R. and Tomei, P. (1995) Nonlinear Control Design, Prentice Hall Europe, London. Mir, S.A., Zinger, D.S., and Elbuluk, M.E. (1994) Fuzzy controller for inverter fed induction machines. IEEE Transactions on Industry Applications, 30(1), 78–84. Narendra, K.S. and Mukhopadhyay, S. (1996) Intelligent control using neural networks, in Intelligent Control Systems: Theory and Applications (eds M.M. Gupta and N.K. Sinha) IEEE Press, New Jersey. 30 Applied Intelligent Control of Induction Motor Drives Rajashekara, K., Kawamura, A., and Matsuse, K. (1996) Speed sensorless control of induction motor, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura, and K. Matsuse), IEEE Press, New Jersey. Salvatore, L., Stasi, S., and Tarchioni, L. (1993) A new EKF-based algorithm for flux estimation in induction machines. IEEE Transactions on Industrial Electronics, 40(5), 496–504. Shi, K.L., Chan, T.F., and Wong, Y.K. (1997) A new direct self-control scheme for an inverter-fed induction motor. Second International Power Electronics and Motion Control Conference, Hangzhou, November. Simoes, M.G. and Bose, B.K. (1995) Neural network based estimation of feedback signals for a vector controlled induction motor drive. IEEE Transactions on Industry Applications, 31, 620–629. Sousa, G.C.D. and Bose, B.K. (1994) A fuzzy set theory based control of a phase-controlled converter DC machine drive. IEEE Transactions on Industry Applications, 30(1), 34–44. Sousa, G.C.D., Bose, B.K., and Cleland, J.G. (1995) Fuzzy logic based efficiency optimization control of an indirect vector controlled induction motor drive. IEEE Transactions on Industrial Electronics, 42(2), 192–198. Tang, Y.F. and Xu, L.Y. (1994) Fuzzy logic application for intelligent control of a variable speed drive. IEEE Transactions on Energy Conversion, 9(4), 679–685. Trzynadlowski, A.M. (1994) The Field Orientation Principle in Control of Induction Motors, Kluwer Academic Publishers, Boston. Vidyasagar, M. (1993) Nonliear Systems Analysis, Prentice-Hall Inc., New Jersey. Wright, A.H. (1991) Genetic algorithms for real parameter optimization, in Foundations of Genetic Algorithms (ed. J.E. Rawlins), Morgan Kaufmann, San Francisco, CA, pp. 205–218. Xu, X. and Doncker, R.D. (1988) A stator flux oriented induction machine drive. IEEE Power Electronics Specialists Conference, pp. 870–876. Zadeh, L.A. (1965) Fuzzy sets. Information and Control, 8, 338–353. 3 Modeling and Simulation of Induction Motor1 3.1 Introduction Evaluation of an induction motor control system can be performed in two ways. The first approach (at hardware level) uses a real motor with an inverter and a controller. The controller is usually constructed using electronic devices, such as ICs (integrated circuits), or a DSP (digital signal processor) with the algorithm coded in assembler or ‘C’ language. The advantages of the experimental approach are that it includes the actual noise present, the practical inverter voltage and current waveforms, and sensor characteristics that may not be included in a computer simulation. The main disadvantage of the practical approach is that the experimental results are valid only for the system being investigated such as motor type, rating, and inverter supply. Besides, some of the electrical parameters may be difficult or impossible to measure. The second approach (at algorithm level) is a computer simulation of the system (Krause and Thomas, 1965; Chan, Jiang and Chen, 1993; Mohan et al., 1997). In the computer simulation environment, all quantities can be readily observed and the parameters can be altered to investigate their effect on the system, thereby providing useful information for controller design. Process noise and sensor noise can be added to simulate the performance. Motor type, size, and power supply may be changed easily. Development of a new motor drive often involves expensive prototypes. Advanced computer simulation and mathematical modeling techniques with solution procedures can produce optimal designs with minimum time, cost, and effort. 1 (a) Portions reprinted from K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling and simulation of the three-phase induction motor,” International Journal on Electrical Engineering Education, 36(2), 163–172, Ó 1999, with permission from Manchester University Press. (b) Portions reprinted by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK,” The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, May 18–21, 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE. (c) Portions reprinted from K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Modeling and simulation of a novel two-stage controller for an induction motor,” International Association of Science and Technology for Development (IASTED) Journal on Power and Energy Systems, 19(3), 257–264, Ó 1999, with the permission from ACTA Press. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 32 Applied Intelligent Control of Induction Motor Drives Modeling and simulation of the three-phase induction machine is well documented in the literature and digital computer solution can be performed using several methods, such as numeric programming, symbolic programming and the electromagnetic transient program (EMTP) (Domijan and Yin, 1994). Throughout this book, MATLABÒ/Simulink software will be used for the dynamic modeling of the induction motor and simulation studies. The main advantage of Simulink over other programming softwares is that, instead of compilation of program code, the simulation model is built up systematically by means of basic function blocks. A set of machine differential equations can thus be modeled by interconnecting appropriate function blocks, each of which performing a specific mathematical operation. Programming efforts are drastically reduced and error debugging is easy. Since Simulink is a model operation program, the simulation model can be easily developed by addition of new sub-models to cater for various control functions. As a sub-model, for example, the induction motor could be incorporated in a complete electric motor drive system. 3.2 Modeling of Induction Motor Three simulation models of induction motor are developed using MATLABÒ/Simulink in this chapter. They are the current-input model, the voltage-input model, and the discrete-state model, which can be used to study different induction motor drive systems. The current-input model is more suitable for the study of a current-controlled drive system, while the voltage-input model and the discrete-state model are more suitable for the study of inverter-fed induction motor control. The current-input model is based on Equation (2.15), the reduced-order equation of the 11th fifth-order equation in the excitation reference frame, while the discrete-state model is based on a discrete-time form of Equation (2.14), the 11th fifth-order equation in the stator reference frame. Modeling of the voltage-input model is based on the 8th fifth-order equation, which can be expressed in matrix form as follows (Trzynadlowski, 1994): 3 2 P P 2 oo LM oo Lr LM Rs Lr 0 7 Rr L M 6 2 2 72 3 6 2 s 3 7 is 6 ids P 7 ds 6 P 6 oo L2M oo Lr LM Rs Lr Rr LM 0 76 7 6 s 7 76 i s 7 6 2 6 iqs 7 76 qs 7 6 2 6 7 76 7 6 7 P P d6 76 s 7 6 is 7 ¼ 1 6 o o R L L R L L L 0 L 76 idr 7 6 o s M r s o s M s M dr 7 2 76 7 2 2 dt 6 6 7 Lc 6 76 s 7 6 6 is 7 74 iqr 5 6P P 4 qr 5 6 oo Ls LM oo Ls Lr Rs LM Rr Ls 0 7 7 62 2 7 oo 6 oo 7 6 2 4 PLM L2 PLM Lc Cf 5 c iqs ids 0 0 3J 3J J 3 2 Lr 0 LM 0 0 2 s 3 V 6 0 Lr 0 LM 0 7 76 ds 6 s 7 Vqs 7 6 7 6 16 L 0 Ls 0 0 76 7 þ 26 M ð3:1Þ 0 76 7 74 Lc 6 0 L 0 L 0 5 M s 0 7 6 4 L2c 5 TL 0 0 0 0 J pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 where Lc ¼ Ls Lr LM . 33 Modeling and Simulation of Induction Motor Rotating transformation from abc to dq coordinates, also called 3/2 rotating transformation, projects balanced three-phase quantities (voltages or currents) to rotating two-axis coordinates at a given angular velocity. The transformation is defined as follows: " Vd Vq # 2 6 cosðyÞ 6 ¼ Cdq 6 4 sinðyÞ 2p cos y 3 2p sin y 3 cosðyÞ 6 Va 6 2p 6 cos y 6 7 6 Vb 7 ¼ Cabc 6 3 6 4 5 6 4 2p Vc cos y þ 3 2 2 3 32 3 2p Va cos y þ 3 7 6 76 7 7 7 4 Vb 5 2p 5 sin y þ Vc 3 3 sinðyÞ 7 2p 7" V # 7 d sin y 3 7 7 Vq 7 2p 5 sin y þ 3 ð3:2Þ ð3:3Þ where Cdq Cabc ¼ 2=3. Note that the transform matrices and multiplying factors are the same for both voltages and currents. In the original Park’s transformation, the factor Cdq for abc to dq transformation is 2/3, while the factor Cabc for p dqﬃﬃﬃﬃﬃﬃﬃ to abc ﬃ transformation is 1. In some publications, however, Cdq and Cabc are (Trzynadlowski, 1994). both defined to be 2=3. In this book, Cdq is defined as 1 and Cabc as 2/3p ﬃﬃﬃ For example, the peak value of a line-linepvoltage of 220 V is 220 2 ¼ 311:13 V and the ﬃﬃﬃ pﬃﬃﬃ peak value of each phase voltage is 220 2= 3 ¼ 179:63 V. After a rotating transformation pﬃﬃﬃ from abc to dq coordinate, the peak value of Vd or Vq is 220 2 Cdq 3 p1ﬃﬃ 2 3 ¼ 269:444 Cdq . When Cdq ¼ 1, the peak value of Vd or Vq is 269.444 V. Accordingly, the multiplying factor in the torque equation of the induction motor may be different depending on the value of Cdq defined. Another transformation, which converts three phase quantities to two phase quantities without rotation of coordinates, is called the abc to ab coordinate transformation. It is used to simplify the analysis of three-phase quantities, and is defined as follows. " Vds Vqs 2 # Va ¼ Cdqs 3 " 1 0 2 1=2 pﬃﬃﬃ 3=2 1 6 6 7 6 Vb 7 ¼ Cabcs 6 1=2 4 4 5 Vc where Cdqs Cabcs ¼ 2=3. 1=2 2 3 # Va 1=2 6 7 6 Vb 7 pﬃﬃﬃ 4 5 3=2 Vc 3 0 " # pﬃﬃﬃ 7 Vds 7 3=2 5 Vqs pﬃﬃﬃ 3=2 ð3:4Þ ð3:5Þ 34 Applied Intelligent Control of Induction Motor Drives In this book, ab axes are defined as ds-qs. Cdqs is 1 and Cabcs in the ab transform is 2/3 (Trzynadlowski, 1994). The various induction motor models being studied are summarized in Table 3.1. Table 3.1 Induction motor models. Models Equivalent Circuit and Reference Frame Modeling Equations Computer Execution Time Applications Current-input model Voltage-input Model Discrete-state model ‘T’ in excitation reference frame ‘T’ in stator reference frame ‘T’ in stator reference frame Equation (2.15) Fast Equation (3.1) Medium Discrete form of Equation (2.14) Slow Currentcontrolled drive Voltage-source invert-fed drive State-space expression 3.3 Current-Input Model of Induction Motor The current-input model is based on the reference-frame theory of coordinate transformation (Krause, Wasynczuk and Sudhoff, 1995). The simulation model is implemented using MATLABÒ/Simulink and it possesses the following characteristics: 1. It takes current source and load torque as inputs and gives the rotor speed as output. 2. The parameters may be continuously changed. 3. The model may be easily expanded and has a good user interface. The current-input model of an induction motor consists of (1) a current (3/2) transformation sub-model, (2) an electrical sub-model, and (3) a mechanical sub-model, as shown in Figure 3.1. 4 Load TL Ids 1 Current magnitude Iqs 2 Current phase 3 Current frequency 1 Te 3 P/2 Figure 3.1 Current 3/2Trans sub-model Electrical sub-model Slip frequency Mechanical sub-model + Sum wo w Current-input model of an induction motor in Simulink. Rotor speed 35 Modeling and Simulation of Induction Motor 3.3.1 Current (3/2) Rotating Transformation Sub-Model The current (3/2) rotating transformation sub-model consists of a current source block and a current 3/2 rotating transformation block. The current source block is used to build a current source based on input frequency, phase, and magnitude. The current (3/2) rotating transformation block is used to convert the three-phase stator current to the corresponding vectors in the excitation reference frame. The current source block is based on the following current equation. Ð 8 i ¼ A cos odt as > > < Ð ibs ¼ A cos odt 2p=3 > > Ð : ics ¼ A cos odt þ 2p=3 ð3:6Þ The representation of one supply phase using Simulink blocks is shown in Figure 3.2. Ampl. Phase Output cos(u) Freq 1 s Integrator Product Fcn ibs Figure 3.2 Simulink block diagram of one supply phase. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) The three-phase to two-phase (3/2) rotating transformation block is based on the current equations for phase transformation Equation (3.7). 2 3 Ð Ð Ð # ias " e # " ids cos odt cos odt 2p=3 cos odt þ 2p=3 6 7 7 ¼ ð3:7Þ Ð Ð Ð 6 4 ibs 5 e iqs sin odt sin odt 2p=3 sin odt þ 2p=3 ics The representation of 3/2 rotating transformation by Simulink blocks is shown in Figure 3.3. The current source blocks and the 3/2 rotating transformation blocks are grouped together to form the current 3/2 rotating transformation sub-model in the induction motor model. 3.3.2 Electrical Sub-Model Let the rotor time constant tr ¼ Lr /Rr. Equation (2.15) can be rewritten as: T¼ P LM e e ði l 3Rr tr qs dr e e ids lqr Þ ð3:8Þ 36 Applied Intelligent Control of Induction Motor Drives . Cosine vector 3 phase stator current ias ibs ics Current vector Mux e i ds Inner Product . Sine vector e i qs Inner Product1 Figure 3.3 Simulink blocks of 3/2 rotating transformation sub-model. (Reproduced by permission of K. L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) 1 LM e ¼ i p tr ds 1 LM e i leqr ¼ p tr qS 1 e e l þ or lqr tr dr 1 e lqr or ledr : tr ledr ð3:9Þ ð3:10Þ Figure 3.4 shows the electrical sub-model of an induction motor as described by e e Equations (3.8), (3.9), and (3.10). Components ids and iqs of the stator current vector and slip frequency or are the input variables and the torque T is the output variable. 3.7 input1 e i ds 0.1 Lm /τr + + τr 1/s * Integrator Sum * Product1 Product2 input3 ωr Product3 + Sum2 38. output P/3Rr Torque * input2 e i qs 0.1 Lm /τr1 * + Sum1 1/s Integrator1 Product4 3.7 τr Figure 3.4 Electrical sub-model in Simulink. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) 37 Modeling and Simulation of Induction Motor Construction of the electromechanical block in Simulink only requires the basic blocks of Sum, Gain, Product, and Integrator in the Simulink library. These blocks can be easily opened in separate windows for modification of parameters. The completed model is illustrated in Figure 3.4. The electrical blocks are grouped into the electrical sub-model in the induction motor model. 3.3.3 Mechanical Sub-Model When the friction coefficient of an induction motor is considered, the mechanical sub-model based on the first line of Equation (2.15) is expressed by Equations (3.11) and (3.12), which is constructed as shown in Figure 3.5. doo ¼ dt oo ¼ cf T TL oo þ Jm þ JL Jm þ JL ð1=Jm þ JL Þ ðT p þ cf =ðJm þ JL Þ ð3:11Þ TL Þ ð3:12Þ where p is a differential operator. 1 TL 1/0.8 s+0.124 2 Te Figure 3.5 Sum Transfer Fcn 1 Rotor Speed Simulink blocks of mechanical sub-model. For the induction motor being studied, Jm þ JL ¼ 0.8 and cf /(Jm þ JL) ¼ 0.124. The slip speed or can be calculated and fed back into the electromechanical block by Equation (3.13). or ¼ o P oo 2 ð3:13Þ The mechanical blocks are grouped into the mechanical sub-model in the induction motor model. 3.3.4 Simulation of Current-Input Model of Induction Motor In order to test the current-input model, a power source block involving internal resistance and a calculation block of stator voltage are configured with the current-input model as shown in Figure 3.6. 38 Applied Intelligent Control of Induction Motor Drives T Current source i e qs ias ibs ics Load dynamics calculation Electromechanical calculation 3/2 ωo i e ds |Is | e E −|Vs | RE |V | or | Is | = I − s RI | Is |= ω,θ |Vs | Stator voltage calculation E or I Figure 3.6 e λ dr , λ qr , e e pλ dr , p λ qr TL Block diagram of the current-input model. In Figure 3.6, the block in dotted line is the current-input induction motor model which can be used alone when the motor operates in the current controlled mode. In addition, a power supply block is included to adapt the model for motor operation on a voltage source (E) or a current source (I). In the excitation reference frame, stator flux equation and stator voltage equation can be expressed as (Trzynadlowski, 1994): les ¼ Ls L2M e LM e l i þ Lr s Lr r Vse ¼ Rs ise þ ðp þ joÞles ð3:14Þ ð3:15Þ e e e e where ise ¼ ids þ jVqs and les ¼ leds þ jleqs . þ jiqs , Vse ¼ Vds The stator voltage calculation block is based on Equations (3.14) and (3.15). The flux ler ¼ ledr þ jleqr and pler can be obtained directly from the outputs of the electromechanical block. When the two-phase quantities (voltages or currents) are transformed to three-phase coordinates, the peak value of the three phase quantities is 2/3 times of the two-phase quantities. Hence, the peak value of |Vs| in three-phase coordinates in Figure 3.6 is jVs j ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 e 2 e 2 3 ðVds Þ þ ðVqs Þ . The parameters of the induction motor used for simulation are listed under ‘Motor 1’ of Appendix B. To illustrate the application of the dynamic model of the induction motor to transient motor operation, a simulation study of direct-on-line starting is demonstrated. At the initial time instant (t ¼ 0), the motor, previously de-energized and at standstill, is connected to a three-phase, 220pVﬃﬃﬃ (line-to-line pﬃﬃﬃvoltage) and 60 Hz supply. The peak value of each phase voltage equals 2 220= 3 ¼ 179:63 V. The power source is simulated by a signal generator block in the Simulink library. It is assumed that the load TL ¼ 0.5oo (N.m). The moment of inertia JL of the load equals 0.4 kg m2. 39 Modeling and Simulation of Induction Motor Figures 3.7–3.12 show the results of computer simulation using the Simulink model which also accounts for the effect of internal resistance in the power source. When the power supply has a large internal resistance, the torque oscillations in the torque/speed characteristic are reduced and damped more rapidly, but the run up time of the motor is longer. 300 stator current(A) 250 250 stator voltage(V) 200 Torque (N.m) 200 150 speed (rad/sec) 100 150 100 50 50 0 0 0 0.5 1 1.5 2 2.5 -50 3 0 20 Time (s) 40 60 80 100 120 Speed (rad/s) Figure 3.8 Dynamic torque-speed characteristic when internal resistance of power supply is 0.2 O. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) Figure 3.7 Speed response, stator current, and stator voltage when internal resistance of power supply is 0.2 O. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) 300 stator current of ias (A) 200 100 0 -1 0 0 -2 0 0 -3 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Time (s) Figure 3.9 Stator current when internal resistance of power supply is 0.2 O. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) 40 Applied Intelligent Control of Induction Motor Drives 300 250 stator current(A) 250 Torque (N.m) 200 200 stator voltage(V) 150 100 50 0 0.5 1 100 50 0 speed (rad/sec) 0 150 -50 1.5 Time (s) 2 2.5 0 3 20 40 60 80 100 120 Speed (rad/s) Figure 3.10 Speed response, stator current, and stator voltage when internal resistance of power supply is 0.05 O. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) Figure 3.11 Dynamic torque-speed characteristic when internal resistance of power supply is 0.05 O. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK”, The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, 18–21 May 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) 300 stator current of ias (A) 200 100 0 -100 -200 -300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Time (s) 1.8 2 2.2 2.4 2.6 2.8 3 Figure 3.12 Phase current when internal resistance of power supply is 0.05 O. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Modelling of the three-phase induction motor using SIMULINK,” The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper WB3-6, May 18–21, 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE.) 3.4 Voltage-Input Model of Induction Motor The voltage-input model is based on the 8th fifth-order equation of induction motor. In this modeling scheme, the induction motor consists of an electrical sub-model, a torque sub-model and a mechanical sub-model as shown in Figure 3.13. It is more convenient to split the induction motor model into smaller sub-models for drive design purpose. 41 Modeling and Simulation of Induction Motor Vds Vqs Equation (3.16) Equation (3.17) Electrical sub-model Torque sub-model Rotor speed Equation (3.12) Mechanical sub-model Load 3 Gain Figure 3.13 outputs). Modeling of an induction motor in Simulink (thick arrows representing vector inputs or The equation for computing the current vector may be derived from Equation (3.1). 82 > Ls > > > 6 s 7 ðt > 6 > <6 0 6 iqs 7 6 7 6 ¼ 6 s 7 6 > 6i 7 6 LM > 4 dr 5 0 > 4 > > > : 0 s iqr 2 0 s B Vds B6 B6 V s 7 B6 qs 7 7 B6 B4 0 7 5 B @ 0 2 3 2 6 6 6 6 6 6 6 4 s ids 3 0 LM Ls 0 0 Lr LM 0 Rs 0 0 0 Rs 0 0 P oo LM 2 Rr P oo LM 2 0 0 7 LM 7 7 7 0 7 5 Lr 0 P oo Lr 2 1 3 3 s 7 ids 0 76 s 76 i 76 qs P oo Lr 7 76 is 2 74 dr 5 is qr Rr 2 Matrix [A] and matrix [B] are defined as follows. 2 6 6 6 6 ½ A ¼ 6 6 6 6 4 Rs 0 0 0 Rs 0 0 P oo LM 2 Rr P oo LM 2 0 P oo Lr 2 0 3 7 0 7 7 7 7 P oo Lr 7 7 2 7 5 Rr 19 > 3 > > C> > C > 7 C> 7 C= 7C dt 7 C> 5 C> > > A> > > ; Ls 0 LM 6 6 0 6 ½ B ¼ 6 6 LM 4 Ls 0 0 Lr LM 0 2 0 ð3:16Þ 0 3 1 7 LM 7 7 7 0 7 5 Lr By using the matrices [A] and [B], we can implement Equation (3.16) by the Simulink blocks as shown in Figure 3.14. In Figure 3.14, the voltage vector [Vds, Vqs] is the input vector and the current vector [ids, iqs, idr, iqr] is the output vector. Mux1, Mux2, Sum, Integrator, and Matrix Gain [B] are basic blocks 42 Applied Intelligent Control of Induction Motor Drives Vds Vqs Vdr Vds Vqs Vdr Vqr 0 Mux1 0 [B] ids iqs idr iqr 1/s Sum Integrator Matrix Gain Vqr ids iqs idr iqr Wo [A] Matrix Calculator Figure 3.14 outputs). 3 Rotor speed Gain Mux2 Electrical model of an induction motor in Simulink (thick arrows represent vector inputs or of Simulink. The function blocks of electrical sub-model in Figure 3.14 may be grouped together and then included in the motor model in Figure 3.13. 1. Torque calculation model of induction motor The torque equation of an induction motor is expressed as: T¼ PLM ðidr iqs 3 iqr ids Þ: ð3:17Þ By using Equation (3.17), we can construct the torque calculation blocks as shown in Figure 3.15. In Figure 3.15, Demux, Product, Sum, and Gain are basic blocks of Simulink. The torque calculation blocks in Figure 3.15 may be grouped together and then included in the motor model in Figure 3.13. 2. Mechanical model of induction motor The mechanical model is same as that in the current-input model, as expressed in Equation (3.8) and illustrated in Figure 3.5. 1 Current Vector ids iqs idr iqr Product Demux Product1 Figure 3.15 0.082 Sum1 Gain P*Lm/3 1 Torque Torque calculation blocks in Simulink. All function blocks of the induction motor in Figure 3.13 may be grouped together to form an induction motor block as shown in Figure 3.16. The two scope blocks enable the speed and torque of the motor to be observed. 43 Modeling and Simulation of Induction Motor Power Speed Sower Supply Scope Torque 20 N.m Load Figure 3.16 3.4.1 Scope1 Induction Motor Simulink model of an induction motor. Simulation Results of ‘Motor 1’ The parameters of the induction motor used for simulation are listed under ‘Motor 1’ of Appendix B, but cf ¼ 0. To illustrate the transient operation of the induction motor, a simulation study of direct-on-line starting is demonstrated. At the initial time instant (t ¼ 0), the motor, previously de-energized and at standstill, is connected to a three-phase, 220 V (line-to-line) and 60 Hz supply with an internal resistance of 0.05 O per phase. The power source is constructed using a signal generator block from the Simulink library. The load torque TL is assumed to be 20 N m, and is independent of speed. The moment of inertia JL of the load is 0.4 kg m2. Figures 3.17 and 3.18 show the results of computer simulation using the Simulink model. 140 120 Rotor speed (rad/s) 100 80 60 40 20 0 -20 0 Figure 3.17 3.4.2 0.5 1 1.5 2 2.5 Time (s) 3 Speed response of the induction motor with direct-on-line starting. Simulation Results of ‘Motor 2’ The parameters of the induction motor are listed in ‘Motor 2’ of Appendix B. A simulation study of direct-on-line starting is carried out. At the initial instant of time, t ¼ 0, the motor, previously de-energized and at standstill, is connected to a 220 V, 60 Hz supply. The power 44 Applied Intelligent Control of Induction Motor Drives 200 Rotor speed (rad/s) 150 100 50 0 -50 -100 0 0.5 Figure 3.18 1 1.5 2 2.5 Time (s) 3 Torque response of the induction motor with direct-on-line starting. source is constructed using a signal generator block from the Simulink library. The load torque TL is assumed to be 2 N m, and independent of the speed. The moment of inertia JL of the load is 0.05 kg m2. Figures 3.19–3.21 show the results of computer simulation using the voltageinput model. 40 Current (A) 20 0 -20 -40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 3.19 3.4.3 Stator current of the induction motor with direct-on-line starting. Simulation Results of ‘Motor 3’ ‘Motor 3’ is an experimental motor (model 295) manufactured by Bodine Electric Company. The motor parameters listed in ‘Motor 3’ of Appendix B have been obtained from standard tests as outlined in Appendix H. To illustrate the transient operation of the induction motor, 45 Modeling and Simulation of Induction Motor 25 Torque (N.m) 20 15 10 5 0 -5 0 Figure 3.20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (s) 2 Torque response of the induction motor with direct-on-line starting. 200 Speed (rad/s) 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 3.21 Speed response of the induction motor with direct-on-line starting. a simulation study of direct-on-line starting is carried out. At the initial time instant, t ¼ 0, the motor, previously de-energized and at standstill, is connected to a 220 V, 60 Hz supply. The power source is constructed using a signal generator block from the Simulink library. The load torque TL is assumed to be 0.1 N m, and independent of speed. The moment of inertia JL of the load is assumed to be 0.001 kg m2. Figures 3.22–3.24 show the results of computer simulation over a period of 0.4 s using the voltage-input model. 3.5 Discrete-State Model of Induction Motor Equation (2.14) expresses a state-space equation of induction motor. The solution to the differential equation x_ ¼ Ax þ Bu is given by (Lewis, 1992): 46 Applied Intelligent Control of Induction Motor Drives 10 Current (A) 5 0 -5 -10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 3.22 Phase-A stator current of the induction motor with direct-on-line starting. 4 Torque (N.m) 3 2 1 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 3.23 Torque response of the induction motor with direct-on-line starting. xðtÞ ¼ e Aðt t0 Þ xðt0 Þ þ ðt e Aðt t0 Þ BuðtÞdt: ð3:18Þ t0 In digital computation, the measurements are taken only at integral multiples of the sampling period M. Thus, we can convert the continuous-time model of an induction motor to the discrete-time model: x n þ 1 ¼ A n xn þ B n u n ð3:19Þ yn ¼ Cn xn : ð3:20Þ 47 Modeling and Simulation of Induction Motor 200 Speed (rad/s) 150 100 50 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 3.24 Speed response of the induction motor with direct-on-line starting. Defining t0 ¼ nM, t ¼ (n þ 1)M, and the sampled sequence xn ¼ x(nM), we may write xn þ 1 ¼ e AM xn þ ðn þð1ÞM eA½ðn þ 1ÞM t BuðtÞdt: ð3:21Þ nM Assuming that u(t) is constant between the samples, the parameters in Equations (3.19) and (3.20) become An ¼ e AM ; Bn ¼ M ð e AM Bdt; Cn ¼ C: ð3:22Þ 0 The conversion is accomplished by the following approximate formulas: An ¼ e AM I þ AM Bn ¼ M ð ð3:23Þ e AM Bdt BM ð3:24Þ Cn ¼ C: ð3:25Þ 0 where we denote the system matrix, the input and output matrices of the continuous system with A, B, and C, and those of the discrete system with An, Bn, and Cn. We also assume that our sampling time is very short compared with the dynamics of the system. Making use of the rotor time constant tr ¼ Lr =Rr ; Kr ¼ Rs þ L2M Rr =L2r and Kl ¼ ð1 L2M =Lr =Ls Þ*Ls , the discrete form of induction motor equation is derived from Equation (2.14) as follows: 48 Applied Intelligent Control of Induction Motor Drives 2 6 6 6 6 7 6 6 6 ðn þ 1Þ 7 6 7 6 6 iqs 7 6 6 6 ðn þ 1Þ 7 6 7¼6 6l 7 6 6 dr 7 6 6 6 ðn þ 1Þ 7 6 7 6 6 lqr 5 6 4 6 6 ðn þ 1Þ 6 oo 6 4 2 ðn þ 1Þ ids 3 Kr M Kl 1 LM Rr M L2r Kl 0 0 1 Kr M Kl ðnÞ PLM oo M 2Lr Kl LM M tr 0 0 LM M tr P ðnÞ o M 2 o PLM ðnÞ l M 3JLr dr 0 PLM ðnÞ l M 3JLr qr 2M 6 KL 6 6 6 0 6 þ6 6 0 6 6 6 0 4 0 0 0 1 1 M tr ðnÞ PLM oo M 2Lr Kl LM Rr M L2r Kl P ðnÞ o M 2 o 1 1 M tr 0 0 7 72 7 ðnÞ 3 7 ids 76 76 ðnÞ 7 0 76 iqs 7 7 76 7 76 76 ðnÞ 7 76 ldr 7 7 0 76 7 76 76 lðnÞ 7 74 qr 7 5 7 0 7 ðnÞ 7 oo 7 MCf 5 1 J 3 72 3 7 ðnÞ 7 Vds 0 7 7 76 ðnÞ 7 76 7 6 Vqs 7 5 0 74 7 ðnÞ 0 7 TL 5 M J M KL 0 0 0 3 ð3:26Þ Equation (3.26) can be implemented by an ‘S-function’ block of MATLABÒ/Simulink. The S-function is a program description of a dynamic system. With the power source block, the load block, and the scope block, the S-function block of induction motor is configured in Simulink as shown in Figure 3.25. ids iqs Vds Vqs λdr λqr TL Mux Induction_motor Demux 20 Power supply Load Figure 3.25 S-Function Mux ωo Demux Speed Discrete-state model of induction motor in Simulink. s s In the discrete-state model of induction motor, the discrete state is ½ids iqs lsdr lsqr oo , the s s s s s s input is [Vds Vqs TL ], and the output is [ids iqs ldr lqr oo ]. The power source which produces the stator voltage vectors is constructed using a signal generator block in the Simulink library. The ‘S-function’ block accommodates a short program called M-file which implements Equation (3.26). The M-file is given in Appendix C. 49 Modeling and Simulation of Induction Motor To illustrate the transient operation of the induction motor, a simulation of direct-on-line starting is done. The induction motor parameters for the computer simulation are listed under ‘Motor 1’ of Appendix B. The load torque, TL, is assumed to be 20 N m, and independent of speed. The moment of inertia JL of the load equals that of the motor. At the initial time instant (t ¼ 0), the motor, previously de-energized and at standstill, is connected to a three-phase, 220 V (line-to-line), 60 Hz supply with an internal resistance of 0.05 O per phase. Figure 3.26 shows the results of computer simulation using the discrete-state model with sampling time M ¼ 0.0005s. The speed-time curve is similar to that obtained using the voltageinput model (Figure 3.17). 140 120 Rotor speed (rad/s) 100 80 60 40 20 0 -20 0 0.5 1 1.5 2 2.5 3 Time (s) Figure 3.26 Speed response of the induction motor with direct-on-line staring. 3.6 Modeling and Simulation of Sinusoidal PWM Adjustable frequency operation of motors requires a symmetrical set of three-phase sine modulated PWM (pulse-width-modulated) waveforms, adjustable in both amplitude and frequency. The reference voltages (which are sinusoidal waves) should be adjustable in the full speed range, normally in the area from several Hz to several hundred Hz. The PWM patterns were typically generated by comparing these analog reference voltages with a high-frequency triangular carrier wave at the desired switching frequency (typically between 5 and 20 kHz). The results of the comparisons between the sinusoidal references and the carrier waveform are the PWM signals used to control the power devices of the voltage source inverter that supplies the motor. The desired pulse widths are usually calculated in a microprocessor or DSP chip and then a PWM generation unit is used to produce the output patterns. In order to supply the motor, a power converter is needed that translates the low level PWM signals from the processor to the appropriate high voltage levels. The most common of such a power converter is the voltage source inverter that comprises six power switching devices such as MOSFETs or IGBTs. To study the sinusoidal PWM for induction motor control, a Simulink program module of the sinusoidal PWM shown in Figure 3.27 is used. 50 Applied Intelligent Control of Induction Motor Drives PWM 2*pi*60 V-frequency Relay 3-phase sine waves Polar A (V) Relay1 line A-B (V) 1 V-amplitude Polar B (V) Relay2 tri-wave generator Polar C (V) Figure 3.27 Simulation program of the sinusoidal PWM in Simulink. In the simulation program, two ‘Constant’ blocks are used to produce the frequency and the amplitude of the reference voltage. The block ‘3-phase sine waves’ yields three-phase sinusoidal signals according to the frequency and amplitude of the reference voltage, while the block ‘tri-wave generator’ yields a high-frequency triangular carrier wave. By using three ‘Relay’ blocks (thresholds of switch on and switch off in the ‘Relay’ blocks are set as 10 4 and 10 4), we can output the three-phase sinusoidal PWM waveforms. The five ‘Scope’ blocks are used for viewing the simulation results. The reference voltages and the triangular wave carrier of the three-phase sinusoidal PWM are shown in Figure 3.28, which can be observed from the ‘PWM’ scope shown in Figure 3.27. 1.2 phase A 1 phase C phase B 0.8 0.6 Voltage (V) 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 0 20 40 60 80 100 120 140 160 1/10000 s Figure 3.28 Reference voltages and triangular wave carrier. 180 200 51 Modeling and Simulation of Induction Motor Voltage (V) Pole-A and pole-B voltages of the three-phase sinusoidal PWM are shown in Figures 3.29 and 3.30 and these can be observed from the ‘Polar A (V)’ and ‘Polar B (V)’ scopes shown in Figure 3.27. 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 20 40 60 80 100 120 140 160 180 200 180 200 1/10000 s Voltage (V) Figure 3.29 Pole-A voltage of three-phase sinusoidal PWM. 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 20 40 60 80 100 120 140 160 1/10000 s Figure 3.30 Pole-B voltage of three-phase sinusoidal PWM. The line voltage of the three-phase sinusoidal PWM is shown in Figure 3.31, which can be observed by the ‘line A-B (V)’ scope in Figure 3.27. 3.7 Modeling and Simulation of Encoder The encoder for measuring rotor speed is an optoelectronic feedback device that uses a patterned optical mask and an LED light source and transistor photo-sensor pairs. As the induction motor shaft rotates, the light source either passes through the disk, or is blocked by 52 Applied Intelligent Control of Induction Motor Drives 2 1.5 Voltage (V) 1 0.5 0 -0.5 -1 -1.5 -2 0 20 40 60 80 100 120 140 160 180 200 1/10000 s Figure 3.31 Line A-B voltage of three-phase sinusoidal PWM. the disk. The emitter/detector pairs produce a digital output waveform. The encoder can be modeled by Simulink as shown in Figure 3.32. 1 Shaft angle 1 Rotor speed Constant 1 s |u| Integrator Abs 1 Switch Speed code 0 Constant1 Transport Delay S/H Sample and Hold Figure 3.32 Encord simulation block Simulation model of speed encoder in Simulink. In the encoder model, the input is rotor speed of the induction motor and the output is a pulse string of the angular speed code. The rotor speed is transformed to a shaft angle by using an ‘Integrator’ block of Simulink, while a ‘Transport Delay’ block is used to control the pulse width of the encoder output. Two ‘Constant’ blocks are used to control the magnitude of the encoder output pulse. The ‘Switch’ block is used to control the encoder precision. If the encoder 53 Modeling and Simulation of Induction Motor precision is defined as N pulses/revolution, the threshold of the ‘Switch’ is set as 2 p/N. Figure 3.33 shows the rotor speed of the induction motor and Figure 3.34 shows the corresponding pulse string of the rotor speed code when the encoder precision is set to be 200 pulses/revolution. 90 80 Rotor speed (rad/s) 70 60 50 40 30 20 10 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Time (s) Figure 3.33 Rotor speed of induction motor input to the encoder model. 1.2 1 Voltage (V) 0.8 0.6 0.4 0.2 0 -0.2 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Time (s) Figure 3.34 Pulse string output from the encoder model with a precision of 200 pulses/revolution. 54 3.8 Applied Intelligent Control of Induction Motor Drives Modeling of Decoder The function of the decoder is to transform the output pulses of an encoder into the rotor speed signal. It can be implemented by special decoder hardware or DSP processor in a practical application. A mathematical model of the decoder may be expressed by Equations (3.27) and (3.28): yo ðtÞ ¼ f ðScode Þ oo ¼ yo ðtÞ yo ðt Dt ð3:27Þ DtÞ ð3:28Þ : where Scode is output pulse of an encoder, yo is the shaft angle. A Simulink model of the decoder is shown in Figure 3.35. θo(t) 1 Speed code Clk Up Cnt 2.6 Gain 1 Rotor speed Counter Transport Delay Figure 3.35 Decoder model in Simulink window. In this decoder model, a ‘Counter’ block implements Equation (3.27). A ‘Transport Delay’ block, a ‘Sum’ block, and a ‘Gain’ block implement the difference calculation according to Equation (3.28). The value of the ‘Gain’ block equals 2 p Dt/N, where N is the encoder precision in pulses/revolution. 3.9 Simulation of Induction Motor with PWM Inverter and Encoder/Decoder To simulate the induction motor with a PWM inverter power supply and an encoder device, the PWM model built in Section 3.6, the encoder model built in Section 3.7, and the decoder model built in Section 3.8 are configured with the voltage-input model of induction motor in Section 3.4. A ‘Gain’ block is used to simulate an inverter whose input is the PWM model’s output and whose output is the polar voltages for an induction motor. The parameters of an experimental induction motor used for the simulation are listed under ‘Motor 3’ of Appendix B. The load torque TL is assumed to be 0.1 N m, and independent of speed. The moment of inertia JL of the load is assumed to be 0.001 kg m2, and the PWM switch voltage is set as 180 V. Figure 3.36 shows the pole-A output voltage of the inverter and Figure 3.37 shows the line voltage VAB supplied to the induction motor. Figure 3.38 shows the phase-A stator current of the induction motor and Figure 3.39 shows the torque response of the induction motor. 55 Modeling and Simulation of Induction Motor 200 150 Voltage (V) 100 50 0 -50 -100 -150 -200 0 0.5 1 1.5 2 2.5 3 Time (10-3 s) Figure 3.36 Pole-A voltage of the inverter output to the induction motor. 300 200 Voltage (V) 100 0 -100 -200 -300 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) Figure 3.37 Line voltage VAB supplied to the induction motor. Figure 3.40 shows the rotor speed measured by the encoder and decoder models built in Sections 3.7 and 3.8 respectively. Figure 3.41 shows the rotor speed measured by the encoder and decoder models, when the encoder precision is set as 2000 pulses/revolution. 3.10 MATLABÒ/Simulink Programming Examples MATLABÒ (The MathWorks, Inc., 2008a) is a popular computing software. Using easy-tounderstand program language, MATLABÒ can manipulate matrices, functions, algebraic 56 Applied Intelligent Control of Induction Motor Drives 10 Current (A) 5 0 -5 -10 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) Figure 3.38 Phase-A stator current of the induction motor. 4 Torque (N.m) 3 2 1 0 -1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) Figure 3.39 Torque response of the induction motor with PWM inverter supply. expressions, and it is provided with facilities for plotting of computed data. Simulink (The MathWorks, Inc., 2008b) is a graphical programming tool that must run in the MATLABÒ environment. Simulink (The MathWorks, Inc., 2008c) can be used to model, simulate and analyze dynamic systems by using graphical blocks. It should be mentioned that the functions supported by Simulink is only a subset of those supported by MATLABÒ. Some complex algorithms, such as Genetic Algorithm or algebra operation, can only be performed by MATLABÒ codes. Nevertheless, graphical programming proves very helpful for a nonprofessional programmer. Basically, there are three ways to simulate a dynamic system on 57 Modeling and Simulation of Induction Motor 200 Rotor speed (rad/s) 150 100 50 0 0 Figure 3.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) Rotor speed measured by an encoder with a precision of 200 pulses/revolution. 200 Rotor speed (rad/s) 150 100 50 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) Figure 3.41 Rotor speed of the induction motor with an encoder of 2000 pulses/revolution. MATLABÒ/Simulink. The first method is to write program codes of MATLABÒ language and to perform the codes in the MATLABÒ command window. The second method is to create a simulation model with various blocks from the Simulink library and to execute the simulation of the model in Simulink. The third method is simulation using hybrid MATLABÒ codes and Simulink blocks. When MATLABÒ is started, a main window will appear as shown in Figure 3.42. In the MATLABÒ window, various calculation and simulation may be performed by typing corresponding commands into the command line. The commands may be an equation, a function, or a sequence of codes. 58 Applied Intelligent Control of Induction Motor Drives Figure 3.42 MATLABÒ window. In this section, six examples will be given to illustrate programming of Park’s transform with MATLABÒ codes, Simulink blocks, and hybrid methods. The six different programming examples are useful for mastering the basic steps of MATLABÒ/Simulink programming. Example Example Example Example Example Example 3.1 3.2 3.3 3.4 3.5 3.6 Programming by MATLABÒ commands Programming by Simulink blocks Programming by Simulink blocks with self-defined expression Programming by Simulink blocks which calls a MATLABÒ function Programming by MATLABÒ function which calls a Simulink model Programming by calling an ‘abc_to_qd0’ block Example 3.1 uses only MATLABÒ commands and Example 3.2 uses only Simulink blocks. Example 3.3 illustrates using self-defined expression to simplify a Simulink model. The Examples (3.4–3.6) illustrate how to program with hybrid MATLABÒ function and Simulink blocks. The hybrid programming method is useful in genetic algorithm and extended Kalman filter simulations, as these are functions of MATLABÒ in the present MATLABÒ/Simulink version. When a Simulink model is optimized by the Genetic Algorithm, it needs to call the Simulink model from MATLABÒ function. When an extended Kalman filter of MATLABÒ function is embedded in a Simulink model, the Simulink model needs to call the MATLABÒ function. 59 Modeling and Simulation of Induction Motor Example 3.1 Programming of Park’s Transformation by MATLABÒ Commands The original Park’s transformation of voltage is expressed as " Vds Vqs # 2 cos ðyÞ 26 6 ¼ 6 34 sin ðyÞ 2p cos y 3 2p sin y 3 32 3 2p Vas cos y þ 7 3 76 7 6 Vbs 7 7 4 5 2p 5 sin y þ Vcs 3 ð3:29Þ In Park’s transformation, the inputs are the vector [Vas, Vbs, Vcs] and the reference angle y, while the output vector is [Vds, Vqs]. To simulate Park’s transformation, the input data needs to be created first. Then the transformation function needs to be expressed by MATLAB codes. Finally, the results of the transformation need to be plotted. Step 1 Create Data of Three Phase Voltages The three phase voltages [Vas, Vbs, Vcs] with a frequency of 60 Hz and amplitude of 1 V may be expressed as follows: Vas ¼ sin ð2p 60tÞ 2 p Vbs ¼ sin 2p 60t 3 2 Vcs ¼ sin 2p 60t þ p : 3 ð3:30Þ ð3:31Þ ð3:32Þ In the example, simulation time is set as 0.03 s and step size is set as 0.0001s. Type the following code in the MATLABÒ command line to create the time variable, ‘t’. >> t = [0:0.0001:0.03]; Type the following code to create data of the three phase voltages. >> Vas = sin(2*pi*60*t); >> Vbs = sin(2*pi*60*t - 2/3*pi); >> Vcs = sin(2*pi*60*t + 2/3*pi); Type the following code for plotting the waveforms of the three phase voltages. >> >> >> >> >> plot(t, Vas, ‘blue’); hold on; plot(t, Vbs, ‘red’); plot(t, Vcs, ‘black’); hold off; The ‘plot’ command is used to show the waveforms of the three phase voltages. Vas is plotted in blue, Vbs is plotted in red, and Vcs is plotted in black. Use the ‘hold on’ and ‘hold off’ commands to keep the waveforms of the three phase voltages in one picture frame. 60 Applied Intelligent Control of Induction Motor Drives The above codes may be combined as follows: clear t = [0:0.0001:0.03]; Vas = sin(2*pi*60*t); Vbs = sin(2*pi*60*t - 2/3*pi); Vcs = sin(2*pi*60*t + 2/3*pi); plot(t, Vas, ’blue’); hold on; plot(t, Vbs, ’red’); plot(t, Vcs, ’black’); axis([0 0.03 -1.2 1.2]); hold off; The entire code sequence may be copied into the MATLABÒ command line. The results of executing the code are shown in Figure 3.43. Figure 3.43 Waveforms of three phase voltages Vas, Vbs, and Vcs. Step 2 Create Reference Angle of Transformation The reference angle of transformation is represented by a 100 Hz sawtooth wave with amplitude equal to 2p rad. Type the following code in the MATLABÒ command line to create data of the reference angle which is saved in variable ‘Ra’. The time variable ‘t’ in the codes has been created in Step 1. >> Ra = pi + pi*sawtooth(2*pi*100*t); The reference angle created may be plotted by following commands. >>plot(t, Ra); >>axis([0 0.03 0 2*pi]); Modeling and Simulation of Induction Motor 61 The command ‘axis’ is used to set the x-axis and y-axis limits. In the example, the x-axis is time ‘t’ with range from 0 to 0.03 s and the y-axis is angle with range from 0 to 2p rad. The waveform of the reference angle is shown in Figure 3.44. Figure 3.44 Waveform of the reference angle. Step 3 MATLABÒ Code of Park’s Transformation In Step 1, the simulation time is set as 0–0.03 s with a step size of 0.0001s, hence, the data size of the simulation is 301 (including one data at t ¼ 0 s). Park’s transformation is implemented by the following code, the results being saved in the variables Vds and Vqs. >>for i = 1:301; >>Vds(i)= 2/3*[cos(Ra(i))’, cos(Ra(i)-2/3*pi)’, cos(Ra(i) + 2/3*pi)’]*[Vas(i);Vbs(i);Vcs(i)]; >>Vqs(i) = 2/3*[sin(Ra(i))’, sin(Ra(i)-2/3*pi)’, sin(Ra(i) + 2/3*pi)’]*[Vas(i);Vbs(i);Vcs(i)]; >>end It is easily seen that the Park’s transformation given by Equation (3.29) is implemented by the looping statements. The results may be plotted by following commands. >>plot(t, Vds, ’blue’); >>hold on; >>plot(t, Vqs, ’red’); >>hold off; Step 4 Create a New MATLABÒ Function of Park’s Transformation A new MATLABÒ file may be created by clicking ‘File’ and selecting ‘New’ in MATLABÒ window. Copy all the codes in Steps 13 into the new file and save it with the name ‘Example1_Park_transform’ with suffix ‘.m’ (the extension ‘m’ means MATLABÒ file), that is, ‘Example1_Park_transform.m’. The file may be executed by typing the filename 62 Applied Intelligent Control of Induction Motor Drives ‘Example1_Park_transform’ in the MATLABÒ command line. The file ‘Example1_Park_transform.m’ is listed as follows: % Clear all variables in workspace clear % Step 1 t = [0:0.0001:0.03]; Vas = sin(2*pi*60*t); Vbs = sin(2*pi*60*t - 2/3*pi); Vcs = sin(2*pi*60*t + 2/3*pi); subplot(3,1,1); plot(t, Vas, ’blue’); hold on; plot(t, Vbs, ’red’); plot(t, Vcs, ’black’); axis([0 0.03 -1.2 1.2]); hold off; % Step 2 Ra = pi + pi*sawtooth(2*pi*100*t); subplot(3,1,2); plot(t, Ra); axis([0 0.03 0 2*pi]); % Step 3 for i = 1:301; Vds(i)= 2/3*[cos(Ra(i))’, cos(Ra(i)-2/3*pi)’, cos(Ra(i) + 2/3*pi)’]*[Vas(i);Vbs(i);Vcs(i)]; Vqs(i) = 2/3*[sin(Ra(i))’, sin(Ra(i)-2/3*pi)’, sin(Ra(i) + 2/3*pi)’]*[Vas(i);Vbs(i);Vcs(i)]; end subplot(3,1,3); plot(t, Vds, ’blue’); hold on; plot(t, Vqs, ’red’); axis([0 0.03 -1.2 1.2]); hold off; Note: 1. ‘%’ is comment line. 2. Command ‘subplot’ is used to place multiple plots in same figure frame. Command ‘subplot (n, m, k)’ place m n pictures in a figure frame where m is size of rows, n is size of columns and k is the index of current plot. The results are shown in Figure 3.45. Example 3.2 Programming of Park’s Transformation by Simulink Blocks Step 1 Creating a New Simulink Model From the MATLABÒ window, Simulink may be called by typing ‘Simulink’ in the MATLABÒ command line or by clicking the ‘Simulink’ icon on the upper left corner of the MATLABÒ window. The ‘Simulink Library Browser’ window shown in Figure 3.46 will appear. 63 Modeling and Simulation of Induction Motor Waveforms of three phase voltages Reference angle Waveform of Vqs voltage Waveform of Vds voltage Figure 3.45 Simulation results of Example 3.1. Click the icon as indicated in Figure 3.46 (or select ‘New’ and ‘Module’ from ‘File’) to create a blank model as shown in Figure 3.47. Click to create a new Simulink model Figure 3.46 Simulink library browser. Step 2 Building a Simulink Model of Park’s Transformation Figure 3.48 shows the library of ‘Simulink/Source’. In the library, the ‘Constant block’, ‘Sine wave’ block, and ‘Repeating Sequence’ block can be found. Paths of other blocks can be found 64 Applied Intelligent Control of Induction Motor Drives Figure 3.47 A blank Simulink model. in Table 3.2 (in the rightmost column named ‘Libraries and path’). Drag these blocks into the new model and connect them to build the Simulink model as shown in Figure 3.48. Click to run the model Figure 3.48 Simulink model of Park’s transformation. Step 3 Parameter Configuration of Simulink Model The Simulink block parameters and simulation parameters need to be configured, separately. The parameters of the Simulink blocks are listed in Table 3.2. Click to open each block to edit the parameters. The simulation parameters need to be configured with the following values. 1. Simulation time is from 0 to 0.03 s. 2. Max step size is 0.0001s. 65 Modeling and Simulation of Induction Motor Table 3.2 Parameters of Simulink blocks. Blocks Parameters (unspecified is default value) Libraries and path Vas Vbs Simulink/Sources/Sine wave Simulink/Sources/Sine wave Constant1 Constant2 sin Amplitude: 1; Frequency: 60 2 pi; Phase: 0 Amplitude: 1; Frequency: 60 2 pi; Phase: 2/3 pi Amplitude: 1; Frequency: 60 2 pi; Phase: 2/3 pi Time values: [0 0.01]; Output values: [0 2 pi] Constant value: 2/3 pi Constant value: 2/3 pi Function: sin cos Function: cos product Add Gain Scope2 Default value List of signs: þ þ þ Gain: 2/3 Default value Vcs angle Simulink/Sources/Sine wave Simulink/Sources/Repeating Sequence Simulink/Sources/Constant Simulink/Sources/Constant Simulink/Math Operations/ Trigonometric Function Simulink/Math Operations/ Trigonometric Function Simulink/Math Operations/Product Simulink/Math Operations/Add Simulink/Math Operations/Gain Simulink/Sinks/Scope 3. Other parameters are default values. Press down ‘Ctrl þ E’ keys to open and edit the simulation parameters as shown in Figure 3.49. Figure 3.49 Configuration parameters of the simulation. 66 Applied Intelligent Control of Induction Motor Drives Step 4 Running the Simulink Model of Park’s Transformation Click the run icon shown in Figure 3.49 to start the simulation of Park’s transformation. The simulation results may be observed by clicking the ‘Scope2’ block as shown in Figure 3.50. Figure 3.50 Simulation results of Example 3.2. Example 3.3 Programming of Park’s Transformation using Simulink Blocks and Self-Defined Expression In order to simplify the Simulink model of Park’s transformation, a user-defined function block, named ‘Fcn’, is employed. The block may be found through the library path ‘Simulink/ User-Defined Functions’. Drag the block from the library into the Simulink model to build the model of Park’s transformation as shown in Figure 3.51. Click the two ‘Fcn’ blocks as shown in Figure 3.51 separately to input the self-defined functions into the expression line. In ‘Fcn1’ block, ‘Sample time’ is the default value and the following expression is input: 2/3 (cos(u(4)) u(1) þ cos(u(4) 2/3 pi) u(2) þ cos(u(4) þ 2/3 pi) u(3)). Figure 3.52 shows how the expression is input into the ‘Fcn1’ block. For ‘Fcn2’ block, the following expression is input: 2/3*(sin(u(4))* u(1) + sin(u(4)-2/3*pi)* u(2) + sin(u(4) + 2/3*pi)* u(3)) In Example 3.3, simulation parameters, such as simulation time and step size are same as those in Example 3.2. The simulation results may be observed by clicking ‘Scope2’ in the Simulink model as shown in Figure 3.51. The simulation results of Example 3.3 are same as those in Example 3.2. Modeling and Simulation of Induction Motor 67 Figure 3.51 Simulink model of Example 3.3. Figure 3.52 Self-defined function being entered into ‘Fcn1’. Example 3.4 Programming of Park’s Transformation Using Simulink Blocks which Calls a MATLABÒ Function In this example, a MATLABÒ function is called by a Simulink model to implement Park’s transformation. MATLABÒ function calls are useful in some applications, for example, in the implementation of extended Kalman filter in a Simulink model. Step 1 Create a MATLABÒ Function of Park’s Transformation which may be Called by Simulink Model As in Example 3.1, a new MATLABÒ file may be created by clicking ‘File’ and selecting ‘New’ in MATLABÒ window. Input the following code into the new file and save it with name 68 Applied Intelligent Control of Induction Motor Drives ‘Example4_Park_Transform.m’. function Vdqs = Example4_Park_Transform(x) Vdqs(1) = 2/3*(cos(x(4))*x(1) + cos(x(4)2/3*pi)*x(2) + cos(x(4) + 2/3*pi)*x(3)); Vdqs(2) = 2/3*(sin(x(4))*x(1) + sin(x(4)2/3*pi)*x(2) + sin(x(4) + 2/3*pi)*x(3)); end The above code defines a MATLABÒ function whose name is ‘Example4_Park_Transform. m’. The output of the function is a vector ‘Vdqs’ which includes two elements, Vdqs(1) and Vdqs(2), which represent Vds and Vqs, respectively. ‘x’ is input of the function. Elements of ‘x’, x(1), x(2), and x(3) represent Vas, Vbs, and Vcs separately, while x(4) represents the transformation reference angle. Step 2 Building a Simulink Model to Call the MATLABÒ Function A ‘MATLAB Fcn’ block is used to call a MATLABÒ function. The block may be found through library path ‘Simulink/User-Defined Functions’. Drag the block from the library into a Simulink model to build the model of Park’s transformation as shown in Figure 3.53. Click the ‘MATLAB Fcn’ block in Figure 3.53 to open it as shown in Figure 3.54. In the ‘MATLAB function’ window, type in ‘Example4_Park_Transform’ and other parameters are default values. Click the ‘OK’ icon to finish the block configuration. Figure 3.53 Simulink model of Example 3.4. Step 3 Running the Simulink Model of Example 3.4 The simulation results of Example 3.4 are the same as those in previous examples, and they may be observed by clicking ‘Scope1’ and ‘Scope2’ in the Simulink model as shown in Figure 3.53. The waveforms in ‘Scope1’ are the same as those in Figure 3.43 in Example 3.1 and the waveforms in ‘Scope2’ are same as those in Figure 3.50. Modeling and Simulation of Induction Motor Figure 3.54 69 ‘MATLAB Fcn’ block configuration. Example 3.5 Programming of Park’s Transformation by a MATLABÒ Function which Calls a Simulink Model This example illustrates how to call a Simulink model from a MATLABÒ code. This operation is convenient for some applications, for example, optimization of a Simulink model using genetic algorithm (which is a MATLABÒ function in the present MATLABÒ/Simulink version). Step 1 Building a Simulink Model A ‘To Workspace’ block is employed to store data into workspace and the data will be called by MATLABÒ function. The block may be found through library path ‘Simulink/Sinks’. Drag the block from the library into the Simulink model to build the Simulink model of Example 3.5, as shown in Figure 3.55. Click to open the ‘To Workspace’ block in Figure 3.55. Enter ‘x’ into the ‘Variable name’ window and select ‘Array’ in the ‘Save format’ window. Other parameters are the default values as shown in Figure 3.56. Click the ‘OK’ icon to finish the block configuration. The new Simulink is saved with name ‘Example5_Park_transform.mdl’, where the suffix ‘.mdl’ means Simulink model. Step 2 Creating a New MATLABÒ Function which Calls the Simulink Model A new MATLABÒ file may be created by clicking ‘File’ and selecting ‘New’ in the MATLABÒ window. Enter the following code sequence and save it with the filename ‘Example5_Park_transform.m’. 70 Applied Intelligent Control of Induction Motor Drives clear sim(’Example5_Park_transform’,0.03); Vas = x(:,1); Vbs = x(:,2); Vcs = x(:,3); Ra = x(:,4); t = tout; A = size(x); for i = 1:A(1); Vds(i)= 2/3*[cos(Ra(i))’, cos(Ra(i)-2/3*pi)’, cos(Ra(i) + 2/3*pi)’]* [Vas(i);Vbs(i);Vcs(i)]; Vqs(i) = 2/3*[sin(Ra(i))’, sin(Ra(i)-2/3*pi)’, sin(Ra(i) + 2/3*pi)’]*[Vas(i);Vbs(i);Vcs(i)]; end plot(t, Vds, ’blue’); hold on; plot(t, Vqs, ’red’); In the file, ‘sim’ is a MATLABÒ function which is used to simulate a Simulink model. It takes two parameters: one is name of the Simulink model (‘Example5_Park_transform’) and the other is the simulation time (0.03 s). Figure 3.55 Simulink model of Example 3.5. Step 3 Running the MATLABÒ Function of Example 3.5 In MATLABÒ command line, type ‘Example5_Park_transform’ to run Example 3.5 and the results are obtained automatically, as shown in Figure 3.57. The simulation results shown in Figure 3.57 are same as the previous examples. 71 Modeling and Simulation of Induction Motor Figure 3.56 Figure 3.57 Parameter configuration. Simulation results of Example 3.5. 72 Applied Intelligent Control of Induction Motor Drives Figure 3.58 Simulink model of Park’s transformation using ‘abc_to_dq0’ block. Example 3.6 Programming of Park’s Transformation by Calling ‘abc_to_dq0 Transform’ Block In this example, a simulink model of Park’s transformation is built by employing the block ‘abc_to_dq0 Transform’ in Simulink library. The block may be found from path ‘SimPowerSystem/Extra_Library/Measurements’. Drag the block into the Simulink model as shown in Figure 3.58. Figure 3.59 Descriptions of ‘abc_to_dq0 Transformation’ block. Modeling and Simulation of Induction Motor Figure 3.60 73 Simulation results of Example 3.6. As shown in Figure 3.58, input of transformation reference in the block is ‘sin_cos’. In order to match the input format, two trigonometric function blocks, ‘sin’ and ‘cos’ are used. Click the ‘abc_to_dq0 Transformation’ block to see the description as shown in Figure 3.59. There are differences between the ‘abc_to_dq0’ transformation and the original Park’s transformation by comparing Equation (3.26). Vd defined in the Simulink block is Vqs in the original Park’s transformation while Vq defined in the Simulink block is Vds. In using the ‘abc_to_dq0’ block, Vd has to be interpreted as Vqs in the original Park’s transformation and Vq has to be interpreted as Vds. Figure 3.60 shows the simulation results of Example 3.6 which calls the ‘abc_to_dq0’ block. Compared with Figure 3.50, it is seen that Vd lags Vds by 2/3p rad and Vq lags Vqs by the same angle. 3.11 Summary Based on the 8th and 11th fifth-order equations, the Simulink models of induction motor presented in this chapter are useful for transient analysis of the induction motor. The currentinput model of induction motor involves the least amount of calculations and, hence, is computationally efficient and can be used for the study of a current-controlled induction motor drive system. The voltage-input model is realized using the matrix calculation blocks and can be used for the study of a voltage-controlled induction motor drive system. The discrete-state model uses an ‘S-function’ block with a short M-file (which consists of about twenty program lines) to implement the discrete fifth-order equation of a three-phase induction motor, giving the most compact modeling form. Because the discrete-state model involves lengthy calculations and gives accurate simulation results only when the sampling time M is less than 0.8 ms, a long 74 Applied Intelligent Control of Induction Motor Drives program execution time is required. Each block of the models may be connected and modified easily in the MATLABÒ/Simulink environment. Some limit conditions, such as saturation of magnetic circuit and stator current limit, may be easily inserted into the function blocks. The object modeling methods of the current-input model and voltage-input model are convenient because program compilation is not required. As a subsystem, the three models may be easily incorporated into a sophisticated control system of the induction motor. The sinusoidal PWM model and encoder model may be used to simulate a PWM generator and a speed measurement device making the system model of the induction motor drive more realistic. Further work on induction motor modeling may include: (1) incorporating more practical factors in the model, such as magnetic saturation, temperature rise, motor vibration, and unbalanced parameters, (2) automatically generating a computer model based on measured data of the actual induction motor. This chapter has also provided a primer for readers to familiarize with the MATLABÒ/ Simulink programming environment. The techniques introduced will be employed in the intelligent control of induction motor drives detailed later in the book. References Chan, C.C., Jiang, J.Z., and Chen, G.H. (1993) Computer simulation and analysis of a new polyphase multipole motor drive. IEEE Transactions on Industrial Electronics, 40(1), 62–77. Domijan, A. Jr and Yin, Y. (1994) Single phase induction machine simulation using the electromagnetic transients program: theory and test cases. IEEE Transactions on Energy Conversion, 9(3), 535–542. Krause, P.C. and Thomas, C.H. (1965) Simulation of symmetrical induction machinery. IEEE Transactions on Power Apparatus and System, PAS-84(11), 1038–1053. Krause, P.C., Wasynczuk, O., and Sudhoff, S.D. (1995) Analysis of Electric Machinery, IEEE Press, New Jersey. Lewis, F.L. (1992) Applied Optimal Control and Estimation, Prentice-Hall, Inc., New Jersey. The MathWorks, Inc. (2008a) MATLABÒ Getting Started Guide. The MathWorks, Inc. The MathWorks, Inc. (2008b) Simulink Getting Started Guide. The MathWorks, Inc. The MathWorks, Inc. (2008c) Simulink Graphical User Interface. The MathWorks, Inc. Mohan, N., Robbins, W.P. et al. (1997) Simulation of power electronic and motion control system, in Power Electronics and Variable Frequency Drives: Technology and Applications (ed. B.K. Bose), IEEE Press, New Jersey. Trzynadlowski, A.M. (1994) The Field Orientation Principle in Control of Induction Motors, Kluwer Academic Publishers, Boston. 4 Fundamentals of Intelligent Control Simulation 4.1 Introduction Computer simulation provides a fast way to verify new designs and improvements at the algorithm level, without incurring hardware cost and possible device damage. Currently, MATLABÒ (The MathWorks, Inc., 2008a) software is an ideal tool for simulating most intelligent control systems. A large number of function blocks have been developed in the Simulink libraries (The MathWorks, Inc., 2008b) by Mathworks Inc. Various mathematical operations, engineering models, and software tools are packaged into the blocks. With the aid of these blocks, users can avoid repeated effort in modeling when verifying or developing a custom design. In this chapter, readers will learn how to model and simulate a fuzzy logic based PI controller, neural network based Park’s transformation, signal measurement using Kalman filter, and a genetic algorithm optimized PID controller using MATLABÒ/Simulink. Control System Toolbox, Fuzzy Logic Toolbox, Neural Network Toolbox, Signal Processing Blockset in Simulink libraries will be employed for the simulation examples. 4.2 Getting Started with Fuzzy Logic Simulation MATLABÒ (version R2008b) delivers a ‘Fuzzy Logic Toolbox’ (The MathWorks, Inc., 2008c). In the toolbox, a block named ‘Fuzzy Logic Controller’ may be used to simulate a fuzzy logic controller in Simulink platform. The MATLABÒ command ‘Fuzzy’ calls the FIS (Fuzzy Inference System) editor that enables membership functions and fuzzy inference rules to be input and edited. In this section, an example of fuzzy PI control system is presented. 4.2.1 Fuzzy Logic Control A basic fuzzy inference system is described as shown in Figure 4.1. The basic fuzzy inference system may be simulated in MATLABÒ, and the operations are summarized in Table 4.1. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 76 Applied Intelligent Control of Induction Motor Drives FIS (fuzzy inference system) Input Output Fuzzy reasoning Fuzzify Figure 4.1 Defuzzify A basic fuzzy inference system. Operations of fuzzy inference system in MATLABÒ. Table 4.1 Name Action Parameter Edit Window How to Enter FIS (fuzzy inference system) Fuzzy inference Membership functions and rulebase FIS Editor Fuzzify Map inputs to membership values Fuzzy reasoning based on fuzzy rulebase and if-then logic Input membership function Membership Function Editor FIS Editor/ Membership Function Editor FIS Editor/Rule Editor Entering command ‘fuzzy’ on the MATLABÒ main window Enter from FIS Editor window (see Figure 4.9) Enter from FIS Editor window (see Figure 4.9) Fuzzy reasoning Output membership function Fuzzy rulebase Defuzzify Transfer fuzzy values to crisp outputs N/A N/A Enter from FIS Editor window (see Figure 4.10) N/A The steps of developing a fuzzy simulation model are shown in Figure 4.2. Figure 4.2 shows the basic steps of developing a fuzzy inference system in MATLABÒ/ Simulink. Firstly, the fuzzy inference system is created and its parameters are configured by the ‘FIS Editor’ of MATLABÒ. Then, the fuzzy inference system is exported under MATLABÒ path with its own filename. After the filename is entered into a ‘Fuzzy Logic Controller’ block, the fuzzy inference system may be called by the Simulink model. Start Create and configure an FIS in “FIS Editor” Export the FIS with a file name under MATLAB® path Adjust rules Figure 4.2 Enter the filename into “Fuzzy Logic Controller” block in Simulink model Run the Simulink model Satisfied ? End Yes No Steps of developing a fuzzy model in MATLABÒ/Simulink. 77 Fundamentals of Intelligent Control Simulation 4.2.2 Example: Fuzzy PI Controller An example of a basic fuzzy controller (Sousa and Bose, 1995) is presented in this section. The purpose is to demonstrate the programming process of fuzzy logic simulation in MATLABÒ/ Simulink. For comparison purpose the performance of a PI controller is also studied. Step 1 Building a PI Control System in Simulink Ð A PI controller is described by the expression uðtÞ ¼ Kp eðtÞ þ Ki eðtÞdt, where e(t) is input of the controller, u(t) is output of the controller, Kp is the proportional gain, and Ki is the integral gain. A Simulink model of PI control system may be constructed as shown in Figure 4.3. 1 Kp u(t) Step e(t) Add 1 1 s 1 Ki Figure 4.3 s2 +s+1 Integrator Add1 Transfer Fcn Scope A PI control system in Simulink. The PI control system in Figure 4.3 consists of ‘Step’, ‘Add’, ‘Gain’, ‘Integrator’, ‘Transfer Fcn’, and ‘Scope’ blocks. These blocks may be found in ‘Simulink Library’. The properties of the blocks are summarized in Table 4.2. For example, the block ‘Step’ is used to generate a step function from the Sources Group in the Simulink libraries. The ‘Transfer Fcn’ is provided in Table 4.2 Simulation blocks in PI control system. Block Functions Parameters Libraries/Group Step Generate a step function Simulink/Sources Add Add or subtract inputs Step time ¼ 5 s Initial value ¼ 0 Final value ¼ 1 þ Gain Multiply input by a constant Integrator Transfer Fcn Integrate signal Transfer function Scope Display signals generated during simulation þþ Proportional Gain ¼ 1 Integral Gain ¼ 1 N/A Numerator coefficient ¼ 1 Denominator coefficient ¼ [1 1 1] Y_min ¼ 0.5 Y_max ¼ 1.5 Simulink/Math Operations Simulink/Math Operations Simulink/Continuous Simulink/Continuous Simulink/Sinks 78 Applied Intelligent Control of Induction Motor Drives Continuous Group in the Simulink libraries. The parameters of the blocks may be set by clicking the individual blocks. Step 2 Running the Simulation for the PI Control System After running the Simulink model of PI control system as shown in Figure 4.3, the simulation results of controller command (dot line) and system output (solid line) are obtained as shown in Figure 4.4. 1.5 1 0.5 0 -0.5 0 10 20 30 40 50 Time (s) Figure 4.4 Simulation results of PI controller. The performance of the PI controller may be further optimized by tuning the proportional gain Kp and the integral gain Ki. Step 3 Fuzzy Logic Control Modeling in Simulink In the previous PI controller, both the proportional gain Kp and the integral gain Ki are constant. In order to improve the controller performance, the gains should be varied as e(t) varies. This is accomplished by varying Kp and KI according to some fuzzy rules when the absolute value of error of ‘Transfer Fcn’ block output and input command, e(t) (controller’s input) varies. For example, the rules may be defined as follows: If abs(e(t)) is large, then Kp is large and Ki is large. If abs(e(t)) is small, then Kp is large and Ki is zero. If abs(e(t)) is zero, then Kp is large and Ki is small. A Simulink model of fuzzy PI control system is shown in Figure 4.5 and parameters of the Simulink blocks are listed in Table 4.3. 79 Fundamentals of Intelligent Control Simulation Product |u| Step Add Abs Fuzzy Logic Controller 1 1 s Product1 Integrator s2 +s+1 Add1 Transfer Fcn Scope Figure 4.5 Modeling fuzzy PI control system in Simulink. Table 4.3 Simulation blocks in Fuzzy PI control system. Name Function Libraries/Group Parameter Abs Output absolute value of input Fuzzy inference system Simulink/Math Operations Fuzzy Logic Toolbox N/A Multiply the inputs Simulink/Math Operations Number of inputs is 2 Fuzzy Logic Controller Product FIS file is ‘fis2’ Step 4 Configuring the Fuzzy Inference System in MATLABÒ After the command ‘Fuzzy’ is entered in the MATLABÒ command window, a FIS (Fuzzy Inference System) editor window will appear as shown in Figure 4.6. Figure 4.6 FIS (Fuzzy Inference System) editor. 80 Applied Intelligent Control of Induction Motor Drives There is only one input and one output in the newly opened FIS by default, whereas the proposed fuzzy controller has two outputs, one for adjusting Kp and another for adjusting Ki. One more output should thus be added. This is done by clicking ‘Edit’ on the FIS Editor and selecting ‘Add Variable’ and ‘Output’, as shown in Figure 4.7. Figure 4.7 Adding an output variable in FIS editor. After the above operation, a new output, ‘output2’, is added in the FIS editor as shown in Figure 4.8. Double-click any one input or output box in the ‘FIS Editor’. A ‘Membership Function Editor’ window appears as shown in Figure 4.9. The membership function of the input and output need to be configured manually in the ‘Membership Function Editor’ with parameter values given in Table 4.4. Double-click the fuzzy rule box ‘Untitled mamdani’ in the center of the FIS editor to bring up the ‘Rule Editor’ window as shown in Figure 4.10. Fuzzy inference rules may be configured manually in the ‘Rule Editor’ with the contents in Table 4.5. When the editing of the Fuzzy Inference System is completed, click the ‘File’ icon and export the Fuzzy Inference System with a filename. The filename should match the parameter in the ‘Fuzzy Logic Controller’ block as listed in Table 4.3. In this example, the filename is ‘fis2’. Also, the file should be saved to current MATLABÒ paths, in order that it can be called by the Simulink model of Fuzzy based PI controller as shown in Figure 4.5. Step 5 Running the Simulation for the PI Controller and Fuzzy Controller Run the Simulink model of the PI control system as shown in Figure 4.3 and the Simulink model of the fuzzy PI control system as shown in Figure 4.5. The simulation results of PI controller (dot line) and fuzzy controller (solid line) are displayed, as shown in Figure 4.11. Fundamentals of Intelligent Control Simulation Figure 4.8 Figure 4.9 One output added in FIS editor. Membership function editor. 81 82 Applied Intelligent Control of Induction Motor Drives Table 4.4 Parameters of membership function. Membership Function Range Type Parameters Input1 Output1 Output2 [0 1] [0 1] [0 1] Trimf Trimf Trimf [ 0.5 0 0.5] [ 0.5 0 0.5] [ 0.5 0 0.5] Figure 4.10 Table 4.5 Rule No Rule editor. Fuzzy inference rules. Conditions 1 If input is zero abs(e(t)) is zero 2 If input is small abs(e(t)) is small 3 If input is large abs(e(t)) is large Actions output1 is large and output2 is small output1 is large and output2 is zero output1 is large and output2 is large Kp is large and KI is small Kp is large and KI is zero Kp is large and KI is large 83 Fundamentals of Intelligent Control Simulation 1.5 1 0.5 0 -0.5 0 10 20 30 40 50 Time (s) Figure 4.11 Performance of PI controller and fuzzy PI controller. The above simulation results show that the basic fuzzy controller presented gives better performance than a conventional PI controller with fixed gains. It should be noted that optimization of structure and parameters has not been performed on the fuzzy controller yet. 4.3 Getting Started with Neural-Network Simulation MATLABÒ/Simulink delivers a ‘Neural Network Toolbox’ and some learning functions for simulating various neural networks (The MathWorks, Inc., 2008d). A neural network may be built and trained in MATLABÒ command line or in a graphic-guide window. In the toolbox, various neuron transfer functions are packaged into blocks that can be dragged into a Simulink block diagram for building a neural-network model. Alternatively, a neural-network model may be built by entering appropriate commands into MATLABÒ command window. In this section, neural-network based Park’s transformation will be implemented by MATLABÒ/ Simulink. 4.3.1 Artificial Neural Network An artificial neural network consists of neurons and connection lines. A two-layer neural network is shown in Figure 4.12, where layer 1 is also called the hidden layer and layer 2 is also called the output layer. In a practical application, a network may have several layers each having a different number and type of neurons. 84 Applied Intelligent Control of Induction Motor Drives layer 1 layer 2 Input Figure 4.12 Output A two-layer network consisting of five neurons and connection lines. A neuron consists of net weight (product operator), net bias (constant), net sum (add operator), and a transfer function as shown in Figure 4.13. Parameters of a neuron are listed in Table 4.6. neuron Input Output Weight + Transfer function Bias Figure 4.13 Table 4.6 Internal structure of artificial neuron. Parameters of an artificial neuron. Name Properties Achieved by Weight Bias Transfer function Scalar or vector gain Scalar or vector constant linear or nonlinear function Learning Learning Depends on function relationship of input and output The weights and bias of neurons may be obtained by a training process as shown in Figure 4.14. The initial weights and biases for a back-propagation network may be created randomly. Update equation of the weight and bias of neurons is given as: 85 Fundamentals of Intelligent Control Simulation Target Input Output Adjust weight and bias Figure 4.14 Training process of neural network. wðt þ 1Þ ¼ wðtÞ þ Z qE : qwðtÞ ð4:1Þ where w(t þ 1) is a vector of the new weight and bias, w(t) is a vector of the old weight and bias, qE Z is learning rate, qwðtÞ is gradient descent, and E is sum squared error of the output and the target of the neural network as shown in Figure 4.14. 4.3.2 Example: Implementing Park’s Transformation Using ANN Park’s transformation is also called a-b-c to d-q rotating transformation. With a rotating reference angle, the three-phase variables in stationary frame are transferred to the rotating d-q reference frame by Park’s transformation. In this example, Park’s transformation will be implemented by a neural network. Park’s transformation may be expressed as 2 6 cos ðyÞ 6 2 4 5¼ 6 36 4 Vq sin ðyÞ 2 Vd 3 2p cos y 3 2p sin y 3 32 3 2p Va cos y þ 6 7 3 7 76 7 76 7 7 6 Vb 7 2p 54 5 sin y þ Vc 3 ð4:2Þ where Va, Vb, Vc, and y are the input vector, and Vd and Vq are the output vector. Step 1 Design of Neural Network of Park’s Transformation Equation (4.2) expresses a product of the transformation matrix and vector [Va, Vb, Vc]. Product operation is defined as an input function and no training is necessary in MATLABÒ. (Due to no suitable neuron support, training a product operation is difficult in MATLABÒ.) However, the transformation matrix may be implemented by a neural network with one input (angle y) and six outputs (elements of the transformation matrix). The neural network thus consists of four ‘tansig’ type neurons and six ‘purelin’ type neurons. Using the neural network, the transformation matrix is implemented with a parallel calculation structure as shown in Figure 4.15. Park’s transformation in Equation (4.2) may be implemented by a product of [Va, Vb, Vc] and the outputs of the neural network in Figure 4.15. 86 Applied Intelligent Control of Induction Motor Drives 4 tansig neurons 6 purelin neurons cos(θ ) sin(θ ) cos(θ -2π/3) θ sin(θ -2π/3) cos(θ +2π/3) sin(θ +2π/3) Figure 4.15 Neural network of Park’s transformation matrix. Step 2 Acquiring Samples for Training Neural Network A Simulink model is designed to yield input and target sample sets which will be used to train a neural network, as shown in Figure 4.16. In the model, ‘Repeating Sequence’ block outputs repeating sequence with amplitude varying from zero to 4p rad and period equal to 2 s, which yields the rotor angle y. The sample data of the rotor angle y is sent to workspace with name ‘sin_in’ as the neural network input. The six elements of the transformation matrix in Equation (4.2) are given by six ‘sin’ and ‘cos’ blocks, separately, whose sample data are stored to ‘Workspace’ with name ‘sin_out’ as the target of training neural network. The sample rate is set as 0.001 s, so 1000 data pairs (input and target samples) are obtained by running the model for 1 second. Further details of the blocks in the model are given in Table 4.7. sin_in To Workspace1 cos sin cos sin_out Repeating Sequence -2*pi/3 sin Constant To Workspace cos 2*pi/3 sin Constant1 Figure 4.16 Simulink model for acquiring samples. It is emphasized that the data in ‘sin_in’ and ‘sin_out’ blocks are stored with column formats in the workspace, while input and target arrays of the network training function in MATLABÒ 87 Fundamentals of Intelligent Control Simulation Table 4.7 Simulation blocks in Park’s transformation matrix. Name Function Libraries/Group Parameter Repeating Sequence Generate angle reference Simulink/Sources Time values [0,2] Output values [0,4 pi] Sin Trigonometric Perform trigonometric function Simulink/Math Operations To Workspace Write data to MATLABÒ workspace Manage simulation process Simulink/Sinks Cos Save format: Array N/A Start time: 0 s Simulation parameters End time: 1s Sample time: 0.001 s are in row formats. In order to match the network training function, the input and target samples have to be transposed. This is achieved by entering the following commands: >> sinin = sin_in’; >> sinout = sin_out’; Step 3 Creating a New Neural Network After Step 2, the sample sets of input and target are stored in row format with the new names ‘sinin’ and ‘sinout’. Enter the following command to create a feed-forward backpropagation network: >> net = newff(sinin,sinout,4); The parameters of the command are listed in Table 4.8. Table 4.8 Parameters of a feed-forward backpropagation network. Name Function newff() Create a new feed-forward backpropagation network default is ‘tansig’ for hidden layer and ‘purelin’ for output layer Name of new network Input of the network Output of the network 4 ‘tansig’ neurons in hidden layer 6 ‘purelin’ neurons in output layer net sinin sinout 4 sinout is 6-dimension vector Step 4 Training the Neural Network Enter the following command in order to train the new network with name ‘net’: >> [net,tr] = train(net,sinin,sinout); The parameters of the command are listed in Table 4.9. 88 Applied Intelligent Control of Induction Motor Drives Table 4.9 Parameters for network training. Name Function train() create a new feed-forward backpropagation network default transfer function is ‘tansig’ Name of created network input of the network Train target Store training records net sinin sinout tr The training function will return new weight and bias values and these are stored in the network ‘net’, while the training records are stored in ‘tr’. After entering the training command, a ‘Neural Network Training’ window as shown in Figure 4.17 appears and a training process starts automatically. Figure 4.17 Training window. 89 Fundamentals of Intelligent Control Simulation After the training of network completed, clicking the ‘Performance’ box in the ‘Neural Network Training’ window may display the epoch process as shown in Figure 4.18. If the result is unsatisfactory, the training process may be repeated by entering the following commands again until a satisfactory result is obtained: Figure 4.18 Network training performance: the mean squared error is less than 10 training epochs. 5 after 660 >> net = newff(sinin,sinout,4); >> [net,tr] = train(net,sinin,sinout); It should be noted that the results are different for each training process because the initial weight and bias of the network being trained are randomly created. Step 5 Generating a Simulink Block of the Trained Neural Network Enter the following command to generate a Simulink block for simulating the trained neural network ‘net’ for further use: >> gensim(net,-1); where -1 means inherited sample time. After entering the above command, a Simulink model is automatically created as shown in Figure 4.19. 90 Applied Intelligent Control of Induction Motor Drives x{1} Input 1 x{1} y{1} y{1} Neural Network Figure 4.19 Creating a neural network by the command ‘gensim(net,-1)’. Copy the ‘Neural Network’ block in Figure 4.19 and paste it into a new Simulink model named as Park’s Transform as shown in Figure 4.20. In the model, the ‘Vabc’ block yields three phase voltage [Va, Vb, Vc] with frequency 60 Hz and magnitude 1 V. The ‘Neural Network’ block yields Park’s transformation matrix. The ‘Matrix Product’ block implements product operation of [Va, Vb, Vc] and the Park’s transformation matrix to give Vd and Vq. Scope2 Vabc Vdq x{1} Vabc y {1} Matrix Scope1 Neural Network Matrix Product Repeating Sequence Figure 4.20 Scope3 Simulink model of Park’s transformation. Step 6 Running the Simulink Model After running the Park_ANN model, ‘Scope2’ displays the three phase voltage [VaVbVc], ‘Scope3’ displays the output of neural work based Park’s transformation, and ‘Scope1’ displays the voltage [VdVq] of rotating d-q reference frame. The simulation results are shown in Figures 4.21–4.23. 4.4 Getting Started with Kalman Filter Simulation By using recursive calculations, the Kalman filter is capable of estimating the state of a linear dynamic system from a series of noisy measurements. In this section, the theory of the Kalman filter is briefly reviewed. An example of signal measurement in the presence of noise will then be presented to show how the Kalman filter can be modeled. 91 Fundamentals of Intelligent Control Simulation 1.5 1 0 -0.5 -1 -1.5 0 0.002 0.004 0.006 0.008 0.01 Time (s) Figure 4.21 Three phase voltage [VaVbVc]. 1.5 1 0.5 Voltage (V) Voltage (V) 0.5 0 -0.5 -1 -1.5 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 Time (s) Figure 4.22 Output of neural-network based Park’s transformation. 92 Applied Intelligent Control of Induction Motor Drives 1.5 1 Voltage (V) 0.5 0 -0.5 -1 -1.5 0 0.002 0.004 0.006 0.008 0.01 Time (s) Figure 4.23 4.4.1 Voltage [VdVq] output of rotating d-q reference frame. Kalman Filter A discrete state-space representation of a linear dynamic system with noises may be written in the following form. xn ¼ Axn 1 þ Bun 1 þ w ð4:3Þ yn ¼ Cxn þ v The discrete model may be constructed as a flowchart as shown in Figure 4.24. un-1 Ax n-1 +Bun-1 + w Figure 4.24 Delay xn Cx n + v yn Discrete model of a linear dynamic system. u (input of system) and y (output of system) are the two input variables of a basic Kalman filter and estimated state x and estimated y are the two output variables, as illustrated in Figure 4.25. The equations of state estimation of the basic discrete Kalman filter may be expressed as follows: 1. Prediction of state: n ¼ A^ x xn 1 þ Bun 1 ð4:4Þ 93 Fundamentals of Intelligent Control Simulation u Ax + Bu + w Delay x y Cx + v Estimated y Kalman Filter Estimated x Figure 4.25 A system model and a basic Kalman Filter. Prediction of error covariance matrix: n ¼ AP ^ n 1 AT þ Q P ð4:5Þ 2. Computation of Kalman filter gain: n CT ðC P n C T þ RÞ Kn ¼ P 1 ð4:6Þ State estimation: ^n ¼ x n þ Kn ðyn C x xn Þ ð4:7Þ Update of the error covariance matrix: ^n ¼ P n Kn C P n P ð4:8Þ The recursive calculation process of the basic Kalman filter shown in Figure 4.26 is useful for understanding the Kalman filter at work. The definitions of symbols in the Kalman filter are listed in Table 4.10. System u Ax +Bu + w Delay y x Cx + v Estimated y Kalman Filter Ax +Bu Predicted Delay Estimated -+ Cx x + + x Estimated x K Eq.(4.7) Eq.(4.4) Update Estimated Eq.(4.5) P K Eq.(4.6) Eq.(4.8) Delay Updated Figure 4.26 Kalman filter calculations. P 94 Applied Intelligent Control of Induction Motor Drives Table 4.10 Parameters of the Kalman filter. Symbol Definition Initial Value Update A B C K P ^ P Q R u v w x x ^ x y State transition matrix Input matrix Measurement matrix Kalman gain Predicted error covariance Estimated error covariance Process noise covariance Measurement noise covariance System input Measurement noise Process noise State Predicted state Estimated state Measurement Constant matrix Constant matrix Constant matrix N/A N/A Matrix Constant matrix Constant matrix N/A N/A N/A N/A N/A Matrix N/A No No No Yes Yes Yes No No Yes N/A N/A N/A Yes Yes Yes 4.4.2 Example: Signal Estimation in the Presence of Noise by Kalman Filter In this example, measured random DC voltage accompanying various noises is estimated by a Kalman filter in order to demonstrate how to simulate a Kalman filter using MATLABÒ/ Simulink. Step 1 Mathematical Model of the Signal Measurement In processing measurement data, Kalman filter may be used to separate signal from random noises (Kalman, 1960). In this example, it is reasonable to assume that the measured signal is from a linear dynamic system with noises as described in Equation (4.3). If we assume that the measured signal is same as the system state, then the measurement matrix C is equal to 1. The measured data is a one-dimensional array, and the state has no change from step n 1 to step n, that is, xn ¼ xn 1. Hence, the state transition matrix A is 1. There is no control input in the system, hence u equals 0. The state-space representation in Equation (4.3) becomes xn ¼ xn 1 þw yn ¼ xn þ v ð4:9Þ Step 2 Modeling the Signal Measurement Process MATLABÒ software delivers a ‘Kalman Filter’ block in ‘Signal Processing Blockset’. The block can simulate a simple Kalman filter action (The MathWorks, Inc., 2008e). In the example, value of DC voltage is arbitrarily selected to be measured and it is accompanied by random measurement noise. Mean of the noise is set as 0 and variance of the noise is set as 0.1, hence the measurement noise variance R is set as 0.1. Since only measurement noise is injected into the DC voltage in this example, the process noise covariance Q is set as 0, exactly. It should be noted that the noise covariance is unknown in practical measurements. 95 Fundamentals of Intelligent Control Simulation Step Scope1 Z Random Number Kalman Filter Z_est Add Scope2 Kalman Filter Scope3 Figure 4.27 Simulink model of Kalman Filter for signal measurement. The simulation model is constructed in Simulink as shown in Figure 4.27 and the model parameters as listed in Table 4.11. Table 4.11 Parameters of blocks in Simulink model of Kalman filter. Name Function Parameter Libraries/Group Kalman Filter Estimating measured signal under noise condition Initial estimated state ¼ 0; Signal Processing Blockset/Filtering/ Adaptive Filters Step Random Number Scope 1 Scope 2 Scope 3 Parameters of simulation Generating a step DC signal Generating a random number to simulate measurement noise Show original signal without noise Show estimated signal by Kalman filter Show measured signal with noise Manage simulation Initial estimated error covariance ¼ 1; State transition matrix A ¼ 1; Process noise covariance Q ¼ 0; Measurement matrix C ¼ 1; Measurement noise covariance R ¼ 0.1 Step time ¼ 0 Simulink/Sources Initial value ¼ 0 Final value ¼ 10 Mean ¼ 0; Simulink/Sources Variance ¼ 0.1; Seed ¼ 0. N/A Simulink/Sinks N/A Simulink/Sinks N/A Simulink/Sinks Fixed-step with step size ¼ 0.02 Start time ¼ 0.0 Stop time ¼1 N/A 96 Applied Intelligent Control of Induction Motor Drives To observe the output of Kalman filter in each iteration, the simulation step is set as 0.02 s and the simulation time is set as 1 s. Thus, the simulation calculation will yield 50 measurement samples and 50 outputs. The parameter configuration window of the ‘Kalman Filter’ block is shown in Figure 4.28. Figure 4.28 Configuring parameters of Kalman filter for the example. Step 3 Simulation of the Kalman Filter Based Signal Measurement In a practical application, the measurement noise covariance R may be unidentified. Hence, R may be arbitrarily set. To observe the convergence process of Kalman filter calculation in the presence of various noises, the simulation is performed three times with the following measurement noise covariances which are input into the ‘Kalman Filter’ blocks in each simulation, separately. R ¼ 0:1 ðtrue value of simulating the measurement systemÞ R ¼ 0:001 R¼1 ðarbitrary valueÞ ðarbitrary valueÞ Run the Simulink model shown in Figure 4.27. The simulation results are summarized in Figures 4.29 and 4.30. 97 Fundamentals of Intelligent Control Simulation 12 11 Voltage (V) 10 9 8 7 6 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (s) Figure 4.29 Simulation results: original voltage (solid line) and 50 measured samples (dots). 10.5 Voltage (V) 10 9.5 9 8.5 8 0 10 20 30 40 50 Iteration Figure 4.30 Simulation results: original voltage (solid line) and estimated voltages by Kalman filter in 50 iterations, with noise covariance R ¼ 0.1 (dots), with R ¼ 0.001 (crosses), and with R ¼ 1 (asterisks). 98 Applied Intelligent Control of Induction Motor Drives The simulation results show that Kalman filter has the ability to separate signal from random noises. However, Kalman filter is sensitive to the measurement noise covariance R. Various R values will result in different convergence results as shown in Figure 4.30. Because noise covariance is usually unknown in practical applications, it will be of interest to investigate further how the noise covariance in the Kalman filter can be tuned in order to yield the best estimation result. 4.5 Getting Started with Genetic Algorithm Simulation MATLABÒ (version R2008b) delivers a ‘Genetic Algorithm and Direct Search Toolbox’ (The MathWorks, Inc., 2008f). In the toolbox, the ‘ga’ function may be used to optimize a MATLABÒ function. In the toolbox User’s Guide, some MATLABÒ functions are used as GA’s fitness function and they can be optimized by the ‘ga’ function. In this section, an example is presented to optimize a Simulink model by the ‘ga’ function. 4.5.1 Genetic Algorithm Genetic Algorithm (GA) may be employed to optimize a model or a function. The model or a function is called a fitness function in a GA optimization problem. The basic steps of genetic algorithm are as follows. Step 1 Start: Generate a random population of n chromosomes which have a proper form for the problem. Step 2 Run Fitness Function: Evaluate the fitness function using each chromosome in the population. Step 3 Result Test: Judge the n evaluated results. If conditions are satisfied, then GA stops and outputs the best chromosome of current population. Step 4 Selection: Select two or more parent chromosomes from a population according to their fitness (the better the fitness of a chromosome, the greater is its chance of being selected). Step 5 Crossover: With a crossover probability cross over the parents to form a new offspring (children). If no crossover was performed, the offspring is an exact copy of the parents. Step 6 Mutation: With a mutation probability mutate new offspring at each locus (position in chromosome). Step 7 Replace: Place new offspring in the old population to create a new population and use a new generated population for a further run of the algorithm. Step 8 Loop: Go to step 2. 99 Fundamentals of Intelligent Control Simulation The calculation procedure of basic genetic algorithm may be summarized in Figure 4.31. Start Generate random population of n chromosomes First generation evaluation 1 evaluation 2 • • • evaluation nn chromosome 1 chromosome 2 • • • chromosome n Pass Run fitness function Result test Stop Next generation Fail Mutation Replace Figure 4.31 Crossover Selection Calculation process of basic genetic algorithm. The parameters of genetic algorithm are listed in Table 4.12. Table 4.12 Parameters of genetic algorithm. Name Function Input Output Start Initialize n random chromosomes N/A Run fitness function Result test Evaluate fitness function n chromosomes First generation of population has n chromosomes n evaluated results Judge n evaluated results If conditions satisfied, then stop Select good parent chromosomes according to rank of evaluation Create new chromosomes Improve chromosomes n chromosomes Pass or Fail n chromosomes Good chromosomes Parent chromosomes Child chromosomes Child chromosomes Improved child chromosomes n chromosomes of next generation of population Selection Crossover Mutation Replace Create next generation of population by replacing old chromosomes Child chromosomes and parent chromosomes 100 4.5.2 Applied Intelligent Control of Induction Motor Drives Example: Optimizing a Simulink Model by Genetic Algorithm This example demonstrates that a PID controller is optimized by Genetic Algorithm function ‘ga’ of MATLABÒ when the control system is a Simulink model. In order to call the Simulink model from MATLABÒ, the Simulink model must first be built, and then a MATLABÒ programming function is used to call the Simulink model. Step 1 Building a PID Control Model in Simulink A Simulink model of PID (proportional–integral–derivative) control system is built as shown in Figure 4.32. 1 Out1 1 PID Step s(s+1) Add Figure 4.32 PID Controller Scope Zero-Pole A Simulink model of PID control system. This PID control system will be optimized by genetic algorithm. It is simulated by a ‘Zeropole’ block. A ‘Step’ block is used to create a control reference. An ‘Out1’ block is used to export calculation results of the Simulink model. The Simulink model is saved with the filename ‘PID_controller.mdl’. Parameters of the PID control system are listed in Table 4.13. Table 4.13 Parameters of Simulink model ‘PID_controller.mdl’. Name Function Parameter Plant Simulate a plant PID Controller Step Feedback control Create control reference Out1 Export calculation results of the Simulink model Manage simulation process 1 sðs þ 1Þ Kp ¼ x1, Ki ¼ x2, Kd ¼ x3 step time ¼ 0 initial value ¼ 0 and final value ¼10 N/A Simulation Parameters Type of solver is Fixed-step Fixed-step size 0.001 s Start time 0.0 s Stop time 10 s Fundamentals of Intelligent Control Simulation 101 Parameters of the PID controller consist of three variables, namely, proportional gain Kp ¼ x1, integral gain Ki ¼ x2, and derivative gain Kd ¼ x3, which are set in the ‘PID Controller’ block as shown in Figure 4.33. Figure 4.33 Configuration of PID parameters. Step 2 Programming a Function to Run the Simulink Model In order to call the Simulink model from MATLABÒ platform, a MATLABÒ function ‘Call_PID.m’ is programmed as follows. function s = Call_PID(x) assignin(’base’,’x1’,x(1)); assignin(’base’,’x2’,x(2)); assignin(’base’,’x3’,x(3)); [tout,xout,yout] = sim(’PID_controller’,10); z = yout; [m,n] = size(z); V = 0; R = 10; %command reference for i = 1:m V = V + (R-z(i))^2; end s = V/m; end In MATLABÒ/Simulink, there two workspaces, one is named as ‘caller’ which stores variable values of MATLABÒ function. Another workspace is named as ‘base’ which stores 102 Applied Intelligent Control of Induction Motor Drives variable values of input and output of Simulink model. Because the ‘ga’ function is a MATLABÒ function, an ‘assignin’ function is employed to transfer data in the two workspaces. In this way, the variable values may be exchanged between function ‘Call_PID.m’ and model ‘PID_controller.mdl’. Descriptions of the program Call_PID.m are listed in Table 4.14. Table 4.14 Descriptions of Programming Call_PID.m. Description Function Parameter function s ¼ Call_PID(x) Function head assignin Exchange variable value in ‘caller’ and ‘base’ workspaces sim Perform a Simulink model siz Calculating number of rows and number of columns ‘for’ cycle sentence and s ¼ V/m sentence Calculating mean square error of the plant output and command reference x: input variable of function s: output variable of function Call_PID: function name x1, x2, x3: variables in ‘base’ workspace may be called by Simulink model x: array in ‘base’ workspace used by ‘ga’ function Output: [tout,xout,yout] PID_controller: Simulink model 10: simulation time (secs) input: a matrix output: m is number of rows and n is number of columns of the matrix s: output of Call_PID function R ¼ 10: command reference Step 3 MATLABÒ Programming of Genetic Algorithm In the example, the fitness function is the Call_PID.m which calls Simulink model ‘PID_ controller.mdl’. The chromosome is the PID controller’s parameters [x1, x2, x3]. Parameters of GA performance use default values of the ‘ga’ function which are listed in Table 4.15. When the performance needs to be improved, the parameters may be changed by ‘gaoptimset’ function. Table 4.15 Elements of GA. Elements of GA Representation Reference Fitness function Evaluate value Call_PID.m Mean square error of Simulink model output and command reference PID controller’s parameters x1, x2, and x3 in Simulink model Default value Function Call_PID.m Function Call_PID.m and ‘PID_controller.mdl’ Figure 4.33 Chromosome GA parameters See ‘Options of GA’ later 103 Fundamentals of Intelligent Control Simulation Enter the following commands to run the simulation on genetic algorithm. clc clear options = gaoptimset(@ga); options = gaoptimset(options,’PlotFcns’,{@gaplotbestf},’Display’, ’iter’); lb = [0 0 0]; ub = [100 100 100]; [x,fval] = ga(@Call_PID,3,[],[],[],[],lb, ub,[],options); Descriptions of above commands are listed in Table 4.16. Table 4.16 Descriptions of commands to run genetic algorithm. Command Function Parameter Ouput clc clear gaoptimset() Clear old commands Clear old workspaces Get GA parameters N/A N/A @ga gaoptimset() Change GA option, Plot GA’s optimizing process Lower bound on x Upper bound on x Perform GA options, ‘PlotFcns’, {@gaplotbestf}, ‘Display’, ‘iter’ Lower bound of PID Upper bound of PID @Call_PID: Fitness function 3: size of chromosome N/A N/A Default values of options New parameters of options lb ub ga() Options: Plotting GA process Options of GA (Default) options = PopulationType: ’doubleVector’ PopInitRange: [2x1 double] PopulationSize: 20 EliteCount: 2 CrossoverFraction: 0.8000 ParetoFraction: [] MigrationDirection: ’forward’ MigrationInterval: 20 MigrationFraction: 0.2000 Generations: 100 TimeLimit: Inf FitnessLimit: -Inf StallGenLimit: 50 StallTimeLimit: Inf TolFun: 1.0000e-006 TolCon: 1.0000e-006 InitialPopulation: [] [0 0 0] [100 100 100] x: chromosome fval: value of the fitness function at x 104 Applied Intelligent Control of Induction Motor Drives InitialScores: [] InitialPenalty: 10 PenaltyFactor: 100 PlotInterval: 1 CreationFcn: @gacreationuniform FitnessScalingFcn: @fitscalingrank SelectionFcn: @selectionstochunif CrossoverFcn: @crossoverscattered MutationFcn: {[1x1 function_handle] [1] [1]} DistanceMeasureFcn: [] HybridFcn: [] Display: ’final’ PlotFcns: [] OutputFcns: [] Vectorized: ’off’ UseParallel: ’never’ Step 4 Optimizing the PID Parameters by Genetic Algorithm In order to compare the results of GA optimized PID controller, two simulations are first performed with a random set x ¼ [0.0310, 0.6467, 0.0563] and x ¼ [5,5,5] and the simulation results are shown in Figure 4.34. 40 15 30 20 10 10 0 -10 5 -20 -30 -40 0 2 4 6 (a) 8 10 0 0 Time (s) 2 4 6 (b) 8 10 Time (s) Figure 4.34 Two simulation results of PID control model. (a) With random PID parameter x ¼ [0.0310, 0.6467, 0.0563]; (b) With x ¼ [5,5, 5]. Run the GA command set described in Step 3. clc; clear; options = gaoptimset(@ga); options = gaoptimset(options,’PlotFcns’,{@gaplotbestf},’Display’, ’iter’); lb = [0 0 0]; ub = [100 100 100]; [x,fval] = ga(@Call_PID,3,[],[],[],[],lb, ub,[],options); 105 Fundamentals of Intelligent Control Simulation Because initial chromosomes in the genetic algorithm are randomly created, the program may need to be run several times in order to obtain satisfactory results. Figures 4.35 and 4.36 show that the best output is 1.997 with the final PID parameters x ¼ [25.20, 0.045, 4.25]. Best: 1.9975 Mean: 2.045 Fitness value 15 10 5 0 0 20 40 60 Generation 80 100 Figure 4.35 Best evaluated outputs of the fitness function at each generation. 15 10 5 0 0 2 4 6 8 10 Time (s) Figure 4.36 The final simulation output of Simulink model ‘PID_controller.mdl’ with the optimized PID parameters x ¼ [25.20, 0.045, 4.25] and the mean square error 1.997. Step 5 Improving the GA Performance Results In order to improve the performance of the GA, several GA option parameters may be adjusted with the following commands. 106 Applied Intelligent Control of Induction Motor Drives 1. Increase population size to 40 by command by entering options = gaoptimset(options,’PopulationSize’,40); 2. Increase better individuals in old population to 10 that are guaranteed to survive to the next generation by entering options = gaoptimset(options, ’EliteCount’,10); 3. Decrease crossover fraction to 0.6 by entering options = gaoptimset(options, ’CrossoverFraction’,0.6); 4. Increase generations to 140 by entering options = gaoptimset(options, ’Generations’,140); Insert the above four commands into GA run commands described in Step 3. The GA run commands become: clc clear options = options = ’iter’); options = options = options = options = gaoptimset(@ga); gaoptimset(options,’PlotFcns’,{@gaplotbestf},’Display’, gaoptimset(options,’PopulationSize’,40); gaoptimset(options, ’EliteCount’,10); gaoptimset(options, ’CrossoverFraction’,0.6); gaoptimset(options, ’Generations’,140); Best: 1.2943 Mean: 1.295 Fitness value 15 10 5 0 Figure 4.37 0 20 40 60 80 Generation 100 120 140 Best and mean evaluated outputs of the fitness function at each generation. 107 Fundamentals of Intelligent Control Simulation 15 10 5 0 0 2 4 6 8 10 Time (s) Figure 4.38 Simulation output of Simulink model ‘PID_controller.mdl’ with the final optimized PID parameters x ¼ [59.99, 0.03, 6.73] and mean square error 1.294. options = gaoptimset(options,’MutationFcn’,@mutationadaptfeasible); lb = [0;0;0]; ub = [60;10;10]; [x,fval] = ga(@Call_PID,3,[],[],[],[],lb, ub,[],options); After running the above revised set of GA commands, better chromosomes (PID parameters) are obtained as shown in Figure 4.37 and the evaluated output of the Simulink model ‘PID_controller.mdl’ is smaller, as shown in Figure 4.38. The best output is 1.294 and the final PID parameters are x ¼ [59.99, 0.03, 6.73]. By comparing Figure 4.37 with Figures 4.35 and 4.38 with Figure 4.36, we conclude that the GA optimization result can be improved by adjusting the GA performance parameters. The mean square error is decreased from 1.997 to 1.294. 4.6 Summary The example of fuzzy PI controller illustrates how to start using ‘Fuzzy Logic Toolbox’ of MATLABÒ/Simulink. The example of neural network based Park’s transformation demonstrates using a neural network of parallel calculation structure to implement multi-output nonlinear functions. In the Kalman filter example, linear measured signal is separated from random noises by the ‘Kalman Filter’ block of Simulink. It is also demonstrated that the performance of the Kalman filter is sensitive to the measurement noise covariance R. The example of genetic algorithm optimized PID controller illustrates how to get started using the ‘ga’ function delivered by MATLABÒ software. After working through these four examples, the readers should have acquired the basic techniques of intelligent control simulation. 108 Applied Intelligent Control of Induction Motor Drives References Kalman, R.E. (1960) A new approach to linear filtering and prediction problems. ASME Journal of Basic Engineering, 82, 34–45. The MathWorks, Inc. (2008a) MATLABÒ Getting Started Guide. The MathWorks, Inc. The MathWorks, Inc. (2008b) Simulink Getting Started Guide. The MathWorks, Inc. The MathWorks, Inc. (2008c) Fuzzy Logic Toolbox User’s Guide. The MathWorks, Inc. The MathWorks, Inc. (2008d) Neural Network Toolbox User’s Guide. The MathWorks, Inc. The MathWorks, Inc. (2008e) Signal Processing Blockset Reference. The MathWorks, Inc. The MathWorks, Inc. (2008f) Genetic Algorithm and Direct Search Toolbox User’s Guide. The MathWorks, Inc. Sousa, G.C.D. and Bose, B.K. (1995) Fuzzy logic application to power electronics and drives – an overview. Proceedings of the 1995 IEEE IECON 21st International Conference on Industrial Electronics, Control, and Instrumentation, Orlando, FLA, pp. 57–62. 5 Expert-System-based Acceleration Control1 5.1 Introduction Conventional vector control of the induction motor includes field-oriented control (FOC) and direct self control (DSC). In recent years, FOC and DSC have been applied to inverter-fed induction motor drives for improving the transient response (Bose, 1986; Novotny and Lipo, 1996). Although the implementation of both methods has largely been successful, they both suffer from sensitivity to parameter variations and error accumulation when evaluating the definite integrals (Shi et al., 1999). In both methods, the control must be continuous and the calculation must begin from an initial state. If the control time is long, degradation in the steady-state and transient responses will result due to drift in parameter values and excessive error accumulation. An expert system is a computer program that is designed to emulate a human’s skills in a specific problem domain (George and William, 1989). As the forerunner among all the AI techniques, expert systems have been researched since the early 1960s and have now become the most important branch of artificial intelligence. Since then, expert systems have found wide applications in many areas. If an expert system is used as part of a feedback controller to emulate the expertise of a human in performing control of plant, it is called ‘expert-system control’ (Passino and Lunardhi, 1996a). Expert-system control was originally proposed by Astr€ om and Anton (1984) (Astr€ om and Anton, 1984). Due to the complexity existing in many real-world control problems, not all of them can be well represented, solved and implemented 1 (a) Portions reprinted from K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A new acceleration control scheme for an inverter-fed induction motor,” Electric Power Components and Systems, 27(5), 527–554, Ó 1999, by permission of Taylor & Francis Ltd, http://www.tandf.co.uk/journals (b) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE. (c) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” Proceedings of IEEE International Electric Machines and Drives Conference (IEMDC ’99), pp. 613–615, Seattle, Washington, U.S.A. Ó 1999 IEEE. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 110 Applied Intelligent Control of Induction Motor Drives by the traditional mathematical methodologies and tools. Consequently, the applications of human-like expert system in real-time dynamic control have been an attractive research area. The core parts of expert-system control are the knowledge-base and the inference engine. The knowledge base consists of facts and rules that characterize strategies on how to control the plant. The inference engine is designed to emulate the control expert’s decision-making process. In addition, an expert-system controller may have a user interface to interpret the control process and to modify the knowledge base by a user. In this chapter, the expert-system principle is employed to control the rotor acceleration of an induction motor, the main objective being to overcome the drawbacks of common vector control schemes. Based on the relationship between stator voltage vector and rotor acceleration, a control method with voltage vector comparison and voltage vector retaining is proposed to control the rotor acceleration. This method uses a trial-and-error strategy to determine the best of seven voltage vectors in every interval of the control process, which is then selected and retained. To decrease the number of voltage vectors to be compared, the production knowledge base is modified by tracking the angle of the stator current vector. After using the heuristic knowledge, the number of voltage vectors compared is decreased to two, and the influence of sub-optimal voltage vectors is reduced to a minimum. Fourteen rules represent the rotor acceleration control knowledge and the inference engine based on a production system (Buchanan and Shortliffe, 1984; HayesRoth, 1985) processes the rules in order to arrive at the desired control goals. 5.2 Relationship between the Stator Voltage Vector and Rotor Acceleration The usual vector controllers rely on flux calculations. Since flux is calculated from an integral of input electrical energy, the controller cannot thoroughly eliminate the flux accumulation error. However, by using rotor acceleration control instead of electromagnetic torque control, flux calculations will no longer be needed. In practice, most of the inverters in use can produce only seven discrete space vector values of actuating variables. Usually none of these is exactly equal to the desired instantaneous value of the space vector. In the proposed rotor acceleration controller, one voltage vector is selected in every period so as to decrease the error between the actual rotor acceleration and the acceleration command. Because there is no direct relationship between the rotor acceleration and the stator voltage vector, the optimum voltage vector has to be selected by comparing the incremental acceleration produced by every voltage vector. The formulations of incremental acceleration and stator voltage vector are deduced as follows. The dynamic equation of the mechanical system may be expressed as (Krause, Wasynczuk, and Sudhoff, 1995): g doo ¼ T TL : dt ð5:1Þ where g is the normalized mechanical time constant, TL is the load torque, and T is the electromagnetic torque given by: T ¼ lsm iss : ð5:2Þ 111 Expert-System-based Acceleration Control From Equations (5.1) and (5.2), the rotor acceleration is: doo 1 s lm iss TL : ¼ g dt ð5:3Þ The stator flux can be expressed as: lsm ðt0 Þ ¼ ðt0 0 or VsðkÞ Rs iss dt ð5:4Þ dlsm ¼ VsðkÞ Rs iss dt: ð5:5Þ ðkÞ When t > t0 , the stator voltage vector Vs determines the increment of the stator flux, dlsm , which is shown in Figure 5.1. If the rotor acceleration is denoted by a, then Equation (5.1) becomes a¼ doo 1 ¼ ðT TL Þ g dt ð5:6Þ Vs(2) 2 Vs(3) 2 Vs(1) 1 3 dλ 2 3 1 dλ 1 dλ 3 λ sμ Vs(4) 6 4 6 4 5 dλ 4 Vs(6) 5 dλ 6 Vs(5) dλ 5 Figure 5.1 Flux increment of induction motor. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) The differential rotor acceleration is 1 da ¼ ½dT dTL g ð5:7Þ dT ¼ dlsm iss þ lsm diss : ð5:8Þ From Equation (5.2), 112 Applied Intelligent Control of Induction Motor Drives Substituting Equations (5.5), (5.8) into (5.7), daðkÞ ¼ i 1 h ðkÞ Vs Rs iss dt iss þ lsm diss dTL : g ð5:9Þ Because iss iss ¼ 0, Equation (5.9) becomes daðkÞ ¼ i 1 h ðkÞ Vs iss dt þ lsm diss dTL g ð5:10Þ where k (mod(k) ¼ 7) denotes one of the seven voltage vectors. The incremental acceleration of the rotor is, from Equation (5.10), i 1 h ðkÞ Vs iss Dt þ lsm Diss DTL g ð5:11Þ i 1h Dt Ro jVsðkÞ jjiss jsin Wi þ lsm Diss DTL g ð5:12Þ DaðkÞ ¼ DaðkÞ ¼ Incremental Acceleration ∆a(k) where Ro is a unit vector. ðkÞ Equation (5.12) explains that the stator voltage vector Vs determines the incremental accelerations of the rotor. When t > t0 , the incremental accelerations that result from the six stator voltage vectors are shown in Figure 5.2. ∆a(i+1) ∆a(i+2) ∆a(i) Vs(i+3) Vs(i+4) Vs(i+5) Vs(i) Vs(i+1) Vs(i+2) Stator voltage vector Vs(k) ∆a(i+5) ∆a(i+3) ∆a(i+4) Figure 5.2 Rotor acceleration increments of six stator voltage vectors. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) Two important results are obtained from Equation (5.12). 1. Incremental acceleration of the rotor is determined by the stator voltage vector. 2. If Da(j) < 0, there is at least one number m such that Da(j þ m) > 0. If Da( j) > 0, there is at least one number n such that Da(j þ n) < 0. According to these two results, a controller may be designed using a voltage vector comparison and retaining method. 113 Expert-System-based Acceleration Control 5.3 Analysis of Motor Acceleration of the Rotor An example is given to illustrate rotor acceleration controlled by stator voltage vectors. If two stator voltage vectors are supplied to the motor in succession for t > t0, they will produce two different accelerations of rotor as shown in Figure 5.3. Accelerations ∆a(Vs(1), is(ξ1)) ∆a(Vs(2), is(ξ2)) a(Vs(2) ) Voltages a(Vs(1) ) a2(Vs(2) ) Vs(1) t0 Figure 5.3 a1(Vs(1) ) Vs(1) or Vs(2) Vs(2) t1 t2 t3 Time Effect of applied voltage vector on rotor acceleration. ð1Þ During t2 < t < t3 , selecting and retaining the voltage vector Vs that results in a larger incremental acceleration of the rotor will produce a larger acceleration. This may be proved as follows. Let Dt ¼ t1 t0 ¼ t2 t1 ¼ t3 t2 . Then from Equation (5.11), the incremental acceleration of the rotor may be written as, 1h i Da VsðkÞ ; iss ðxÞ ¼ Dt VsðkÞ iss ðxÞ þ lsm Diss DTL g ð5:13Þ where t0 < x < t0 þ Dt. The rotor accelerations at instants t1, t2 and t3 are as follows: aðt1 Þ ¼ aðt0 Þ þ Da Vsð1Þ ; iss ðx1 Þ ; t0 < x1 < t1 aðt2 Þ ¼ aðt1 Þ þ Da Vsð2Þ ; iss ðx2 Þ ; t1 < x2 < t2 a1 ðt3 Þ ¼ aðt2 Þ þ Da Vsð1Þ ; iss ðx3 Þ ; t2 < x3 < t3 a2 ðt3 Þ ¼ aðt2 Þ þ Da Vsð2Þ ; iss ðx4 Þ ; t2 < x4 < t3 : Suppose iss ðx3 Þ iss ðx1 Þ and iss ðx4 Þ iss ðx2 Þ, then a1 ðt3 Þ ¼ aðt2 Þ þ Da Vsð1Þ ; iss ðx3 Þ aðt2 Þ þ Da Vsð1Þ ; iss ðx1 Þ ð5:14Þ ð5:15Þ ð5:16Þ ð5:17Þ ð5:18Þ 114 Applied Intelligent Control of Induction Motor Drives a2 ðt3 Þ ¼ aðt2 Þ þ Da Vsð2Þ ; iss ðx4 Þ aðt2 Þ þ Da Vsð2Þ ; iss ðx2 Þ : ð5:19Þ ð2Þ ð1Þ If Da Vs ; iss ðx1 Þ > Da Vs ; iss ðx2 Þ , then a1 ðt3 Þ > a2 ðt3 Þ. In this case, if we wish to increase the acceleration of the rotor during the subsequent time interval, the voltage vector ð1Þ ð2Þ Vs should be retained and the voltage vector Vs should be discarded. To find the optimum voltage vector at every period, a control strategy of voltage vector comparison and voltage vector retaining is proposed. 5.4 Control Strategy of Voltage Vector Comparison and Voltage Vector Retaining In the proposed control method, the time is divided into many small intervals each consisting of a voltage vector comparison period and a voltage vector retaining period. In the comparison period, several voltage vectors are supplied to the induction motor in proper order, and the incremental acceleration of each voltage vector is recorded. At the end of the comparison period, the optimum voltage vector that produces a larger incremental acceleration is selected for the retaining stage. In the latter stage, the controller retains this optimum voltage vector to the motor. If the rotor acceleration is above or below a certain threshold during the voltageretaining period, a zero voltage vector is supplied. A cycle of the control process for the induction motor is illustrated in Figure 5.4. Three problems need to be solved before the proposed method can be applied directly to control an induction motor. The first problem is how to assign the comparison time and retaining time, as this will affect the results of control for the induction motor. The second problem is how to select heuristically the voltage vectors to be compared, because too many voltage vector comparisons will degrade the performance of the induction motor. The third problem is how to compare the rotor acceleration, because the voltage vector of maximum rotor acceleration may not be the optimum voltage vector. When the rotor accelerations produced by different voltage vectors are compared, the maintenance of the current amplitude should also be considered. Assign the comparison time and retaining time. To determine the appropriate cycle time, a heuristic approach may be used. Because there are six nonzero voltage vectors supplied during a revolution and the stator voltage vector rotation is faster than the rotor by the asynchronous principle, the cycle time should be shorter than the time for the rotor to rotate through 1/6 of a revolution. The cycle time should thus be shorter when the speed of rotor is faster. By this heuristic, the cycle time may be fuzzily determined and adjusted by measuring the rotor speed. Strategy of selecting the voltage vectors to be compared. In order to decrease the number of voltage vectors to be compared, a method of selecting these voltage vectors heuristically is used by tracking the angle of stator current vector. Equation (5.3) may be written as doo 1 s s jlm jjis jsin ji TL : ¼ dt g ( ) doo TL ¼ 0; ji do¼0 ¼ arcsin When ¼ j0 dt dt jlsm jjiss j ð5:20Þ ð5:21Þ 115 Expert-System-based Acceleration Control Acceleration command ath ath Acceleration of rotor Threshold Retaining voltage Vs(2) Vs(1) Vs(2) Vs(3) Vs(4) Vs(5) Vs(6) Clock Control Signal amax a* amin Time Comparing period Retaining period Comparing signal Time Selecting signal Time Retaining signal Time Zero voltage signal Time Figure 5.4 A cycle of voltage comparison and voltage retaining. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) doo > 0; j0 < ji < p j0 dt ð5:22Þ doo 0; p j0 ji j0 dt ð5:23Þ When When After the actual acceleration of the rotor has been known, the angle range between the stator current vector and the flux vector may be determined from Equations (5.22) and (5.23). Once the actual angle of the stator current vector is detected, the flux angle range may be estimated. Because the estimated angle range of the flux vector should not exceed p rad, the incremental acceleration of the rotor can be determined by comparing only two voltage vectors. An example of voltage vector comparison based on the position of the stator current vector is shown in Figure 5.5. When the rotor acceleration is larger than zero and the stator current vector is in area 5, the flux lsm may be in area 2, 3, or 4 according to Equation (5.22). According to a predictive (optimal) principle of current control (Nabae, Ogasawara, and Akagi, 1986), the incremental current Di1, Di3, Di4, Di5 and Di6 are as shown in Figure 5.5. From Equation (5.11) and Figure 5.5, when the rotor acceleration is larger than zero and the stator current vector is in area 5, six rules may be summarized as follows: 116 Applied Intelligent Control of Induction Motor Drives Vs(2) Vs(3) 2 2 3 1 4 6 Flux λsμ Vs(4) ∆i3 Vs(1) 1 3 6 4 5 is 5 Vs(6) Vs(5) ∆i1 ∆i6 ∆i4 ∆i5 Figure 5.5 An example of selecting the voltages to be compared. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) 1. If Vs(5) is chosen, then the current amplitude and the rotor acceleration will be increased. 2. If Vs(6) is chosen, then the current amplitude will be maintained and the rotor acceleration will be increased. 3. If Vs(1) is chosen, then the current amplitude will be decreased and the rotor acceleration will be increased. 4. If Vs(3) is chosen, then the current amplitude will be decreased and the rotor acceleration will be decreased. 5. If Vs(4) is chosen, then the current amplitude will be maintained and the rotor acceleration will be decreased. 6. If Vs(0) is chosen, then the current amplitude and the rotor acceleration will be decreased. The selection pattern of compared voltage vectors can be derived from the above six rules. When the rotor acceleration command is larger than zero (a counterclockwise acceleration command), the supply current should be maintained at a larger value, because a positive torque is needed to accelerate the rotor. Hence, the compared voltage vectors should be Vs(5) and Vs(6) and the voltage vectors Vs(1), Vs(2), Vs(3) and Vs(4) are discarded. When the rotor acceleration command is less than zero (a clockwise deceleration command), magnitude of the supply current should be maintained at a larger value, because a negative torque is needed to decelerate the rotor. Hence, the compared voltage vectors should be Vs(5) and Vs(4) and the voltage vectors Vs(1), Vs(2), Vs(3) and Vs(6) are discarded. When the rotor acceleration command is equal to zero, the supply current should be maintained at a smaller value. Hence, the compared voltage vectors should be Vs(5) and Vs(1) when rotor speed command is larger than zero (a counterclockwise rotation command); or should be Vs(5) and Vs(3) when rotor speed command is less than zero (a clockwise rotation command); and the voltage vectors Vs(6), Vs(2), and Vs(4) are discarded. These selection patterns are expressed in Table 5.1. 117 Expert-System-based Acceleration Control Table 5.1 a Selection of the vectors to be compared according to rotor acceleration and speed commands. o*o a 0 a 0 a 0 o*o > 0 a 0 o*o < 0 Voltage vectors compared when stator current vector is in area n ¼ 5 ð1Þ Vs ð2Þ Vs ð3Þ Vs ð4Þ ð5Þ Retained voltage vector ð6Þ ð0Þ Vs Vs Vs Vs Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) When stator current vector is in any area n, the general patterns of selecting the voltage vectors to be compared can be summarized as follows: ðnÞ 1. If a 0, and stator current vector is in area n, the compared voltage vectors are Vs and ðn þ 1Þ Vs . ðnÞ 2. If a 0, and stator current vector is in area n, the compared voltage vectors are Vs and ðn 1Þ Vs . ðnÞ 3. If a 0, o*o > 0, and stator current vector is in area n, the compared voltage vectors are Vs ðn þ 2Þ . and Vs ðnÞ 4. If a 0, o*o < 0, and stator current vector is in area n, the compared voltage vectors are Vs ðn 2Þ . and Vs Comparison strategy of rotor acceleration: According to the above rules, the amplitude ðnÞ ðn þ 1Þ ðn þ 2Þ ðn 1Þ increment of stator current produced by Vs is larger than Vs , Vs or Vs when the stator current vector is in area n. In order to maintain the amplitude of stator current, once the ðn þ 1Þ ðn þ 2Þ rotor acceleration produced by Vs or Vs is larger than zero (for the case a 0, or, ðn 2Þ ðn 1Þ * is less than zero (for the case a 0, or, a 0 and or Vs a 0 and oo > 0), or, Vs ðnÞ * oo < 0), they should preferentially be selected as the retained voltage vector rather than Vs . The method of the voltage vectors comparison can be expressed as follows. n o ðRÞ ðnÞ ðn þ 1Þ Da Vs ¼ max Da Vs ; ZDa Vs when a* 0 n ðRÞ ðnÞ ðn ¼ min Da Vs ; ZDa Vs Da Vs 1Þ o when a* 0 n o ðRÞ ðnÞ ðn þ 2Þ ¼ max Da Vs ; ZDa Vs when a* 0 and o*o > 0 Da Vs n ðRÞ ðnÞ ðn Da Vs ¼ max Da Vs ; ZDa Vs 2Þ o when a* 0 and o*o < 0 118 Applied Intelligent Control of Induction Motor Drives Z is a preferential parameter that is larger than 1 to implement the preferential selection. A ðRÞ satisfactory value of Z is 500 from the results of computer simulation. Vs is the optimum voltage vector that will be supplied in the retaining stage of the control process. 5.5 Expert-System Control for Induction Motor The functions of an expert-system controller are to interpret plant outputs and reference inputs, to reason about alternative control strategies, and to generate inputs in order to improve the performance of the closed-loop system. An expert-system controller functionally works as follows (Astr€ om and Bj€ orn, 1995; Passino and Lunardhi, 1996a): 1. Through the input interface, the controller receives information that is numerical (quantitative) or linguistic (qualitative). Through the output interface, the controller sends electrical signals to the plant. 2. Based on the real-time information received, a knowledge base and an inference engine provide the decision making to control the system under an uncertain environment, such as changes of noise, parameter, load, or power supply. The decision making can be achieved just by tuning the parameters of the controller, changing the algorithm, or modifying the control structure. 3. Monitoring performance faults, consulting with the control expert, and modifying the knowledge base via a user interface. The knowledge-base modification based on consultation with the control expert can make the controller more flexible and adaptive than the prototype controller. The control system proposed consists of the expert-system controller, inverter, and induction motor as shown in Figure 5.6. Expert-system controller a a* ω* Commands Input interface Inference engine Output interface Inverter iss Knowledge base User User interface Explanation of performance Knowledge acquisition and modification Figure 5.6 Induction motor control system with expert-system controller. IM Expert-System-based Acceleration Control 119 The expert-system controller consists of a knowledge base, an inference engine, an input interface, an output interface, and a user interface. The knowledge base includes a database and a rulebase. The data can be separated into facts and goals. Examples of facts are statements such as ‘acceleration is zero,’ and ‘in retaining period.’ An example of goals is ‘rotor acceleration is between super-value and under-value.’ New facts can also be created by the rules. The rulebase contains production rules of the type: ‘if premise then conclusion (action).’ The premise is the fact or the goal of the database. The conclusion results in an action and may add a new fact to the database or modify an existing fact. In this way, the knowledge base can choose the most appropriate strategy to control the induction motor. In collecting command input (rotor acceleration command), induction motor output (rotor acceleration), and the inference engine output (working state of controller), the inference engine is designed to emulate the control expert’s decision-making process to operate the rules to arrive at the conclusion or to satisfy the goals. The input interface implements the numerical and linguistic coding of electrical signals. The output interface implements the transformation from the numerical values and linguistic commands to electrical signals. In order to improve the performance of the prototype controller, the user interface may be designed to monitor the performance faults, to consult the control expert, and to modify the knowledge base of the controller. The task of knowledge representation is to capture the essential features of a problem domain and make that information accessible to a problem-solving procedure. The rotor acceleration control knowledge can be represented as 14 rules by the logical language, ‘if premise then conclusion (action).’ At the beginning of the comparison period, the space region n of stator current vector is detected. Then, depending on the rotor acceleration command, two voltage vectors are supplied to the induction motor in succession, and the corresponding rotor accelerations are obtained from the speed sensor. By comparing the two accelerations, the optimum voltage vector is obtained and is held constant in the next period (retaining period). In the comparison period, the control knowledge is expressed as 10 rules as follows. 1. If in comparison period (denote as E) and comparison voltage vectors have not been input (denote as :H), then to detect the region of stator current space vector (denote as n ¼ i). 2. If in comparison period (E), rotor acceleration command is much larger than zero (A1), and comparison voltage vectors have not been input (:H), then supply Vs(n) and Vs(n þ 1) to induction motor in succession (X1). 3. If in comparison period (E), rotor acceleration command is near zero (A2), and comparison voltage vectors have not been input (:H), then supply Vs(n) and Vs(n þ 2) to induction motor in succession (X2). 4. If in comparison period (E), rotor acceleration command is much less than zero(A3), and comparison voltage vectors have not been input (:H), then supply Vs(n) and Vs(n 1) to induction motor in succession (X3). 5a. If in comparison period (E), rotor acceleration command is much larger than zero (A1), comparison voltage vectors have been input (H), and Da(Vs(n)) > ZDa(Vs(n þ 1)) (B1), then Vs(n) is supplied to induction motor and is retained (k ¼ n, Vs(k), counter t ¼ 0). 5b. If in comparison period (E), rotor acceleration command is near zero (A2), comparison voltage vectors have been input (H), and Da(Vs(n)) > ZDa(Vs(n þ 2)) (B3), then Vs(n) is supplied to induction motor and is retained (k ¼ n, Vs(k), counter t ¼ 0). 120 Applied Intelligent Control of Induction Motor Drives 5c. If in comparison period (E), rotor acceleration command is much less than zero (A3), comparison voltage vectors have been input (H), and Da(Vs(n)) < ZDa(Vs(n 1)) (B5), then Vs(n) is supplied to induction motor and is retained (k ¼ n, Vs(k), counter t ¼ 0). 5d. If in comparison period (E), rotor acceleration command is near zero (A2), comparison voltage vectors have been input (H), and Da(Vs(n)) < ZDa(Vs(n 2)) (B7), then Vs(n) is supplied to induction motor and is retained (k ¼ n, Vs(k), counter t ¼ 0). 6. If in comparison period (E), rotor acceleration command is much larger than zero(A1), comparison voltage vectors have been input (H), and Da(Vs(n)) ZDa(Vs(n þ 1)) (B2), then Vs(n þ 1) is supplied to induction motor and is retained (k ¼ n þ 1, Vs(k), counter t ¼ 0). 7. If in comparison period (E), rotor acceleration command is near zero (A2), o*o > 0 (F), comparison voltage vectors have been inputted (H), and Da(Vs(n)) ZDa(Vs(n þ 2)) (B4), then Vs(n) is supplied to induction motor and is retained (k ¼ n þ 2, Vs(k), counter t ¼ 0). 8. If in comparison period (E), rotor acceleration command is near zero (A2), o*o < 0 (:F), comparison voltage vectors have been inputted (H), and Da(Vs(n)) ZDa(Vs(n 2)) (B8), then Vs(n) is supplied to induction motor and is retained (k ¼ n 2, Vs(k), counter t ¼ 0). 9. If in comparison period (E), rotor acceleration command is much less than zero (A3), comparison voltage vectors have been input (H), and Da(Vs(n)) ZDa(Vs(n 1)) (B6), then Vs(n) is supplied to induction motor and is retained (k ¼ n 1, Vs(k), counter t ¼ 0). In the voltage vector retaining period, the voltage vector supplied is unchanged if the rotor acceleration is within the range (amin, amax), where amin ¼ a ath and amax ¼ a þ ath, a is the rotor acceleration command and ath is a specified threshold value (Figure 5.4). When the rotor acceleration is larger than amax and if the rotor acceleration command is larger than zero, then a zero voltage vector is supplied; if the rotor acceleration command is less than zero, then optimum voltage vector is supplied. When the rotor acceleration is less than amin and if the rotor acceleration command is less than zero, then zero voltage vector is supplied; if the rotor acceleration command is larger than zero, then the optimum voltage vector is supplied. In the retaining period, the control knowledge is therefore expressed as five rules as follows. 10a. If in retaining period (denote as :E), rotor acceleration command is much larger than zero (denote as A1), zero voltage vector is supplied (denote as C1), and rotor acceleration is larger than amax (Figure 5.4) (denote as D1), then the zero voltage vector is kept (Vs(k), k ¼ 0). 10b. If in retaining period (:E), rotor acceleration command is much less than zero (A3), zero voltage vector is supplied (C1), and rotor acceleration is less than amin (D3), then zero voltage vector is supplied (Vs(k), k ¼ 0). 11a. If in retaining period (:E), rotor acceleration command is much larger than zero (A1), nonzero optimum voltage vector is supplied (C2), and rotor acceleration is larger than amax (D1), then the nonzero voltage vector is recorded in m (m ¼ k, k ¼ 0), and zero voltage vector is supplied (Vs(k)). 11b. If in retaining period (:E), rotor acceleration command is much less than zero (A3), nonzero optimum voltage vector is supplied (C2), and rotor acceleration is less than amin (D3), 121 Expert-System-based Acceleration Control 12. 13a. 13b. 14a. 14b. then the nonzero voltage vector is recorded in m (m ¼ k, k ¼ 0), and zero voltage vector is supplied (Vs(k)). If in retaining period (:E), rotor acceleration is between amax and amin of reference value (D2), then voltage vector supplied (the optimum voltage vector or zero voltage vector) is unchanged (Vs(k)). If in retaining period (:E), rotor acceleration command is much larger than zero(A1), zero voltage vector is supplied (C1), and rotor acceleration is less than amin (D3), then the optimum voltage vector is restored and supplied (k ¼ m, Vs(k)). If in retaining period (:E), rotor acceleration command is much less than zero (A3), zero voltage vector is supplied (C1), and rotor acceleration is larger than amax (D1), then the optimum voltage vector is restored and supplied (k ¼ m, Vs(k)). If in retaining period (:E), rotor acceleration command is much larger than zero (A1), nonzero optimum voltage vector is supplied (C2), and rotor acceleration is less than amin (D3), then the optimum voltage vector supplied is unchanged (Vs(k)). If in retaining period (:E), rotor acceleration command is much less than zero (A3), nonzero optimum voltage vector is supplied (C2), and rotor acceleration is larger than amax (D1), then the optimum voltage vector supplied is unchanged (Vs(k)). The detailed algorithm of the expert-system acceleration control for an induction motor is given in APPENDIX D. A typical sequence of the expert-system acceleration control is illustrated in Table 5.2. Table 5.2 A typical sequence of the expert-system acceleration control. Iteration No. Working memory Conflict Set Rule fired i i i i i i i i i A1^:E^ D1^C2 :E^D2 A1^:E^ D3^C1 E^:H E^A1^:H E^A1^H^B1 :E^D3^C2 :E^D2 :E^D1^C2 .. . S 11 12 13 1,2,3,4 2 6 14 12 11 .. . 11 12 13 1 2 6 14 12 11 .. . Halt þ1 þ2 þ3 þ4 þ5 þ6 þ7 þ8 .. . iþk Remarks Modify database m ¼ k, k ¼ 0 Retaining voltage vector Modify database k ¼ m Modify database n ¼ i Input comparing voltage vectors Modify database k ¼ n þ 1, t ¼ 0 Keep voltage vector Retaining voltage vector Modify database m ¼ k, k ¼ 0 .. . Motor stops (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) 122 Applied Intelligent Control of Induction Motor Drives 5.6 Computer Simulation and Comparison Five computer simulation examples are presented to prove the feasibility of expert-system based control. In the first example, the performance of an inverter-fed induction motor driving a constant torque load is investigated. The simulation results of DSC and the proposed expertsystem controller are compared. The second example compares the robustness of the two controllers. The third example verifies that the expert-system controller has exchangeability, that is, the same controller can be used for different induction motors. The fourth example demonstrates that the expert-system controller can work in a very low speed range. The fifth example simulates the expert-system controller working with an encoder model and establishes that the encoder should have a minimum required precision. A computer simulation of the expert-system acceleration controller is implemented using MATLABÒ/Simulink software as shown in Figure 5.7. 1 Rotor acceleration Commands 2 Stator current Current vector Time control signal Acceleration selection 3 Voltage Select 1 Rotor speed 1 Deceleration selection out_1 Switch Votage hold Voltage Select 2 Figure 5.7 Simulink model of the expert-system acceleration controller. The simulation model of the acceleration controller consists of a ‘Current vector’ block, a ‘Commands’ block, a ‘Time control signal’ block, an ‘Acceleration selection’ block, a ‘Deceleration selection’ block, a ‘Voltage select 1’ block, a ‘Voltage select 2’ block, 123 Expert-System-based Acceleration Control a ‘Switch’ block, and a ‘Voltage hold’ block. The inputs of the model are the rotor acceleration a (which may be obtained from the rotor speed by a differential calculation), stator current is, and rotor speed signal o. The output is the stator voltage vector supplied to the induction motor. The ‘Current vector’ block (which stores the expert-system rule 1) transfers the stator current into current vector. The ‘Commands’ block issues rotor speed command o , rotor acceleration command a , and rotor acceleration error Da. The ‘Time control signal’ block generates time control signals of the comparison period and retaining period. The ‘Acceleration selection’ block and ‘Deceleration selection’ block implement the rotor acceleration/deceleration comparisons and selections. The ‘Voltage select 1’ block (which stores the expert-system rules 2, 3, 5a, 5b, 6, 7, 8) issues comparison voltage vectors according to rotor acceleration command. The ‘Voltage select 2’ block (which stores rules 4, 5c, 5d, 9) issues comparison voltage vectors according to the deceleration command. The ‘Switch’ block is used to switch control signals of the rotor acceleration and deceleration. The ‘Voltage hold’ block (which stores rules 10–14) generates and retains stator voltage vector signals according to the results of the rotor acceleration/deceleration comparisons and selections. 5.6.1 The First Simulation Example This example is a comparison of DSC and the expert-system controller in respect of rotor acceleration, torque, current, and flux. The induction motor parameters chosen for the simulation studies are listed in ‘Motor 1’ of Appendix B, and the load torque is 20 Nm. Speed command: o*o ¼ 40ðrad=sÞ 0 s t < 0:4 s o*o ¼ 20ðrad=sÞ 0:4 s t < 0:8 s Rotor acceleration command: a* ¼ 300ðrad=s2 Þ o*o ¼ 40 ^ oo < 40 a* ¼ 0ðrad=s2 Þ o*o ¼ 40 ^ oo ¼ 40 a* ¼ 300ðrad=s2 Þ t 0:4 s ^ oo > 20 a* ¼ 0ðrad=s2 Þ o*o ¼ 20 ^ oo ¼ 20 Figure 5.8a, Figure 5.9a, Figure 5.10a, and Figure 5.11a are the simulation results for the expert-system controller. Figure 5.8b, Figure 5.9b, Figure 5.10b, and Figure 5.11b are the simulation results for the DSC controller. As shown in the above figures, the responses of speed, torque and rotor acceleration of the two controllers are almost the same. With the proposed controller, however, oscillations in rotor acceleration and torque are produced during the transition period. Although the flux is not directly controlled by the proposed scheme, the stator current and flux do not deviate significantly from the corresponding curves of DSC. 124 Applied Intelligent Control of Induction Motor Drives 50 (a) 50 (b) 40 Speed (rad/s) Speed (rad/s) 40 30 20 10 30 20 10 0 -10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -10 0.8 0 0.1 0.2 0.3 0.4 0.5 Time (s) 0.6 0.7 0.8 Time (s) 400 Acceleration (rad/s2) Torque (N.m) (a) 200 0 -200 -400 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (b) 400 Acceleration (rad/s2) Torque (N.m) Figure 5.8 (a) Rotor speed response of expert-system controller; (b) Rotor speed response of DSC. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) 300 200 100 0 -100 -200 -300 -400 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Time (s) Figure 5.9 (a) Controlled acceleration and torque response of expert-system controller; (b) Acceleration response and controlled torque of DSC controller. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) (a) 400 (b) 200 100 0 -100 -200 -300 -400 -400 400 300 d component (A) d component (A) 300 200 100 0 -100 -200 -300 -200 0 200 q component (A) 400 -400 -400 -200 0 200 400 q component (A) Figure 5.10 (a) Stator current vector of expert-system controller, time ¼ 0 s 0.15 s; (b) Stator current vector of DSC, time ¼ 0 s 0.13 s. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) 125 Expert-System-based Acceleration Control 1.5 (b) 1 d component (Wb) d component (Wb) (a) 0.5 0 -0.5 -1 -1.5 -1.5 -1 -0.5 0 0.5 1 1.5 1 0.5 0 -0.5 -1 -1.5 -1.5 1.5 q component (Wb) -1 -0.5 0 0.5 1 1.5 q component (Wb) Figure 5.11 (a) Primary flux vector of expert-system controller, time ¼ 0 s 0.15 s; (b) Primary flux vector of DSC, time ¼ 0 s 0.13 s. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) 5.6.2 ~is s The Second Simulation Example s s Let ¼ iss þn (~is : current with noise, iss : current, n: sensor noise). Substituting ~is to Equation (5.4) which is DSC flux calculation model (Takahashi and Noguchi, 1986), Equation (5.24) may be obtained and the flux error may be calculated by Equation (5.25). lsm ðt0 Þ ¼ ðt0 ðVsðkÞ s Rs~is Þdt ¼ ðt0 ðVsðkÞ Dlsm ðt0 Þ ¼ ðt0 ðt0 Rs ndt ð5:24Þ 0 0 0 Rs iss Þdt Rs ndt ð5:25Þ 0 When the control time is long, it is difficult to ensure that there is no noise source of nonzero mean value in a practical control system (Engberg and Larsen, 1995). Accumulation of flux error in DSC may be produced by a current sensor noise with nonzero mean value. In order to verify the robustness of the new controller to load changes and noise, an oscillating load is applied to the motor and a drift noise (nonzero mean value) is added to the current. Figure 5.12a shows that the expert-system controller has good noise immunity and effective control is obtained over a long period of time. On the other hand, DSC is sensitive to the noise and the load. At t ¼ 2 s, the motor speed drops to zero and the controller fails (Figure 5.12b). It has been said that DSC can achieve an instantaneous torque response. However, this is true only when the integral calculation of flux does not have excessive error accumulation over a long period. When an excessive error accumulation (such as that created by noise) occurs, the instantaneous torque response is not assured and the error would not be corrected, as shown in this simulation example. Since the new expert-system controller does not 126 Applied Intelligent Control of Induction Motor Drives 50 Speed 50 (rad/s) 40 40 30 Load 30 (N.m) 20 20 10 Noise 10 of is(A) 0 0 -10 -10 0 0.5 1 1.5 2 2.5 3 (a) 3.5 4 0 0.5 1 1.5 2 2.5 3 (b) Time (s) 3.5 4 Time (s) Figure 5.12 (a) Expert-system controller with drift noise and oscillating load; (b) DSC controller with drift noise and oscillating load. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A rule-based acceleration control scheme for an induction motor,” IEEE Transactions on Energy Conversion, 17(2), 2002: 254–259. Ó 2002 IEEE.) require the calculation of integrals, the control is more effective and accurate over a longer period than DSC. 5.6.3 The Third Simulation Example 50 40 (b) 400 300 Acceleration (rad/s2) (a) Torque (N.m) Speed (rad/s) Because the expert-system controller is independent of motor parameters, the third example will verify that the new controller has exchangeability when it is used for different induction motors. When the expert-system controller is used to control a 0.75 kW induction motor, only the inverter needs to be changed. The controller is the same as that used for the 7.5 kW induction motor in the first simulation example. The 0.75 kW induction motor parameters chosen for the simulation studies are listed in ‘Motor 2’ of Appendix B with load 2 Nm. The speed command and the rotor acceleration command are the same as the first simulation example. The simulation results shown in Figure 5.13a and b are almost the same as those obtained from the 7.5 kW induction motor in the first simulation example. 30 20 10 0 -10 200 100 0 -100 -200 -300 -400 -20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 5.13 (a) Speed and torque of 0.75 kW induction motor with expert-system controller; (b) Controlled rotor acceleration of 0.75 kW induction motor with expert-system controller. 127 Expert-System-based Acceleration Control When the expert-system controller is applied to control a 0.147 kW induction motor (model 295, Bodine Electric Company), only the inverter needs to be changed. The controller is the same as that used for the 7.5 kW induction motor in the first simulation example. The 0.147 kW induction motor parameters chosen for the simulation studies are listed in ‘Motor 3’ of APPENDIX B with load 1 Nm. The speed command and the rotor acceleration command are the same as the first simulation example. Figure 5.14 shows stator voltage and current of the 0.147 kW induction motor. Figure 5.15 shows controlled rotor acceleration and torque responses of the induction motor, while Figure 5.16 shows rotor speed response of the induction motor. 10 200 Stator current (A) Stator voltage (V) 300 100 0 -100 -200 -300 5 0 -5 -10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 Time (s) Figure 5.14 3 2 200 Torque (N.m) Acceleration (rad/s2) 0.8 Stator voltage and current of 0.147 kW induction motor. 400 0 -200 -400 0.7 Time (s) 1 0 -1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) -2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 5.15 Controlled rotor acceleration and torque response of 0.147 kW induction motor. The controlled rotor acceleration, torque response, and speed response shown in Figures 5.15 and 5.16 are almost the same as those obtained from the 7.5 kW induction motor in Figures 5.8a and 5.9a of the first simulation example and from the 0.75 kW induction motor in Figure 5.13a and b. 5.6.4 The Fourth Simulation Example The fourth simulation example will demonstrate that the expert-system controller can work very well in very low speed range. The same 0.147 kW induction motor (Bodine Electric Company model 295) is used and all the simulation parameters and conditions are the same 128 Applied Intelligent Control of Induction Motor Drives 60 Speed (rad/s) 40 20 0 -20 -40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 5.16 Speed response of 0.147 kW induction motor. those in third simulation example, except that the speed command is reset. Figure 5.17 shows the controlled acceleration and torque response of the 0.147 kW induction motor with the expert-system controller when the speed command is set as 6 rad/s and 6 rad/s, while Figure 5.18 shows the rotor speed response of the induction motor. 3 200 Torque (N.m) Acceleration (rad/s2) 300 100 0 -100 -200 2 1 0 -300 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -1 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 Time (s) 0.7 0.8 Time (s) Figure 5.17 Controlled rotor acceleration and torque response of 0.147 kW induction motor when speed command is 6 rad/s and 6 rad/s. 6 Speed (rad/s) 4 2 0 -2 -4 -6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 5.18 Speed response of 0.147 kW induction motor when speed command is 6 rad/s and 6 rad/s. 129 Expert-System-based Acceleration Control 400 2 200 1.5 Torque (N.m) Acceleration (rad/s2) Figure 5.19 shows controlled acceleration and torque response of the 0.147 kW induction motor with the expert-system controller when the speed command is set as 1 rad/s and 1 rad/s, while Figure 5.20 shows the rotor speed response of the induction motor. 0 -200 1 0.5 -400 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 Time (s) 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 5.19 Controlled rotor acceleration and torque response of 0.147 kW induction motor when speed command is 1 rad/s and 1 rad/s. 2 Speed (rad/s) 1 0 -1 -2 -3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 5.20 5.6.5 Speed response of 0.147 kW induction motor when speed command is 1 rad/s and 1 rad/s. The Fifth Simulation Example The fifth simulation example demonstrates rotor speed responses of the expert-system acceleration controller working with speed encoders of various encoder precisions. The simulation program consists of the encoder and decoder models built in Chapter 3, the 0.147 kW voltage-input model of induction motor built in Chapter 3, and the expert-system controller model in Figure 5.7. The motor parameters are listed in ‘Motor 3’ of Appendix B and the speed command is from 0 rad/s to 40 rad/s. The encoder model receives rotor speed of the induction motor model and outputs speed code strings to the decoder model, while output of the decoder model is sent to the expert-system controller as rotor speed signal. Figure 5.21 shows the rotor speed responses of the induction motor with and without the encoder and decoder models, the encoder precision being set as 2000 pulses/revolution. 130 Applied Intelligent Control of Induction Motor Drives 50 Speed (rad/s) 40 30 20 With encoder/decoder (dotted line) 10 Without encoder/decoder (solid line) 0 -10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 5.21 revolution. Speed responses of 0.147 kW induction motor with and without an encoder of 2000 pulses/ The rotor speed response with encoder and decoder models is different from the speed response without encoder and decoder models, because an encoder of lower precision can decrease control precision of the expert-system controller. Figure 5.22 show the rotor speed responses of the induction motor with and without the encoder and decoder models, the encoder having a precision of 20 000 pulses/ revolution. 50 Speed (rad/s) 40 30 20 With encoder/decoder (dotted line) 10 Without encoder/decoder (solid line) 0 -10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 5.22 Speed responses of 0.147 kW induction motor with and without an encoder of 20 000 pulses/revolution. Figure 5.23 shows the rotor speed responses of the induction motor with and without the encoder and decoder models, the encoder now having a resolution of 200 000 pulses/ revolution. Figures 5.21–5.23 show that the encoder’s precision is extremely important for the expert-system acceleration controller. When the encoder precision is up to 200 000 pulses/ revolution, the expert-system controller can have a good performance. Therefore, a high precision encoder, such as an expensive Gurley Model 8435H hollow-shaft optical encoder 131 Expert-System-based Acceleration Control 50 Speed (rad/s) 40 30 With encoder/decoder (dotted line) 20 10 Without encoder/decoder (solid line) 0 -10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 5.23 Speed responses of 0.147 kW induction motor with and without an encoder of 200 000 pulses/revolution. with 900 000 counts/revolution is needed for hardware implementation of the expert-system acceleration controller. 5.7 Summary The expert-system based control scheme of induction motor is quite different from the usual vector control schemes that depend on flux and torque calculations. Due to the use of inference instead of algebraic calculations, the expert-system controller has a small control error but no cumulative error. Another valuable property is that the controller is independent of the parameters of the induction motor, so the same controller can be used for different induction motors. Lastly, the control may be performed at any time, whereas conventional vector control must be performed from an initial state. Since the expert-system algorithm consists mainly of logic operations, the execution time of the control algorithm should be shorter than that of the conventional vector-control algorithm. But, since the rotor acceleration values are obtained by a differential operation on the angular speed, a high precision encoder is needed and control error may be produced by the noise present in the signal from the speed encoder. Expert system is an effective method for induction motor control. It is envisaged that more and more advanced induction motor drives will be controlled using AI principles and algorithms (Bose, 1993; Passino, 1996b). The possible developments of the expert-system based acceleration controller are: (1) to systematize further the principle of rotor acceleration control, (2) to optimize further the control rules and algorithms, (3) to tackle the problem of noise in the measured rotor acceleration, and (4) DSP based hardware implementation with a high-precision speed sensor. References Astr€ om, K.J. and Anton, J.J. (1984) Expert control. Proceedings, 9th IFAC (International Federation of Automatic Control) World Congress, Budapest, Hungary. Astr€ om, K.J. and Bj€ orn, W. (1995) Adaptive Control, Addison Wesley Publishing Company, Reading, MA. Bose, B.K. (1986) Power Electronics and AC Drives, Prentice Hall, Englewood Cliffs, NJ. 132 Applied Intelligent Control of Induction Motor Drives Bose, B.K. (1993) Power electronics and motion control-technology status and recent trends. IEEE Transactions on Industry Applications, 29, 902–909. Buchanan, B. and Shortliffe, E.H. (1984) Rule-Based Expert Systems, MYCIN, Addison-Wesley, Reading, MA. Engberg, J., and Larsen, T., (1995) Noise Theory of Linear and Nonlinear Circuits, John Wiley & Sons Ltd, Chichester. George, F.L. and William, A.S. (1989) Artificial Intelligence and the Design of Expert System, Benjamin-Cummings Publishing Company, Inc., San Francisco, CA. Hayes-Roth, F. (1985) Building Expert Systems, Addison-Wesley, Reading, MA. Krause, P.C., Wasynczuk, O., and Sudhoff, S.D. (1995) Analysis of Electric Machinery, IEEE Press, New Jersey. Nabae, A., Ogasawara, S., and Akagi, H. (1986) A novel control scheme for current-controlled PWM Inverters. IEEE Transactions on Industry Applications, 22(4), 697–701. Novotny, D.W. and Lipo, T.A. (1996) Vector Control and Dynamics of AC Drives, Oxford University Press, Oxford. Passino, K.M. and Lunardhi, A.D. (1996a) Qualitative analysis of expert control systems, in Intelligent Control Systems: Theory and Applications (eds M.M. Gupta and N.K. Sinha) IEEE Press, New Jersey. Passino, K.M. (1996b) Towards bridging the perceived gap between conventional and intelligent control, in Intelligent Control Systems: Theory and Applications (eds M.M. Gupta and N.K. Sinha) IEEE Press, New Jersey. Shi, K.L., Chan, T.F., Wong, Y.K., and Ho, S.L. (1999) A new acceleration control scheme for an inverter-fed induction motor. Electric Machines and Power Systems, USA, 27(5), 527–541. Takahashi, I. and Noguchi, T. (1986) A new quick-response and high-efficiency control strategy of an induction motor. IEEE Transactions on Industry Applications, 22(5), 820–827. 6 Hybrid Fuzzy/PI Two-Stage Control1 6.1 Introduction Field orientation principle is one of the most promising methods to achieve high performance in adjustable speed inductionmotor drives(Bose,1993). But, due to the dependence ofperformance on the motor parameters and the complicated calculations involved, accurate vector control is difficult to implement in practice. Two features of field-oriented control, however, deserve attention.Firstly, althoughthe field-oriented controllerdoes not control the frequency directly, its supply frequency does change and its slip frequency is constant during the acceleration/ deceleration period. Secondly, when the torque command is constant, the supply current magnitude will remain constant. The first feature may be proved by noting the relationship between the supply frequency o, the slip frequency or, and the rotor angular speed oo: o ¼ or þ P oo : 2 ð6:1Þ 1 (a) Portions reprinted by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “A novel two-stage speed controller for an induction motor,” The 1997 IEEE Biennial International Electrical Machines and Drives Conference, Paper MD2-4, May 18–21, 1997, Milwaukee, Wisconsin, U.S.A. Ó 1997 IEEE (b) Portions reprinted by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE. (c) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “An improved two-stage control scheme for an induction motor,” Proceedings of the IEEE 1999 International Conference on Power Electronics and Drive Systems, pp. 405–410, July 27–29, 1999, Hong Kong. Ó 1999 IEEE. (d) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A novel hybrid fuzzy/PI two-stage controller for an induction motor drive,” IEEE International Electric Machines and Drives Conference (IEMDC 2001), pp. 415–421, June 17–20, 2001, Cambridge, MA, U.S.A. Ó 2001 IEEE. (e) Portions reprinted from K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Modeling and simulation of a novel two-stage controller for an induction motor,” International Association of Science and Technology for Development (IASTED) Journal on Power and Energy Systems, 19(3), 257–264, Ó 1999, with permission from ACTA Press. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 134 Applied Intelligent Control of Induction Motor Drives The slip frequency or is given by Equation (2.18): or ¼ 3Rr T * Pledr * 2 ð6:2Þ where Rr is the rotor resistance, P is the number of poles, T denotes the torque command, and ledr * denotes rotor flux command. If T is maintained constant during acceleration, or is also constant. As oo changes during acceleration and deceleration, o has to be varied so that Equation (6.1) is satisfied. The second feature may be proved using the following field orientation conditions (Trzynadlowski, 1994): leqr ¼ 0 ledr ¼ const: ð6:3Þ Substituting Equation (6.3) into Equation (2.15), e ids ¼ ledr ¼ const: LM ð6:4Þ T* kq ledr ð6:5Þ Equation (2.17) may be rewritten as: e iqs ¼ where kq ¼ PLM . 3Lr Stator phase current magnitude j^I s j can be expressed by: 2 j^I s j ¼ 3 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ e 2 e Þ2 ðids Þ þ ðiqs ð6:6Þ Substituting Equations (6.4) and (6.5) into Equation (6.6), 2 j^I s j ¼ 3 sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ e 2 * 2ﬃ ldr T þ : kq ledr LM ð6:7Þ When the torque command T is constant, Equation (6.7) becomes: 2 j^I s j ¼ 3 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ e2 e2 ¼ const: ids þ iqs In this chapter, the above two features of field-oriented control are employed in the design of a novel two-stage control scheme for an induction motor. A simulation study on the proposed hybrid fuzzy/PI two-stage controller is carried out using the software MATLABÒ/Simulink and the results are compared with that obtained from an indirect field-oriented controller. 135 Hybrid Fuzzy/PI Two-Stage Control 6.2 Two-Stage Control Strategy for an Induction Motor The current-input induction motor model shown in Figure 6.1 has three inputs, namely the stator current magnitude Is, supply frequency o, and load torque TL. It has an output, namely the rotor speed oo. The relationship between the output and inputs may be expressed as: oo ¼ IMðIs ; o; TL Þ: ð6:8Þ 1 Current frequency 2 1 Current amplitude Rotor speed 3 Load Induction motor Figure 6.1 An induction motor model with current input. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) Speed (rad/sec) The speed response of the motor may be divided into two stages, an initial acceleration/ deceleration stage, and a final steady-state stage, as shown in Figure 6.2. 80 60 40 20 Time (sec) 0 0 0.5 1 Acceleration period 1.5 2 2.5 3 3.5 Final steady state period Figure 6.2 Typical speed response of an induction motor. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) The basic principle of the two-stage controller may be described as follows (Shi, Chan and Wong, 1997; Shi, Chan and Wong, 1999). 1. During the acceleration/deceleration stage, the stator current magnitude |Is| is maintained constant and the rotor accelerates or decelerates depending on the input frequency o. 136 Applied Intelligent Control of Induction Motor Drives 2. During the final steady-state stage, the input frequency o is held constant and the speed of rotor oo is maintained constant by controlling the stator current magnitude |Is|. In the two-stage speed control scheme, the relationship between inputs and outputs is described by Table 6.1. Table 6.1 Two-stage speed control scheme. Stages Inputs Output Control o |Is| oo objective Acceleration or deceleration change constant change Steady-state constant change constant change speed eliminate oscillations (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) A problem arises as how to vary the supply frequency from zero to the final frequency of the command speed. If the supply frequency rises too fast, the torque will produce oscillations so that the acceleration/deceleration period is longer, but if the supply frequency rises too slowly, the torque will be so small that the acceleration/deceleration period is again prolonged. To tackle this problem, a fuzzy controller is designed using the equations of field-oriented control. 6.3 Fuzzy Frequency Control Fuzzy-logic control is an important intelligent control method which uses fuzzy rule sets and linguistic representation of a human’s knowledge to control a plant. In the proposed two-stage control scheme, fuzzy logic frequency control based on the frequency feature of the field orientation principle is developed. During the acceleration stage, the torque command has a larger value, whereas during the steady-state stage, the torque command has a smaller value. These commands can be determined from the difference between rotor speed oo and speed command oo : T* ¼ ( Tacceleration when Doo 6¼ 0 Tsteady when Doo ¼ 0 where speed error Doo ¼ oo oo. Substituting Equations (6.2)–(6.9), the slip frequency of field-oriented control is 8 3Rr Tacceleration > > when Doo 6¼ 0 > > < Pledr * 2 or ¼ > > > 3Rr Tsteady when Doo ¼ 0 > : Pledr * 2 ð6:9Þ ð6:10Þ 137 Hybrid Fuzzy/PI Two-Stage Control At steady state, the torque command Tsteady is equal to the load torque TL. If TL is a function of the motor speed, that is, TL ¼ TL(oo), then Tsteady ¼ TL ðoo Þ: ð6:11Þ For the present investigation, the following load characteristic is assumed (Wade, Dunnigan and Williams, 1997): TL ¼ moo ð6:12Þ where coefficient m ¼ 0.18 Nm/(rad/s). When Do ¼ 0, replacing oo with oo , and substituting Equation (6.12) into Equation (6.10), the steady-state slip frequency may be written as: or ¼ 8 3R r > T > > < Pledr * 2 acceleration > 3Rr > > : e 2 moo * Pldr * when Doo 6¼ 0 ð6:13Þ : when Doo ¼ 0 Because the slip frequency or is a function of variables Do and oo , it can be written as: * or ¼ f ðoo ; Doo Þ ð6:14Þ According to (6.14), the speed error Do and speed command oo can be used as the inputs of the fuzzy frequency control which consists of fuzzification, fuzzy logic inference, rulebase, database and defuzzification. Figure 6.3 shows a fuzzy frequency control system. Fuzzy frequency controller ω 0* + - Fuzzification Fuzzy logic inference Δω 0 ωr Defuzzification + + ω I Current-controlled inverter Rule base IM Data base ω0 Figure 6.3 Fuzzy frequency control system. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) 138 Applied Intelligent Control of Induction Motor Drives The fuzzification operation is the process which converts the crisp input values (Do, oo ) to fuzzy sets. A fuzzy set consists of elements each having a degree of membership and associated with linguistic values. The defuzzification operation is the process which determines the best numerical value os to represent a given fuzzy set. The database stores the memberships of fuzzy variables, while the rulebase provides the necessary linguistic control rules for the fuzzy inference (Sousa and Bose, 1994). 6.3.1 Fuzzy Database The fuzzy slip frequency control uses two fuzzy state variables (speed command and speed error) and one control variable (slip frequency). Consequently, the fuzzy database consists of membership functions of speed command, speed error, and slip frequency. 6.3.1.1 Membership Functions of Speed Command Let the normal range of speed (oo) be from 120 rad/s to 120 rad/s. The universe of discourse of the speed command fuzzy variable is divided into seven overlapping fuzzy sets: Fwo ¼ {NBwo, NMwo, NSwo, Zwo, PSwo, PMwo, PBwo}, as shown in Figure 6.4, where m(wo) denotes the degree of membership of speed command. µ (wo) 1 NBwo NMwo NS wo Zwo PSwo PMwo PBwo 0.5 0 -160 -120 -80 -40 0 40 80 120 160 “wo” (rad/s) Figure 6.4 Membership function of speed command. NB: negative big; NM: negative medium; NS: negative small; Z: zero; PB: positive big; PM: positive medium; PS: positive small. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) 6.3.1.2 Membership Functions of Speed Error When the range of speed command (oo ) is from 120 rad/s to 120 rad/s, the range of the speed error (Doo) is from 240 rad/s to 240 rad/s. The universe of discourse of the speed error fuzzy variable is divided into three overlapping fuzzy sets: FDwo ¼ {NDwo, ZDwo, PDwo} as shown in Figure 6.5, where m(Dwo) denotes the degree of membership of speed error. 6.3.1.3 Membership Functions of Slip Frequency For the induction motor to be studied, Rr ¼ 0.151 O, P ¼ 6, and T(acceleration) ¼ 100 Nm. If ledr * ¼ 0:67 Wb during the acceleration stage, then or ¼ 16.8 rad/s by Equation (6.13). For the 139 Hybrid Fuzzy/PI Two-Stage Control µ(Dwo) 1 NDwo ZDwo PDwo 0.5 0 -240 -5 5 240 “Dwo” (rad/s) Figure 6.5 Membership function of speed error. N: negative; Z: zero; P: positive. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) steady-state stage, the values of steady-state slip frequency can be calculated from (6.13). The speed command, slip frequency, and fuzzy linguistic values are shown in Table 6.2. Table 6.2 Speed, slip frequency, and fuzzy linguistic values. Stages Deceleration Steady state Acceleration oo — 120 80 40 0 40 80 120 — or 16.8 3.64 2.42 1.21 0 1.21 2.42 3.64 16.8 Fwr NBwr NMwr Nwr NSwr Zwr PSwr Pwr PMwr PBwr (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) For the acceleration/deceleration stage, the slip frequencies are larger, so that their universe of discourse is defined as F 0 wr ¼ fPBwr ; NBwr g. For the steady-state stage, the slip frequencies 00 are smaller so that their universe of discourse is defined as Fwr ¼ fPMwr ; PSwr ; Pwr ; Zwr ; 00 Nwr ; NSwr ; NMwr g. The universe of discourse of the slip frequency is Fwr ¼ fF 0 wr ; Fwr g, and m(wr) denotes the degree of membership of slip frequency. Using the slip frequency values given in Table 6.2, the slip fuzzy membership functions are defined using the triangular distribution as shown in Figure 6.6. 6.3.2 Fuzzy Rulebase For induction motors from 3 to 50 hp, the torque computed using the steady-state equivalent circuit is approximately equal to the average of the transient torque given by 140 Applied Intelligent Control of Induction Motor Drives µ(ws) (NMBwr) (NBBwr) 1 NBwr (NSBwr) NMwr Pwr Zwr Nwr (PMBwr) PSwr PMwr (PSBwr) NSwr PBwr (PBBwr) 0.5 “wr” (rad/s) Figure 6.6 18 15 16.8 4.85 3.64 2.42 0 1.21 -1.21 -2.42 -3.64 -4.85 -15 -16.8 -18 0 Membership function of slip frequency. the free-acceleration torque-speed characteristic (Krause, Wasynczuk and Sudhoff, 1995). Accordingly the steady-state characteristics are used in the control formulations. The torque-speed curves in Figure 6.7 illustrate the four operating states of an induction motor. When the induction motor is operated in regions I or IV, it works in the normal motoring mode. When the induction motor is operated in regions II or III, it works in the generating mode. The slip speed or of the induction motor may be expressed as: or ¼ o P oo : 2 ð6:15Þ T III ωo (III) I IV ω ωo (IV) 0 II ωo (I) ω ωo ωo (II) Figure 6.7 Torque-speed curves of an induction motor in four operating states. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) From Figure 6.7, it is seen that T(oo(I)) > 0, T(oo(II)) 0, T(oo(IV)) 0, and T(oo(III)) > 0. In order to obtain larger acceleration/deceleration torque, when oo > 0 and oo oo > 0 (operating state I), or when oo 0 and oo oo > 0 (operating state III), the instantaneous slip frequency command or should have a positive value and its fuzzy linguistic value is PBwr. When oo > 0 and oo oo < 0 (operating state II), or when oo 0 and oo oo < 0 (operating state IV), the instantaneous slip frequency command or should have a negative value and its fuzzy linguistic value is NBwr. The slip frequency control rules for the acceleration/deceleration stage may be summarized in Table 6.3. 141 Hybrid Fuzzy/PI Two-Stage Control Table 6.3 Slip speed control rules for the acceleration/deceleration stage. (oo oo > 0 oo) > 0 oo > 0 (oo oo) < 0 (oo (oo I or is PBwr II or is NBwr III or is PBwr IV or is NBwr Control Conditions Operation States Action Rules oo 0 oo) > 0 oo 0 oo) < 0 (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) Let ‘wo’ denote the speed command oo , ‘Dwo’ denote the speed error (oo oo), and ‘wr’ denote the slip frequency or. With reference to the control rules of the acceleration/ deceleration stage in Table 6.3 and the steady-state control rules in Table 6.2, 21 slip frequency control rules are formulated and input to the fuzzy rulebase as shown in Table 6.4. Table 6.4 Dwo NDwo ZDwo PDwo Fuzzy rulebase of slip frequency control. wo NBwo NMwo NSwo Zwo PSwo PMwo PBwo NBwr NMwr PBwr NBwr Nwr PBwr NBwr NSwr PBwr NBwr Zwr PBwr NBwr PSwr PBwr NBwr Pwr PBwr NBwr PMwr PBwr (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) 6.3.3 Fuzzy Inference The fuzzy inference includes a linguistic inference and a degree of membership calculation which gives the degree of membership of the output variable according to the rules. The inputs of the linguistic inference consist of two fuzzy linguistic values F(wo)i and F(Dwo)j, and the output is u(k) (crisp fuzzy linguistic value of slip frequency). The inputs of the degree of membership calculation consists of two degrees of membership m(wo)s and m(Dwo)t, and the output is m(wr)(yk) (degree of slip frequency membership). 6.3.3.1 Linguistic Inference Using the 21 rules of fuzzy rulebase in Table 6.4, the linguistic inference of the fuzzy linguistic values can be expressed as: IFFðwoÞi AND FðDwoÞj ; THEN FðwrÞk ð6:16Þ where FðwoÞi 2 fNBwo ; NMwo ; NSwo ; Zwo ; PSwo ; PMwo ; PBwo g; FðDwoÞj 2 fNDwo ZDwo PDwo g; and FðwrÞk 2 fNBwr ; NMwr ; Nwr ; NSwr ; Zwr ; PSwr ; Pwr ; PMwr ; PBwr g: ð6:17Þ 142 Applied Intelligent Control of Induction Motor Drives The crisp value of fuzzy linguistic F(wr)k is: uðkÞ ¼ uðFðwrÞk Þ where u(k) 2{ 16.8 3.64, 2.42, ð6:18Þ 1.21, 0, 1.21, 2.42, 3.64, 16.8}. 6.3.3.2 Degree of Membership Calculation The MAX-MIN principle (Bose, 1997) is adopted in the degree of membership calculation. If the input signals are x1 (speed command) and x2 (speed error), then the degree of membership of speed command is m(wo)(x1), and the degree of speed error is the m(Dwo)(x2). If the output signal is y, then the degree of membership of slip frequency is m(wr)(y). Because the operation between ‘wo ¼ ’ and ‘Dwo’ is ‘AND’ according to (6.16), the ‘MIN’ (Intersection) operation is used. For any inference rule, the degree of membership of output ‘wr’ is m(wr) and the degree of membership calculation of the slip frequency can be expressed as: mðwrÞq ¼ MIN½mðwoÞs ðx1 Þ; mðDwoÞt ðx2 Þ ð6:19Þ where s 2 {NBwo, NMwo, NSwo, Zwo, PSwo, PMwo, PBwo}, t 2 {NDwo ZDwo PDwo}, and q 2 {NBwr, NMwr, Nwr, NSwr, Zwr, PSwr, Pwr, PMwr, PBwr}. Because the logic relationships between the 21 fuzzy rules are ‘OR’ in Table 6.4, the degree of membership of output y is calculated by ‘MAX’ (Union) operation. mðwrÞ ðyk Þ ¼ MAXðmðwrÞpjp¼1;2;...21 Þ 6.3.4 ð6:20Þ Defuzzification After the fuzzy inference, the fuzzy output needs to be converted into a crisp value required by the inverter control. The inputs of defuzzification are u(k) and m(wr)(yk), which are the outputs of fuzzy inference. The output is the numerical value of slip frequency, y. In this design, the centroid method is used to implement the defuzzification operation (Kosko, 1997). y¼ n X uðkÞmðwsÞ ðyk Þ k¼1 n X ð6:21Þ mðwsÞ ðyk Þ k¼1 6.3.5 Fuzzy Frequency Controller Simulation of the frequency controller may be implemented using the software MATLABÒ/ Simulink with Fuzzy Logic Toolbox as shown in Figure 6.8. The inputs of the controller are the speed command and the rotor speed. The output is the frequency command to the inverter. The controller has three characteristics: (1) its supply frequency is almost the same as fieldoriented control, hence it can maintain a large acceleration/deceleration torque in the four 143 Hybrid Fuzzy/PI Two-Stage Control wr Mux + Mux 2 Speed Command Fuzzy Logic + Sum1 + wo Sum2 1 Frequency 1 Rotor Speed Figure 6.8 Simulink blocks of frequency controller. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) operating states; (2) it is insensitive to motor parameter changes; (3) the speed response over the whole speed range, even subjected to large noise and load disturbances, is very satisfactory. 6.4 Current Magnitude PI Control During the acceleration/deceleration stage, the stator current magnitude is regulated as the maximum permissible value of the inverter drive system. During the final steady-state period, the supply frequency is maintained constant, while the stator current magnitude is adjusted to control the rotor speed. When the supply frequency is fixed, the torque-current relationship may be expressed as Equation (6.22) (Krause, Wasynczuk and Sudhoff, 1995) and is illustrated in Figure 6.9. P oo L2m Is2 Rr o 3P 2 T¼ ðN mÞ ð6:22Þ 2 2 P oo ðLm þ Llr Þ2 Rr 2 þ o 2 Figure 6.9 shows the process of controlling the speed oo by stator current magnitude according to the speed error. The decaying oscillations of speed about the final operating point have been eliminated. The following proportional-and-integral control with output saturation is used in the nonlinear control. Is ¼ Kp ðoo jIs j ¼ ( * ð oo Þ þ KI ðoo * oo Þ dt jIs j jIs j < 50 A steady--state stage 50 jIs j 50 A acceleration stage ð6:23Þ ð6:24Þ 144 Applied Intelligent Control of Induction Motor Drives Torque (N.m) 400 350 300 250 Increasing Is T a 200 150 b c 100 time 50 0 0 15 30 60 45 90 75 105 ωο(rad/sec) ωο a’ b’ c’ time Figure 6.9 Speed controlled by stator current magnitude. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) When a PI controller is used to control the nonlinear system, it must be tuned very conservatively in order to provide stable behavior over the entire range of operating conditions (Henson and Seborg, 1997). In this study, coordination of the current magnitude control for the two stages is achieved using the following strategy: 1. When |oo oo| 3, the current magnitude control changes from a steady-state stage to an acceleration stage. 2. When 2.5 < |oo oo| < 3, the control pattern is unchanged. 3. When |oo oo| 2.5, the current magnitude control changes from an acceleration stage to a steady-state stage. During the steady-state stage, stator current Is has a small value. When |oo oo| 3, the current magnitude control changes from the steady-state stage to an acceleration stage. If we let Kp(oo oo) > 50, that is, Kp > 16.6, then Is of Equation (6.23) is larger than 50 A, and hence the proportional coefficient Kp may be chosen as 17. The maximum value of the integral part of Equation (5.63) can be estimated from an acceleration process with oo ¼ 120, oo(t ¼ 0 s) ¼ 0, assuming that the rotor speed rises at uniform acceleration and oo(t ¼ 0.2 s) 120, that is, 0:2 ð t¼0 ðoo * oo Þdt 12 ð6:25Þ 145 Hybrid Fuzzy/PI Two-Stage Control When the current magnitude control changes from an acceleration stage to a steady-state stage, substituting (oo oo) ¼ 2.5, Kp ¼ 17, and Equation (6.25) into Equation (6.23), and let Is < 50, then KI < 0.625. Therefore the integral coefficient KI is chosen as 0.6. A current magnitude controller can be designed as shown in Figure 6.10. 1 Speed command + Sum PI PI controller 1 Saturation Current amplitude 2 Rotor speed Figure 6.10 Simulink blocks of current magnitude controller. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) The current magnitude controller consists of a sum block to calculate speed error, a PI block to implement Equation (6.23), and a saturation block to implement Equation (6.24). During acceleration or deceleration stage, there is a larger difference between the speed command and the rotor speed. Consequently, the PI controller has a larger output. Due to the function of the saturation block, the supply current amplitude is maintained constant during acceleration or deceleration stage. During the steady-state stage, there is a smaller difference between speed command and rotor speed. Consequently, the output of the PI controller is smaller than the limit of the saturation block and the rotor speed is controlled by the current amplitude. 6.5 Hybrid Fuzzy/PI Two-Stage Controller for an Induction Motor By combining the fuzzy frequency controller and the current magnitude PI controller, a hybrid fuzzy/PI two-stage controller can be formed. During the acceleration/deceleration period, the current magnitude controller outputs the maximum permissible current. During the final steady-state period, the fuzzy frequency controller outputs the frequency that corresponds to the speed command. The model of two-stage speed controller for the induction motor is constructed using MATLABÒ/Simulink as shown in Figure 6.11. The current-input model of induction motor in Chapter 3 is employed. The simulation model of the two-stage controller consists of the induction motor model, the frequency control sub-model (Figure 6.8), the current magnitude control sub-model (Figure 6.10), a load block, a command block, and a scope sink for display of rotor speed. In addition, three scope sinks are configured inside the sub-models for observing the current, slip frequency, and torque. The load block implements the load function of Equation (6.12). 6.6 Simulation Study on a 7.5 kW Induction Motor Computer simulations were performed on the fuzzy/PI two-stage controller shown in Figure 6.11 for a 7.5 kW induction motor. Five investigations were undertaken: (1) comparison 146 Applied Intelligent Control of Induction Motor Drives Current frequency Frequency control Current amplitude Rotor speed Speed command Current control Induction motor Load Fcn Figure 6.11 Simulink blocks of the hybrid fuzzy/PI control system. (Reproduced by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Hybrid fuzzy two-stage controller for an induction motor,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1898–1903, October 11–14, 1998, San Diego, U.S.A. Ó 1998 IEEE.) with field-oriented control, (2) effects of parameter variation, (3) effects of noise in the measured speed and input current, (4) effects of magnetic saturation, and (5) effects of load torque variation. The parameters of the 7.5 kW induction motor chosen for the simulation studies are listed in ‘Motor 1’ of Appendix B. It is assumed that the induction motor is taken through the following control cycle: Speed Command oo ¼ 120 rad/s oo ¼ 120 rad/s oo ¼ 120 rad/s oo ¼ 0 rad/s Period 0 s t < 4s 4 s t < 8s 8 s t < 12s 12 s t < 15s Permissible magnitude of stator current of the induction motor is 50 A. The moment of inertia, JL, of the load equals that of the motor. 6.6.1 Comparison with Field-Oriented Control Figures 6.12, 6.14, 6.16 and 6.18 show the simulation results of the hybrid fuzzy/PI controller. Very fast speed response is obtained with the two-stage control method. Due to the current control in the final steady-state stage, the oscillations of speed about the final operating point are completely eliminated. In order to compare the new controller with a field-oriented controller, an indirect rotor flux field-oriented controller was investigated. In the computer simulation, the acceleration torque T ¼ 100 Nm, the rotor flux command ledr * ¼ 0:67 Wb, Rr ¼ 0.151 O, LM ¼ 0.042 H/ph and 147 Hybrid Fuzzy/PI Two-Stage Control 100 Stator current (A) 100 80 60 40 20 0 -20 -40 -60 -80 -100 50 0 -50 0 5 10 15 Time (s) Figure 6.12 -100 0 5 10 15 Time (s) Stator current of fuzzy controller. Figure 6.13 Stator current of FOC controller. 30 Slip frequency (rad/s) 30 20 20 10 10 0 0 -10 -10 -20 -20 -30 0 5 10 -30 15 0 5 10 Figure 6.14 15 Time (s) Time (s) Slip frequency of fuzzy controller. Figure 6.15 Slip frequency of FOC controller. 400 400 Torque (N.m) 300 200 200 100 0 0 -100 -200 -200 -300 -400 0 5 10 15 -400 0 Time (s) Figure 6.16 Torque response of fuzzy controller. Figure 6.17 5 10 15 Time (s) Torque response of FOC controller. 148 Applied Intelligent Control of Induction Motor Drives 150 150 100 Speed (rad/s) 100 50 50 0 0 -50 -50 -100 -100 -150 0 5 10 15 -150 0 5 10 15 Time (s) Time (s) Figure 6.18 Speed response of fuzzy controller. Figure 6.19 Speed response of FOC controller. kq ¼ 2, hence the magnitude of phase current is about 50 A from Equation (6.7) (same as that for the hybrid fuzzy/PI controller), while the slip frequency is 16.8 rad/s from (6.13). Figures 6.13, 6.15, 6.17, and 6.19 show the simulation results of the indirect FOC controller. Since the hybrid fuzzy/PI two-stage controller has almost the same current and slip frequency responses as FOC, it has approximately the same torque response, although in the former case, the torque has not been directly controlled. Consequently, the speed response of the new controller is almost the same as the field-oriented controller (Figures 6.18 and 6.19). But the torque oscillations and the transient torque peaks (Figure 6.16) may increase the mechanical stress of the motor shaft. 6.6.2 Effects of Parameter Variation In order to illustrate the insensitivity of the hybrid fuzzy/PI two-stage controller to the variation of motor parameters, the rotor resistance and the mutual inductance are assumed to be changed to 2Rr and 0.7LM respectively. Figure 6.20 shows the stator current of the induction motor drive, while Figures 6.21 and 6.22 show that the torque and speed responses of the fuzzy controller are insensitive to parameter variations. 400 Torque (N.m) 300 Stator current (A) 100 80 60 40 20 0 -20 -40 -60 -80 -100 0 200 100 0 -100 -200 -300 -400 0 5 10 15 Time (s) 5 10 Time (s) 15 Rr LM 2Rr, 0.7LM Figure 6.20 Stator current of the induction motor Figure 6.21 Torque response of fuzzy controller with parameter variations. drive with parameter variations. 149 Hybrid Fuzzy/PI Two-Stage Control 150 Speed (rad/s) 100 50 0 -50 -100 -150 0 5 10 15 Time (s) Rr LM 2Rr, 0.7LM Figure 6.22 6.6.3 Speed response of fuzzy controller with parameter variations. Effects of Noise in the Measured Speed and Input Current In order to evaluate the effects of the noise of speed sensor and the noise of the input current, distributed random noises are added into the feedback speed and input current. The simulation is achieved using the random number blocks of Simulink, which generate a pseudo-random, normally distributed (Gaussian) number (Simulink, 1994). The speed response with the measured speed noise (mean of zero and variance of 3) and in the current noise (mean of zero and variance of 10) shows that the hybrid fuzzy/PI two-stage controller has good disturbance rejection (Figure 6.23). 150 Speed (rad/s) 100 50 0 -50 -100 -150 0 5 10 15 Time (s) Figure 6.23 6.6.4 Rotor speed response with current noise and measured speed noise. Effects of Magnetic Saturation In order to study the effect of magnetic saturation of the induction motor on the controller performance, two saturation blocks are included in the induction motor model to simulate the 150 Applied Intelligent Control of Induction Motor Drives nonlinear relationship between the current and flux, where ledr and leqr are assumed to be less than 0.8 Wb due to saturation. Figures 6.24–6.26 show the simulation results of the rotor speed, stator phase current and torque responses. As a result of magnetic saturation, flux increase is limited so that the torque oscillations are reduced significantly, but excessive magnetic saturation during the acceleration/deceleration stage will produce larger losses and a higher temperature rise. 150 Speed (rad/s) 100 without limit of magnetic saturation 50 0 with limit of magnetic saturation -50 - 100 - 150 0 5 10 15 Time (s) Figure 6.24 Magnetic saturation effect on speed response of fuzzy controller. 100 Stator current (A) 80 60 40 20 0 24 -20 -40 -60 -80 -100 0 5 10 15 Time (s) Figure 6.25 6.6.5 Magnetic saturation effect on stator current of fuzzy controller. Effects of Load Torque Variation The simulation will investigate effects of load torque variation on the hybrid fuzzy/PI control system. The load torque variation may be implemented by changing parameters of the load function block in the simulation program (see Figure 6.11). In the simulation, the control system experiences sudden changes in the load torque: at t ¼ 2.5 s, the load increases from 100% to 200% of the rated torque, TL, at t ¼ 7 s, the load decreases to 100% of TL, and at t ¼ 10 s, the load increases to 200% of TL again. Figure 6.27 shows the rotor speed of the fuzzy 151 Hybrid Fuzzy/PI Two-Stage Control 400 Torque (N.m) 300 without magnetic saturation 200 100 0 with magnetic saturation -100 -200 -300 -400 0 5 10 15 Time (s) Figure 6.26 Magnetic saturation effect on torque response of fuzzy controller. 150 Speed (rad/s) 100 50 0 -50 -100 -150 0 5 10 15 Time (s) Figure 6.27 Rotor speed of the fuzzy control system with the load torque variation. control system with load torque variation. At about 2.5 s, following the load changes, the speed, initially at 120.08 rad/s, drops to 119.94 rad/s, but is restored to 120.08 rad/s in 0.2 s. Figures 6.28–6.30 show the stator current, slip frequency, and torque response with load torque variation. 30 20 Slip frequency (rad/s) Stator current (A) 100 80 60 40 20 0 -20 -40 -60 -80 -100 0 5 10 15 Time (s) 10 0 -10 -20 -30 0 5 10 Time (s) Figure 6.28 variation. Stator current with load torque Figure 6.29 Slip with load torque variation. 15 152 Applied Intelligent Control of Induction Motor Drives 400 Torque (N.m) 300 200 100 0 -100 -200 -300 -400 0 5 10 15 Time (s) Figure 6.30 Torque response with load torque variation. The above simulation results show that the fuzzy/PI controller can accommodate larger changes in load torque. 6.7 Simulation Study on a 0.147 kW Induction Motor The fuzzy/PI controller has been simulated using the current-input model of the induction motor. In this section, the voltage-input model of an induction motor built in Chapter 3 is used in simulation studies on a 0.147 kW induction motor (Bodine Electric Company model 295) for the fuzzy/PI two-stage controller. Parameters of the 0.147 kW induction motor for the simulation studies are listed in ‘Motor 3’ of Appendix B. The simulation program of fuzzy/PI two-stage control system is shown in Figure 6.31. The current frequency and magnitude are transformed to stator current commands (ia , ib , ic ) by the ‘3-phase current’ block which is described in Figure 3.2 in Chapter 3. The stator voltages (Va, Vb, Vc) are produced by three ‘PI’ blocks of stator-current control with difference of the stator current commands (ia , ib , ic ) and the actual stator currents (ia, ib, ic) as input. The load characteristic of Equation (6.12) is assumed with the coefficient m ¼ 0.00 532 Nm/ (rad/s). When the rotor speed is 188 rad/s, the load torque equals 1 Nm. Because the pole number of the induction motor is 4, the normal range of speed (oo) is from 188 rad/s to 188 rad/s. The membership function of speed command has to be designed again and is shown in Figure 6.32. When the range of speed command (oo ) is from 188 rad/s to 188 rad/s, the range of the speed error (Doo) is from 376 rad/s to 376 rad/s. The membership function of speed error is designed as shown in Figure 6.33. For the 0.147 kW induction motor, Rr ¼ 12.76 O, P ¼ 4, and T(acceleration) ¼ 1.3 Nm. If ledr * ¼ 0:8 Wb during the acceleration stage, then or ¼ 19.53 rad/s from Equation (6.3). For the steady-state stage, the value of steady-state slip frequency can be calculated from s ¼ 0.03. Hybrid Fuzzy/PI Two-Stage Control ia ib ic Current frequency PI ia* Fuzzy-PI controller Speed Command 3-phase current Current magnitude PI ib* PI Va Vb Vc K 3/2 ic* IM Scope of speed f(u) Load Scope of ic Scope of Vc Rotor speed Figure 6.31 Simulink program of fuzzy/PI control system with voltage-input model of induction motor. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A novel hybrid fuzzy/PI two-stage controller for an induction motor drive,” IEEE International Electric Machines and Drives Conference (IEMDC 2001), pp. 415–421, June 17–20, 2001, Cambridge, MA, U.S.A. Ó 2001 IEEE.) 153 154 Applied Intelligent Control of Induction Motor Drives µ(wo) NBwo 1 NMwo NS wo Zwo PSwo PMwo PBwo 0.5 0 -250 -188 -126 -63 0 63 126 188 250 “wo” (rad/s) Figure 6.32 Membership function of speed command. NB: negative big; NM: negative medium; NS: negative small; Z: zero; PB: positive big; PM: positive medium; PS: positive small. µ(Dwo) 1 NDwo ZDwo PDwo 0.5 0 -376 Figure 6.33 -3 3 376 “Dwo” (rad/s) Membership function of speed error. N: negative; Z: zero; P: positive. The speed command, slip frequency, and fuzzy linguistic values of the membership functions of slip frequency are shown in Table 6.5. When permissible magnitude of stator current of the induction motor is assumed as 3 A, the proportional and integral parameters in the ‘fuzzy-PI controller’ block in Figure 6.31 may be Table 6.5 Speed, slip frequency, and fuzzy linguistic values. Stages oo or Deceleration Steady state — 188 80 40 0 40 80 188 — 19.53 5.64 2.4 1.2 0 1.2 2.4 5.64 19.53 Acceleration Fwr NBwr NMwr Nwr NSwr Zwr PSwr Pwr PMwr PBwr 155 Hybrid Fuzzy/PI Two-Stage Control designed according to Equations (6.23), (6.24), and (6.25) as: Kp ¼ 1 KI ¼ 0:03 The three PI controllers of stator currents in the ‘PI’ blocks in Figure 6.31 would force the error between the stator current commands and actual stator currents to zero. The inner current loops were tuned with constant stator current command. (i.e. with the fuzzy-PI controller disabled). Once satisfactory results were obtained, the fuzzy-PI controller was tuned. The transfer function of the PI controller of stator currents is represented by GPI ðsÞ ¼ Kp þ KI : s ð6:26Þ The controller has a zero at: s¼ KI Kp ð6:27Þ and a pole at the origin. s¼1 Let L2m Ls Lr ð6:28Þ Substituting Equations (6.28) and (3.10) into Equation (3.11) gives: Ves ¼ Rs ise þ sLs d e Lm d e i þ l joles : dt s Lr dt r ð6:29Þ In this equation, the stator voltage is represented by four terms. The last two can be considered as disturbance terms and can be neglected in the PI controller design. The first two terms represent the plant to be controlled. The transfer function of the plant is represented by: Gmotor ¼ 1 sLs s þ Rs ð6:30Þ which has a pole at: s¼ Rs : sLs ð6:31Þ To give a critically damped response, the ratio of Kp and KI can be chosen to place the controller zero at the plant pole: KI Rs ¼ : Kp sLs ð6:32Þ 156 Applied Intelligent Control of Induction Motor Drives The open-loop transfer function of the PI controller of stator currents and the motor can be expressed as: Gopenloop ¼ GPI Gmotor ¼ Kp 1 : sLs s ð6:33Þ Making the following substitution: K ¼ Kp 1 sLs ð6:34Þ gives the following equation: Gopenloop ¼ K : s Closing the feedback loop with unity gain results in the following closed-loop transfer function: Gclosedloop ¼ K : sþK ð6:35Þ This is recognized to be a single-pole low pass filter with 3-dB corner frequency at: F3dB ¼ K : 2p ð6:36Þ Choosing the simulation controller bandwidth of 100 Hz results in: K ¼ 2p 100: ð6:37Þ Kp can be obtained by substituting K into Equation (6.34): Kp ¼ 200p sLs : ð6:38Þ From Appendix H and Equation (6.28), s ¼ 0.208 and Ls ¼ 0.3185 H. Substituting these values into Equation (6.38), Kp ¼ 200p 0:208 0:3185 Kp ¼ 42 : ð6:39Þ KI can be obtained from Equation (6.32) with s ¼ 0.208, Ls ¼ 0.3185 H, and Rs ¼ 14.6 O: 42 14:6 0:208 0:3185 : KI ¼ 9256 KI ¼ ð6:40Þ 157 Hybrid Fuzzy/PI Two-Stage Control It is assumed that the induction motor is taken through the following control cycle: Speed Command Period oo ¼ 180 rad/s oo ¼ 20 rad/s 0 s t < 0.5 s 0.5 s t 1.5 s Figure 6.34 shows that, when permissible magnitude of stator current of the induction motor is 3 A, the actual stator current ic (dotted line) of the voltage-input model of the induction motor is able to track the stator current command ic (solid line). 5 Stator current (A) 3 1 -1 -3 -5 Figure 6.34 0 0.02 0.04 0.06 0.08 0.1 Actual stator current ic (dotted line) and stator current command ic (solid line). 30 5 20 3 Stator current (A) Slip frequency (rad/s) Figure 6.35 shows controlled slip frequency and controlled stator current of the fuzzy/PI control system. 10 0 -10 -20 -30 0 0.25 0.5 0.75 Time (s) Figure 6.35 1 1.25 1.5 1 -1 -3 -5 0 0.25 0.5 0.75 1 1.25 1.5 Time (s) Controlled slip frequency and controlled stator current. Figure 6.36 shows the phase voltage and rotor speed response of the voltage-input model of the 0.147 kW induction motor. 158 Applied Intelligent Control of Induction Motor Drives 300 200 Speed (rad/s) Phase voltage (V) 200 100 0 -100 150 100 50 -200 -300 0 0.25 0.5 0.75 1 1.25 1.5 0 0 0.25 0.5 Time (s) 0.75 1 1.25 1.5 Time (s) Figure 6.36 Phase voltage and rotor speed response of the voltage-input model of the 0.147 kW induction motor. 6.8 MATLABÒ/Simulink Programming Examples Two examples are given to illustrate programming of a fuzzy/PI two-stage controller using MATLABÒ/Simulink. The voltage-input model of an induction motor is first developed, and it is then used in a fuzzy/PI two-stage controller for an induction motor. 6.8.1 Programming Example 1: Voltage-Input Model of an Induction Motor This example demonstrates programming of the voltage-input model of a 0.147 kW induction motor, which is the ‘IM’ block in Figure 6.31. The electrical model of the induction motor is described by Equation (3.16) and the mechanical model is described by Equation (3.17). Step 1 Implementing the Induction Motor Model The induction motor model is implemented by using Simulink blocks as shown in Figure 6.37. The inputs of the induction motor model are dq-axis stator voltages (Vds, Vqs) and the load. The outputs of the model are the three-phase stator currents (iasibsics), rotor speed, and torque. In the induction motor model, the ‘Matrix A’ block is implemented by a ‘MATLAB Function’ block and the ‘Matrix B’ block is implemented by a ‘Matrix Gain’ block. The two matrix blocks in Equation (3.16) are used to simulate the electrical model of induction motor. The ‘2/3’ block is implemented by a ‘Matrix Gain’ block, which simulates dq-axis to three-phase transformation described in Equation (3.5). The mechanical model of the induction motor is simulated by the ‘Mechanical model’ block in Figure 6.37 and its details are shown in Figure 6.38. The inputs of the mechanical model are stator currents, rotor currents, and torque. The outputs of the mechanical model are torque and rotor speed. The stator currents and rotor currents come from the electrical model in Figure 6.37. Calculation of the torque in the Is 2/3 1 Wo_ Vds,Vqs 0 1 Hybrid Fuzzy/PI Two-Stage Control K*u K*u Sum 1/s Matrix B 2 Integrator Sum1 0 Vdr Initial Speed 0 2 Vqr Load Ids,Iqs,Idr,Iqr Rotor spped T Mechanical model 3 Torque MATLAB Function Matrix A Figure 6.37 Voltage-input model of 0.147 kW induction motor. 159 160 Applied Intelligent Control of Induction Motor Drives 1 -K- Is, Ir 2 Torque 1/0.001 2 s+0.000124 Load Transfer Fcn1 Figure 6.38 1 Rotor speed Mechanical model of induction motor. mechanical model is based on Equation (3.17) and calculation of the rotor speed is based on Equation (3.12). The motor parameters (‘Motor 3’ in Appendix B) are given as follows. 0.147 kW induction motor (Bodine Electric Company model 295) Stator resistance: Rs ¼ 14.6 O/ph Rotor resistance Rr ¼ 12.77 O/ph Stator inductance, Ls ¼ 0.3185 H/ph Mutual inductance, LM ¼ 0.2963 H/ph Rotor inductance Lr ¼ 0.3482 H/ph Moment of inertia of the rotor JM ¼ 0.001 kg m2 Coefficient of friction Cf ¼ 0.000 124 Number of poles P ¼ 4 Step 2 Configuring the Parameters of the Simulink Blocks With the above electrical parameters of the induction motor, matrix A is as shown in Table 6.6, while matrix B is obtained by a matrix inverse according to Equation (3.16), as follows: B ¼ invð½0:3185; 0; 0:2963; 0; 0; 0:3185; 0; 0:2963; 0:2963; 0; 0:3482; 0; 0; 0:2963; 0; 0:3482Þ Upon entering the above MATLABÒ command, the matrix B is obtained: 2 15:0684 6 6 0 6 B¼6 6 12:8224 4 0 0 12:8224 15:0684 0 0 13:7831 12:8224 0 0 3 7 12:8224 7 7 7 7 0 5 13:7831 The functions and parameters of the main blocks of the induction motor are listed in Table 6.6. 161 Hybrid Fuzzy/PI Two-Stage Control Table 6.6 Function and parameters of the blocks of the 0.147 kW induction motor. Block Name Function Parameters Matrix A ‘MATLAB Function’ block Implement matrix A in Equation (3.16) Matrix B ‘Matrix Gain’ block Implement matrix B in Equation (3.16) [u(1) 14.6; u(2) 14.6; u(2) u(5) 2 0.2963 þ u(3) 12.77 þ u(4) u(5) 2 0.3482; ( 0.2963) u(1) u(5) 2 þ ( 0.3482) u(3) u(5) 2 þ u(4) 12.77] [15.0684 0 12.8224 0; 2/3 ‘Matrix Gain’ block Transfer Fcn1 ‘Transfer Fcn’ block Vdr, Vqr ‘Constant’ blocks Implement dq-axis to 3-phase transform in Equation (3.5) Calculate rotor speed in Equation (3.12) 0 15.0684 0 12.8224; 12.8224 0 13.7831 0; 0 12.8224 0 13.7831] [1 0; 1/2 sqrt(3)/2; 1/2 sqrt(3)/2] Numerator coefficient: [1/0.001] Denominator coefficient: [1 0.000 124] Vdr ¼ 0; Vqr ¼ 0. Simulate rotor voltages Step 3 Adding a Voltage Source and the Load to the Induction Motor Model For testing of the motor model, a ‘dq-axis Voltage source’ block and a ‘Load’ block are added to the motor model, as shown in Figure 6.39. Stator current dq-axis Voltage source 0.8 IM Speed of rotor Load Torque Figure 6.39 Test model of the 0.147 kW induction motor. The ‘Load’ block with a constant value 0.8 simulates a load torque of 0.8 Nm. The ‘dq-axis Voltage source’ block yields the dq-axis voltages Vds and Vqs, and its details are shown in Figure 6.40. 162 Applied Intelligent Control of Induction Motor Drives 269.4 1 Constant Vds Vqs Polar to Cartesian Repeating Sequence Figure 6.40 A dq-axis voltage source with output Vds, Vqs. The ‘dq-axis Voltage source’ block consists of a ‘Constant’ block (which contains the amplitude of the voltage source), a ‘Repeating Sequence’ block (which yields the phase angle of the voltage source), and a ‘Polar to Cartesian’ block (which transforms the amplitude and phase angle into dq-axis voltages Vds and Vqs). To simulate a voltage source with an amplitude of 269.4 Vand a frequency of 60 Hz, the value 269.4 is input into the ‘Constant’ block and the ‘Repeating Sequence’ block is filled with time values of [0,0.001667] and an output value of [0,2 pi]. Step 4 Running the Simulink Model The Simulink test model as shown in Figure 6.39 is run with following parameters. Simulation type: variable-step Max step ¼ 0.0001 Min step ¼ auto Initial step ¼ 0.0001 Simulation time ¼ 0.5 s The simulation results for rotor speed, torque, and three-phase stator currents are shown in Figures 6.41–6.43, respectively. 200 Speed (rad/s) 150 100 50 0 -50 0 0.1 0.2 0.3 0.4 0.5 Time (s) Figure 6.41 Rotor speed of the 0.147 kW induction motor. 163 Hybrid Fuzzy/PI Two-Stage Control 12 10 Torque (N.m) 8 6 4 2 0 -2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time (s) Figure 6.42 Torque of the 0.147 kW induction motor. 10 Currents (A) 5 0 -5 -10 0 0.1 0.2 0.3 0.4 0.5 Time (s) Figure 6.43 6.8.2 Three-phase stator currents of the 0.147 kW induction motor. Programming Example 2: Fuzzy/PI Two-Stage Controller This example illustrates programming of the fuzzy/PI two-stage controller for the 0.147 kW induction motor using MATLABÒ/Simulink. The controller is the ‘fuzzy-PI controller’ block in Figure 6.31. Step 1 Implementing a Simulink Model A model of the fuzzy/PI two-stage controller is implemented as shown in Figure 6.44. The fuzzy/PI two-stage controller consists of a ‘Frequency Control’ block and a ‘PI Controller’ block. Details of the two blocks are shown in Figures 6.8 and 6.10, respectively. A ‘Saturation2’ block in Simulink library is employed to limit the amplitude of the stator current. 164 Applied Intelligent Control of Induction Motor Drives 1 1 Frequency Speed command Frequency Control PI 2 Rotor speed Sum1 Figure 6.44 PI Controller 2 Saturation2 Current Fuzzy/PI two-stage controller. Step 2 Choosing Parameters for the Simulink Blocks The ‘PI Controller’ employs a ‘PID Controller’ in Simulink library with a derivative parameter of 0. Assuming the permissible magnitude of the stator current of the induction motor to be 3 A, the proportional and integral parameters in the ‘PID Controller’ block is designed as described in Section 6.7 and the following parameters are input into the block: Proportional ¼ 1 Integral ¼ 0.03 Derivative ¼ 0 The Simulink block ‘Fuzzy Logic Controller’ shown in Figure 6.8 contains the parameter ‘ACCELE’ which is a file name of FIS (Fuzzy Inference System). The file ‘ACCELE’ may be edited by the FIS editor using the command ‘Fuzzy’ in the MATLABÒ window. The FIS edit operation steps have been described in Section 4.2.2. The ‘Fuzzy Logic Controller’ block has two inputs and one output. They are the rotor speed command, rotor speed error, and reference slip frequency, respectively. The fuzzy membership functions are input and edited by ‘Membership Function Editor’ on FIS editor platform. The fuzzy membership function of the rotor speed command is shown in Figure 6.32, the fuzzy membership function of speed error is shown in Figure 6.33, and the fuzzy linguistic values of reference slip frequency are listed in Table 6.4. The fuzzy rules of the fuzzy controller are given in Table 6.5 and the fuzzy rulebase is input and edited by ‘Rule editor’ on the FIS editor platform. Step 3 Implementing an Induction Motor Drive with Fuzzy/PI Two-Stage Controller To study the performance of the induction motor drive with the fuzzy/PI two-stage controller, the latter model is connected to the induction motor model built earlier with a ‘3-phase current’ block (which is described in Figure 3.2), three ‘PI’ blocks of stator-current control designed from Equations (6.26)–(6.40), a load which is described by Equation (6.12), a ‘Speed Command’ block which employs a ‘Repeating Sequence’ block in Simulink library, and a 3/2 transformation block which is described by Equation (3.5). These models are connected together to simulate the fuzzy/PI control system with a voltage-input model of the induction motor, as shown in Figure 6.31. 165 Hybrid Fuzzy/PI Two-Stage Control Step 4 Running the Simulink Model of Fuzzy/PI Control System The model shown in Figure 6.31 is run with following parameters. Simulation type: variable-step Max step ¼ 0.0001 Min step ¼ auto Initial step ¼ 0.0001 Simulation time ¼ 1.5 s The rotor speed commands are as follows, oo * ¼ 180 rad=s 0 s t < 0:5 s oo * ¼ 20 rad=s 0:5 s t 1:5 s The following parameters are input into the ‘Speed Command’ block. Time values ¼ [0 0.5 0.5 1.5]; Output values ¼ [180 180 20 20]. The ‘load’ block is a ‘Fcn’ block in Simulink library, which contains the parameter ‘u(1) 0.00 532’ to simulate the load described by Equation (6.12) with coefficient m ¼ 0.00 532 Nm/(rad/s), and the input u(1) is the rotor speed. The simulation results of the fuzzy/PI control system are shown in Figures 6.34–6.36. 6.9 Summary Based on the two-stage strategy and the heuristics deduced from the field-oriented principle, a hybrid fuzzy/PI controller is proposed. The controller has almost the same frequency and current characteristics as the field-oriented controller. During the acceleration/deceleration stage, the stator current magnitude is maintained at the maximum permissible value to give a large torque, and during the steady-state stage, the stator current magnitude is adjusted to control the rotor speed. Because the two features of fieldoriented control are exploited, the performance of the two-stage controller is superior to a scalar controller (Garcia, Stephan and Watanabe, 1994). Besides, the hybrid fuzzy/PI controller has the advantages of simplicity and insensitivity to motor parameter changes, input current noise, noise in the measured speed, magnetic saturation, and load torque variation. Very encouraging results are obtained from a computer simulation using MATLABÒ/Simulink. Due to the excellent speed response over the whole speed range, the method should find applications in practical industrial drive systems. The possible developments of the hybrid fuzzy/PI two-stage control are (1) to develop a design method of the fuzzy controller in the presence of disturbances and parameter variations, (2) optimizing the fuzzy rules and membership functions of the controller with self-learning methods such as neuro-fuzzy and genetic algorithm. 166 Applied Intelligent Control of Induction Motor Drives References Bose, B.K. (1993) Power electronics and motion control-technology status and recent trends. IEEE Transactions on Industry Applications, 29, 902–909. Bose, B.K. (1997) Expert system, fuzzy logic, and neural networks in power electronics and drives, in Power Electronics and Variable Frequency Drives: Technology and Applications (ed. B.K. Bose) IEEE Press, New Jersey. Garcia, G.O., Stephan, R.M., and Watanabe, E.H. (1994) Comparing the indirect field-oriented control with a scalar method. IEEE Transactions on Industrial Electronics, 41(2), 201–207. Henson, M.A. and Seborg, D.E. (1997) Nonlinear Process Control, Prentice-Hall, Upper Saddle River, NJ. Kosko, B. (1997) Fuzzy Engineering, Prentice-Hall, Inc., New Jersey. Krause, P.C., Wasynczuk, O., and Sudhoff, S.D. (1995) Analysis of Electric Machinery, IEEE Press, New Jersey. The MathWorks, Inc. (1994) Simulink User’s Guide, The MathWorks, Inc. Shi, K.L., Chan, T.F., and Wong, Y.K. (May 1997) A novel two-stage speed controller for an induction motor. The 1997 IEEE International Electric Machines and Drives Conference, USA. Shi, K.L., Chan, T.F., and Wong, Y.K. (1999) Modeling and simulation of a novel two-stage controller for an induction motor. International Association of Science and Technology for Development (IASTED) Journal on Power and Energy Systems, USA, 19(3), 257–264. Sousa, G.C.D. and Bose, B.K. (1994) A fuzzy set theory based control of a phase-controlled converter DC machine drive. IEEE Transactions on Industry Applications, 30(1), 34–44. Trzynadlowski, A.M. (1994) The Field Orientation Principle in Control of Induction Motors, Kluwer Academic Publishers, Boston. Wade, S., Dunnigan, M.W., and Williams, B.W. (1997) Modeling and simulation of induction machine vector control with rotor resistance identification. IEEE Transactions on Power Electronics, 12(3), 495–505. 7 Neural-Network-based Direct Self Control1 7.1 Introduction Nonlinear dynamical control research usingthe neural network has been proposed for almost two decades (Narendra and Parthasarathy, 1990). Recently, it has been proposed that neural networks can be applied to parameter identification and state estimation of induction motor control systems(Simoes and Bose, 1995). However, complete ANN vectorcontrol ofinduction motors is seldom reported, one of the reasons being the complexity of the controller. Direct self controller (DSC) is a dynamic, recurrent, and nonlinear signal processing method which theoretically can give an inverter-fed three-phase induction motor an excellent performance (Kazmierkowski and Kasprowicz, 1995). Because complicated calculations are involved, it is difficult to implement DSC using common integrated circuit (IC) circuit hardware. The DSC algorithms are usually studied by serial calculations on a digital signal processor (DSP) board. However, as a predictive control scheme, DSC has a steady-state control error produced by the time delay of the lengthy computations, which depends largely on the control algorithm and hardware performance. Typical DSP (TMS32010) execution time of the DSC algorithm is about 250 ms (Habetler et al., 1992), hence the maximum switching frequency of the inverter has to be limited to 4 kHz. Consequently, DSC is usually suitable for motor drives with low switching frequencies. With simple architecture and the inherent parallel computation capability, a neural-network controller is superior to a DSP board in execution time and hardware structure. The execution times of neural devices are less than 0.5 ms (analog) 1 (a) Portions reprinted by permission of K.L. Shi, T.F. Chan and Y.K. Wong, “Direct self control of induction motor using artificial neural network,” 1998 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1696–1701, October 11–14, 1998, San Diego, U.S.A. 1998 IEEE (b) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Industry Applications Society (IEEE-IAS) 2000 Meeting, vol. 3, pp. 1380–1387, October 8–12, 2000, Rome, Italy. 2000 IEEE. (c) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 168 Applied Intelligent Control of Induction Motor Drives or 0.8 ms (digital) per neuron (Zaghloul, Meador and Newcomb, 1994). Two neural devices have been suggested (Simoes and Bose, 1995) for induction motor control. Micro Devices MD1220, a digital VLSI device, takes 0.8 ms to process any synaptic input (or bias) when the clock rate is 20 MHz. Intel 80170NX (Electrically Trainable Analog Neural Network), on the other hand, is an analog device which takes only 3 ms to process through each layer. This chapter presents an ANN algorithm with 7 layers and 58 neurons to replace the DSP serial calculations of the classical DSC system. Because the 58 neurons take only 46.4 ms (using the digital MD1220) or 21 ms (using the analog 80170NX), the control precision of DSC can be significantly improved using the neural-network algorithm. 7.2 Neural Networks In general, a neural model is mathematically represented by a basis function (net function) and an activation function (neuron function). The selection of these functions often depends on the applications of the neural network. In other words, application-driven neural models are only loosely tied to the biological realities. Linear basis function u(wi,x) is a hyperplane-type function, where wi stands for the weight matrix, x for the input vector, and yi for the bias or threshold. Mathematically (Kung, 1993), ui ðwi ; xÞ ¼ n X j¼1 wij xj þ yi ð7:1Þ where j is the dimension of input. The net value as expressed by the basis function, ui(wi,x), will be immediately transformed by an activation function of the neuron. Thus, yi ¼ f ðui Þ ð7:2Þ where yi is net output and f() is the activation function. The activation functions used in this design include linear, square, log-sigmoid, tan-sigmoid, and hard limit functions (Appendix E). The memory of a neural network lies in the weights and biases. The neural networks can be classified, in terms of how the weights and biases are obtained, into three categories (Kung, 1993; Fausett, 1994). They are fixed-weight, unsupervised and supervised networks. In this design, the fixed-weight networks and the supervised networks are used. The constructions of the two networks are shown in Figure 7.1. The training data consist of pairs of input and target produced by the DSC mathematical model. The characteristic of the fixed-weight network is that the weights and biases are precomputed and pre-stored from training data. The fixed-weight network, which is also called the direct design method, can be used to implement an exact mathematical model. In same cases, its implementation is easier than the supervised network. In the supervised network, the weights and biases are adaptively trained by a learning mechanism, which has been the mainstream of neural model development. The backpropagation learning rule (Kung, 1993) is used to design the supervised networks for the DSC, details of which are presented as follows. It is convenient to regard the threshold y just as an extra weight, that is y ¼ wn þ 1 (Kung, 1993). The net value given by Equation (7.1) can be rewritten as: 169 Neural-Network-based Direct Self Control ANN input output wθ output + input wθ target ANN w and θ are precomputed from mathematical model (a) Fixed-weight network (b) Supervised network Figure 7.1 Neural networks using different training algorithms. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) ui ðwi ; xÞ ¼ nX þ1 j¼1 wij zj ¼ Wi Z ð7:3Þ where Wi ¼ [wi1wi2 . . . win yi] and Z ¼ [x1x2 . . . xn 1]T The sum squared error E (cost function) for the set of M patterns of input is given by Equation (7.16) (Simoes and Bose, 1995) E¼ M M X I 1X 1X 2 Em ¼ ðtm ym i Þ 2 m¼1 2 m¼1 i¼1 i ð7:4Þ where Em is the squared output error of the output layer, I is the dimension of the output vector, ym is the actual output vector, and tm is the corresponding desired output vector. The weights are changed to reduce the cost function E to a minimum value by the gradient descent method. The best initial weights and biases for back-propagation networks are created at random utilizing the minimum and maximum value of each input. The jth weight-update equation of the ith neuron is given as: qEm wij ðt þ 1Þ ¼ wij ðtÞ þ Z qwij ðtÞ ð7:5Þ where Z is the learning rate, wij(t þ 1) is the new weight, and wij(t) is the old weight. The training strategies may be divided as mutual (whole) and individual (local) (Kung, 1993). In mutual training, the training of all the weights is influenced by all the input/output values. In individual training, the training of an individual subnet will not be influenced by the inputs and outputs of other subnets. Pure mutual training is almost impossible for DSC, due to three reasons. Firstly, the direct self controller is a dynamic (there are integrators), recurrent (there are hysteresis comparators), and nonlinear system. Secondly, the eight input variables (Va, Vb, Vc, ia, ib, ic, T , jlsm j ) constitute a huge training set. Thirdly, it may take substantially more iterations to reach a mutual agreement between all the nodes. For simpler and faster design, the individual training strategy is adopted. 170 Applied Intelligent Control of Induction Motor Drives 7.3 Neural-Network Controller of DSC A DSC scheme consists typically of 3/2 transformations of current and voltage, flux estimation, torque calculation, flux angle encoder, flux magnitude computation, hysteresis comparator, and optimum switching table. Figure 7.2 shows a DSC system in the MATLAB/Simulink window, which consists of a DSC controller, an inverter, and an induction motor (Shi, Chan and Wong, 1998). DSC controller Torque Calculator Hysteresis Comparator Switching Table Inverter Stator Current 1 Flux estimation Flux Amplitude i Flux V IM Torque, Flux Command Output Voltage Flux Angle Cartesian to Polar Figure 7.2 A construction of the direct self control system in MATLAB/Simulink window. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) Based on DSC principle, the neural-network controller is divided into five sub-nets, which are individually trained: (1) flux estimation sub-net (fixed-weight) with dynamic neurons, (2) torque calculation sub-net (fixed-weight) with square neurons, (3) flux angle encoder and magnitude calculation sub-net (supervised) with log-sigmoid neurons and tan-sigmoid neurons, (4) hysteresis comparator sub-net (fixed-weight) with recurrent neurons, and (5) optimum switching table sub-net (fixed-weight or supervised) with hard limit neurons. 7.3.1 Flux Estimation Sub-Net Based on Equation (2.6) and 3/2 transformation, the flux estimation is mathematically expressed as: dlsdm 1 1 ðVb Rs ib Þ ðVc Rs ic Þ ¼ ðVa Rs ia Þ 2 2 dt dlsqm dt ¼ pﬃﬃﬃ pﬃﬃﬃ 3 3 ðVb Rs ib Þ ðVc Rs ic Þ 2 2 ð7:6Þ ð7:7Þ 171 Neural-Network-based Direct Self Control where Va, Vb, Vc are the phase voltages and ia, ib, ic are phase currents, which come from the voltage and current sensors. Neuron models can be divided in two basic types, namely static and dynamic. A dynamic neuron is one whose output is described by a differential equation (Delgado, Kambhampati and Warwick, 1995). Hence, the flux estimation sub-net should be constructed using two dynamic neurons which consist of linear neurons and integrators, as shown in Figure 7.3. Va Vb w1,θ1 Vc w2,θ2 ia ∫ λsdμ ∫ λsqμ ib ic Figure 7.3 A dynamic net of the flux estimation. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) A supervised method, viz. the back-propagation learning rule, is used to train the linear neurons until they can approximate Equations (7.6) and (7.7). Figure 7.3 shows the flux estimation network. Using a random generator function of MATLAB ‘randnc’, 10 random inputs of the vector [Va, Vb, Vc, ia, ib, ic] are produced. The target outputs can be obtained from Equations (7.6) and (7.7). Since the network is linear, convergence can be obtained in relatively few training epochs. For the induction motor being studied, the weights and biases have been obtained as follows: w¼ " 0:5725 0:3899 0:2910 0:7790 1:3073 0:2469 y¼ 7.3.2 0:3740 " 0:4546 0:2029 0:2836 # 0:7496 0:0172 0:7029 0:4575 # : Torque Calculation Sub-Net Based on Equation (2.6), the torque equation for a DSC system is given by: T¼ P2 s s ðl i ls is Þ 2 3 dm qs qm ds where P is the number of motor poles. ð7:8Þ 172 Applied Intelligent Control of Induction Motor Drives s s Since there are four inputs, lsdm ; lsqm ; ids ; and iqs , the data of all training patterns will be huge if high precision is required. To avoid training difficulties, the fixed-weight method is adopted. Equation (7.8) may be rewritten as a sum of square functions: T¼ i Ph s s2 s 2 s 2 s2 s2 ðldm þ iqs Þ ðlsqm þ ids Þ ls2 þ l þ i i dm qm ds qs 6 ð7:9Þ where " s ids s iqs # ¼ " 2 3 # ia 1=2 6 7 6 ib 7 pﬃﬃﬃ 4 5 3=2 ic 1 1=2 pﬃﬃﬃ 0 3=2 A two-layer, fixed-weight neural network is used to implement Equation (7.9) directly as shown in Figure 7.4. The first layer is a square activation function with the weight and bias w1 and y1, while the second layer is a linear active function with the weight and bias w2 and y2. 2 1 6 6 60 6 6 61 6 w1 ¼ 6 60 6 6 6 60 4 0 pﬃﬃﬃ 3=2 0 0 1 1 0 0 0 1 0 0 0 1 0 1=2 1=2 pﬃﬃﬃ 0 3=2 pﬃﬃﬃ 3 2 3 3=2 0 7 6 7 7 7 6 1=2 7 607 7 7 6 7 607 7 0 7 6 7 7 7 y1 ¼ 6 7 6 7 0 7 6 0 7 7 6 7 6 7 7 7 6 1=2 7 405 5 pﬃﬃﬃ 0 3=2 w2 ¼ ½1 1 1 1 1 1 y2 ¼ ½0 : λsdμ λsqμ ia ib ic Torque T Linear Activation Function Neuron Square Activation Function Neuron Figure 7.4 Neural network for torque calculation. (Reproduced by permission of K.L. Shi, T.F. Chan, Y. K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 173 Neural-Network-based Direct Self Control 7.3.3 Flux Angle Encoder and Flux Magnitude Calculation Sub-Net The flux angle a and flux magnitude f can be calculated from the flux space vectors lsdm and lsqm . Then the flux angle is encoded as B1B2B3. f ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ s2 ls2 dm þ lqm ð7:10Þ a ¼ tan 1 ðlsdm =lsqm Þ ð7:11Þ B1 B2 B3 ¼ encoderðaÞ ð7:12Þ In order to obtain accurate results and to simplify the design, Equations (7.10) and (7.11) are rewritten as: s2 u ¼ ls2 dm þ lqm ð7:13Þ vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ " #ﬃ u 1 u f ¼ tu 1 ð7:14Þ x ¼ 1=lsqm ð7:15Þ z ¼ lsdm x ¼ ½ðlsdm þ xÞ2 lsdm 2 x2 =2 ð7:16Þ B1 B2 B3 ¼ encoderðzÞ: ð7:17Þ The network of flux angle encoder and flux magnitude calculation consists of five nets as shown in Figure 7.5. Net1 with two square neurons implements Equation (7.13). Net2 with four tansig neurons implements Equation (7.14). Net3 with four logsig neurons, net4 with three square neurons, and net5 with ten hard limit neurons implement Equations (7.15)–(7.17), respectively. Net1, net4, and net5 are designed using the fixed weight method. Net2 and net3 are designed using the supervised method. The output layers of the net1, net2, net3, and net4 will be merged with the input layers of their next sub-nets according to the rule shown in Figure 7.14. Hence, weights and biases of the output layers of these nets will not be listed hereinafter. Design of net1 is similar to that used for the torque calculation sub-net described in Section 7.2. Weight w and bias y of net1 with two square neurons can be directly designed according to Equation (7.13) as follows: 174 Applied Intelligent Control of Induction Motor Drives s2 s2 s2 λ qμ + λ dμ s2 λ dμ + λ qμ net1 net2 s λ dμ s s s λ qμ / λ dμ 1/ λ dμ Flux codes net3 s λ qμ net5 net4 Figure 7.5 Individual training scheme for flux angle and magnitude calculations. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) wðnet 1Þ ¼ " 1 0 0 1 # yðnet 1Þ ¼ " # 0 0 The back-propagation learning rule is used to train net 2. 500 input/output pairs for training net 2 are produced by the square root function. After 50 000 training epochs, the sum-squared error E is less than 0.01. Weight w and bias y of net2 with tansig neurons is as follows. 2 0:1781 6 6 2:5008 6 wðnet 2Þ ¼ 6 6 2:9325 4 0:5233 0:1781 3 7 2:5008 7 7 7 2:9325 7 5 0:5233 2 1:5851 3 7 6 6 6:0920 7 7 6 yðnet 2Þ ¼ 6 7 6 6:2367 7 5 4 0:3963 Figure 7.6 shows the implementation of the flux magnitude calculation using net 1 and net2. The back-propagation learning rule is used to train net 3 until they can approximate the reciprocal function. 1000 input/output pairs are produced by the reciprocal function to train net3. After 100 000 training epochs, the sum-squared error E is less than 0.02. 2 31:6560 6 6 2:8829 6 wðnet 3Þ ¼ 6 6 14:8182 4 47:8563 3 2 0:7218 3 7 6 7 6 0:0022 7 7 7 6 7 7 7 yðnet 3Þ ¼ 6 6 0:0207 7 7 5 4 5 0:7360 175 Neural-Network-based Direct Self Control Square activation function neuron λ ds Tansig activation function neuron λ qs λ2ds + λ2qs net 1 Linear activation function neuron net 2 Figure 7.6 Implementation of the flux magnitude calculation. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) With three square neurons, net 4 implements Equation (6.13) using the same technique described in Section 7.2. 2 1=2 1=2 6 wðnet 4Þ ¼ 6 4 1=2 0 0 1=2 3 7 7 5 2 3 0 6 7 7 yðnet 4Þ ¼ 6 405 0 Net5 implements the flux angle encoding directly from lsdm =lsqm (output of net4), lsdm , and lsqm . To improve the algorithm, the trigonometric function computations of flux angle, which are necessary in previous DSC schemes, are replaced by logic operations. With reference to Figure 7.7, the flux angle code (B1 B2 B3) can be directly derived from the following equations: λ sqμ (100) II (110) (101) I III λµs λsdμ VI (010) IV V (001) (011) Figure 7.7 Space flux encoder (B1 B2 B3). (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 176 Applied Intelligent Control of Induction Motor Drives B1 ¼ B2 ¼ If we define: 8 1 > > > < > > > : 0 ( 1 if lsqm 0 0 otherwise if ðlsqm =lsdm ð7:18Þ tan p=3 and lsdm < 0Þ or if ðlsqm =lsdm < tan p=3 and lsqm < 0Þ ð7:19Þ otherwise 8 1 if ðlsqm =lsdm < tan p=3 and lsdm 0Þ > > > < B3 ¼ or if ðlsqm =lsdm tan p=3 and lsqm < 0Þ > > > : 0 otherwise M ¼ lsqm =lsdm tan p=3 ð7:20Þ ¼ lsqm =lsdm < tan p=3 M ð7:21Þ ¼ lsqm =lsdm < tan p=3 N ð7:22Þ K ¼ lsdm 0 ¼ lsdm < 0 K ð7:23Þ L ¼ lsqm 0 ¼ lsqm < 0 L ð7:24Þ N ¼ lsqm =lsdm tan p=3 then the encoder Equations (7.18)–(7.20) can be written as: (positive logic expression) B1 ¼ L ð7:25Þ [ ðN \ LÞ B2 ¼ ðN \ KÞ ð7:26Þ \ KÞ [ ðM \ LÞ: B3 ¼ ð M ð7:27Þ Equations (7.21)–(7.27) show that trigonometric function calculations are not needed for the flux angle encoding, hence the complexity of implementation is decreased. The flux angle encoder can be accomplished by the hard limit neurons as shown in Figure 7.8 (Fausett, 1994). The five nets are linked together to form the network of flux angle encoder and flux magnitude computation, which has 24 different neurons as shown in Figure 7.9. 177 Neural-Network-based Direct Self Control B1 N5 N1 W=1 b=0 s λ qμ N2 s W=1 b=-tanπ/3 N3 N4 s λ dμ N9 W=[1 1] N6 s λ dμ /λ qμ W=[-1 -1] b=-0.5 B2 b=0 W=[1 -1] b=0.5 N7 W=1 b=tanπ/3 W=[-1 1] b=-0.5 W=[1 1] N8 W=1 b=0 N10 W=[-1 1] b=-0.5 B3 b=0 Equation (7.24) is implemented by the neuron . N1. Equation (7.22) is implemented by the neuron N2. 2. Equation (7.21) is implemented by the neuron N3. 3. Equation (7.23) is implemented by the neuron N4. 4. Equation (7.25) is implemented by the output of neuron N1. 1. Equation (7.26) is implemented by the neurons N5, N6, and N9. Equation (7.27) is implemented by the neurons N7, N8, and N10. Figure 7.8 Flux angle encoder (net5) with hard limit neurons. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) Net5 Net3 Net4 B1 Hard Limit Activation Function Neuron Square Activation Function Neuron λsdμ B2 Tan-sigmoid Activation Log-sigmoid Activation Function Neuron λsqµ B3 Linear Activation Function Neuron λ s2dµ + λ s2qµ Net1 Net2 Figure 7.9 Network of flux angle encoder and flux magnitude computation. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 178 7.3.4 Applied Intelligent Control of Induction Motor Drives Hysteresis Comparator Sub-Net Using the hysteresis comparator as shown in Figure 7.10, the flux error between stator flux jlsm j and its command jlsm j can be limited within Djlsm j, and the flux error code B6 produced by the hysteresis comparator will be used to select the space voltage vector (Takahashi and Noguchi, 1986). Figure 7.10 Flux magnitude hysteresis comparator. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) The flux error code B6 can be expressed as: B6 ¼ ðif jlsm j < jlsm j* þ Djlsm j and B6 ¼ 0Þ 8 0 > > > > > > > > > < or ðif jlsm j < jlsm j* Djlsm j and B6 ¼ 1Þ ðif > > > 1 > > > > > > : jlsm j jlsm j* þ Djlsm j and B6 ¼ 0Þ : ð7:28Þ or ðif jlsm j jlsm j* Djlsm j and B6 ¼ 1Þ Equation (7.28) represents a recurrent calculation: To obtain B6, we have to do a calculation using B6, and in order to do the calculation, we have to obtain B6. In order to derive the weight and bias of network, Equation (7.28) is rewritten as: B6 ¼ ( 0 if ðw1 B6 þ jlsm j jlsm *j Djlsm j < 0Þ 1 if ðw1 B6 þ jlsm j jlsm *j Djlsm j 0Þ ð7:29Þ where w1 ¼ 2Djlsm j. The output B6 is connected as an input, which forms a recurrent network (The MathWorks, Inc., 1994). Using the basis function given by Equation (7.1) for a neural network, the weight and bias can be pre-computed. The input of network x ¼ [B6, |l|, |l |]. Its output is B6, its weight w ¼ [2D|l| 1 1], and its bias y ¼ [ D|l|]. The flux hysteresis comparator is implemented by a recurrent network with hard limit function as shown in Figure 7.11. 179 Neural-Network-based Direct Self Control Flux error code B6 Flux |λ µs | Hard limit activation function neuron [0 1] Flux command Figure 7.11 Flux hysteresis comparator of neural network. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) The difference between the motor torque T and the torque command T is compared with DT and the error flag is used to produce a torque error code for selecting the voltage space vector (Takahashi and Noguchi, 1986), that is. T* DT T T* ð7:30Þ (when lsm rotates in the clockwise direction) T* T T* þ DT ð7:31Þ (when lsm rotates in the counterclockwise direction) The torque hysteresis comparator expressed by Equations (7.30) and (7.31) can be designed in a similar manner as the flux hysteresis comparator, which is shown in Figure 7.12. The torque error code consists of two bits B4 and B5. The weight of u1 is [DT 1 1] and the bias of u1 is [0], while the weight of u2 is [DT 1 1] and the bias of u2 is [DT]. u1 Torque T Torque error code B4 Torque command T* u2 Torque error code B5 Figure 7.12 Torque hysteresis comparator of neural network. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 180 7.3.5 Applied Intelligent Control of Induction Motor Drives Optimum Switching Table Sub-Net The DSC optimum switching table is expressed in Table 7.1. The flux angle code B1B2B3, the torque error code B4, B5, and the flux magnitude error code B6 determine the output voltage codes Sa, Sb, Sc. The output voltage codes of the optimum switch table represent the on/off status of the inverter switches (Takahashi and Noguchi, 1986).A two-layer network with a total of 26 hard limit neurons is employed to implement the optimum switching table. The first layer has 23 neurons and the second layer has 3 neurons. Utilizing the 36 pairs of input and output patterns shown in Table 7.1, the network is trained by a supervised method with perceptron training rule (The MathWorks, Inc., 1994). After 321 training epochs, the sum squared error E arrives at zero. Table 7.1 DSC optimum switching table. (Sa,Sb,Sc) B4B5B6 ¼ 010 B4B5B6 ¼ 000 B4B5B6 ¼ 100 B4B5B6 ¼ 011 B4B5B6 ¼ 001 B4B5B6 ¼ 101 B1B2B3 ¼ 001 B1B2B3 ¼ 010 B1B2B3 ¼ 011 B1B2B3 ¼ 100 B1B2B3 ¼ 101 B1B2B3 ¼ 110 (0,1,1) (1,1,1) (1,0,1) (0,1,0) (0,0,0) (1,0,0) (1,1,0) (1,1,1) (0,1,1) (1,0,0) (0,0,0) (0,0,1) (0,1,0) (0,0,0) (0,0,1) (1,1,0) (1,1,1) (1,0,1) (1,0,1) (1,1,1) (1,1,0) (0,0,1) (0,0,0) (0,1,0) (0,0,1) (0,0,0) (1,0,0) (0,1,1) (1,1,1) (1,1,0) (1,0,0) (0,0,0) (0,1,0) (1,0,1) (1,1,1) (0,1,1) (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) An optimum switching table implemented by a hard limit neural network is shown in Figure 7.13. B1 W1 W2 θ1 θ 2 B2 … B6 B3 B5 W 24 θ24 W 26 θ26 Sa Sb B4 … W 23 θ23 Sc Figure 7.13 Optimum switching table implemented by neural network. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 181 Neural-Network-based Direct Self Control Weights and biases of the trained network of the optimum switching table are as follows: 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 w1 ¼ 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 0:3550 0:2885 0:7253 0:9269 0:0369 0:2401 0:8712 0:5187 0:2029 0:4311 0:1012 0:8907 0:0085 0:0325 0:5237 0:1668 0:8606 0:1340 0:3676 0:1286 0:0511 0:5529 0:1546 0:4239 0:6203 0:6865 0:2845 0:0241 0:8728 0:3333 0:8429 0:6309 0:2998 0:8419 0:0831 0:4301 0:8902 0:4835 0:4559 0:0767 0:7310 0:8661 0:9935 0:5583 0:8899 0:9817 0:2867 0:5424 0:3540 0:2792 0:1941 0:4154 0:1969 0:1388 0:5978 0:1585 0:0047 0:3297 0:9324 0:7765 0:9794 0:6219 0:7241 0:4927 0:2107 0:3663 0:5114 0:7814 0:3536 0:4784 0:4391 0:3123 0:4460 0:4094 0:5830 0:2659 0:2422 0:4385 0:4762 0:9414 0:9226 0:8008 0:6726 0:9360 0:0432 0:6741 0:4552 0:9438 0:2675 0:0007 0:2443 0:2400 0:9482 0:4688 0:4291 0:2412 0:7092 0:8132 0:7693 0:9648 0:0102 0:7978 0:7402 0:0252 0:4314 0:5715 0:4626 0:7834 0:1893 0:1831 0:9659 0:1633 0:1369 0:6547 0:9621 0:2690 3 7 7 0:0932 7 7 7 7 0:9459 7 7 7 7 0:4709 7 7 7 0:4498 7 7 7 7 0:9635 7 7 7 7 0:9462 7 7 7 7 0:9813 7 7 7 7 0:0070 7 7 7 7 0:6442 7 7 7 7 0:0162 7 7 7 7 0:9993 7 7 7 0:5643 7 7 7 7 0:2400 7 7 7 7 0:4980 7 7 7 7 0:7044 7 7 7 7 0:4455 7 7 7 7 0:1331 7 7 7 7 0:7321 7 7 7 7 0:4792 7 7 7 0:7769 7 7 7 7 0:6458 7 7 5 0:2571 182 Applied Intelligent Control of Induction Motor Drives 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 y1 ¼ 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 0:4346 3 2 41:0738 7 6 7 6 7 6 37:7507 0:2551 7 6 7 6 7 6 7 6 6:3355 0:6687 7 6 7 6 7 6 6 41:5267 0:4239 7 7 6 7 6 7 6 6 14:9610 0:5796 7 7 6 7 6 7 6 6 29:8704 0:3578 7 7 6 7 6 7 6 6 45:2122 0:3410 7 7 6 7 6 7 6 6 53:3863 0:2098 7 7 6 7 6 7 6 6 22:1699 0:0808 7 7 6 7 6 7 6 0:8631 7 6 25:7650 7 6 7 6 7 6 0:9978 7 6 57:7658 7 6 7 6 7 6 T 0:2047 7 w2 ¼ 6 32:7479 7 6 7 6 7 6 0:4015 7 6 40:8303 7 6 7 6 7 6 27:3672 0:9724 7 6 7 6 7 6 7 6 24:7633 0:5862 7 6 7 6 7 6 7 6 13:0352 0:5770 7 6 7 6 7 6 7 6 28:9413 0:9197 7 6 7 6 7 6 7 6 54:7596 0:5717 7 6 7 6 7 6 7 6 39:4737 0:8491 7 6 7 6 7 6 7 6 76:8339 0:5232 7 6 7 6 7 6 7 6 15:8100 0:2756 7 6 7 6 7 6 7 6 21:6393 0:9595 7 6 5 4 0:5518 38:4350 74:4303 46:8430 97:5883 5:9237 53:1857 9:3693 8:3780 7:1366 0:0711 73:9106 7:8811 17:4653 31:5257 75:5551 69:1695 40:2875 49:3222 33:2641 23:4507 136:3204 25:8781 6:4111 63:6614 44:9270 3 7 7 48:6175 7 7 7 7 79:2760 7 7 7 7 62:7760 7 7 7 7 36:3249 7 7 7 7 40:7466 7 7 7 7 77:5973 7 7 7 7 11:0640 7 7 7 7 7 7:3889 7 7 7 58:8391 7 7 7 7 47:1295 7 7 7 7 29:2237 7 7 7 7 76:5592 7 7 7 44:8241 7 7 7 7 7 4:9325 7 7 7 122:2603 7 7 7 7 26:6222 7 7 7 7 48:0328 7 7 7 7 58:4754 7 7 7 7 21:3997 7 7 7 7 10:4552 7 7 7 7 85:3883 7 7 5 2:7575 183 Neural-Network-based Direct Self Control 2 58:6962 3 6 7 7 y2 ¼ 6 4 7:9228 5 48:4529 7.3.6 Linking of Neural Networks When the sub-nets are linked to each other, some neurons of the output layer may be merged with the input neurons of the next sub-net. For example, if an output neuron of a sub-net has a linear activation function, it may be merged with the input neuron of the next sub-net. As shown in Figure 7.14, the activation function of neuron A is linear, and its output is: Output layer xa x1 Input layer Input layer B Merging Process y1 x2 xa y2 Previous Sub-net Next Sub-net y1 xd x2 C Previous Sub-net B x1 x2 xd A x1 y2 C Next Sub-net Figure 7.14 Merging of neurons with linear activation functions. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) xa ¼ w1 x1 þ w2 x2 þ y1 : ð7:32Þ Let the basis function of neuron B be u1 ¼ w3 xa þ w4 xd þ y2 : ð7:33Þ u1 ¼ w3 w1 x1 þ w3 w2 x2 þ w4 xd þ w3 y1 þ y2 : ð7:34Þ Substituting (7.32) into (7.33), If the new weight and bias of neuron B are denoted by w0 and y0 2 respectively, then w0 ¼ ½w3 w1 w3 w2 w4 ð7:35Þ y0 2 ¼ ½w3 y1 þ y2 : ð7:36Þ In this way, neuron A is merged with neuron B as well as the neuron C. 184 Applied Intelligent Control of Induction Motor Drives If an output neuron of a sub-net has a hard limit function, it can also be merged into next subnet’s input neuron that has also a hard limit function. Employing this strategy, the number of layers and neurons of the linked network can be decreased. With the merging of input and output neurons, the five sub-nets (flux estimation, torque calculation, flux angle encoder and flux magnitude calculation, hysteresis comparator, and optimum switching table) are assembled into the DSC neural network as shown in Figure 7.15. Vc 1/s B1 B2 Vb ia Va ib ic λ sµ T* 1/s B3 B6 Sa Sb B5 B4 Sc Figure 7.15 Neural-network implementation of DSC. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) The complete neural network consists of 7 layers and 58 neurons. It may be implemented using special neural devices. If the device 80170NX (Intel analog IC chip) is used, the processing time for the seven layers will be 21 ms. If the device MD-1220 (digital IC chip) is used, the processing time for 58 neurons will be 46.4 ms (at a clock rate of 20 MHz). Parallelism of neural device computation renders it extremely fast compared with the DSP serial computation. 7.4 Simulation of Neural-Network-based DSC A MATLAB/Simulink program with Neural Network Toolbox is used to simulate the neuralnetwork DSC, which is shown in Figure 7.16. The voltage-input model of an induction motor presented in Chapter 3 is used for the simulation studies. The parameters of the 7.5 kW induction motor are listed in Appendix B. The stator flux command and torque command for ANN-DSC and classical DSC simulation are as follows: 185 Neural-Network-based Direct Self Control Torque calculator 1 2 1 T* λ* Current Hysteresis Switch table On/off signals to inverter Flux Angle encoder and calculation amplitude computation 3 Voltage Figure 7.16 Neural-network-based DSC in Simulink. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) Stator flux commands: jlsm j* ¼ 0:86 Wb Torque commands: 0s<t 4s T* ¼ 100 N m T* ¼ 20 N m T* ¼ 0 s < t 0:8 s 0:8 s < t 2 s 100 N m T* ¼ 20 N m 2 s < t 2:3 s 2:3 s < t 4 s Figures 7.17, 7.18 and 7.21 show the torque response, speed response, and flux response of the classical DSC system with 100 ms controller delay (typical of a DSP-based controller), while Figures 7.19, 7.20 and 7.22 show the torque response, speed response, and flux response Torque (N.m) 100 50 0 -50 -100 0 1 2 3 4 Time (s) Figure 7.17 Torque response of DSC with 100 ms delay. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 186 Applied Intelligent Control of Induction Motor Drives Rotor speed (rad/s) 100 80 60 40 20 0 0 1 2 3 4 Time (s) Figure 7.18 Speed response of DSC with 100 ms delay. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) Torque (N.m) 100 50 0 -50 -100 0 1 2 Time (s) 3 4 Figure 7.19 Torque response of ANN-DSC with 25 ms delay. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 100 Rotor speed (rad/s) 80 60 40 20 0 0 1 2 Time (s) 3 4 Figure 7.20 Speed response of ANN-DSC with 25 ms delay. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) 187 Neural-Network-based Direct Self Control 0.5 0.5 Flux-qs (Wb) 1 Flux-qs (Wb) 1 0 0 -0.5 -0.5 -1 -1 -0.5 0 0.5 Flux-ds (Wb) 1 Figure 7.21 Flux response of DSC with 100 ms delay (time ¼ 0–0.2 s). (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) -1 -1 -0.5 0 0.5 Flux-ds (Wb) 1 Figure 7.22 Flux response of ANN-DSC with 25 ms delay (time ¼ 0–0.2 s). (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Direct self control of induction motor based on neural network,” IEEE Transactions on Industry Applications, 37(5), 2001: 1290–1298. 2001 IEEE.) of the neural-network control system with 25 ms controller delay. The results demonstrate that DSP-based DSC produces large torque and flux errors, whereas the neural-network controller eliminates almost all these errors. In the simulation studies, it is evident that (1) torque and flux errors increase with increasing controller delay time, (2) the large torque and flux errors decrease the robustness of the drive system against current noise and load changes. It can be concluded that neural-network-based DSC is a more effective algorithm for the control of an inverter-fed induction motor. 7.5 MATLAB/Simulink Programming Examples In this section, two examples are given to illustrate programming of a direct self controller (DSC) (Shi et al., 2003) and a neural-network-based optimum switching table in MATLAB/ Simulink. 7.5.1 Programming Example 1: Direct Self Controller The direct self control system shown in Figure 7.2 consists of the following function blocks: (1) flux estimation, (2) torque calculation, (3) flux angle encoder and magnitude calculation, (4) hysteresis comparator, and (5) optimum switching table. The realization of the neuralnetwork-based controller in MATLAB/Simulink involves the following steps. Step 1 Building the Flux Estimation Model Based on Equations (7.6) and (7.7), a flux estimation model is built as shown in Figure 7.23, where the gain block represents the stator resistance Rs of the motor (0.294 O). 188 Applied Intelligent Control of Induction Motor Drives 2 Vs 1 1/s 0.294 1 Is Flux Rs Figure 7.23 Simulink model of flux estimation. In the Simulink model of flux estimation, the inputs are the dq-axis stator voltage vector and dq-axis stator current vector; while the output is the dq-axis flux vector. Step 2 Building the Torque Calculation Model Based on Equation (7.8), a torque calculation model is built for the induction motor (in which the number of poles P ¼ 6) as shown in Figure 7.24. 2 Flux 2 Gain 1 Is Figure 7.24 1 Torque Simulink model of torque calculation. In the torque calculation model, the input dq-axis flux vector is the output of the flux estimation model and the other input is the dq-axis stator current vector, while the output is the torque. Step 3 Building the Flux Angle Encoder and Magnitude Calculation Model With the dq-axis flux vector obtained in Step 1 and based on Equations (7.10) and (7.11), the flux angle and magnitude is computed by employing a ‘Cartesian to Polar’ block in Simulink library, as shown in Figure 7.25. 1 1 Flux Amplitude Cartesian to Polar 2 Angle Figure 7.25 Flux angle and magnitude calculation. Based on Equations (7.18), (7.19), and (7.20), a Simulink model of flux angle encoder is implemented as shown in Figure 7.26. In the flux angle encoder model, the input is the flux angle and the output is the flux angle codes (B1 B2 B3) of the DSC optimum switching table in Table 7.1. 189 Neural-Network-based Direct Self Control 1 Angle 0 >= pi < AND >= pi/1.5 OR -pi/3 < -pi/1.5 >= pi/3 < 1 B1_B2_B3 AND Figure 7.26 Simulink model of flux angle encoder. Step 4 Building the Hysteresis Comparator Model Based on Equations (7.28), (7.30), and (7.31), the hysteresis comparator may be built by ‘Relay’ blocks in Simulink library as shown in Figure 7.27. 1 Torque Sum1 1 B4_B5 Relay1 2 T* Relay2 3 Flux 2 B6 Relay3 29 Figure 7.27 Simulink model of hysteresis comparator. The outputs of the hysteresis comparator model are the codes (B4 B5 B6) of the DSC optimum switching table in Table 7.1. When the flux command jlsm j ¼ 0:86 Wb, Djlsm j ¼ 0:2 Wb, control error of torque D|T | ¼ 5 N m, the parameters of the hysteresis comparator model are as shown in Table 7.2. Table 7.2 Parameters of Simulink model of the hysteresis comparator. Block Relay 1 Equation (7.30) Relay 2 Equation (7.31) Relay 3 Equation (7.28) Switch on point 0 5 0.88 Switch off point 5 0 0.84 Output when on Output when off 0 1 1 1 0 0 190 Applied Intelligent Control of Induction Motor Drives Step 5 Building the Optimum DSC Switching Table The DSC optimum switching table given in Table 7.1 is implemented by a ‘Combinatorial Logic’ block in Simulink library, as shown in Figure 7.28. 1 1 B1~B6 Sa-Sb-Sc Figure 7.28 Combinatorial Logic Simulink model of DSC optimum switching table. The inputs of the ‘Combinatorial Logic’ block are the codes (B1 B2 B3 B4 B5 B6) and the outputs are the output voltage codes (Sa, Sb, Sc). The 36 states of the output voltage codes (Sa, Sb, Sc) listed in Table 7.1 are used as the parameters of the truth table in the ‘Combinatorial Logic’ block, as shown below: [1 0 1;1 0 1;1 0 1;1 0 1;1 0 1;1 0 1;1 0 1;1 0 1;0 0 0;0 0 0;0 1 1;0 1 0;1 0 1;1 0 0;1 1 1;1 1 1;0 0 0; 0 0 0;1 1 0;1 0 0;0 1 1;0 0 1;1 1 1;1 1 1;0 0 0;0 0 0;0 1 0;1 1 0;0 0 1;1 0 1;1 1 1;1 1 1;0 0 0;0 0 0; 1 0 1;0 0 1;1 1 0;0 1 0;1 1 1;1 1 1;0 0 0;0 0 0;0 0 1;0 1 1;1 0 0;1 1 0;1 1 1;1 1 1;0 0 0;0 0 0;1 0 0; 1 0 1;0 1 0;0 1 1;1 1 1;1 1 1;1 1 1;1 1 1;1 1 1;1 1 1;1 1 1;1 1 1;1 1 1;1 1 1] After the above parameters have been input into the ‘Combinatorial Logic’ block, the block may be used to simulate the optimum switching table. Step 6 Implementing the Direct Self Controller The direct self controller is implemented by linking the models of flux estimation, torque calculation, flux angle encoder and magnitude calculation, hysteresis comparator, and optimum switching table obtained in Step 1 to Step 5, as shown in Figure 7.29. 2 Is Is Torque Flux 3 Torque calculation T* Torque B4_B5 T* B6 Flux 1 Combinatorial Logic Hysteresis Is Flux 1 Vs Angle B1_B2_B3 Vs Flux calculation Cartesian to Polar Angle encoder Figure 7.29 Simulink model of direct self controller. Sa_Sb_Sc 191 Neural-Network-based Direct Self Control Step 7 Building the Direct Self Control System To study the performance of the DSC induction motor system, the direct self controller model is combined with the voltage-input model of the induction motor, a ‘decode’ block, a load block, a ‘T ’ block, and a ‘Transport Delay’ block, as shown in Figure 7.30. Wo TL Scope1 T 20 IM Transport Delay Scope Vs Vs Sa_Sb_Sc Is T* Decode DSC Figure 7.30 T* Simulink model of direct self control system. The voltage-input model of the 7.5 kW induction motor used in this study has been built in Programming example 1 in Section 6.8. The ‘decode’ block consists of a ‘Combinatorial Logic’ block and a ‘Polar to Cartesian’ block in Simulink library, which is used to transform the output voltage codes Sa, Sb, Sc to the corresponding dq-axis voltage vector, as shown in Figure 7.31. 1 1 Vs Sa_Sb_Sc Polar to Cartesian Figure 7.31 vector. Combinatorial Logic ‘Decode’ block for transforming the output voltage codes Sa, Sb, Sc to dq-axis voltage The parameters in the truth table of the ‘Combinatorial Logic’ block represent the amplitudes and angles of the six voltage vectors and zero voltage vector. When the amplitude of nonzero voltage vector is 270 V, the parameters will be as follows. ½0 0; 270 pi=6; 270 5* pi=6; 270 pi=2; 270 pi=2; 270 pi=6; 270 5* pi=6; 0 0 192 Applied Intelligent Control of Induction Motor Drives The truth table consists of eight vectors (six nonzero vectors and two zero vectors). The first value of each vector represents the amplitude of the voltage vector and the second value represents the angle of the voltage vector. The ‘T ’ block in Figure 7.30 employs a ‘Repeating Sequence’ block in Simulink library to yield torque commands. To simulate the stator torque commands as listed in Section 7.4, the ‘T ’ block is provided with the following parameters. Time value ¼ [0,0.8, 0.8, 2, 2, 2.3, 2.3, 4] Output value ¼ [100 100, 23, 23, 100, 100, 22, 22] The ‘Transport Delay’ block in Figure 7.30 simulates the controller delay. When the controller delay is 100 ms, the parameter of the block is 0.0001. Step 8 Running the Simulink Model The Simulink model of direct self control system shown in Figure 7.29 is run with following parameters. Simulation type: Fixed-step Fixed-step size ¼ 0.00 002 s Simulation time ¼ 4 s Controller delay ¼ 100 ms The simulation results are obtained as shown in Figures 7.17 and 7.18. When a ‘XY Graph’ block in Simulink library is connected to the two outputs of the flux angle and magnitude calculation in Figure 7.25, the flux response shown in Figure 7.21 is obtained. To simulate the control system without the controller delay, the parameter of the ‘Transport Delay’ block should be set to 0. 7.5.2 Programming Example 2: Neural-Network-based Optimum Switching Table In this example, the optimum switching table is implemented by a two-layer neural network with hard limit neurons. The neural network is trained by a supervised method with perceptron training rule (The MathWorks, Inc., 1994). Step 1 Entering Samples of Input and Target into Workspace of MATLAB From the truth table in Table 7.1, the codes (B1 B2 B3 B4 B5 B6) have 36 combinations and these are used as input samples for training the neural network. The codes are listed below: B1 B2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 B3 B4 1 0 1 0 1 1 1 0 1 1 1 0 0 0 B5 1 0 0 1 0 0 1 B6 0 0 0 1 1 1 0 Neural-Network-based Direct Self Control 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 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 193 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 Enter the above samples as a [6 36] array into the workspace of MATLAB and name the array as variable ‘P’ which is used later as input samples for training the network. In Table 7.1, the output voltage codes (Sa, Sb, Sc) have 36 states corresponding to the 36 input samples. The 36 states are used as target samples for training the neural network and they are listed below. Sa 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 Sb Sc 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 194 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 Applied Intelligent Control of Induction Motor Drives 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 Enter the above samples as a [3 36] array into the workspace of MATLAB and name the array as variable ‘T’ which is used as target samples. Step 2 Training the Neural-Network-based Optimum Switching Table The following program is based on Neural Network Toolbox Version 1.0 (The MathWorks, Inc., 1994), 2.0 or 3.0 on MATLAB 4.x or MATLAB 5.x platforms. S1 = 23; tp = [100 500]; % Set 23 neurons in first layer % Set training parameters to show results of 100 epochs % Max training epochs is 500 [W1,b1] = initp(P,S1); % Initialize weight and bias of first-layer net [W2,b2] = initp(S1,T); % Initialize weight and bias of second-layer net nntwarn off % Turn off the warning A1 = simup(P,W1,b1); % Yield data from first-layer net [W2,b2,epochs] = trainp(W2,b2,A1,T,tp); % Training weight and bias % of the second-layer net The above training program is run repeatedly until the sum squared error (SSE) of the performance program arrived at zero. In some cases, SSE cannot arrive at zero within 500 epochs due to the random initial parameters in the training program. A successful training result with SSE ¼ 0 in 463 epochs is listed as follows. TRAINP: 0/500 epochs, SSE ¼ 58. TRAINP: 100/500 epochs, SSE ¼ 31. TRAINP: 200/500 epochs, SSE ¼ 27. TRAINP: 300/500 epochs, SSE ¼ 21. TRAINP: 400/500 epochs, SSE ¼ 20. TRAINP: 463/500 epochs, SSE ¼ 0. The network training performance is shown in Figure 7.32. 195 Neural-Network-based Direct Self Control Sum-Squared Network Error for 463 Epochs 100 90 80 Sum-Squared Error 70 60 50 40 30 20 10 0 -10 0 50 100 150 200 250 Epoch 300 350 400 450 Figure 7.32 Network training performance: the sum squared error (SSE) arrived at zero after 463 training epochs. Upon entering ‘W1’, ‘b1’, ‘W2’, and ‘b2’ into the MATLAB window, the weight matrices and bias vectors of the network are shown on computer screen. They are listed following Figure 7.13 in Section 7.3 with name w1, y1, w2, and y2, respectively. Step 3 Building the Neural-Network-based Optimum Switching Table The neural-network-based optimum switching table consists of a ‘Matrix Gain’ block, a ‘Constant’ block, a ‘Sum’ block, and a ‘hardlim’ block in Simulink library, as shown in Figure 7.33. 1 W in_1 Weight 1 Sum hardlim out_1 b Bias Figure 7.33 A neural network with hard limit neurons. The ‘Matrix Gain’ block stores the weight matrix, the ‘Constant’ block stores the bias vector, and the ‘hardlim’ block simulates the hard limit neurons and the number of the neurons as determined by the size of weight matrix. The blocks are grouped and duplicated as two 196 Applied Intelligent Control of Induction Motor Drives neural-network blocks named as ‘Net1’ and ‘Net2’ to simulate the first layer and second layer of the network, respectively. The weight matrices and bias vectors obtained in Step 2 are directly input into the ‘Matrix Gain’ blocks and the ‘Constant’ blocks in the ‘Net1’ and ‘Net2’, respectively. Step 4 Verifying the Neural-Network-based Optimum Switching Table To verify the neural-network-based optimum switching table, the ‘Combinatorial Logic’ block that represented the optimum switching table in Figure 7.29 are replaced by ‘Net1’ and ‘Net2’. The modified Simulink model of direct self controller is shown in Figure 7.34. 2 Is Is Torque Flux Torque calculation Torque 3 T* T* Flux B4_B5 B6 1 Sa_Sb_Sc Net1 Net2 Hysteresis Is Flux 1 Vs Angle B1_B2_B3 Vs Flux calculation Cartesian to Polar Angle encoder Figure 7.34 Simulink model of direct self controller with neural-network-based optimum switching table. With a controller delay of 25 ms and other simulation parameters same as those in Example 1, the simulation results of the direct self control system with neural-network-based optimum switching table shown in Figures 7.19 and 7.20 are obtained. When a ‘XY Graph’ block is connected to the outputs of the flux angle and magnitude calculation in Figure 7.25, the flux response in Figure 7.22 can be viewed. 7.6 Summary The flexible neural-network structures are used to implement the computationally intensive DSC principle. Based on the understanding of DSC, the fixed weight and supervised networks with individual training strategy are employed for the ANN controller design. Neural-network-based DSC can greatly reduce the execution time of the controller, hence the steady-state control error is eliminated almost completely. The results of simulation demonstrate that the neural-network algorithm has a better precision in the torque and flux responses than the classical DSC method. Using neural-network techniques, hardware implementation of DSC presents less problems and it is envisaged that ANN-DSC induction motor drives will gain wider acceptance in future. The possible developments of the neuralnetwork-based direct self control are (1) to improve the neural network in order to decrease the neuron types, number and layers, (2) to design a neural-network-based sensorless DSC by developing a sub-network of speed estimation, (3) to develop a neural-network-based DSC controller whose performance is immune to disturbances and motor parameter variations. Neural-Network-based Direct Self Control 197 References Delgado, A., Kambhampati, C., and Warwick, K. (1995) Dynamic recurrent neural network for system identification and control. IEE Proceedings – Control Theory and Applications, 142(4), 307–314. Fausett, L. (1994) Fundamentals of Neural Networks, Prentice-Hall, Inc., New Jersey. Habetler, T.G., Profumo, F., Pastorelli, M., and Tolbert, L.M. (1992) Direct torque control of induction machines using space vector modulation. IEEE Transactions on Industry Applications, 28(5), 1045–1053. Kazmierkowski, M.P. and Kasprowicz, A.B. (1995) Improved direct torque and flux vector control of PWM inverterfed induction motor drives. IEEE Transactions on Industrial Electronics, 42(4), 344–350. Kung, S.Y. (1993) Digital Neural Networks, PTR Prentice-Hall, Inc., New Jersey. The MathWorks, Inc. (1994) Neural Network Toolbox User’s Guide. The MathWorks, Inc. Narendra, K.S. and Parthasarathy, K. (1990) Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1, 4–27. Shi, K.L., Chan, T.F., and Wong, Y.K. (May 1998) Modelling and simulation of direct self control system. IASTED International Conference: Modelling and Simulation, Pittsburgh, USA. Shi, K.L., Chan, T.F., Wong, Y.K., and Ho, S.L. (2003) Modeling and simulation of direct self control for induction motor. International Journal of Engineering Education. U.K., 19(4), 646–654. Simoes, M.G. and Bose, B.K. (1995) Neural network based estimation of feedback signals for a vector controlled induction motor drive. IEEE Transactions on Industry Applications, 31, 620–629. Takahashi, I. and Noguchi, T. (1986) A new quick-response and high-efficiency control strategy of an induction motor. IEEE Transactions on Industry Applications, 22(5), 820–827. Zaghloul, M.E., Meador, J.L., and Newcomb, R.W. (1994) Silicon Implementation of Pulse Coded Neural Networks, Kluwer Academic Publishers, Boston. 8 Parameter Estimation Using Neural Networks 8.1 Introduction A three-phase induction motor for drive applications may be described and studied by a set of differential equations. Generally speaking, the differential equations give satisfactory results in motor transient analysis when the input voltages are smooth functions. In a modern machine drive, however, the motor is invariably fed from a power electronic converter, typically a pulsewidth modulated (PWM) inverter. Non-differentiable points therefore exist in the motor current due to rapid turn-on or turn-off of the ideal power electronic switches, resulting in possible divergences when the motor drive simulation program is executed. Design and simulation of an induction motor drive require an accurate knowledge of the machine parameters. When differential operators are used for parameter measurement, magnitude of noise may be amplified and the computational accuracy will be degraded. In order to secure convergence in performance analysis of an ac motor drive, integration loops are usually employed instead of the differential operations. Methods of parameter estimation for an induction motor have been proposed in many publications. In (Moon and Keyhani, 1994), electrical parameters of induction motor are estimated under standstill conditions, using transfer functions with the acquired time-domain data. In (Attaianese et al., 1998), model reference adaptive control (MRAC) is employed to estimate the parameters of an induction motor. In (Zai, Li-Cheng, DeMarco, and Lipo, 1992), the extended Kalman filter (EKF) is used to measure the rotor time constant of an induction motor. Recently, artificial intelligence (AI) techniques, such as fuzzy logic (Bose and Patel, 1998), Artificial Neural Network (ANN) (Wishart and Harley, 1995), and genetic algorithm (Pillay, Nolan, and Haque, 1997), have been applied to motor parameter estimation. Online parameter estimation of an induction motor has been reported (de Souza Ribeiro et al., 2000). However, most published methods using the conventional differential equations have complex structures and some of them may be sensitive to noise. In (Zamora and GarciaCerrada, 2000), some integral operators have been used to simplify parameter estimation. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 200 Applied Intelligent Control of Induction Motor Drives Among the various AI techniques, neural networks are particularly suitable for motor drive applications as they have the ability to process and acquire information in a complex system. Nonlinearities and uncertainties in parameters of the motor drive system can therefore be modeled with ease with the aid of neural networks. In this chapter, integral models of an induction motor will be implemented by using an artificial neural network (ANN) approach. By using the proposed ANN-based integral models, almost all the machine parameters can be derived directly from the measured data, namely the stator currents, stator voltages and rotor speed. With the estimated parameters, load, stator flux, and rotor speed may be estimated. 8.2 Integral Equations Based on the ‘T’ Equivalent Circuit In the stator reference frame, the ‘T’ equivalent circuit (Slemon, 1989) of an induction motor is shown in Figure A.2 of Appendix A, where ir ¼ ls Ls is : LM ð8:1Þ Substituting (8.1) into the conventional differential equations in which the state variables are the stator currents and rotor currents, the induction motor ‘T’ equivalent circuit model (Slemon, 1989) can be expressed in terms of five nonlinear equations in the stator reference frame: dids ¼ kT ðRr Ls þ Lr Rs Þids dt Poo iqs diqs ¼ kT ðRr Ls þ Lr Rs Þiqs þ Poo ids dt 1 L2M Lr Ls kT Lr Vds ð8:2Þ kT Rr lqs þ Poo kT Lr lds kT Lr Vqs ð8:3Þ dlds ¼ Vds dt Rs ids ð8:4Þ dlqs ¼ Vqs dt Rs iqs ð8:5Þ doo 2 P ðlds iqs ¼ 3 2J dt where kT ¼ Poo kT Lr lqs kT Rr lds lqs ids Þ TL J Foo J ð8:6Þ . The stator fluxes may be obtained by integrating (8.4) and (8.5): lds ðtÞ ðt lds ð0Þ ¼ Vds dt 0 ðt Rs ids dt 0 ð8:7Þ 201 Parameter Estimation Using Neural Networks ðt lqs ðtÞ ðt lqs ð0Þ ¼ Vqs dt ð8:8Þ Rs iqs dt: 0 0 With the initial conditions lds(0) ¼ 0 and lqs(0) ¼ 0, substitution of Equations (8.7) and (8.8) into Equation (8.2), Equations (8.3) and (8.6) results in the integral forms of ids, iqs, and oo, as follows: ðt ids ð0Þ ¼ kT ðRr Ls þ Lr Rs Þ ids dt ids ðtÞ 0 0t 1 ð ðt þ PkT Lr Rs oo @ iqs dtAdt 0 ðt ðt 0 1 ðt ðt P oo iqs dt þ kT Rr Rs @ ids dtAdt 0 kT Lr Vds dt 0 0 0 0 0 0t 1 ; ð PkT Lr oo @ Vqs dtAdt ðt 1 0 ðt ðt kT Rr @ Vds dtAdt 0 0 0 1 0 ðt ðt ðt ðt iqs ð0Þ ¼ kT ðRr Ls þ Lr Rs Þ iqs dt þ P oo ids dt þ kT Rr Rs @ iqs dtAdt iqs ðtÞ 0 oo ðtÞ 0 ðt 1 TL dt J 0 kT Lr Vqs dt 0 0 t ðt ð 2P @ oo ð0Þ ¼ Rs ids iqs dt 3 2J 0 0 iqs 0 0 1 0t 1 ; ðt ðt ðt ð kT Rr @ Vqs dtAdt þ PkT Lr oo @ Vds dtAdt ðt 0 0 0 0 0t 1 ðt ð PkT Lr Rs oo @ ids dtAdt ðt 0 ðt 0 0 0 t ðt ð 2 P A @ iqs Vds dt ids dt dt þ 3 2J 1 0 0 0 ðt 1 ids Vqs dtAdt 0 : F oo dt J 0 The induction motor can therefore be modeled by the above equations that involve explicitly only three variables, namely, ids, iqs and oo. For convenience, when ids(0) ¼ 0, iqs(0) ¼ 0, and oo(0) ¼ 0, the above integral equations may be written in the following concise forms: ids ¼ A1 X1 þ A2 X2 þ A3 X3 þ A4 X4 þ A5 X5 þ A6 X6 þ A7 X7 iqs ¼ A1 Y1 A2 Y2 þ A3 Y3 A4 Y4 þ A5 Y5 þ A6 Y6 oo ¼ C1 Z1 þ C2 Z2 þ C3 Z3 þ C4 Z4 A7 Y 7 ð8:9Þ ð8:10Þ ð8:11Þ 202 Applied Intelligent Control of Induction Motor Drives where ðt Y1 ¼ iqs dt A1 ¼ kT ðRr Ls þ Lr Rs Þ 0 ðt ðt ðt A2 ¼ X1 ¼ ids dt 0 X2 ¼ oo iqs dt Y2 ¼ oo ids dt 0 ðt 0 0t 1 ð X3 ¼ @ ids dtAdt 0 0 1 ðt ðt Y3 ¼ @ iqs dtAdt 0 ðt 0 0 1 0t ð Y4 ¼ oo @ ids dtAdt 0 0 ðt X5 ¼ Vds dt 1 0 ðt ðt Y6 ¼ @ Vqs dtAdt 0 0 0t 1 ð ðt X7 ¼ oo @ Vqs dtAdt ðt ðt Z1 ¼ @ids iqs dt 0 ðt 0 0 0 0 t ð ðt @ Z2 ¼ iqs Vds dt 0 0 ðt Z3 ¼ TL dt A5 ¼ kT Lr A6 ¼ k T Rr A7 ¼ PkT Lr 0 1 0 ðt ðt X6 ¼ @ Vds dtAdt 0 A4 ¼ PkT Lr Rs 0 ðt Y5 ¼ Vqs dt 0 A3 ¼ kT Rr Rs 0 ðt 1 0t ð X4 ¼ oo @ iqs dtAdt 0 P 0t 1 ð Y7 ¼ oo @ Vds dtAdt 0 ðt 1 iqs ids dtAdt 0 0 C1 ¼ 2P Rs 3 2J C2 ¼ 2P 3 2J C3 ¼ 1 J C4 ¼ F J 0 ðt 1 ids Vqs dtAdt ð8:12Þ 0 0 ðt Z4 ¼ oo dt 0 Equations (8.9)–(8.11) expresses a set of linear functions of ids iqs and oo with variables X ¼ [X1, X2, X3, X4, X5, X6, X7], Y ¼ [Y1, Y2, Y3, Y4, Y5, Y6, Y7], and Z ¼ [Z1, Z2, Z3, Z4], 203 Parameter Estimation Using Neural Networks which may in turn be calculated by integral operations on the measured stator voltages, stator currents, and rotor speed. If the coefficients A1, A2, A3, A5, A6, C2, and C4 are known, the parameters P, Rs, Ls, F, J, and the rotor time constant, may be obtained from Equation (8.12): P¼ A2 ; Rs ¼ A3 ; A6 Ls ¼ Rr A6 ¼ L r A5 A5 A3 A1 A6 A26 J¼ ; 2 P ; 3 2C2 F¼ ðRotor time constantÞ: JC4 ; ð8:13Þ If the coefficients, A1, A2, A3, A4, A5, A6, A7, C1, C2, C3, and C4 are known, the induction motor model is completely described by Equations (8.9)–(8.11). It is well known that the rotor parameters, Rr and Lr cannot be independently obtained (Stephan, Bodson, and Chiasson, 1994) from the ‘T’ equivalent circuit because the motor equations are not sufficient for identification of these parameters. Only when the assumption Lr ¼ Ls is made can all the parameters be obtained from Equation (8.12). In order to reduce the complexity without loss in computational accuracy, the ‘G’ equivalent circuit is frequently used instead (Slemon, 1989). Using the ‘G’ equivalent circuit, all the machine parameters can be derived from the corresponding integral equations as detailed in Section 8.3. 8.3 Integral Equations based on the ‘G’ Equivalent Circuit The ‘G’ equivalent circuit (Slemon, 1989) of an induction motor in the stator reference frame is shown in Figure A.1 of Appendix. As in the case of the ‘T’ equivalent circuit, the induction motor model based on a ‘G’ equivalent circuit may be described by five nonlinear differential equations in the stator reference frame: dids ¼ kG ðLs RR þ LR Rs Þids dt Poo iqs diqs ¼ kG ðLs RR þ LR Rs Þiqs þ Poo ids dt 1 Ls LR L2s . kG LR Vds ð8:14Þ kG RR lqs þ PkG LR oo lds kG LR Vqs ð8:15Þ dlds ¼ dt Rs ids þ Vds ð8:16Þ dlqs ¼ dt Rs iqs þ Vqs ð8:17Þ doo 2 P ðlds iqs ¼ 3 2J dt where kG ¼ PkG LR oo lqs kG RR lds lqs ids Þ TL J Foo J ð8:18Þ 204 Applied Intelligent Control of Induction Motor Drives The mechanical Equation (8.18) for the ‘G’ equivalent circuit is the same as Equation (8.6) for the ‘T’ equivalent circuit. The integrals of the stator fluxes Equations (8.16) and (8.17) for the ‘G’ equivalent circuit are the same as Equations (8.7) and (8.8) for the ‘T’ equivalent circuit. Substituting Equations (8.7) and (8.8) into Equations (8.14), (8.15), and (8.18), the integral forms of the ‘G’ equivalent circuit may be derived: ðt ids ðtÞ ðt 0 1 ðt ðt P oo iqs dt þ kG RR Rs @ ids dtAdt ids ð0Þ ¼ kG ðLs RR þ LR Rs Þ ids dt 0 ðt 0t 1 ð þ PkG Rs oo @ iqs dtAdt 0 0 ðt kG LR Vds dt 0 0 k G RR 0 ðt 0 ðt 0t 1 ð @ Vds dtAdt 0 PkG LR 0 ðt ðt 0 0t 1 ; ð oo @ Vqs dtAdt 0 0 1 ðt ðt iqs ð0Þ ¼ kG ðLs RR þ LR Rs Þ iqs dt þ P oo ids dt þ kG RR Rs @ iqs dtAdt iqs ðtÞ 0 0 oo ðtÞ 0 t ð ðt 2P @ Rs ids iqs dt oo ð0Þ ¼ 3 2J 1 TL dt J 0 0 iqs 0 0 0t 1 ; 0 1 ð ðt ðt ðt kG RR @ Vqs dtAdt þ PkG LR oo @ Vds dtAdt 0 0 0 0 ðt 0 ðt kG LR Vqs dt 0t 1 ð ðt PkG Rs oo @ ids dtAdt ðt 0 ðt 0 0 0 0 t ðt ð 2 P @ A iqs Vds dt ids dt dt þ 3 2J 1 0 0 ðt 1 ids Vqs dtAdt 0 : F oo dt J 0 The above integral equations may be written as: ids ¼ B1 X1 þ B2 X2 þ B3 X3 þ B4 X4 þ B5 X5 þ B6 X6 þ B7 X7 ð8:19Þ iqs ¼ B1 Y1 ð8:20Þ B2 Y2 þ B3 Y3 B4 Y4 þ B5 Y5 þ B6 Y6 oo ¼ C1 Z1 þ C2 Z2 þ C3 Z3 þ C4 Z4 : B7 Y7 ð8:21Þ 205 Parameter Estimation Using Neural Networks where X1 X7, Y1 Y7, Z1 Z4 and C1 C4 are the same as the corresponding variables in Equations (8.9)–(8.11), while B1 B7 are defined by: B1 ¼ kG ðRR Ls þ LR Rs Þ B2 ¼ P B3 ¼ k G RR Rs B4 ¼ PkG LR Rs B5 ¼ kG LR B6 ¼ k G RR B7 ¼ PkG LR ð8:22Þ It should be noted that the elements of coefficient matrix [A] in Equation (8.9) and the elements of coefficient matrix [B] in Equation (8.19) are identical, despite the fact that corresponding elements may be given by different expressions. If the coefficients B1, B2, B3, B4, B5, B6, B7, C1, C2, C3, and C4 are known, all the parameters of the induction motor may be estimated from Equation (8.22): P¼ B2 ; Rs ¼ B3 ; B6 Ls ¼ B5 B 3 J¼ 8.4 B 1 B6 B26 2 P ; 3 2C2 ; F¼ LR ¼ B5 L2s ; B5 Ls 1 RR ¼ B6 ðLs LR JC4 : L2s Þ; ð8:23Þ Parameter Estimation of Induction Motor Using ANN Accurate knowledge of the parameters of the induction motor model is required for analysis and control purposes. Specifically, we wish to identify the coefficients A1 A7 in Equation (8.9) or Equation (8.10), B1 B7 in Equation (8.19) or Equation (8.20), and C1 C4 in Equation (8.11) or Equation (8.21). An examination of the equations concerned reveals that the quantities ids, iqs, and oo may each be modeled by a single-layer linear network with multiple inputs and a single output. The neural network contains only a neuron which is characterized by a linear transfer function. With obtained sample pairs of input and target, the linear network can be trained by a MATLABÒ function ‘newlind’ in Neural Network Toolbox (The MathWorks Inc., 2008). Specific network weights and biases may be obtained to minimize the mean square error by using this MATLABÒ function. A Simulink model of induction motor drive is used for the parameter estimation as shown in Figure 8.1. The Simulink model consists of a ‘Signal Source’ block, a ‘SVPWM’ block, a ‘Load’ block, and an ‘Induction Motor’ block. The ‘Signal Source’ block outputs three-phase 60 Hz 206 Applied Intelligent Control of Induction Motor Drives 3-phase 60Hz Signal Source SVPWM Inverter w Vdq Scope T 20 N.m Speed Torque Scope1 Load is Load Induction Motor Figure 8.1 Simulink model of induction motor drive with a SVPWM inverter. sinusoidal signals. The ‘Load’ block is a ‘Constant’ block in Simulink library to simulate a 20 N.m load. The ‘SVPWM’ block simulates a space-vector PWM inverter, which outputs dq-axis voltages Vds and Vqs with a magnitude of 300 V to drive the induction motor. The ‘Induction Motor’ block is a voltage-input model of induction motor based on the ‘T’ equivalent circuit, which is described in Section 3.4 and a programming example in Section 6.8. 8.4.1 Estimation of Electrical Parameters Measurement data Figure 8.2 shows a training scheme of neural network with a single linear neuron for obtaining the coefficients A1 A7 or B1 B7. The stator voltages (Vds, Vqs), stator currents (ids, iqs), are input to the integral module which gives the seven variables X1, X2, X3, X4, X5, X6, and X7 to the single-layer neural network ANN1. The error between the output of ANN1 and the stator current ids (target) is used to train the network parameters. ids iqs Vds Vqs ωo ∫ , ∫∫ module X1 X2 X3 X4 X5 X6 X7 ids ANN1 Figure 8.2 Training scheme of ANN-based electrical model of induction motor (oo 6¼ 0). Upon completion of the training, the coefficients A1 A7 of the ‘T’ equivalent circuit (or B1 B7 of the ‘G’ equivalent circuit) are obtained from the weights of the network ANN1 by Equations (8.13) and (8.23). The biases of the network should be very close to zero if the training process converges. Consequently, ANN1 may be used to give ids in the integral Equations (8.9) and (8.19) with a feedback line as shown in Figure 8.3. By using a similar method, a second neural network ANN2 with only a linear neuron may be designed and trained to simulate iqs in the integral Equations (8.10) or (8.20) with a feedback line as shown in Figure 8.3. 207 Parameter Estimation Using Neural Networks ∫ , ∫∫ Vds Vqs Eq.(8.12) ωo ∫ , ∫∫ Eq.(8.12) x1 x2 x3 x4 x5 x6 x7 ANN1 ids y1 y2 y3 y4 y5 y6 y7 iqs ANN2 Figure 8.3 ANN-based electrical model of induction motor. After the training is completed, the ANN-based electrical model of the induction motor is established as shown in Figure 8.3. The electrical parameters of induction motor may be also estimated without rotor speed information. Under blocked-rotor conditions, that is, rotor speed oo ¼ 0, the electrical equations of the induction motor are also valid. Hence, a simple method to obtain the electrical parameters is presented in Figure 8.4. When the rotor speed oo ¼ 0, Equations (8.9) and (8.19) are reduced to ids ¼ A1 X1 þ A3 X3 þ A5 X5 þ A6 X6 ð8:24Þ ids ¼ B1 X1 þ B3 X3 þ B4 X4 þ B6 X6 : ð8:25Þ Measurement data where [A1, A3, A5, A6] ¼ [B1, B3, B5, B6]. Equation (8.24) or (8.25) therefore expresses ids as a linear function of the variables X1, X3, X5, X6, obtainable with the motor under blocked-rotor conditions. Figure 8.4 oo ¼ 0. ids iqs Vds Vqs ∫ , ∫∫ Integral X1 X3 X5 X6 ids ANN3 Training scheme of estimating electrical parameter of induction motor with condition As shown in Figure 8.4, the stator voltages (Vds, Vqs) and stator currents (ids, iqs) under blocked-rotor conditions are input into the integral module to yield the four outputs X1, X3, X5, 208 Applied Intelligent Control of Induction Motor Drives and X6 to the neural network ANN3. After the training of ANN3 is completed, the coefficients A1, A3, A5, and A6 are determined and the electrical parameters in the ‘T’ equivalent circuit are obtained from Equation (8.13). If the number of poles P is known, the remaining three coefficients A2, A4, and A7 in Equation (8.9) may be computed from the coefficients, A1, A3, A5, and A6 already obtained: A2 ¼ P; A4 ¼ P A3 A5 ; A6 A7 ¼ PA5 : The coefficients B1, B3, B5, and B6 in the ‘G’ equivalent circuit are also equal to the weights of the linear network ANN3. Consequently, all the electrical parameters in the ‘G’ equivalent circuit may be obtained from Equation (8.23). If P is known, the remaining three coefficients B2, B4, and B7 in Equation (8.19) can be determined from the coefficients B1, B3, B5, B6 already obtained: B2 ¼ P; B4 ¼ P B 3 B5 B6 B7 ¼ PB5 : When the motor is under blocked-rotor condition, the rotor load equals the rotor torque. With a connection line from the torque port to load port, the Simulink model of induction motor drive in Figure 8.1 may simulate the motor under blocked-rotor condition as shown in Figure 8.5. 3-phase 60Hz Signal Source SVPWM Inverter w Speed Vdq Scope T Torque Scope1 Load is Induction Motor Figure 8.5 8.4.2 Simulink model of induction motor drive with motor under blocked-rotor condition. ANN-based Mechanical Model Figure 8.6 shows the proposed training scheme for the ANN-based mechanical model. With the load torque TL set to zero, the network ANN4 with a single linear neuron is used to compute the rotor speed using the inputs Z1, Z2, and Z4 from the integral module. The error between the output of ANN4 and the rotor speed (target) is used to train the network parameters. After the training is completed, the coefficients C1, C2, and C4 in Equation (8.11) are obtained from the weights of ANN4. All the mechanical parameters of the ‘T’ or ‘G’ equivalent circuit may be obtained from Equation (8.13). The input Z3, which is the integral of load torque 209 Measurement data Parameter Estimation Using Neural Networks Figure 8.6 ωo ids iqs Vds Vqs Z1 ∫ Z2 Eq. (8.12) ωo ANN4 Z4 Training scheme of ANN-based mechanical model of induction motor with TL ¼ 0. with weight ( 1/J), is then added into the trained network to complete the mechanical model as shown in Figure 8.7. Measurement data TL ωo ids iqs Vds Vqs Figure 8.7 Z1 ∫ Z2 Eq. (8.12) ANN4 ωo Z4 Completed ANN-based mechanical model of induction motor. The four linear neural networks for induction motor parameter estimation are summarized in Table 8.1. Table 8.1 Four linear neural networks for induction motor parameter estimation. Name Function Input Output Neuron and training function ANN1 Electrical model Equation (8.9), Equation (8.19) Electrical model Equation (8.10), Equation (8.20) Electrical model (oo ¼ 0) Equation (8.24) Mechanical model Equation (8.11), Equation (8.21) X1, X2, X3, X4, X5, X6, and X7 X1, X2, X3, X4, X5, X6, and X7 X1, X3, X5, and X6 ids Z1, Z2, and Z4 oo One linear neuron Training function ‘newlind’ One linear neuron Training function ‘newlind’ One linear neuron Training function ‘newlind’ One linear neuron Training function ‘newlind’ ANN2 ANN3 ANN4 iqs ids 210 Applied Intelligent Control of Induction Motor Drives 8.4.3 Simulation Studies Simulation studies are carried out on a three-phase induction motor (‘Motor 1’ in Appendix B) with the following ‘T’ equivalent circuit parameters: Stator resistance Stator inductance Mutual inductance Rotor resistance Rotor inductance Total inertia of motor Viscous friction coefficient Number of poles Rs ¼ 0.294 O Ls ¼ 0.0424 H LM ¼ 0.041 H Rr ¼ 0.156 O Lr ¼ 0.0417 H J ¼ 0.8 kg m2 F ¼ 0.1 N m s/rad P¼6 The corresponding electrical parameters of the ‘G’ equivalent circuit are: Stator resistance Stator inductance Rotor resistance Rotor inductance Rs ¼ 0.294 O Ls ¼ 0.0424 H RR ¼ 0.167 O LR ¼ 0.0446 H The Simulink model of sampling data consists of the induction motor drive in Figure 8.1 and a ‘Sample Model’ block based on Equation (8.12), as shown in Figure 8.8. To simulate current measurement noise, two ‘Random Number’ blocks are introduced to inject Gaussian white noise to the stator currents ids and iqs before the data is sampled. The ‘Equation (8.12)’ block outputs the variables X1 X7 and the variables Z1 Z4 based on Equation (8.12). The four ‘To Workspace Input’ blocks are employed to store samples of vector X ¼ [X1, X2, X3, X4, X5, X6, X7], variable Y (stator current ids), vector Z ¼ [Z1, Z2, Z4], and variable W (rotor speed oo), respectively. From the motor simulation results, the variables X1 X7 are obtained from the ‘Equation (8.12)’ block based on ten sets of data acquired at 0.04 s intervals for training the network ANN1. Since the model in Equation (8.9) is linear, a fairly small number of data samples suffice to ensure convergence in the ANN training. The values of the input samples are listed below: x1 0.94692 0.22678 0.72640 0.71875 0.79240 0.43001 0.49282 x2 1.98520 0.58155 9.75612 15.27895 0.19296 4.41782 7.49746 x3 0.00755 0.01918 0.03498 0.06303 0.05244 0.04821 x4 0.11399 0.50539 1.19009 2.37681 4.15943 6.02133 8.04367 x5 0.46359 0.68192 0.69432 0.41458 0.01956 0.42286 0.69515 0.64079 0.41185 0.08396 x6 0.00459 0.00311 0.00363 0.00600 0.00258 0.00572 0.00320 0.00237 0.00355 0.00103 x7 0.04492 0.20875 0.41957 0.79826 1.21903 1.72559 2.41915 3.03928 3.94426 4.82695 0.05994 0.14841 0.72756 20.83614 19.24096 0.12109 18.17365 0.04847 0.04608 0.04035 10.44622 13.30458 16.44377 The following ten samples of the stator current extracted over the same time period are used as the targets for the training: y 43.33115 197.23973 292.50222 278.07246 127.70671 40.97748 190.20088 275.99749 258.02238 138.12246 211 Parameter Estimation Using Neural Networks 3-phase 60Hz Signal Source w SVPWM Inverter Speed w Vdq Scope T 20 N.m To Workspace input3 Torque Scope1 Load is Load X1 Induction Motor Wo X2 X3 X4 x X5 To Workspace input1 Vdq X6 X7 Random Number1 idq Z1 Z2 Stator current z Z3 em TL Z4 To Workspace input2 Eq.(8.12) y Random Number2 Figure 8.8 To Workspace input4 Simulink model of sampling data. where y is ids. With the above sample pairs of input and target, the linear network is trained by a MATLABÒ function ‘newlind’ (The MathWorks Inc., 2008). The following is a program for training the linear network. P¼6; y1¼y(2:11)’; x1¼x(2:11,:)’; net ¼ newlind(x1,y1); Y ¼ sim(net,x1); E¼y1-Y; SSE¼sumsqr(E) Weight¼net.IW{1,1} A¼Weight; Biase¼net.b{1} Ls¼(A(5) A(3)-A(1) A(6))/A(6)/A(6) %Pole number of motor is 6 %Training neural network %Y is outputs of the trained network %Error of Y and sample outputs %Calculate sum squared error %Output weight of network %Output bias of network %Calculate Ls in ‘T’ equivalent %circuit based on Equation(8.13) 212 Applied Intelligent Control of Induction Motor Drives Rs¼-A(3)/A(6) %Calculate Rs in ‘T’ equivalent %circuit based on Equation(8.13) %Calculate Rr/Lr in ‘T’ equivalent %circuit based on Equation(8.13) %Calculate LR in ‘G’ equivalent %circuit based on Equation (8.23) %Calculate LR in ‘G’ equivalent %circuit based on Equation (8.23) RrLr¼A(6)/A(5) LR¼A(5) Ls Ls/(A(5) Ls-1) RR¼A(6) (Ls LR-Ls Ls) It should be noted that value of matrix [A] in ‘T’ equivalent circuit and matrix [B] in ‘G’ equivalent circuit are identical. After running above MATLABÒ program, the following results are shown in computer screen. SSE ¼ 1.7565e-020 Weight ¼ [ 216.7; 3; Bias ¼ 3.9154e-011 Ls ¼ 0.0424 Rs ¼ 0.2940 RrLr ¼ 3.7410 LR ¼ 0.0446 RR¼ 0.1668 526.7; 422.4; 478.9; 1791.5; 1436.6] The sum squared error (SSE) between the output of ANN1 and the target ids arrives at 1.7565e-020. The network weights are found to be ½ 216:7 3 526:7 422:4 478:9 1791:5 1436:6 and the network bias is 3.9154e-011, which may be considered to be equal to zero. The network weights are the coefficients of [A] in the ‘T’ equivalent circuit or of [B] in the ‘G’ equivalent circuit, that is, ½A1 ; A2 ; A3 ; A4 ; A5 ; A6 ; A7 ¼ ½ 216:7 3 526:7 422:4 478:9 1791:5 1436:6 ð8:26Þ ½B1 ; B2 ; B3 ; B4 ; B5 ; B6 ; B7 ¼ ½ 216:7 3 526:7 422:4 478:9 1791:5 1436:6 ð8:27Þ With the above coefficients of [A], the parameters of the ‘T’ equivalent circuit are obtained from Equation (8.13): P ¼ 6; RS ¼ 0:294 O; Ls ¼ 0:0424 H; and rotor time constant Rr =Lr ¼ 3:741 s: In a similar manner, with the above coefficients of [B], the parameters of the ‘G’ equivalent circuit are obtained from Equation (8.23): P ¼ 6; RS ¼ 0:294 O; Ls ¼ 0:0424 H; RR ¼ 0:167 O; LR ¼ 0:0446 H: 213 Parameter Estimation Using Neural Networks For training of ANN4 in Figure 8.7, the following data sets, which are simulation results obtained from the ‘Equation (8.12)’ block in Figure 8.8, are used as inputs, z1 z2 z4 8.57757 3.86035 0.07599 20.20110 8.91320 0.29626 27.29074 12.53849 0.66223 37.56554 16.88888 1.17180 50.62150 22.20011 1.82807 57.04781 25.73052 2.63694 68.12547 30.69521 3.60462 75.90780 34.73047 4.73717 84.74541 39.12689 6.04035 95.57365 44.17282 7.52038 while the following samples of rotor speed, also obtained from the ‘Equation (8.12)’ block in Figure 8.8, are used as the targets. oo 3.33687 7.39816 11.20479 14.46507 18.06499 22.06658 26.21527 30.44186 34.77437 39.24546 The program for training ANN4 is shown below: P¼6; Z¼ z(2:11,:)’; w1¼w(2:11)’; net ¼ newlind(Z,w1); Y ¼ sim(net,Z); E¼w1-Y; SSE¼sumsqr(E) Weight ¼ net.IW{1,1} Bias ¼ net.b{1} D¼net.IW{1,1}; J¼P/3/D(2) F¼-J D(3) C¼[D(1), D(2), -1/J, D(3)] %Pole number of motor is 6 %Training neural network %Y is outputs of the trained network %Error of Y and sample outputs %Calculate sum squared error %Output bias of network %Output bias of network %Calculate J based on Equation (8.13) %Calculate F based on Equation (8.13) %See Equation(8.28) After running the above code, the following results are displayed on the computer screen. SSE ¼ 8.7306e-025 Weight ¼ [0.7350, 2.5000, 0.1250] Bias ¼ 7.5608e-013 J ¼ 0.8000 F ¼ 0.1000 C ¼ 0.7350 2.5000 1.2500 0.1250 With the sample pairs of input and target obtained, the linear network is trained by the MATLABÒ function ‘newlind,’ the sum squared error (SSE) between the output of ANN4 and 0:1250, and the target oo arrives at 8.7306e-25. The network weights are ½0:735 2:500 the network bias is 7.5608e-13. The network bias may be considered to be equal to zero. The network weights are the coefficients [C] in the mechanical model in Equation (8.11), that is, 214 Applied Intelligent Control of Induction Motor Drives ½C1 ; C2 ; C4 ¼ ½0:7350 2:5000 0:1250. From Equation (8.12), C3 ¼ ½C1 ; C2 ; C3 ; C4 ¼ ½0:7350 2:5000 1=J 1/J, hence ð8:28Þ 0:1250 Since the pole number P ¼ 6 (obtained from the weights of ANN1), the following mechanical parameters of the induction motor are obtained from Equation (8.13): J¼ 8.5 2 P and F ¼ 3 2C2 JC4 ; i:e:; J ¼ 0:8 kg:m2 and F ¼ 0:1 N:m:s=rad: ANN-based Induction Motor Models The induction motor model may be implemented by using the ANN-based electrical model (Figure 8.3) and mechanical model (Figure 8.7), as shown in Figure 8.9. A double integral of a sinusoidal function may result in data overflow in the computer memory, caused by the second integral operation on an integration constant which has arisen from the first definite integral. When the period of program simulation is long, data overflow may occur when evaluating the double integrals in Equation (8.12). To overcome the above difficulty, Equations (8.9) to (8.12) are rewritten as ids ðtÞ ðt ids ð0Þ ¼ ðA1 X10 þ A2 X20 þ A3 X30 þ A4 X40 þ A5 X50 þ A6 X60 þ A7 X70 Þdt ð8:29Þ 0 iqs ðtÞ ðt A2 Y20 þ A3 Y30 oo ðtÞ ðt iqs ð0Þ ¼ ðA1 Y10 A4 Y40 þ A5 Y50 þ A6 Y60 A7 Y70 Þdt ð8:30Þ 0 oo ð0Þ ¼ ðC1 Z10 þ C2 Z20 þ C3 Z30 þ C4 Z40 Þdt ð8:31Þ 0 Vds Vqs ∫ , ∫∫ Eq.(8.12) ∫ , ∫∫ Eq.(8.12) Figure 8.9 x1 x2 x3 x4 x5 x6 x7 y1 y2 y3 y4 y5 y6 y7 TL ANN1 ids ∫ Eq. (8.12) ANN2 iqs ANN model of induction motor. z1 z2 z3 z4 ANN4 ωo 215 Parameter Estimation Using Neural Networks where X10 ¼ ids Y10 ¼ iqs A1 ¼ kT ðRr Ls þ Lr Rs Þ X20 ¼ oo iqs Y20 ¼ oo ids A2 ¼ X30 ðt Y30 ¼ ids dt 0 X40 ðt ¼ iqs dt P A3 ¼ kT Rr Rs 0 ðt Y40 ¼ oo iqs dt ðt ¼ oo ids dt A4 ¼ PkT Lr Rs 0 0 X50 ¼ Vds Y50 ¼ Vqs A5 ¼ kT L r ðt X60 ¼ Vds dt ðt Y60 ¼ Vqs dt A6 ¼ kT R r ðt X70 ¼ oo Vqs dt ðt Y70 ¼ oo Vds dt A7 ¼ 0 0 0 ð8:32Þ PkT Lr 0 C1 ¼ 2P Rs 3 2J 0 ðt iqs ids dt ðt ðt C2 ¼ 2P 3 2J Z30 ¼ TL C3 ¼ 1 J Z40 ¼ oo C4 ¼ F J ðt Z10 ¼ ids iqs dt Z20 ¼ iqs Vds dt 0 0 ids Vqs dt 0 Note that only simple integral operators are involved when evaluating the variables X, Y and Z in Equation (8.32). Based on Equations (8.29)–(8.32), an improved ANN model for the induction motor is shown in Figure 8.10. For comparison in simulation studies, the ANN model in Figure 8.10 is packed in a Simulink block (ANN IM) and is connected in parallel with the conventional induction motor model (Figure 8.1), as shown in Figure 8.11. 216 Applied Intelligent Control of Induction Motor Drives Vds Eq. (8.30) Vqs Eq. (8.30) Figure 8.10 X'1 X'2 X'3 X'4 X'5 X'6 X'7 Y' 1 Y' 2 Y' 3 Y' 4 Y' 5 Y' 6 Y' 7 TL ids ∫ ANN1 Eq. (8.30) ∫ ANN2 ωo Z 1' Z 2' Z 3' Z 4' ANN4 ∫ iq ANN model of induction motor without involving double integrals. 3-phase 60Hz Signal Source SVPWM Inverter w Speed Vdq Scope1 T 20 N.m Load is Current Load Scope2 Induction Motor Speed V wo Scope3 Current TL is Scope4 ANN IM Figure 8.11 Neural network and conventional models of induction motor drive. A study of direct-on-line starting of the induction motor is made in order to compare the performance of the ANN model with the conventional model in predicting motor transient operation. At time t ¼ 0 the motor is at standstill with a constant load torque. Pertinent data for the simulation study are shown below: Parameters of the induction motor: listed under ‘Motor 1’ of Appendix B. Frequency of three-phase sinusoidal signal source ¼ 60 Hz 217 Parameter Estimation Using Neural Networks Amplitude of three-phase sinusoidal signal source ¼ 0.866 V Switching frequency of SVPWM ¼ 20 kHz Modulation index ¼ 0.866 Magnitude of the SVPWM output ¼ 300 V Load torque ¼ 20 N m The moment of inertia JL of the load ¼ 0.4 kg m2 Simulation type: Variable-step Max-step size ¼ 0.00002 s Simulation time ¼ 2 s. 140 140 120 120 Rotor speed ω 0 (rad/s) Rotor speed ω 0 (rad/s) The rotor speed computed from the conventional model is shown in Figure 8.12a and that computed from the ANN model is shown in Figure 8.12b. It is noticed that the ANN model gives similar motor run-up performance as the conventional model. 100 80 60 40 20 80 60 40 20 0 0 -20 100 0 0.5 1 Time (s) (a) Figure 8.12 1.5 2 -20 0 0.5 1 Time (s) 1.5 2 (b) Computed motor run-up performance: (a) Conventional model; (b) ANN model. The above comparison of the conventional model and the ANN model has shown that the ANN modeling approach is feasible. The ANN model can be established through proper training of the neural networks using the data acquired from a simulation model or from an actual motor drive. 8.6 Effect of Noise in Training Data on Estimated Parameters The data acquired in a practical inverter-fed induction motor drive will usually contain noise. In order to test the efficacy of the ANN-based model under such conditions, Gaussian white noise with various variance values is injected into the stator currents ids and iqs before the data samples are input to the neural networks for training. The two ‘Random Number’ blocks in Figure 8.8 are connected and added into the stator currents with various variances. Figure 8.13a shows the current waveform of ids without noise and Figure 8.13b shows the corresponding waveform when noise with a variance value of unity is present. From Table 8.2, it is noticed that the estimated mechanical parameters J and F are practically unaffected by noise. The error in Applied Intelligent Control of Induction Motor Drives 300 300 295 295 290 290 Stator current (A) Stator current (A) 218 285 280 275 270 265 260 285 280 275 270 265 0.285 0.2855 0.286 0.2865 0.287 0.2875 260 0.285 0.2855 0.286 0.2865 0.287 0.2875 Time (s) (a) Time (s) (b) Figure 8.13 Waveform of ids when motor is fed from an SVPWM inverter: (a) without noise; (b) noise variance equal to 1. the estimated electrical parameters, on the other hand, increases when the noise content increases. With a noise variance of unity, the estimated values of Ls, LR and RR are smaller than the ideal values by 6.1 %, 5.8 %, and 13.4 %, respectively, whereas the estimated value of Rs is larger than the ideal value by 8.4 %. The value of the estimated rotor resistance is therefore more sensitive to noise. Despite the errors in the individual estimated machine parameters, the ANN model gives satisfactory prediction of the speed response as reflected by the small rotor speed error shown in the right-most column of Table 8.2, where o0 and o01 are the rotor speed computed from the ANN model and the conventional model, respectively. 8.7 Estimation of Load, Flux and Speed Using the estimated parameters of the induction motor obtained in Section 8.5, load, stator flux, and rotor speed may be estimated, respectively. 8.7.1 Estimation of Load To estimate the load torque, Equation (8.6) is written as TL ¼ 2P ðlds iqs 32 lqs ids Þ J doo dt ð8:33Þ Foo Substituting Equations (8.7) and (8.8) into Equation (8.33), load torque TL may be estimated by the following equation. TL ðtÞ 0 t ð 2P @ Rs ids iqs dt TL ð0Þ ¼ 32 0 iqs ðt 0 0 t ð 2 P A @ iqs Vds dt ids dt þ 32 1 0 ðt 1 ids Vqs dtA J doo dt Foo 0 ð8:34Þ Error in parameter estimation when Noise is present in training data. Variance of noise Motor Parameters Estimated by ANN1 and ANN4 Ls (H) Rs (O) LR (H) RR (O) J (kg m2) F (N m s/rad) Steady-state (t ¼ 1.5 s) value of rotor speed oo (rad/s) 0.0424 0.0415 0.0410 0.0406 0.0402 0.0398 0.2940 0.3046 0.3092 0.3129 0.3161 0.3188 0.0446 0.0437 0.0432 0.0428 0.0424 0.0420 0.1667 0.1573 0.1531 0.1498 0.1470 0.1444 0.8000 0.7999 0.7998 0.7998 0.7998 0.7998 0.1000 0.1001 0.1002 0.1002 0.1003 0.1003 125.35 125.65 125.79 125.91 126.00 126.07 Electrical parameters 0 0.2 0.4 0.6 0.8 1 Rotor speed error (simulation time 02 s, speed range 0130 rad/s) Mechanical parameters Average error (t ¼ 02 s) of oo1 and oo 0.0201 0.5168 0.6998 0.8666 0.9942 1.1085 Parameter Estimation Using Neural Networks Table 8.2 n X 1. Rotor speed error E ¼ 1n joo oo1 j, where oo is rotor speed computed using the ANN model, oo1 is rotor speed computed using the conventional model, and n is sample number during 02 s. i¼1 2. Without current noise injection, steady-state (t ¼ 1.5 s) value of rotor speed using the conventional model, oo1 ¼ 125.335 rad/s. 219 220 Applied Intelligent Control of Induction Motor Drives With the motor parameters obtained in Section 8.4, the load torque of the induction motor may be calculated by Equation (8.34). A Simulink model of load estimation is shown in Figure 8.14. 3-phase 60Hz Signal Source SVPWM Inverter Rotor speed Torque Radom load Induction Motor estload To Workspace Wo Stator current butter idq Load Vdq Stator voltage Analog Filter Design Estimated load Load Estimation load To Workspace1 Figure 8.14 A Simulink model of load estimation. The model consists of the induction motor drive (Figure 8.1), a ‘Load Estimation’ block, and an ‘Analog Filter Design’ block in Simulink library. The ‘Load Estimation’ block is used to estimate the load torque based on Equation (8.34). The ‘Analog Filter Design’ block is used to reduce the differential noise in the estimated load and noise caused by the differential operation of rotor speed in Equation (8.34). The Simulink model of load estimation as shown in Figure 8.14 is run with the following parameters. Parameters of the induction motor: listed under ‘Motor 1’ of Appendix B. Frequency of three-phase sinusoidal signal source ¼ 60 Hz Amplitude of three-phase sinusoidal signal source ¼ 0.866 V Switching frequency of SVPWM ¼ 20 kHz Modulation index ¼ 0.866 Magnitude of the SVPWM output ¼ 300 V The moment of inertia JL of the load ¼ 0.4 kg m2 Simulation type: Variable-step Max-step size ¼ 0.00002 s Simulation time ¼ 0.4 s 221 Parameter Estimation Using Neural Networks With a desired passband frequency of 500 Hz (3142 rad/s), the ‘Analog Filter Design’ block has following parameters. Design method: Butterworth Filter type: Lowpass Filter order ¼ 1 Passband edge frequency (rad/s) ¼ 3142 rad/s 30 30 25 25 20 20 Load (N.m) Load (N.m) The simulation results are shown in Figure 8.15 and two arrays ‘load’ and ‘Est_load’ are stored in MATLABÒ workspace at the end of the simulation. 15 10 5 0 15 10 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) (a) Actual load Figure 8.15 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) (b) Estimated load Actual load and estimated load from simulation; (a) Actual load; (b) Estimated load. Mean square error between the actual load torque and the estimated load torque may be calculated by error ¼ n 1X ðload n 1 estloadÞ2 ð8:35Þ where n is the number of data samples. The following MATLABÒ code is used to calculate the mean square error between the actual load torque and the estimated load torque: s = size(load); %Acquire sample number e = 0; for i = 1:s(1) e = e + (load(i)-Est_load(i))^2; end error = e/s(1) %Yield mean square error 222 Applied Intelligent Control of Induction Motor Drives The calculation result shows that the mean square error of actual load and estimated load is 0.0153 with 155 276 samples taken in 0.4 s. When measurement noise with variance of 1 A and mean of 0 A are added into the measured stator currents ids and iqs, the mean square error of actual load and estimated load is 0.1503 with 155 239 samples taken in 0.4 s. The simulation result is shown in Figure 8.16. 30 25 Load (N.m) 20 15 10 5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 8.16 8.7.2 Estimated load with noise. Estimation of Stator Flux To estimate the stator flux, Equations (8.2) and (8.3) are written in the following concise forms: Aa lds þ Ba lqs ¼ Ca ð8:36Þ Ab lds þ Bb lqs ¼ Cb ð8:37Þ where Aa ¼ k T Rr Ba ¼ Poo kT Lr Poo iqs kT Lr Vds dids dt Cb ¼ kT ðRr Ls þ Lr Rs Þiqs þ Poo ids kT Lr Vqs diqs dt Ca ¼ kT ðRr Ls þ Lr Rs Þids Ab ¼ Poo kT Lr Bb ¼ k T Rr 223 Parameter Estimation Using Neural Networks Because Bb ¼ Aa and Ab ¼ Ba, Equations (8.36) and (8.37) may be written as " #" A a Ba Ba A a V lqs # ¼ " Ca Cb # ð8:38Þ : The stator flux in Equation (3.38) is solved as follows: " lds lqs # 3 Aa Ca Ba Cb 6 A2a þ B2a 7 6 7 ¼6 7: 4 Ba Ca þ Aa Cb 5 2 ð8:39Þ A2a þ B2a From Equation (8.12), the elements in Equation (8.39) are as follows: Aa ¼ Ba ¼ A6 ð8:40Þ A7 oo ð8:41Þ Ca ¼ A1 ids þ A2 oo iqs þ A5 Vds dids dt ð8:42Þ Cb ¼ A1 iqs diqs dt ð8:43Þ A2 oo ids þ A5 Vqs The following values are obtained from Equation (8.26), A1 ¼ 216:7 A2 ¼ 3 A5 ¼ 478:9 A6 ¼ 1791:5 A7 ¼ 1436:6 The elements in Equation (8.39) may be expressed as follows. Aa ¼ Ba ¼ Ca ¼ 216:7ids 1791:5 ð8:44Þ 1436:6oo ð8:45Þ 3oo iqs þ 478:9 Vds dids dt ð8:46Þ 224 Applied Intelligent Control of Induction Motor Drives Cb ¼ 216:7iqs þ 3oo ids þ 478:9 Vqs diqs dt ð8:47Þ Based on Equation (8.39), a Simulink model for estimating stator flux is built as shown in Figure 8.17. 3-phase 60Hz Speed Signal Source SVPWM Inverter Scope Torque Scope1 20 N.m Load Fds Induction Motor conventional Flux calculate To Workspace1 Fqs To Workspace2 Est_Fds is uds To Workspace3 uqs Est_Fqs Vs Wo Flux Estimation Figure 8.17 To Workspace4 Simulink model of stator flux estimation. The Simulink model consists of the induction motor drive as shown in Figure 8.1, a ‘Flux calculate’ block and a ‘Flux Estimation’ block. The ‘Flux calculate’ block performs a conventional flux estimation based on Equations (8.7) and (8.8). The ‘Flux Estimation’ block performs the differential flux estimation based on Equation (8.39). Stator flux vector (lds, lqs) yielded by the conventional flux estimation method and flux vector (^lds, ^lqs) yielded by the differential flux estimation method are stored into MATLABÒ workspace with four arrays named ‘Fds,’ ‘Fqs,’ ‘Est_Fds,’ and ‘Est_Fqs,’ respectively. Due to the SVPWM inverter and the differential operations of dq-axis stator currents in Equations (8.50) and (8.51), four low-pass filters are used to reduce ripples of input (Vds, Vqs, ids, iqs) caused by the PWM inverter and two output low-pass filters are used to reduce the ripples of output (^lds, ^lqs) caused by the differential operations. The six filters are simulated by ‘Analog Filter Design’ block in Simulink library and they are set inside of the ‘Flux Estimation’ block in Figure 8.17. 225 Parameter Estimation Using Neural Networks The Simulink model of stator flux estimation in Figure 8.17 is run with following parameters. Parameters of the induction motor are listed under ‘Motor 1’ of Appendix B. Frequency of three-phase sinusoidal signal source is 60 Hz Amplitude of three-phase sinusoidal signal source is 0.866 V Switching frequency of SVPWM is 20 kHz Modulation index is 0.866 Magnitude of the SVPWM output is 300 V Load ¼ 20 N m The moment of inertia JL of the load is 0.4 kg m2 Simulation type: Variable-step Max-step size ¼ 0.00002 s Simulation time ¼ 0.4 s With a desired passband frequency of 500 Hz (3142 rad/s), the six ‘Analog Filter Design’ blocks in the ‘Flux Estimation’ block have following parameters. Design method: Butterworth Filter type: Lowpass Filter order ¼ 1 Passband edge frequency (rad/s) ¼ 3142 rad/s 0.8 1 0.6 0.8 0.4 0.6 Flux λ qs (Wb) Flux λ ds (Wb) The simulation results are shown in Figure 8.18 and Figure 8.19 and the four arrays ‘uds,’ ‘uqs,’ ‘Est_uds,’ and ‘Est_uqs’ are stored in MATLABÒ workspace after the simulation run. 0.2 0 -0.2 0.4 0.2 0 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) (a) Flux λ ds of conventional estimation 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) (b) Flux λ qs of conventional estimation Figure 8.18 Flux vector components lds and lqs of conventional estimation method; (a) Flux lds of conventional estimation; (b) Flux lqs of conventional estimation. With the two arrays ‘Fds’ and ‘Est_Fds’ in MATLABÒ workspace, the following MATLABÒ program is used to calculate the mean square error of direct-axis flux obtained by the conventional estimation method and the differential estimation method: 226 Applied Intelligent Control of Induction Motor Drives 0.8 1 0.6 0.8 0.4 0.6 Flux λ qs (Wb) Flux λ ds (Wb) s = size(Fds); %Acquire sample number e = 0; for i = 1:s(1) e = e + (Fds(i)-Est_Fds(i))^2; end error = e/s(1) %Yield mean square error 0.2 0 -0.2 0.4 0.2 0 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) (a) Flux λ ds of differential estimation 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) (b) Flux λ qs of differential estimation Figure 8.19 Flux vector components ^lds and ^lqs of differential estimation method; (a) Flux ^lds of differential estimation; (b) Flux ^lqs of differential estimation. The computed result shows that the mean square error of direct-axis flux is 0.0016 with 289 274 samples during 0.4 s. In a similar manner, the following MATLABÒ program is used to calculate the mean square error of quadrature-axis flux obttained from the conventional estimation method and the differential estimation method: s ;= size(Fqs); %Acquire sample number e = 0; for i = 1:s(1) e = e+ (Fqs(i)-Est_Fqs(i))^2; end error = e/s(1) %Yield mean square error The computed result shows that the mean square error of quadrature-axis flux is also 0.0016 with 289 274 samples during 0.4 s. The differential estimation method does not suffer from error accumulation caused by integrators in conventional flux estimation (Shi et al., 1999). 8.7.3 Estimation of Rotor Speed Using the estimated parameters of the induction motor obtained in Section 8.5, we can also estimate the rotor speed. 227 Parameter Estimation Using Neural Networks With lds(0) ¼ 0, lqs(0) ¼ 0, substitution of Equations (8.7) and (8.8) into Equations (8.2) and (8.3) separately enables the following equations to be derived: dids ¼ kT ðRr Ls þ Lr Rs Þids dt ðt ðt Poo iqs þ kT Rr Rs ids dt þ PkT Lr Rs oo iqs dt 0 kT Lr Vds ðt kT Rr Vds dt 0 ðt ðt PkT Lr Rs oo ids dt kT Rr Vqs dt þ PkT Lr oo Vds dt ðt oo @PkT Lr Vqs dt þ Piqs 0 ðt 0 ðt 1 PkT Lr Rs iqs dtA ¼ 0 ðt PkT Lr Vds dt 0 kT Lr Vqs ðt dids dt ðt diqs dt kT Rr Vds dt þ kT ðLs Rr þ Lr Rs Þids þ kT Rr Rs ids dt 0 oo @ 0 ðt 0 0 ð8:49Þ ðt 0 kT Lr Vds ; 0 ðt diqs ¼ kT ðRr Ls þ Lr Rs Þiqs þ Poo ids þ kT Rr Rs iqs dt dt 0 ð8:48Þ PkT Lr oo Vqs dt 0 kT Lr Vqs ; ðt : ð8:51Þ 1 Pids þ PkT Lr Rs oo ids dtA ¼ kT Rr Vqs dt þ kT ðLs Rr þ Lr Rs Þiqs þ kT Rr Rs iqs dt 0 ð8:50Þ 0 0 ðt ; 0 For convenience, the above integral equations may be written in the following concise forms. oo ð A7 X1 A2 X 2 A4 X3 Þ ¼ A 5 X4 þ A6 X5 þ A 1 X6 þ A3 X7 þ A8 X8 oo ðA7 Y1 þ A2 Y2 þ A4 Y3 Þ ¼ A5 Y4 þ A6 Y5 þ A1 Y6 þ A3 Y7 þ A8 Y8 ð8:52Þ ð8:53Þ 228 Applied Intelligent Control of Induction Motor Drives where ðt X1 ¼ Vqs dt ðt Y1 ¼ Vds dt A7 ¼ 0 X2 ¼ iqs ðt X3 ¼ iqs dt 0 Y2 ¼ ids ðt Y3 ¼ ids dt ðt X5 ¼ Vds dt Y4 ¼ Vqs kT Lr ð8:54Þ k T Rr 0 Y6 ¼ iqs Y7 ¼ iqs dt dids dt Y8 ¼ 0 X8 ¼ A5 ¼ Y5 ¼ Vqs dt A6 ¼ ðt X7 ¼ ids dt P A4 ¼ PkT Lr Rs ðt 0 X6 ¼ ids A2 ¼ 0 0 X4 ¼ Vds PkT Lr A1 ¼ kT ðRr Ls þ Lr Rs Þ ðt A3 ¼ k T R r Rs diqs dt A8 ¼ 0 1 Equations (8.52) and (8.53) are functions of the rotor speed and these may further be written as: oo Da ¼ Db ð8:55Þ oo Qa ¼ Qb ð8:56Þ where Da ¼ A 7 X1 A2 X2 A 4 X3 Db ¼ A5 X4 þ A6 X5 þ A1 X6 þ A3 X7 þ A8 X8 : Qa ¼ A7 Y1 þ A2 Y2 þ A4 Y3 ð8:57Þ Qb ¼ A5 Y4 þ A6 Y5 þ A1 Y6 þ A3 Y7 þ A8 Y8 From Equations (8.49) and (8.50), it is seen that Da and Qb are q-axis sinusoidal variables, whereas Qa and Db are d-axis sinusoidal variables. From Equations (8.55) and (8.56), oo ¼ Db Da and oo ¼ Qb Qa. However, they cannot be used to estimate the rotor speed directly because the sinusoidal variables Da and Qa may equal zero. In orderp toﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ avoid division by zero, the pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ magnitudes of the sinusoidal variables Da2 þ Qa2 and Db2 þ Qb2 are employed for estimation of the rotor speed. 229 Parameter Estimation Using Neural Networks Squaring Equations (8.55) and (8.56) adding the resulting equations, o2o ðDa2 þ Qa2 Þ ¼ ðDb2 þ Qb2 Þ ð8:58Þ Equation (8.58) can thus be written as follows: pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Da2 þ Qa2 ¼ Db2 þ Qb2 ð8:59Þ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ where Da2 þ Qa2 is magnitude of the q-axis sinusoidal variables and Db2 þ Qb2 is magnitude of the d-axis sinusoidal variables. When magnitude of the sinusoidal variables is larger than zero, the rotor speed may be estimated by oo pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Db2 þ Qb2 oo ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ : Da2 þ Qa2 ð8:60Þ Finally, substitution of Equations (8.57) into (8.60) gives the following equation: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðA5 X4 þ A6 X5 þ A1 X6 þ A3 X7 þ A8 X8 Þ2 þ ðA5 Y4 þ A6 Y5 þ A1 Y6 þ A3 Y7 þ A8 Y8 Þ2 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ oo ¼ ð A7 X1 A2 X2 A4 X3 Þ2 þ ðA7 Y1 þ A2 Y2 þ A4 Y3 Þ2 ð8:61Þ With the value of the matrix [A] obtained in Equation (8.26), Equation (8.61) may be used to estimate the rotor speed. A Simulink model of rotor speed estimation is built as shown in Figure 8.20. 3-phase 60Hz Signal Source SVPWM Inverter w Speed Speed Vdq To Workspace1 T 20 N.m Load Load is Induction Motor is Est_Speed wo Vs To Workspace2 Speed Estimation Figure 8.20 Simulink model of rotor speed estimation. The Simulink model consists of the induction motor block (Figure 8.1) and a ‘Speed Estimation’ block. The ‘Speed Estimation’ block is used to estimate the rotor speed according 230 Applied Intelligent Control of Induction Motor Drives to Equation (8.61). The ‘To Workspace1’ and ‘To Workspace2’ blocks in Figure 8.20 are used to store the actual rotor speed and the estimated speed into MATLABÒ workspace with the two arrays ‘Speed’ and ‘Est_Speed,’ respectively. Four low-pass filters are used to reduce ripples of inputs (Vds, Vqs, ids, iqs) caused by the SVPWM inverter (Equations (8.50) and (8.51)) and one output low-pass filter is used to reduce the ripples of the output oo. These five filters are simulated by ‘Analog Filter Design’ blocks in Simulink library and they are set inside of the ‘Speed Estimation’ block in Figure 8.20. The Simulink model of rotor speed estimation in Figure 8.20 is run with following parameters. Parameters of the induction motor are listed under ‘Motor 1’ of Appendix B. Frequency of three-phase sinusoidal signal source is 60 Hz Amplitude of three-phase sinusoidal signal source is 0.866 V Switching frequency of SVPWM is 20 kHz Modulation index is 0.866 Magnitude of the SVPWM output is 300 V Torque ¼ 20 N m The moment of inertia JL of the load is 0.4 kg m2 Simulation type: Variable-step Max-step size ¼ 0.000001 s Simulation time ¼ 1.5 s When the desired passband frequency is 500 Hz (3142 rad/s), the five ‘Analog Filter Design’ blocks have the following parameters: Design method: Butterworth Filter type: Lowpass Filter order ¼ 1 Passband edge frequency (rad/s) ¼ 3142 rad/s The simulation results are shown in Figure 8.21 and the two arrays ‘Speed’ and ‘Est_Speed’ are stored in MATLABÒ workspace. With the two arrays ‘Speed’ and ‘Est_Speed’ in MATLABÒ workspace, the following MATLABÒ program is used to calculate the mean square error between the actual rotor speed and the estimated speed. s = size(Speed); %Acquire sample number e = 0; for i = 1:s(1) e = e + (Speed(i)-Est_Speed(i))^2; end error = e/s(1) %Yield mean square error The result shows that the mean square error of the actual rotor speed the and estimated speed is 0.0132 with 1 908 527 samples during 1.5 s. The simulation results demonstrate that the rotor speed estimation method has a wide estimation range even near zero speed and the estimation error is small. However, the 231 140 140 120 120 Rotor speed (rad/s) Rotor speed (rad/s) Parameter Estimation Using Neural Networks 100 80 60 40 20 0 100 80 60 40 20 0 0.5 1 1.5 0 0 Time (s) (a) Actual rotor speed Figure 8.21 0.5 1 Time (s) (b) Estimated speed 1.5 Simulation result of rotor speed estimation; (a) Actual rotor speed; (b) Estimated speed. estimation method yields only absolute value of the rotor speed. Using the model of rotor speed estimation, a sensorless FOC will be given in next section. 8.8 MATLABÒ/Simulink Programming Examples In this section, two examples are given to illustrate programming of a field-oriented control (FOC) system and sensorless control of induction motor using MATLABÒ/Simulink. 8.8.1 Programming Example 1: Field-Oriented Control (FOC) System Field-oriented control (FOC) is a vector control method as both the magnitude and the phase of current and voltage vectors are regulated. Using field-oriented control, an induction motor drive can be made to exhibit satisfactory torque and speed responses because both the flux magnitude and the torque are controlled to desired values. A Simulink model of field-oriented control system of induction motor is built with following steps. Step 1 Building a Flux Estimation Model With the given value of stator resistance Rs (0.294 O in this example) and based on Equation (8.7), Equation (8.8), and Cartesian to polar transformation block, a Simulink model of flux estimation is built as shown in Figure 8.22. 1 Mag vs 2 2 is 0.294 1/s em Ang 1 Rs Cartesian to Polar Figure 8.22 Simulink model of flux estimation. 232 Applied Intelligent Control of Induction Motor Drives In the flux estimation model, the inputs are the dq-axis stator voltage vector and dq-axis stator current vector; while the output is magnitude and angle of dq-axis flux vector. Step 2 Building a Field-Oriented Control System Model A Simulink model of field-oriented control (FOC) system is shown in Figure 8.23. The field-oriented control system model consists of a ‘Speed ’ block, a ‘Flux ’ block, four ‘PI’ blocks, a ‘Park(for)’ block, a ‘Park(rev)’ block, a ‘Flux calculation’ block, an ‘IM’ block, and a ‘Load’ block. Flux* Load PI PI Torque Vds ids* PI IM iqs* Vqs PI Park (rev) SVM Speed* Vs ids |Flux| iqs Park (for) is Wo Flux calculate |Flux| Figure 8.23 Simulink model of field-oriented control system. The ‘IM’ block is a voltage-input induction motor model described in Section 3.4 and programmed in Section 6.8.1. The ‘Park(for)’ and ‘park(rev)’ blocks are Park’s transformation expressed in Equations (3.2) and (3.3). The programming of Park’s transformation is described in Section 3.8. The ‘Flux calculate’ block is built in Step 1. The ‘SVM’ block simulates a space vector PWM inverter which is given on the book companion website. The ‘Speed ’ block employs a ‘Repeating Sequence’ block in Simulink library. Pertinent details of these blocks, including their functions and programming references, are summarized in Table 8.3. Table 8.3 Function and parameters of the blocks in field-oriented control system. Block Name Function Programming References IM Voltage-input model of induction motor Park’s transformation Park’s inverse transformation Estimation of stator flux space vector PWM inverter Rotor speed command Section 3.4 and Section 6.8.1 Park(for) Park(rev) Flux calculate SVM Speed Flux Load PI Stator flux command Load of rotor Control rotor speed, stator flux, stator currents Equation (3.2), Section 3.8 Equation (3.3), Section 3.8 Step 1, Equations (8.7) and (8.8) Book companion website ‘Repeating Sequence’ block in Simulink library ‘Step’ block in Simulink library ‘Step’ block in Simulink library ‘PID’ block in Simulink library 233 Parameter Estimation Using Neural Networks Step 3 Running the Simulink Model of Field-Oriented Controller with Parameter Set The parameters of the motor are listed in Section 8.4.3. The flux command employs a ‘Step’ block with following stator flux commands. s l * ¼ 0:86 Wb 0 s < t 2 s m The following parameters are input into the ‘Step’ block. Step time ¼ 0 Initial value ¼ 0 Final value ¼ 0.86 The speed command employed the ‘Repeating Sequence’ block with following speed commands. oo * ¼ 0 rad=s 0 s < t 0:1 s Building flux stage oo * ¼ 0 50 rad=s 0:1 s < t 0:65 s Speed ramp rise stage oo * ¼ 50 rad=s 0:65 s < t 1 s Steady-state stage oo * ¼ 50 20 rad=s 1 s < t 1:5 s Speed ramp fall stage oo * ¼ 20 rad=s Steady-state stage 1:5 s < t 2 s The following parameters are entered into the ‘Repeating Sequence’ block. Time values ¼ ½0 0:1 0:65 0:65 1 1:5 2 Output values ¼ ½0 0 50 50 50 20 20 The 20 N m load employs a ‘Step’ block with following parameters. Step time ¼ 0.1 Initial value ¼ 0 Final value ¼ 20 The parameters of the four PI controllers are listed in Table 8.4. The parameters of the flux PI controller and the current ids PI controller are first tuned to guarantee that the magnitude of flux of the motor reaches the flux command value when the speed command equals zero. In this example, the speed command equals zero before 0.1 s during which the flux is building up. From 0.1 s onwards, the flux is controlled. The variation of the stator flux from 0 s to 0.4 s is shown in Figure 8.24. The parameters of the speed PI controller and the current iqs PI controller are next tuned to guarantee a good torque response. The Simulink model of field-oriented control system shown in Figure 8.23 is run with the following parameters. Switching frequency of SVPWM ¼ 20 kHz Magnitude of the SVPWM output ¼ 300 V 234 Applied Intelligent Control of Induction Motor Drives Load ¼ 20 N m Simulation type: Variable-step Max-step size ¼ 0.000001 s Simulation time ¼ 2 s Table 8.4 Parameters of the four PI controllers. Output Flux PI controller Speed PI controller Current ids PI controller Current iqs PI controller Error of magnitude of flux command and estimated flux Error of speed command and rotor speed Error of current ids reference and measured current ids Error of current iqs reference and measured current iqs current ids reference current iqs reference Stator voltage Vds Stator voltage Vqs 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Flux magnitude (Wb) Input Flux magnitude (Wb) Name 0 0.02 Figure 8.24 0.04 0.06 Time (s) 0.08 0.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Proportional Integral 400 1000 800 100 1 10 80 100 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Stator flux build-up during 0 0.1 s and controlled during 0.1 0.4 s. The simulation results are shown in Figures 8.25 and 8.26. 8.8.2 Programming Example 2: Sensorless Control of Induction Motor By connecting the estimator of rotor speed described in Section 8.7.3 to the field-oriented control system in programming example 1, sensorless control of the induction motor may be simulated. Step 1 Building the Model of a Sensorless Control System A Simulink model of sensorless control of induction motor is built by a ‘Speed Estimation’ block and the field-oriented control system described in the programming example 1 as shown in Figure 8.27. 235 Parameter Estimation Using Neural Networks 100 Torque (N.m) 80 60 40 20 0 -20 -40 0 0.5 1 1.5 2 Time (s) Figure 8.25 Torque of field-oriented control system. 60 Rotor speed (rad/s) 50 40 30 20 10 0 -10 0 0.5 1 1.5 2 Time (s) Figure 8.26 Rotor speed of field-oriented control system. Step 2 Building Sub-models Da, Db, Qa and Qb in the ‘Speed Estimation’ Block Simulink models of Da, Db, Qa, and Qb in the ‘Speed Estimation’ block are built based on Equation (8.57), using the values of A1 to A7 obtained from Equation (8.26) and the value of A8 obtained from Equation (8.54). The models are shown in Figures 8.28–8.31. Step 3 Building the Speed Estimation Model With the models of Da, Db, Qa, and Qb developed in Step 2, the speed estimation model is built as shown in Figure 8.32. 236 Applied Intelligent Control of Induction Motor Drives Flux* Load PI PI Torque Vds ids* PI iqs* IM Park (rev) Vqs PI SVM Speed* Speed Vs Wo is ids |Flux| Park (for) iqs Flux calculate Vs wo is Est_Speed Speed Estimation To Workspace Figure 8.27 Simulink model of sensorless control of induction motor. -A7 1 -A7*X1 1 s -K- Vqs -A2 2 -A2*X2 3 1 Da iqs -A4 -K- Figure 8.28 -A4*X3 1 s Simulink model of Da. A5 1 Vds A5*X4 -K- A6 -K- 1 s A1 2 ids A6*X5 A1*X6 -K- 1 Db A3 -K- 1 s A8 -1 du/dt A3*X7 A8*X8 Sum Figure 8.29 Simulink model of Db. To Workspace1 237 Parameter Estimation Using Neural Networks A7 1 A7*Y1 1 s -K- Vds A2 A2*Y2 -3 2 1 Qa ids A4 A4*Y3 1 s -K- Figure 8.30 Simulink model of Qa. A5 1 Vqs A5*Y4 -KA6 1 s -KA1 2 iqs A6*Y5 A1*Y6 -K- 1 Qb A3 -K- 1 s A8 -1 du/dt A3*Y7 A8*Y8 Sum Figure 8.31 Simulink model of Qb. Filter 1 butter Vds Db 1 Vs em ids Filter 2 butter Vqs Qb butter iqs butter f(u) 2 is em Filter 3 1 Vqs Da butter iqs Filter 4 Vds Fcn Switch Clock Qa ids 0 Constant Figure 8.32 Speed estimation model. Filter 5 wo 238 Applied Intelligent Control of Induction Motor Drives The speed estimation model consists of five filter blocks which employ ‘Analog Filter Design’ block in Simulink library, blocks of Da, Db, Qa, and Qb built in Step 2, a ‘Fcn’ block in Simulink library to implement Equation (8.60) with parameters, (sqrt(u(1)^2 þ u(2)^2))/ sqrt(u(3)^2 þ u(4)^2), a ‘Switch’ block in Simulink library, a ‘Clock’ block in Simulink library, and a ‘Constant’ block in Simulink library. The last three blocks are used to avoid output estimated speed when time is less than 0.1 s. while the speed command equals zero before 0.1 s which is flux setup time. Value of the ‘Constant’ block is 0 and threshold value of the ‘Switch’ block is 0.1. Five analog low-pass Butterworth filters are employed to filter noises of input stator current (ids,iqs), stator voltage, (Vds, Vqs), and estimated speed (oo). With a desired frequency passband of 500 Hz (3142 rad/s), the five filters have the following parameters. Design method: Butterworth Filter type: Lowpass Filter order ¼ 1 Passband edge frequency (rad/s) ¼ 3142 rad/s The above parameters are input into the five ‘Analog Filter Design’ blocks in Figure 8.33. Step 4 Building the Induction Motor Drive Model with Sensorless Control With the Simulink model of field-oriented control system built in the example 1 and the Simulink model of speed estimation built in Step 3, a Simulink model of sensorless control of induction motor is built as shown in Figure 8.32. With the two ‘To Workspace’ blocks in Figure 8.33, realistic rotor speed and estimated rotor speed may be stored into MATLABÒ workspace with two arrays named ‘Speed’ and ‘Est_Speed,’ respectively. Flux* PI PI Load Vds ids* Torque PI iqs* PI Park (rev) Vqs IM SVM Speed* Speed Vs ids |Flux| iqs Park (for) is Wo To Workspace1 Flux calculate Vs wo Est_Speed To Workspace Figure 8.33 is Speed Estimation Simulink model of sensorless control of induction motor. 239 Parameter Estimation Using Neural Networks Step 5 Running the Simulation Model The Simulink model of sensorless control of induction motor shown in Figure 8.33 is run with same parameters as in Step 3 of example 1, but the simulation time is changed to 1 s. Since speed estimation is implemented, the loop gains of the FOC drive are different from those in example 1, as listed in Table 8.5. Using these adjusted parameters for the PI controllers, the FOC sensorless drive is able to give satisfactory performance. Table 8.5 Parameters of the four PI controllers. Name Input Output Flux PI controller Error of magnitude of flux command and estimated flux Error of speed command and rotor speed Error of current ids reference and measured current ids Error of current iqs reference and measured current iqs Speed PI controller Current ids PI controller Current iqs PI controller Proportional Integral current ids reference 600 1000 current iqs reference 200 400 Stator voltage Vds 1 100 Stator voltage Vqs 50 1000 The simulation results are shown in Figures 8.34 and 8.35. The two arrays ‘Speed’ and ‘Est_Speed’ are stored in MATLABÒ workspace, after the simulation. 100 90 80 Torque (N.m) 70 60 50 40 30 20 10 0 -10 0 0.2 0.4 0.6 0.8 Time (s) Figure 8.34 Torque of the sensorless control system. 1 Applied Intelligent Control of Induction Motor Drives 60 60 50 50 40 40 Rotor speed (rad/s) Rotor speed (rad/s) 240 30 20 10 30 20 10 0 0 -10 -10 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 Time (s) Time (s) (a) (b) 0.8 1 Figure 8.35 (a) Rotor speed of the sensorless control system; (b) Estimated speed used to control the induction motor. With the two arrays ‘Speed’ and ‘Est_Speed’ in MATLABÒ workspace, the following MATLABÒ program is used to calculate the mean square error between the actual rotor speed and the estimated speed. s = size(Speed); %Acquire sample number e = 0; for i = 1:s(1) e = e + (Speed(i)-Est_Speed(i))^2; end error = e/s(1) %Yield mean square error The result shows that the mean square error of actual rotor speed and estimated speed is 0.0019 with 1 224 441 samples during 1 s. 8.9 Summary The chapter describes an integral model for the induction motor which can be implemented conveniently using artificial neural networks. In the integral model, all the variables are directly measurable from the actual machine. The coefficients of the integral equations may be obtained by proper training of the linear neural networks and a realistic simulation model of the induction motor may be constructed. With the estimated coefficients of the integral equations, load, stator flux, and rotor speed of an induction motor may be estimated. Sensorless control of induction motor is given as a programming example. The simplicity of the neural network structure implies that implementation of online parameter identification is possible based on a general digital signal processor (DSP) technique, in which case the algorithm of network training should be written into the processor for online training. Simulation studies on a typical induction motor have confirmed the validity of the ANNbased integral model. Parameter Estimation Using Neural Networks 241 References Attaianese, C., Damiano, A., Gatto, G., et al. (1998) Induction motor drive parameters identification. IEEE Transactions on Power Electronics, 13(6), 1112–1122. Bose, B.K., and Patel, N.R., (1998) Quasi-fuzzy estimation of stator resistance of induction motor. IEEE Transactions on Power Electronics, 13(6), 401–409. de Souza Ribeiro, L.A., Jacobina, C.B., Lima, A.M.N., and Oliveira, A.C., (2000) Real-time estimation of the electric parameters of an induction machine using sinusoidal PWM voltage waveforms. IEEE Transactions on Industry Applications, 36(3), 743–754. The MathWorks Inc. (2008). Neural Network Toolbox User’s Guide. The MathWorks Inc. Moon, S., and Keyhani, A., (1994) Estimation of induction machine parameters from standstill time-domain data. IEEE Transactions on Industry Applications, 30(6), 1609–1615. Pillay, P., Nolan, R., and Haque, T., (1997) Application of genetic algorithms to motor parameter determination for transient torque calculations. IEEE Transactions on Industry Applications, 33(5), 1273–1282. Shi, K.L., Chan, T.F., Wong, Y.K., and Ho, S.L., (1999) A new acceleration control scheme for an inverter-fed induction motor. Electric Machines and Power Systems, 27(5), 527–541. Slemon, G.R., (1989) Modelling of induction machine for electric drives. IEEE Transactions on Industry Applications, 25(6), 1126–1131. Stephan, J., Bodson, M., and Chiasson, J., (1994) Real-time estimation of the parameters and flux of induction motors. IEEE Transaction on Industry Applications, 30(3), 746–759. Wishart, M.T., and Harley, R.G., (1995) Identification and control of induction machines using artificial neural networks. IEEE Transactions on Industry Applications, 31(3), 612–619. Zai, Li-Cheng, DeMarco, C.L., and Lipo, T.A., (1992) An extended kalman filter approach to rotor time constant measurement in pwm induction motor drives. IEEE Transactions on Industry Applications, 28(1), 96–104. Zamora, J.L., and Garcia-Cerrada, A., (2000) Online estimation of the stator parameters in an induction motor using only voltage and current measurements. IEEE Transactions on Industry Applications, 36(3), 805–816. 9 GA-Optimized Extended Kalman Filter for Speed Estimation1 9.1 Introduction Elimination of the speed sensor and measurement cables results in a lower cost and increased reliability of an induction motor drive system. Hence, in recent years, speed estimation methods have aroused great interest among induction motor control researchers. Kalman filter is a special kind of observer which provides optimal filtering of the noises in measurement and inside the system if the covariances of these noises are known. When rotor speed (as an extended state) is added into the dynamic model of an induction motor, the extended Kalman filter (EKF) can be used to re-linearize the nonlinear state model for each new estimate as it becomes available. Recently, some advances have been obtained for the extended Kalman filter of induction motor drives (Henneberger, Brunsbach and Klepsch, 1996; Kim, Sul and Park, 1996; Salvatore, Stasi and Tarchioni, 1993; Texas Instruments Incorporated, 1997) and the extended Kalman filter has been considered to be the best solution for the speed estimation of induction motor (Manes, Parasiliti and Tursini, 1994). However, these extended Kalman filters do not yield the best drive performance, due to the fact that the correct noise matrices cannot be obtained from traditional theories. The noise matrices are usually tuned experimentally using a trial-and-error method (Manes, Parasiliti and Tursini, 1994; Bolognani, Oboe and Zigliotto, 1999). In this chapter, a real-coded GA method (Goldberg, 1989; Wright, 1991) is used to optimize the noise matrices for improving the EKF performance. Simulation studies are carried out on a closed-loop V/Hz controller, a sensorless direct self controller (DSC), and a field-oriented controller (FOC) and the effects of stator current noise and machine parameter changes are investigated. 1 (a) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of induction motor using extended Kalman filter,” IEEE 2000 Winter Meeting, vol. 1, pp. 243–248, January 23–27, 2000, Singapore. Ó 2000 IEEE. (b) Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. Ó 2002 IEEE. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 244 9.2 Applied Intelligent Control of Induction Motor Drives Extended State Model of Induction Motor A dynamic electrical model for a three-phase induction motor has four state variables, namely the stator currents (ids, iqs) and the rotor fluxes (ldr, lqr). An extended induction motor model results if the rotor speed is included as an extended state variable. The extended model can be expressed as follows (Lewis, 1992): x_ ¼ Ax þ Bu þ GðtÞwðtÞ ðSystemÞ ð9:1Þ y ¼ Cx þ vðtÞ ðMeasurementÞ ð9:2Þ where 2 ðnÞ 3 ids 6 6 ðnÞ 6 iqs 6 6 ðnÞ xn ¼ 6 6 ldr 6 6 ðnÞ 6 lqr 4 ðnÞ oo 7 7 7 7 7 7; 7 7 7 7 5 2 Kr M 61 Kl 6 6 6 6 6 0 6 6 6 An ¼ 6 L 6 MM 6 6 tr 6 6 6 0 6 4 2 yn ¼ 4 0 1 Kr M Kl 0 0 ðnÞ ids ðnÞ iqs 3 2 5; un ¼ 4 ðnÞ LM Rr M L2r Kl P ðnÞ o M 2 o 1 M tr P ðnÞ o M 2 o 0 0 5; PLM oo M 2Lr Kl PLM oo M 2Lr Kl LM M tr ðnÞ Vqs 3 ðnÞ LM Rr M L2r Kl 1 ðnÞ Vds 1 1 M tr 0 M 6 Kl 6 6 6 60 6 Bn ¼ 6 6 60 6 6 60 4 0 3 07 7 7 M7 " 7 1 0 Kl 7 7; Cn ¼ 7 0 1 07 7 7 07 5 0 0 0 0 0 0 0 07 7 7 7 7 07 7 7 7 7; 07 7 7 7 7 7 07 5 1 where tr ¼ Lr =Rr , Kr ¼ Rs þ L2M Rr =L2r and Kl ¼ ð1 L2M =Lr =Ls Þ*Ls . 2 3 # ; 245 GA-Optimized Extended Kalman Filter for Speed Estimation In Equations (9.1) and (9.2), G(t) is the noise-weight matrix, w(t) is noise matrix of state model (system noise), and v(t) is noise matrix of output model (measurement noise). The covariance matrices Q and R of these noises are defined as: Q ¼ covðwÞ ¼ Efwwt g ð9:3Þ R ¼ covðvÞ ¼ Efvvt g ð9:4Þ where E{} denotes the expected value. 9.3 Extended Kalman Filter Algorithm for Rotor Speed Estimation The recursive form of Kalman filter may be expressed by the following system of equations, where all symbols in the formulations denote matrices or vectors (Goldberg, 1989): 9.3.1 Prediction of State xn þ 1 n ¼ Fðn þ 1; n; xnn 1 ; un Þ ð9:5Þ Fðn þ 1; n; xnn 1 ; un Þ ¼ An ðxnn Þxnn þ Bn ðxnn Þun : ð9:6Þ where 9.3.2 Estimation of Error Covariance Matrix Pn þ 1 n ¼ @F @x Pnn x¼xnn @FT @x þ Gn QGTn ð9:7Þ x¼xnn where G¼ nð þ1 ð9:8Þ Fðtn þ 1 ; tÞGðtÞdt: n and initial value of Pnn is a constant matrix. 9.3.3 Computation of Kalman Filter Gain Kn ¼ Pnn @H T 1 @x x¼xnn 1 @H @x Pnn x¼xnn 1 @H T 1 @x þR x¼xnn 1 ! 1 ð9:9Þ 246 Applied Intelligent Control of Induction Motor Drives where Hðxnn 1 ; nÞ ¼ Cn ðxnn 1 Þxnn 1 : 9.3.4 State Estimation xnn ¼ xnn 9.3.5 ð9:10Þ 1 þ Kn ðyn Hðxnn 1 ; kÞÞ ð9:11Þ Update of the Error Covariance Matrix Pnn ¼ Pnn Kn 1 @H @x Pnn x¼xnn ð9:12Þ 1 1 Using Equations (9.1), (9.2), (9.6), and (9.10), the matrices F, H, @F/@x and @H/@x are obtained as follows: 3 ðnÞ Kr L R PL o M o M r M ðnÞ ðnÞ ðnÞ ðnÞ 6 1 M ids þ 2 Mldr þ Mlqr þ Vds 7 7 6 K K L K 2L K l l r l l r 7 6 7 6 ðnÞ 6 Kr LM Rr M ðnÞ 7 7 6 ðnÞ PLM oo ðnÞ ðnÞ M iqs Mldr þ 2 Mlqr þ Vqs 7 6 1 7 6 Kl Kl Lr Kl 2Lr Kl 7 6 7 6 F ¼ 6 LM ðnÞ 7 1 P ðnÞ ðnÞ ðnÞ 7 6 o Ml M l þ 1 Mi o qr dr ds 7 6 tr t 2 r 7 6 7 6 7 6 LM P ðnÞ ðnÞ 1 ðnÞ 7 6 ðnÞ Miqs þ oo Mldr þ 1 M lqr 7 6 2 tr 7 6 tr 5 4 ðnÞ oo 2 2 H ¼ Cn xn ¼ 4 2 Kr M 61 Kl 6 6 6 6 6 0 6 @F 6 6 ¼6 @x 6 LM M 6 6 tr 6 6 6 0 6 4 0 1 0 LM Rr M L2r Kl Kr M Kl PLM oo M 2Lr Kl 0 1 ðnÞ 1 M tr LM M tr P ðnÞ o M 2 o 0 0 ðnÞ ids ðnÞ iqs 3 ð9:14Þ 5 ðnÞ PLM oo M 2Lr Kl LM R r M L2r Kl P ðnÞ o M 2 o 1 ð9:13Þ 1 M tr 0 3 LM ðnÞ Mlqr 7 Lr Kl 7 7 7 7 PLM ðnÞ 7 Mldr 7 2Lr Kl 7 7 7 7 ðnÞ Mlqr 7 7 7 7 ðnÞ 7 Mldr 7 5 1 ð9:15Þ 247 GA-Optimized Extended Kalman Filter for Speed Estimation @H ¼ @x " 1 0 0 0 0 0 1 0 0 0 # ð9:16Þ The speed estimation algorithm of the extended Kalman filter can be simulated by using MATLABÒ/Simulink, as shown in Figure 9.1. The EKF algorithm is coded in an M-file (written in the MATLABÒ language) which is then placed in the S-function block. The M-file is listed in Appendix F. i(n)ds i(n)qs 1 λ(n)dr Currents λ(n)qr Kalman_filter Mux kal_1 2 Voltages Demux S-Function Mux 1 Estimated speed Demux Figure 9.1 Simulink model of Extended Kalman filter speed estimator. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. Ó 2002 IEEE.) 9.4 Optimized Extended Kalman Filter To justify the need for an optimized extended Kalman filter, the EKF speed estimation algorithm is applied to a closed-loop constant V/Hz controller (Shi et al., 2002) as shown in Figure 9.2. Rotor speed 20 Induction motor load Closed-loop V/Hz controller Stator voltage Speed command Torque Stator current Kalman filter u Scope Estimated speed Clock Figure 9.2 Extended Kalman filter speed estimation for a voltage-frequency controlled drive system. Simulink model of Extended Kalman filter speed estimator. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. Ó 2002 IEEE.) 248 Applied Intelligent Control of Induction Motor Drives Details of the Kalman filter block are shown in Figure 9.1 and the induction motor block is the voltage-input model built in Chapter 3, while the block of closed-loop V/Hz controller is shown in Figure 9.3. Parameters of the induction motor chosen for the simulation studies are listed in ‘Motor 1’ of Appendix B. It is assumed that the induction motor is taken through the following control cycle: oo * ¼ 0 120 ðrad=sÞ 0 s < t 1:5 s oo * ¼ 120 ðrad=sÞ 1:5 s < t 3 s oo * ¼ 120 20 ðrad=sÞ 3 s < t 4:25 s oo * ¼ 20 ðrad=sÞ 4:25 s < t 6 s oo * ¼ 20 120 ðrad=sÞ 6 s < t 7:25 s oo * ¼ 120 ðrad=sÞ 7:25 s < t 9 s In the simulation, initial values of the error covariance matrix P of EKF is set as a unit matrix while the noise covariance matrices R, Q, and noise-weight matrix G of EKF are assumed as follows: 1 0 0 0 0 6 60 1 6 6 P¼6 60 0 6 60 0 4 0 0 7 07 " 7 10 7 07 7 R¼ 7 0 07 5 2 3 3 0 # 1 0 0 1 0 0 0 0 x 0 0 0 0 l 0 0 0 0 6 60 6 6 Q¼6 60 6 60 4 x 0 0 l 0 0 0 x 0 0 l 0 0 0 x 0 0 l 0 0 0 6 7 60 07 6 7 6 7 60 G ¼ 07 6 7 6 7 60 7 05 4 0 0 0 7 07 7 7 07 7 7 07 5 2 0 10 3 1 d 3 2 0 3 m Traditionally, the values of x, d, l and m are determined using a trial-and-error process which is time consuming and may not yield the best filter performance. Figure 9.4 shows the performance of the EKF speed estimation algorithm when applied to the closed-loop constant V/Hz controller, with x, d, l and m set at different values. The example demonstrates that the EKF speed estimation algorithm is sensitive to the noise covariance matrix Q and the noiseweight matrix G. The ‘goodness’ of speed estimation of the EKF with various compositions of Q and G may be evaluated by the mean squared error between the actual rotor speed and the estimated speed. 2 Speed command |V| 10s+0.5 Volts/hertz s speed controller 1 slip_limit 3 Gain Figure 9.3 1 Angle s Integrator Simulink program of closed-loop V/Hz controller. Polar to Cartesian Stator voltages GA-Optimized Extended Kalman Filter for Speed Estimation 1 Rotor speed 249 250 Applied Intelligent Control of Induction Motor Drives 140 λ=μ=ξ=δ =1e-6 Estimated speed (rad/s) 120 100 λ=μ=ξ=δ=1e-3 80 60 40 λ=μ=ξ=δ=1e-2 20 0 -20 λ=ξ=1e-6, μ=δ=1e-2 0 1 2 3 4 5 6 7 8 9 Time (sec) Figure 9.4 Estimated speed of constant V/Hz induction motor drive with the various matrices. Simulink model of Extended Kalman filter speed estimator. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. Ó 2002 IEEE.) Using this criterion, it is found that very good performance of the EKF is obtained with the matrices Q ¼ Diag[10 6, 10 6, 10 6, 10 6, 10 2] and G ¼ Diag[10 6, 10 6, 10 6, 10 6, 10 2], as illustrated in Table 9.1. Fine tuning of the elements of G, however, is tedious and it is difficult to check whether the optimum values have been obtained. Table 9.1 Performance of EKF for a constant V/Hz induction motor drive in terms of the mean squared error between the actual rotor speed and the estimated speed. Matrices G and Q l ¼ m ¼ x ¼ d ¼ 1e-2 l ¼ m ¼ x ¼ d ¼ 1e-3 l ¼ m ¼ x ¼ d ¼ 1e-6 l ¼ x ¼ d ¼ 1e-3, m ¼ 1e-2 l ¼ x ¼ 1e-3, m ¼ d ¼ 1e-2 l ¼ x ¼ 1e-6, m ¼ d ¼ 1e-2 E¼ n 1X ðsi ei Þ2 n i¼1 417.1220 772.4852 2.5927e þ 003 1.5331 1.0164 0.9985 Estimation Results Poor Poor Poor Good Good Very good s: actual rotor speed; e: estimated speed; n: number of data samples (¼ 45 000); E: mean squared error of estimated speed. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. Ó 2002 IEEE.) 9.5 Optimizing the Noise Matrices of EKF Using GA In order to find the best matrices G, Q, and R for the EKF, a real-coded GA is employed. The real-coded GA has many advantages (Wright, 1991) in numerical function optimization over GA-Optimized Extended Kalman Filter for Speed Estimation 251 binary encoding. Efficiency of the real-coded GA is increased as there is no need to convert chromosomes to phenotypes before each fitness evaluation; less memory is required; there is no loss in precision by the conversion between binary and real values. The procedures of the real-coded are outlined as follows: a. Population Representation of the Natural Parameter. The five diagonal elements (Gd) of the matrix G, five diagonal elements (Qd) of covariance matrix Q, and two diagonal elements (Rd) of covariance matrix R are coded into a long real-coded string, chromosome. A coding example of the real-coded GA is given as follows: Gd ¼ ½0:0637; 0:0769; 0:0054; 0:0115; 0:0846 Qd ¼ ½0:0172; 0:0037; 0:0313; 0:0817; 0:0235 Rd ¼ ½0:0587; 0:0924 chromosome ¼ ½Gd ; Qd ; Rd ¼ ½0:0637; 0:0769; 0:0054; 0:0115; 0:0846; 0:0172; 0:0037; 0:0313; 0:0817; 0:0235; 0:0587; 0:0924 b. Initial Generation. It begins by randomly generating an initial population of the long realcoded strings. c. Fitness Evaluation. In the current generation, each of the strings is decoded back to the corresponding diagonal elements of the three matrices, Gd, Qd, and Rd. Then, these diagonal elements from each string are separately sent to the EKF speed estimator of the induction motor drive to yield the objective function (which is the mean squared error of the estimated speed). Finally, these strings are ranked according to the value of the objective function by a linear ranking method. d. Reproduction. Reproduction is a process in which parent structures are selected to form new offspring. In the present study, the stochastic universal sampling method is employed. e. Recombination (Crossover). The single-point recombination method is used to exchange the information between two chromosomes. f. Mutation. Breeder Genetic Algorithm (Muhlenbein and Schlierkamp-Voosen, 1993) is used to implement the mutation operator for the real-coded GA, which uses a nonlinear term for the distribution of the range of mutation applied to gene values. This mutation algorithm is able to generate most points in the hypercube defined by the variables of the individual and range of the mutation. By biasing mutation towards smaller changes in gene values, the mutation can be used in conjunction with recombination as a foreground search process. g. Iteration. The real-coded GA runs iteratively repeating the processes (c) to (g) until a population convergence condition is met or the given maximum number of iterations is reached. 252 Applied Intelligent Control of Induction Motor Drives The real-coded GA for EKF (GA-EKF) can be implemented on a PC by MATLABÒ language. For optimizing the matrices G, Q, and R of EKF for the constant V/Hz controller, the parameters of the GA are set as follows. 1. 2. 3. 4. 5. 6. Initial population size: 100 Maximum number of generations: 20 Probability of crossover: 0.8 Mutation probability: 0.01 Initial range of real-coded strings: [0.0001; 0.1] Performance measure: the mean squared error between the actual rotor speed and the estimated speed. Table 9.2 shows a gradient convergence process of the real-coded GA. At the twentieth generation, the mean squared error of the rotor speed and the estimated speed has decreased to 0.1543 with the optimized matrices G ¼ Diag([0.0020 0.0050 0.0010 0.0246 0.1000]), Q ¼ Diag([0.0024 0.0875 0.0527 0.0001 0.0978]), and R ¼ Diag([0.0524 0.0094]). Comparing with the results of the trial-and-error method (Table 9.1), the real-coded GA method has found better matrices G, Q, and R. Table 9.2 Generations 0 1 2 3 4 5 6 7 8 9 10 Iteration process of the GA. E¼ n 1X ðsi ei Þ2 n i¼1 8.3137 5.2311 3.8212 2.9570 2.3951 1.5648 0.9142 0.8853 0.7271 0.6370 0.6286 Generations 11 12 13 14 15 16 17 18 19 20 E¼ n 1X ðsi ei Þ2 n i¼1 0.5713 0.5247 0.3943 0.3306 0.2425 0.1794 0.1731 0.1618 0.1662 0.1543 s: actual rotor speed; e: estimated speed; n: number of data samples (¼ 45 000); E: mean squared error of estimated speed. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. Ó 2002 IEEE.) Figure 9.5 shows the simulation results for the closed-loop constant V/Hz controller with the optimized matrices G, Q, and R. . Effect of current noise and machine parameter changes Figures 9.6 and 9.7 show the rotor speed responses of the constant V/Hz controller and the estimated speed of the GA-EKF when the rotor resistance of the induction motor, Rr, is changed 253 GA-Optimized Extended Kalman Filter for Speed Estimation 150 140 Torque (N.m) 120 100 Estimated speed (rad/sec) 100 80 50 60 0 40 Rotor speed (rad/sec) 20 -50 0 -100 0 1 2 3 4 5 6 7 8 9 -20 0 1 2 3 Time (sec) Figure 9.5 GA-EKF. 4 5 6 7 8 9 Time (sec) Torque, rotor speed, and estimated speed of the closed-loop constant V/Hz controller by 140 120 Rotor speed (rad/sec) 100 80 60 40 Estimated speed (rad/sec) 20 Rotor resistance 2Rr Noise variance 5A 0 -20 0 1 2 3 4 5 6 7 8 9 Time (sec) Figure 9.6 Rotor speeds and the estimated speeds of the constant V/Hz controller with the machine parameter variations and the current sensor noise. separately to 2Rr and 0.8Rr and a random noise (variance 5 A) is present in the current sensor of the controller. The extended Kalman filter is less sensitive to the machine parameter variations because these variations are handled as noise. Figures 9.5 and 9.6 and Table 9.3 also show that the EKF has disturbance rejection for the current sensor noise. 9.6 Speed Estimation for a Sensorless Direct Self Controller To further investigate the performance of the optimized EKF, simulation studies on a sensorless direct self controller (DSC) (Shi, Chan and Wong, 1998) for an induction motor drive is carried out. Figure 9.8 shows the MATLABÒ/Simulink program developed. 254 Applied Intelligent Control of Induction Motor Drives 140 120 Rotor speed (rad/sec) 100 80 60 40 Estimated speed (rad/sec) 20 Rotor resistance 0.8Rr Noise variance 5A 0 -20 0 1 2 3 4 5 6 7 8 9 Time (sec) Figure 9.7 Rotor speeds and the estimated speeds of the constant V/Hz controller with the machine parameter variations and the current sensor noise. Table 9.3 Mean squared error of rotor speed and estimated speed with the machine parameter variations and the current noise for the closed loop V/Hz controller. n 1X Stator Resistance Rotor Resistance Variance of E¼ ðsi ei Þ2 Rs ¼ 0.288 O Rr ¼ 0.161 O Current Noise n i¼1 Rs 0.8Rs 2Rs 0.8Rs 2Rs Rr 0.8Rr 2Rr 0.8Rr 2Rr 0A 0A 0A 5A 5A 0.1543 8.9731 25.0374 10.2616 29.7503 The induction motor, the EKF parameters, and the matrices G, Q, and R used for the simulation studies are the same as those used in the closed-loop constant V/Hz controller simulation. The speed, stator flux and torque commands are set as: oo * ¼ 60 rad=s 0s < t 0:8 s oo * ¼ 20 rad=s 0:8s < t 1:6 s oo * ¼ 60 rad=s 1:6s < t 2:5 s jls j* ¼ 0:86 Wb 0s < t 4 s T* ¼ 200 N m oo < oo * T* ¼ 200 N m oo oo * T* ¼ 20 N m oo > oo * 255 GA-Optimized Extended Kalman Filter for Speed Estimation Rotor speed Stator voltage Torque Induction motor 20 Stator current Scope Load Direct self Inverter T* Torque command controller Speed command Kalman filter Estimated speed Figure 9.8 GA-EKF. Speed estimation for a sensorless direct self controlled induction motor drive using Figure 9.9 shows the simulation results of the sensorless DSC induction motor drive using EKF with the GA-optimized matrices G, Q, and R while the mean squared error of the rotor speed and the estimated speed is 0.1528. 250 200 70 50 40 30 20 -100 -150 -200 -250 10 Estimated speed (rad/sec) 0 0 0.5 1 1.5 Time (sec) Figure 9.9 9.7 Rotor speed (rad/sec) 60 Torque (N.m) 150 100 50 0 -50 2 2.5 -10 0 0.5 1 1.5 2 2.5 Time (sec) Torque, rotor speed, and estimated speed of the sensorless direct self controller. Speed Estimation for a Field-Oriented Controller To further explore the feasibility of the extended Kalman filter for speed estimation, simulation studies are also carried out on a field-oriented controlled (FOC) induction motor drive with direct stator flux orientation (Xu and Novotny, 1991). 256 Applied Intelligent Control of Induction Motor Drives Figure 9.10 shows the block diagram of the FOC system. From the stator voltages (Vds, Vqs) and stator currents (ids, iqs), the stator flux can be obtained by a ‘Flux calculate’ block based on Equation (2.6). Two PI blocks control the stator flux and rotor speed, while another two PI blocks control the stator currents (iDS, iQs) in field coordinates. Coordinate transformation of voltages from the field frame (VDs,VQs) to the stator frame (Vds, Vqs) is implemented by an inverse Park calculation. At the same time, the 3-phase voltage signals and 3-phase current signals are sent to a GA-EKF program for rotor speed estimation. A voltage-input model of induction motor built in Chapter 3 is used to simulate a 0.147 kW induction motor (USA Bodine Electric Company model 295). VDs iDs* PI Torque load PI Flux* VQs iQs* PI PI Park (rev) Vs K IM Speed* iDs |Flux| iQs Park (for) Flux calculate ia ib ic is Speed Kalman estimator Figure 9.10 Speed estimation of FOC induction motor drive using EKF. Simulink model of Extended Kalman filter speed estimator. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. Ó 2002 IEEE.) The four PI controllers (one flux controller, one speed controller, and two current controllers) in the control system are tuned individually by adjusting the proportional constant Kp and the integral constant KI. The goal of this tuning is to choose parameters that would enable the controller to drive the error signal to zero. The four signals related to each controller (reference, actual, error and output) may be observed by ‘Scope’ blocks and examined during the simulation studies. The inner current loops are tuned first with constant values on their reference inputs (i.e. the speed and flux controllers disabled). For the 0.147 kW induction motor, the parameters of the current PI controllers can be obtained from Equations (6.26)–(6.40) in Chapter 6. Kp ¼ 42 KI ¼ 9256 257 GA-Optimized Extended Kalman Filter for Speed Estimation After the parameters of the current PI controllers have been set, the speed and flux PI controllers in Figure 9.10 are tuned by observing the responses of the ‘Scope’ blocks. It is found that the parameters of the speed and flux PI controllers should be tuned as follows: Parameters of the speed PI controller : Kp ¼ 100; KI ¼ 1 Parameters of the flux PI controller : Kp ¼ 2; KI ¼ 1 The parameters of the 0.147 kW induction motor for the simulation studies are listed in ‘Motor 3’ of Appendix B. The load torque is constant at 0.5 N m. It is assumed that the induction motor is taken through the following control cycle: Period Speed Command Flux Command 0 s t < 0.1 s t ¼ 0.1 s 0.25 s t ¼ 0.25 s 1 s t ¼ 1 s 1.1 s t ¼ 1.1 s 2 s oo ¼ 0 rad/s oo ¼ 0180 rad/s oo ¼ 180 rad/s oo ¼ 18020 rad/s oo ¼ 20 rad/s ls ¼ 0.6 Wb ls ¼ 0.6 Wb ls ¼ 0.6 Wb ls ¼ 0.6 Wb ls ¼ 0.6 Wb Figure 9.11 shows the phase-A stator voltage and current of the field-oriented control system in Figure 9.10. The torque and rotor speed responses are shown in Figure 9.12. 4 3 200 Phase-A current (A) Phase-A voltage (V) 300 100 0 -100 -200 2 1 0 -1 -2 -3 -300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 9.11 -4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Phase-A voltage and current of the field-oriented control system. The EKF program in Figure 9.10 is listed in Appendix F with the following 0.147 kW motor parameters used: Lr K ¼ 0:3481; Ls K ¼ 0:3185; Lh K ¼ 0:2963; Rs K ¼ 14:6; Rr K ¼ 12:77; H pole ¼ 4=2 ðpole number P ¼ 4Þ: Figure 9.13 shows rotor speed estimated by the EKF, when the matrices G, Q, and R of the EKF are initially set as: 258 Applied Intelligent Control of Induction Motor Drives 2 Rotor speed (rad/s) Torque (m.N) 1.5 1 0.5 0 -0.5 -1 -1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 200 180 160 140 120 100 80 60 40 20 0 -20 0 0.2 0.4 0.6 0.8 1 Time (s) Speed (rad/s) Figure 9.12 200 180 160 140 120 100 80 60 40 20 0 -20 1.2 1.4 1.6 1.8 2 Time (s) Torque and rotor speed responses of the field-oriented control system. Rotor speed (solid line) Estimated speed (dotted line) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 9.13 Rotor speed and estimated speed of induction motor drive with EKF. G ¼ Diagð½0:01; 0:01; 0:01; 0:01; 0:5Þ; Q ¼ Diagð½0:01; 0:01; 0:01; 0:01; 0:5Þ; R ¼ Diagð½0:01; 0:01Þ; With these selected matrices, the EKF fails to give a good speed estimation and divergence occurs eventually. Figure 9.14 shows the rotor speed estimated by the EKF when the matrices G, Q, and R of the EKF are tuned, using a trial-and-error method, as follows: G ¼ Diagð½0:01; 0:01; 0:01; 0:01; 1:5Þ; Q ¼ Diagð½0:01; 0:01; 0:01; 0:01; 1:5Þ; R ¼ Diagð½0:01; 0:01Þ; 259 Speed (rad/s) GA-Optimized Extended Kalman Filter for Speed Estimation 200 180 160 140 120 100 80 60 40 20 0 -20 Rotor speed (solid line) Estimated speed (dotted line) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 9.14 Rotor speed and estimated speed of induction motor drive with EKF. In this case the estimation error (i.e. mean squared error between the estimated speed and the actual rotor speed) is 106.5209. The trial-and-error method has improved the speed estimation accuracy but fails to yield the best EKF performance. In order to obtain the optimum matrices G, Q, and R for the EKF, the real-coded GA employed in Sections 9.5 and 9.6 is used. The parameters of the GA for optimizing the matrices G, Q, and R of EKF from the experimental data are the same as those in Section 9.5 except that the initial range of real-coded strings is set as [0.01; 5]. A different initial range is necessary in order to guarantee convergence and short iteration time. Table 9.4 shows the convergence process. Figure 9.15 shows the actual speed and the speed estimated using GA-EKF with the optimized matrices. The GA optimization method has improved the EKF performance by decreasing the mean squared error of estimated speed from 106.5209 (Figure 9.14) to 0.1105 (Figure 9.15). The optimized matrices are: G ¼ Diag[0.0525, 0.0602, 0.0319, 0.01302, 1.809], Q ¼ Diag([0.108, 0.081, 0.0716, 0.1308, 2.307]), and R ¼ Diag([0.0101, 0.0104]). Table 9.4 Iteration process of the GA. Generations 0 1 2 3 4 5 6 7 8 9 10 E¼ n 1X ðsi ei Þ2 n i¼1 42.3431 23.6518 12.7427 7.1624 3.4261 1.6421 0.8934 0.9518 0.6615 0.5933 0.4821 Generations 11 12 13 14 15 16 17 18 19 20 E¼ n 1X ðsi ei Þ2 n i¼1 0.4632 0.4728 0.3572 0.3147 0.2143 0.2315 0.1623 0.1372 0.1252 0.1105 s: actual rotor speed; e: estimated speed; n: number of data samples (¼ 40 000); E: mean squared error of estimated speed. 260 Applied Intelligent Control of Induction Motor Drives 200 Speed (rad/s) 180 160 140 Rotor speed (solid line) 120 100 80 60 Estimated speed (dotted line) 40 20 0 -20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 9.15 9.8 Rotor speed and estimated speed using GA-EKF with optimized matrices. MATLABÒ/Simulink Programming Examples Four programming examples are given to illustrate the development of a voltage-frequency controlled (VFC) drive, a GA-optimized EKF for speed estimation, an EKF-based sensorless VFC of induction motor, and an EKF-based sensorless field-oriented control (FOC) of induction motor. 9.8.1 Programming Example 1: Voltage-Frequency Controlled (VFC) Drive Voltage A voltage-frequency controlled drive is based on constant volts/Hz operation to maintain constant torque in the induction motor. A typical constant volts/Hz characteristic (The MathWorks, Inc., 2008) is shown in Figure 9.16. The straight line has a small voltage boost in order to compensate for resistance drop at low frequencies. Base Voltage Boost Voltage Frequency Base Frequency Figure 9.16 Volts/Hz characteristic. 261 GA-Optimized Extended Kalman Filter for Speed Estimation Step 1 Building a Lookup Table of Constant Volts/Hz Characteristic The volts/Hz characteristic of a 7.5 kW induction motor is assumed as follows: Base frequency Fb ¼ 60 Hz (2p 60 Hz ¼ 377 rad/s) Base voltage Vb ¼ 300 V Slope rate ¼ Vb/Fb ¼ 300/377 ¼ 0.7958 Boost voltage Vboost ¼ 4 V The following MATLABÒ program is first written to generate the lookup table of constant volts/Hz characteristic: % Program ’Give_VF_table.m’ Base_F=60*pi*2; Slop=300/377; F_input=[-1*Base_F*2:4:Base_F*2]; B3=[8*Slop:Slop*4: 300]; B2=fliplr(B3); [sF1 sF2]=size(F_input); [sB1 sB2]=size(B3); M= (sF2-1)/2-sB2-1; B1=ones(1,M)*300; V_output=[B1,B2,5,4,5,B3,B1]; plot(F_input, V_output); axis([-800 800 -20 350]); The result of running the above program is shown in Figure 9.17. 350 300 V_output (V) 250 200 150 100 Boost Voltage 50 0 -800 -600 -400 -200 0 200 400 600 800 F_input (rad/s) Figure 9.17 Lookup table of constant volts/Hz characteristic for the 7.5-kW motor. The two arrays ‘F_input’ and ‘V_output’ are stored in MATLABÒ workspace after the program ‘Give_VF_table.m’ has been run. The array ‘F_input’ contains the values of frequency and the ‘V_output’ contains the corresponding magnitudes of output voltage. 262 Applied Intelligent Control of Induction Motor Drives Constant volts/Hz operation can then be simulated by using a ‘Lookup’ block in Simulink library, as detailed in the next step. Step 2 Building a Simulink Model of the Constant Volts/Hz Controller The Simulink model of the constant volts/Hz controller is built as shown in Figure 9.18. 1 Speed* PID 1 3 Sum1 slip_limit Lookup Sum 2 Vdq Polar to Cartesian Gain 1 s Rotor Speed Integrator Figure 9.18 Simulink model of constant volts/Hz controller. The Simulink model consists of a ‘PID’ block, a ‘slip_limit’ block, a ‘Gain’ block, a ‘Lookup’ block, an ‘Integrator’ block, and a ‘Polar to Cartesian’ block. The inputs are the speed command and the rotor speed, while the output is the stator voltage vector (Vds, Vqs). The parameters of the ‘slip_limit’ block are set as follows: Upper limit: 37.7 Lower limit: 37.7 The parameters of the ‘PID’ block are set as follows: Proportional: 3 Integral: 0.02 Derivative: 0 Since the induction motor has 3 pole-pairs, the parameter of the ‘Gain’ block is set as follows: Gain: 3 The ‘Lookup’ block has two parameters set as follows: Vector of input values: F_input Table data: V_output Input of the ‘Lookup’ block is the array ‘F_input’ and the output is the array ‘V_output’. With the two arrays in workspace (created in Step 1), the ‘Lookup’ table can be used to simulate the constant volts/Hz characteristic. The ‘Integrator’ block is used to calculate the angle of the stator voltage vector. Using the magnitude from the ‘Lookup’ block and the angle from the ‘Integrator’ block, the ‘Polar to Cartesian’ block outputs the stator voltage vector (Vds, Vqs). 263 GA-Optimized Extended Kalman Filter for Speed Estimation Step 3 Building a Simulink Model of the Voltage-Frequency Controlled Drive The Simulink model of voltage-frequency controlled drive is built as shown in Figure 9.19. Speeds 20 Load Repeating Sequence Figure 9.19 Induction Motor idq VF Controler Simulink model of voltage-frequency controlled (VFC) drive. In Figure 9.19, the ‘VF Controller’ block is the Simulink model of constant volts/Hz controller built in Step 2. The ‘Induction Motor’ block is a 7.5 kW voltage-input model of induction motor described in Section 3.4 with parameters of ‘Motor 1’ listed in Appendix B. The ‘Repeating Sequence’ block outputs the speed commands with following parameters: Time values ¼ [0 1 2 4 6 8 10 12 14 16 17 20] Output values ¼ [0 0 100 100 100 100 100 100 100 100 0 0] The ‘Load’ block outputs a constant load torque of 20 N m and the parameter of the block is set as follows: Constant ¼ 20 Step 4 Simulating the Voltage-Frequency Controlled Drive Before performing the simulation of the voltage-frequency controlled drive in Figure 9.19, the MATLABÒ program ‘Give_VF_table.m’ in Step 1 should first be run to create the two arrays ‘F_input’ and ‘V_output’ for use by the ‘Lookup’ block in the constant volts/Hz controller. The Simulink model is run with following parameters. Simulation type: Variable-step Max-step size ¼ 0.001 s Simulation time ¼ 18 s The simulation results are shown in Figure 9.20. 264 150 150 100 100 Rotor speed (rad/s) Rotor speed (rad/s) Applied Intelligent Control of Induction Motor Drives 50 0 -50 -100 50 0 -50 -100 -150 -150 0 2 4 6 8 10 12 14 16 18 0 2 4 6 Time (s) (a) 8 10 12 14 16 18 Time (s) (b) Figure 9.20 (a) Speed command and (b) Rotor speed. 9.8.2 Programming Example 2: GA-Optimized EKF for Speed Estimation This example describes how the matrices [Gd, Qd, Rd] described in Section 9.5 of an extended Kalman filter (EKF) can be optimized for speed estimation of an induction motor. The MATLABÒ program consists of a GA program ‘Start_GA.m’, a fitness evaluation program ‘Call_kal.m’, and a Simulink model ‘kal_train.mdl’ of an induction motor drive with EKF speed estimation. Their relationship is shown in Figure 9.21. Start_GA.m (1) Set GA parameters Call (2) ga (@ Call_kal.m,..) Call_kal.m (3) Output best (1) sim( kal_train.mdl ) kal_train.mdl (2) Calculate mean squared error (mse) of estimated speed by “yout” (1) Simulation of induction motor drive and EKF speed estimation Call chromosome [Gd, Qd, Rd] Return mse Output: mse Return “yout” Figure 9.21 (2) Output: “yout” (error of estimated speed) Relationship between programs in GA-optimized EKF. The functions of programs in the GA-optimized EKF are listed in Table 9.5. 265 GA-Optimized Extended Kalman Filter for Speed Estimation Table 9.5 Functions of programs in GA-optimized EKF. Name of Program Function Input Output Start_GA.m Set GA parameters and perform ‘ga’ function in MATLABÒ which calls the fitness evaluation function ‘Call_kal.m’ Fitness evaluation which calls the Simulink model ‘kal_train.mdl’ and calculates the mean squared error (mse). Simulink models of induction motor drive and EKF speed estimation N/A best chromosome matrix [Gd, Qd, Rd] Chromosome [Gd, Qd, Rd] ‘mse’ mean squared error of estimated speed as value of evaluation fitness ‘yout’ error of estimated speed Call_kal.m Kal_train.mdl Chromosome [Gd, Qd, Rd] Notes: The chromosome matrix [Gd, Qd, Rd] is described in Section 9.5. Step 1 Programming GA Program ‘Start_GA.m’ The following MATLABÒ program ‘Start_GA.m’ is first written: function x1=Start_GA() clc clear all warning off all %Give_VF_table_GA; X0=rand(1,12); lb=ones(1,12)*0.00001; lb=lb’; ub=ones(1,12)*100; ub=ub’; options = gaoptimset(@ga); options = gaoptimset(options,’MutationFcn’,@mutationadaptfeasible); options = gaoptimset(options,’PopulationSize’,100); options = gaoptimset(options,’Generations’,20); options = gaoptimset(options, ’EliteCount’,2); options = gaoptimset(options, ’CrossoverFraction’,0.8); options = gaoptimset(options,’PlotFcns’,{@gaplotbestf },’Display’, ’iter’); [xx,fval,exitflag]=ga(@Call_kal,12,[],[],[],[],lb, ub,[], options) assignin(’base’,’fval’,fval); x1=xx; assignin(’base’,’x1’,x1); [A,B]=size(x1); Error=sum(x1.^2)/A; assignin(’base’,’Error’,Error); G=diag(x1(1:5)); Q=diag(x1(6:10)); R=diag(x1(11:12)); assignin(’base’,’G’,G); assignin(’base’,’Q’,Q); assignin(’base’,’R’,R); end 266 Applied Intelligent Control of Induction Motor Drives The programming information is described in Step 3 of Section 4.5.2. Step 2 Programming Fitness Evaluation ‘Call_kal.m’ The following program ‘Call_kal.m’ is next written: function mse=Call_kal(xx) x1=xx; G=diag(x1(1:5)); Q=diag(x1(6:10)); R=diag(x1(11:12)); assignin(’base’,’G’,G); assignin(’base’,’Q’,Q); assignin(’base’,’R’,R); [tout,xout,yout]=sim(’kal_train’,1.5); [A,B]=size(yout); y=yout; y(1)=[]; mse=sum(y.^2)/A; end Step 3 Programming Simulink Model ‘kal_train.mdl’ of Induction Motor Drive and EKF Speed Estimation Direct-on-line starting of a 7.5 kW induction motor is employed for the fitness evaluation of GA optimization. The Simulink model ‘kal_train.mdl’ of induction motor drive and EKF speed estimation is shown in Figure 9.22. Rotor Speed 20 load Scope Power Supply Induction Motor 3-phase 269.4 V 60Hz 1 Estimated Speed Out1 EKF Figure 9.22 Simulink model for fitness evaluation of GA optimization. The Simulink model ‘kal_train.mdl’ is called by the program ‘Call_kal.m’ in Step 2 and returns error of EKF speed estimation to ‘Call_kal.m’ for calculating the fitness evaluation (mean squared error of estimated speed). The Simulink model consists of an ‘Induction Motor’ 267 GA-Optimized Extended Kalman Filter for Speed Estimation block, an ‘EKF’ block, and a ‘Power Supply’ block. The ‘Induction Motor’ block may be a 7.5 kW voltage-input model (described in Section 3.4 and programmed in Section 6.8.1) or a 7.5 kW discrete-state model (described in 3.5) of induction motor. The ‘EKF’ block is described in Figure 9.1 and its MATLABÒ program is listed in Appendix F. The ‘Power Supply’ block is a dq-axis voltage source with output Vds, Vqs, which is programmed in Section 6.8.1 and shown in Figure 6.39. The parameters of the Simulink model are set as follows. Simulation type: Variable-step Max-step size ¼ 0.0002 s Simulation time ¼ 1.5 s Step 4 Running the GA Programs to Optimize EKF Speed Estimation Upon entering command ‘Start_GA’ in the MATLABÒ window, the GA optimizing process starts. The optimizing process may be time-consuming, depending on the computer speed and the following parameters in the programs. 1. the simulation time in ‘sim’ function of the program ‘Call_kal.m’; 2. ‘PopulationSize’; and 3. ‘Generations’ in the program ‘Start_GA.m’. 140 140 120 120 Rotor speed (rad/s) Rotor speed (rad/s) After the program ‘Start_GA.m’ has stopped, the optimum matrices [Gd, Qd, Rd] of EKF speed estimation are stored in MATLABÒ workspace. With the optimum matrices [Gd, Qd, Rd], the Simulink model ‘kal_train.mdl’ built in Step 3 is run, and the simulation results are shown in Figure 9.23. 100 80 60 40 20 0 -20 0 100 80 60 40 20 0 0.5 1 1.5 -20 0 0.5 1 Time (s) Time (s) (a) (b) 1.5 Figure 9.23 Rotor speed response of direct-on-line starting: (a) rotor speed of motor (b) estimated speed by the optimized EKF. 268 9.8.3 Applied Intelligent Control of Induction Motor Drives Programming Example 3: GA-based EKF Sensorless Voltage-Frequency Controlled Drive The Simulink model of a GA-based EKF sensorless voltage-frequency controlled drive is shown in Figure 9.24. Scope1 20 load Repeating Sequence Induction Motor Kalman Estimater VF Controller Figure 9.24 Sensorless voltage-frequency controlled drive with GA-based EKF. The model consists of the Simulink model of voltage-frequency controlled drive built in Section 9.8.1 and an embedded optimized EKF speed estimation built in Section 9.8.2. The parameters of the ‘Repeating Sequence’ block and the ‘load’ block in Figure 9.24 are described in Step 3 in Section 9.8.1, and the speed response of the GA-based sensorless voltage-frequency controlled drive is shown in Figure 9.25. 150 Rotor speed (rad/s) 100 50 0 -50 -100 -150 0 2 4 6 8 10 12 14 16 18 Time (s) Figure 9.25 Speed response of the GA-based EKF sensorless voltage-frequency controlled drive. 269 GA-Optimized Extended Kalman Filter for Speed Estimation 9.8.4 Programming Example 4: GA-based EKF Sensorless FOC Induction Motor Drive The Simulink model of a GA-based EKF sensorless FOC induction motor drive is shown in Figure 9.26. Vds ids* PI Torque load PI Flux* Vqs iqs* PI PI Park (rev) Vs IM Speed* ids |Flux| iqs Park (for) Flux calculate is Speed Kalman estimator Figure 9.26 Simulink model of a sensorless FOC induction motor drive with GA-based EKF. The sensorless FOC drive employs a 0.147 kW induction motor (‘Motor 3’ of Appendix B). Replacing the 7.5 kW induction motor by the 0.147 kW induction motor and repeating the GA optimizing program in Section 9.8.2, we obtain the optimized matrices [Gd, Qd, Rd] in EKF speed estimation for the 0.147 kW induction motor drive. The Simulink model of FOC induction motor drive built in Section 9.7 and shown in Figure 9.10 is employed for constructing the sensorless FOC induction motor drive, the speed estimated by the optimized EKF being fed back to the speed PI controller, as shown in Figure 9.26. The parameters of the four PI controllers are set as follows. Parameters Parameters Parameters Parameters of of of of the current ids PI controllers the current iqs PI controllers the flux PI controller: the flux PI controller: Kp ¼ 20 Kp ¼ 20 Kp ¼ 100 Kp ¼ 1 KI ¼ 1 KI ¼ 1 KI ¼ 1 KI ¼ 100 The speed commands are created by a ‘Repeating Sequence’ block with following parameters. Time values ¼ [0 0.1 0.25 0.25 1 1.1 2] Output values ¼ [0 0 180 180 180 20 20] 270 Applied Intelligent Control of Induction Motor Drives The ‘Load’ block outputs a constant load of 0.5 N m and the parameter of the block is set as follows: Constant ¼ 0.5 The simulated rotor speed response of the sensorless FOC induction motor drive with GA-based EKF is shown in Figure 9.27. 200 180 Rotor speed (rad/s) 160 140 120 100 80 60 40 20 0 0 0.5 1 1.5 2 Time (s) Figure 9.27 Rotor speed response of the sensorless FOC induction motor drive with GA-based EKF. 9.9 Summary This chapter has presented a novel method to achieve good performance of an EKF for speed estimation of an induction motor drive. Based on a real-coded GA, the optimization procedure enables the noise covariance and weight matrices, on which the EKF performance critically depends, to be properly selected. Simulation studies on different induction motor drives have confirmed the efficacy of the approach. Real-coded GA is found to be a powerful technique for optimizing the EKF algorithm as applied to the three different controllers and two different induction motors. Computer simulation results have demonstrated that the GA-EKF has good noise rejection and its performance is less sensitive to the machine parameter variations. Possible future developments of the extended Kalman filter are (1) to find a relationship between the motor parameters and the initial range of the matrices G, Q, and R of EKF for the GA optimization, and (2) to implement the GA-EKF on a DSP board. References Bolognani, S., Oboe, R., and Zigliotto, M. (1999) Sensorless full-digital PMSM Drive with EKF estimation of speed and rotor position. IEEE Transactions on Industrial Electronics, 46(1), 184–191. GA-Optimized Extended Kalman Filter for Speed Estimation 271 Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley Publishing Company, Reading, MA. Henneberger, G., Brunsbach, B.J., and Klepsch, Th. (1996) Field-oriented control of synchronous and asynchronous drives without mechanical sensors using a Kalman filter, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura, and K. Matsuse), IEEE Press, pp. 207–214. Kim, F Y.R., Sul, S.K., and Park, M.H. (1996) Speed sensorless vector control of induction motor using extended Kalman filter, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura, and K. Matsuse), IEEE Press, New Jersey, pp. 215–223. Lewis, F.L. (1992) Applied Optimal Control and Estimation, Prentice-Hall, Inc., New Jersey. Manes, C., Parasiliti, F., and Tursini, M. (1994) A comparative study of rotor flux estimation in induction motors with a nonlinear observer and the extended Kalman filter. IECON 94 Conference, pp. 2149–2154. Muhlenbein, H. and Schlierkamp-Voosen, D. (1993) Predictive models for the breeder genetic algorithm. Evolutionary Computation, 1(1), 25–49. Salvatore, L., Stasi, S., and Tarchioni, L. (1993) A new EKF-based algorithm for flux estimation in induction machines. IEEE Transactions on Industrial Electronics, 40(5), 496–504. Shi, K.L., Chan, T.F., and Wong, Y.K. (May (1998)) Modelling and simulation of direct self control system. IASTED International Conference: Modelling and Simulation, Pittsburgh, USA. Shi, K.L., Chan, T.F., Wong, Y.K., and Ho, S.L.(February (2002)) Speed estimation of an induction motor drive using an optimized extended Kalman filter. IEEE Transactions on Industrial Electronics, 49(1), 124–134. Texas Instruments Incorporated (July 1997) Sensorless Control with Kalman Filter on TMS320 Fixed-Point DSP, Literature Number: BPRA057. Texas Instruments Europe. The MathWorks, Inc. (2008) SimPowerSystemsÔ 5 User’s Guide. Wright, A.H. (1991) Genetic algorithms for real parameter optimization, in Foundations of Genetic Algorithms (ed J.E. Rawlins), Morgan Kaufmann, San Mateo, CA, pp. 205–218. Xu, X. and Novotny, D.W. (1991) Implementation of direct stator flux orientation control on a versatile DSP based system. IEEE Transactions on Industry Applications., 27, 694–700. 10 Optimized Random PWM Strategies Based on Genetic Algorithms 10.1 Introduction Many new pulse width modulation (PWM) techniques have been developed in order to give inverters a wider linear modulation range, lower switching loss, wider spread of energy over the harmonic spectrum, and reduced total harmonic distortion (THD) (Zhou and Wang, 2002). These new techniques may be categorized as (1) selected harmonic elimination method, (2) random PWM (RPWM) method, and (3) genetic algorithm (GA) optimization techniques. The selected harmonic elimination method suppresses the chosen harmonics by controlling the switching angles (Chiasson et al., 2004). On the other hand, the random PWM inverter achieves very small magnitude of switching harmonics compared with a standard PWM inverter by spreading the harmonic energy over a wide frequency range. Two major advantages of the RPWM over the standard PWM are (Bech et al., 1999): (1) the whistling acoustic noise emitted by standard PWM is converted into less annoying broad-band noise, (2) the size of filter components required for the inverter to comply with standards for conducted electromagnetic interference (EMI) is reduced. However random PWM techniques cannot significantly improve the total harmonic distortions (THD). To overcome this problem, genetic algorithm (GA) optimization techniques have recently been proposed (Shi and Li, 2003; Ozpineci, Tolbert and Chiasson, 2004) to reduce the THD of PWM waveforms. In this chapter, a random carrier-frequency PWM, a random pulse-position PWM, a random pulse-width PWM, and a hybrid random pulse-position and random pulse-width PWM will be optimized by genetic algorithm. Compared with standard PWM and random PWM inverters, the GA-optimized random PWM inverters have the same switching loss, but they have a wider linear modulation range, lower value of THD (and hence less copper loss), and smaller harmonic amplitudes (which require a smaller filter size). The harmonic energy of the Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 274 Applied Intelligent Control of Induction Motor Drives GA-optimized random PWM is spread over a wide range, and the energy the fundamental component is also enhanced. In practical applications, these advantages are obtained without any extra hardware cost and programming complexity. The optimized random PWM strategy may be implemented by adding only arrays including the optimized carrier series or pulse series with some instructions included in the DSP program. A single-phase inverter is employed for this optimization study. The validity of the proposed methods has been verified by simulation and experimental studies on a DSP-based voltage-controlled inverter. As steadystate performance is being considered, the GA-optimized random PWM inverter proposed may be used as an uninterruptable power supply (UPS) or used to drive a single-phase induction motor for low performance applications, such as pumps, fans and mixers. 10.2 PWM Performance Evaluation In a single-phase two-arm bridge PWM inverter, a triangular-carrier wave is employed for comparison with sinusoidal modulation waves to generate signals to control the semiconductor switching devices as shown in Figure 10.1. IGBT IGBT DC Ua Ub IGBT IGBT Gate drive PWM generator Va Triangular carrier Vb Sinusoidal modulation waves Figure 10.1 A single-phase two-arm bridge PWM inverter. For convenience, assume that the amplitude of the triangular-carrier wave Vc shown in Figure 10.2 is 1 V. Then, Vc may be expressed mathematically as Vc ¼ Vc ¼ 4 t 4n þ 3 ðVÞ Tc 4 t þ 4n 1 ðVÞ Tc when ðn 1ÞTc < t < nTc when nTc where n ¼ 1, 2, . . ., N, and Tc is the carrier period. Tc < t < nTc 2 Tc 2 ð10:1Þ 275 Optimized Random PWM Strategies Based on Genetic Algorithms Vc(V) 1V 0V t -1 V Tc (n-1)Tc nTc - nTc /2 (n+1) Tc nTc Figure 10.2 Tc (n+2) Tc Triangular carrier wave. The sinusoidal modulation waves in the single-phase PWM inverter are known as reference signals or modulating signals, which may be expressed as Va ¼ V sin ðotÞ ð10:2Þ Vb ¼ V sin ðotÞ where o is the frequency and V is the amplitude of the sinusoidal waveform. For a carrier frequency of 1 kHz, a reference sinusoidal frequency of 50 Hz, and a modulation index of 0.8, the carrier wave and the modulating waves are as shown in Figure 10.3. The points of intersection between the carrier and modulating waves generate the control signals for the PWM inverter. Voltage (V) 1 Vb Va 0.5 0 -0.5 -1 0 Figure 10.3 0.005 0.01 0.015 0.02 Time (s) Two sinusoidal waves and triangular carrier wave. When the value of the reference sinusoidal wave is larger than value of the triangular-carrier wave, the PWM output is in the high state; otherwise it is in the low state. In this chapter, the single-phase triangular-carrier PWM is referred to as the standard PWM. For a DC source of 1 V, the outputs of the PWM inverter are Ua, Ub, and, Uab, as shown in Figure 10.4. 276 Applied Intelligent Control of Induction Motor Drives 1V Ua 0V 1V Ub 0V 1V Uab 0V -1V Figure 10.4 Ua and Ub). Output waveforms of PWM inverter (The pulse frequency of Uab is about two times of 10.2.1 Fourier Analysis of PWM Waveform The PWM-inverter output waveform Uab may be expressed by a trigonometric form of Fourier series (Lathi, 2005): Uab ðtÞ ¼ A0 þ N X ½Ai cos ðio0 tÞ þ Bi sin ðio0 tÞ ðVÞ ð10:3Þ i¼1 Ð Ð Ð where A0 ¼ T10 T0 Uab ðtÞdt, Ai ¼ T20 T0 Uab ðtÞ cos no0 tdt, Bi ¼ T20 T0 Uab ðtÞsin no0 tdt, o0 is the fundamental frequency, and T0 ¼ o2p0 . The compact trigonometric form of the Fourier series is Uab ðtÞ ¼ C0 þ N X Ci cosðio0 t þ yi Þ ðVÞ ð10:4Þ i¼1 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ where C0 ¼ A0 , Ci ¼ A2i þ B2i , and yi ¼ tan 1 ABi i . The PWM output waveform may be evaluated by Fourier coefficients as follows. a. Amplitude of the fundamental wave of PWM-inverter output: U F ¼ C1 ðVÞ ð10:5Þ Amplitude of the maximum harmonic: U max H ¼ maxðCi¼2;...N Þ ðVÞ ð10:6Þ Total harmonic distortion (THD): vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u N X 1 u t THD ¼ C2 C1 i¼2 i ð10:7Þ 277 Optimized Random PWM Strategies Based on Genetic Algorithms Power of PWM signal in time domain is defined as P PWM ¼ Tð0 UðtÞ2 dt 0 ð10:8Þ T0 where U(t) is the PWM-inverter output waveform in the time domain, T0 is the period, and P_PWM is power of the PWM signal. b. Power of a discrete PWM signal is defined as (Lathi, 2005) P PWM ¼ N 1 X Ui2 i¼0 N where Ui is the ith sample of PWM output waveform in the time domain, and N is the total sample number. According to Parseval’s theorem (Lathi, 2005), the sum of the power of all discrete FFT components equals the power of the continuous signal in the time domain, that is, P PWM ¼ C02 þ N 1 1X C2 : 2 i¼1 i ð10:9Þ The power of the fundamental component of PWM output waveform is defined as P F 1 ¼ C12 : 2 ð10:10Þ The power of all the harmonic components of PWM output waveform is defined as P H ¼ N 1 1X C2 : 2 i¼2 i ð10:11Þ 10.2.2 Harmonic Evaluation of Typical Waveforms Example 10.1 Square Wave A square wave and its Fourier series are shown in Figure 10.5. The period of the square wave T0 is 0.02 s and the fundamental frequency o0 ¼ 2p/T0 ¼ 100p rad. The square wave may be evaluated as follows. The fundamental components are calculated from Equation (10.3): 20:01 3 0:02 ð ð 24 A1 ¼ 1 cos o0 tdt þ ð 1Þ cos o0 tdt5 ¼ 0 V T0 0 0:01 20:01 3 0:02 ð ð 2 4 B1 ¼ 4 1 sin o0 tdt þ ð 1Þ sin o0 tdt5 ¼ V: T0 p 0 0:01 278 Applied Intelligent Control of Induction Motor Drives 1.5 Magnitude (V) Voltage (V) 1 0.5 0 -0.5 -1 0 0.005 0.01 0.015 0.02 1 0.5 0 0 5 10 15 20 Time (s) Figure 10.5 25 30 i th component A square wave and its Fourier series. The amplitude of fundamental component is then obtained from Equation (10.5): U F ¼ C1 ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 4 A21 þ B21 ¼ V p The power of signal of the square wave is obtained from Equation (10.8): P PWM ¼ Tð0 UðtÞ2 dt 0 T0 00:01 1 0 0:02 1 ð ð 1 @ 1 @ ¼ 12 dtA þ ð 1Þ2 dtA ¼ 1: 0:02 0:02 0 0:01 The power of the fundamental component of PWM output is obtained from Equation (10.10): P F 2 1 1 4 ¼ 0:811: ¼ C12 ¼ 2 2 p The power of all the harmonic components of PWM output is obtained from P H ¼P PWM P F ¼ 1 0:811 ¼ 0:189: Because the square wave is an odd function, the harmonic components have the following properties: 1. Ai ¼ 0, for all i 2. Ci ¼ 0, when i is even, which implies that there are no even harmonic components in the square wave. 2 3. Ci ¼ ip , when i is odd. The 3rd and 5th harmonics are large in the square wave. Elimination of the harmonics of low frequency will require a large filter. PWM techniques are therefore employed in order to reduce the amplitudes of the low-frequency harmonics. 279 Optimized Random PWM Strategies Based on Genetic Algorithms Example 10.2 Four-Pulse PWM Wave A four-pulse waveform, Uab, is produced by the triangular-carrier PWM inverter as shown in Figure 10.1 with following parameters. Frequency of carrier wave ¼ 100 Hz Amplitude of carrier wave ¼ 1 V Frequency of reference sinusoidal wave ¼ 50 Hz Amplitude of reference sinusoidal wave ¼ 0.8 V (Modulation index ¼ 0.8) DC source ¼ 1 V. Using a computer simulation program, we obtain the four-pulse PWM wave and its Fourier series as shown in Figure 10.6. t1 t2 t3 t4 t5 t6 t7 t8 1 Magnitude (V) Voltage (V) 1 0.5 0 -0.5 -1 0 0.8 0.6 0.4 0.2 0 0.005 0.01 0.015 0.02 0 5 10 15 20 Time (s) Figure 10.6 25 30 ith component A four-pulse PWM waveform and its Fourier series. The pulse width of the four-pulse PWM wave is 0.00291s and the pulse positions are as follows: t 1 ¼ 0:00156 s; t 2 ¼ 0:00447 s; t 3 ¼ 0:00553 s; t 4 ¼ 0:00844 s; t 5 ¼ 0:01156 s; t 6 ¼ 0:01447 s; t 7 ¼ 0:01553 s; t 8 ¼ 0:01844 s: The four-pulse PWM wave is an odd function and its fundamental component is calculated as follows. The fundamental components are calculated from Equation (10.3): A1 ¼ 0; 2 t2 tð4 tð6 ð 24 1 sin o0 tdt þ 1 sin o0 tdt þ ð 1Þ sin o0 tdt B1 ¼ T0 t1 tð8 t3 # þ ð 1Þ sin o0 tdt ¼ 0:912 V t7 where T0 ¼ 0.02 s and o0 ¼ 100p rad. t5 280 Applied Intelligent Control of Induction Motor Drives Amplitude of fundamental component is obtained from Equation (10.5): U ¼ C1 ¼ F qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ A21 þ B21 ¼ 0:912 V Power of signal of the wave is obtained from Equation (10.8): P PWM ¼ Tð0 UðtÞ2 dt 0 ¼ 0:582: T0 Power of the fundamental component of the wave is obtained from Equation (10.10): P F 1 1 ¼ C12 ¼ ð0:912Þ2 ¼ 0:416: 2 2 Power of all the harmonic components of the wave is P H ¼P PWM P F ¼ 0:582 0:416 ¼ 0:166: Because the four-pulse PWM wave is an odd function, the harmonic components have the following properties: 1. Ai ¼ 0, for all i 2. Ci ¼ 0 when i is an even number, which implies that there are no even harmonic components in the four-pulse PWM wave. Comparing with the square wave in Example 10.1, the amplitude of the 3rd harmonic has been reduced in the four-pulse PWM wave. Example 10.3 Four-Pulse Wave with Moved Positions When the pulses in Figure 10.6 are moved to certain positions, the energy of the harmonics may be spread over a wide frequency range. The harmonic amplitudes are reduced, and the fundamental amplitude is increased as shown in Figure 10.7. t1 t2 t3 t4 t5 t6 t7 t8 1 Magnitude (V) Voltage (V) 1 0.5 0 -0.5 -1 0 0.8 0.6 0.4 0.2 0 0.005 0.01 0.015 0.02 0 5 10 15 Time (s) Figure 10.7 A four-pulse waveform and its Fourier series. 20 25 30 ith component 281 Optimized Random PWM Strategies Based on Genetic Algorithms The pulse width of the four-pulse wave is also 0.00291s and the pulse positions are as follows: t 1 ¼ 0:00199 s; t 2 ¼ 0:0049 s; t 3 ¼ 0:005 s; t 4 ¼ 0:00791 s; t 5 ¼ 0:0119 s; t 6 ¼ 0:01481 s; t 7 ¼ 0:0152 s; t 8 ¼ 0:01811 s: The four-pulse wave is neither even nor odd and its fundamental component is calculated as follows. Fundamental components are calculated from Equation (10.3): 2 t2 tð4 tð6 ð 2 A1 ¼ 4 1 cos o0 tdt þ 1 cos o0 tdt þ ð 1Þ cos o0 tdt T0 t1 þ tð8 t3 t5 # ð 1Þ cos o0 tdt ¼ 0:0073 V t7 2 t2 tð4 tð6 ð 24 B1 ¼ 1 sin o0 tdt þ 1 sin o0 tdt þ ð 1Þ sin o0 tdt T0 t1 þ ðt8 t3 t5 # ð 1Þ sin o0 tdt ¼ 0:9879 V t7 where T0 ¼ 0.02 s and o0 ¼ 100p rad. The amplitude of the fundamental component is obtained from Equation (10.5): U ¼ C1 ¼ F qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ A21 þ B21 ¼ 0:988 V: The power of the wave is obtained from Equation (10.8): P PWM ¼ Tð0 UðtÞ2 dt 0 T0 ¼ 0:582: The four-pulse wave with moved pulse positions has the same power of signal as the PWM wave in Example 10.2 because of equal pulse widths. The power of the fundamental component of the wave is obtained from Equation (10.10): P F 1 1 ¼ C12 ¼ ð0:988Þ2 ¼ 0:488: 2 2 282 Applied Intelligent Control of Induction Motor Drives The power of the all harmonic components of the wave is P H ¼P P PWM F ¼ 0:582 0:488 ¼ 0:094: The 5th harmonic is prominent in the four-pulse wave. To reduce the lower frequency harmonics, PWM with a higher carrier frequency should be employed. Example 10.4 Standard PWM Output with a 5-kHz Triangular Carrier Wave The standard PWM inverter (Figure 10.1) is simulated with the following parameters: Frequency of carrier wave ¼ 5 kHz Amplitude of carrier wave ¼ 1 V Frequency of reference sinusoidal wave ¼ 50 Hz Amplitude of reference sinusoidal wave ¼ 0.8 V (Modulation index ¼ 0.8) DC source ¼ 1 V. The spectrum of the output wave Uab of the standard PWM inverter is shown in Figure 10.8 and several prominent harmonics are present. As shown in Figure 10.4, the pulse frequency of Uab is about two times of the triangular-carrier frequency, hence the prominent harmonic has a frequency of 10 kHz. 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 104 Hz Figure 10.8 Spectrum of the standard PWM output Uab. The evaluation results for various PWM waveforms are summarized in Table 10.1. Comparing the results for Examples 10.2 and 10.3 in Table 10.1, we may conclude that when pulse positions are changed, 1. 2. 3. 4. the THD is reduced; the energy of the harmonics is spread; power and amplitude of the harmonic components are reduced; power and amplitude of fundamental component are enhanced; 283 Optimized Random PWM Strategies Based on Genetic Algorithms Table 10.1 Evaluation results of various PWM waveforms. Performance of PWM Example 10.1 Example 10.2 Example 10.3 Example 10.4 THD Equation (10.7) Power of signal Equations (10.8) and (10.9) Power of fundamental component Equation (10.10) Power of all harmonic components Equation (10.11) Amplitude of fundamental component Equation (10.5) Amplitude of max harmonic component Equation (10.6) 0.483 1 0.631 0.582 0.438 0.582 0.774 0.508 0.811 0.416 0.488 0.318 0.189 0.166 0.094 0.190 1.273 V 0.912 V 0.988 V 0.797 V 0.424 V 0.385 V 0.301 V 0.318 V at 10 kHz 5. the power of signal (summation of the power of fundamental component and the power of all harmonic components) is unchanged. 10.3 Random PWM Methods To improve the performance of the PWM inverter by using traditional mathematical methods, very complex calculation is involved. Hence, random PWM methods optimized by genetic algorithm (GA) are proposed. Various random pulse-width modulation techniques for dc-ac inverters have been reported and summarized in (Trzynadlowski et al., 1994). The three basic random PWM strategies are: 1. random carrier-frequency modulation (Habetler and Divan, 1991; Boys and Handley, 1992; Pedersen and Blaabjerg, 1992), in which the carrier frequencies are randomly varied; 2. random pulse-position modulation (Kirlin, Kwok and Trzynadlowski, 1993; Kirlin et al., 1994), in which the switching pulses are randomly placed in individual switching intervals; 3. random switching or random pulse-width modulation (Legowski and Trzynadlowski, 1989; Legowski and Trzynadlowski, 1990; Tse et al., 2000), in which the pulse width is randomly varied relative to the output-pulse width of the standard PWM. 10.3.1 Random Carrier-Frequency PWM Random carrier-frequency modulation may be regarded as a special frequency shift keying (FSK) technique (Habetler and Divan, 1991). The instantaneous carrier half period can be 284 Applied Intelligent Control of Induction Motor Drives described in terms of the half switching period Tn, as follows: fi ¼ 1 Tn ð10:12Þ Tn ¼ nðti Þ where n ¼ 1, 2,. . ., N, and Tn is the time period determined by the random function n(ti). A triangular carrier waveform with random frequency is shown in Figure 10.9. Ti Ti+1 Ti+2 Ti+3 1V 0V -1V tk Figure 10.9 tk+1 tk+2 tk+3 tk+4 Triangular carrier waveform with random frequency. In computer simulation, pseudo Gaussian ‘white’ noise is used as the random function n(ti), while in DSP-based PWM inverter implementation, the random function is generated by a pseudo-random function generator. When the DC supply is 1 V, the mean random-carrier frequency is 5 kHz and its amplitude is 1 V, frequency of sinusoidal wave is 50 Hz and amplitude is 0.8 V (modulation index equals 0.8), and FFT is based on 4096 samples, the spectrum of output Uab of the random carrier-frequency PWM inverter is as shown in Figure 10.10. 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 4 10 10 Hz Figure 10.10 Spectrum of output Uab of random carrier-frequency PWM inverter. 285 Optimized Random PWM Strategies Based on Genetic Algorithms 10.3.2 Random Pulse-Position PWM In random pulse-position PWM, harmonic components of the output waveform are suppressed by moving the PWM positions randomly in a pulse interval, while keeping all pulse widths unchanged. The random pulse position PWM may be expressed as follows. Pcenter ðnÞ ¼ PPWM center ðnÞ RðnÞ ð10:13Þ where n ¼ 1, 2,. . ., N; P_center and PPWM_center are center positions of nth pulse of the random PWM and the standard PWM, and R(n) the is nth random number. An example of random pulse-position PWM waveform is shown in Figure 10.11 together with a standard PWM for comparison. Standard PWM Random pulse-position PWM 1 2 1 2 3 3 4 4 5 5 6 6 7 8 7 9 10 8 9 10 Figure 10.11 Comparison between random pulse-position PWM and standard PWM. A random pulse-position PWM is simulated and evaluated by the following steps. Step 1 Obtain a standard PWM pulse series by using a 5 kHz triangular-carrier wave of amplitude 1 V and a 50 Hz modulating sinusoidal waveform of amplitude as 0.8 V, giving a modulation index of 0.8. Step 2 Move the pulse positions of the standard PWM output randomly in each half cycle. Step 3 Calculate the FFT of random pulse-position PWM output based on 4096 samples. When DC supply is 1 V, the spectrum of output Uab of the random pulse-position PWM inverter is shown in Figure 10.12. 10.3.3 Random Pulse-Width PWM Random pulse-width PWM may be expressed as follows: Wrand ðnÞ ¼ WPWM ðnÞ RðnÞ ð10:14Þ where n ¼ 1, 2,. . ., N; WPWM and Wrand are widths of the nth pulse of standard PWM and random pulse-width PWM, and R(n) is the nth random number. 286 Applied Intelligent Control of Induction Motor Drives 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 4 10 10 Hz Figure 10.12 Typical spectrum of random pulse-position PWM inverter output. An example of random pulse-width PWM is shown in Figure 10.13 together with a standard PWM for comparison. 1 2 3 4 1 2 3 4 5 6 7 8 9 10 6 7 8 9 10 Standard triangular PWM Random pulse-width PWM Figure 10.13 5 Comparison between random pulse-width PWM and standard PWM. When DC supply is 1 V, carrier frequency is 5 kHz and amplitude is 1 V, frequency of sine wave is 50 Hz and amplitude is 0.8 V (modulation index equals 0.8), and FFT is based on 4096 samples, the spectrum the random pulse-width PWM inverter output Uab is shown in Figure 10.14. 10.3.4 Hybrid Random Pulse-Position and Pulse-Width PWM Both the pulse position and pulse width are randomly changed in a hybrid random pulseposition and pulse-width PWM. When DC supply is 1 V, carrier frequency is 5 kHz and amplitude is 1 V, frequency of sine wave is 50 Hz and amplitude is 0.8 V (modulation index equals 0.8), and FFT is based on 4096 287 Optimized Random PWM Strategies Based on Genetic Algorithms 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 4 10 10 Hz Figure 10.14 Typical spectrum of random pulse-width PWM inverter output. samples, the spectrum of output Uab of the hybrid random pulse-position and random pulsewidth PWM inverter is shown in Figure 10.15. 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 4 10 10 Hz Figure 10.15 Typical spectrum of hybrid random pulse-position and random pulse-width PWM inverter output. 10.3.5 Harmonic Evaluation Results The standard and random PWM output waveforms are generated using the following conditions: DC supply ¼ 1 V Frequency of carrier wave ¼ 5 kHz 288 Applied Intelligent Control of Induction Motor Drives Amplitude of carrier wave ¼ 1 V Frequency of sinusoidal wave ¼ 50 Hz Amplitude of sinusoidal wave ¼ 0.8 V (Modulation index ¼ 0.8) Sample number of FFT ¼ 4096. The output waveforms are then evaluated by Equations (10.5)–(10.11) and the results are summarized in Table 10.2. Table 10.2 Evaluation results of standard and random PWM output waveforms. Evaluation results and equations Standard PWM Random carrier frequency PWM Random pulseposition PWM Random pulsewidth PWM Hybrid random pulseposition and pulsewidth PWM THD Equation (10.7) Signal power Equation (10.8) Power of fundamental Equation (10.10) Power of all harmonics Equation (10.11) Amplitude of fundamental Equation (10.5) Amplitude of max harmonic Equation (10.6) 0.7739 0.5078 0.3176 0.7721 0.5093 0.3191 0.7820 0.5061 0.3141 0.7840 0.5078 0.3142 0.7997 0.5044 0.3076 0.1902 0.1902 0.1920 0.1931 0.1967 0.7970 V 0.7988 V 0.7925 V 0.7927 V 0.7843 V 0.3182 V 0.1219 V 0.1096 V 0.0956 V 0.0757 V Comparing the results in Tables 10.1 and 10.2, we observe that the harmonic amplitudes of various random PWM methods are greatly reduced. However, other evaluated values of the various random PWM methods are not improved compared with the standard PWM inverter. Hence, genetic algorithm is proposed to improve the PWM output waveform. 10.4 Optimized Random PWM Based on Genetic Algorithm Genetic algorithms have been applied to optimize electrical drive systems recently (Zhang et al., 2001; Shi et al., 2002; Shi and Li, 2003). In Chapter 9, the application of real-coded genetic algorithm (GA) to an extended Kalman filter based sensorless induction motor drive is described. In this chapter, the same technique will be employed for optimizing various PWM strategies. The THD of the PWM output waveform is selected as the fitness value of chromosomes, hence the fittest individual in GA optimization will have the best PWM waveform evaluation result. A flowchart for optimizing a random PWM inverter waveform using GA is shown in Figure 10.16. The simulation results for different PWM strategies are listed in Table 10.3. Optimized Random PWM Strategies Based on Genetic Algorithms 289 Start Initialize GA parameters Set iteration number gen = 0 Initialize population of first generation with M random chromosomes gen = gen + 1 Use the chromosomes to generate M PWM output waveforms Calculate fitness values (THD) of the chromosomes of the output waveforms Select the best N individuals based on the fitness values Recombination to exchange the information among the N chromosomes Mutation to overcome local minimum Reinsertion to keep population size as M No gen > L Yes Stop and output the best fit individual Figure 10.16 Flowchart for optimizing random PWM inverter output waveform using GA. (Reproduced by permission of K.L. Shi and H. Li, “Optimized PWM strategy based on genetic algorithms,” IEEE Transaction on Industrial Electronics, 52(5), 2005: 1458–1461. Ó 2005 IEEE.) 10.4.1 GA-Optimized Random Carrier-Frequency PWM The GA program with following parameters is used to optimize a random carrier-frequency PWM. 1. DC supply ¼ 1 V 2. Mean of the carrier frequencies: 5 kHz 290 Applied Intelligent Control of Induction Motor Drives Table 10.3 Comparison of various PWM evaluation results. Simulation results Calculation equations Standard GA carrier GA pulse- GA pulse- GA pulsePWM frequency position width position width THD Power of signal Power of fundamental Power of all harmonics Amplitude of fundamental Amplitude of max harmonic Equation (10.7) Equation (10.8) Equation (10.10) Equation (10.11) Equation (10.5) 0.7739 0.5078 0.3176 0.1902 0.7970 V 0.7478 0.5152 0.3304 0.1848 0.8129 V 0.6420 0.5078 0.3596 0.1482 0.8481 V 0.6489 0.5078 0.3573 0.1505 0.8453 V 0.6085 0.5098 0.3719 0.1377 0.8625 V Equation (10.6) 0.3182 V 0.0877 V 0.1165 V 0.1102 V 0.1423 V 3. 4. 5. 6. 7. 8. 9. 10. 11. Amplitude of carrier wave ¼ 1 V Frequency of sinusoidal wave ¼ 50 Hz Amplitude of sinusoidal wave ¼ 0.8 V (modulation index: 0.8) Total pulse number in 0.02 s: equals total pulse number yielded by the standard PWM Chromosome: time period series of triangular-carrier wave Fitness value of chromosome: THD of PWM inverter output Population size: 200 Maximum number of generations: 200 Sample number of FFT ¼ 4096 By proper scaling, the total pulse number of the GA-optimized random PWM equals exactly the total pulse number yielded by the standard PWM in a fundamental cycle (0.02 s). Hence, the total switching loss in the GA-optimized random PWM is same as that in the standard PWM inverter. Computer simulation shows that the fitness value THD has decreased to 0.7478 at the 200th generation, as shown in Figure 10.17. The spectrum of output Uab of the optimized random-carrier-frequency PWM inverter is shown in Figure 10.18. The real-coded GA method has spread the harmonic energy over a wide frequency range. Comparing with the standard PWM, the THD of the GA-optimized random-carrierfrequency PWM is reduced by about 3.4 %, the power of fundamental component is increased by 4 %, the power of all harmonic components is reduced by 2.8 %, the amplitude of the maximum harmonic component is reduced by about 72.4 %, and the amplitude of the fundamental component is increased by about 2 %. 10.4.2 GA-Optimized Random-Pulse-Position PWM The GA program with following parameters is used to optimize a random pulse-position PWM inverter. 1. DC supply ¼ 1 V 2. Mean of the carrier frequencies: 5 kHz 3. Amplitude of carrier wave ¼ 1 V 291 Optimized Random PWM Strategies Based on Genetic Algorithms Best: 0.74781 0.764 0.762 0.76 Fitness value 0.758 0.756 0.754 0.752 0.75 0.748 0.746 Figure 10.17 0 20 40 60 80 100 120 Generation 140 160 180 200 Convergence process of optimizing a random carrier-frequency PWM inverter. 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 104 Hz Figure 10.18 Spectrum of GA-optimized random-carrier-frequency PWM inverter output. 4. 5. 6. 7. Frequency of sinusoidal wave ¼ 50 Hz Amplitude of sinusoidal wave ¼ 0.8 V (Modulation index: 0.8) Total pulse number in 0.02 s: equals total pulse number yielded by the standard PWM Chromosome: time series of pulse position 292 8. 9. 10. 11. 12. Applied Intelligent Control of Induction Motor Drives Fitness value of chromosome: THD of PWM inverter output Population size: 100 Maximum number of generations: 50 Initial population: Pulse-position series produced by the standard PWM inverter Sample number of FFT ¼ 4096 As shown in Figure 10.19, the fitness value THD has decreased to 0.6420 at the 50th generation. Best: 0.6420 0.75 0.73 Fitness value 0.71 0.69 0.67 0.65 0 10 20 30 40 50 Generation Figure 10.19 Convergence process of optimizing a random pulse-position PWM inverter. The spectrum of output Uab of the optimized random-pulse-position PWM inverter is shown in Figure 10.20. 10.4.3 GA-Optimized Random-Pulse-Width PWM The GA program with following parameters may yield satisfactory results to optimize pulsewidth PWM. 1. 2. 3. 4. DC supply ¼ 1 V Mean of the carrier frequencies: 5 kHz Amplitude of carrier wave ¼ 1 V Frequency of sinusoidal wave ¼ 50 Hz 293 Optimized Random PWM Strategies Based on Genetic Algorithms 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Figure 10.20 5. 6. 7. 8. 9. 10. 11. 12. 0 2 4 6 8 104 Hz 10 Spectrum of GA-optimized random-pulse-position PWM inverter output. Amplitude of sinusoidal wave ¼ 0.8 V (Modulation index ¼ 0.8) Total pulse number in 0.02 s: equals total pulse number yielded by the standard PWM Chromosome: time series of pulse width Fitness value of chromosome: THD of PWM inverter output Population size: 200 Maximum number of generations: 50 Initial population: pulse-width series produced by standard PWM inverter Sample number of FFT ¼ 4096 As shown in Figure 10.21, the fitness value THD has decreased to 0.64895 at the 50th generation. The spectrum of output Uab of the optimized random-pulse-width PWM inverter is shown in Figure 10.22. 10.4.4 GA-Optimized Hybrid Random Pulse-Position and Pulse-Width PWM The GA program with following parameters is used to optimize a hybrid random pulse-position and pulse-width PWM. 1. 2. 3. 4. 5. 6. 7. 8. 9. DC supply ¼ 1 V Mean of the carrier frequencies: 5 kHz Amplitude of carrier wave ¼ 1 V Frequency of sinusoidal wave ¼ 50 Hz Amplitude of sinusoidal wave ¼ 0.8 V (Modulation index ¼ 0.8) Total pulse number in 0.02 s: equals total pulse number yielded by the standard PWM Chromosome: time series of pulse position and pulse width Fitness value of chromosome: THD of PWM inverter output Population size: 200 294 Applied Intelligent Control of Induction Motor Drives Best: 0.64895 0.76 0.74 Fitness value 0.72 0.7 0.68 0.66 0.64 0 10 20 30 40 50 Generation Figure 10.21 Convergence process of optimizing a random pulse-width PWM inverter. 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 104 Hz Figure 10.22 Spectrum of GA-optimized random-pulse-width PWM inverter output. 10. Maximum number of generations: 50 11. Initial population: pulse-position and pulse-width series produced by standard PWM inverter 12. Sample number of FFT ¼ 4096 295 Optimized Random PWM Strategies Based on Genetic Algorithms As shown in Figure 10.23, the fitness value THD has decreased to 0.60853 at the 50th generation. Best: 0.60853 0.76 0.74 Fitness value 0.72 0.7 0.68 0.66 0.64 0.62 0.6 0 10 20 30 40 50 Generation Figure 10.23 Convergence process of optimizing a hybrid random pulse-position and pulse-width PWM inverter. The spectrum of output Uab of the optimized hybrid random pulse-position and pulse-width PWM inverter is shown in Figure 10.24. 10.4.5 Evaluation of Various GA-Optimized Random PWM Inverters Computer evaluation results of various GA-optimized random PWM methods are listed in Table 10.3 for comparison. In order to compare various PWM methods, we define a parameter DEval as follows: DEval ¼ ðEvaluation GA Evaluation SÞ 100%: Evaluation S ð10:15Þ where Evaluation_S is evaluation value of the standard PWM and Evaluation_GA is evaluation value of the GA-optimized random PWM. The computed values of DEval for different GAoptimized random inverters are summarized in Table 10.4. 296 Applied Intelligent Control of Induction Motor Drives 1 0.9 0.8 Magnitude (V) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 104 Hz Figure 10.24 Spectrum of GA-optimized hybrid random pulse-position and pulse-width PWM inverter output. Table 10.4 DEval (%) of GA-optimized random PWM inverters. Simulation results GA random carrier-frequency PWM GA random pulse-position PWM GA random pulse-width PWM GA Hybrid pulse-position and pulse-width PWM THD % Power of signal of PWM output Power of fundamental component Power of all harmonic components Amplitude of fundamental Amplitude of max harmonic 3.4 % 1.5 % 17.04 % 0.0 % 16.2 % 0.0 % 21.4 % 0.4 % 4.0 % 13.22 % 12.50 % 17.1 % 2.8 % 2.0 % 72.4 % 22.08 % 6.41 % 63.4 % 20.9 % 6.1 % 65.4 % 27.6 % 8.2 % 55.3 % 10.4.6 Switching Loss of GA-Optimized Random Single-Phase PWM Inverters Switching energy losses of semiconductor devices are caused by charging and discharging output capacitance at turn-on and turn-off periods, which may be expressed as (Kazimierczuk, 2008), 2 Esw ¼ Np Co Vdc ð10:16Þ 297 Optimized Random PWM Strategies Based on Genetic Algorithms where Co is the output capacitance, Vdc is the DC voltage, Np is number of pulses, and Esw is the switching energy loss. Hence, the total switching loss in a fundamental cycle increases in proportion to the total pulse number in the cycle. Since the same pulse number is used, the total switching losses in various GA-optimized random PWM inverters are same as the total switching loss in the standard PWM inverter. 10.4.7 Linear Modulation Range of GA-Optimized Random Single-Phase PWM Inverters In the linear modulation range, that is, modulation index is less than or equals 1, the average value of pulse width of the standard PWM inverter varies directly with the amplitude of the sinusoidal reference signal. Since the total number of pulses and average width of pulses are unchanged, the GA-optimized random PWM inverters retain the features of linear modulation. To demonstrate the linear modulation capability of the GA-optimized random PWM inverters, the GA-optimized random-pulse-position series at a modulation index of 0.8 (obtained in Section 10.3.2) is applied to the PWM inverter with various modulation indices and the harmonic evaluation results are listed in Table 10.5. Table 10.5 Evaluation values of the GA-optimized random-pulse-position PWM. Modulation index THD Power of signal Power of fundamental Power of all harmonics Amplitude of fundamental Amplitude of max harmonic 1 0.9 0.8 0.6 0.4 0.2 0.1 0.5036 0.5699 0.6420 0.8479 1.1828 1.9573 3.4643 0.6377 0.5713 0.5078 0.3818 0.2529 0.1250 0.0566 0.5085 0.4311 0.3596 0.2221 0.1054 0.0259 0.0044 0.1292 0.1402 0.1482 0.1597 0.1475 0.0991 0.0523 1.0083 0.9285 0.8481 0.6665 0.4592 0.2275 0.0933 0.1081 0.0797 0.1165 0.2082 0.2280 0.1507 0.0713 Evaluation values of the standard PWM are listed in Table 10.6 for comparison. Table 10.6 Evaluation values of the standard PWM. Modulation index THD Power of signal Power of fundamental Power of all harmonics Amplitude of fundamental Amplitude of max harmonic 1 0.9 0.8 0.6 0.4 0.2 0.1 0.5235 0.6509 0.7739 1.0664 1.4791 2.3360 3.5540 0.6377 0.5713 0.5078 0.3818 0.2529 0.1250 0.0566 0.5005 0.4013 0.3176 0.1787 0.0793 0.0194 0.0042 0.1372 0.1700 0.1902 0.2031 0.1736 0.1056 0.0525 1.0005 0.8958 0.7970 0.5978 0.3984 0.1968 0.0912 0.2104 0.2605 0.3182 0.3724 0.3255 0.1881 0.0920 298 Applied Intelligent Control of Induction Motor Drives Since the total pulse width remains unchanged, the power of the output signal of the GA-optimized random PWM is same as the standard PWM. The values of DEval computed by Equation (10.15) are listed in Table 10.7. Table 10.7 DEval (%) for GA-optimized random PWM at different modulation indices. Modulation index THD 1 0.9 0.8 0.6 0.4 0.2 0.1 3.80 12.44 17.04 20.49 20.03 16.21 2.52 Power of signal Power of fundamental 0 0 0 0 0 0 0 1.56 7.40 13.22 24.29 32.91 33.51 4.76 Power of all harmonics 6.05 17.65 22.08 21.37 15.03 6.16 0.38 Amplitude of fundamental 0.78 3.65 6.41 11.49 15.26 15.60 2.30 Amplitude of max harmonic 48.62 69.40 63.39 44.09 29.95 19.88 22.50 The GA-optimized random-pulse-position PWM inverter has very good linear modulation capacity with lower THD and good evaluation values when the modulation index is between 0.2 and 0.9. When the modulation index equals 0.1 and 1, the GA-optimized random-pulseposition PWM is also superior to the standard PWM as observed from Table 10.7. 10.4.8 Implementation of GA-Optimized Random Single-Phase PWM Inverter 10.4.8.1 GA-Optimized Random-Carrier-Frequency PWM Inverter The GA-optimized random-carrier-frequency series will be repeatedly applied to control the PWM inverter to replace the standard triangular carrier generator in order to minimize the total harmonic distortion. 10.4.8.2 GA-Optimized Random Pulse-Position and Pulse-Width PWM Inverters The other three GA-optimized random PWM inverters are (1) random-pulse-position PWM inverter, (2) random-pulse-width PWM inverter, and (3) hybrid random pulse-position and pulse-width PWM inverter. The states of Uab of the inverter must be translated into the switching states of the semiconductor switches, and this process is repeated in every fundamental cycle. For the inverter shown in Figure 10.25, the transformation relationship is as listed in Table 10.8. 10.4.9 Limitations of Reference Sinusoidal Frequency of GA-Optimized Random PWM Inverters Because the optimization process is based on a fixed sinusoidal reference frequency, the optimum performance of the GA-optimized random PWM inverter is obtained for that 299 Optimized Random PWM Strategies Based on Genetic Algorithms IGBT 1 IGBT 3 DC Uab IGBT 2 Figure 10.25 IGBT 4 Semiconductor devices and Uab pulse sequence. Table 10.8 State of semiconductor switches according to the states of Uab. Uab 1 1 0 0 IGBT 1 IGBT 2 IGBT 3 IGBT 4 Off On On Off On Off Off On On Off On Off Off On Off On particular frequency. When the GA-optimized random PWM is used at a different reference frequency, the carrier frequency should be modified as follows: f new carrier ¼ f GA carrier f f new reference ð10:17Þ GA reference where f_new_carrier is the new carrier frequency, f_new_reference is the new reference frequency, f_GA_carrier is the carrier frequency when PWM inverter is optimized, and f_GA_reference is the reference sinusoidal frequency when PWM inverter is optimized. An alternative solution is to construct a look-up table which stores the GA-optimized random switching series at various reference sinusoidal frequencies for the variable-frequency inverter. It is also possible to model the data in the look-up table by using a regression function or a neural network in order to maintain a lower THD. 10.5 MATLABÒ /Simulink Programming Examples Three MATLABÒ /Simulink programming examples are presented in this section. (1) Singlephase sinusoidal PWM; (2) Evaluation of a four-pulse wave; (3) Random carrier-frequency PWM. 10.5.1 Programming Example 1: A Single-Phase Sinusoidal PWM In this programming example, the reference sine wave has a frequency of 50 Hz and an amplitude of 0.8 V, while the triangular carrier wave has a frequency of 5 kHz and an amplitude of 1 V. The single-phase sinusoidal PWM may be modeled and simulated by the following steps. 300 Applied Intelligent Control of Induction Motor Drives Step 1 Build a Simulink model of the triangular carrier PWM ‘single_phase_inverter.mdl’ as shown in Figure 10.26. The PWM model consists of a ‘Sine Wave’ block, two ‘Relational Operator’ blocks, a ‘Repeating Sequence’ block, and an ‘Out1’ block. The ‘Relational Operator’ blocks simulate the modulation operation, the ‘Repeating Sequence’ block simulates the triangular-carrier wave, and the ‘Out1’ block outputs Uab for evaluation. The parameters of these blocks are as listed in Table 10.9. Repeating Sequence Scope1 Scope2 <= 1 Out1 Sine wave <= Uab -1 Gain Ua Ub Figure 10.26 Table 10.9 Simulink model of triangular carrier PWM. Parameters of Simulink model ‘single_phase_inverter.mdl’. Name Function Parameter Sine Wave Generate sinusoidal reference wave Repeating Sequence Generate 5 kHz triangular carrier wave Simulation parameter Manage simulation process Amplitude ¼ 0.8 Frequency ¼ 2 pi 50 Phase ¼ 0 Time values: T_V created by the MATLABÒ program Output values: o_V created by the MATLABÒ program Solver options: Fixed-step Fixed-step size:1/204800 Simulation time: 0–0.2 s Optimized Random PWM Strategies Based on Genetic Algorithms 301 Step 2 Write the following MATLABÒ program (with filename ‘Evaluation.m’ on the book companion website) for waveform evaluation. function y¼Evaluation(x) N¼1024 4; H_pwm¼fft(x,N); Harmonica ¼ H_pwm(1:N/2); ss¼abs(Harmonica); s_V¼ss/(N/2); assignin(‘base’,‘s_V’,s_V); s_THD¼0; for i¼3:N/2, s_THD¼s_THD þ s_V(i)^2; end THD¼sqrt(s_THD)/s_V(2) V_Fundamental¼s_V(2) s_Vh¼s_V; s_Vh(2)¼[ ]; Max_Harmonic ¼max(s_Vh) P_Fundamental¼s_V(2)^2/2 DC¼s_V(1)/2 s_Vfft¼s_V; Pt_FFT¼DC^2 þ sum(s_Vfft.^2)/2 Pt_PWM¼sum(x.^2)/4098 s_Vfft(1)¼[ ]; s_Vfft(1)¼[ ]; P_all_harmonics ¼ sum(s_Vfft.^2)/2 tx¼(0:1:(N/2-1)) 50; bar(tx,s_V) axis([-5000 50000 0 1]); end % Evaluate x % FFT calculation % Cut half of FFT % Calculate magnitude of FFT components % Calculate real amplitude of output components % Assign array ‘s_V’ into workspace % Calculate THD of waveform % Obtain amplitude of fundamental waveform % Cut off fundamental component % Calculate amplitude of max harmonic component % Calculate power of fundamental component % Obtain amplitude of DC component % % % % % Total power of FFT components Total power of standard PWM signal Cut off DC component Cut off fundamental component Calculate power of all harmonic components % Set x-axis as Hz % Plot spectrum of PWM output % Set x-axis and y-axis ranges Step 3 Enter the following code to create the two arrays T_V and o_V in the MATLABÒ workspace. Run the Simulink model ‘single_phase_inverter.mdl’, and run the evaluation program written in Step 2. The two arrays (T_V and o_V) are used by the ‘Repeating Sequence’ block to simulate the triangular carrier wave with a frequency of 5 kHz and an amplitude of 1 V. NN=200; % Switch frequency 5kHz, 200 points during 0.02 seconds for I=1:NN/2 % Create +1 and -1V voltage series o_V(2*I)=1; o_V(2*I-1)=-1; end o_V(NN+1)=-1; T_V=(0:0.02/NN:0.02); % Create time series of carrier wave assignin(’base’,’T_V’,T_V); % Save to workspace assignin(’base’,’o_V’,o_V); % Save to workspace 302 Applied Intelligent Control of Induction Motor Drives Then enter the following MATLABÒ commands to evaluate the PWM output: [tout,xout,yout]¼sim (‘single_phase_inverter ’,0.02); Evaluation(yout); % Run Simulink model ‘single_phase_ inverter.mdl’ % Call MATLAB program ‘Evaluation.m’ The evaluation results are shown on the computer screen as follows and a spectrum of the PWM output wave is shown in Figure 10.8. THD= 0.7739 V_Fundamental= 0.7970 Max_Harmonic= 0.3182 P_Fundamental= 0.3176 DC= 0 Pt_FFT= 0.5078 Pt_PWM= 0.5076 P_all_harmonics= 0.1902 The evaluation results are as listed in the column ‘Uab of standard 5 kHz PWM’ in Table 10.1. Step 4 Enter the command ‘plot(tout, yout)’ to plot the single-phase sine PWM output waveform Uab with 5 kHz carrier frequency, as shown in Figure 10.27. 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.002 0.004 0.006 0.008 Figure 10.27 0.01 0.012 0.014 0.016 0.018 0.02 Waveform Uab of sine PWM output with 5 kHz carrier frequency. 10.5.2 Programming Example 2: Evaluation of a Four-Pulse Wave A four-pulse wave is modeled and simulated by the following steps. 303 Optimized Random PWM Strategies Based on Genetic Algorithms Step 1 Build a Simulink model ‘Four_pulse.mdl’ as shown in Figure 10.28. Repeating Sequence5 Scope 1 Out1 Figure 10.28 Simulink model of the four-pulse wave. Step 2 Input the following vectors into the ‘Repeating Sequence’ block. Time Values = [0,0.00199,0.00199,0.0049,0.0049,0.005,0.005,0.00791,0.00791,0.0119, 0.0119,0.01481,0.01481,0.0152,0.0152,0.01811,0.01811,0.02] Output Values = [0,0,1,1,0,0,1,1,0,0,-1,-1,0,0,-1,-1,0,0] Step 3 Enter the following MATLABÒ commands (or run the program ‘Run_Exp2.m’ on the book companion website). [tout,xout,yout]¼sim (‘Four_pulse’,0.02); Evaluation(yout); bar(s_V); axis([-1 30 0 1.1]); % Call Simulink model named as ‘Four_pulse.mdl’ % Call MATLAB program ‘Evaluation.m’ % Plot bar graph % Set x-axis and y-axis ranges The evaluation results are as follows and a spectrum of the PWM output shown in Figure 10.6 is also obtained. THD = 0.4376 V_Fundamental = 0.9882 Max_Harmonic = 0.3007 P_Fundamental = 0.4883 DC = 2.4414e-004 Pt_FFT = 0.5818 Pt_PWM = 0.5815 P_all_harmonics = 0.0935 10.5.3 Programming Example 3: Random Carrier-Frequency PWM A random carrier-frequency PWM may be modeled and simulated by the following steps. 304 Applied Intelligent Control of Induction Motor Drives Step 1 Open the Simulink model ‘single_phase_inverter.mdl’ in Programming Example 1 and save it as ‘triangle.mdl’. Step 2 Replace the elements of the arrays T_V in the ‘Repeating Sequence’ block in the Simulink model with random numbers by entering following MATLABÒ code: clear; clc; NN=200; % Switch frequency 5kHz, 200 points during 0.02 seconds for I=1:NN/2 % Create +1 and -1V voltage series o_V(2*I)=1; o_V(2*I-1)=-1; end o_V(NN+1)=-1; T_V(1) =0; % Create time series of carrier wave with random number for i=2:NN+1, T_V(i)=T_V(i-1)+0.00002+rand(1)*0.00016; % rand(1) yields a pseudorandom number range as -1~ +1 End assignin(’base’,’T_V’,T_V); % Save to workspace assignin(’base’,’o_V’,o_V); ‘% Save to workspace Step 3 Enter the following MATLABÒ commands to simulate the random carrier-frequency PWM and evaluate the waveforms by the evaluation program written in Step 2 in Programming Example 1. [tout,xout,yout]¼ sim(‘triangle’,0.02); Evaluation(yout); % Call Simulink model named as ‘triangle.mdl’ % Call MATLAB program ‘Evaluation.m’ After running the above MATLABÒ program and the evaluation program, a possible evaluation result is obtained as follows: THD= 0.7708 V_Fundamental= 0.8009 Max_Harmonic= 0.0813 P_Fundamental= 0.3207 DC= 0.0034 Pt_FFT= 0.5112 Pt_PWM= 0.5110 P_all_harmonics= 0.1905 A spectrum of the PWM output similar to that in Figure 10.10 will also be obtained. Because the carrier frequency is randomly produced, the evaluation results may vary from one simulation to another. 305 Optimized Random PWM Strategies Based on Genetic Algorithms Step 4 Enter the command ‘plot(tout, yout)’ to plot the random carrier-frequency PWM output Uab, as shown in Figure 10.29. 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Figure 10.29 Waveform Uab of the random carrier-frequency PWM. 10.6 Experiments on Various PWM Strategies The GA-optimized single-phase random-carrier-frequency PWM inverter is implemented and compared with the standard PWM inverter by the hardware setup in Figure 10.30. The experimental facility consists of a TMS320F2812 DSP board, an IRAMX16UP60A inverter module, a digital oscilloscope, a PC host computer, and a DC power supply. The DSP facilitates the implementation of various PWM strategies in real-time. 10.6.1 Implementation of PWM Methods Using DSP DSP TMS320F2812 is able to generate two types of PWM waveform, viz. symmetric waveform and asymmetric waveform. The symmetric PWM has less harmonic distortion (Texas Instruments Incorporated, 2003) than the asymmetric PWM, but the latter gives twice the resolution. In this chapter, the symmetric PWM is chosen for implementing the various PWM methods. The main steps (Texas Instruments Inc., 2003) to operate PWM in TMS320F2812 DSP chip are: a. Initialize a 16-bit ‘Timer Period Register’ and a 16-bit ‘Full Compare Register’, respectively. 306 Applied Intelligent Control of Induction Motor Drives IRAMX16UP60A Module IGBT 1 IGBT 3 Ua DC Ub IGBT 2 IGBT 4 Gate drive PC TMS320F2812 DSP board Figure 10.30 PWM inverter experimental system. (Reproduced by permission of K.L. Shi and H. Li, “Optimized PWM strategy based on genetic algorithms,” IEEE Transaction on Industrial Electronics, 52(5), 2005: 1458–1461. Ó 2005 IEEE.) b. Load the PWM period into the ‘Timer Period Register’ and the sinusoidal reference value into the ‘Full Compare Register’, respectively. c. Compare the output of a ‘General Purpose Timer’ with the ‘Timer Period Register’. When they are equal, two pairs of pulse signals are generated from a ‘Full Compare Unit’ and a software interrupt is triggered. d. Upon receiving the software interrupt signal, the program updates the value in the ‘Timer Period Register’ and the value in the ‘Full Compare Register’ according to the desired carrier frequency requested by different PWM methods. e. Repeat from step (b) to step (d). Three PWM methods are implemented by the DSP-based inverter. The operating strategies are described as follows: A. Standard PWM method, which applies a constant carrier frequency; B. Random carrier-frequency PWM, which employs a random carrier frequency generated by a pseudorandom function that depends on a special seed sequence; and C. GA-optimized random-carrier-frequency PWM method, in which the random-carrierfrequency series is stored in a DSP, the optimization having been performed optimized off-line by GA. It should be noted that the above implementation of the GA-optimized PWM method does not incur extra hardware cost and programming complexity compared with other PWM techniques. Optimized Random PWM Strategies Based on Genetic Algorithms 307 10.6.2 Experimental Results In order to compare the performance of three PWM methods, the normalized output voltage of PWM inverter and the corresponding harmonic spectrum at different switching frequencies are displayed on a digital oscilloscope as shown in Figures 10.31–10.33. Figure 10.31 Output waveforms of standard PWM inverter. Upper trace: Voltage Uab (Time scale: 4 ms/ div; voltage scale: 2 V/div) Lower trace: Frequency spectrum (Frequency scale: 2.5 kHz/div; voltage scale: 300 mV/div). (a) Carrier frequency ¼ 1 kHz (b) Carrier frequency ¼ 5 kHz (c) Carrier frequency ¼ 10 kHz (d) Carrier frequency ¼ 15 kHz. (Reproduced by permission of K.L. Shi and H. Li, “Optimized PWM strategy based on genetic algorithms,” IEEE Transaction on Industrial Electronics, 52(5), 2005: 1458–1461. Ó 2005 IEEE.) 10.6.2.1 Standard PWM When the carrier frequency is constant, the DSP-controlled inverter outputs standard PWM waves. Figure 10.31 shows the output voltage Uab when the carrier frequency is 1 kHz, 5 kHz, 10 kHz, and 15 kHz, respectively. 308 Applied Intelligent Control of Induction Motor Drives 10.6.2.2 Random Carrier-Frequency PWM When the carrier frequency is randomly changed, the DSP generates a random carrierfrequency PWM. Figure 10.32 shows the output voltage Uab when the mean frequency of the carrier is 1 kHz, 5 kHz, 10 kHz, and 15 kHz, respectively. Figure 10.32 Output waveforms of random PWM inverter. Upper trace: Voltage Uab (Time scale: 4 ms/ div; voltage scale: 2 V/div) Lower trace: Frequency spectrum (Frequency scale: 2.5 kHz/div; voltage scale: 300 mV/div) (a) Mean random carrier frequency ¼ 1 kHz (b) Mean random carrier frequency ¼ 5 kHz (c) Mean random carrier frequency ¼ 10 kHz (d) Mean random carrier frequency ¼ 15 kHz. (Reproduced by permission of K.L. Shi and H. Li, “Optimized PWM strategy based on genetic algorithms,” IEEE Transaction on Industrial Electronics, 52(5), 2005: 1458–1461. Ó 2005 IEEE.) Optimized Random PWM Strategies Based on Genetic Algorithms 309 10.6.2.3 GA-Optimized Random-Carrier-Frequency PWM The GA-optimized random-carrier-frequency series is obtained off-line by a MATLABÒ program and then copied to the DSP PWM program to replace conventional carrier operation. When the optimized program is loaded into the experimental DSP device, the inverter gives optimized performance as presented in Figure 10.33. Figure 10.33 Output waveforms of GA-optimized random PWM inverter Upper trace: Voltage Uab (Time scale: 4 ms/div; voltage scale: 2 V/div). Lower trace: Frequency spectrum (Frequency scale: 2.5 kHz/div; voltage scale: 300 mV/div). (a) Mean of GA-optimized carrier frequency ¼ 1 kHz (b) Mean of GA-optimized carrier frequency is 5 kHz (c) Mean of GA-optimized carrier frequency ¼ 10 kHz (d) Mean of GA-optimized carrier frequency ¼ 15 kHz. (Reproduced by permission of K.L. Shi and H. Li, “Optimized PWM strategy based on genetic algorithms,” IEEE Transaction on Industrial Electronics, 52(5), 2005: 1458–1461. Ó 2005 IEEE.) 310 10.7 Applied Intelligent Control of Induction Motor Drives Summary In this chapter, real-coded genetic algorithm has been employed to optimize a single-phase inverter by using four random PWM methods. They are (1) GA-optimized random-carrierfrequency PWM, (2) GA-optimized random-pulse-position PWM, (3) GA-optimized randompulse-width PWM, and (4) GA-optimized hybrid random pulse-position and pulse-width PWM. Simulation studies have demonstrated that the GA-optimized random PWM is superior to conventional PWM techniques when harmonic energy spread and THD are considered. DSP-based inverter experiments confirm the feasibility of implementation of GA-optimized random-carrier-frequency PWM. The present investigation has demonstrated the capability of the GA-optimized random PWM technique in improving the power quality of inverters. Further work would be to extend the technique to three-phase PWM inverters that find wider applications in induction motor drives. References Bech, M.M., Pedersen, J.K., Blaabjerg, F., and Trzynadlowski, A.M. (1999) A methodology for true comparison of analytical and measured frequency domain spectra in random pwm converters. IEEE Transactions on Power Electronics, 14(3), 578–586. Boys, J.T. and Handley, P.G. (1992) Spread spectrum carrier: low noise modulation technique for PWM inverter drives. Proc IEE, Part B, 139(3), 252–260. Chiasson, J.N., Tolbert, L.M., McKenzie, K.J., and Du, Z. (2004) A complete solution to the harmonic elimination problem. IEEE Transactions on Power Electronics, 19(2), 491–499. Habetler, T.G. and Divan, D.M. (1991) Acoustic noise reduction in sinusoidal PWM drives using a randomly modulated carrier. IEEE Transactions on Power Electronics, 6(3), 356–363. Kazimierczuk, M.K. (2008) Pulse-width DC-DC Power Converters, John Wiley & Sons, Inc., New York, NY. Kirlin, R.L., Kwok, S., and Trzynadlowski, A.M. (1993) Power spectra of a PWM inverter with randomized pulse position. Proc. PESC’93, pp. 1041–1047. Kirlin, R.L., Kwok, S., Legowski, S., and Trzynadlowski, A.M. (1994) Power spectra of a PWM inverter with randomized pulse position. IEEE Transactions on Power Electronics, 9(5), 463–472. Legowski, S. and Trzynadlowski, A.M. (1989) Hypersonic MOSFET-based power inverter with random pulse width modulation. Conference Record 1989 IEEE-IAS Annual Meeting, pp. 901–903. Legowski, S. and Trzynadlowski, A.M. (1990) Power-MOSFET, hypersonic inverter with high quality output current. Proc. APEC’90, pp. 3–7. Lathi, B.P. (2005) Linear System and Signals, Second edition, Oxford University Press, Oxford, pp. 247–634. Ozpineci, B., Tolbert, L.M., and Chiasson, J.N. (June 2004), Harmonic optimization of multilevel converters using genetic algorithms. Proceedings of Power Electronics Specialists Conference (PESC 04) and vol. 5, pp. 3911–3916. Pedersen, J.K. and Blaabjerg, F. (1992) Implementation and test of a digital quasi-random modulated SFAVM PWM in a high performance drive system. Proceedings of IECON’92 pp. 256–270. Shi, K.L., Chan, T.F., Wong, Y.K., and Ho, S.L. (2002) Speed estimation of an induction motor drive using an optimized extended Kalman filter. IEEE Transactions on Industrial Electronics, 49(1), 124–134. Shi, K.L. and Li, H. (November 2003) An optimized PWM method using genetic algorithms. Proceedings of IECON’03 – 29th Annual Conference of the IEEE Industrial Electronics Society Roanoke, Virginia, USA, pp. 7–11. Texas Instruments Incorporated (November 2003) TMS320F28x DSP Event Manager (EV) Reference Guide, Literature Number: SPRU065B. Trzynadlowski, A.M., Blaabjerg, F., Pedersen, J.K. et al. (1994) Random pulse width modulation techniques for converter-fed drive systems – a review. IEEE Transactions on Industry Applications, 30(5), 1166–1175. Optimized Random PWM Strategies Based on Genetic Algorithms 311 Tse, K.K., Chung, H., Hui, S.Y.R., and So, H.C. (2000) A comparative investigation on the use of random modulation schemes for dc/dc converters. Transactions on Industrial Electronics, 47, 245–252. Zhang, J., Chung, H.S.-H., Lo, W.-L. et al. (2001) Implementation of a decoupled optimization technique for design of carrier regulators using genetic algorithms. IEEE Transactions on Power Electronics, 16(6), 752–763. Zhou, K. and Wang, D. (2002) Relationship between space-vector modulation and three-phase carrier-based PWM: a comprehensive analysis. IEEE Transactions on Industrial Electronics, 49(1), 186–196. 11 Experimental Investigations 11.1 Introduction This chapter discusses how the algorithms of induction motor intelligent control are realized physically by hardware. The inverter, the controller, and the induction motor are essential components for implementing the control algorithms. Different control algorithms, however, may require different hardware configurations. For example, the open-loop V/Hz controller can be implemented using analog components, and the vector controller can be implemented using digital devices such as a DSP (Ben-Brahim and Kawamura, 1992; Kubota, Matsuse and Nakano, 1993; Xu and Novotny, 1996) or a PC (Zhong, Messinger and Rashad, 1991). The fuzzy control algorithm can be implemented using a fuzzy microcontroller or a DSP device with a fuzzy-logic program; the neural-network algorithm can be implemented with neural network devices; the expert system algorithm may be implemented by a DSP device with an expert-system control program. It should be mentioned that the implementation of the expert-system control algorithm requires a high-precision speed sensor, such as the expensive Gurley’s Model R158 Rotary Incremental Encoder. Induction motor controllers with analog components have several drawbacks. Aging and temperature rise bring about component variations and regular system adjustments are required. As the parts count increases the reliability of the system decreases. Analog components also raise tolerance issues and upgrades are difficult to achieve as the design is hardwired. Digital systems offer improvements over analog designs. Drift is eliminated since most functions are performed digitally. Upgrades can easily be made in software and parts count is also reduced since most calculation functions can be handled on a single chip. Two fixed-point-DSP motor controllers, namely Analog Devices Inc.’s ADMC331 and Texas Instruments’s TMS320F240, are available commercially. Each system integrates a digital signal processor chip with the peripherals of a micro-controller and hence is suitable for induction motor control applications. The fixed-point DSP is preferred for two reasons. Firstly, its cost is much less than that of floating point DSPs. Secondly, a dynamic range of 16 bits and the capability of executing 26 MIPS (million instructions per second) are sufficient for most motor controllers. ADMC331 and TMS320F240 have comparable technical specifications and performance levels, such as the executing capability, memory size, and micro-controller Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 314 Applied Intelligent Control of Induction Motor Drives peripherals, but the former is less expensive. Hence, a Development Tool Kit ADMC331ADVEVALKIT (delivered by Analog Devices Inc.) is chosen for the experimental studies. The kit is complete with hardware (ADMC331 processor board and ADMC connector board), software (assembler, linker and debugger), and serial cable for connection to a PC. With the ADMC331 as the core element, a DSP-based hardware system is configured to implement some of the intelligent control algorithms. The system consists of a power module, a DSP-processor, 3-phase current sensors, an encoder, an induction motor, a host PC, a data-acquisition card and a data-acquisition PC. Based on the special hardware configuration and some Assembly and Cþþ referencing programs and manuals delivered by Analog Devices Inc. Amirix Inc., and Advantech Co., the following program files in Assembly language and Cþþ language have been developed for the experimental studies: (a) DSP main program and subroutines for induction motor run-up experiment, (b) DSP main program, routines, and subroutines of fuzzy/PI controller, (c) DSP FOC main program for the GA-EKF experiment, (d ) a data-acquisition Cþþ program for the DSP code debug on a PC. Four experiments have been performed: (1) determination of the electrical parameters of the 147-W induction motor used in the drive system, (2) an induction motor run-up experiment to verify the induction motor model, PWM model, encoder model, and decoder model built in Chapter 3, (3) a DSP based experiment on the fuzzy/PI two-stage controller to verify the control algorithm proposed in Chapter 6, and (4) an experiment to verify the GA-EKF speed estimation algorithm proposed in Chapter 9. Section 11.8 presents four DSP Programming examples on a floating-point digital signal processor (DSP) TMS320F28335 delivered by Texas Instruments Inc. 11.2 Experimental Hardware Design for Induction Motor Control The experimental hardware of the intelligent control is configured by the following components and is shown in Figure 11.1, while photographs of the experimental system are shown in Figure G.1 and G.2 of Appendix G. 11.2.1 Hardware Description 11.2.1.1 DSP ADMC331 Processor Board Analog Devices Inc.’s ADMC331 is a low cost, single-chip DSP-based controller, which is suitable for implementing an induction motor drive. The ADMC331 integrates a 26 MIPS, fixed-point DSP core with a complete set of motor control peripherals. The DSP core of the ADMC331 is the ADSP-2171 with ADSP-2100 based architecture, which is completely code compatible with the ADSP-2100 DSP family and combines three computational units, dataaddress generators and a program sequencer. The computational units comprise an ALU, a multiplier/accumulator (MAC) and a barrel shifter (comprising the shifter array, the OR/ PASS logic, the exponent detector, and the exponent compare logic). The ADSP-2171 has instructions for bit manipulation, multiplication (X squared), biased rounding and global interrupt masking. In addition, two flexible, double-buffered, bidirectional, and synchronous serial ports are included in the ADMC331. 315 Experimental Investigations 6 Data acquisition PC 10 Host PC Data acquisition card PCL818HG 9 ADMC 2 Connector board J6 RS-232 port 1 12-bit DAC AD7568 DSP ADMC331 (26MIPS) 3-phase PWM J3 4 Encoder 1/5 hp 3-phase induction motor IM J4 Current sensor board Gate drive IR2132 DSP system power supply Power module IRPT1058A 3 Integrated Power Stage J1 5 Isolating transformer 8 7 220V single-phase AC Figure 11.1 Hardware configuration for the experiments on intelligent control of induction motor. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. 2002 IEEE.) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Component ADMC331 Processor Board ADMC Connector Board Integrated Power Stage (IRPT1058A) Encoder (GBZ02) Current Sensor Board (3I411A) Data-Acquisition Card (PCL818HG) Isolating Transformer AC Induction Motor (Model 295) Data-Acquisition PC (PII350) Host PC (ThinkPad 600E PII 300) Manufacturer Analog Devices Inc. Analog Devices Inc. International Rectifier Inc. China Sichuan Opto-electronic Co. China WB Automation Institute. Taiwan Advantech Co. Ltd. China Chengdu Transformer Co. USA Bodine Electric Co. Intel Inc. IBM Co. 316 Applied Intelligent Control of Induction Motor Drives The ADMC331 provides 2K 24-bit program memory RAM, 2K 24-bit program memory ROM and 1K 16-bit data-memory RAM. The program and data-memory RAM can be bootloaded through the serial port from a serial ROM (SROM), E2PROM, asynchronous (UART) connection or synchronous connection. The program memory ROM includes a monitor that adds software-debugging features through the serial port. In addition, a number of pre-programmed mathematical and motor control functions are included in the program memory ROM. The motor control peripherals of the ADMC331 include a 16-bit center-based PWM generation unit that can be used to produce high accuracy PWM signals with minimal processor overhead and seven analog input channels. The device also contains two auxiliary 8-bit PWM channels, a 16-bit watchdog timer and it has expansion capability through the serial ports and 24-bit digital I/O ports. 11.2.1.2 ADMC Connector Board The ADMC connector board is a part of the development tool kit ADMC331-ADVEVALKIT produced by Analog Devices Inc. The connector board offers the following functions: . . . . Connector (J1) accepts speed signals from the encoder. Connector (J3) provides analog inputs that are fed to the ADC interface circuitry of the ADMC331 processor chip. It can receive the signals from the current sensors. Connector (J4) brings the six PWM output signals from the DSP ADMC331 to International Rectifier PowIRtrain module. An eight-channel, 12-bit serial Digital to Analog Converter (DAC AD7568 chip) interfaces to the DSP-based motor controller through serial port SPORT0 on the ADMC331 chip. The eight analog outputs are brought to the data-acquisition PC through connector (J6). 11.2.1.3 Integrated Power Stage The integrated power stage adopts the IRPT1058C PowIRtrain of International Rectifier Inc., which provides the complete conversion function for a 0.75 hp (0.56 kW) induction motor controller with variable frequency and variable voltage. The PowIRtrain combines a power module IRPT1058A with a Driver-Plus Board IRPT1058D. The power module IRPT1058A contains a single-phase input bridge rectifier and a 3-phase IGBT inverter. Figure 11.2 shows the block diagram of the power module. The specifications of IRPT1058A are as follows. . . . . . . . Input Power: Voltage 220 V, single-phase, 50/60 Hz Output Power: Voltage 0–230 V (defined by external PWM control) Pulse deadtime: 0.8 ms Minimum input pulse width: 1 ms DC link voltage: 230 V Isolation voltage: 2500 V rms DC bus filter capacitor: 2 680 mF, 400 V The Driver-Plus Board IRPT1058D contains DC link capacitors, capacitor soft charge function, gate driver IR2132 for insulated gate bipolar transistors (IGBT), DC bus voltage 317 Experimental Investigations Voltage source inverter Single phase rectifier IGBT 1 IGBT 3 IGBT 5 U V W AC input (220V) IGBT 2 G1 G2 Figure 11.2 IGBT4 G3 G4 IGBT 6 G5 G6 Power module IRPT1058A. and current feedback circuit, protection circuitry and system power supply. Pulse-Width Modulated (PWM) signals from the DSP ADMC331 are input to the gate drive of the inverter IGBT switches to produce a 3-phase voltage of variable magnitude and frequency. The system power supply offers the user 5 and 15 V to power the DSP controller. 11.2.1.4 Encoder An encoder manufactured by China Sichuan Opto-electronic Co. is used for the motor speed measurement. The encoder is an optoelectronic feedback device that uses a patterned optical mask and a LED light source and transistor photosensor pair. As the motor shaft rotates, the light source either passes through the disk, or is blocked by the disk. The two-emitter/detector pairs produce two digital output waveforms which are 90 degrees out of phase with each other. The various components making up the encoder are shown in Figure 11.3. Figure 11.3 Various components making up the encoder. Because the ADMC331 does not have an on-chip encoder interface, the encoder is interfaced to the AMDC331 using programmable I/O (PIO) lines. A DSP software, ENCODER.DSP is used to calculate the shaft speed. 318 Applied Intelligent Control of Induction Motor Drives Encoder features: Model GBZ02 . . . . . 200 pulses/revolution Rise time <100 ns Fall time <100 ns Output voltage VH ¼ 2.5 V, VL ¼ 0 V Single þ 5 V DC supply. 11.2.1.5 Current Sensor Board The current sensor board is used to produce three analog voltages proportional to the motor phase currents. These analog voltages are scaled for input to the ADC on the connector (J3) of the ADMC331 DSP. This board is used to sense currents up to 10 A and provides a voltage output suitable for sampling with an analog to digital converter (ADC). The current sensor board is useful in motion control and power supply designs. It has the following features: . . . . Two phase current sensing based on closed-loop Hall effect current transducer. Single þ5 V DC supply. Working current: 42 mA. Low pass filtering on outputs. 11.2.1.6 PC Data-Acquisition Card Analog to digital (A/D) conversion changes analog voltage or current levels into digital information. The conversion is necessary for the computer to process or store the signals. PCL-818HG of Advantech Co. is a low-cost high-performance data-acquisition board. It is also called a PC-based data-acquisition board. PCL818HG is configured on an ISA slot of PC motherboard and is used to acquire the information of voltages, currents, and rotor speed from the induction motor drive. Specifications of the PCL818HG board are listed as follows. . . . . . . . . . A/D conversion time: Maximum data throughput: Accuracy: Channels: Resolution: Input range selection: Data transfer: Input impedance: Input overvoltage: 8 ms 100 kHz for input range 10 V and 5 V 35 kHz for input range 1 V, 0.5 V, and 0.1 V 0.01–0.04 % 16 single-ended or 8 differential analog inputs 12 bits A/D converter Software controlled Interrupt (IRQ) in Chapter 1 or DMA in Chapter 3 10 MO 30 V DC max. 319 Experimental Investigations 11.2.1.7 Isolation Transformer An isolation transformer (Single-phase 220 V 300 W) manufactured by China Chengdu Transformer Company is used to provide the following benefits: . . Improved safety. Reduced EMI emissions onto the power lines. As the controller is modified by adjusting parameters, power quality issues may arise. 11.2.1.8 AC Induction Motor The motor is a Bodine Electric Company (USA) model 295, 147-W (1/5 HP), 230-V induction motor. The motor is star or ‘Y’ connected with no access to the neutral point. The motor ratings are as follows: Rated voltage, per phase: Rated current, per phase: . Starting current: . Stator resistance per phase: . Pole number: . Net weight: . . 230 V AC 2A 4.5 A 14.6 O 4 30 pounds 11.2.1.9 Data-acquisition PC A Pentium II 350 PC is used for the data-acquisition PC in the experiments of the DSP-based induction motor drive. It performs the following functions: . . Monitoring the drive system by acquiring data from the ADMC connector board, through the data-acquisition card PCL818HG mounted on an ISA port of the personal computer. Storing, plotting, and analyzing the acquired data. 11.2.1.10 Host PC A notebook computer (IBM ThinkPad 600E PII 300) is used as a host PC in the experiments of the DSP-based induction motor drive. It is used for: . . Loading an executable program to the DSP ADMC311 via a RS232 port on the host computer. Starting and debugging the program for driving the induction motor. 11.2.1.11 Power Budget of DSP Controller Table 11.1 summarizes the power budget for the electronics in the experimental system. Note that this budget does not include the drive current required by the induction motor. The motor power requirements (147 W) are well within the PowIRtrain’s 560 W rating. 320 Applied Intelligent Control of Induction Motor Drives Table 11.1 Power budget for the electronics in the experimental system. Component Voltage ADMC connector board, ADMC331 processor board PowIRtrain Encoder Current sensor board 11.3 Current(max) 5VDC 5VDC 15VDC 5VDC 5VDC Total 200 mA 25 mA 25 mA 25 mA 50 mA 325 mA Software Development Method Figure 11.4 shows the software development process for creating an application to run on the ADMC331. It comprises the following steps: 1. A source code in ADSP-21xx assembly language is created by an editor that produces plain text files [.DSP]. 2. The assembly language code is translated by the ADSP-2100 Family Assembler into object code. 3. The ADSP-21xx Linker generates an executable program [.exe] by linking together separately-assembled modules. 4. The executable program is run at debug state on ADMC331 board by using the software ‘ADMC331 Motion Control Debugger’ of Analog Devices Inc. 5. Modify the source program and repeat steps (2) to (4) until the desired output is obtained. Generate code (1) (2) (3) Assembler source files [.DSP] Assembler Linker Debug Analysis of data, variable, or output (5) Executable files [.exe] Motion control debugger on ADMC331 board (4) Figure 11.4 Software development procedure on ADMC331. Each DSP program is organized into a number of source code files (with .DSP extension) each handling a separate function. Each DSP source code file (except the main program) has an accompanying header file (.H extension) which is used to declare functions and variables located within its associated .DSP file. A program structure using multiple files and header files results in minimal coupling between blocks. . A ‘program’ is one that can run independently. Its source file has the extension .DSP or .C, for example, main program MAIN.DSP or ACQUIRE.C. Experimental Investigations . . 321 A ‘routine’ may be called by a ‘program’. It has the extension .DSP, for example, CAPTURE. DSP. A ‘subroutine’ is not an independent DSP program, but only a program segment located in a ‘program’ or a ‘routine’ and called only by a ‘program’ or a ‘routine’. In ADSP-21xx assembly language structure, a ‘subroutine’ begins from a label and ends with ‘RTS’. In program debugging, one of the following three methods may be employed to monitor the data, variable, and input/output of the developed program: 1. Multimeter: Certain steady-state values in the running program may be observed at the DAC output ports on the ADMC connector board by a digital multimeter. 2. Reading the data memory on the DSP: ADMC331 DSP has a 1k x 16-bit data memory (RAM with address form 0x3C00 to 0x3FFF) which can store successive data values to aid in debugging the code and tuning the controller parameters. The stored data values may then be examined by displaying them with Motion Control Debugger’s plot memory function, or by dumping them to a file on the PC using a dump memory command. From a memory dump file, the data can be further analyzed. Due to limitation of the data memory size on the DSP, the number of captured data is less than 1000. 3. Acquiring data by PCL818HG: A Visual Cþþ program is designed to implement the data acquisition from the DAC to the PC. The eight-way signals can be acquired at a sampling rate up to 100 kHz. 11.4 Experiment 1: Determination of Motor Parameters Tests were performed to determine the electrical parameters of the 147-W induction motor manufactured by Bodine Electric Company. These parameters are required in the simulation studies as well as in tuning of the PI controllers. The details are given in Appendix H. 11.5 Experiment 2: Induction Motor Run Up In order to verify the voltage-input model, sinusoidal PWM model, encoder model, and decoder model built in Chapter 3, the ADMC331 pulse-width-modulator (PWM switching frequency of 10 kHz) block is used to generate a 3-phase, 60-Hz supply to run the motor up to its base speed of 1800 r/min. The encoder GBZ02 is used to measure the angular speed of the motor, while the data-acquisition board PCL818HG is used to acquire signals of the angular speed into the data-acquisition PC from the DAC port on the ADMC connector board. The basic programs designed for this experiment are: (1) main program MAIN.DSP, (2) routine PWM331.DSP (ADSP-21xx assembly language), to produce three PWM signals, (2) routine DAC.DSP, to write the reference phase voltages to the AD7568 digital to analog converter (DAC), (3) routine ENCO.DSP, to detect pulses from the encoder, and (4) PC program ACQUIRE.C (Cþþ language), to acquire the signals of voltage and angular speed from the DAC, as well as the encoder output signal to the data-acquisition PC for observation and analysis. 322 Applied Intelligent Control of Induction Motor Drives File Name Description 1. MAIN.DSP: 2. pwm331.dsp: 3. pwm331.h: 4. ENCODER.DSP: 5. DAC.DSP: DSP source code for main program (listed in Appendix I). pulse width modulator initialization and use routines. header file containing definitions for PWM331.DSP. calculate shaft speed by reading the signal from an encoder. writing to the AD7568 digital to analog converter (DAC) on the ADMC connector board. The DAC is a 12-bit, 8-channel device, and is accessed using the SPORT0 serial port on the DSP. header file containing definitions for DAC.DSP. batch file to convert the DSP source code into an executable file, main.exe which can be downloaded and run on the DSP. Cþþ source code for acquiring phase voltage signals and encoder output signal to the PC. This is built into an executable file acquire.exe to run on the data-acquisition PC with the data-acquisition card PCL818HG. header file containing definitions for ACQUIRE.C. 6. DAC.H: 7. build.bat: 8. ACQUIRE.C: 9. ACQUIRE.H: 11.5.1 Program Design 11.5.1.1 PWM Algorithm The algorithm produces three PWM signals whose fundamental outputs may be described in normalized variables as: Vref A ¼ ksinðyÞ ð11:1Þ Vref B ¼ ksinðy þ 2p=3Þ ð11:2Þ Vref C ¼ ksinðy þ 4p=3Þ ð11:3Þ where k 2 [0,1] is the amplitude and frequency scale factor. The angle y is calculated incrementally for each PWM cycle as: yðnÞ ¼ yðn ¼ yðn 1Þ þ 2pkfmax Ts 1Þ þ kD ð11:4Þ where Ts is the PWM switching period and fmax is the maximum fundamental frequency at k ¼ 1. For an assumed maximum frequency fmax of 100 Hz and a PWM switching frequency of 10 kHz (i.e., Ts ¼ 0.0001s), D ¼ 0.0628 rad. A suitable sine approximating function (Analog Devices, 1992) is given by: sinðxÞ ¼ 3:140625x þ 0:020264x2 5:325196x3 þ 0:544678x4 þ 1:800293x5 ð11:5Þ The sine function is implemented by calling a subroutine ADMC_SIN in ADMC331 ROM. Having calculated the sine functions and scaled by k to produce the reference voltages, the 323 Experimental Investigations PWM on-times may be calculated as: TA ¼ Ts Ts þ Vref A : 2 2 ð11:6Þ Similar equations can be written for the other two phases. 11.5.1.2 Estimating the Actual Stator Frame Voltages In order to estimate the actual 3-phase voltages (Vac_a, Vac_b, Vac_c) applied to the motor, the VDC_HANDLING subroutine in MAIN.DSP uses the DC bus voltage value to perform the following calculations: Vdc measured Vac a ¼ Va ð11:7Þ Vdc max ¼ Vb Vdc measured Vdc max ð11:8Þ Vac c ¼ Vc Vdc measured : Vdc max ð11:9Þ Vac b Va, Vb, and Vc are the requested voltages, but if the DC bus voltage is less than the maximum value, such as when the motor is heavily loaded, the applied voltages will be reduced. 11.5.1.3 Digital to Analog Converter The routine DAC.DSP writes digital values via the AR register to the appropriate location in a buffer. The resulting polarity is then correct at the DAC screw terminals on the ADMC connector board. Table 11.2 gives some examples of digital values used as parameters to the DAC subroutines and the resulting analog voltages produced. When a stator phase-voltage is 0 V in an algorithm and its digital value in the DSP program is defined as 0x0000 or 0xFFFF, the analog voltage output from the DAC is 2.5 V, according to Table 11.2. When the stator phase-voltage magnitude is 188 V in the algorithm and its digital value in the DSP program is defined as 0x3FFF, the analog voltage output from the DAC is 3.75 V. Table 11.2 Digital Value 0x8000 0xBFFF 0xFFFF 0x0000 0x3FFF 0x7FFF DAC output voltages for various digital inputs. Analog Voltage 0V 1.25 V 2.5 V 2.5 V 3.75 V 5V 324 Applied Intelligent Control of Induction Motor Drives 11.5.1.4 Encoder Functions The routine ENCO.DSP is used to detect pulses from the encoder, and a programmable timer on ADMC331 enables the motor speed to be determined. The file contains three subroutines: (1) Init_encoder subroutine: it is used to initialize the encoder subsystem; (2) Timer_isr (interrupt service routine) subroutine: on each timer interrupt, the counter variable is incremented. ALU saturation mode is enabled so that the counter value will only go as high as 0x7FFF. (3) Pio_isr subroutine handles changes detected on the encoder PIO line with a rising edge interrupt. 11.5.1.5 Data Acquisition A Cþþ code file ACQUIRE.C is written to acquire stator voltages and encoder signals via the PCL818HG card to the data-acquisition PC using the direct memory access (DMA) method. DMA is a fast data-transfer method by allowing external devices to transfer data directly to the PC memory without involving the interrupt commands of the system CPU. An executable program ACQUIRE.EXE is produced from the Cþþ code ACQUIRE.C and is run in the dataacquisition PC. 11.5.2 Program Debug The program debug procedure comprises the following steps: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Disconnect the inverter PowIRtrain from the DSP ADMC331. Produce an executable program main.exe using the batch file BUILD.BAT. Invoke the ‘Motion Control Debugger’ program on the host PC. Download the main.exe program from the host PC to DSP. Click the run button on the host PC. Observe and analyze the data, variable, and input/output values, by a digital multimeter, by reading the data memory of ADMC331, or on the data-acquisition PC with the dataacquisition card PCL818HG. Modify the source code of assembly language and iteratively repeat steps (2) to (7), until satisfactory voltage waveforms are obtained. Connect the inverter PowIRtrain to the DSPADMC331 and replace the induction motor by a larger resistor load (three 5K resistors with ‘Y’ connection). The inverter output terminals are connected to the voltage sensor (model 3V411A), so that the output line voltages, Vab and Vac can be transferred to the data-acquisition PC via the data-acquisition card PCL818HG. Download the main.exe program from the host PC to DSP. Run the acquire.exe program on the data-acquisition PC. Click the run button on the host PC and click the start button on the data-acquisition PC. Observe the inverter output line voltages on the data-acquisition PC. When the output of the inverter is satisfactory, program debug is complete and the PowIRtrain may be connected to drive the induction motor. 325 Experimental Investigations 11.5.2.1 Results of Debug At Step (6) 5 4.5 5 4.5 4 3.5 4 3.5 Voltage Vb (V) Voltage Va (V) Figure 11.5 shows the voltage waveforms Va, Vb, and Vc (requested three phase voltages) which are directly acquired by the data-acquisition card PCL818HG via the DAC on the ADMC connector board. 3 2.5 2 1.5 1 0.5 0 0.2 0.25 0.3 0.35 0.4 Time (s) 3 2.5 2 1.5 1 0.5 0 0.2 0.25 0.3 0.35 0.4 Time (s) Voltage Vc (V) 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 11.5 Requested three phase voltages Va, Vb, and Vc output directly from DAC. In Figure 11.5, the requested phase-voltage magnitudes from DAC are 1.25 V (¼ 3.75 V 2.5 V). From Table 11.2, the requested phase-voltage magnitude should be 188 V in the control algorithm and its digital value in the DSP program should be defined as 0x3FFF. Figure 11.6 shows the output waveforms Vah, Val, Vbh, and Vch (three high-side PWM signals and a low-side PWM signal) which are directly acquired by the data-acquisition card PCL818HG from terminals J4 on the ADMC connector board at a sampling rate of 35 kHz. Because the signal values of PWM output are smaller (about 50 mV), they have to be amplified by the PCL818HG card before A/D transformation. With an amplification factor of 10, the maximum sampling rate of the PCL818HG card is limited to 35 kHz. If the four signals Vah, Val, Vbh, and Vcb, are to be acquired simultaneously, the sampling rate of each signal is 8.75 kHz (35/4 kHz), which is much lower than the minimum of 20 kHz (for 10 kHz PWM switching frequency). Hence, the acquired signals in Figures 11.6 and 11.7 have larger distortions and very narrow switching pulses cannot be shown. Nevertheless, it is confirmed that the three PWM signals produce a balanced three-phase system at the desired output frequency of 60 Hz. 326 Applied Intelligent Control of Induction Motor Drives 0.5 Vah 0 Val Voltage (V) -0.5 -1 Vbh -1.5 Vch -2 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Time (s) Figure 11.6 Output waveforms Vah, Val, Vbh, and Vch (three high-side PWM signals and a low-side PWM signal) acquired at a sampling rate of 8.75 kHz at debug Step (6). Figure 11.7 shows the waveform of the difference of the two PWM outputs Vah and Vbh. The line-voltage modulation process may be clearly seen. Comparing Figure 11.7 with Figure 3.31, the experimental PWM waveform verified that the PWM Simulink model built in Chapter 3 is viable. 0.8 Va-Vb 0.6 Voltage (V) 0.4 0.2 0 -0.2 -0.4 -0.6 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Time (s) Figure 11.7 PWM output waveform of Vah – Vbh acquired at a sampling rate of 8.75 kHz. 11.5.2.2 Results of Debug at Step (11) At debug Step (11), the inverter PowIRtrain output line voltage is measured by the voltage sensor (model 3V411A) with gain 0.01 and transferred to the data-acquisition PC via the dataacquisition card PCL818HG at 20 kHz sampling rate. Figure 11.8 shows the line voltage Vab at the inverter PowIRtrain output terminals. Because the voltage sensor gain is 0.01, the actual magnitude of the line voltage in Figure 11.8 is 325 V. The waveform suggests that the inverter is operating at the desired output frequency of 60 Hz. 327 Experimental Investigations 4 3 Voltage (V) 2 1 0 -1 -2 -3 -4 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Time (s) Figure 11.8 Output line voltage Vab of the inverter PowIRtrain acquired at a sampling rate of 20 kHz. After satisfactory debug results have been obtained, the PWM control program may be used to drive the induction motor. 11.5.3 Experimental Investigations The experimental investigations start with the following steps: 1. 2. 3. 4. 5. Invoke the ‘Motion Control Debugger’ program on the host PC. Download the main.exe program from the host PC to DSP. Run the acquire.exe program on the data-acquisition PC. Click the run button on the host PC. Click the start button on the data-acquisition PC. When the executable program main.exe is downloaded into DSP, it is converted into a binary file and located in ADMC331 program memory at address from 0x0030 to 0x010D (occupying 222 12 bit space), while the interrupt vector table is stored at address from 0x0000 to 0x002F. Due to the unavailability of the ADSP-2100 Family Simulators software, program execution time cannot be estimated. Test Results The rotor speed is calculated by calling the ENCO.DSP routine which reads the signal from the encoder. Then, the rotor speed signal and signals of 3-phase voltages (Vac_a, Vac_b, Vac_c) are acquired via DAC at a sampling rate of 40 kHz (sampling rate of each signal is 10 kHz) by the acquire.exe program and are displayed on the data-acquisition PC. The 3-phase voltages (Vac_a, Vac_b, Vac_c) have been estimated by the VDC_HANDLING subroutine on the DSP as described in Equations (11.7), (11.8), and (11.9). Figure 11.9 shows the estimated 3-phase voltages which are applied to the induction motor. According to Table 11.2, the analog values of the stator voltages shown in Figure 11.9 have been modified by: Vestimated ¼ ðVacquire 2:5Þ 188 ðVÞ: 1:25 ð11:10Þ 328 300 300 200 200 Voltage Vac_b (V) Voltage Vac_a (V) Applied Intelligent Control of Induction Motor Drives 100 0 -100 -200 -300 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 100 0 -100 -200 -300 0.1 0.2 0.3 Time (s) 0.4 0.5 0.6 0.7 0.8 Time (s) Voltage Vac_c (V) 300 200 100 0 -100 -200 -300 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 11.9 Estimated 3-phase voltages (Vac_a, Vac_b, Vac_c). where Vacquire represents the voltage signal acquired by PCL818HG card from DAC on the ADMC connector board, while Vestimated represents the estimated value of the stator phase voltage. Figure 11.10 shows the rotor speed response (time ¼ 0 s 0.8 s) calculated by the routine ENCO.DSP and acquired by the data-acquisition card PCL818HG via the DAC port on the ADMC Connector Board. At steady state, the motor runs at a speed of about 187 rad/s, confirming that the output frequency of the inverter is 60 Hz. Rotor speed (rad/s) 180 130 80 30 -20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) Figure 11.10 Rotor speed response (time ¼ 0 s 0.8 s). 329 Experimental Investigations 11.5.3.1 Verifying the Encoder and Decoder Models Figure 11.11 shows the encoder output signal which is acquired at a sampling rate of 10 kHz, while Figure 11.12 shows the rotor speed calculated from the encoder output signal, using the decoder model shown in Figure 3.35 of Chapter 3. 5 20 Speed (rad/sec) Voltage (V) 4 3 2 1 0 -1 0.14 0.143 0.146 0.149 0.152 0.155 0.158 15 10 5 0 -5 0.14 Time (s) Figure 11.11 Encoder output signal acquired at a sampling rate of 10 kHz. 0.143 0.146 0.149 0.152 0.155 0.158 Time (s) Figure 11.12 Actual speed response calculated by the decoder model. Figure 11.13 shows the encoder output signal which is acquired at a sampling rate of 20 kHz while Figure 11.14 shows the speed response calculated using the decoder model. 5 30 Speed (rad/sec) Voltage (V) 4 3 2 1 0 25 20 15 10 5 -1 0.27 0.275 0.28 0.285 0.29 0.295 0.3 0.305 0.31 0.315 0.32 Time (s) Figure 11.13 Encoder output signal acquired at a sampling rate of 20 kHz. 0 0.27 0.275 0.28 0.285 0.29 0.295 0.3 0.305 0.31 0.315 0.32 Time (s) Figure 11.14 Actual speed response calculated by the decoder model. The simulation models of the PWM inverter, encoder, and decoder (which have been built in Chapter 3) may be compared with the experimental results, for example, Figure 3.34 versus Figures 11.11,11.13 and 3.40 versus Figures 11.12 and 11.14. Although a number of uncertain factors in the experimental system (such as the load, motor parameter changes, calculation tolerance, and noise) have not been accounted for, the simulation results of the encoder and decoder in Chapter 3 are approximately the same as the experimental results. The encoder and decoder models developed in Chapter 3 are thus verified. 330 11.6 Applied Intelligent Control of Induction Motor Drives Experiment 3: Implementation of Fuzzy/PI Two-Stage Controller This experiment is designed to verify the algorithm of the fuzzy/PI two-stage controller which has been described in Section 6.5 in Chapter 6. Source codes of the fuzzy/PI two-stage controller are written by ADSP-21xx assembly language. The hardware system has been described in Figure 11.1 and the software development method has been described in Section 11.3. The contents of the .DSP and .H files of the DSP-based fuzzy/PI controller are summarized as follows. File Name Description MAIN.DSP FUZZY.DSP, FUZZY.H CURRENTMC.DSP CURRENTMC.H STCPI.DSP, STCPI.H ADC331.DSP, ADC331.H DAC.DSP, DAC.H DIVIDE.DSP, DIVIDE.H FPMATH.DSP, FPMATH.H MATH_32B.DSP, MATH_32B.H PWM331.DSP, PWM331.H ROMUTIL.H ENCO.DSP, ENCO.H SPEEDSET.DSP, SPEEDSET.H CONST331.H CAPTURE.DSP, CAPTURE.H build.bat: Induction machine control main program Fuzzy frequency controller Current magnitude PI controller Stator-current PI controller Analog to digital converter of stator currents Writing to DAC on ADMC connector board Divide function Floating point math routines 32 bit math routines PWM functions ROM utility definitions Encoder functions Speed setpoint function ADMC331-related constants Capturing variables to data memory of ADMC331 Batch file to build the DSP source code into an executable file main.exe which can be downloaded and run on the DSP. Cþþ source codes for acquiring signals to PC ACQUIRE.C, ACQUIRE.H: 11.6.1 Program Design 11.6.1.1 Control Main Program (MAIN.DSP) The main program is MAIN.DSP (listed in Appendix J), and the file CONST331.H has constant definitions. The file MAIN.DSP contains the initialization code, the main loop, and top level software architecture. The initialization code makes calls to all of the various subroutines which initialize a given function such as the encoder, DAC, and so on. Design details of the fuzzy frequency controller, PI current magnitude controller, and stator current controllers are described as follows. 11.6.1.2 Fuzzy Slip Frequency Controller (FUZZY.DSP) Source code of the fuzzy frequency controller FUZZY.DSP contains (1) subroutine of fuzzification operation of speed command, (2) subroutine of fuzzification operation of error 331 Experimental Investigations between speed command and actual speed, (3) subroutine of fuzzy inference operation, INFERE.DSP, and (4) subroutine of defuzzification operation. Fuzzification Subroutine of Speed Command The subroutine of fuzzification operation of speed command converts the crisp input values of speed command oo to fuzzy sets. Fuzzy conversion involves the calculation of triangular degrees of membership and calculation of linguistic values. With reference to Figure 6.32 (Membership function of speed command), the degrees of membership and linguistic values can be calculated. The six constants of fuzzification operation of speed command in Figure 11.15 are defined in Table 11.3, while Table 11.4 summarizes the fuzzification operations of the speed command. UWO NBWO NMWO NSWO ZWO PSWO PMWO PBWO 1 0.5 0 WO1 WO2 WO3 WZ WO4 WO5 WO6 "WO" (rad/s) Figure 11.15 Membership function of speed command. NBWO: negative big; NMWO: negative medium; NSWO: negative small; ZWO: zero; PBWO: positive big; PMWO: positive medium; PSWO: positive small. Table 11.3 Fuzzification operation constants of speed command. WO1 188 WO2 WO3 126 63 WZ WO4 WO5 WO6 0 63 126 188 The subroutine segment (written in ADSP-21xx assembly language) to implement the fuzzification operation of speed command is listed as follows. FUZW: {subroutine begin} FUZA: AR = WOC-WO1; IF GE JUMP FUZB; UWO1 = 1; UWO2 = 1; lingu1= NBWO; lingu2= NBWO; JUMP FUZEND {label} {AR: ALU result register} {Program flow controlled by ALU result} { Degrees of membership} { Linguistic value} {Jump to label FUZEND} 332 Applied Intelligent Control of Induction Motor Drives Table 11.4 Fuzzification operations of speed command. Label Condition Degrees of membership Linguistic value FUZA WOC LT WO1 UWO1 ¼ 1 UWO2 ¼ 1 NBWO NBWO FUZB WOC GE WO1 AND WOC LT WO2 UWO1 ¼ (WO2-WOC)/(WO2-WO1) UWO2 ¼ (WOC-WO1)/(WO2-WO1) NBWO NMWO FUZC WOC GE WO2 AND WOC LT WO3 UWO1 ¼ (WO3-WOC)/(WO3-WO2) UWO2 ¼ (WOC-WO2)/(WO3-WO2) NMWO NSWO FUZD WOC GE WO3 AND WOC LT WZ UWO1 ¼ (WZ-WOC)/(WZ-WO3) UWO2 ¼ (WOC-WO3)/(WZ-WO3) NSWO ZWO FUZE WOC GE WZ AND WOC LT WO4 UWO1 ¼ (WO4-WOC)/(WO4-WZ) UWO2 ¼ (WOC-WZ)/(WO4-WZ) ZWO PSWO FUZF WOC GE WO4 AND WOC LT WO5 UWO1 ¼ (WO5-WOC)/(WO5-WO4) UWO2 ¼ (WOC-WO4)/(WO5-WO4) PSWO PMWO FUZG WOC GE WO5 AND WOC LT WO6 UWO1 ¼ (WO6-WOC)/(WO6-WO5) UWO2 ¼ (WOC-WO5)/(WO6-WO5) PMWO PBWO FUZH WOC GE WO6 UWO1 ¼ 1 UWO2 ¼ 1 PBWO PBWO WOC: Speed command; LT: Less than (ADSP-2100 assembler expression); GT: Greater than (ADSP-2100 assembler expression); GE: Greater than or equal (ADSP-2100 assembler expression); /: divide (ADSP-2100 assembler expression); -: subtraction (ADSP-2100 assembler expression). FUZB: AR = WOC-WO2; IF GE JUMP FUZC; UWO1 = (WO2-WOC)/(WO2-WO1); UWO2 = ( WOC-WO1)/(WO2-WO1) lingu1= NBWO; lingu2= NMWO; JUMP FUZEND FUZC: . . . FUZEND: RTS; { Subroutine ends here } Fuzzification Subroutine of Speed Error Speed error ‘WE’ is the difference between rotor speed ‘WO’ and speed command ‘WOC’, which can be expressed as: WE ¼ WO WOC 333 Experimental Investigations where WO is obtained from the output of the encoder program, ENCO, and WOC is the speed set value. The subroutine of fuzzification operation of speed error converts the crisp input values of speed error Do to fuzzy sets. Table 11.5 defines the five constants of fuzzification operation of speed error and the fuzzification operations of speed error are summarized in Table 11.6. Table 11.5 E1 376 Constants of fuzzification operation of speed error. E2 3 E3 E4 E5 0 3 376 Table 11.6 Fuzzification operations of speed error. Label Condition Degrees of membership Linguistic value FUZI WE LT E1 UWO3 ¼ 1 UWO4 ¼ 1 NDWO NDWO FUZJ WE GE E1 AND WE LT E2 UWO3 ¼ (E3-WE)/(E3-E1) UWO4 ¼ 0 NDWO ZDWO FUZK WE GE E2 AND WE LT E3 UWO3 ¼ (E3-WE)/(E3-E1) UWO4 ¼ (WE-E2)/(E3-E2) NDWO ZDWO FUZD WE GE E3 AND WE LT E4 UWO3 ¼ (W4-WE)/(E4-E3) UWO4 ¼ (WE-E3)/(E5-E3) ZDWO PDWO FUZE WE GE E4 AND WE LT E5 UWO3 ¼ 0 UWO4 ¼ (WE-E3)/(E5-E3) ZWO PDWO FUZF WE GE E5 UWO3 ¼ 1 UWO4 ¼ 1 PDWO PDWO Subroutine of Fuzzy Inference Operation The subroutine of fuzzy inference operation implements the linguistic inference of Equations (6.16) and (6.18), and the degree of membership calculation of Equations (6.19) and (6.20). The details of the fuzzy inference operations are summarized in Table 11.7. Table 11.7 Fuzzy inference operations. Variable names Description Inputs UWO1, UWO2, UWO3, UWO4 Lingu1, lingu2, lingu3, lingu4, Degrees of membership of speed command and speed error Linguistic values of speed command and speed error Outputs UC1, UC2 UD1, UD2 Crisp values of fuzzy linguistic Degrees of membership 334 Applied Intelligent Control of Induction Motor Drives Subroutine of Defuzzification Operation The subroutine of defuzzification operation implements the defuzzification for outputs of the fuzzy inference. The centroid method given by Equation (6.21) is used to implement the defuzzification operation. The details of the defuzzification operations are summarized in Table 11.8. Table 11.8 Defuzzification operations. Variable names Description Inputs UC1, UC2 UD1, UD2 Crisp values of fuzzy linguistic Degrees of membership Outputs WEC Numerical value of slip frequency 11.6.1.3 PI Current Magnitude Controller (CURRENTMC.DSP) When the permissible magnitude of stator current of the induction motor is 2 A, proportional and integral parameters of the PI current magnitude controller are designed, from Equations (6.23)–(6.25), as Kp ¼ 0.7 and KI ¼ 0.014. The discrete time difference equations which implement the PI controller are as follows: Iðk þ 1Þ ¼ IðkÞ þ KI eðk þ 1Þ Ufk þ 1Þ ¼ Kp eðk þ 1Þ þ Iðk þ 1Þ ð11:11Þ ð11:12Þ where: KI ¼ integral constant I(k þ 1) ¼ integral of error x integral constant I(k) ¼ previous integral of error x integral constant e(k þ 1) ¼ error for iteration k þ 1 Kp ¼ proportional constant U(k þ 1) ¼ controller output Equations (11.11) and (11.12) are implemented by a routine of PI current magnitude controller, CURRENTMC.DSP. 11.6.1.4 Generate Stator Current Command (Subroutine SINCURRENT) The slip frequency command WEC of the fuzzy controller output, the current magnitude command U of the output of current magnitude PI controller, and the speed command WO are converted into three stator current commands, IAC, IBC, and ICC by a subroutine 335 Experimental Investigations SINCURRENT in the main program MAIN.DSP. Algorithm of the subroutine SINCURRENT is described as follows: {initialize phase angles} Wað0Þ ¼ 0; Wbð0Þ ¼ 2p=3; Wcð0Þ ¼ 2p=3; {calculate supply frequency} W com ¼ WO þ WEC; {increment phase angles} Waðn þ 1Þ ¼ WaðnÞ þ W com DT; where DT ¼ 2 p (1/10000); (PWM frequency ¼ 10 kHz) {calculate 3-phase current command} IAC ¼ UsinðWaðn þ 1ÞÞ; IBC ¼ UsinðWbðn þ 1ÞÞ; ICC ¼ UsinðWcðn þ 1ÞÞ; The sine function is implemented by calling a function ADMC_SIN stored in ADMC331 ROM. 11.6.1.5 Stator Current Controllers (STCPI.DSP) The design of the current PI controller shown in Figure 6.31 has been described in Equation (6.26)–(6.40). Because the feedback gains in the experimental system is different from the simulation system in Chapter 6, the parameters of the current PI controller must be modified as follows. The open-loop transfer function, Equation (6.33), of the PI controller and the motor is modified as: Gopenloop ¼ GPI K1 Gmotor ¼ Kp K1 where K1 is all other gains in the systems. 1 sLs s ð11:13Þ 336 Applied Intelligent Control of Induction Motor Drives If a constant K2 is introduced as follows, K2 ¼ Kp K1 1 sLs ð11:14Þ K2 . s Closing the feedback loop with unity gain results in the following closed-loop transfer function: then, Gopenloop ¼ Gclosedloop ¼ K2 : s þ K2 ð11:15Þ This is recognized as a single-pole low-pass filter with 3-dB corner frequency at: F3dB ¼ K2 : 2p ð11:16Þ Choosing a filter corner frequency (or a controller bandwidth) of 1 kHz results in: K2 ¼ 2p 103 : ð11:17Þ The feedback gain term K1 is made up of the following terms: PWM Gain ¼ DC bus voltage Current sensor gain ADC gain Scaling Total 230 V 0.825 V/A 0.17041 3.4566 111.770 that is, K1 ¼ 111:770 From Equation (11.14): Kp ¼ K2 sLs : K1 ð11:18Þ From Appendix H, the parameters of the experimental induction motor are: s ¼ 0.208, Ls ¼ 0.3185 H and Rs ¼ 14.6 O. From Equation (11.18), the proportional constant is Kp ¼ 2p 103 0:208 0:3185=111:770 or Kp ¼ 3:724 From Equation (6.23), the integral constant KI is KI ¼ 3:724 14:6 0:208 0:3185 : ð11:19Þ 337 Experimental Investigations or KI ¼ 821: ð11:20Þ 11.6.1.6 Analog to Digital Converter (ADC331.DSP) The file ADC331.DSP contains subroutines used to read analog voltages which represent the three-phase stator currents and the DC bus voltage. 11.6.1.7 Divide Function (DIVIDE.DSP) The file DIVIDE.DSP contains a function called Division which divides a 32-bit dividend by a 16-bit divisor, and returns a 16-bit quotient. 11.6.1.8 Floating Point Math Routines (FPMATH.DSP) The routines in the file FPMATH.DSP implement floating point numbers in the program. In the floating point format used here, each number is represented by two 16-bit words, one for the mantissa in 1.15 format (i.e., 1 signed bit, 15 fractional bits), and the other for the exponents in 16.0 format (i.e., 16-bit binary strings). The value of the floating point number is given by: Value ¼ Mantissa 2Exponent : ð11:21Þ Table 11.9 gives some representations of the floating point number for the speed error between the speed command and actual speed. Table 11.9 Floating point representation examples. Speed error 188 126 1.0 0.25 126 188 Mantissa (dec) 0.734375 0.984375 1.0 1.0 0.984375 0.734375 Mantissa (hex) 0xA1FF 0x81FF 0x8000 0x7FFF 0x7E00 0x5E00 Exponent (dec) 8 7 0 2 7 8 Exponent (hex) 0x0008 0x0007 0x0000 0xFFFE 0x0007 0x0008 11.6.1.9 Speed Setpoint Function (SPEEDSET.DSP) This DSP program implements reading of a speed setpoint from a potentiometer on the ADMC connector board to ADMC331 as the speed command of the controller. The program reads the auxiliary ADC input channel and scales the resulting value so that analog input voltages of 0.3–3.3 V produced by the potentiometer result in speed setpoints of 0 to 188 rad/s. 338 Applied Intelligent Control of Induction Motor Drives 11.6.1.10 Capturing Signals to DSP Memory (CAPTURE.DSP) The file CAPTURE.DSP contains routines used to aid in debugging the code and tuning the fuzzy controller parameters. They provide a means to capture 100 successive values (floating point number) for each of four variables, which is limited by the 1k 16-bit data memory of the ADMC331. The data values can then be examined by displaying them with Motion Control Debugger’s (MCD) plot memory function, or by dumping them to a file using MCDs dump memory command. From a memory dump file, the data can be further analyzed. 11.6.2 Program Debug 11.6.2.1 Debug for Program FUZZY.DSP 1. Disconnect the inverter PowIRtrain from the DSP ADMC331. 2. Open the control loop by disconnecting the encoder input terminal from the DSP and set a static speed value in the program to replace the actual rotor speed. 3. Produce an executable program main.exe using the file BUILD.BAT. 4. Invoke the ‘Motion Control Debugger’ program on the host PC. 5. Download the main.exe program from the host PC to DSP. 6. Click the run button on the host PC. 7. Check the speed setpoint (speed command) by a digital multimeter. 8. Observe and analyze the speed error (input of the program FUZZY.DSP) and the slip frequency (output of the program FUZZY.DSP) by reading the data memory of ADMC331. 9. Modify the source code of assembly language and iteratively repeat steps (3) to (9) until satisfactory data values are obtained. The speed setpoint is read by the program SPEEDSET.DSP from a potentiometer on the ADMC connector board to ADMC331 as a speed command of the controller. At debug Step (7), the speed command value is written to DAC channel 1 and is examined by a digital multimeter. The DAC converts digital values (12 bit fixed point data) of the speed command to analog voltage values. For convenience of observation, the digital values are multiplied by 100 before they are converted to the analog voltage values. According to the DAC algorithm (Table 11.2), the DAC output voltage can be calculated by: Vout ¼ Hinput 2:5 þ 2:5ðVÞ 32767 ð11:22Þ where 32 767 represents the hex number 0x7FFF, Hinput is the speed command 100 (decimal number), and Vout is the DAC output voltage. Table 11.10 shows the analog voltage values of DSP output, which is observed on a digital multimeter. After the speed command is set and checked, the speed error (input of the program FUZZY. DSP) and the slip frequency (output of the program FUZZY.DSP) are read from the data memory (DM) of ADMC331 (DM address 0x3894). The speed error and slip frequency are floating point numbers in the DSP control program, which has been captured to the 339 Experimental Investigations Table 11.10 Speed command observed on a digital multimeter. Speed command (rad/s) (fixed point) 100 before DAC Output value (V) Observed value on multimeter (V) 0 (0x0000) 0 (0x0000) 2.500 2.50 40 (0x0028) 4000 (0x0FA0) 2.805 2.80 80 (0x0050) 8000 (0x1F40) 3.110 3.10 188 (0x00BC) 18800 (0x4970) 3.934 3.90 data memory on ADMC331 by the program CAPTURE.DSP. Table 11.11 shows the slip frequencies captured at various speed setpoints and speed errors during the acceleration and steady-state stages. Table 11.11 Speed error and the slip frequencies read from the DSP data memory. Control stages Stop Speed setpoint (fixed point) Speed error (floating point) Captured Slip frequency Acceleration Steady Acceleration Steady Acceleration Steady 0 40 (0x0000) (0x0028) 0 40 40 80 (0x0028) (0x0050) 0 80 80 188 (0x0050) (0x00BC) 0 188 188 (0x00BC) 0 0.026 0.730 2.272 5.678 18.228 18.317 18.198 After the desired slip frequencies have been obtained by the program FUZZY.DSP, the debug for the fuzzy control program is complete. 11.6.2.2 Debug for Other Programs The stator current control program STCPI.DSP has been tested alone by a demo program delivered by Amirix Inc., while the program ENCO.DSP has been tested in experiment 2 and a test result is shown in Figure 11.10. The debug method and procedure for other programs of the experimental control program are similar to those in Experiment 2 in Section 11.5. After all the programs have been debugged, the encoder is connected to the DSP ADMC331 for performing a closed-loop control experiment. 11.6.3 Performance Tests 11.6.3.1 Performance Test 1 Speed set point ¼ 175 (rad/s). Seven-way signals (Va, Vb, Vc, ia, ib, ic, oo) are acquired to the data-acquisition PC at same time. Sampling rate ¼ 40 kHz. Sampling time ¼ 1.4 s. The test procedure is similar to that of Experiment 2 in Section 11.5. 340 Applied Intelligent Control of Induction Motor Drives Test Results The induction motor is started by the fuzzy/PI controller from standstill to 175 rad/s. During the time interval 0 s 0.14 s, the 3-phase stator voltage, current, and speed response are acquired by the PCL818HG card to the data-acquisition PC. Figure 11.16 shows the phase-A stator voltage estimated by the VDC_HANDLING subroutine and modified by Equation (11.10), phase-A stator current acquired from the current sensor board 3I411A, and rotor speed response acquired from the output of DAC on the ADMC connector board. In Figure 11.16, it is demonstrated that the stator current magnitude is maintained at about 2 A in the acceleration stage, which is a distinct characteristic of the two-stage fuzzy/PI controller. 4 200 Stator current (A) Phase voltage (V) 300 100 0 -100 -200 -300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) 2 0 -2 -4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) Rotor speed (rad/s) 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) Figure 11.16 Phase-A stator voltage, phase-A stator current, and rotor speed response. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “A novel hybrid fuzzy/PI two-stage controller for an induction motor drive,” IEEE International Electric Machines and Drives Conference (IEMDC 2001), pp. 415–421, June 17–20, 2001, Cambridge, MA, U.S.A. 2001 IEEE.) The 3-phase stator voltage, current, and speed response in the acceleration stage are shown in Figures 11.17–11.19 respectively. Figure 11.18 shows that 3-phase stator current magnitudes are maintained at about 2 A in the acceleration stage. Figure 11.19 shows the rotor speed response of the induction motor with the fuzzy/PI controller, the signal being acquired from the output of DAC on the ADMC Connector Board. 341 Experimental Investigations 300 Phase-B voltage (V) Phase-A voltage (V) 300 200 100 0 -100 -200 -300 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 200 100 0 -100 -200 -300 0 0.05 0.1 Time (s) 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Phase-C voltage (V) 300 200 100 0 -100 -200 -300 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 11.17 Estimated 3-phase voltages applied to the induction motor. 4 Phase-B current (A) Phase-A current (A) 4 2 0 -2 2 0 -2 -4 -4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 Time (s) Time (s) Phase-C current (A) 4 2 0 -2 -4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 11.18 Three-phase stator currents in the acceleration stage. 0.35 0.4 342 Applied Intelligent Control of Induction Motor Drives Rotor speed (rad/s) 200 150 100 50 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 11.19 Rotor speed response in the acceleration stage. 11.6.3.2 Performance Test 2 Speed set point ¼ 120 rad/s. Seven-way signals (Va, Vb, Vc, ia, ib, ic, oo) are captured to the data-acquisition PC at same time. Sampling rate ¼ 40 kHz. Sampling time ¼ 1.4 s. The test procedure is similar to that of Experiment 2 in Section 11.5. Test Results The induction motor is started by the fuzzy/PI controller from standstill to 120 rad/s. Figure 11.20 shows the 3-phase stator voltage, current, and speed response acquired by the PCL818HG card to the data-acquisition PC. 4 200 Stator current (A) Phase voltage (V) 300 100 0 -100 -200 -300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) 2 0 -2 -4 0 0.2 0.4 0.6 0.8 1 1.2 Time (s) Rotor speed (rad/s) 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) Figure 11.20 Phase-A stator voltage, phase-A stator current, and rotor speed response. 1.4 343 Experimental Investigations The variations of the 3-phase stator voltages and currents in the acceleration stage are shown in Figure 11.21, while the rotor speed response in the acceleration stage is shown in Figure 11.22. 300 Phase B voltage (V) Phase A voltage (V) 300 200 100 0 -100 -200 -300 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 200 100 0 -100 -200 -300 0 0.05 0.1 Time (s) Phase A current (A) Phase C voltage (V) 100 0 -100 -200 0 0.05 0.1 0.15 0.2 0.25 0.3 2 0 -2 -4 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Time (s) 4 Phase C current (A) 4 Phase B current (A) 0.35 0.4 4 200 2 0 -2 -4 0.25 0.3 Time (s) 300 -300 0.15 0.2 0 0.05 0.1 0.15 0.2 0.25 0.3 Time (second) Figure 11.21 0.35 0.4 2 0 -2 -4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (second) Three-phase stator voltages and currents in the acceleration stage. When real-time data are acquired to the PC memory with the DMA method, the data size is limited to 32 000 by the actual memory assigned by the PC hardware manager. Hence, to observe and record the performance of the fuzzy/PI controlled drive over a longer period, a powerful digital scope is required. Experiment 3 has basically verified the feasibility of the Fuzzy/PI two-stage controller proposed in Chapter 5. Better performance, however, will necessitate further simulation studies for improving and tuning the Fuzzy/PI control algorithm, for example, by using more advanced 344 Applied Intelligent Control of Induction Motor Drives Rotor speed (rad/s) 200 150 100 50 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s) Figure 11.22 Rotor speed response in the acceleration stage. methods (such as ANN-Fuzzy or GA-Fuzzy) to optimize the membership functions instead of the classical fuzzy method. 11.7 Experiment 4: Speed Estimation Using a GA-Optimized Extended Kalman Filter This experiment is designed to verify the efficacy of the real-coded genetic algorithm for optimizing the extended Kalman filter which has been proposed and simulated in Chapter 7. Figure 11.23 shows the block diagram of the experimental system of the GA-optimized extended Kalman filter for rotor speed estimation. INVERTER IM PWM ωo iDs* VDs PI PI PI VQs λs* Vds Vqs Va 2/3 PI INV. PARK ω o* Vb Vc iQs* iQs λs iDs PARK FLUX CALC. ids iqs 3/2 ia ib ic ωo GA-EKF Figure 11.23 Block diagram of experimental EKF drive system. 345 Experimental Investigations 11.7.1 Program Design The GA-EKF experimental software includes a DSP software to drive an induction motor using the Field Oriented Control (FOC) technique, a PC Cþþ software to acquire actual signals of 3-phase stator voltages, currents, and encoder, and a MATLAB software to optimize EKF by using GA and EKF speed estimation. The basic principle of the FOC technique is to control the torque-producing and flux-producing components of the motor current independently of each another. The FOC algorithm and computer simulation have been described in Section 7.7 of Chapter 7. The C þþ data-acquisition software has been designed in Section 11.5, and the MATLAB GA software has been designed in Chapter 7. The MATLAB EKF program is given in Appendix F. Following is the list of program units and the functions that they perform: File Name Description ACIM.DSP ADC331.DSP, ADC331.H CAPTURE.DSP, CAPTURE.H CNTRL.DSP, CNTRL.H CONST331.H DAC.DSP, DAC.H Induction machine controller main program ADC routines Debugging functions for capturing variables to memory Speed, flux, Iqs, and Ids PI controllers ADMC331-related constants Debugging functions for writing to DAC on ADMC connector board Divide function Field oriented control constants Floating point math routines Initialization of IR PowIRtrain module 32 bit math routines Flux estimation PWM functions ROM utility definitions Encoder functions Vector transformation functions Batch file to build the DSP source code into an executable file main.exe which can be downloaded and run on the DSP. Cþþ source codes for acquiring signals to PC MATLAB program to optimize EKF by using GA MATLAB program to implement EKF algorithm DIVIDE.DSP, DIVIDE.H FLUX.H FPMATH.DSP, FPMATH.H IR_INIT.DSP, IR_INIT.H MATH_32B.DSP, MATH_32B.H MODEL.DSP, MODEL.H PWM331.DSP, PWM331.H ROMUTIL.H ENCO.DSP, ENCO.H VECT_TRA.DSP, VECT_TRA.H build.bat: ACQUIRE.C, ACQUIRE.H: GA.M EKF.M 11.7.2 GA-EKF Experimental Method The GA-EKF experiment is divided into the training phase and the verification phase. In the training phase, three-phase voltage and current are acquired as training samples from the experimental system and the actual rotor speed is acquired from the encoder as the target function. After the matrices G, Q, and R have been obtained off-line using the real-coded GA, the performance of the GA-EKF is examined in the verification phase by acquiring new data samples. Figure 11.24 shows the GA training phase procedure and Figure 11.25 shows the verification phase procedure. 346 Applied Intelligent Control of Induction Motor Drives Loading FOC program to DSP ADMC331 and running it Acquiring Va, Vb, Vc, ia, ib, ic, ωo from sensors to PC [Va, Vb, Vc, ia, ib, ic] Generate initial population of noise matrices for EKF EKF speed estimation on PC GA ωo ωo Reproduction Is optimization criterion met? no Recombination yes Output the best G, Q, R, to EKF Mutation Figure 11.24 Flowchart of GA-EKF program for the training phase. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. 2002 IEEE.) Rerunning program on DSP ADMC331 with setting ωo* Reacquiring Va, Vb, Vc, ia, ib, ic, ωo from sensors EKF with GA optimized noise matrices ωo ωo Comparing estimated speed with actual speed ωo Figure 11.25 GA-EKF speed estimation procedure in the verification phase. 11.7.3 GA-EKF Experiments The hardware system for the experimental investigations has been described in Figure 11.1 and the following parameters have been chosen for data acquisition via the PCL818HG card: Sampling rate ¼ 20 kHz for scanning 7-way signals (Va, Vb, Vc, ia, ib, ic, Encoder) Sampling rate of each way signal ¼ 2.857 kHz (¼20/7 kHz) Sampling time ¼ 1.4 s 347 Experimental Investigations Total sample number ¼ 28 000 Sample number of each signal ¼ 4000 11.7.3.1 GA EKF in the Training Phase Figure 11.26 shows the acquired phase voltage and phase current when the induction motor is run up from standstill to 105 rad/s. Phase voltage (V) 300 200 100 0 -100 -200 -300 0 0.2 0.4 0.6 0.8 1 1.2 0.8 1 1.2 Time (s) Phase current (A) 3 2 1 0 -1 -2 -3 0 0.2 0.4 0.6 Time (s) Figure 11.26 Phase voltage and phase current waveforms of the induction motor when run up to 105 rad/s. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. 2002 IEEE.) Figure 11.27 shows the actual speed and the speed estimated using EKF with matrices G ¼ Q ¼ Diag[10 3, 10 3, 10 3, 10 3, 10 2] and R ¼ Diag[10 3, 10 3]. In this case, the mean squared error of the estimated speed is 48.1632. The real-coded GA used to optimize the matrices G, Q, and R of the EKF has been described in Chapter 9. In the training stage, the real-coded GA parameters for the EKF experiment are set as follows: 1. Initial population size: 100 2. Maximum number of generations: 20 348 Applied Intelligent Control of Induction Motor Drives 120 Rotor speed (rad/s) 100 80 Actual speed (solid line) 60 Estimated speed (dotted line) 40 20 0 -20 0 0.2 0.4 0.6 0.8 1 1.2 Time (s) Figure 11.27 3. 4. 5. 6. Actual speed of rotor and speed estimated using EKF. Probability of crossover: 0.8 Mutation probability: 0.01 Initial range of real-coded strings: [0.01; 5]. Performance measure: the mean squared error between the estimated speed and the actual rotor speed. Table 11.12 shows the convergence process in EKF training. The GA optimization method has improved the EKF performance by decreasing the mean squared error of estimated speed from 48.1632 to 1.2980. The optimized matrices are found to be: G ¼ Diag[0.1264, 0.1306, 0.1847, 0.1945, 1.5603], Q ¼ Diag[0.0648, 0.0993, 0.0816, 0.0963, 1.5000], and R ¼ Diag[0.0101, Table 11.12 Iteration process of the off-line GA. Generations 0 1 2 3 4 5 6 7 8 9 10 E¼ n 1X ðsi n i¼1 12.6931 4.0216 4.3045 3.1341 3.0235 2.8401 2.5294 2.1983 2.2631 1.9578 1.8653 ei Þ2 Generations 11 12 13 14 15 16 17 18 19 20 E¼ n 1X ðsi n i¼1 ei Þ2 1.6493 1.6320 1.5234 1.6019 1.4820 1.4397 1.3589 1.3740 1.3138 1.2980 s: actual rotor speed; e: estimated speed; n: number of data samples (¼ 4000); E: mean squared error of estimated speed. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. 2002 IEEE.) 349 Experimental Investigations 0.0104]. It is apparent that the noise covariance and weight matrices required depend on the motor whose speed is to be estimated. Figure 11.28 shows the actual speed and the estimated speed by using the optimized EKF. The mean squared error of the estimated speed is 1.2980. 120 Rotor speed (rad/s) 100 80 60 Actual speed (solid line) 40 20 Estimated speed (dotted line) 0 -20 0 0.2 0.4 0.6 0.8 1 1.2 Time (s) Figure 11.28 Actual speed of rotor and speed estimated using GA-EKF. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. 2002 IEEE.) 11.7.3.2 GA EKF in Verification Phase In the verification phase, the induction motor is run up from standstill to 188 rad/s by the same FOC program. Data samples are acquired from the DSP drive system to the PC and the GA-EKF program is run again to check the accuracy of the speed estimation. Figure 11.29 shows the phase voltage, phase current, and estimated speed of the motor. The mean squared error of the estimated speed is found to be 1.7387, which is very close to that obtained in the training phase. The experimental results demonstrate that the off-line GA method is efficacious for optimizing an EKF speed estimator. In order to obtain satisfactory covariance and weight matrices by the off-line GA, a short sampling period must be chosen for actual data acquisition. In this experiment, DMA method is used to implement high-speed data acquisition for the 7-way signals (Va, Vb, Vc, ia, ib, ic, and o). At a sampling rate of 20 kHz, which corresponds to a sampling time interval of 0.00035s (¼7/20 000), very satisfactory GA training and EKF verification results have been obtained. 11.7.4 Limitations of GA-EKF Because the real-coded genetic algorithm begins from a randomly generated initial population of the long real-coded strings, the distribution of values in the initial population may affect the convergence process of the algorithm. The optimization process may need to be repeated several times before the global optimum is obtained. In the simulation studies 350 Applied Intelligent Control of Induction Motor Drives 300 Phase voltage (V) 200 100 0 -100 -200 -300 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1 1.2 1.4 1.2 1.4 Time (s) 3 Phase current (A) 2 1 0 -1 -2 -3 0 0.2 0.4 0.6 0.8 Time (s) Rotor speed (rad/s) 180 130 Actual speed (solid line) 80 Estimated speed (dotted line) 30 -20 0 0.2 0.4 0.6 0.8 1 Time (s) Figure 11.29 Phase voltage, phase current and speed estimated using GA-EKF when the motor is run up to 188 rad/s. (Reproduced by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of an induction motor drive using an optimized extended Kalman filter,” IEEE Transactions on Industrial Electronics, 49(1), 2002: 124–133. 2002 IEEE.) and the experimental studies, it is also found that an improper initial range of the covariance matrices may result in extremely long time for GA iterations or even GA optimization failure. The initial range is different for various induction motor types, for example, the initial range is [0.0001; 0.1] for the 7.5 kW motor in Chapter 7 and is [0.01; 5] for the 147 W motor. 351 Experimental Investigations As an example, consider the case where the initial range of EKF covariance matrices is set as [0.0001; 0.1] for the experimental 147-W motor. The GA iteration process is shown in Table 11.13. Table 11.13 Iteration process of a GA failure case. E¼ Generations 0 1 2 3 4 5 6 7 8 9 10 n 1X ðsi n i¼1 ei Þ2 E¼ Generations 38.2961 31.7557 29.9381 30.2317 30.0430 29.9381 30.0021 29.9376 29.9175 29.8982 29.9378 11 12 13 14 15 16 17 18 19 20 n 1X ðsi n i¼1 ei Þ2 29.9377 29.8982 29.9147 29.9344 29.8982 29.8982 29.8819 29.8392 29.8425 29.8949 s: actual rotor speed; e: estimated speed; n: number of data samples (¼ 4000); E: mean squared error of estimated speed. At the 20th iteration step, the mean squared error of the estimated speed is still at a large value of 29.8949 and the corresponding EKF matrices are: G ¼ Diag[0.0326, 0.0425, 0.02764, 0.0139, 0.0832], Q ¼ Diag[0.0174, 0.0268, 0.0460, 0.0533, 0.09524], and R ¼ Diag[0.0230, 0.0147]. Figure 11.30 shows the actual speed and the speed estimated by the sub-optimal EKF. 120 Rotor speed (rad/s) 100 80 Actual speed (solid line) 60 40 Estimated speed (dotted line) 20 0 -20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (s) Figure 11.30 Actual speed and the estimated speed using the sub-optimal EKF. 352 11.8 Applied Intelligent Control of Induction Motor Drives DSP Programming Examples TMS320F28335 processor (Texas Instruments Inc., 2009a) is employed for the DSP programming examples. Working in association with MATLAB software, TMS320F28335 is suitable for implementing an intelligent induction motor control system with the following features: 1. Up to 150 MIPS (million instructions per second) or 6.67-ns instruction cycle time, 32-bit floating-point CPU, up to 18 PWM outputs, 6 event capture inputs, and 16 channels 12-bit ADC (analog-to-digital converter) with 80-ns conversion rate. 2. Standard IEEE 1149.1 JTAG (Joint Test Action Group) interface is implemented on TMS320F28335 processor. With JTAG-based emulator hardware, the processor may be connected to a host PC through a USB (Universal Serial Bus) interface. 3. Supports RTDX (Real Time Data exchange) technique. RTDX enables real-time, asynchronous exchange of data between the target DSP and the host PC, without stopping the tasks in the target DSP. When a motor control program is running in the DSP, another complex intelligent control program, such as ANN or GA, may be run simultaneously on the host PC to support the motor control program running in the target DSP. 4. Supports Code Composer Studio (CCS) IDE (integrated development environment) and Cþþ compiler/assembler/linker, DSP/BIOS, and digital motor control software. 4 2 VDC ic ib 3 Encoder TMS320 F28335 Figure 11.31 PWM 1 ADC JTAG Target DSP CAP Host PC USB In this section, four examples are presented to demonstrate basic DSP programming of an induction motor control system. The four examples are (1) generation of 3-phase sinusoidal PWM pulses for driving a 3-phase inverter; (2) RTDX for exchange of real-time data between the DSP and MATLAB software; (3) acquisition of analog signals to the DSP by using an ADC; (4) capturing rotor encoder pulses to DSP by CAP programming. The hardware for the four programming examples includes a host PC, DSP experiment board, and an oscilloscope. The DSP experiment board may be an eZdspF28335 development board (delivered by Spectrum Digital, Inc.) or a TMS320F28335 experimenter kit (delivered by Texas Instruments Inc.). The two boards have an on board JTAG connector that provides interface to a PC via a USB connection. The oscilloscope is used for observing the output waveforms of the DSP board. The hardware configuration is shown in Figure 11.31. Oscilloscope Hardware configuration of DSP programming examples. 353 Experimental Investigations In the TMS320F28335 target DSP, the three peripherals (PWM, CAP, ADC) and JTAG port implement the four functions. 1. The PWM ports output the six PWM pulses which control the inverter that feeds the induction motor. 2. Stator currents and voltage of inverter DC supply are acquired by the ADC ports to the DSP. With the acquired voltage of inverter DC supply and the PWM signals produced in the DSP, output voltages of the inverter may be obtained by their product. 3. Pulses yielded by a rotor speed encoder may be captured by the CAP port. 4. Through the on-board JTAG hardware interface, values of stator voltage, stator current, and rotor speed may be transferred to the host PC for real-time analysis and calculation. Complex intelligent algorithms that cannot run in the present-day DSP, such as ANN and GA, may be asynchronously run on the host PC by MATLAB software with data acquired in real-time. The optimized parameters obtained by the intelligent algorithm in the host PC may be instantly transferred to the DSP to update the running program. The software for the four programming examples include CCStudio_v3.3 with bios_5_33_06 software package (Texas Instruments Inc., 2009b) and MATLAB 2008b with Embedded IDE Link CC software package (The MathWorks, Inc. 2008). The software configuration in the host PC and the application program loaded in the target DSP are shown in Figure 11.32. Host PC 1) CCS IDE Edit/Debug GUI Code generation tools DSP/BIOS API RTDX host library 2) MATLAB ® Embedded IDE Link CC Figure 11.32 JTAG interface Target DSP 1) Application program 2) RTDX Target Library Software configuration of the host PC and target DSP. In the software configuration, CCS IDE includes integrated Edit/Debug GUI (graphical user interface), code generation tools, DSP/BIOS, and RTDX host library. DSP/BIOS kernel is a real-time, multi-tasking software, also called a real-time DSP operating system (Texas Instruments Inc., 2009b). DSP/BIOS provide standardized API (Application Program Interface) functions for even the most sophisticated DSP applications. RTDX software consists of the target library and the host library. A small RTDX software library runs on the target DSP. This library transfers the required data to or from the host PC in real-time through a JTAG interface when the DSP application is running. On the host PC, the RTDX host library operates in conjunction with MATLAB to obtain the target data or to send data to the target DSP application through the JTAG interface. ‘Embedded IDE Link CC’ software package of MATLAB may be embedded to the Code Composer Studio software. Using RTDX technique, bi-directional real-time data exchange between MATLAB software and the TMS320F28335 processor program can be easily implemented. 354 Applied Intelligent Control of Induction Motor Drives To verify that the board has been connected to the host PC, start MATLAB and enter ‘ccsboardinfo’ in the MATLAB command line. If the development board eZdspF28335 is connected to the host PC, the following information will be shown in the MATLAB window. >> ccsboardinfo Board Board Proc Processor Processor Num Name Num Name Type --- -------------------------------- --- ---------------0 F28335_eZdsp 0 cpu_0 If the TMS320F28335 experimenter kit is connected to the host PC, the following information will be shown in the MATLAB window. >> ccsboardinfo Board Board Proc Processor Processor Num Name Num Name Type --- -------------------------------- --- ---------------0 F28335 XDS100 0 TMS320C2800_0 USB Emulator 11.8.1 Generation of 3-Phase Sinusoidal PWM This example demonstrates programming 3-phase sinusoidal PWM for an inverter-fed induction motor in a TMS320F28335 processor (Texas Instruments Inc., 2009c). The 3-phase PWM operates at a synchronization frequency of 1 kHz. The three-phase PWM waveforms are produced by three events, namely PWM1, PWM2 and PWM3. PWM1 works as a master and a PWM1 event is started by the processor timer. Next, PWM1 triggers a hardware interrupt to start event PWM2 which then works as a slave. Finally, PWM2 triggers a hardware interrupt to start event PWM3 which then works as a slave. Step 1 Connect the TMS320F28335 experiment board to the PC via USB interface. Start Code Composer Studio (CCS) and create a new project named as ‘F28335_example_PWM.pjt’ by selecting the ‘New’ item from the ‘Project’ menu on CCS. Step 2 Write a main program ‘Main_PWM.c’ and add it to the project. The main program is listed below: #include ’DSP2833x_Device.h’ #include ’F28335_example_PWM.h’ void main(void) { InitSysCtrl(); InitPieCtrl(); (Peripheral Interrupt Expansion) InitGpio(); InitEPwm(); } // Peripheral address definitions // Main include file // Initialize the CPU // Initialize and enable the PIE / Initialize the shared GPIO pins // Initialize the 3-phase PWM 355 Experimental Investigations Step 3 Write the four initialization functions and add them to the project. ‘InitSysCtrl()’: Configure the registers of clocking and system control (Texas Instruments Inc., 2009d). The system clock is set at 75 MHz with a register script SysCtrlRegs.PLLSTS.bit. DIVSEL ¼ 0x2. ‘InitGpio()’: Configure the GPIO (General-Purpose Input/Output) ports as PWM ports with following scripts (Texas Instruments Inc., 2009d). GpioCtrlRegs.GPAMUX1.bit.GPIO0 = GpioCtrlRegs.GPAMUX1.bit.GPIO1 = GpioCtrlRegs.GPAMUX1.bit.GPIO2 = GpioCtrlRegs.GPAMUX1.bit.GPIO3 = GpioCtrlRegs.GPAMUX1.bit.GPIO4 = GpioCtrlRegs.GPAMUX1.bit.GPIO5 = 1; 1; 1; 1; 1; 1; // // // // // // Set GPIO0 Set GPIO1 Set GPIO2 Set GPIO3 Set GPIO4 Set GPIO5 port as EPWM1A port as EPWM1B port as EPWM2A port as EPWM2B port as EPWM3A port as EPWM3B port port port port port port ‘InitEPwm()’: This example implements symmetrical PWM with PWM1 configured as a master, PWM2 and PWM3 configured as slaves. There are seven control register modules in the enhanced PWM (EPWM) system to implement various PWM control techniques as shown below: . . . . . . . Time-Base Module Counter Compare Module Action Qualifier Module Dead-Band Generator Module PWM Chopper (PC) Module Trip Zone Module Event Trigger Module (TBCTL registers) (CMPCL registers) (AQCTLA/B registers) (DBCTL registers) (PCCTL registers) (TZCTL registers) (ETSEL registers) The configuration in the EPWM registers has a long script (please refer to the book companion website). To understand the full technical details, readers should consult the Enhanced Pulse Width Modulator (ePWM) Module Reference Guide (Texas Instruments Inc., 2009c). After completing the configuration of EPWM registers, the following scripts in ‘InitEPwm()’ are necessary to make PWM interrupts work. /* Enable CPU INT3 which is connected to EPWM1-3 INT */ IER |= M_INT3; /* Enable EPWM INTn in the PIE: Group 3 interrupts 1-3 */ PieCtrlRegs.PIEIER3.bit.INTx1 = 1; PieCtrlRegs.PIEIER3.bit.INTx2 = 1; PieCtrlRegs.PIEIER3.bit.INTx3 = 1; /* Clear three PWM interrupt flags */ EPwm1Regs.ETCLR.bit.INT = 1; EPwm2Regs.ETCLR.bit.INT = 1; EPwm3Regs.ETCLR.bit.INT = 1; Step 4 Write a header file ‘F28335_example_PWM.h’ including the following scripts and add it to the project. // Set half period of the PWM and initial duty cycle #define PWM_HALF_PERIOD 37500 // 1 kHz PWM at 75MHz system clock #define PWM_DUTY_CYCLE 18750 //50% duty cycle 356 Applied Intelligent Control of Induction Motor Drives Step 5 Create a new DSP/BIOS configuration ‘f28335_example_PWM.tcf’ by selecting ‘New’ and ‘DSP/BIOS configuration’ from the ‘File’ menu in CCS and add the new DSP/BIOS to the project. PWM hardware interrupts may be set by assigning the three interrupt service routines, ‘_EPWM1_INT_ISR’, ‘_EPWM2_INT_ISR’, and ‘_EPWM3_INT_ISR’ to the three PIE (Peripheral Interrupt Expansion) interrupt items ‘PIE_INT3_1’ ‘PIE_INT3_2’, and ‘PIE_INT3_3’, respectively. The assignment is done in the ‘PIE INTERRUPTS’ folder of the DSP/BIOS. Step 6 Write PWM interrupt service routines (ISR) to adjust the duty cycle according to the sinusoidal reference function as follows and add them to the project. #include ’DSP2833x_Device.h’ // Peripheral address definitions #include ’F28335_example_PWM.h’ // Main include file #include ’math.h’ // Include sine function double A1=0.0, A2=0.0, A3=0.0, B; Uint32 C; double TWO_PI_div20 = 0.3141592653589795; // = 2p/20 void EPWM1_INT_ISR(void) // PIE3.1 @ 0x000D60 EPWM1_INT (EPWM1) { PieCtrlRegs.PIEACK.all = PIEACK_GROUP3; // Must acknowledge the PIE group A1=A1+TWO_PI_div20; if (A1 >= TWO_PI) A1=0.0; B = sin(A1); // Call a sine function B=18750-0.8* B*18750; C= (Uint32) B; // Converter to 32 bit Uint data EPwm1Regs.CMPA.half.CMPA=C; // Update compare register EPwm1Regs.ETCLR.bit.INT = 1; // Clear PWM1 interrupt flag } void EPWM2_INT_ISR(void) // PIE3.2 @ 0x000D62 EPWM2_INT (EPWM2) { PieCtrlRegs.PIEACK.all = PIEACK_GROUP3; // Must acknowledge the PIE group A2=A2+TWO_PI_div20; if (A2 >= TWO_PI) A2=0.0; B = sin(A2-TWO_PI/3); // Call a sine function with phase as -2p/3 B=18750-0.8* B*18750; C= (Uint32) B; // Converter to 32 bit Uint data EPwm2Regs.CMPA.half.CMPA=C; // Update compare register EPwm2Regs.ETCLR.bit.INT = 1; // Clear PWM2 interrupt flag } void EPWM3_INT_ISR(void) // PIE3.3 @ 0x000D64 EPWM3_INT (EPWM3) { PieCtrlRegs.PIEACK.all = PIEACK_GROUP3; // Must acknowledge the PIE group A3=A3+TWO_PI_div20; if (A3 >= TWO_PI) A3=0.0; B = sin(A3+TWO_PI/3); // Call a sine function with phase as 2p/3 B=18750-0.8* B*18750; C=(Uint32) B; // Converter to 32 bit Uint data EPwm3Regs.CMPA.half.CMPA=C; // Update compare register EPwm3Regs.ETCLR.bit.INT = 1; // Clear PWM3 interrupt flag } Experimental Investigations 357 Note: The execution time of the sin function is 37 instruction cycles (Texas Instruments Inc., 2008). Step 7 By selecting ‘Rebuild All’ in the ‘Project’ menu of the CCS window, the executable code is generated. The filename of the executable code may be set in the ‘Build Options’ window in the ‘Project’ menu. In this example, it is named as ‘F28335_example_PWM.out’. Step 8 Connect the Code Composer Studio (CCS) to the TMS320F28335 processor by selecting the item ‘Connect’ from the CCS ‘Debug’ menu. Step 9 Reset the CPU and load the executable code ‘F28335_example_PWM.out’ into the processor by selecting the item ‘Load Program’ from the CCS ‘File’ menu. Step 10 Connect pins GPIO0 (PWM1A) and GPIO1 (PWM1B) in the processor to the oscilloscope channel 1 and channel 2, and click key ‘F5’ to start the program in the processor. Waveforms of PWM1A and PWM1B can be observed on the oscilloscope as shown in Figure 11.33. Figure 11.33 Waveforms of PWM1A and PWM1B displayed on the oscilloscope. Click key ‘Shift-F5’ to halt the executable code. Connect pins of the processor, GPIO0 (PWM1A), GPIO2 (PWM2A), and GPIO4 (PWM3A) to the oscilloscope channels 1, 2, and 3, respectively. Click key ‘F5’ to start the program again. The three-phase sinusoidal PWM output PWM1A, PWM2A and PWM3A can be observed on the oscilloscope as shown in Figure 11.34. Connect a low-pass filter consisting of a 1-kO resistance and a 4.7-mF to the pin GPIO0 (PWM1) of the processor and connect the output of the filter to channel 1 of the oscilloscope. The output waveform shown in Figure 11.35 may be observed. 358 Applied Intelligent Control of Induction Motor Drives Figure 11.34 Waveforms of PWM1A, PWM2A, and PWM3A in the oscilloscope. Figure 11.35 Filter output waveform from PWM1A. 359 Experimental Investigations 11.8.2 RTDX Programming This example demonstrates RTDX programming to exchange data between the TMS320F28335 processor and MATLAB. In this example, the application program in the processor is started by a MATLAB script and an array is sent to the processor from MATLAB. In the main program in the processor, a software interrupt is posted to call an interrupt service routine for receiving the array from MATLAB. After the processor has received the array, the value of every element in the array is increased by 1 and a second software interrupt is posted to call an interrupt service routine for sending the new array to MATLAB from the processor. Step 1 Create a new project ‘RTDX.pjt’. Step 2 Write a main program ‘swi.c’ as listed below and add it to the project. #include <rtdx.h> #include ‘swicfg.h’ RTDX_CreateInputChannel(ichan); RTDX_CreateOutputChannel(ochan); double A[64]; void main(Int argc, Char *argv[]) { RTDX_enableInput(&ichan); RTDX_enableOutput(&ochan); SWI_post(&SWI0); } // RTDX header file // Header file created by BIOS // Create a input channel // Create a output channel // Enable the input channel // Enable the output channel // Post software interrupt SWI0 Step 3 Create a new DSP/BIOS configuration ‘swi.tcf’ and add it to the project. Two software interrupts are set by adding two software interrupt items ‘SWI0’ and ‘SWI1’ into the DSP/ BIOS. The two software interrupts are assigned to trigger the interrupt service routines ‘_swiFxn0’ and ‘_swiFxn1’. By entering ‘_swiFxn0’ and ‘_swiFxn1’ into the items ‘SWI0’ and ‘SWI1’, respectively, the configuration is completed. Step 4 Write the interrupt service routines and add them to the project. void swiFxn0(void) // Interrupt service routine called by software interrupt SWI0 { RTDX_read( &ichan, &A, sizeof(A) ); // Read data from MATLAB RTDX_disableInput(&ichan); // Disable the input channel SWI_post(&SWI1); // Post software interrupt SWI1 } void swiFxn1(void) // Interrupt service routine called by software interrupt SWI1 { int i; for (i = 0; i < 64; i + +) A[i] = A[i] + 1; // Add 1 to every element of the array RTDX_write( &ochan, &A, sizeof(A) ); // Write data to MATLAB RTDX_disableOutput(&ochan); // Disable the output channel } 360 Applied Intelligent Control of Induction Motor Drives Step 5 Create an executable code ‘RDTX.out’. The filename of the executable code may be set in ‘Build Options’ in CCS. Step 6 Connect the Code Composer Studio (CCS) to the TMS320F28335 processor by selecting the item ‘Connect’ from the CCS ‘Debug’ menu. Step 7 Reset the CPU, and load the executable code ‘RDTX.out’ into the processor. Step 8 Enable RTDX in CCS by opening the ‘RTDX Control’ window from the ‘RTDX’ folder in the ‘Tools’ menu on the CCS, then selecting the ‘RTDX Enable’ box from the opened ‘RTDX Control’ window. Step 9 Start MATLAB and write a program ‘Example_RTDX.m’ as follows: function void = Example_RTDX() clear(’all’) A = 0:0.1:6.3; Send_array = sin(A); % Create a array of sine function % Connect MATLAB to CCS cc = ticcs; rx = cc.rtdx; open(rx,’ichan’,’w’) enable(rx,’ichan’) open(rx,’ochan’,’r’) enable(rx,’ochan’) flush(rx,’ochan’); % Get a handle to Code Composer Studio (CCS) % created an alias rx to the RTDX portion of cc % Open a channel for write access % Enable write access % Open a channel for read access % Enable read access % Flush data from ochan channels % Start processor application and write data from MATLAB to processor cc.run(’run’); % Start the processor program writemsg(rx,’ichan’,Send_array); % Write data to the processor % Read the data from processor to MATLAB % Determine the number of messages number_msgs = msgcount(rx,’ochan’) if ( number_msgs >=1) Read_array = cc.rtdx.readmsg(’ochan’,’double’, number_msgs); end % Read data to MATLAB halt(cc); % Halt the processor disable(rx,’all’) close all; % Plot waveforms plot(Send_array); hold on; plot(Read_array); axis([1 64 -1.5 2.5]); end % Plot the write data % Plot the read data Step 10 Run the program ‘Example_RTDX.m’ in MATLAB platform. The results are shown in Figure 11.36. 361 Experimental Investigations 2.5 2 Received data Value 1.5 1 0.5 0 Sent data -0.5 -1 -1.5 10 20 30 40 50 60 Index n Figure 11.36 Data sent to the processor and data received from it. 11.8.3 ADC Programming This example demonstrates ADC (analog-to-digital converter) programming to acquire analog signals from an ADC port of the TMS320F28335 processor and to transfer them to MATLAB by RTDX technique. The ADC module in TMS320F28335 has following features (Texas Instruments Inc., 2007). . . . . . 12-bit ADC core with built-in sample-and-hold Analog input range: 0.0–3.0 V Fast conversion rate: Up to 80 ns at 25-MHz ADC clock. 16 ADC channels Sixteen result registers to store conversion values and the digital value of the input analog voltage is derived by: Digital Value ¼ 4096 (Input Analog Voltage)/3. In this example, the application program in the processor is started by a MATLAB script. The ADC in the processor is triggered by PWM4 timer at a sampling rate of 2.5 kHz. From the ‘ADCINA0’ port of the processor, analog voltage is converted to digital value. After the conversion is completed, a hardware interrupt is triggered to call an interrupt service routine ‘ADCINT_ISR’. In the routine ‘ADCINT_ISR’, a software interrupt is posted to call an interrupt service routine ‘AdcSwi’. In the routine ‘AdcSwi’, the digital value is saved to an array. After 50 samples have been acquired, a task interrupt is issued by the routine ‘AdcSwi’ to call an interrupt service routine ‘task’ which sends the samples acquired to MATLAB. Step 1 Create a new project ‘F28335_example_ADC.pjt’. Step 2 Write the main program ‘Main_ADC.c’ as follows: 362 Applied Intelligent Control of Induction Motor Drives #include ‘DSP2833x_Device.h’ #include ‘F28335_example.h’ #include <rtdx.h> Uint16 AdcBuf[50]; RTDX_CreateOutputChannel(ochan); // Peripheral address definitions // Main include file // RTDX // ADC data buffer allocation void main(void) { InitSysCtrl(); InitAdc(); InitEPwm(); RTDX_enableOutput(&ochan); } // Initialize the CPU // Initialize the ADC // Initialize the PWM // Enable the output channel Step 3 Write the initialization functions as in Step 3 in Section 11.8.1. Step 4 Create a new DSP/BIOS configuration ‘f28335_example_ADC.tcf’ and add it to the project. ADC hardware interrupt is set by entering ‘_ADCINT_ISR’ into ‘PIE_INT1_6’ in the DSP/BIOS. The hardware interrupt ‘PIE_INT1_6’ will call the interrupt service routine ‘ADCINT_ISR’. A software interrupt is set by adding a software interrupt item ‘ADC_swi’ into the DSP/BIOS and entering ‘_AdcSwi’ into ‘ADC_swi’. The software interrupt ‘ADC_swi’ will call the interrupt service routine ‘AdcSwi’. A task interrupt is set by adding task interrupt item ‘TSK1’ into the DSP/BIOS and entering ‘_task’ into the task interrupt item ‘TSK1’which will call the interrupt service routine ‘task’. Step 5 Write the software interrupt service routines and task interrupt service routines: void AdcSwi(void) interrupt ADC_swi // Interrupt service routine called by software { static Uint16 *AdcBufPtr = AdcBuf; AdcRegs.ADCTRL2.bit.RST_SEQ1 = 1; Registers SEQ1 AdcRegs.ADCST.bit.INT_SEQ1_CLR = 1; *AdcBufPtr++ = AdcRegs.ADCRESULT0 >> 4; if( AdcBufPtr == (AdcBuf + 50) ) { AdcBufPtr = AdcBuf; TSK_yield(); } // Pointer to buffer // Reset Sequencing Control // Clear ADC SEQ1 interrupt flag // Read the ADC result // Rewind the pointer to beginning // Yield a task interrupt } void task(void) interrupt TSK1 // Interrupt service routine called by task { RTDX_write( &ochan, &AdcBuf, sizeof(AdcBuf) ); // Write data to MATLAB RTDX_disableOutput(&ochan); // Disable the output channel } 363 Experimental Investigations Step 6 Create an executable code ‘F28335_ADC.out’. The filename of the executable code may be set in the item ‘Build Options’ in CCS. Step 7 Connect the Code Composer Studio (CCS) to the TMS320F28335 processor by selecting the item ‘Connect’ from the CCS ‘Debug’ menu. Step 8 Reset the CPU, and load the executable code ‘F28335_ADC.out’ into the processor. Step 9 Enable RTDX in the CCS window as described in Step 7 of the example in Section 11.8.2. Step 10 Start MATLAB and write a program ‘Example_ADC.m’ as follows: function void = Example_ADC() clear(’all’) % Connect MATLAB to CCS cc = ticcs; rx = cc.rtdx; open(rx,’ochan’,’r’) enable(rx,’ochan’) % Get a handle to Code Composer Studio (CCS) % created an alias rx to the RTDX portion of cc % Open a channel for read access % Enable read access % Start processor application from MATLAB platform cc.run(’run’); % Start the processor program % Read the ADC data from processor to MATLAB number_msgs = msgcount(rx,’ochan’) % Determine the number of messages Read_array = cc.rtdx.readmsg(’ochan’,’int16’, number_msgs); % Read data from the processor to MATLAB Voltage = double(Read_array)*3/4096; % Coverter ADC digital value % to analog voltage value halt(cc); % Halt the processor % Plot waveform plot(Voltage); end % Plot the read voltage waveform Step 11 Connect the pin ‘ADCINA0’ on the TMS320F28335 processor to ground. Step 12 Run the program ‘Example_ADC.m’ in the MATLAB window. The results are shown in Figure 11.37. Step 13 Connect the positive terminal of a battery to the pin ‘ADCINA0’ on the TMS320F28335 processor and the negative terminal to the ground of the processor. The battery voltage measured using a multimeter is about 1.6 V. Step 14 Restart the processor application by selecting ‘Restart’ in the ‘Debug’ menu on CCS. 364 Applied Intelligent Control of Induction Motor Drives -3 x 10 5 4 Voltage (V) 3 2 1 0 -1 -2 -3 -4 -5 0 10 5 15 20 25 30 35 40 45 50 Index n Figure 11.37 ADC result of zero voltage from the processor. Step 15 Run the program ‘Example_ADC.m’ in MATLAB. The results are shown in Figure 11.38. 1.7 1.68 Voltage (V) 1.66 1.64 1.62 1.6 1.58 1.56 1.54 1.52 1.5 0 5 10 15 20 25 30 35 40 45 50 Index n Figure 11.38 Battery voltage acquired by the DSP via an ADC. 11.8.4 CAP Programming The enhanced capture (eCAP) module (Texas Instruments Inc., 2009e) in TMS320F28335 processor may be used to capture a pulse and to measure its period and duty cycle. In this example, the application program in the processor is started by a MATLAB script. The continuous sinusoidal PWM pulse created from GPIO0 port of the processor serves as the signal source. By connecting the GPIO0 pin to GPIO5 pin, the PWM pulse is captured to the processor from GPIO5 port. After the eCAP module has captured two pulses, a hardware interrupt ‘PIE_INT4_1’ is triggered. The hardware interrupt will call an interrupt service routine ‘ECAP1_INT_ISR’ which calculates the period and duty cycle of the captured 365 Experimental Investigations pulse and then post a software interrupt ‘SWI0’. In an interrupt service routine ‘swi_RTDX’, the period and duty cycle of the pulses are sent to MATLAB. After the period and duty cycle of the pulses are received by MATLAB, the waveform of the pulses is reconstructed and plotted. Figure 11.39 shows a pulse capture process. Period Pulse 1 Pulse 2 t1 Figure 11.39 t2 t3 t4 Time Capture process of two pulses in TMS320F28335. In the capture process: Time ‘t1’, which coincides with a rising edge, is captured into register ‘ECap1Regs.CAP1’; Time ‘t2’, which coincides with a falling edge, is captured into register ‘ECap1Regs.CAP2’; Time ‘t3’, which coincides with a rising edge, is captured into register ‘ECap1Regs.CAP3’; Time ‘t4’, which coincides with a falling edge, is captured into register ECap1Regs.CAP4’. The period and duty cycle of the pulses may be calculated by the values in the registers as follows: Duty cycle of pulse 1 ¼ t1 Duty cycle of pulse 2 ¼ t4 Period ¼ [(t3 t1) þ (t4 t2; t3; t2)]/2. Step 1 Create a new project ‘F28335_example_CAP.pjt’. Step 2 Write a main program ‘F28335_example_CAP.c’ as follows and add it to the project. #include ‘DSP2833x_Device.h’ #include ‘F28335_example_CAP.h’ #include <rtdx.h> RTDX_CreateOutputChannel(ochan); Uint32 PwmDuty; Uint32 PwmPeriod; Uint32 PwmDuty2; Uint32 PwmPeriod2; Uint32 To_pc[4]; void main(void) { InitSysCtrl(); InitGpio(); InitEPwm(); InitECap(); } // Peripheral address definitions // Main include file // RTDX // Measured PWM duty cycle // Measured PWM period // Measured PWM duty cycle 2 // Measured PWM period 2 // Initialize the CPU // Initialize the GPIO pins // Initialize the PWM // Initialize the Capture units 366 Applied Intelligent Control of Induction Motor Drives Step 3 Write initialization functions which are similar to Step 3 in Section 11.8.1. Step 4 Write a header file ‘F28335_example_CAP.h’ and add it to the project, as in Step 4 in Section 11.8.1. Step 5 Create a new DSP/BIOS configuration ‘F28335_example_CAP.tcf’ and add it to the project. CAP hardware interrupt may be set by entering ‘_ECAP1_INT_ISR’ into ‘PIE_INT4_1’ in the DSP/BIOS. The hardware interrupt ‘PIE_INT4_1’ will call the interrupt service routine ‘ECAP1_INT_ISR’. A software interrupt may be set by adding a software interrupt item ‘SWI0’ into the DSP/BIOS and entering ‘swi_CAP’ into the item ‘SWI0’. The software interrupt ‘SWI0’ will call the interrupt service routine ‘swi_CAP’. Step 6 Write an interrupt service routine to create a PWM pulse as follows and add the routine to the project. #include ‘DSP2833x_Device.h’ // Peripheral address definitions #include ‘F28335_example_CAP.h’ // Main include file #include ‘math.h’ double AA=0.0, CC; Uint32 BB; double TWO_PI = 6.28318530717959; double TWO_PI_div20 = 0.3141592653589795; void EPWM1_INT_ISR(void) // PIE3.1 @ 0x000D60 EPWM1_INT (EPWM1) { PieCtrlRegs.PIEACK.all = PIEACK_GROUP3; // Must acknowledge the PIE group AA=AA+TWO_PI_div20; if (AA >= TWO_PI) AA=0.0; CC = sin(AA); CC=CC*18750; CC=18750-CC*0.8; BB=(Uint32)CC; EPwm1Regs.CMPA.half.CMPA=BB; EPwm1Regs.ETCLR.bit.INT = 1; } // Call sine function // Converter to 32 bit Uint data // Update compare register // Clear PWM1 interrupt flag Step 7 Write a CAP interrupt service routine to calculate the period and duty cycle of the captured pulses as follows and add the routine to the project. void ECAP1_INT_ISR(void) // PIE4.1 @ 0x000D70 ECAP1_INT (ECAP1) { PieCtrlRegs.PIEACK.all = PIEACK_GROUP4; // Must acknowledge the PIE group PwmDuty = (int32)ECap1Regs.CAP2 - (int32)ECap1Regs.CAP1; PwmPeriod = (int32)ECap1Regs.CAP3 - (int32)ECap1Regs.CAP1; PwmDuty2 = (int32)ECap1Regs.CAP4 - (int32)ECap1Regs.CAP3; PwmPeriod2 = (int32)ECap1Regs.CAP4 - (int32)ECap1Regs.CAP2; PwmPeriod = (PwmPeriod + PwmPeriod2)/2; SWI_post(&SWI0); // Post software interrupt SWI0 ECap1Regs.ECCLR.bit.CEVT4 = 1; // Clear the CEVT4 flag } Experimental Investigations 367 Step 8 Write an interrupt service routine ‘swi_CAP’ as follows. void swi_CAP(void) { To_pc[0] = PwmDuty; // Duty cycle of pulse 1 To_pc[1] = PwmPeriod; // Period of pulse 1 To_pc[2] = PwmDuty2; // Duty cycle of pulse 2 To_pc[3] = PwmPeriod; // Period of pulse 2 as same as pulse1 RTDX_write( &ochan, &To_pc, sizeof(To_pc) ); // Write data to MATLAB } Step 9 Create an executable code ‘F28335_example_CAP.out’. The filename of the executable code may be set in the ‘Build Options’ in CCS. Step 10 Connect the Code Composer Studio (CCS) to the TMS320F28335 processor by selecting item ‘Connect’ from the CCS ‘Debug’ menu. Step 11 Reset the CPU, and load the executable code ‘F28335_example_CAP.out’ into the DSP. Step 12 Enable RTDX in CCS window as described in Step 7 in the RTDX programming example in Section 11.8.2. Step 13 Start MATLAB and write a MATLAB program ‘Example_CAP.m’ as follows. function void = Example_CAP() clear(’all’) % Connect MATLAB to CCS cc = ticcs; %Get a handle to Code Composer Studio (CCS) rx = cc.rtdx; % created an alias rx to the RTDX portion of cc open(rx,’ochan’,’r’) % Open a channel for read access enable(rx,’ochan’) % Enable read access % Start processorP cc.run(’run’); pause(0.02); halt(cc); application from MATLAB platform %Start the processor application program %Pause MATLAB 0.02s %Halt the processor application program % Read the captured data from processor to MATLAB number_msgs = msgcount(rx,’ochan’) %Obtain number of unread message in RTDX channel out_array = 0; if ( number_msgs > = 1) out_array = cc.rtdx.readmsg(’ochan’,’int32’, number_msgs); %Read data from RTDX channel A = cell2mat(out_array); %Convert data to a single matrix end % Separate duty and period from the matrix A Period = []; 368 Applied Intelligent Control of Induction Motor Drives Duty = []; B = double(A) C = B/(75*1e6)/2 [n,m] = size(C) for i = 1:m/2 Period(i) = C(i*2); Duty(i) = C(i*2-1); end %Convert int32 to double %Convert to real value at processor Clock as 75 MHz %Separate Period from the matrix %Separate Duty from the matrix % Build waveform of a sine cycle by captured duties and periods t = 0:1e-6:1e-3; %Create 1001 points on every pulse period [nt,mt] = size(t); Period(1) = []; %Clear first period sample -3 1 x 10 0.9 Duty cycles (s) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 4 6 8 10 12 14 16 18 20 Index n Figure 11.40 Duty cycles of pulses captured by the processor. 1 Amplitude (V) 0.8 0.6 0.4 0.2 0 -0.2 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Time (s) Figure 11.41 Waveform of pulses reconstructed by the data captured by the processor. 369 Experimental Investigations Duty(1) = []; %Clear first Duty sample mm = 20; %20 samples in a cycle with 50 Hz reference and 1kHz carrier p = []; timeplot = []; for j = 1:mm, if(t(i)<Duty(j)) p(i + mt*(j-1)) = 1.0; else p(i + mt*(j-1)) = 0.0; end timeplot(i + mt*(j-1)) = (i + mt*(j-1))*1e-6; end end % Plot pulse waveform and duty cycle data plot(Duty,’.’) % Plot duty cycle axis([1 20 0 2e-3]); plot(timeplot, p); % Plot pulse waveform axis([0 max(timeplot) -0.2 1.2]); end Step 14 Connect the GPIO0 pin of the processor to the GPIO5 pin by a wire and connect GPIO0 pin to the oscilloscope channel 1. Step 15 Run the program ‘RTDX_ MATLAB_CAP.m’ in MATLAB. Duty cycles of pulses are shown in Figure 11.40 and waveform of pulses is shown in Figure 11.41. On the oscilloscope channel 1, waveform of continuous sinusoidal PWM source may be observed as shown in Figure 11.42. Figure 11.42 Waveform of continuous 1 kHz sinusoidal PWM. 370 11.9 Applied Intelligent Control of Induction Motor Drives Summary This chapter has presented four experiments for verifying some of the intelligent control algorithms developed in previous chapters. The experimental system consists of an ADMC331 fixed-point DSP board (Analog Devices Inc.), an IGBT inverter power module IRPT1058A (International Rectifier Inc.), a data-acquisition board PCL818HG (Advantech Co.Ltd.), an encoder GBZ02 with a resolution of 200 pulses/revolution (China Sichuan Opto-electronic Co.), three-phase current sensor 3I411A (China WB institute), a host PC, a data-acquisition PC, and a three-phase induction motor. The hardware systems and devices from different manufacturers have been successfully integrated to give a functional experimental drive system. The system has the features of low cost, convenience in data acquisition, and expansion capability. However, program development at assembly code level is tedious and time-consuming. Based on the simulation models developed in previous chapters, three experimental programs (motor run up, fuzzy/PI control, and GA-EKF speed estimation) are developed with DSP assembly language, Cþ þ language, and MATLAB language. Experiment 2 has verified the accuracy of the voltage-input model, PWM model, encoder model, and decoder model in Chapter 3. Experiments 3 and 4 have basically verified the feasibility of the Fuzzy/PI two-stage controller developed in Chapter 6 and the GA-EKF speed estimator developed in Chapter 9. The insight and experience gained have provided a firm foundation for the practical implementation of other intelligent control algorithms. Additional technical problems need to be tackled, however, in order to advance the drive technology to production on a commercial scale. These include program code optimization, writing code to PROM, temperature rise consideration, vibration, and packaging. In Section 11.8, basic DSP programming techniques necessary for induction motor control are presented by way of four examples with reference to the TMS320F28335 processor. These techniques enable the necessary feedback signals, stator voltages, stator currents, and rotor speed to be acquired and transferred to MATLAB of a host PC in real-time for use by a complex intelligent algorithm. References Analog Devices (1992) Digital Signal Processing Applications using the ADSP-2100 Family, Volume 1, Analog Devices. Ben-Brahim, L. and Kawamura, A. (1992) A fully digitized field-oriented controlled induction motor drive using only current sensors. IEEE Transactions on Industrial Electronics, 39(3), 241–249. Kubota, H., Matsuse, K., and Nakano, T. (1993) DSP-based speed adaptive flux observer of induction motor. IEEE Transactions on Industry Applications, 29(2), 344–348. Texas Instruments Inc. (2007) TMS320x2833x Analog-to-Digital Converter (ADC) Module Reference Guide, Literature Number: SPRU812A. Texas Instruments Inc. (2008) C28x Floating Point Unit fast RTS Library, Module User’s Guide, C28x Foundation Software. Texas Instruments Inc. (2009a) TMS320F28335, TMS320F28334, TMS320F28332 Digital Signal Controllers (DSCs) Data Manual, Literature Number: SPRS439F. Texas Instruments Inc. (2009b) TMS320C28x DSP/BIOS 5.x Application Programming Interface (API) Reference Guide, Literature Number: SPRU625K. Texas Instruments Inc. (2009c) TMS320x2833x, 2823x Enhanced Pulse Width Modulator (ePWM) Module Reference Guide, Literature Number: SPRUG04A. Experimental Investigations 371 Texas Instruments Inc. (2009d) TMS320x2833x, 2823x System Control and Interrupts Reference Guide, Literature Number: SPRUFB0C. Texas Instruments Inc. (2009e) TMS320x2833x, 2823x Enhanced Capture (eCAP) Module Reference Guide, Literature Number: SPRUFG4A. The MathWorks Inc. (2008a) Embedded IDE Link 4, User’s Guide, For Use with Texas Instruments’ Code Composer Studio. Xu, X. and Novotny, W. (1996) Implementation of direct stator flux orientation control on a versatile DSP based system, in Sensorless Control of AC Motor Drives (eds K. Rajashekara, A. Kawamura, and K. Matsuse), IEEE Press, New Jersey. Zhong, H.Y., Messinger, H.P., and Rashad, M.H. (1991) A new microcomputer-based direct torque control system for three-phase induction motor. IEEE Transactions on Industry Applications, 27(2), 294–298. 12 Conclusions and Future Developments This book has investigated the induction motor control problem from three perspectives, namely the theory level, algorithm design level, and hardware implementation level: 1. Modern nonlinear control theory and artificial intelligence principles form the basis of induction motor control. Development of a control theory should be based on an understanding of the physical system, from which an abstract mathematical model (principle or formulation) is derived. 2. Control algorithm of the drive system is based on an understanding of the control theory from which a calculation model is produced for achieving the desired performance. In the book, the intelligent control algorithms presented are based on modern nonlinear control theory as well as Kalman filter, expert-system, fuzzy-logic, artificial neural-network, and genetic algorithm principles. 3. Hardware implementation is based on the fine details of the control algorithm, from which a real physical model is constructed. An ADMC331 DSP-based experimental system has been constructed for verifying the fuzzy-logic control algorithm and GA-EKF speed estimation algorithm for an induction motor. ADSP-21xx Family Assembler and Linker are used for generating an executable program for the experimental investigations. Based on an understanding of induction motor control and nonlinear feedback control theory, the induction motor control algorithms and speed estimation algorithms are presented systematically in Chapter 2. This book has presented four intelligent induction motor control schemes mainly at the algorithm level, namely expert-system acceleration control, hybrid fuzzy/PI two-stage control, neural-network DSC control, and GA-EKF sensorless control. The expert-system is based on hard or precise computation, whereas the fuzzy-logic, neural-network, and genetic algorithm are based on soft or approximate computation (Bose, 1997). At the control algorithm level, this book has demonstrated that expert-system, fuzzy-logic, neural-network, and genetic algorithm are effective in different aspects of induction motor control. At the hardware level, Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 374 Applied Intelligent Control of Induction Motor Drives feasibility of the fuzzy/PI two-stage control and GA-EKF sensorless control has essentially been verified. 12.1 Main Contributions of the Book The main contributions of the book are as follows: 1. The relationship between the 12 fifth-order nonlinear equations of an induction motor is investigated. Based on an understanding of induction motor control and nonlinear feedback control theory, the induction motor control algorithms and speed estimation algorithms are summarized systematically. 2. Three induction motor models are developed using the MATLAB /Simulink software. They are the current-input model, voltage-input model, and discrete-state model. The current-input model requires the least amount of calculations and is suitable for the study of current-controlled induction motor drives. The voltage-input model involves matrix calculations and can be used to study voltage-controlled induction motor drive systems. The discrete-state model has the most compact representation, but is computationally intensive. In addition, a PWM model, an encoder model, and a decoder model have been developed. 3. Expert-system-based acceleration control principle and a production system algorithm are presented in this book. The control scheme is quite different from the usual vector control schemes that depend on flux and torque calculations. The expert-system controller has the following characteristics: (1) rotor acceleration of an induction motor is controlled, (2) it has a small control error but no cumulative error, (3) it is independent of the parameters of the induction motor, so the same controller can be used for different induction motors, (4) the control may be performed at any time and state, whereas conventional vector control must be continuously performed starting from an initial state, (5) its execution time should be less than that of the conventional vector-control, because the expert-system algorithm consists mainly of logic operations, and (6) since the acceleration values are obtained by a differential operation on the angular speed, some error may be produced by the speed sensor noise in a practical system. 4. A hybrid fuzzy/PI two-stage control algorithm is presented. The fuzzy-logic-based twostage control strategy enables a scalar controller to give a performance approaching that of a field-oriented controller. Consequently, the rotor speed response is almost the same as a field-oriented controller. The fuzzy controller has the advantages of simplicity and robustness such as insensitivity to motor parameter changes, input current noise, noise in the measured speed, and magnetic saturation. Due to the excellent speed response over the whole speed range, the method should find applications in practical industrial drive systems. 5. A neural-network-based direct self control algorithm is presented. The neural-networkbased DSC with seven layers of neurons is developed to improve the performance of a DSP-based direct self controller. The execution time of control is decreased from 250 ms (for the DSP-based controller) to 21 ms (for the ANN-based controller). Simulation results show that the torque and flux errors resulting from the long execution time are almost eliminated. Hence, the ANN-based DSC drive system has better robustness against current noise and load changes than a DSP-based DSC drive system. Using neural-network Conclusions and Future Developments 6. 7. 8. 9. 10. 375 techniques, hardware implementation of DSC presents less problems and it is envisaged that neural-network-based DSC will gain wider acceptance in future. A novel method is presented to achieve good performance of an extended Kalman filter (EKF) for speed estimation of an induction motor drive. A real-coded genetic algorithm (GA) is used to optimize the noise covariance and weight matrices of the EKF, thereby ensuring filter stability and accuracy in speed estimation. Simulation studies on a constant V/Hz controller, a direct self controller, and a field-oriented controller demonstrate the efficacy of the presented method. Integral equations of the induction motor are presented. Using the integral equations, a linear-neural-network model of induction motor may be trained with measured data from a running induction motor. Almost all the machine parameters can be derived directly from the trained neural network models. With the estimated parameters, load, stator flux, and rotor speed may be estimated for induction motor control. With the estimated rotor speed, a simulation programming example of integral model-based sensorless control of induction motor is presented. Performance of conventional PWM inverter is improved by genetic algorithms. To reduce total harmonic distortion and to spread the harmonic energy of PWM inverter output waveform, four GA optimization strategies are presented in the book. They are (1) GAoptimized random-carrier-frequency PWM, (2) GA-optimized random-pulse-position PWM, (3) GA-optimized random-pulse-width PWM, and (4) GA-optimized hybrid random pulse-position and pulse-width PWM. A single-phase inverter is employed for the optimization study. This book has presented five experiments to verify the intelligent control algorithms for an induction motor: (1) An experiment to determine the electrical parameters of an induction motor, (2) a motor run-up experiment to verify the induction motor model, PWM model, encoder model, and decoder model, (3) a DSP-based experiment for the fuzzy/PI two-stage controller to verify the feasibility of the fuzzy/PI two-stage control algorithm, (4) a GAEKF experiment to verify the feasibility of the GA-EKF speed estimation algorithm, (5) GA-optimized single-phase random-carrier-frequency PWM inverter implemented by a TMS320F2812 DSP board and an IRAMX16UP60A inverter module. Source codes of the programming examples and control algorithms presented in the book are included on the book companion website for easy reference by the reader. These program modules could form the basis for more advanced intelligent induction control applications that the readers may wish to investigate. 12.2 Industrial Application of New Induction Motor Drives The demand for high-performance induction motor drives is rapidly increasing, particularly in the area of traction, electric vehicles, oil-drilling and aerospace applications. An ideal induction motor drive should have the following functions: A. High-performance control B. Performance should be unaffected by machine parameter variations C. Possibility of speed-sensorless control D. Low cost and fast dynamic response 376 Applied Intelligent Control of Induction Motor Drives Currently, vector control technique has only provided a practical solution for target A and parameter estimation technique may be a possible solution for target B, while speed and position estimation techniques are being developed to achieve target C. Addressing the unresolved problems with present-day induction motor controllers, this book investigated and presented four artificial intelligence (AI) control techniques for the induction motor drive. They include an expert-system-based controller which gives a complete solution for targets A and B, a genetic algorithm optimized extended Kalman filter with high-precision speed estimation for a sensorless drive and an integral model based sensorless drive which give a practical solution for target C, and a low-cost neural-network-based vector controller will give a hardware solution for target D. In future, ANN-based induction motor controller may be integrated in several ASIC (application specific integrated circuit) chips with fast parallel calculation and low hardware cost to replace the present DSP (digital signal processor) based controller. A comparison of various controllers on advantages, disadvantages, and cost is summarized in Table 12.1 that may serve as an application reference. The various controllers are designed to suit different application conditions, while their technical details could be found from the relevant chapters. The constant V/Hz controller may be used in a low-performance drive, but it has a low control accuracy and slow transient response. On the other hand, FOC, DSC, and expertsystem acceleration controller are suitable for high-performance applications and they have high control accuracy and a fast transient response. The fuzzy/PI two-stage controller has a performance that is intermediate between that of a constant V/Hz controller and FOC. In practical industrial applications, induction motor drives are generally selected according to the desired performance and cost of the controllers. A high-performance controller (except the ANN-based controller) is currently implemented by a DSP device that will result in high cost. A low or medium performance controller is generally implemented by a dedicated microprocessor that helps to reduce the cost. Although the software implementation of low performance controller is easier compared with a high-performance controller, the hardware implementation of the two controllers presents almost the same level of complexity, because different a.c. drives employ basically the same components, such as an inverter, a controller, an induction motor, and some sensors. In applications requiring a high-performance a.c. drive which is unaffected by machine parameter variations, such as electric vehicles and precision machine tools, the expert-system controller presented in the book should be considered. When a low cost drive is desired, such as oil-drilling, civil-engineering equipment and pump, it is recommended to replace the current constant V/Hz controller by the fuzzy/PI two-stage controller developed. Elimination of the speed sensor will increase the reliability and ruggedness of the overall drive system, hence the GA-EKF sensorless drive may be used for applications that require speed control in adverse environments or submerged drive systems. The ANN-based induction motor controller has fast parallel performance and low cost. It is envisaged that when special ANN chips for motor control are available on the market, the ANN-based induction motor controller will gradually supersede the expensive DSP device for implementing an induction motor drive. 377 Conclusions and Future Developments Table 12.1 Comparison of various induction motor controllers. Controller Advantages Constant V/Hz controller . Fuzzy controller ANN controller . Low-performance . Low . Performance dependent on machine parameters . Micro-processor based Low . Medium-performance . Micro-processor based . Performance is less dependent on machine parameters High-performance . . Higher . Stable . Performance is dependent on machine parameters Integral error accumulation . DSP based . Flux and torque are controlled High-performance . Performance is dependent on highprecision speed sensor . Highest . DSP based and high precision encoder Performance is dependent on machine parameters Integral error accumulation . Lowest . Neural device based Performance is dependent on machine parameters . Higher DSP based Performance is dependent on machine parameters . . Expert system controller Cost Performance approximates that of FOC Stable . . FOC and DSC Stable Disadvantages . . . Performance is independent of machine parameter variations . . No integral error accumulation High-performance . . Flux and torque are controlled . . Shortest time delay of controller . Controller with GA-EKF estimator . Controller with integral model estimator . 12.3 Robust structure No speed sensor No speed sensor . . . . Higher DSP based Future Developments Future developments on intelligent control of induction motor are briefly discussed as follows: 378 Applied Intelligent Control of Induction Motor Drives 12.3.1 Expert-System-based Acceleration Control 1. Although feasibility of the expert-system-based acceleration controller has been confirmed from computer simulation studies, it should be verified at the hardware level. The controller hardware may be implemented on a DSP (digital signal processor) with a high-precision encoder. 2. In order to improve the expert-system controller performance, the control rules and control knowledge could be refined by other AI techniques, such as Fuzzy logic, ANN or GA. 12.3.2 Hybrid Fuzzy/PI Two-Stage Control 1. To develop a current-magnitude fuzzy control in place of the PI control. 2. To develop a design method for the fuzzy controller that can accommodate the effect of load changes, disturbances, and parameter variations. 3. To improve the fuzzy/PI control algorithm at the computer simulation stage by using some AI techniques such as ANN-Fuzzy or GA-Fuzzy to optimize the membership functions instead of using the fairly standard and straightforward fuzzy method. 12.3.3 Neural-Network-based Direct Self Control 1. The neural-network-based DSC should be further improved in order to decrease the types and number of neurons. 2. A neural-network-based speed sensorless DSC can be developed by designing a subnetwork for speed estimation. 3. To develop a neural-network controller whose performance is immune to disturbances and motor parameter variations. 12.3.4 Genetic Algorithm for an Extended Kalman Filter Kalman filter technique has been widely used in different engineering disciplines. Further application of the GA-EKF method presented in this book need to be explored. 12.3.5 Parameter Estimation Using Neural Networks Neural-network-based parameter estimation employs integral models of induction motor. The advantage of the integral models is that they are insensitive to measurement noise created by rapid turn-on or turn-off of the semiconductor switch devices. New control algorithm based on integral equations of induction motor and real-time parameter measurement based on resetintegral method need to be developed. 12.3.6 Optimized Random PWM Strategies Based on Genetic Algorithms GA-optimized random PWM strategies will obviously reduce total harmonic distortion and boost energy converter efficiency for PWM inverters. Further work would be to extend the technique to three-phase PWM inverters that find wider applications in induction motor drives. Conclusions and Future Developments 379 12.3.7 AI-Integrated Algorithm and Hardware With the aid of modern nonlinear control theory and development of artificial intelligence techniques, induction motor drives will continue to evolve. It is envisaged that more advanced drives employing AI-integrated algorithm and ANN-integrated hardware will emerge, for example, a novel fuzzy-expert induction motor controller with GA-EKF speed estimator and implemented by ANN-integrated chips. Reference Bose, B.K. (1997) Intelligent control and estimation in power electronics and drives. The 1997 IEEE International Electric Machines and Drives Conference, Milwaukee, Wisconsin, USA, May 18–21. Appendix A Equivalent Circuits of an Induction Motor The ‘G’ equivalent circuit model of an induction motor in the stator reference-frame is shown in Figure A.1. iss V ss isR Rs dλsμ /dt LR RR dλsR/dt Lμ + - isμ jω oλsRP/2 Figure A.1 ‘G’ equivalent circuit model of an induction motor. The ‘T’ equivalent circuit model of an induction motor in the stator reference-frame is shown in Figure A.2. is s V ss Rs Ls-LM dλ ss /dt dλsM /dt isr LM isM Figure A.2 Lr-LM Rr dλsr /dt + - jωoλsrP/2 ‘T’ equivalent circuit model of an induction motor. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 Appendix B Parameters of Induction Motors The parameters of the three induction motors used for the simulation studies in the book are listed below. Table B.1 Motor 1. Type three-phase, wye-connected, squirrel-cage induction motor Rated power Rated stator voltage Rated frequency Rated speed Number of poles Stator resistance Stator leakage reactance Rotor resistance referred to stator Rotor leakage reactance referred to stator Magnetizing reactance Moment of inertia of the rotor Coefficient of friction KWrat ¼ 7.5 kW Vs,rat ¼ 220 V frat ¼ 60 Hz nM,rat ¼ 1160 r/min P¼6 Rs ¼ 0.282 O/ph Xls ¼ 0.512 O/ph Rr ¼ 0.151 O/ph Xlr ¼ 0.268 O/ph Xm ¼ 14.865 O/ph JM ¼ 0.4 kg m2 Cf ¼ 0.124 Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 384 Table B.2 Applied Intelligent Control of Induction Motor Drives Motor 2. Type three-phase, wye-connected, squirrel-cage induction motor Rated power Rated stator voltage Rated frequency Rated speed Number of poles Stator resistance Stator leakage reactance Rotor resistance referred to stator Rotor leakage reactance referred to stator Magnetizing reactance Moment of inertia of the rotor KWrat ¼ 0.75 kW Vs,rat ¼ 220 V frat ¼ 60 Hz nM,rat ¼ 1770 r/min P¼4 Rs ¼ 3.353 O/ph Xls ¼ 1.073 O/ph Rr ¼ 1.991 O/ph Xlr ¼ 1.073 O/ph Xm ¼ 1.029 O/ph JM ¼ 0.05 kg m2 Table B.3 Motor 3 (Bodine Electric Company model 295). Type three-phase, wye-connected, squirrel-cage induction motor Rated power Rated stator voltage Rated frequency Rated speed Number of poles Stator resistance Stator leakage reactance Rotor resistance referred to stator Rotor leakage reactance referred to stator Magnetizing reactance Moment of inertia of the rotor Coefficient of friction kWrat ¼ 0.147 kW Vs,rat ¼ 230 V frat ¼ 60 Hz nM,rat ¼ 1790 r/min P¼4 Rs ¼ 14.6 O/ph Xls ¼ 8.37 O/ph Rr ¼ 12.76 O/ph Xlr ¼ 19.53 O/ph Xm ¼ 111.7 O/ph JM ¼ 0.001 kg m2 Cf ¼ 0.000124 Appendix C M-File of DiscreteState Induction Motor Model M-file: Induction_motor.m function [sys,x0] = Induction_motor(t,x,u,flag,M) global Tr Ts Lr Ls Lm K1 Kr Rs Rr J Pole; Lr=0.0417; Ls=0.0424; Lm=0.041; Rs=0.294; Rr=0.156; Tr=Lr/Rr; J=0.8;Pole=6; K1=(1-Lm*Lm/Ls/Lr)*Ls; Kr=Rs+Lm*Lm*Rr/Lr/Lr; if flag==0 x0=zeros(5,1); sys=[0,5,5,3,0,0]; elseif flag==2 diff_FI=[(1-Kr/K1*M)*x(1)+Lm*Rr/Lr/Lr/K1*x(3)*M +Lm/Lr*x(5)/K1*x(4)*M*Pole/2; (1-Kr/K1*M)*x(2)-Lm/Lr*x(5)*M/K1*x(3) *Pole/2 +Lm*Rr/Lr/Lr/K1*x(4)*M; Lm/Tr*x(1)*M+(1-1/Tr*M)*x(3)-x(5)*x(4)*M*Pole/2; Lm/Tr*x(2)*M+x(5)*x(3)*M*Pole/2+(1-1/Tr*M)*x(4); x(5)+Pole*Lm*(x(3)*x(2)-x(4)*x(1))*M/(J*Lr)/3-u(3)*M/J] +[u(1)/K1*M;u(2)/K1*M;0;0;0]; sys=diff_FI; elseif flag==3 sys=x; elseif flag==4 sys=(round(t/M)+1)*M; else sys=[]; end Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 Appendix D Expert-system Acceleration Control Algorithm The expert-system acceleration control algorithm is implemented by a production system (Buchanan and Shortliffe, 1984; Hayes-Roth, 1985). The knowledge base of the controller is represented by the set of production rules that represents the expertise of the control area. Casespecific data of the knowledge base are kept in the working memory of production system. Finally, the inference engine is implemented by the recognize-act cycle of the production system. The following set of symbols is defined as: a a Da i n m t th A1 A2 A3 B1 B2 B3 B4 B5 B6 B7 B8 C1 C2 acceleration command actual acceleration an increment of acceleration Da ¼ a(t þ Dt) a(t) denotes area in which the stator current vector lies a number which denotes a stator voltage vector (mod(n) ¼ 7) a temporary register of the stator voltage vector time counter retaining time a 0 a 0 a 0 Da(Vs(n)) > ZDa(Vs(n þ 1)) Da(Vs(n)) ZDa(Vs(n þ 1)) Da(Vs(n)) > ZDa(Vs(n þ 2)) Da(Vs(n)) ZDa(Vs(n þ 2)) Da(Vs(n)) < ZDa(Vs(n 1)) Da(Vs(n)) ZDa(Vs(n 1)) Da(Vs(n)) < ZDa(Vs(n 2)) Da(Vs(n)) ZDa(Vs(n 2)) n ¼ 0 number of zero voltage vector n 6¼ 0 nth number of non-zero voltage vector Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 388 Applied Intelligent Control of Induction Motor Drives D1 D2 D3 E :E F :F H :H S Vs(k) X1 X2 X3 o*o oo e Z a a þ e a e < a < a þ e a a e t th (comparison stage) 0 < t < th (retaining stage) o*o > 0 o*o < 0 X1, X2 or X3 has been performed when t > th X1, X2 or X3 has not been performed when t > th a ¼ 0^oo ¼ 0 a stator voltage supplied to induction motor Supply Vs(n) and Vs(n þ 1) to induction motor in succession Supply Vs(n) and Vs(n þ 2) to induction motor in succession Supply Vs(n) and Vs(n 1) to induction motor in succession rotor speed command actual rotor speed threshold of acceleration error preferential parameter The production system consists of the following set of rules: Rule#Condition Action Note 1. E^:H ! n ¼ i 2: E ^ A1 ^ :H ! X1 3: E ^ A2 ^ :H ! X2 4: E ^ A3 ^ :H ! X3 Detect region of current vector 9 = 5: ðE ^ A1 ^ H ^ B1 Þ _ ðE ^ A2 ^ H ^ B3 Þ _ ðE ^ A3 ^ H ^ B5 Þ _ðE ^ A2 ^ H ^ B7 Þ ! k ¼ n; t ¼ 0 6: E ^ A1 ^ H ^ B2 ! k ¼ n þ 1; t ¼ 0 7: E ^ A2 ^ F ^ H ^ B4 ! k ¼ n þ 2; t ¼ 0 8: E ^ A2 ^ :F ^ H ^ B8 ! k ¼ n 2; t ¼ 0 9: E ^ A3 ^ H ^ B6 ! k ¼ n 1; t ¼ 0 10. (A1^:E^ D1^C1)_(A3^:E^ 11. (A1^:E^ D1^C2)_(A3^:E^ 12. :E^D2 ! Vs(k) 13. (A1^:E^ D3^C1)_(A3^:E^ 14. (A1^:E^ D3^C2)_(A3^:E^ Input comparison voltages ; D3^C1) ! Vs(k) D3^C2) ! m ¼ k, k ¼ 0, Vs(k) D1^C1) ! k ¼ m, Vs(k) D1^C2) ! Vs(k) 9 > > > > > > > = > > > > > > > ; Select an optimum voltage vector, and modify the rule base Keep zero voltage Insert zero voltage Retaining voltage Restore optimum voltage Keep optimum voltage A production system is defined by (George, 1989): 1. The set of production rules. These are called productions. A production is a conditionaction pair. Appendix D Expert-system Acceleration Control Algorithm 389 2. Working memory contains a description of the current state in a reasoning process. This description is a pattern that is matched against the condition part of a production to select appropriate problem-solving action. 3. The recognize-act cycle. The patterns in working memory are matched against the conditions of the production rules; this produces a subset of the productions, called the conflict set, whose conditions match the patterns in working memory. One of the productions in the conflict set is then selected (conflict resolution) and the production is fired. After the selected production rule is fired, the control cycle repeats with the modified working memory. References Buchanan, B. and Shortliffe, E.H. (1984) Rule-Based Expert Systems, MYCIN, Addison-Wesley, Reading, MA. George, F.L. and William, A.S. (1989) Artificial Intelligence and the Design of Expert System, Benjamin/Cummings Publishing Company, Inc. Hayes-Roth, F. (1985) Building Expert Systems, Addison-Wesley, Reading, MA. Appendix E Activation Functions of Neural Network y u Activation function of linear neuron: y ¼ u. Figure E.1 ⎧0 y =⎨ 1 u<0 u≥0 y y 1 0 Figure E.2 u <0 u ≥0 ⎧− 1 y =⎨ 1 1 u 0 -1 u Activation function of Hard Limit neuron. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 392 Applied Intelligent Control of Induction Motor Drives y 30 25 20 15 10 5 0 u -5 -4 -3 -2 -1 0 1 2 3 4 5 Figure E.3 Activation function of Square neuron: y ¼ u2 . y 1 0.5 0 -0.5 -1 -6 -4 -2 0 2 4 6 u Activation function of Tan-sigmoid neuron: y ¼ tanhðuÞ. Figure E.4 y 1 0.8 0.6 0.4 0.2 0 -0.2 -6 -4 -2 0 2 4 6 u Figure E.5 Activation function of Log-sigmoid neuron: y ¼ 1 þ1e u . Appendix F M-File of Extended Kalman Filter1 function [sys,x0] = kalman(t,x,u,flag,T) % input, u: Vds, Vqs, Ids, Iqs % states, x: Ids, Iqs, Fids, Fiqs, speed % output: Ids, Iqs, Fids, Fiqs, speed %sample time: T global Tr Ts Lr Ls Lh K1 Kr Rs Rr Q R GQG G x_1 P_1 K P h Y out; % Motor parameters Lr=0.0417; Ls=0.0424; Lh=0.041; Rs=0.294; Rr=0.156; H_pole=6/2;Tr=Lr/Rr; Kl=(1-Lh*Lh/Ls/Lr)*Ls; Kr=Rs+Lh*Lh*Rr/Lr/Lr; % initial parameters and states if flag==0 x0=zeros(5,1); K=zeros(5,2); P=[1 0 0 0 0; 0 1 0 0 0; 0 0 1 0 0; 0 0 0 1 0; 0 0 0 0 1]; G=[1e-10 0 0 0 0; 0 1e-10 0 0 0; 0 0 1e-10 0 0; 0 0 0 1e-10 0; 0 0 0 0 1e-10]; 1 Portions reprinted by permission of K.L. Shi, T.F. Chan, Y.K. Wong and S.L. Ho, “Speed estimation of induction motor using extended Kalman filter,” IEEE 2000 Winter Meeting, vol. 1, pp. 243–248, January 23–27, 2000, Singapore. Ó 2000 IEEE. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 394 Applied Intelligent Control of Induction Motor Drives Q=[1e-5 0 0 0 0; 0 1e-5 0 0 0; 0 0 1e-5 0 0; 0 0 0 1e-5 0; 0 0 0 0 1e-5]; R=[0.001 0 0 0.001]; GQG=G*Q*G’; sys=[0,5,5,4,0,0]; %Update discrete states elseif abs(flag)==2 % Set measurement variable U=[u(1);u(2)]; Y=[u(3);u(4)]; % Equation (7.5): Prediction of state dif_F=[1-Kr/K1*T,0,Lh*Rr/Lr/Lr/K1*T,Lh/Lr*x(5)*H_pole/K1*T,Lh/Lr*x (4)/K1*T; 0,1-Kr/K1*T,-Lh/Lr*x(5)*H_pole/K1*T,Lh*Rr/Lr/Lr/K1*T, -Lh_K/Lr_K*x(3)/K1_K*T; Lh/Tr*T,0,1-T/Tr,-x(5)*H_pole*T,-x(4)*T; 0,Lh/Tr*T,x(5)*H_pole*T,1-T/Tr,x(3)*T; 0,0,0,0,1]; x_1=[ dif_F(1,1)*x(1)+dif_F(1,3)*x(3)+dif_F(1,4)*x(4); dif_F(2,2)*x(2)+dif_F(2,3)*x(3)+dif_F(2,4)*x(4); dif_F(3,1)*x(1)+dif_F(3,3)*x(3)+dif_F(3,4)*x(4); dif_F(4,2)*x(2)+dif_F(4,3)*x(3)+dif_F(4,4)*x(4); dif_F(5,5)*x(5)]+T*[u(1)/K1;u(2)/K1;0;0;0 ]; % Equation(7.7): Estimation of error covariance matrix GQG=GQG-dif_F*GQG*dif_F’*T; P_1=dif_F*P*dif_F’+GQG; % Equation(7.14): Calculation of h and diff_h h=[x(1);x(2)]; dif_h=[1 0 0 0 0;0 1 0 0 0]; % Equation(7.9): Calculation of Kalman Filter K=P_1*dif_h’*inv(dif_h*P_1*dif_h’+R); % Equation(7.11): Estimation of Kalman Filter out=x_1+K*(Y-h); sys=out; % Equation(7.12): Update of the error covariance matrix P=P_1-K*dif_h*P_1; elseif flag==3 sys=out; elseif flag==4 sys=(round(t/T)+1)*T; else sys=[]; end Appendix G ADMC331-based Experimental System Figure G.1 Complete experimental system with host PC and notebook computer for data acquisition. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 396 Applied Intelligent Control of Induction Motor Drives Figure G.2 Close-up view of the ADMC331 kit and the induction motor. Appendix H Experiment 1: Measuring the Electrical Parameters of Motor 3 The motor is a three-phase 147-W, 230-V induction motor (Model 295 Bodine Electric Co.). The motor is Y-connected with no access to the neutral point. 1. DC Resistance Test As shown in Figure H.1, a DC voltage VDC is applied so that the current IDC is close to the motor rating. Because the machine is Y-connected, Rs ¼ Rdc/2 ¼ (VDC/IDC)/2. From measurement, VDC ¼ 30.6 V, IDC ¼ 1.05 A. Hence, Rs ¼ RDC ð30:6=1:05Þ ¼ 14:6 O=phase: ¼ 2 2 Idc A V Vdc Open a b IM c Figure H.1 Circuit for DC resistance test. 2. No Load Test The setup for the no-load test and locked-rotor test is shown in Figure H.2. Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 398 Applied Intelligent Control of Induction Motor Drives V A A Three-phase wattmeter B IM C AC 220V 3 phase N Figure H.2 Circuit for no-load and locked-rotor test. With the motor running at no load, measure V, I & P to find the machine reactance Xn Xls þ Xm. The measured data are as follows: Frequency (Hz) Voltage (V) Current (A) Real power (W) 50 220 1.22 128.2 At no load the per-unit slip s is approximately zero, hence the equivalent circuit is as shown in Figure H.3. Rs Xls Xr + Ia Xm Va s ≈ 0 means Rr /s ≈ infinite (open circuit) – Figure H.3 Equivalent circuit of three-phase induction motor under no-load test. The real power P represents, 1. Hysteresis and Eddy current losses (core losses) 2. Friction and windage losses (rotational losses) 3. Copper losses in stator and rotor (usually small at no load) Phase voltage V 220 Va ¼ pﬃﬃﬃ ¼ pﬃﬃﬃ ¼ 127 V 3 3 Appendix H Experiment 1: Measuring the Electrical Parameters of Motor 3 399 Phase current Ia ¼ 1:22 A Phase real power Pa ¼ P=3 ¼ 128:2 3 ¼ 42:73 W Phase reactive power Qa ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðVa Ia Þ2 P2a ¼ ð127 1:22Þ2 42:732 Þ ¼ 148:93 VAr Xn ¼ Qa 148:93 ¼ ¼ 100:06 O Ia2 1:222 Since s 0, Xn Xls þ Xm : 3. Locked-rotor Test With the rotor locked, the rotor speed is zero and the per-unit slip is equal to unity. The equivalent circuit is as shown in Figure H.4 or Figure H.5. Rs Xls Xr + Ia Xm Va Rr – Figure H.4 Equivalent circuit of three-phase induction motor under locked-rotor test. Rs Xls + Ia R2 Va X2 – Figure H.5 Simplified equivalent circuit of three-phase induction motor under locked-rotor test. 400 Applied Intelligent Control of Induction Motor Drives The test data are: Frequency (Hz) Voltage (V) Current (A) Real power (W) 50 69.32 1.2 103.35 Phase voltage V 69:32 Va ¼ pﬃﬃﬃ ¼ pﬃﬃﬃ ¼ 40:02 V 3 3 Phase current Ia ¼ 1:2 A Active power per phase P 103:35 ¼ ¼ 34:45 W 3 3 Pa ¼ Reactive power per phase Qa ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðVa Ia Þ2 P2a ¼ ð40:02 1:2Þ2 34:452 Þ ¼ 33:46 VAr For a class C motor, Xls ¼ 0:3 Xlr ¼ 0:7 Qa 33:46 ¼ 0:3 ¼ 6:97 O Ia2 1:22 Qa 33:46 ¼ 0:7 ¼ 16:27 O: 2 Ia 1:22 From the no-load test, Xn ¼ 100:06 O, so Xm ¼ Xn Xls ¼ 100:06 R¼ 6:97 ¼ 93:09 O Pa 34:45 ¼ ¼ 23:92 O: Ia2 1:22 From Figure H.5, R2 ¼ R Rs ¼ 23:92 14:6 ¼ 9:32 O: Appendix H Experiment 1: Measuring the Electrical Parameters of Motor 3 Comparing Figures H.4 and H.5, R2 þ jX2 ¼ R2 Rr ¼ R2 Xlr þ Xm Xm 2 ðRr þ jXlr Þ jXm ðRr þ jXlr Þ þ jXm Rr Xm2 Rr þ ðXlr þ Xm Þ2 ¼ 9:32 16:27 þ 93:09 93:09 Summarizing, 1. Stator winding resistance Rs ¼ 14.6 O/phase 2. Rotor winding resistance Rr ¼ 12.76 O/phase 3. Magnetizing reactance Xm ¼ 93.09 O/phase The magnetizing inductance per phase is Lm ¼ Xm 93:09 ¼ 0:2963 H: ¼ 2pf 2p 50 Stator leakage reactance Xls ¼ 6.97 O/phase The stator inductance per phase is Lls ¼ Xls 6:97 ¼ 0:0222 H: ¼ 2pf 2p50 Rotor leakage reactance Xlr ¼ 16.27 O/phase, The rotor leakage inductance per phase is Llr ¼ Xlr 16:27 ¼ 0:0518 H: ¼ 2pf 2p50 2 ¼ 12:86 O: 401 Appendix I DSP Source Code for the Main Program of Experiment 2 .MODULE/RAM/SEG=USER_PM1/ABS=0x30 main; #include <c:\ADMC331\TgtFiles\admc331.h> #include <c:\ADMC331\TgtFiles\romutil.h> #include <c:\ADMC331\TgtFiles\macro.h> #include <c:\ADMC331\TgtFiles\constant.h> #include <dac.h> #include <pwm331.h> .VAR/DM/RAM/SEG=user_dm .VAR/DM/RAM/SEG=user_dm .VAR/DM/RAM/SEG=user_dm .VAR/DM/RAM/SEG=user_dm .VAR/DM/RAM/SEG=user_dm .VAR/DM/RAM/SEG=user_dm VphaseA; ThetaA; VphaseB; ThetaB; VphaseC; ThetaC; .ENTRY PWMSYNC_ISR; .ENTRY PWMTRIP_ISR; .VAR/DM/RAM/SEG=USER_DM Vdc; .VAR/DM/RAM/SEG=USER_DM Vdc_max_inv; .INIT Vdc_max_inv : Vdc_INV; { Phase increment constant : Desired frequency = 60 Hz PWM frequency = 10 kHz PWM cycles per period = 10000/60 = [-1,1] = [-pi, pi] phase increment = 2 * 60 * 32768 / 10000 = 393 } .CONST delta = 393; { Initialization Code } STARTUP: Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 404 Applied Intelligent Control of Induction Motor Drives ICNTL = 0x00; {Configure interrupt format: disable nested interrupts IRQ0,1,2 level sensitive } ay0 = 0x00E; {Enable s/w and SPORT1 interrupts for debugger } ar = IMASK; ar = ar OR ay0; IMASK = ar; { initialize DAC routines } call init_DAC; { initialize the PWM block } call init_PWM; { initialize phase angles } ar = 0x0000; dm(ThetaA) = ar; ay0 = TwoPiOverThree; ar = ar + ay0; dm(ThetaB) = ar; ar = ar + ay0; dm(ThetaC) = ar; IFC = 0x80; {Clear any pending IRQ2 interrupt } ay0 = 0x200; {Enable IRQ2 interrupts } ar = IMASK; ar = ar OR ay0; IMASK = ar; { do first DAC write to start autobuffer process } call update_DAC; { Main loop : empty, just waits for interrupts } MAINLOOP: jump MAINLOOP; PWMSYNC_ISR: IMASK = 0x06; { enable Sport1 interrupts for debugger } { increment phase angles } ax0 = dm(ThetaA); ay0 = delta; ar = ax0 + ay0; dm(ThetaA) = ar; ax0 = dm(ThetaB); ay0 = delta; ar = ax0 + ay0; dm(ThetaB) = ar; ax0 = dm(ThetaC); ay0 = delta; ar = ax0 + ay0; dm(ThetaC) = ar; Appendix I DSP Source Code for the Main Program of Experiment 2 405 { calculate phase voltages by taking sine of angleand then mulitplying by 0.5 to put on the range[-0.5, 0.5] } ax0 = dm(ThetaA); M5 = 1; L5 = 0; call ADMC_SIN; my1 = ar; mr = 0; mx0 = 0x4000; mr = mr + mx0 * my1 (SS); dm(VphaseA) = mr1; ax0 = dm(ThetaB); M5 = 1; L5 = 0; call ADMC_SIN; my1 = ar; mr = 0; mx0 = 0x4000; mr = mr + mx0 * my1 (SS); dm(VphaseB) = mr1; ax0 = dm(ThetaC); M5 = 1; L5 = 0; call ADMC_SIN; my1 = ar; mr = 0; mx0 = 0x4000; mr = mr + mx0 * my1 (SS); dm(VphaseC) = mr1; { write to PWM generator } sr1 = dm(VphaseA); ay1 = dm(VphaseB); my1 = dm(VphaseC); call WR_PWM_DUTY; call read_ADC; dm(Vdc) = ar; call Vdc_HANDLING; { write to DAC } write_DAC(Vdc_as, DAC1) write_DAC(Vdc_bs, DAC2) write_DAC(Vdc_cs, DAC3) rti; PWMTRIP_ISR: imask = 0x06; { unmask SPORT1 interrupts for debugger} { check the PWMTRIP input, if it has gone high restart the PWM block } AR = DM(SYSSTAT); 406 Applied Intelligent Control of Induction Motor Drives AR = TSTBIT 0 of AR; IF NE JUMP RESTART_PWM; CNTR = H#3FF ; DO Wait0 UNTIL CE; { wait 10us } Wait0: NOP; { check the PWMTRIP input again, if it has gone high restart the PWM block } AR = DM(SYSSTAT); AR = TSTBIT 0 of AR; IF NE JUMP RESTART_PWM; RTI; { After a shutdown - restart the PWM. } RESTART_PWM: CNTR = H#3FF ; DO Wait20 UNTIL CE; { wait 10us } Wait20: NOP; IFC = 0X80; { clear IRQ2 interupt } AR = DM(IRQFLAG); call INIT_PWM; RTI; { Measure the bus-voltage for correction of the phase voltages. } Vdc_HANDLING: { calculate Vdc(measured) / Vdc(max) } MX0 = DM(Vdc_max_inv); MY0 = DM(Vdc); MR = MX0*MY0 (SS); { Vdc_as = VphaseA * Vdc(measured) / Vdc(max) } MX0 = MR1; MY0 = DM(VphaseA); MR = MR1*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Vdc_as) = SR1; { Vdc_bs = VphaseB * Vdc(measured) / Vdc(max) } MY0 = DM(VphaseB); MR = MX0*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Vdc_bs) = SR1; { Vdc_cs = VphaseC * Vdc(measured) / Vdc(max) } MY0 = DM(VphaseC); MR = MX0*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Vdc_cs) = SR1; RTS; .ENDMOD; Appendix J DSP Source Code for the Main Program of Experiment 3 .MODULE/RAM/SEG=USER_PM1/ABS=0x30 main; #include <c:\adi\mcd331\TgtFiles\admc331.h>; #include <c:\adi\mcd331\TgtFiles\macro.h>; #include <c:\adi\mcd331\TgtFiles\romutil.h> {Local program variable definitions} { Three phase stator currents } .VAR/DM/RAM/SEG=USER_DM Ias; .VAR/DM/RAM/SEG=USER_DM Ibs; .VAR/DM/RAM/SEG=USER_DM Ics; .VAR/DM/RAM/SEG=user_dm ThetaA; .VAR/DM/RAM/SEG=user_dm ThetaB; .VAR/DM/RAM/SEG=user_dm ThetaC; { Phase current offsets, measured at startup } .VAR/DM/RAM/SEG=USER_DM Ia_offset; .VAR/DM/RAM/SEG=USER_DM Ib_offset; .VAR/DM/RAM/SEG=USER_DM Ic_offset; { DC bus voltage: actual and 1/max } .VAR/DM/RAM/SEG=USER_DM Vdc; .VAR/DM/RAM/SEG=USER_DM Vdc_max_inv; { Three reference voltages } .VAR/DM/RAM/SEG=USER_DM VrefA; .VAR/DM/RAM/SEG=USER_DM VrefB; .VAR/DM/RAM/SEG=USER_DM VrefC; .VAR/DM/RAM/SEG=USER_DM Omega_set; { Real time clock variables } .VAR/DM/RAM/SEG=USER_DM Count; .VAR/DM/RAM/SEG=USER_DM Time; Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 408 Applied Intelligent Control of Induction Motor Drives { Flag indicating whether first PWMSYNC has occurred } .VAR/DM/RAM/SEG=USER_DM firstFlag; { Direction flag } .VAR/DM/RAM/SEG=USER_DM dir_flag; .CONST CW_FLAG = 0x01; .CONST CCW_FLAG = 0x00; { for debugging only } .VAR/DM/RAM/SEG=USER_DM StepTime; { Local program variable initialization } .INIT Vdc_max_inv : Vdc_INV; .INIT StepTime : 1; { time to apply speed command from potentiometer, in 0.1s increments } { Subroutines defined in this module } .ENTRY PWMSYNC_ISR; .ENTRY PWMTRIP_ISR; {PWM frequency = 10 kHz 2 * pi * time increment = 2 * 32768 / 10000 = 7} .CONST delta = 7; { Subroutines defined in other modules } #include #include #include #include #include #include #include #include #include #include #include <dac.h> <admc331.h> <pwm331.h> <ir_init.h> <model.h> <mathfix.h> <math_32b.h> <enco.h> <cntrl.h> <capture.h> <speedset.h> { Global variable definitions } .GLOBAL VrefA; .GLOBAL VrefB; .GLOBAL VrefC; .GLOBAL Omega_set; .GLOBAL ImRef; .GLOBAL Freq; .GLOBAL Fslip .GLOBAL IaRef; .GLOBAL IbRef; .GLOBAL IcRef; { Initialization Code } Appendix J DSP Source Code for the Main Program of Experiment 3 STARTUP: ay0 = 0x00E; {Enable s/w, and SPORT1 interrupts } ar = IMASK; ar = ar OR ay0; IMASK = ar; ICNTL = 0x00; {Configure interrupt format: disable nested interrupts IRQ0,1,2 level sensitive } { set PIO(23) as output } ax0 = 0x80; dm(PIODIR2) = ax0; ax0 = 0x00; dm(PIODATA2) = ax0; { set time to 0 } ax0 = 0x0000; dm(Time) = ax0; call init_speed_est; { initialize the data capture functions: number of samples = 100 1 sample per 200 PWM cycles 1 sample per 20 ms 50 Hz sample rate 2s of total time } call init_capture; ar = 99;{199;} call init_undersample; { initialize current magnitude PI controllers } call init_ MCPI_Controller; { initialize fuzzy frequency controllers } call init_ FUZZY_Controller; { initialize stator current PI controllers } call init_SCPI_Controllers; { initialize the IR PowIRtrain module } call init_IR; { initialize the DAC } call init_DAC; { initialize the ADC } call init_ADC; { initialize the encoder } call init_enco; { initialize a counter to measure current offsets } ax0 = 16; dm(Count) = ax0; ax0 = 0x0001; 409 410 Applied Intelligent Control of Induction Motor Drives dm(firstFlag) = ax0; ax0 = 0x0000; dm(Ia_Offset) = ax0; dm(Ib_Offset) = ax0; dm(Ic_Offset) = ax0; { initialize phase angles } ar = 0x0000; dm(ThetaA) = ar; ay0 = TwoPiOverThree; ar = ar + ay0; dm(ThetaB) = ar; ar = ar + ay0; dm(ThetaC) = ar; { initialize counters used for a real time clock subsystem } ax0 = 0x0000; dm(Count_01s) = ax0; dm(Time) = ax0; { initialize the speed setpoint functions } call init_speed; call INIT_PWM; {Initialize PWM registers and ISRs } IFC = 0x80; {Clear any pending IRQ2 interrupt } ay0 = 0x200; {Enable IRQ2 interrupts } ar = IMASK; ar = ar OR ay0; IMASK = ar; call update_DAC; MAINLOOP: ax0 = dm(Time); ay0 = dm(StepTime); ar = ax0 - ay0; if ne jump MAINLOOP; ar = ax0 + 1; { increment time } dm(Time) = ar; { enable capture } call enable_A; call enable_B; call enable_C; call enable_D; { do initial capture } call record; { apply apply speed command request from potentiometer} ax0 = dm(Omega_set); ay0 = dm(speedset); ar = ax0 + ay0; dm(Omega_set) = ar; Appendix J DSP Source Code for the Main Program of Experiment 3 jump MAINLOOP; { end of main loop } PWMSYNC_ISR: { PWM Interrupt Service Routine } imask = 0x20E;{unmask IRQ2, s/w, SPORT1 interrupts} { IRQ2 used for tacho or resolver pulses } { s/w, SPORT1 used for debugger } ena sec_reg; ax0 = dm(Count_0s); ar = ax0 + 1; ay0 = 1000; af = ax0 - ay0; if eq jump tic; dm(Count_0s) = ar; jump cont3; tic: ax0 = 0x0000; dm(Count_0s) = ax0; ax0 = dm(Time); { increment Time } ar = ax0 + 1; dm(Time) = ar; cont3: nop; { do nothing in the first PWMSYNC cycle since the ADCs do not yet have valid values. } ar = dm(firstFlag); ar = pass ar; if eq jump not1st; ar = 0x0000; dm(firstFlag) = ar; jump end_PWM; { in PWMSYNC cycles 2 through 17 measure the current offsets. } not1st: ar = dm(Count); ar = pass ar; if eq jump cont4; call read_ADC; call Calc_I_Offsets; jump end_PWM; cont4: call read_ADC; dm(Vdc) = ar; call Vdc_HANDLING; { stator current PI Controllers } { decide if it is time to execute the fuzzy and current magnitude controllers } ar = dm(Vel_count); af = pass ar; if le jump do_speed; ar = ar - 1; dm(Vel_count) = ar; jump CHECK_Vabc; 411 412 Applied Intelligent Control of Induction Motor Drives do_speed: ar = VEL_COUNT_MAX-1; dm(Vel_count) = ar; { speed encoder} call enco; call Fuzzy; call Currentmc; call SINCURRENT; call Stcpi; CHECK_Vabc: SR1 = DM(Vac_as); MR1 = DM(Vac_bs); MR2 = DM(Vac_cs); { Calculate the three phase-voltages. } DM(VrefA) = SR1; DM(VrefB) = MR1; DM(VrefC) = MR2; JUMP V_CW_CCW; { Limit the voltages before calculating the duty-cycles } CALL LIMIT_VrefABC; { Update PWM duty cycles based on calculated VrefA, B, C} SR1 = DM(VrefA); AY1 = DM(VrefB); MY1 = DM(VrefC); call WR_PWM_DUTY; call calc_enco; write_DAC(VrefA, DAC1) write_DAC(VrefB, DAC2) write_DAC(VrefC, DAC3) write_DAC(Fslip, DAC4) write_DAC(ImRef, DAC5) write_DAC(Ias, DAC6) write_DAC(Ibs, DAC7) write_DAC(Ics, DAC8) call record; end_PWM: dis sec_reg; rti; SINCURRENT: ax0 = dm(ThetaA); ay0 = delta * dm(Freq); ar = ax0 + ay0; dm(ThetaA) = ar; ax0 = dm(ThetaB); ay0 = delta * dm(Freq); Appendix J DSP Source Code for the Main Program of Experiment 3 413 ar = ax0 + ay0; dm(ThetaB) = ar; ax0 = dm(ThetaC); ay0 = delta * dm(Freq); ar = ax0 + ay0; dm(ThetaC) = ar; ax0 = dm(ThetaA); M5 = 1; L5 = 0; call ADMC_SIN; my1 = ar; mr = 0; mr = mr + my1 * dm(ImRef); dm(IaRef) = mr; ax0 = dm(ThetaB); M5 = 1; L5 = 0; call ADMC_SIN; my1 = ar; mr = 0; mr = mr + my1 * dm(ImRef); dm(IbRef) = mr; ax0 = dm(ThetaC); M5 = 1; L5 = 0; call ADMC_SIN; my1 = ar; mr = 0; mr = mr + my1 * dm(ImRef); dm(IcRef) = mr; { Subroutine : record Description : record variables of interest in buffers using the routines defined in capture.dsp.} record: ar = dm(Fslip); call capture_A; ar = dm(ImRef); call capture_B; ar = dm(Enco); call capture_C; ar = dm(IasRef); call capture_D; rts; { Calc_I_Offsets - measure the three phase current offsets. This code is only executed for the first 16 PWM cycles.} 414 Applied Intelligent Control of Induction Motor Drives Calc_I_Offsets: ay1 = ar; { store the measured values as the offsets } ay0 = dm(Ia_offset); { load old Ia_offset } SR = ASHIFT sr1 BY -4 (LO); { divide latest reading by 16 } ar = sr0 + ay0; dm(Ia_offset) = ar; { keep running total } ay0 = dm(Ib_offset); { load old Ib_offset } SR = ASHIFT sr1 BY -4 (LO); { divide latest reading by 16 } ar = sr0 + ay0; { keep running total } dm(Ib_offset) = ar; ay0 = dm(Ic_offset); { load old Ic_offset } SR = ASHIFT mr1 BY -4 (LO); { divide latest reading by 16 } ar = sr0 + ay0; dm(Ic_offset) = ar; { keep running total } { decrement the count value } skip:ar = dm(Count); ar = ar - 1; dm(Count) = ar; rts; { PWMTRIP - stops the PWM on the outputs.} PWMTRIP_ISR: imask = 0x0E; { unmask s/w, SPORT1 interrupts for debugger } { check the PWMTRIP input, if it has gone high restart the PWM block } AR = DM(SYSSTAT); AR = TSTBIT 0 of AR; IF NE JUMP RESTART_PWM; CNTR = H#3FF ; DO Wait0 UNTIL CE; Wait0: NOP; { wait 10us } { check the PWMTRIP input again, if it has gone high restart the PWM block } AR = DM(SYSSTAT); AR = TSTBIT 0 of AR; IF NE JUMP RESTART_PWM; DIS SEC_REG; RTI; { After a shutdown - restart the PWM. RESTART_PWM: CNTR = H#3FF ; DO Wait20 UNTIL CE; Wait20: NOP; { wait 10us } } 415 Appendix J DSP Source Code for the Main Program of Experiment 3 IFC = 0X80; { clear IRQ2 interupt } AR = DM(IRQFLAG); call INIT_PWM; RTI; {Return From Interrupt} CURRENT_HANDLING: AX1 = MR1; { save Ics } MY0 = Vi_Scale; { scaling factor } { Calculate Ias } AY1 = DM(Ia_offset); AR = SR1 - AY1; { SR1 = Ias_ADC } MR = AR*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Ias) = sr1; AR = -SR1; AX0 = AR; { Calculate Ibs } AY1 = DM(Ib_offset); AR = SR1 - AY1; { SR1 = Ibs_ADC } MR = AR*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Ibs) = sr1; AR = -SR1; AX0 = AR; { Calculate Ics } AY1 = DM(Ic_offset); AR = AX1 - AY1; { AX1 = Ics_ADC } MR = AR*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); AY1 = SR1; DM(Ics) = SR1; { Measure the bus-voltage for correction of the phase voltages. Vdc_HANDLING: { calculate Vdc(measured) / Vdc(max) } MX0 = DM(Vdc_max_inv); MY0 = DM(Vdc); MR = MX0*MY0 (SS); { Vac_as = VrefA * Vdc(measured) / Vdc(max) } MX0 = MR1; MY0 = DM(VrefA); } 416 Applied Intelligent Control of Induction Motor Drives MR = MR1*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Vac_as) = SR1; { Vac_bs = VrefB * Vdc(measured) / Vdc(max) } MY0 = DM(VrefB); MR = MX0*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Vac_bs) = SR1; { Vac_cs = VrefC * Vdc(measured) / Vdc(max) } MY0 = DM(VrefC); MR = MX0*MY0 (SS); SR = ASHIFT MR1 BY 2 (HI); DM(Vac_cs) = SR1; RTS; { Limiting of the Va,Vb and Vc, before calculating the duty cycle. } LIMIT_VrefABC: AY0 = Vmax; { limit value } SR1 = DM(VrefA); AR = ABS SR1; AF = AR - AY0; IF GT AR = PASS AY0; AF = PASS SR1; IF LT AR = -AR; DM(VrefA) = AR; SR1 = DM(VrefB); AR = ABS SR1; AF = AR - AY0; IF GT AR = PASS AY0; AF = PASS SR1; IF LT AR = -AR; DM(VrefB) = AR; SR1 = DM(VrefC); AR = ABS SR1; AF = AR - AY0; IF GT AR = PASS AY0; AF = PASS SR1; IF LT AR = -AR; DM(VrefC) = AR; RTS; {Return From Subroutine} .ENDMOD;.ENDMOD; Index acceleration control, 5–6, 15–17, 19, 109–11, 121, 374, 378 activation function, 22, 168, 172, 175, 177, 179, 183 ADMC331 source code Experiment 2, 403–6 Experiment 3, 407–16 ADMC331-based experimental system, 395–6 algorithm acceleration control, 21 direct FOC, 20 DSC control, 21 EKF estimation, 25 fuzzy control, 22, 25 indirect FOC, 20 neural network control, 22 slip frequency and current control, 20 slip frequency and voltage control, 20 ANN, see neural network application specific integrated circuit (ASIC), 376 artificial intelligence, 2–3, 9, 109, 373, 376 ASIC, see application specific integrated circuit assembly language, 314, 320–1, 324, 330–1, 338, 370 back-propagation learning rule, 171, 174 back-propagation network, 169 feed-forward, 87–88 basis function, 22, 168, 178, 183 blocked-rotor, 207–8 Butterworth, 221, 225, 230, 238 CAP programming, 352, 364 carrier wave, 49–50, 274–5, 284–5 chromosomes, 98–9, 105 Code Composer Studio (CCS), 352–4, 357, 360, 363, 367 constant V/Hz characteristic, 260–1 controller, 375–7 continuous-time model, 46 control error, 131, 167, 189 control function, 10, 16, 19–22, 32, 316 Control System Toolbox, 75 covariance matrix, 5, 93–4, 245–6, 248, 251 crossover, 98–99, 106, 251 and mutation, 23 current magnitude PI control, 143, 145, 330, 334 current measurement noise, 210 current noise, 243, 252, 254 decoder, 4, 54–55 default GA options, 103 definite integrals, 2, 109 defuzzification, 17, 22, 137–8, 142, 334 direct self controller, 167, 169, 187–196, 255 sensorless, 243, 253 direct-on-line starting, 38, 43–47, 49, 216, 266–7 discrete-state model M-file, 385 discrete-time model, 46 DSC, see direct self controller Applied Intelligent Control of Induction Motor Drives, First Edition. Tze-Fun Chan and Keli Shi. © 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82556-3 418 Index DSC system flux angle encoder and flux magnitude calculation sub-net, 170, 173–6 flux estimation sub-net, 170–1 hysteresis comparator sub-net, 170, 178 optimum switching table sub-net, 170, 180 torque calculation sub-net, 170–1, 173 digital signal processor (DSP), 4–7, 25, 28, 31, 49, 54, 167–8, 184–5, 187, 270, 274, 284, 305–6, 313–4, 352 ADMC331, 25, 313–318, 320–1, 324, 337–9 TMS320F240, 313 TMS320F2812, 305–6 TMS320F28335, 314, 352–3, 359, 361, 364, 367 dynamic system, 13, 48, 56, 90, 92, 94 fuzzification, 17, 22, 137–8, 330–3 fuzzy frequency control, 136–7 fuzzy frequency controller, 137, 142, 145, 330 Fuzzy Inference System (FIS), 75–6, 79, 164 fuzzy logic, 2, 4, 17, 75–83, 199, 313, 373–4 control, 136 controller, 164 inference, 22 simulation, 75–83 Fuzzy Logic Toolbox, 75, 79, 142 fuzzy rulebase, 76, 139, 141, 164 fuzzy sets, 22, 138 fuzzy variable, 22, 138 fuzzy/PI controller, 314, 330, 340–4 fuzzy/PI two stage controller, 5, 134–5, 145, 148–50, 152, 158, 163 EKF, see extended Kalman filter electrical machines, 1–2 electromagnetic torque, 11, 110 encoder, 4, 6, 51–3 error accumulation, 3, 5, 109, 125, 226, 377 excitation reference frame, 14, 32, 34–5, 38 expert system, 2, 4, 5–6, 17–19, 21–2, 25, 109–10, 313, 373–4, 376 acceleration control algorithm, 378 controller, 110, 118–19, 122–131, 374, 376–7 extended Kalman filter (EKF), 5–6, 18, 25, 58, 67, 243, 245–7, 253, 264, 344, 375–6, 378 algorithm, 245–7 convergence, 348–9 M-file, 393–4 speed estimation algorithm, 247–8 GA, see genetic algorithm GA-EKF speed estimation, 314 experimental method, 345, 346–351 program design, 345 Gaussian white noise, 210, 217, 284 general purpose AC drives, 3 genetic algorithm (GA), 2, 4–7, 17–19, 23, 56, 58, 69, 98–107, 199, 243, 250–3, 273, 283, 288–9, 344, 373, 375–6, 378 real-coded, 18, 243, 250–2, 259, 344, 349 simulation, 98–107 gradient descent, 85 method, 169 field orientation principle, 3, 133, 136 field-oriented control, 3, 6–7, 9, 13–14, 17, 20, 109, 133–4, 136, 146, 231–5, 257–60, 345 field-oriented controller, 9, 17, 133–4, 146, 148, 243, 255, 374–5 FIS, see Fuzzy Inference System FIS Editor, 76, 80–1, 164 fitness evaluation, 251, 264–6 fitness function, 98–9, 102–3, 105 fixed-weight network, 168–9 flux angle encoder, 170, 173, 176–7, 184, 187–90 flux equations, 12 flux increment, 111 flux magnitude calculation, 173–5, 184 flux vector control algorithm, 24 hardware system, 314, 330, 346 harmonic energy, 273, 290 harmonic evaluation, 277, 287, 297 hidden layer, 83, 87 high-performance drives, 3, 133, 375–6 Hopfield, 18 hybrid fuzzy and neural controller, 18 hybrid random pulse-position and random pulse-width PWM, 6, 273, 286–7 hysteresis comparator, 169–170, 178–9, 184, 187, 189–90 flux, 178–9 torque, 179 individual training strategy, 169 induction motor ‘G’ equivalent circuit, 11, 203–6, 208, 381 ‘T’ equivalent circuit, 13, 200, 203–4, 206, 208, 210, 381 Index acceleration control, 5–6, 15–17, 19, 21, 109–110, 119, 121, 373–4, 376, 378 computer modeling of, 4 control, 2, 4, 9–10, 16–17, 19 control algorithms, 19–23 current-input model, 4, 32, 34, 37–8, 42, 145, 152, 374 DC resistance test, 397 discrete-state model, 4, 32, 34, 45, 48, 73–4 electrical model, 4, 25, 42, 158, 244 expert system control, 2, 4, 17, 19, 22, 109–10, 118–21 extended state model, 244 integral equations, 200–1, 203–4, 206, 227 integral models, 5, 200 locked-rotor test, 398–9 mechanical model, 4, 42, 158, 160, 208–9, 213–4 no-load test, 397–8 parameters, 383–4 parameter estimation, 5–6, 199 using ANN, 205–9 two-stage control, 5–6, 17, 133–6, 373–4, 378 voltage-input model, 4, 32, 34, 40, 54, 73–4 induction motor control taxonomy of, 25–6 inference engine, 23, 110, 118–19 inference system, 21, 23, 75–80, 164 initial generation, 251 initial state, 3, 5, 109 integral constant, 256, 334, 336 integral operations, 203 intelligent control, 2–4, 6, 16–17, 19 inverter, 2, 6, 25, 31, 54–5, 110, 118, 170, 180, 273–4, 316–17 switching frequency, 21, 167 iteration, 251–2, 259 JTAG, 352–3 interface, 353 Kalman filter, 25, 75, 90, 92–98 convergence, 96, 98, 251–2, 259 simulation, 90–98 knowledge base, 22–3, 110, 118–9 learning rate, 85, 169 linear modulation range, 273, 297 linguistic inference, 141 linguistic values, 138–9, 141, 154, 164 419 load torque variation, 146, 150–2 look-up table, 299 magnetic saturation, 17, 74, 146, 149–51 MATLABÒ, 6, 75–6, 345, 352–4, 359, 361, 364–5 MATLABÒ/Simulink, 4–6, 32, 34, 39–41, 48, 55, 75–80, 83–90, 94–107, 122, 134, 158, 170, 184 programming examples, 187–196, 205–239, 247–269, 299–305 MATLABÒ window, 58 measurement noise, 94, 245 covariance, 94 mechanical model ANN-based, 208–9 membership function, 75–6, 80, 82, 138–9, 164, 331, 344 editor, 76, 80–1, 164 membership functions slip frequency, 138, 154 speed command, 138 speed error, 138 M-file, 48, 73, 247 model reference adaptive algorithm, 24 modulating signals, 275 modulating wave, 275 modulation index, 275, 284, 297–8 motor controllers, comparison of, 377 multiple-input multiple-output, 10 mutation, 98–9, 251–2 mutual inductance, 13, 148, 160 neural network, 4–5, 17–19, 22, 25, 200, 205–6, 208–9, 216–17, 313, 373–6, 378 algorithm, 25 controller, 167, 170, 187 simulation, 83–90 training, 84–9, 168–9, 171–2, 174, 194–5, 206–9 Neural Network Toolbox, 75, 83, 184, 194, 205 neural networks parameter estimation using, 5–6, 199, 205–226, 378 neuron, 18, 83–87, 168–9, 205 hard limit, 391 linear, 206, 208, 391 log-sigmoid, 168, 170, 177, 392 ‘purelin’, 85–7 square, 392 420 neuron (Continued) tan-sigmoid, 168, 170, 177, 392 ‘tansig’, 85–88, 173–4 Newlind, 205, 209, 211, 213 noise, 16–17, 31, 90, 92, 94, 118, 125, 143, 146, 149, 187, 199, 210, 217–18, 243, 329 random, 94, 98, 107, 149 noise matrix, 245 noise rejection, 18 noise-weight matrix, 245, 248 nonlinear feedback control, 9–10, 373–4 observer algorithm, 24 optimum switching table, 170, 180–1, 184, 187–90, 192, 194–6 output layer, 83, 87, 169, 173, 183 outputs, 10, 22–4, 38, 80, 85, 96, 118, 136, 142, 158, 169, 171, 189–90, 192, 196, 207, 275, 316, 326, 352 parameter changes, 28, 143, 243, 252, 329 parameter identification, 16, 18, 167 parameter variations, 3, 5, 18, 109, 148–9, 196, 253–4, 375–8 Park’s transformation, 33, 59–73, 75, 83, 232 implementing, 75, 83–90 PI controller, 75, 77–8, 80, 83, 144–5, 155–6, 256–7 pole, 155–6 population, 98–9, 106 representation, 251 power electronics, 2–3, 9, 25 preferential parameter, 118 process noise, 31, 94 covariance, 94 proportional constant, 256, 334, 336 pulse width modulation (PWM), 2, 4, 6, 7, 199, 273–4, 276–8, 314–16 PWM waveform Fourier analysis of, 276 fundamental component of, 274, 277–8, 280–1, 290, 296 power of, 277–8, 280–2 THD of, 273, 276, 282 random carrier-frequency PWM, 6, 273, 283, 288, 299, 303–6, 308 random pulse-position PWM, 6, 273, 283, 285–6 random pulse-position PWM, GA-optimized, 290, 292–3 Index random pulse-width PWM, 273, 283, 285, 286 GA-optimized, 292–4, 296 random PWM techniques, 6–7, 273–4, 283, 288, 378 evaluation, 288, 290, 295 switching loss, 290, 296–7 Real Time Data Exchange (RTDX), 6, 352–9 recombination, see crossover recurrent network, 178 recurrent system, 13 reference frame theory, 9, 34 reference input, 10–11, 118, 256 reference signal, 275, 297 reference voltages, 49–50, 322 Repeating Sequence block, 63, 86, 162, 164, 192, 232–3, 263, 268–9 replace, 98–99 reproduction, 23, 251, 346 rotor acceleration command, 116, 119–21, 123 rotor flux angle, 3, 20 rotor inductance, 11, 13, 160 rotor inertia, 11, 13, 160 rotor resistance, 11, 13, 160 rotor speed estimation, 5–6, 229–231, 245, 256, 344 RTDX, see Real Time Data Exchange rule editor, 76, 80, 82,164 rulebase, 17, 22, 76, 137–9 sampling period, 46, 349 sampling rate, 321, 325, 361 saturation block, 145, 149 scalar control, 2–3, 19 selection, 98–9 sensor noise, 28, 31, 125, 253–4 sensorless control, 6, 231, 234, 236, 238–9, 373–5 sensorless FOC drive GA-based, 269–70 sensorless VFC EKF-based, 260 S-function, 48, 247 block, 48, 73 signal measurement, 75, 90, 94, 96 Signal Processing Blockset, 75, 94–5 Simulink library, 37–8, 43–5, 48, 57, 62–3, 72, 77, 163–5, 188–92, 195, 206, 220, 224, 230, 232, 238, 262 sinusoidal PWM, 49–52, 299, 321, 352, 354 Index slip frequency, 5, 20, 36, 133–4, 136–7, 139–42, 145, 152, 330, 334, 338 slip-compensation algorithm, 24 slip-frequency algorithm, 24 speed estimation algorithms, 23–25 speed sensorless control, 4–5, 375 standard PWM, 273, 275, 282, 285–6, 288 state, 9–10, 90, 92, 94, 190, 193, 244–6 state feedback control system, 10–11, 14 state variables, 10–13 stator flux space vector, 3 sub-model current magnitude control, 145 current (3/2) transformation, 34–5 electrical, 34–7, 40–1 frequency control, 145 mechanical, 34, 37, 40–1 sum squared error, 85, 169, 174, 180, 194–5, 212–3 supervised network, 168–9 SVPWM, 205–6, 208, 211, 216, 220, 224, 229–30 system noise, 245 targets, 210, 213 training data, 168 training epochs, 89, 171, 174, 180 transfer function, 77, 83–4, 88, 155–6, 199, 205, 335–6 421 transformation abc to ab, 33 abc to dq, 33 abc to dq0, 72 transient operation, 43–4, 49, 216 universal serial bus (USB), 352, 354 universe of discourse, 138–9 untitled Mamdani, 80 V/Hz control, 2–4, 7, 18–20 V/Hz controller closed-loop, 18, 243, 247–9, 252–4 vector control, 3–5, 11, 16, 19 VFC drive, 260 GA-based, 268 voltage source inverter, 49 voltage vector comparison, 110, 112, 114 voltage vector retaining, 110, 112, 114, 120 voltage vector optimum, 5, 110, 114, 118–21 weight and bias, 22, 84–5, 88–9, 168–9, 171–4, 178–9, 181, 183, 195–6, 205 weight matrix, 5, 168, 195 workspace, 101–3, 261–2, 267 Zadeh, 17 zero, 155

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APPLIED INTELLIGENT CONTROL OF INDUCTION MOTOR DRIVES

APPLIED INTELLIGENT CONTROL OF INDUCTION MOTOR DRIVES

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