Calhoun: The NPS Institutional Archive DSpace Repository Faculty and Researchers Faculty and Researchers' Publications 2013-04 Multicriteria Analysis of L1 Adaptive Flight Control System Dobrokhodov, Vladimir; Xargay, Enric; Hovakimyan, Naira; Kaminer, Isaac; Cao, Chengyu; Gregory, Irene M. SAGE Dobrokhodov V., Xargay E., Hovakimyan N., Kaminer I.I, C. Cao, Gregory I., Multicriteria Analysis of L1 Adaptive Flight Control System, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, April 2013 vol. 227 no. 4 413-427, doi: 10.1177/0959651812468545. http://hdl.handle.net/10945/62684 Downloaded from NPS Archive: Calhoun OriginalArticle Multicriteria analysis of an ..C1 adaptive flight control system Proc/Mee!,£Part I: j Sys:rcms and Conuol Engi11eering 117(4) 4IJ---'!27 <: !MechE2012 Reprints and permissions : sageplJb .c:o.uk/journalsPe:l"IT\issions.n.iv DOI: IO.l I77109S96SI8I246854S pib:agepub.corn ~SAGE 1 , Vladimir Dobrokhodov Enric Xargay2, Naira Hovakimyan2, Isaac Kaminer', Chengyu Cao 3 and Irene M Gregory 4 Abstract This article presents an overview of the application of the Parameter Space Investigation method for the multicriteria design optimization of the C I adaptive flight control system implemented on the two turbine-powered dynamicallyscaled generic transport model Airborne Subscale Transport Aircraft Research aircraft. In particular, this study addresses the improvement of a nominal prototypesolution, obtained using basic design guidelines of .C1 adaptive control theory. The results validate the theoretical claims of { 1 adaptive control in terms of dosed-loop periormance and robustness and illustrate the systematic character of its design procedure. Furthermore. this article shows the suitability of the Parameter Space Investigation method for the mulcicriteria design optimization over a multidimensional design variable space of a flight control system subject to desired control spec:ifications. The use of this particular method is of special interest, as it provides invaluable information about the behavior of the closed-loop system in an extended space of design parameters and periormance criteria. The results and conclusions of this article have led co a deeper understanding of the characteristics of the closed-loop adaptive system and have contributed to the improvement of the flying qualities and the robustness margins of the adaptive [, 1 -augmented aircraft. which has been recently flight tested by National Aeronautics and Space Administration. Keywords £ 1 adaptive control, flying qualities, multicriceria optimization, Pareto optimality, quasi-random sequences Date received: 26 February 2012: accepted: 29 October 2012 Introduction Adaptive control has long been seen as an appealing technoh;gy lo improve aircr:i.ft performance \\•ith n:duccd pilot compensation in adverse llight conditions nr in the event L,f control surface failures and vehicle damage. Under these conditions. which are char:icterized by a high tkgrcc of uncertainty with respect to a nominal aircraft. the achievable levels of perrormancc and 11ying qualities /FQ) that a n,madaptivc night contrnl system (FCS) can provide might he limited. Howe\TL scwral limitatinns of the conventional adaptive systems have prevented this technology from hcing widely used in safely-critical acrospacc applications. 1 ·' In particular. rht: key dcfa-icncics of conventional adap tive (llight) control systems can be surnnwrized as follows: f I) the lack of transient characterization of the closed-loop re,ponsc. (2) the limited framework for analysis of the robustness and performance properties of closed-loop adaptive systems. and ( 3) the b ck of systematic design guidelines to solve the trade-off between adapt:ition. performance. and robustness . The theory of £ 1 adapti\'e control oven.:omes the limitation~ of convenhonal adaptive con t rol arch.itectures described above and enables the design of robust adaptive control arch itectures using fa st adaptalion 4 ,chemes. The key feature of £ 1 adaptive control is the decoupling of the :.idaptarion loop from tbe cnntrol loop. which cnahles fast adaptation without sacriticing robustness. ln fact. in £ 1 adaptive control architectures, the rah: or the adaptation lnnp can be set arbilrarily 'Department of Mechanical and Aerospa ce Engineering, Naval Postgraduate School . Monterey. CA. USA Coordi nated Science Laboratory , University of Illinois at Urbana· Champaign, Urbana, IL, USA 3 Depan:ment of Mechanical Engineering, Univers ity of Conne cticut , Storrs. CT, USA 4 Dynamics Systems and Control Branch, NASA Langley Research Center. Hampton. VA. USA 2 Corresponding author: Vladimir Dobrokhodov, Department of Mechanical and Aerospa ce Engineering. Naval Poscgr-aduate School, Monterey, CA 93943, USA. Email: vldobr@nps.edu Proc/Mech£ PartI:J Systems and ControlEngineering 227(4) 414 high. ,ubkct only w h:inlwarc limitati,)ns (Cl)]11putational power an<l high-frequency sensor noisl!). while the trade-0IT between rcrti.mnance and robustness can be :1ddrcs.,cd v1:1cun,enti,1l1al 111<:tlwJs!"mm c:la~sical and whu,t c·t1ntrol. !-;1st ad;tptati,)n enables L·,1mpensatiun r,1r the undesirable effects ,,f rapidly Yarying uncl:'rtaintics anJ ,;ig:nificanl change, in system dvn;imics and is thus critical t,,,rnr<l ach1cving guaranteed transient pcrform;rnce -.1ithnut enforcing pcrsi,lem;y ort.:xcilati(Hl nr re~orting t(, high-gain fredback. :\hmxwer. the l 1 l1dapL1,-_: Cl>ntr,,l thcc,ry pr,widcs design guidelines that significantlv reduce· Lhe llming .:-ftiJrt of the adaptive t:l'ntro lkr. The main challenge fur the design uf £ 1 FCSs is the optimal tuning or it, elements lt.l prmide desired FQ with ~atisfactory rohustncss margins (>vcr large opcra1ion;d cnvclo1,c-; :111J LllKCrtainL:,se·cnarius. \Vhile lhe thcnr~ ,,r [.1 ad:1pti,e c,)ntrol prnvidcs h:Lsic d,·~ig:n guidelines t,, aJdrcss the trade-off bet 1\ec>n perfnrm,1ne·eand rnbu,rncss. ortimizati(m ,1f the design ,,r l1 adapti,·c n>ntwlkrs i, still J;irgcly open and hard to ;1ddrcss. The main difCLculLyis th,~ ndncum·ex ;111dnonsnw,~th 11;1tureof the'. underlyin2 tiptimizalit>t1 prnhlcm th:t! im oh es the L-11,Jrm nf ,:.t~caekd lincar sy,;tcrns. Randomi1.e·d rararnctrie· ;dgorithni,; lu\e heen pr, 1\cn tn he .-:ffccti\"s:: in cnntwl-rdatc·d 1wm·ll111C.\nptimizatinn rrnh!cms. and therd,)rc they seem attrac ti•:e f,ir the ,,ptimal Je,i~n of [ adapti,e CL)ntrolkrs.-1., ln partie·ular. one of the ;1pproachcs that can help lll s,>lvc this multi,,bj..:1:1i,·e,>ptim1Latil'n pn,hlem is the P:iramcLL·r Space Jn,estigation (PSI) mdlwd."· · This mcthl.ld cxplicitly addres,t'.s the is,ul:'s as,oci:1ted with high dimension:tlity of tho: crill'ri,1 and the functional cnnstraint ~pae·es. It takes into ace·ounl Lhc Cllmph::xity and the nimpulatiuHal expense, nf _;;1mpling.the design space of" high dimensil1nality b~ employing the 4uasi-ranJom sampling i LP-t:tu scqucnce,. see Stalniku,: and Matuso, ." S,)bol and Statnikov. am! refrrem:es the·rcinl. which yield con\erging results by a fac·tl1r or -I~~ smalkr ;amrk ,i.-'c~ c,,m,,ared to the ,1ther methll<l~. Ths: mc·tbud is tmplemented in a u,er -friendly and ··model ag11llstic··Sliftware pac kage ,;ailed ivlu.lticriter ict Opu11111atinnand Vector Idcntilic,1tion ( l\lOVI ).' In this article. we take· ,llh ·,tnta_l!·:orthe d;.:~ign guidelines of t.:1 :td:iptiYe cnntrnl t't1r the dcsign l1ptimi1atiL,n ur ths: l I FCS irnpleml:'nted Dn the generic transptirt model t GT\! J. which is part ,1f 1hc .'\irhnrne Subscak Transport Ain.:ra l't Rcseard1 I AirSTARJ system at the :--ation,tl Aernuau tics and Spac e !\dministrati,m (I'sASA1 Lang:ky Rt!search Center."· 1" ln particular. this study addrc,scs the· applic:ation of the PSl rnetlmd for !he cnnstructi,,n ,,f the kas1ble stilution set and for the suhscq111.:nt1111prmemcnt nf a nominal pnitutypc design. Thi~ artidc dc111t111strarcsthat the c,Jnsis tcnt application of the J-:sign guiddines of L:1 adapti,e cnntrol bcc,, mc, particularly hcnelicial !"tirthe construction ,,J'th-: k,1sibk solution ,cl. In fact. the ability to s:skmaticalh · adjust the contr,11 parameter; in ( 1 adaptive :11Thitectun::s cunsidcrably sirnpli fic:i the identi tic.iti,m 1 of a nominal frasihle solution from 1vhie·htn start the search for other fcasibk s,ilutilmS anJ thi.: subsequent extension of the-fc;1sihle ,nluti,)n set. The availabi lity uf an inili,tl k,1,ibk sc>lution 111;1y nan-.)1\· the design ,ari:ibie ( DV I space ,wcr which th,· search f,,r feasible s,)lllrions should be performed. Furt hcmrnrc. c,1nsidc'ring th<:'henefirs L>fs:1mpling the mu ltidimensinn:d DV space hy the LP-tau quasi-ranJ,1111 sequenct!s. the nnmher nf trials required for the c,rnstruc tion of the kasibk set may be signilic;rn tly reduc~d. This anidc ilhbtratc:, the suitability ,)f the PSI method as a tool for form ulat ing and , c,h ing multicritena oplimiLation pr,,bkms for d~sign of adnpti\·c FCS. The Wl1rk repnrted hcre is n,>t intended tn compare the henelits and drawbacks or various optimization mdlwds: in,tead. it illustraks the cnmplcxity of multicri le ria ana 1:-sisan d suggest,; a \·ia ble ,1pproach to th.-:de-sign ,)f contrnl systems 1'11r sal~·ty-critical applicatil>ns. An explicit compariSl'll of ,·arious 111ultic ritcria anal\ sis 111cthndsc:111be found in the slulh b:- S,,lx, 1 and S1a1nik,n ." 1d1id1 provides ;111 e,;senfrtl ,1ycrvic1\·t)f mnJcm appro:1..:hcs Lt"•multicri tcria decision making. T h is article is organized a, follm,, . Se·i.:tion "'.\iASA A1rST.-'\R ,ind [ , ll1ght c,rnt r,,! let \\ .. intr,1llui.:cs the J-:sign frarncwe >rk consistin g of the GT\1 aircr.1ft nwdd. the adapti,e cnntrnl bw. anJ the ,1ptimizatit>n mcth,ld. This scctwn , t:1rts 1\ith a n ,,\er,iew of the :\.-'\S.-'\ AirST.-\R facility and the [ 1 1light contwl la1v Jere k1pcd l'or the GT\! :iircr;ift: in addition. it rres~nr.- the nominal prototype design. with its main pe rformance and ro busrncss properties. This scL·tiLrn also fonmtlatcs the nrnltiobjecti• .'c op timiz :iti,,n t,tsk and [lfL>vidcsa bricl discussion that jus t ifies th e choi<.:e t)f the nptimi1.ation method. Scc:tion ·-rormulation of ihe oplimiation problem .. formula tes the FCS design t)ptimizatinn prohlcrn and pro1 ides a brief discussion ,1f the PSI munerkal implementation and th.: worktlu\1 (if the (•ptimization prlice,s. The de,ign optimiza tion of the £, 1 FCS l't>r the GTM aircraft. is addr essed in ,ecti,,n "Solmi ,)ns and analysis ... In particul;1 r. th is seL·tinn pr,widcs a detaikd di,cu s,iun of thi.: differen t ~ti:ps of the optimizatilln proc ess. includ ing the c:onstructi, ,n or Lh..::ka sible sciluti,)n and the imprtY,ement ()f th..::protot ype· design. Fine1Uy.section ··Condusi,)11·· summaril't~ the key resul ts an J contains the main c,111..-lusions. NASA AirSTAR and [ 1 flight control law AirSTARfacility During ::1007-2010. thc NASXs ;\nat i,)n Sat',:-ty Program creat ed the lntqirati.:d Ri.:silient Aircraft Contr ol I I R.-\C i pn,ject 1, irh the l•biccti v~ ,,rad-. ancing and transitioning adaptiw flight wntrPI technol,>gies to incr ease aYiatinn safety. The· I RAC pnij i.:Llhad sp~ci,tl int~rt'st in r iloted t1igh1 und.::r :1dvcrsc fligh t c,, nditin11.>such as unusual attitud..:s. contwl surf:.Kc failures. 11 .:mg . anJ stru,.;t ur,il da magi:. As part uf the project. 415 Dobrokhodovet al. roll ra re tp). ,ind a ngle llf ,ideslip (:\OSS. /J). The L:1 adaptivc conlrnlkr pro,i<les thus command-tracking L·apabilitics in b,,th miminal and oll-iwminal ..-unditiuns JS thcr.: is 1w n,111adaptiv;;CAS ba sl'lin.: k 1 assist it. Th.: C 1 CAS consist, ,)f two decuupled £ 1 c,1ntrolh:-r,. clne for the longitudinal channel and another u ne for c:ontrol of the la tc-ral-din:ctional dynami..-s. T he implen1t•ntcd l11ngitudinal £ 1 CllDlwlkr utilizes kcdback m AOA and pitch rate t,1 generate an dev aw r contrnl ~ignal in order to track :\0.\ reference signal. The lateral din:ctll)nal C 1 controller use~ focdback in AOSS. roll rate. and ~a\\ ratc t (> generate aileron and rudder c,.1mmands in order to track sidcslip-ang:le and roll-rate rc{crcrn.:c sigu;Llswith n:ducc:d coupling. ln the current f: FCS. Figure I. AirSTAR GTM unmanned aircraft and its full-scale the pilt1t aJjuslS Jirecriy the thrust level using thc>throtprototype. tle lever. An intcn:slcd n:ad.::r is rcli:rrcd to the study by Xarg:iy et al. 1'· 11• for a more detailed cxpbnatiL,n ,,rthe £ 1 FCS implemented on the \.ASA AirSTA R flight test !',AS.-\ dcYclopcd AirSTAR. a statc-of- thL·-art faL·ility ,..:hide. dcsigncd for the· purpo,c of imcstig.ating and ,alidati ng The design nf the longitudi nal [ 1 FCS is based on liigh-p;1>11lTkchnulngics aimed at the h),, -t,f-contwl the lim:arizeJ ~hort-pcriod dyn.imics of the GTr>.I at rhc prnbkm u~ing remotely piloh:'d ,u h,c all' 1110dds \\ithreCcrcnc.::llighl rnnJitiun ,::;o kl. IOCl<Ht).Sm.:c the air1,ut cxeessi\·.::risk.';·'" ThL· primary flight tL·,t ,chide L)f pla11eLS Level I FQ at this flight ct1nJiti(>n. the· dcsin:d :J..irSTAR is the GT\1 l:1il numhcr T::!_which is sb,1wn dynam ics nf the .11u1,,1m-di,-ror ar~ chos en t,,be cll1sc:r,, in Figur<.: I. Th<.:T2 i, a tw in-engrne jet-pO\\Cr ed and lhuse tile accu,d ain,;r,1ft. For th..-:nnrrnnal pr,,11,tYp<.: dynamically ,cakJ (.'.:i"nl L'l\·il Lran.;pc1rt airnart that dc;;ign. the natur,11 frcqul'.ncy ur thL· p,,ks .,f the syst.::m 11:1s designed :rnd instrumented tn pe r form cuntrt , I is reduced fr,lm r, tt; 5.5 rad s. while the dam11ing rati(1 la-.v CY:ilu:,tion. experime nt lksign. and nwtklin g is increased fwrn i.l.-17to 0),5. A firsr-ord<'r 11.1',\'-pa,s filre,carcb. in-flight failure emul;1ti,rn and tlight in ter ,,ith direct current 1DC) gain I and a bandwidth ,.ir upset cnnditions. 20 rad s \\,IS used in the matched contrihu tinn tn the The AirSTAR facility ab,, inc0rpl1rutc, a highel~\ ·atnr cllrnrn,1nd_ \\'hile tWcl casc:tdc<l first-,)rdcr lnwfidelity nonlinear simulation of the GT\! ai rcraft. The pass filters were u-sed in the unmatched channd. hnrh GT\[ vchidc ha, bcen cxkn,i1 ·cly tested in the KASA having DC gain equal tu l and bamfaidths of 5 and Langley wind tunnds with pani..-ular emphasis on 7 rad s. n::spccti Ycly. Fin a lly. lhc aJaplaliun sampling modding nonlinear reg.inns nf the! e'(tcnded tlig:ht cmcltime was ,et t,) 61HlHz. ,,hich enrresp,)nds ltl the fastest opc \\d] hcyond nominal tlight as 11ell as de-.eloping a inll:gratiun cycle aik,11·cdin the AirSTAR flight control dat ab-isc for ,1 number of strnctural dama~c SL-cnar- comput er . A first-llfdcr prdi ltcr with bamh·idth or ius. 1 1.1: \Vitb thi s capability. AirST\ R pro, ·iJcs a com::!Orads was added to shape the pilot command. The [ 1 111lmresearch cnvinimm:nt ror both sirnulaw:,n a nd FCS. with ib main elements ;is \,ell as the DY,. is rep tlrg.ht. In this article. m: take .Ill\ an tag:,· ,,f thL· high- resented in figu re 2. Thi~ pro1 u1_1p,· lk sign of the state fok litv nonlinc:ar nrndd tJf the GTl\l \Chide fur th:: predictor. the luw-r;1,s filters. the adart:H iun sam pl ing design ui' the £ 1 flight control la\1·. ra tl'. am.I the prelilk r. Jdi1ers an AOA response similar or to th.: desired one [, 1 ffightcontrollaw for the GTM aircra~ Thc L:1 flight L·l1ntrnl la11 de1eloped l<.>rth<' AirSL\R tli,!111k~t ,·d,ide b:1s as tts primary ,)b_jl'.di>l''1chie\ ing rcliahk: tr;1cking for a ,ar iety of t;isks with gt1:.trankcd stabilit, and rnbustncss in the prcscncc ,.,ru111.:rrtain d:. namic,. such as changes Jue to rupi<lly 1arying l11ght conditions during standard mancuvt.'rs. an d un expected fail ures. ,\II thc,c· rcquir,·m,·nb a r;; -::,;pected to be reached while pr m ·iding LeYcl I F(.)1 ·' '" urnkr n,1111inal llight n>nditi,rns, \\·irh a gr:iccful ,kgr :1dati1111unde r signifo:ant :.id\'crsity. Th e L'1 FCS designed for this ap plicat ion consists (1r a nonadapti ,-.::stabi lit~ augmentation ,ystcm (S.\S) for pitch and rnll :ind adapti\e c,,n trol Hll!,-'lncntati,,n sy stem (CAS) for a lhrcc-,\\e~ angk of atta..-k (AOA. a-) . if•J:.•) I Figure 3). Thi: Jniation orth.: resp,msc from the com1rn1ndcd skp is J ui: to th<.: phug nid mt1de of the aircraft. which is stahk. c>scilbtory. and slo1\. T his phugnit! de1iatiPn appears when designing AOA and pitch-r;Jte CASs ;rnd can be easi ly co 111pen sated ft>r by Lb<.: p1k1t ( or a utop1lot in the case AO.\ of ,lllt( >LWlllllllS flight). The 1mm111:ildesign ensures a tim.::-dday marg in ,,r the inner lo op of ;1pproximatd_\, ;:<;5ms and a ga in margin of 7.2 dB. m 11 m gs-k,~J lhgh1 at th<: rc:fi:rcncc flight <.:ondilion. AL this llight 1,:ondition. the FQ ;1re prc::dictcd w he Le,cl I. and the FCS design ha, nn predicted pilot -111Ju-:cdoscillation (PIO) km.kn..-ies (for an acq ui~ition time' of 1.5 s) . .'la turall y. these metrics corr.:-~pond to specific pcrCormann: critcri:i. and thc,c initial nnmina l \a lues will he used as r,·krcncc v,ilucs for thc definition or the nil ~ri:1 n,nstraints during the optimizatinn process . Proc/Mech£ Part/:J Systems and ControlEngineering227(4) 416 (. Flight Control System ,----------------------~-~-----~ ----, Elevator----~ Commanded, ----AOA ' Pilot cmd Prefi!ter : DV4 Control La--.v: ; DVJ Output States S GTM A,rcraft State Predictor: DVl, DV2 Prediction Error Adapt atio n Adaptive Contribution Law '------' '~-----------------------------~ Figure 2. Longitudinal channel of che { 1 flight control architecture. AOA: angle-of-attack; GTM : generic transport mo del. __ ... -(II~ 8 .. l 7.5 T 6.S -1 ij ' . 5.5 •• : ' • • ••• • • ' ; • •• •• •• ' ' ; • • ' • • ''. Si;..;,;~~ 2 4 J 5 bmels,,,!J (a) -3'----'---...,_ D __ 2 _.___ 3 '-------"--...i...---' 4 5 8 llme{sec.1 (b) Figure 3. Prototype design. 3· AOA step respon se . (a) Angle of acL1ck• .,. and (bl elevator deflection . 8, . Multicriteriaoptimization framework The ob_iecti\'e of th.: adaptive rnntrnller tu ning task is tu lind an optimal snlution in the multidimensi o nal C:L'tllwlkr parameter spac e that minimizes tht diffe r ence: hetween th..: ,ksircJ and actual responses of the· airpbne . wlult ensuring: sati:Ja c·tory H.). desir ed robu stns:ss marg ins. and n:a,onahle actuator activity . l t is ckar that the ta,k he longs lt) the dass of mul ticriteria 0ptimization prnh lem. :\ general mult io h_icc ti\ c Jc:,ign prohkm can be pt1scd as r,,llow ~. Min imi Te a vector F<xl l>fk obj ec ti ve functinns F:,lx) m in F(xl f1I.X). Fe(.\.). ' subject c;:0. . . ,,. where 1<1 g ,(x) i = I. 2. .. 111 I. 2. .... n; and /,,/x) = 0. i; th e· numhcr or i11c4 u~tlit~ ct1nstraints. e is the numb er of eq ualit y co1h t ra ints. am! !:.:'is .i vedt>r of DV s. The feasi ble sti lu ti l>n sd X is x "' ddincd as [xgi(X) ~ O.i= 1. 2 ... . ,11a11dlr_.tx) 1). j = 1. 2•. .. <'}. ;11llt the fea;ibk criLcriu n space Z talso called attamabk s-:l) is defined as the sd {F(x)ix ~ X}. 1-·casihili ty of a d esign WL'tDr -' implie~ that n,l eonslr,1int is ,·iolalc'd. Attainability or a crilc'ria Yect,1r implic:s th,1t a poin t 111the criter i,rn sp ace maps Lo a uniqu e po int in the· <.lcsign spa ce . O p timal ity nf solutio ns is deii ned in terms ,,f Pa rct, 1 domin a nce: the Pare tn set con,i sts of solution ; Lh,tl a rc n o t dominated hy any o lh cr solutions . Fnr m tir c <lc1ailsun the fundamenta l ddimtitnb ,md properties nfthe Paret o optimal ity. th e inrcrc,tcd reade r is rd'crred to the m o no gr..iph . · The task pf the [ 1 adaptive contrn!ler op tin11zat 1on c,) nsi s ts uf a mixtur e o f num.:r ica l sim ulation (GT'.1.1 aircrarr) and analy tic al e,tlcularion , i ,1d,1pti,e contrnlkr design and it; pe rfom1ancc mctries) \1-hi :r<:th ere is 110 easy 11ay of cakulatin g derivati1es of the o bJcct i1c funcli, >ns. Th er efore, nongradicnt ,,ptimiz a lion met hod s are bette r can did ates for this problem : a 11nthe r 417 Dobrokhodovet al. important advantag.:: of these n,eth,)ds is that they an: mor.: likely to tind global optima and not tn be stuck nn l,1cal ones. in contra st lLl gradicnl metlwds. The cl;i,;,ificat1<)11of 1wngradiclll mctlwJs 1- dc,igned tu Lackk tlm kmd of prohkm is usually hasc'd L1ll the sta!!c when the deci~ion-ma king process applies the preler~necs on the objectives: ne,er. before. d u ring. nr after the ac:tual optimizaLiLrn proecs,. In contrast to mam of the existin!! apprnachc~. the PSI mdhLxi enables a \·ery pnwert:ul interactiYt: articL1lation or rrekrcno:cs via ,1 ..dic1k,g" with the designer. The key advanta!!cs or this approach are as fol(,_,ws: ( I J there is no need, for a priori pret'crcncc information. 1.:') onl y loc:al prefcn:nci;: info nn at iLm is needed. and (3 I it is a learning proc·css where the decision making impnwes the understanding of the probkm. thus making these tr,1dc-,Jffs , i,ihle. Disadvantages im:lm.k the Cullowing: ( 11 tho: solutions depend L)n hnw well the prd-.:rc1Kes are articulatct.! and (::i) the required comput,1tional etTLJrtis high and depends on the rnmpkxily of th<: undcrlying probkm . .\nnrhcr si!!nifo.:ant advantage ur the PSt method is tha t it aci.:ot;nt:i for a poss ibility of compuwtional inslabilit:, of the 1',1rclcl-nptimal sd whcn e,·,,n sm:111 crrors in thc LTllcria hx ) may kad h) drastic change or the t~asihlc s,llution ,L't X. ror problems th,1t arc neither linc;1r 11<lrconcave. the key metho ds l'nr lh,· Pareto nptim:Ility utiliLe tm.,1 maj o r approaches: (I) minim int ion of v,1rinus functions representing sp,xifi(· metrics k.!!. Hausdl.'rlT. sec Sobol anti Statnikov') and 12) cm·c:ri;H!the feasible snluti,m set with subseb Lll" a spccilic sha;e (c:ubes. sphere,. de.). The PSI meth od falls \\ i thin the' sccond o:atcgPry. emp loying un iforrnly dis1ri buted p~eudnrandom sc4uc:m:c:s puint~ that gu,trantce the fash:st i.:c1merg.::ncc ti) th..:: Pan:tLH)ptimal ,1pproxirnaliL111. In particula r. the LP-tau sequences arc used as a ,ampling m<:drnnism LL>ctner the DV sp~ii.:e. It is abo illl['N tant that the PSI mcthud does not alter the L>plimiL~ll1on task by "map ping"· a sct of mullipk criteria tel ju~t one sca!Dr functional. Details nf the PSI rcaliLatiLl11L·,111be found in the study by Sobol and Statnik,) , . - ,, hik comprehens1\ e o,·er,·ie\\s nf multiohiccuw optimization approaches an: disc:ussed in the 1 ·studies !-n .,\ndcrssn111 • and 1\larlc:r ,tnd Ar<.>r;i. ' Tlie-;c two stud ies a ls,1prnYidc fon nal guiddin,·s ,m the ch,1ice orthe mo ~t ,mtabk meth ()d fo r parti..::ular optimiz,1tion problems. Tn supp ,,n this mult1c:rneria ;ipproach. the 1'-IOV[ package pro,·ides a rich set nf analysis w,)ls. Besides num eric:al result s organized as a test tab le. it pro, idc's a number l)f \·i~ual tLlllls. In part1c:ular. lustn grams ,,f DVs. criteri,1n versu s DV pk,ts. and ffit erion versus cri1erion plots are the most intuiti\T and d kct1 \e LLIL1ls used during tlle inrcractiYe analysis . .-\ comprc-h..:nsi,·<: introdu ct i,111tl) the effro:tiH: use of the J\.lOVl package can bi::found in the stud ies hY Stalnikln · and \latus o, n and Snhol and Statnikov .' · The PSI-based t1p lirni1:1tiLHlmdh,1d,llogy pr,1posed in thi~ wmk cont,1ins rw,) steps . First. takin g the or Figure 4. Optimizatio n framework. AirSTAR, Airborne Sub,cale Tr,n ,po n Airc,aft Research: PSI: parameter space investigat ion. protlltypc solutiLHl as a rc'frre1Kc design. th.:: PSI method is used for the con, lrlJ(:t iLmof the/<'asih/e- sol111io11 sci ;u1d for determining a direction o f improwmcnl for th..: des ign ur the !-'CS. This first step is hascd nn a reduce d and relaxed set of criteria and cunstraillls. Then. al the s-:o:omlstage. the: PSI method is ag:un Lhed w det ermine an oprimaf design tha t sati;Jic~ an extended sci orperformance and rnhuslness cnn,trnints and imprnws thc initial rckrrnce pr ototy pe. !'he arch itcc:turc or the de\dopcd L,ptirnia licm rram.:1, L1rk is presented in Figur e 4. The framework integra tes the GTl'vI mot.Id and the l'. 1 adaptiYe wntrolkr (-b,)th implcrncntcd in Sirnulink). the nilcria calcu l:1ting script, 1_ impkmi.::ntcd in l\lA TLABL and the PSl mc:thod (irnpkmc nk d by the l\.lOVI softwarel. This ~et up allows inLcgrallng the ,apabilitic's 0f a highfidelity simulaliLHl envir~ll1menl with t he v:1stSc'!of features of the l\·IOVI package. We note that althougll hntil the PSI and the "'t"twar e pa<.:kage l\lOVI haw been de\ek,red to ad d ress prnhlem, with hi,:d1 dimen,io nality of bL1lh the design and the nileria ,;aces. for the sa ke of darit y. 11·e keep the design problem within a n:aSLlllablc comp kxity. Th us. the des ign procedure is oniy appli ed Lo the design the l,1twitudinal channel. Fi1wllv, -.ve ;1lsn n,,te that all the: re,t;l!:i included in this study- tire ob tained by the r,.,1ov1 software pao:kagc CL 1mbincd 11it h the MATLAB en,i ronment1 <1 and are based on the full nonlinea r ;imulatit.111nw del of the t110-engine-powered dynam ically scaled AirSTA R GT\1 sy,tem. which 11a~ rde,i:i~d hy NASA in December ~009. or Formulation of the optimization problem rhi, section presents the r,)rmulatiu n llf the i.'.1 PCS de,1gn c)ptimizatilH1pro bkm , indicating tbc sets of DVs and c:ritLTiacons1Lkrc:d in tlus stud y. as well as the critaia constraints to be satisfic:d. DVsand criteria DVs. Since the primar ~ ()b_jccti,·ci~ t,) irnpro,c the FQ 11 hile guar.inh:.::ing satisfactory robustness margrns. ·,1e includ e the natural frequency of the: pro Lo type dc~ign Proc/Mech£ Port/:J Systems and ControlEngineering227(4) 418 and the d:1mping rati,) of th.: .:ig.:1walu.:s or the statc- prediClor dynamics (which .;;in ,peed up or slo11·do1rn the rcspon,.: LJf the augmented ain.:raft) and the hand,1-idth nt lhe hlw-pass filtLT in the m..itchcJ channel 1,, hid1 can be used to ;1dJnst the time-d.::lay margin of the contrul kl,,p) us D\'s (f"igure 2). Funhcrmorc. 1,e alsn rnn,idcr the llptirnizati,111,,rlh<: band\\iJth ()rth<c' piJ,,h:L1mmand prefiltcr. 11·hid1can lx: used to shups: the pilot command as tu pre,ent ek,ator rate limiting and a1nid structural nrntk-llight inlL'ractit•n. The: follLl\\ing list ,umm;1rizes the ,et of optimization parameters tha t ddin-: the D\' space. • • • • DI ·1. :--.;atLtr,tl i'r<c'quency <)I' the st:ne-pred10:tor eigemalues (rad ~). DI·:;_ Damping r;ttin nf the state-predictor eigcn1·alucs !dimen,;ionks,) f)/'3. Bctnd\, ·idth lhc "malchcd" low-pass filkr I.rad SI. !) I·..;_ Bandwidth ot" ihe pil,1t-ct>n1rn,1ndprdilter l_r:td s 1. l,r Criteriaand pseudocriterio. The st:l of design eri teti,t Cl'l1sit.kr.:u in this study i, cho,en !() t:\alt1ate perf,mn un.:e ,md robustness prnperties the GTM aircraf"t au2,rrncntcu 11ith the [ 1 FCS. To pnl1idc an ,1dequatc assessment <)f the performance characteristics an d fQ lh..: L'., -augm~·ntt·<l ain.:r;ifl. bt1th pik1t-off-1he-h,np and pik,t-i11-the-lL1,1pperforrnant·c metric, arc: im:luded in thl.' design prncedurc. The nKtric, t·onsiLkrcd um thus hl.' das,ilied into the follt1\\ing three o:atcgMics. ,,r or I. Pilot-off-th e-lnor perfomrnncc mctncs. 3. Robustm:s, metrics. FQ and PIO metrics. Bt·c,tusc lhL· present m,1tcri,1l addre"es nnly the Lfr,ign of the lnngitudinal channd or the [ 1 !-"CS. the set nf mctri<:s used in this study is mainly hasL·d on the (time-domain) lnngitudi11ul respl1n,.: of Lhc GTM with the t.:1 FCS clusing the k,,,p. W,;: lllHi: that snme nt' the metrics used in this study wer~ als,, proposed in the stuJy by Stepanyan ct al.' 11 for !he e,aluation or aircral't ;tugmcnted 1\ith adapti \e FCS.,. Pilot-off-the-loopperformance metrics. This tirst set of m.::tries e\"aluates the pcrf<.lrman<:t:1)1" th.:'. aug111cn1cd uir<:ral"L by characteriLing its resp onse t,l ,tep inpub. In p,1rticular. the pil,,t -off -Lhc-lo('P perform a nee metric s ,ire based 011the time-domain respon, _.t,l an AOA stc:p cummaml of 3' held for • ~ ( Figure -~), ~tarting from u wings -k vd t1ight condition. The metri cs cq,tur.: the dc,·ia11on of the ao:tual rc,pon,c or the aircraft rrnm ,t gi, en desired response. which is det1neJ to pro\i tk satisfact,)ry FQ 1,ithtlllt tTat:h ing the physll:al linrns of the pk1tf,mn. as \\·ell as d ifferent mea sur es or (.",l lltwl ao:rnity. l,1;1dfactor . and crn ,, -Cl)ltpling. WL· note that in this study. all metric s arc nL1rmalizcJ to the amplitude 1.ll' the step command considered (3n)_ Next. wc pruvidc: a description the metrics inclmkd in thi~ study. Fir,I. ho11e1"er. we need hl i11tr,1ducc key rwr:itions to facilitate thL' Jelinitiou of these metric,;. Along. >.\"1ththe rreYi,)u,ly defined AOA (n) and AOA desireJ rc:sp,rnse (n-,,,., ). c,,,.,dis used here w dcn,llc the AOA rilot command; {3,1,., is the :\OSS desi red respt, 11Sc: /'.i,•.. is the wll-rak desired response: ~_.is the 1ertical acceleration: while ii_.is the ele,ator ddlco:tion command. We lei In be the tim:: inst.Int a l 11hich the ,tep command is applied and dcfi n~· 1, as the tinal time instant c,lllsidered for th<c'perl'unnance e1 aluation 111 - 1,, 1 4s). \Yith the ahll\C nolati,ins. th'-· melrics are l'L>rmallydefined as follow_;_ or Fi1wl dni<1/ 1011. This metric capture, the final devi:1ti,rn ,,f the a.:tual AOA rcsptmM.: rrom the desired AOA response ;1t 4 s ii fter the application t)f the skp command. This me tric ts set to Lero if the al·tu;tl response reaches the :\0.-\ rd'ercncc conunand bel"or.: th<.:end of the -4-, step Pf: P l = { Jdf,) - )u.i, .(1 1 ): if ffti"I < a, ,,,,;. "':'I~ [111.1,,: ot hern ise 1 This metr ic penalizes or cxl'ludcs sluggish resron se, . P:!· .\la.\"i11111111 dniutinn _ti·um desired .-JO.~ re1p o11.,<'. This metric captures the ma:ximurn dc1·i;itinn ( in ah,nlute ,aluc1 ,if the adual AO.-\ r~,p,,us<:' from the desired .-\0.\ resp,,nse p:; -· m,1x ul/) - u.1,-,(/J .•· __ Ii, , l, P3: !11rcgrul devia1ioo/i·,m1 d,•·,ir,·d_10. I rcspo11_1('. This metric is defi ned as the (trunc;1kdf l:-norm ,,r th,; dcviatilll1 L,r tlK' at:tual AOA response frnm the desired AO.-\ respnnsc ,, P3 = Jic,1 !) - n-.,,,,U) d1 P-1. Ore!rslw"t i11 AOA rc.1pn11se. Thi, metric ca pture~ p,issibh: ovcr , buots a nJ luw-d,nnprng .:haracteristics in the :\0:\ response _._IT~'.,1_;.!nfli' if fl'(/) > a,, ,1. for''.-,me I 11 P-1 { !'5 · .\/<1\i11111111 dnii l! ion J i·om clesir l!d [!11.I,: l,therw1se · u ,-,d .-H).-l l"IIIL' This metric captures the maximum rat..:d~, iation (in absuluk v:ilucJ of the actual AO.-\ rcsponsc fn,m ihc:dcs ir.:LIAOA rc:spons.: l'l'.l"J' IIIIS <'. 1'5 - m:tx J't( I) CL/, J /)" 419 Dobrokhodovet al. /'6. lm<'graf devi<uionji-um desired AOA rare re.1po11se. Pl/ maxlli:Uli, Thi~ metric is defined as the (Lrum:akdJ L'.1-iwrm nf ,,: .'1,.i, lhc rate deviation of the actual AOA response from the In L.'.1 adaptiYc control architecture,. the a~·curatc cstidcsin:d AO.-\ responsc ma1inn ,)f system um:ertainLics and the perform.inc,: !; guarantees rely on the (small) ··size" or the prcdi<,;Li on Pti = [ Jc<1 ,i - ri·d,..-(nl,/1 c1Tc1r.,·(I). Thi~ metric is used t(1 nwniwr the c,1rrect functi,rning 1.11' th<:L 1 adaptive controller. Thi: metrics I' 1 /'(, prnvidc a goud characterization nf thc transient re,ponse nf the augmcnt~·J airn~tfl when compared tl> a gi\ell desired respnn;;e. l\cxt. we pri:,t.:nt a set of metrics that can be extracted from the same sli:p resp(111se and cnmpkmcnt the AOA metrics defined aho\c'. 1·crtical accderat/011. Load f,u.:tor land passengt.:r comfurt l requirements can b.: caplL1red b} the rna:-;imnm vertical accekration during the step n.:sp1.1nse P-:': :\l,nimum P'= niaxl.~:(111 PI:'.: .\1u.Yim11m de1i111io11in cm.1·s-rnupli11gdrnam1cs. This metric captures the latcral-direclional c,,upling imluccd by a command in the ll)ngitudinal channel Pl:'. ma.'s )l,.(l)l(i/3(1) i.-_,_._:_ /3.,,,lllr' - tpU) · p,1,.U))\ !'his metric primarily provide s valuable information Cur the design of the lateral-direc tional FCS. l'/3: /11!,'grald<'rialto/1 in ao. 1s-c01rpli11g d_rnw11ic.l'.Th is mctnc is the integral version of the pr<.:•: il'U~ cros,coupling metric and i, tkl ined as follow, , ....'"·' ' PS: Co111mle//i,rt. This metric is ddine<l a, the ( truncated/ l:-nurm Llf the ele\ator dellection command JIr\ Oldl P /J ~ . 1,5 ,.( 1) I !p ( IJ -- f~.:. (; P-- • Ip( (I -- fl.,,.,( I)) ·' )</r J '" Similar l,1 Pl ::. this mdric would he mnre adequate for the design of the Iat.:ral dirn.:ti,inal contrul system. and hnth mt:lri-:s a n: included in this stwh only t\1 illustrate '" a sd ni' addi tional metri<..'sth;tt <,;anbe derived from the This mi:Lric r,en.ilizes !light control Jc~ign, that require resprnhc of the a ugmented ain .:rafl to a command in a high control acti\ily to achieve 1h.: desired control the longitudinal channel. ubji:cti,e. II is impunant w note. h,,wc\c:r. that a high Robustness margins. [n this preliminary sluJy . the contrnl effort might ju,t be the result of a fash:r AOA response, and thcn:fun: a large PS might nl)t ah\ays be onl:- rnbustncss metric considered fnr optimi za tion is the ril!lc-tfelai· 111,rrf{ ill of thc closed-loop :1dap11vesy,an undesirahk respon,c drnractaisllc, Lern. It is defined at rhe input of the air crnrt (tirn<..' deiay in,;erted at the ckrntor ddkction wmmandJ. and it is f' 1i: .lf,1.Yi11wmeleratur rate. L'l.ces~i,c contn,I rat e can derived frnm the timc-dumai n respume of the augmenbt.::identili-:d by the f'olll1wingmctri~-: ti:d aircr,1ft. For a given wings-lcvcl tlight condition Pv = max ,i,(1) and with lhe pillll-uff-th,>lo<Jp. a small pertur bation in ,f;, . .r, the trim (initial) i.:LmditiLrnis introduc ed. The timc-deLiy ma rgin is determined as tht minimum time de lay that This metric pcnafo .cs designs with high eknitor rates prnd1Kes sust:.tined oscillatil1ns in lhc AO.-\ response as in order ltl preYcnt u111.k,irahle effects frnm rate the £ 1 1-{'S tries to stabilize the air,rafL al lh\'. giwn li,mting. trim cundition. In this stLLdy.this rnbu stn.:ss mctric will P/IJ: .\laxim11m ef<'rnior or·n,fcra1io11. High-,n·dn do:1i- he dcnolcd by RI. Nole that the time dela y introduced ,·ati\ ·es of thl' control rnrnm,11lll, arc coupled w the in the elev.itor control d1annd is in addition to the flexible modes ol' thi: aircrnft. The follL1,1ing mctri l-, :!5 ms that is already mod.:kd in th.: A irSTAR ,1mulatio n en viromnL·nt. basc·J on thc second derivative of the di:vator comCriteria addressing FQ and PIO characteristics. Fina lly. mand. captures excessive accclcr at inns and oscillaLi,1ns ·e abo in the control command thal rnuld potentially lead to predid1on, for hnth 1-'Qand PIO tcnLkncies hc11 hccn induded in order to comp lement the pilot-off-theum,,1n1ed structural m11d<.: inti:ractiuns lnnp performance ml"lric< pr.:scnted ,1h,we. Fnr this P J{) = max i\U) study . we CL1nsider the Limi:-d,nnain f\eal-Smit l1 i :i,:,I• (TD'.\iS) 1-'Q and 1'10 criteri a . which w-.:re sp~cilicall:, Pl/ : Jtu.,im11n1 o(C. predil'li 1111 anrr. Thi~ metric i.:ap- devcl npc d lt>r n,>nlincar aircraft dynamics a nd nnn line,lf ~·cs. F,)r a detai led description ur this criterion. turcs the maximum error between the aL·Lual system sta te ,111dthe stale' or the [ 1 st,lte predictor. usua lly an inl<..'rcsli:<ln:adi:r i~ referred to the ,tudy hy Bailey 22 and Bidbck. 21 The reader can als o lin<l in Cho e et al. dc notd by .\·(1l I'S = i Proc /MechE Part/:J Systemsand ControlEngineering22 7(4) 420______________________ Tht' first a nd second conditions address directly the contrnl sre~·ilica1iom. n,1mely. the final value of the step resp,rnse within 10"" uf the de,ir ed. and the predicted Lc'1d I FQ. The third inequa lity imposes a 20" n constraint <111the 01·crsl1<) 0t in the step response. establishing thus a ( luosd bo und on the acci:ptablc transient performance d1arai:tcrbtii:s l'I' t.he actual i\O ,\ response. Dw:: t,1 signiticant di fficulty of defining ;1II FQ I: Tracki,rg 1wrfi,mw11ce. In the TD::--;Scrilcnon. tht'. rLK> t-mt'.an-squared trading errnr is ust>d to cvalt1:1tc criteria i.:nnstraints i:ons1stcnt with kasibilily of the solution. the rest of thc constraints \\ill be i<.kntilicd the dus~d-luPp pt:rformance W!th the pil,)t-in-thc-loop. intc·rai.:Liwlywhile analyLing the test t:1bks . A value of zcrn ffil'ans lh:1t th~ pilN is able to perl'ectl) track ( with zero .:rron the rd~rc-ncc c·omnwnd ;1fh:r the spi:cili~d acquisition time. Solutions and analysis FQ~: Pi/01 1ror!,/uad. [n tht'. TD'.\S criterion. the pilot workload i~ given hy thc pilot compensation phase This ,ectinn pr<:'scnts the tw,l slcps orilcraLive applicaangle (ill degr~c~)- 1rhieh is derived fwm the uplimal tion of the PSI metlwd ll1 the design impro\·e111c·ntof pilut rnudd ubt;1incd fn)m the critcrion. A value Lll' the longitu d inal cha nnel of lhtc £ FCS. A s mentioned 1 zern means that thcTc' is 1w need for either pilnr kad ,H earlier. the first itcra tiLin USL'S a reduced s<:t ,if the conlag compens;irinn. twl rndrics. l\ umerical impkmentati,111 of this first step FQ3.· FQ l,Td Th<"t\1-,) metrics ahm·e. FQJ and F(J!. is rdati \ ely eflicicnt 1vith the '\:um pu t,iti,mal pric·c·· of ar c used t,) dctenninc the pn:dickd H) kvd based on one solution meas ured in m inutes. At the second stcp. the FQ bm111,l-1 rie, prnposcd in the crilcril1n. FQ3 ,~ a wh;,;nusing the extemkd set of criteria. the e fficiency of di,crc:te metric. and it only admits th e values L 2. anJ numcric·al impkm.:ntation bc·rnnu:s critical bl'causc the 3. 1-1hid1 \:l'ITc~pL,ml t,:, L,:\·cl I . I .eve! ~. and level 3 "cnmputatil)nal pri,x" ,,r LlllC sd lllion is meas ured in FQ. respecti vcly. knths of minutes. 'fhe architecture nf thc Llplim ization FQcJ: P!O 1e11dc11e1·. The TD:\"S c,iteri,111al:;,) pr,,vidtc:s framc11-,,rk was prc,cntcd in Figure •. a pn:dic tion h ir the su~ceptihility the augmc-med aircrnft to 1'10. This PIO-suscq, tibilit :- met ric is used to CL,mpkmcnt the FQ metric, di,c·usscJ .ib,,vc. Firstiteration:constructionof the According tn the· TD\:S cnterin11. a value aho'-c 100 feasiblesolutionset implies that the augmcntcd ,iin: raf t is PJO-prnnc. Thtc cnn,tr ucti,)n of tlK' h:asibk Sl1lution sd starts by wherea, a value bck>w lOIJ indicates a PlO-immune defining test intervals for the DVs. These lest inl c'rv a b contigur.1tinn. ha,c hecn identified with respect to the 11l)minal prnt,)type ~nlution obtained frnm the £ 1 de,;ign pnicedure Tilts sc·t of l'Q metrics will be used in section --sdluti<'n, and analysis" IL' impro vc a prol,)type dcsign (L1bie 1). Thc ,,bjcdin:: of the fir,t ,tcp is 10 li nd a dircctinn of urthe illngJtudina l chann el nf the [.,1 FCS. F,ir th..:lirst impr,) \ cmcnl for thi: nominal design . \lore precise!_,. -tagc nf the dc·si~n that aims le> e.'1.pk•retbc fea,ihili ty wt' aim he re at determining tight in ti.:rvab fr,r the DVs set. only a subset of these metrics will be ll',cd. Tile cbar:icterizing t he: , tat e pr ~dicwr (DI ·1 and Di-~) thal ,·,,mplele set ul· m drKs "ill he Li:iedin th<:-s.:-eo nJ stage ll'Ould pnwide Level I FQ and woulJ not dcvial<.:from to optimize th.: <.k,ign or the adaptiv c cnntrnl system. B;iscd c•ll the cih,iecti1·e, llf the Lask and previc1us 11igh1 the dc,i red respon,c defined pre,:iously. Tu thi s end. c,,ntrnl design nperli. ,e. the foll,m111g \ ec1ors 1,f cri- the design is to be minimi,:ed '.1itll rcspeer to the fnlln11ing n:duccd number L1i'crita ia ;P l , P~. I' 3, !'+, f'5, l'f> , teria P'!. P3. P-!. P5. Pn. fl}/ HJ'! FQ3. FQ-/. FQI , FQ~;. RI : ;rnd pseud,x:ritcria ;p~_PS. P9. PIO. Pl!. Pl:!. The rob ustn ess metri c R J and the PIO mi:lrit.: FQ4 P/3; ari.: delined. are n,,t mcludcd 111 thi ~ first st~p bcc au" their a study on the prediction of FQ and ad,·er~e pilot intt'ractit,m in the: GT.'vl ;rngmc:nted with th.: [. 1 FCS. W-: use four difkrcnt mcLril·s. nlracting all of them from the TD-"S crikrinn for an acquisitilHl tim;: l>l' l.5 s. to chantL'k'rizc lhc FQ and PlO tcnclencic, ,)!' the augmented ;1ircr;1ft: or :Pl Criteriaconstraints Table I, Init ial interv als of design variables. l3as-:d on the metrics d-:tinl·d . lhc linal design of the L'. FCS should iclc<1/fy,·cr it\ the set n f contrnl objectives Design variab le at the refcrcncc flight condition or 81)kt nf (c4ui,a len t) <1irspeedand 1000 ft ,,f ,dtitu dc. Corresponding lo th ese llight i.:,111Jition s. a s-:l or three criteria constraint;; was defined a priori Pl ~ ILL HJ] 1, and P• ;; I , DVI DV2 DV3 D!/4 f I prototype 5.SOE+OO 8.SOE-01 2.00E+OI 2.00E+OI Initial inter vals of variation of design variables Min Max 4.00E+OO 5.00E-01 5.00E+OO I.OOE + OI 8.00E+OO I .I OE+OO 3.00E+OI 5.00E+OI - ---- - -··-- - 421 Dobrokhodavet al. e,aluatinn is n1mputationall~ e.\pensiw: these metric~ will be c,,nsidered in tb c next step thi.: optimi1.alilll1 pr(1ce55"hen the dnmain 0f the DY~ becomes signific,ullly rel1nt:t.l.The mi.:trics p-_,,,11 are n,,t indw.kt.l in the set of crikria because imprn,ed FQ may require "high·· values of these metrics. Ncvcrtbcks,. the~ are included in the optirninti,)n process a, pscudocritcria (psc:uducriterion differs frnrn a critcrinn by the fa<:tthat it is nut included m the calculation of the Parern frnnt: for ml1ri: di:tails. see Sratniko, and MatusP\") thus providing useful insights intl1 thi.: dynamics of the ;rngmented ;rneraft. Similarly. thc mctri( Pl!. whi..:h can be used tu monitur the c,)f recr operation of the t adapti,e ctintrolkr. d1.1esLlllt ne-:d IP be: minimized as long as it remains a couple of orlkrs or magnitude beiL>1vthe system srale (truncated) Ci-norm. Finally. the 111etri1:sPl:! and P/3 arc indmkd fnr the sa ke of completenes, and should 1'e considered (1nJy for the design of the lateral directional c0ntrol system. Till' MOVI pack:1ge performs a predefined set of numerical trials :ind then form,; a lest table. lntt:ractin~ 1,ork with rhe test ta hie cnnsists of seque ntial tightening ol' the DV comtrainb and is well sup pom:d hy a number of grapbirnl instruments implem.:nted in \IOVI. The final result achic\cd in this lirst ikratitm of the optimiLa ticm process is based on I024 h~sh. Out of thc·sc I024 tcsh. -C7 vectors did not satisfy the a priori gin~n critcri;1 cc,nstraints. The solutions that di<lnol sati,t~ tlH: n111;tramts enkrcd the 1aNc o( criteria f,1i/11r£'5: or 1 Table 2. Criteria constraints. P2,,;0.2 PJ ,~0.2 P4 s;,1.02 PS<;I P6 ,;.0.3 P7>a0.25 PB,;_5 Min Min Min Min Min Pseudo Pseudo P9,;{ I 5 Pseudo Pseudo Pseudo Pseudo Pseudo Min Min P, o~.;Joo Pl I, ~ 0.25 P/2 ,:; 0.01 Pl 3 ,;: Q.01 FQ/ ,,;O.I FQ2 ,;; 45 e\ery entry pf this tah le is available for a detai led analysis. Thi.:ri.:maining 597 veclor , that did sati sfy a priori given critc:ria constraints were used to constrw.:t the lest table. Wl1ile tlghkning the criteria ct,nstraints in the test tahk. the foll,1wing new cri\cria constra ints were formubted iTahk ~). f\.ote that whih: anal yzing the test tabk. th.: constraint ol' P-1w,1, , ignificantly tightened In the ,·alue of 1.0~. Furthcrnwrc. the rcspotN: on criti.:ri,1 Pl is not presented in T;ible ~ hecausc all solutions pro\·idc<l identical ri.:spt>n,c. Pl= 0. Only ~I) snlutions were f1)und tt1 be frasiblc according lll th1:sc criteria cunstr a ints_ ;ill of them contrihuting tn the Parcw-optimal solutions. /\ fragme nt nf the criteria table is given in Tablc _:\ _ Analysis of th..: criteria tabk ,hows that solution ;f.l)l)_:\ is the most prcfcrahlc 011e.This snlution is cq uivaknt to uth..:rs with 1\.:spcctll>criterion P-1.it is superior to others o,er a set of fi,·e criteria : P:!. P3. Pfi. FQ! . FQl: and is w..:aki:r lh,m the: prototype only with respect to the crit~ri,1n 1'5. Furtherm o re. the o ther 19 solutions are lxttcr than thl' prototype 11·ithrcsp,.x:l tu four l'ri1eri;1 : P:!. P3. F-QI. FQ:!;. However. none of the solutions arc supcriur tl> lhc p rot,1type ll'ith rc:spect t,) criterion 1'5. fn pa rticular. this ,1bsc1Talion implies that if Lht: pwt,,t ype design vector had been sampled by the ,ystem, then it wnu ld bch1ng to lh..: Part:L,, set. On the: t>Lhcr hand. this r..:sult confi rms that the solution obtained following the basic [, 1 de.,ign guidel ines is near opt ima l for this s..:t of ~riti.:riu. Thi~ an ;1lvsis allows ddininf! the direction of further search. In pa rt1cular. the results pro vide tight intcr\'als for the DVs DT'l and DI':! <..:b~1racterizing the st;:ikprcdictor dynamics and suggest extending Lhc in itial imcn·ah or variati(ln of the DVs /JI 3 and IJ 1·-1 {Figure 5). R;1sed on these results and their analysis. a new ..:xpcrimi.:nl is perform ed with the l1bjccti\e to imrr,.Jve I he ft::a,ibk solutilln set and t,> dc:lcrmini: an optimal solutiuu of tile £.1 rCS design that irnprnves th<'!prototype with r.:spl'CI tu an i.:xli.:mkdst:l uf n-iti.:ri,1. Table 3. Fragment of criteria t able. -- ·· ~Criteria P2 PJ P4 PS P6 Pl P8 P9 PIO Pl/ Pl2 P/3 FQ/ FQ2 Prototype Min Min Min Min Min Pseudo Pseudo Pseudo Pseudo Pseudo Pseudo Pseudo Min Min IJOE-0 I l.54E-01 I.OE+OO 3.ISE-01 l.49E-01 I.S I E- 01 3.24E+OO S.96E+OO I .07E+02 7.45E-02 1.01E-04 l I 6E- 05 I 23E-02 5.36 E+OI ·- - Pareto-optimal solutions #241 #281 #329 #409 #649 # 825 #993 l.04E - 01 l.16E-OI I.OOE+OO 5.37E-01 l.97E-01 1.65E- OI 3.3E+OO l.17E+OI 2.42E+02 7.79E-02 l .84E-04 6.1 BE- 05 6.73E-02 4.42E+OI 8.40E - 02 l.03 E-0 I 1.00E+OO 9.36E -0 1 2.21 E-0! 1.74E-0 I 3.29E+OO 7.55E+OO l.34E +02 6.02E-02 l.87E-04 6.87E-05 9.29E-02 4.35E+OI 9 . I 4E- 02 I .06E-01 I.OOE+OO 9 .68E-0 I 2.SBE-0I I.84E-01 3 .31 E+OO 9.IE+OO I .72E+02 6.82E -0 2 2.0SE-04 8.0IE-05 9.74 E-02 4,03E+O I 8.97E-02 l.04E - OI I.OOE+OO 6.29E-0I 2.0JE - 0 I l.72E-0I 3.30E+OO 1.09E+OI 2.16E+02 B.IOE-02 206E-04 7.00E-05 6.86E-02 4.22E+OI 6.0JE-02 8.72E- 02 1.0 I E+OO 8.63E-01 I .74E- 0I l.83E-0 I 3.31E+OO 1. 1IE+OI 2.24E+02 7.72E-02 2.29E-04 8 .1BE - OS 9 .0SE- 02 3.79E+OI 7.44E-02 9.51 E-02 I.OOE+OO 8.58E-OI l.94E - OI l.78E-01 3.30E+OO 9.36E+OO l.76E+02 7.22E-02 2.J4E-04 7.SSE- 05 780E - 02 4.IOE+OI 5.39E-0 2 8.84E- 02 I.OOE+OO 6.89E-OI l.32E - Ol l.?SE-01 3.31 E+OO l.I6E+OI 2.44E+02 7.77E- 02 2.09E-04 7.03E- 05 8.BSE- 02 4.00E+OI _4_22 ______ _______________ P_ro_c_l_M_e_c_hE P,artl:J Systems and ControlEngineering227(4) 5 .,, S4 .," > Direction of improvement 3 i• Nominal 0 -82 E ;E_l design"t] _,_J._ 0 12 20 16 3 h-· ;-; 28 24 36 32 40 44 i 48 DV4 (Pcmshp) Figure 5. A hisrngram of DV4 distribution along with t he nominal des ign (prototype) (th e legend ,·u,1sleft to r ight and top to bottom, respectively). solution and the direction of imp rove ment FQ./, I<I:. All these crite ria ar<: lLl be minimized e:-:cept rur Rl. ,,hich is to be maximized . and critetia Th1: results the second ite ratinn are ha~cd on 512 table jL1Stpresented. w<:adjust lbc- intcflals of varia t ion tests. prod uc ing 124 feasible solu tiom. All thc,e soluol' Lh.:DVs ,L,; gi\en in Table 4. tions arc Pan:ll.1o ptimal. The hi stograms in this secnnd The criteria con,trainb remain unc han ged . 1d1r:r.::1s iteration b;.ivc stronger dist ributi,1ns of tlK kasibk ,uluthc· d.:sig:n is iww lll be optmuzed ,,·ith respect to the tions than in the iirst it.:ration. r igurc 6(a) re pre se nts cxtcmkd set nrcriteria :Pl. P3. P./. P5. Pl\ FQJ. HJ:. th<:distribution of 124solutions for DI· I . As a rc'.sult. anal:vs,s the lest tahlc and histograms leads to a strong<:r set of eritnia and pscudocriteria Table 4. Refined intervals of des ign var iables . constraints. ;1, presenkd in Ta hle 5. Accl1 rding t,, these new constraint s. l1nly six solution, a re feas ible. and all Initial intervals of variation of Design variable Prototype l l f them are Pa ret,1 opti m al. The value, o f the DVs and design v~ri~bles criteria of th e Par eto-opt imal solutions are given in Min Max Tables (1 and 7. n:spectiH:ly. The new dis tributio n of the f..::asibk solution$ for these crikri;1 and pseuJ,1cri7.00E+00 DVI 5.S0E+00 5.S0E+00 Second iteration:design improvement Bas.:d ll • Lh<:analysis of the histogram, or or DV2 DV3 DV4 8.S0E-01 2.00E+0I 2.00E+0I 6.S0E-01 9.80E+00 l.80E+0 I a~ 0.90E+00 4.00E+0I 6.50£+0 I teria comtr;.1ints i~ significantly tightc'r (Fi gure 6(b)i. Th.: nc·•.\ histc>g:ra ms dearly identi(v tight interval; for :Ill the DV, in which the optimal SL>lution,;lie. i 01 (; _ ~ !!!40 oj~g 20 I ~g i;µ !iii c::::'.:::J z::, 5O - ---·:t_ _ _1 ________________ 5.55 5.7 5,85 6 . .. :_f__l .. ~~if mo% 6.15 6.3 6.45 DV1 (PwnAm) ~ Cl 27.42% - r+i... !iii __.l_ _--1 6.6 6.75 6.9 i~tff ?, • 3.23% 0% 1 .·. I (a) El 0% • 0% 0 5.55 5.7 5.85 i 6 ~ • 0% 33.33% 8t;67% IJ 0% Ill 0% 0% 0% • • -~- 6.15 6.3 6.45 6.6 6.75 6.9 OV1 (PwnAm) (b) Figu~e 6. PSI iteration 2. Distribution of feasible solutions of DV( with (a) the original criteria const raints and (b) t he tight ened criteria constn incs (rhe legend run s left to right and top to bottom, r especn vely). 423 Dobrokhodovet al. Further analysis uf Ta bk 7 shnws that all solutiuns c>r this new i1eratinn. as wdl as 1.h:sign #9')} fwrn the tir,t iteration. hdong to the Yery tight intcnab the l'ir,t and ,econd DVs. The' first three !-'<1r;1meters(DI ·1D i '3) or !:.()l/} :md :: !Oh a rc alrnnst idcntil·al. Hml'e\·er. one can see that :-:'99}. \\ hile pro\·iding g:01)dre~ponse pf many c:nh?ria. Uc)CS not satisfy the new constraints on critcri,1 P\I and PIO {ckvator '.H1rkload ). Mcm:l)ver. design #99} also foils \o satisfy the constr~1int 1)11 criter- or or ion FQ3. Analysis l>r tbt' test tables. dcpenJctKie, of criteria and depcmh:ncic:s hd\\ een criteria allow determining: the mclSl preCer,1blesnlutillnS. In parti c·ular on l)Vs. • Figure 7 shows cif th..: "matched" • the inlluence of the bandwidth low-pu~s filtc-r (DI '3) ('ll the Table S. Second iteration, refined criteria constraints. P2~0.I PJ,;;0.I5 P4-;, 1.02 P(0,;;200 Min Min Min Min Min Pseudo Pseudo Pseudo PS,,; I P6 ,,;O 25 P7 ~;0.2 PS-r,5 P9 ,,,_10 Pl Js.: 0.0 I FQ/ ,;;O.I FQ2-;:45 Pseudo Pseudo Pseudo Pseudo Min Min FQ4,,;,5 Min RI ;"'80 Max Pl I ,~O. I P/2 ,;:0.0I Ipiiot-off-the-lnop) trade-off bdween performance critcril1n p::_(P3 shm1·s the same trend ) and ruhustnes;; Rf of the augmented :1ircraft. 1-'rnm this ohscr\;1tion. we condudc thal l'ritni a p::_1P3) and RI i.ll'C contradii.:tor~ 11 ith respect to the DV D 13. Thi~ means tha t improvement the t rac k ing performance rcqnires an im::rcasc in the ban d width of t he lc, w-pass lilkr. which in turn results in <lcgrada ti,m of the timc-dclay m arg in o f the a u gmented aircraft. Thi~ tr..ide-nff is cons iste nt with the predict io ns of the [ 1 aJapt ive control thcon. Figure S shows the Jcpendencie s of the FQ criterion FQ 1 cin the DV D l ·::..\.Vhile the tr end stems tc) indicate that a smaller damping ratio of the- slalL'predictor eigen\'a lues re sults in increased Ile:1d) pilnt rnmpcnsation. Figure X shows th a t the ncw Pareto soluti, 1ns achic,i: a 20" ,, r<::ducti,)ll in criterion FQ l with respect to th e prototype 1ksign Jcspite th1\·ing a smaller damping ratio. A sm1ibr ohsenation t:~tn b1:mJde rnr critcrinn FQ-1 \\l1cn analyzed versus DV DI·::.. The <li:pcndrm:y l)f 1-'Q criccria FQ I and FQ::. in this iteraticin i, also sim ilar to thc1sc obtainc·d in 11lefirst itcrati,)n. thus demo n strating signiticant impro1emcnt predicted FQ 1)\~r the prototype dt:sign. but now in the extended Gil<:ria space. obtained or Table 6. Second ite1·ation. Table of design variables. Design variable DVI DVZ DVJ DV4 Prototype S.50E+OO 8.50E+OO 2.0E+OI 2.0E+Ol #993, first iteration 6.I2E+OO 7.09E-0 I 2.70E+OI 4.93E+O I Pareto-optimal solutions #106 # 202 #254 #318 #358 #462 6.00E+OO 7.34E-01 2.52E+OI 3. I6E+O I S.99E+OO 7.49E-01 I .67E+O I 3.20E+O I 6.24E+OO 7.76E-01 1.SIE+OI 2.1 OE+OI 6.23E+OO 7J3E-0 I 2.I8E+OJ 2.72E+O I 6.IOE+OO 7.SI E-0I l.69 E+Ol 2.57E+Ol 6.I8E+OO 7.ISE-0I 1.58E+OI 3.11 E+OI Table 7. Second ite ration. Table of criteria. Proto type Criteria P2 P3 P4 PS P6 P7 P8 P9 PIO Pl/ P/2 P/3 FQI FQ2 FQ4 RI Min Min Min Min Min Pseudo Pseudo Pseudo Pseudo Pseudo Pseudo Pseudo Min Min Min Max J.30E-00 I I .54E-0 I I .OE+OO ll5E - OI I .49E-01 I.SIE-01 3.24E+OO 5.96E+OO l .07E+02 7.45E 02 I.OIE - 04 3.l6E-05 l.23E-02 5.36E+O I 4.68E+OO 8.50E+O I Pareto-optimal solutions #106 #202 #254 #318 #358 #462 6.0IE-0I 9.60E-02 I.00E+ OO 6.13E-0I l.28E-0I l.6BE-OI 3.29E+OO 9.09E+OO I .77E+02 6.62E-02 I.SIE-04 6.o2E-05 9.93E-0 2 4.J3E+OI 4.0BE+OO 8.SOE+OI 8.45E-02 l.I3E-0I I.OOE+OO 6.SIE - 0I l.67E-OI l.67E-0 I 3.29E+OO 9.1 E+OO l. 78E+02 6 60E-02 J.70E - 04 5.89E-OS 9.BIE-02 4.41 E+OI 4. 19E+OO l .05E+02 9.I7E-02 l.I IE-01 I.OOE+OO 8.8SE- O I 2. I 6E-0 I l.72E-OI 3.29E+OO 7.9E+OO I .43E+02 6.09E-02 I.SOE-04 6.58E-OS 9.34E-02 4.38E+O I 3.87E+OO 8.00E+OI 7.04E-02 9.66E-02 I.OOE+OO 8.43E-01 1 78E-01 l.76E-01 3JOE+OO 9.0SE+OO l.72E+02 6.74E-02 2.0IE-04 7. I 3E- 05 9.26E-02 4.I4E+OI 3.88E+OO 8.50E+OI 9.63E-02 1.ISE-01 I.OI E+OO 7.7IE - OI l.94E-0I l. 68E-01 3.29E+OO 8.43E+OO I .59E+02 6.31 E-0 2 1.69E- 04 6.0IE-05 9.20E-0 2 4.46E+OI 3.84E+OO 9.00E+OI 828E - 02 l.04E-OI I.OOE+ OO 863E-0I 2.I IE-0I I .78E-O I 33 IE+OO 9.54E+OO I 85 E+02 6.95E-02 l.98E - 04 7.27E-05 9.64E -02 4.IOE+OI l97E +OO I.OOE+02 Proc/Mech£ PartI:) Systems and Control Engineering227(4) 424 0.22 z :ii 0 0.2 0.18 ..5 0.16 ~ 0.14 ! C .g ~ u 0.12 0.1 0.08 0.06 12 15 21 18 24 30 27 36 33 39 DV3 (PCsbw) (a) 220 200 0 X <> 180 160 ::; 140 <{ Pareto optimal solutions ts Prototype <>Feasihle Mlutions ::, 0 t:. 120 ~ " -~ c (.) 100 80 60 40 18 15 12 24 21 27 30 33 36 39 DV3 (PCsbw ) (h) Figure 7. PSI iteracion 2. Dependencies of criteria P2 and RI on che design variable DVJ:(a) criterion PZ (max AOA deviation) versus design variable DV3 and (b) cr iterion R / (time-delay margin) versus design variable DV3. 0 O Parelo optimalsolutions z 0. 16 ~ ~ "' E a ~ 4. Prototype 9 Feasible solutions 0 .14 ~ 0. 12 0.1 j 0.08 8 0.06 0.65 0.675 0.7 0.725 0.75 0.775 0.8 0.825 0.85 0 .875 0.9 DV2 (PztAm) Figure 8. PSI iteration 2. Dep e ndencies of criteria FQI (tracking performance) on the design variable DV2. • Fi nail~. Figurs: ') shows the dependency bc'twc:..:n cnteri:.i 1'3 an d RI. which illustrate, the fund:.imental tr;ide-,1ff b<.:tween performance Jnd rnhustn,'ss of lhc closcd-h)op aJ:.ipLiv-: sy,t<.:m \1·ith the pilototl-thc -1',Llp. While all the ,,ptimal sc>lutiuns reduce the Jeviat iuns from the desired response wit h r<:spect to the prototype design. only tin , of thc,c snlutions e\hihit :1 bette r time-dcla :, margin than the prntt1 typ c design ! ii202. ti.+6.") ;rnd t\\·o exhibit a similar margin (:-;106. ;;~lk) . .-'\, a result Llf it..:r ati, e two-step ccq-rection nf initial ,·onstrainLs . six Pa reto -op tima l solutions have hee n found. Analysi s of these sulu tion s shm 1s that designs #106. #202. =::35~.and #-fo2 impr, 1v~d the p rototype dc, ig.n hy six criteria simulL,mco usly. Alt hough :.ill six solutions are pra ct ically equi1alent. pn:krcn..:e is given to the Jcsign 1·ecL,1r#.::'O.".as it 01·crall pr<)\"i de; better track- off between the (predicted) FQ (FQJ. FQ::1 and the timc -(.kby margin (Rl). 11·hikminimizing the difference with the desired rc:; p\m,c ( figure I0) . We noliee Lhat when i.:urnpared tn the time response ,,r the: prototype design. the .-\OA rcspons~ and the ek\a tnr work[l)ad o f th.: <>primal , 1,Iution #2 0.::' prn, ·idcs a foskr respo nse (smalkr rise timl?) \I ilh a minim.LIincrease in the elevator work !oaJ . 425 Dobrokhodovet al. .. .. .. 220 0 .... 200 X <( ::;; 180 ~ Cl 160 140 "'C 120 100 ~ t:. 0 80 8 60 "& 0 <> 0 o Pareto optimal solutions A Q- 0 00 Prototype Feasiblesolutions 0 .. .. 0 0 0 .. .. 40 0.08 0.0850,09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 Criterion 3 (errncnn_L2) -> MIN Figure 9. PSI iteration 2. Relation between criteria RI {time-delay margin) and P3 (integral deviation of AOA). 9.S -a.,.. 9 ,., .... .._ . . O .. . . ' • · •: • L • . 0 0 • ' . ~,. . •• • • 0 • L. : . ¥ , .. • • • L •: O••tH• o - L • • • > ... ~ I'----~-• ... •om......,__, ......··-···. ...... ~ 8.S -«m2 . 8 15 · I 1 "u 6 ..... S5 .s •l'-- --'---....._ 4.50 3 2 -(secl 0 4 __ .__ _ _....__ ..___ _., S 6 7 (b) (a) Figure .,_ __ 3 • lrne[,etj 2 I 0. Optimal design #202. l' AOA seep response. (a) Angle of attack, " and (b) elevator deflection. ii, . z ~0.1 '} § ; 0 l.. i• 2 ~ I ......__ I '•• z --0-- 1 0.12 I ~ Pareto solutions E 0 .11 r;,! 0 E w "' o 0.08 8 I C 0 j Grad"' -0 .04 ~ 0 .06 · · ____ ..______ 6 5.5 8 ~ ---6.5 7 Design Variable 1 (PwnAm) 0.1 --+--- Feasible solutions -G-ra-d-1+--o-.0-0-1l---- 0.09 :;~~to i ' ·-~ l :I~ ---: --0- ...I C j !-' N #202 ,,.1~0. . 0.1 ' 0.13 --+--- Feasible solutions solutions .::O.'··.. I i 25 30 -.__1:=J 0.08 10 15 20 35 40 Design Variable 3 (Pcsbw ) Figure I I. Sensitivity plots. :\s the last stt'p. 11·c vt'ri(v the robustncs, or di:sign TT202w small ,c1ri,1tium of' the DVs hy perfor ming a sensitivity ;1nalys i,. T his analysis calculal\:s a critt!rion rcspn n sc in the di red iun defin ed by a I )V in the ncig:hho rhood o f th e nptima l , nlutinn (in our c,tse. design ir20~L .'\, an example ol' thi, sen, iti\·ity analys is. Fi g:un: l l slww s the dependen cy of cri terion FQ I and desired-model tr acki ng: performance P:: ,111 the DVs Dr / a nJ Di '3. resp cct i\dy; each tig ure represen ts tlK case where only on.: DV is varieJ. l'hi le the remaining: DV, arc kept tixed at the: optimal value defined by desig n ::'202. Co m pac t d istr ibutio n the P:rn:to so lutio ns and sm,1olhncss ,,r the criteria CL1ntirmthe rnhust ncss of dc~ign #202. ,,r 426 Proc/Mech£ Part l:J Systems and Control Engineering 227(4} Conclusion 5. Kim hhh and Hc1' ;1kim>an ,. Dc,elopment ,,r ,·cnfica tion and validatic111ar prnach c, for £ I adapt iv~ control: mult1-<: ritcri:1 ,,pt imi/ "li"n for tilter design ln: Pnw t·ccli1t f.!..,(!( .-ff.~.• g11idt111n·, nari'.,!afion um/ conrro i n111.t,·n11ec.Tnrnnt,1. 0:'.. Canada. 2 5 Au,;u,t ~010. .\mc rin111 !mt itule nr A.:runautic s ,111<.iAstrn11;1u1i.:s. This artick pn:sented results of t he application or lhe PSt m.:tlrnd and the MO\' I solh,are package for the dcsign optimization of the l 1 FCS implemente d on the AirSTAR GT:\! ain.:raft. In particular. this study lws addressed the cnnstruction l'f the 1;.:asiblesoluti,m a~ m~ll as the impro":ment "f a nominal prot ,,t~ re design. F,,r this purp,1, ,,. we ha1e for m uiat.:d and sohed an optimiz;1ti,1n 11rnhkm with ji)llr DJ ·.,--dcti n111g the cigcnstrnclure ,,r the state-prcdii.:t,x state rn;1tri,. the bandwidth of lhL' km-pass filter. and the bandw idth ,,f the· pilot-comman d prefilt.:r----and JS crileria --d1aractcrizing pilnt-llff-lhc-luup performance rnctriL'S. rnbustn..:ss mdrics. a, well as FQ and PIO metrics. This study demonstrates that wnsistent app licat ion th.: ,ksign guidelin~s ,1f l, adapti,·c ,·ontrol becomes particularly bcncfo.:ial for rile con struction nf the feasible: so!uticm set. Additionally. th.::rc,ulLs nrthis ~t udy are consistc:nl with th,· thn,retical cbims of the th,•nry ,,f [.1 adaptive n 1ntrol Ill terms of rohu~tn..-ss and perfor111:1m:c. Mnreo\ ·cr. the d..:\clo ped pro..-cdure and thi.: obtained n:sulrs contirrn the suitabil ity the PSI mcth,,d for the multicrit.:ria optimi1.atinn nf an adapti,c llight control law subjc,·t t,1 ,ksin.:d control spccilica1i,)1b. Finally. we wa111 to emphasize 1hat the insights gaincd during the ,1pti111i7,ationpro,·css with the '.\IOVI ,;(1frn:1re enntrihutcd t,1 th..: SLKcessful fiiuht 1·erificati,ll1 ami \·a!idatiun 1" of the designed .CI ad:pli1·-: -:ontfL)l law at :'a:-\S:\ L\RC. ,,r or Rc,wn. VA.. h. St.it111ho, I{ R :ind \btu,,,-. ..:ng.im·t·rlng. C RB . .\ful!i, ·,-ih'riu a11,1 !_,·s f _, in LtH1d ()n: KIU\\'~r -\G1- Dt1r<lr.:Lhl 81):,,tcJ n dcmic Puhlishers. 21Jti2. s,, h,,I 1\1 aml Starnii,:ci, RB. Scfl'c1i11g op1i111cilpaml11t'frf,\ in n11dlicri1t·i-iu pr(i/ilernY.2nd .:d. \·l,y,;c1.1\ \ : Dn 1fa. 200ti. ~- Statnib), RR :rn<l Statniko\ AR. S11ti,rar c 11c11-/.:<1ge .\/0 I 1 I .-+ t;,,. 1-f·;m/111rs . 11ser:, 111u11u,il.certi/i o//<' o( r,·,:is1r.,11io11. Regi,kr Co p) right,. Umt-:d S1;11c-, of' Amcr- ,,r iGt. Rqiistrat iPn '.'<umber Date: TX.u l-69 R-41X 2111005-:!~. 'I. ford.in Tl .. l.;111µl't1rdWM :.ind Hi ll JS. :-\irhorne , LL h,:,:a lc tr:inspml a ircrart resear ch testbed aircraft nwdd Jc, d c•pn11.:nt. In: Pr111 ·el'dings o ( ..1!. rA guida nce , 111n'(!.!1l1ion {(lfd conrrol n1J."/;n· .11n· . S~lll Francis~o. CA. t 5-1 X .-\ugu,t 20115. Amai .:an Institut e of :\ewn ;tutic, and i\,tr ,111,iutic,. R.cst,111.\'A c\l.\:\-2005-6-1:2 W. 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I vcrtiGLl accekratwn roll rate roll-rate dc,ired rcspnnsc angk of atta..:k anglc-nf-attack pilot Cl1TI7m,md ,111gk-,, f-a ttack desired rcsponsl· angk orsiut:slti:, sidcslip-angk ,ksir~d response cleYator deflection command