1 INTRODUCTION. Enhanced Model Reference Fuzzy Logic Controller for High Performance Induction Motor Drive

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1 Enhand Mod Rfrn Fuzzy Logi Contror for High Prforman Indution Motor Driv. E Dssouky, M. Tarbouhi and D. Bouhard Roya Miitary og of Canada, Etria and Computr Enginring Dpartmnt, Canada Kywords: daptiv fuzzy ontro, Fuzzy Mod Rfrn Larning Contro, indution motor ontro. bstrat: This papr prsnts an nhand thniqu for th adaptation mhanism of Fuzzy Mod Rfrn Larning Contro (FMRLC). th authors proposd a modifiation to th movmnt of th auto-attntiv ara. Th modifiation nhans th transint rspons. Howvr, it was sti unsatisfatory spiay if th input saing fators wr std vry arg. Th sow transint rspons is du to th hattring fft found in th ontro ffort. In this papr, th rsuts of appying th xprin mod to th nhand FMRLC, th ontror was ab to rdu th hattring fft in th ontro ffort, and hn in th transint rspons of th ontro systm. Simuations ar arrid out using an indution motor to vrify th proposd agorithm s prforman. ITRODUCTIO Sf Organizing Fuzzy Contror (SOFC), prsntd in [5], rdus th fuzzy ontror dsign dpndny on xprt knowdg and provids onin adaptation of th ontror paramtrs to ompnsat for pross paramtr variation. Th agorithm adapts th noninar ontro surfa idntifid by th ru bas of th fuzzy ontror, by modifying th ntrs of th output mmbrship funtions Passino t a. proposd an adaptation mhanism [,3,4,6] simiar to SOFC, but, thy mbddd a rfrn mod that dsribs th dsird prforman. Passino agorithm was rfrrd to as Fuzzy Mod Rfrn Larning Contro (FMRLC). Longya t a. appid FMRLC agorithm to an indution motor in a spd ontro oop [7]. Th ontror provd high torqu rjtion apabiity and its potntia to ompnsat for paramtr variations. Morovr, in [7], th authors has prsntd a omparativ study btwn FMRLC, dirt fuzzy ontror, and on-in fuzzy tuning shm. Th rsuts show outstanding prforman for th FMRLC. Passino t a. [6] proposd on ky modifiation to th FMRLC to inras th systm auray without inrasing th omputationa burdn. Th modifiation produs a FMRLC agorithm with th abiity to fous th attntion to th ara that is urrnty of intrst (th ara that has ativ adaptation) and shifts this ara as th attntion movs to othr aras. Th trm uto-ttntiv approah was addd to th FMRLC to dsrib this nw agorithm. Th rsuts showd that th proposd modifiation sudd in traking a trajtory omposd of two sinusoida wavs with diffrnt frqunis. Th authors proposd a modifiation to th movmnt of th auto-attntiv ara. Th modifiation nhans th transint rspons. Howvr, it was sti unsatisfatory spiay if th input saing fators wr std vry arg. Th sow transint rspons is du to th hattring fft found in th ontro ffort. In this papr, th rsuts of appying th xprin mod to th nhand FMRLsing auto-attntiv thniqu ar introdud. Th papr introdus nw modifiations to nhan th auto-attntiv mhanism. Th modifiation aows th auto-attntiv ativ rgion to shift fastr to th ara that is urrnty of intrst. This woud arat th arning pross and nhan th transint ontro ation. In addition, th papr introdus a nw agorithm to updat th rus in th unxpord ara of th univrs of disours whn th auto-attntiv rgion movs. Th papr is organizd as foows: In stion II th auto-attntiv approah is disussd. Stion III is dvotd to th dsription of th proposd modifiation to th movmnt of th auto-attntiv ara. Stion IV th simuation rsuts of th proposd agorithm and th

2 Enhand Mod Rfrn Fuzzy Logi Contror for High Prforman Indution Motor Driv onvntiona on using indution motor spd ontro driv, ar prsntd UTO-TTETIVE MECHISM Th auto-attntiv mhanism for FMRLC aows th ntrs of th input mmbrship funtions to b shiftd on-in. Considr a fuzzy ontror with two inputs givn by: ( = r( y( (-a) ( ( k ) ( = (-b) T hits th bordrs of th auto-attntiv ativ rgion, th auto-attntiv ativ rgion wi mov on stp in th dirtion of th movmnt of th ativ arning rgion. This shift is mad by moving th ntrs of th input mmbrship funtions on stp towards th sgmnt of th input dynami rang that is urrnty of intrst. Th ntrs of th mmbrship funtions for ah input ar givn by: C ( = C ( k ) + K ( w (4-a) i i * C ( = C ( k ) + K ( w (4-b) j j * has th foowing vau: ( rprsnts th rror btwn th st point ( r ( ) and th output of th pross ( y( ), K ( = if min( µ, µ ) > j (5-a) ( rprsnts Th hang rat of (, T is th K ( = if min( µ, µ ) > (5-b) j samping tim and k is th urrnt samp indx In addition, onsidr + mmbrship funtions for K ( = othrwis ah input. ssuming a uniform distribution of th mmbrship funtions in th intrva [-,], th µ width of ah mmbrship funtion is givn by: and µ ar th mmbrship vaus w = of th far right and ft mmbrship funtions for th () input rsptivy. µ is th mmbrship vau j Thn th ntr of ah mmbrship funtions is of th j mmbrship funtion for th nd input givn by: ( j =, +,,,, ). Simiary Ci = Ci + w () K is givn by: K Ci is th ntr of th i = if min( µ, µ ) > (5-a) i mmbrship funtion of th st input (), K = if min( µ, µ ) > (5-b) i i = +, +,,,, and C =. Simiary, th ntrs of th K mmbrship funtions for th nd = othrwis (5-) input () ar givn Th ntrs of th output mmbrship funtions ar by: givn by: u u C ( = C ( k ) + p * µ (6) C j = C j + w (3) p is th adaptation fator (F) (th output of th invrs mod sad by th adaptation gain j = +, +,,,,. g p, µ is th mmbrship vau of th prmis of For FMRLC th mmbrship funtions ovr th th dynami rang of ah input by using th inputsaing fators (input saing fators ar usd to µ = min( µ, µ ) (7) th ru and is givn by: j k sa th inputs to th rang [-,]). Howvr, for th auto-attntiv stratgy, th input mmbrship and = ( i + + ) + ( j + ) *( + ), hn, funtions ovr ony a part of th dynami rang. If th ativ arning rgion (th urrnty fird rus) =,,3, R R rprsnts th tota numbr of rus in th ru-bas ( R = ( + ) ). K

3 Enhand Mod Rfrn Fuzzy Logi Contror for High Prforman Indution Motor Driv 3 In addition to th adaptation of th ntrs of th output mmbrship funtions givn by quation (6), ths ntrs ar aowd to b rst if th autoattntiv rgion movs (i.. ( or/and K ) as foows: K ( = (8) = ( K ( * + + ) + ( j + ) *( + ) if ( (9) K = ( i + + ) + ( K * + ) *( + ) if ( () K and th othr ntrs of th output mmbrship funtion ar givn by: ( k ) = ( k ) () n n n = ( i * + + ) + ( j + ) *( + ), i = +, +,,,, and j =, +,,,, if K ( and i =, +,,,, and j = +, +, L,,,, if K (. Equation (8) indiats that th ntrs of th output mmbrship funtion at th unxpord ara ar st to zro rfting no information about th ontro surfa in this ara. Equation () shows how th rmaining ntrs of th output mmbrship funtions ar shiftd toward th ara that is urrnty of intrst. This agorithm has thr disadvantags that afft th transint prforman of th systm: () Th movmnt of th auto-attntiv ativ ara is sow (sing stp/samp); () Th agorithm wi not b ab to buid nough stab ontro ation to math th transint prforman of th rfrn mod. (3) Th systm is not ab to mmoriz th ovra ontro surfa. Th foowing stion proposs a possib soution to th first disadvantag. 3 EHCED UTO-TTETIVE PPROCH s dsribd in stion II, th auto attntiv ativ ara movs a stp of width ( K and K w hav vaus of,,) in th dirtion of th movmnt of th ativ arning rgion whn th ativ arning rgion hits th boundaris of th auto-attntiv ara. In th as th ara that is urrnty of intrst is too far from th ativ arning rgion, th movmnt mhanism wi b vry sow. s an xamp, assum th auto-attntiv ativ rgion ovrs just % of th dynami rang of two inputs with mmbrship funtions for ah input. In this as, if th auto-attntiv rgion is at th ft dg of dynami rang, and th ara that is urrnty of intrst is at th right dg, thn it woud tak samps from th ontror to mov th auto-attntiv rgion to th ara of intrst. Th proposd modifiation is to shift th ntrs of th input mmbrship funtions simiar to quation (4) but with K and K auatd as foow: K ( = if min( µ, ) > (-a) C µ j K ( = C ifmin( µ, µ ) > (-b) K ( = if min( µ, µ ) > (3-a) C K ( = C if min( µ, µ ) > (3-b) i i j and th ntrs of th output mmbrship funtions ar givn by: ( = (4) for =,,3, R R is th tota numbr of rus at th ru-bas if K > or K > and is idntia to quations () and () if K or K < and th othr ntrs of th < output mmbrship funtions wi b shiftd as foows: ( k ) = ( k ) if K < or K < (5) n n n = ( i * + + ) + ( j + ) *( + ), i = + K, + K +,,,, and j =, +,,,, if ( and i =, +, L,,,, and K j = + K, + K +, L,,,, L if K (., Equation (4) indiats that if th stp width is argr than th ntir auto-attntiv ara th who ntrs wi b rst to zros. In th as th stp width is ss than th auto-attntiv rgion thn just th part that is movd to th unxpord ara wi b rst and th othr part wi b shiftd to th ara that is urrnty of intrst

4 4 Enhand Mod Rfrn Fuzzy Logi Contror for High Prforman Indution Motor Driv 4 SIMULTIOS Th indution motor mod usd for th simuation is givn in [7]. Th paramtrs of th mod ar givn in Tab (). Dsription Vau Units Ratd Powr.5 Hp Ratd urrnt.3 Ratd spd rpm Ratd in votag 8 V Stator indutan H Rotor indutan H Mutua indutan.3784 H Stator rsistan Ω Rotor rsistan Ω Momnt of inrtia.4398 kg-m visous damping m-s onstant umbr of po pairs Tab () Indution motor paramtrs To xamin th prforman of th autoattntiv approah and th nhand on, and to study th advantags and th drawbaks of suh agorithms th input saing fators wr st to high vaus (th auto-attntiv ara ovrs.% of th dynami rang of th inputs). Figurs () and () show th systm rspons whn using th onvntiona auto-attntiv approah and nhand approah rsptivy. It an b notd that both of thm hav vry poor transint prforman. Howvr, th attr is signifianty bttr than th formr. ot that nithr agorithm is ab to buid suffiint urrnt at th transint to math th transint prforman of th rfrn mod known that it is rahab prforman by th indution mahin. This is baus of th adaptation mhanism as indiatd bfor. Th F urvs in both figurs ar high. F urv shows that dspit of th high adaptation ffort th ontro mhanism is not ab to ahiv th dsird prforman. Figurs (3) and (4) show th rspons of th autoattntiv approah with an xprin mod using th onvntiona and nhand mhanisms rsptivy. In both ass th xprin mod ru-bas was buit using avrag knowdg about th indution motor. Th transint prformans hav bn improvd signifianty omparativy to th ontror without an xprin mod. This improvmnt is du to th abiity of th mhanism (in both ass) to oad nar-optima ontro ation from th xprin mod to th auto-attntiv ara as it movs. Hn, th adaptation mhanism starts to updat th rus at th auto-attntiv ara and updat th information savd in th xprin mod at th sam tim using th arning mhanism of th xprin mod. ot that th F urvs in both figurs hav ss vau than in figurs () and () whih indiat ss adaptation ffort and high prforman mhanism. Figurs (3) and (4) indiat that th two agorithms hav suprior rjtion of th variation of th torqu oad (not th prforman at th transint bfor and aftr th torqu oad variation). In th as of th nhand auto-attntiv agorithm th auto-attntiv ara gos dirty to th ara that is urrnty of intrst and oads a th rus at th ru-bas with vaus from th xprin mod. If th vaus ar not optima it nds mor tim to adapt thm. For th onvntiona agorithm, th sow movmnt aows for bttr rspons to suh situation. Howvr, Th arning pross of th xprin mod in th nhand agorithm is mor ffiint it dirty targt th dsignatd ara of th ontro surfa. On othr hand, th arning mhanism of th xprin mod in th onvntiona agorithm is targting othr aras in th first fw samps, whih may dstroy th otd information in th xprin mod in arir training phass. To prov that th nhand agorithm has bttr arning apabiity, stp squns wr appid to both agorithms for ongr durations with no variation in th torqu oad to aow for training. Figurs (5) and (6) show th rspons of th two agorithms aftr sonds of training. It an b notd that th nhand agorithm has bttr arning and transint prforman than th onvntiona on (s rror urvs). Tab () shows a omparison of diffrnt ontro agorithms to th prforman of th systm using som prforman masurmnt fators. Th prforman fators that usd in this work ar th intgra absout rror (IE), th intgra squar rror (ISE), th intgra mutip tim absout rror (ITE).

5 Enhand Mod Rfrn Fuzzy Logi Contror for High Prforman Indution Motor Driv 5 5 REFERECES [] L.. Zadah, Fuzzy sts, Iform. Contr., Vo. 8, 965, pp [] Passino K. M., Stphn Yurkovih Fuzzy Contro ddison-wsy, 998. [3] Layn J. and Passino K., "Fuzzy mod rfrn arning ontro" In Pro. st IEEE Confrn Contro ppiations, Dayton, OH, May/Jun 995, pp [4] Layn, J., Passino K. M Fuzzy Mod Rfrn Larning Contro for Cargo Ship String IEEE Contro Syst. Mag., Vo. 3, o. 6, D. 993, pp [5] Proyk TJ., Mamdani EH. Linguisti Sf- Organizing Pross Contror utomatia, Vo. 5, 979, pp [6] Kwong W.., Passino K. M. Dynamiay Fousd Fuzzy Larning Contro IEEE Transation,.O 6.on Systms, Man and Cybrntis B, Vo pp,996 [7] Li Zhn, Longya Xu Fuzzy Larning Enhand Spd Contro of an Indirt Fid- Orintd Indution Mahin Driv IEEE Transation on Contro Systms Thnoogy, Vo. 8, o., Marh, pp spd (rpm) y (rpm) - - i q () - - Load variation yrf(t) spd (rpm) y (rpm) spd (rpm) y (rpm) - - i q () - - F yrf(t) Tim (s) - Load variation Tim (s) Figur () stp rspons (nhand auto-attntiv approah with arg input saing fators) - - i q () - - F oad variation yrf(t) Tim (s) Figur (3) Contro systm rspons using autoattntiv approah with xprin mod F Tim (s) Figur () stp rspons (onvntiona auto-attntiv approah with arg input saing fators.

6 6 Enhand Mod Rfrn Fuzzy Logi Contror for High Prforman Indution Motor Driv spd (rpm) - oad variation yrf(t) spd (rpm) - yrf(t) - i q () - - y (rpm) F Tim (s) Figur (4) Contro systm rspons using nhand auto-attntiv approah with xprin mod spd (rpm) - - iq() y (rpm) - - F yrf(t) Tim(s) Figur (5) Contro systm rspons aftr s of training using onvntiona auto-attntiv approah with xprin mod - i q () y (rpm) - - F Tim (s) Figur (6) Contro systm rspons aftr s of training using nhand auto-attntiv approah with xprin mod gorithms IE*+3 ISE*+3 ITE*+3 uto ttntiv approah Enhand auto-attntiv approah utoattntiv approah with xprin mod aftr training Enhand uto-attntiv approah with xprin mod aftr training Tab () Prforman omparison of diffrnt ontro agorithms (simuation rsuts)