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1 8 IEEE Systms, Man, & Cybrntics Magazin Octobr X/8 08IEEE

2 Onlin Autotuning of a Srvo Driv Using Wavlt Fuzzy Nural Ntworks to Sarch for th Optimal Bandwidth by Faa-Jng Lin, Shih-Gang Chn, Wi-An Yu, and Hsiao-Ts Chou background: istockphoto.com/kutaytanir Motor: istockphoto/molks To achiv th optimal bandwidth at diffrnt spd commands, an onlin autotuning tchniqu using two two-input, on-output wavlt fuzzy nural ntworks (WFNNs) for intrior prmannt magnt synchronous motor (IPMSM) srvo drivs is proposd in this articl. First, th dynamic prformanc analysis of a fild-orintd control (FOC) IPMSM srvo driv systm is studid. Thn, two two-input, on-output, four-layr WFNNs ar proposd for th onlin autotuning of th gains of a proportional intgral (PI) spd controllr of th srvo motor driv to sarch for th optimal bandwidth without using th information of plant paramtrs and th charactristics of th srvo motor driv. In addition, th ntwork structur and th convrgnc analysis of th WFNNs ar introducd. Finally, xprimntation using th IPMSM srvo driv basd on a floatingpoint digital signal procssor (DSP) is prsntd. Closing in on a Srvo Driv Systm Sinc IPMSMs hav many attractiv charactristics, such as a wid spd-opration rang, high powr dnsity, and larg torqu-to-inrtia ratio, thy hav bn mployd in many industrial applications []. Howvr, ths motors ar also wll known for thir nonlinar machin paramtrs du to magntic saturation, cross-coupling ffcts, and paramtr dpndnc on tmpratur []. Thrfor, high-quality IPMSM srvo drivs ar rquird for highprformanc applications. In addition, th quality of srvo drivs is usually charactrizd by prformanc Digital Obct Idntifir 0.09/MSMC Dat of publication: 7 Octobr 08 paramtrs such as th ris tim, bandwidth, and sampling tim of th controllr. Furthrmor, most srvo motor drivs us a cascadd control structur with an outr position control loop, an intrmdiat spd control loop, and an innr currnt/ torqu control loop. And th prformanc of th outr control loop dpnds on th rspons tim of th currnt control loop. Thrfor, th bandwidth of th currnt control loop must b dsignd to b as high as possibl [3]. In addition, th bandwidth dpnds both on plant paramtrs and th dlay tims, including sampling, pulswidth modulation (PWM), filtr, and calculation [4] [5]. Thrfor, it is vry difficult to quantify th optimal bandwidth of srvo motor drivs in ral applications, and th dsign of an optimal bandwidth of th spd control loop has not bn fully xplord [6]. On th othr hand, th dvlopmnt of autotuning tchniqus for th spd control loop, which usually includs idntification of plant paramtrs, sarching of th optimal bandwidth, and tuning of th spd controllr gains, is ncssary in commrcial srvo motor drivs. Howvr, thr is still no autotuning tchniqu undr dvlopmnt that will sarch for th optimal bandwidth of srvo motor drivs without using th information of plant paramtrs and th charactristics of srvo motor drivs. Th fuzzy nural ntwork (FNN) posssss th charactristic of fuzzy rasoning in handling uncrtain information and th charactristic of artificial nural ntworks in larning from procsss [7]. Morovr, th wavlt nural ntwork (WNN) with rducd ntwork siz has th ability of convrging quickly with high prcision owing to th tim frquncy localization proprtis of wavlts [8]. Bcaus of th aformntiond FNN and WNN Octobr 08 IEEE Systms, Man, & Cybrntics Magazin 9

3 advantags, th WFNN has bn proposd for som advancd applications [9] []. For instanc, a fuzzy wavlt polynomial nural ntwork was proposd to combin th advantags of th polynomial nural ntwork and th WFNN in [] for th applications of tim-sris prdiction and rgrs - sion problms. In this articl, an intllignt onlin autotuning schm for a PI spd controllr using two WFNNs is proposd to sarch th optimal bandwidth without using th information of plant paramtrs and th charactristics of th srvo motor drivs. Th nvisagd WFNN, which has two inputs and on output, uss th first drivativ of a Gaussian function as its mmbrship function. In ad dition, an IPMSM srvo driv systm using a 3-b floating-point DSP, TMS30F8075, is dvlopd. From xpri mntation, it was found that th proposd intllignt control approach can guarant th optimal bandwidth at diffrnt spd commands. Transfr Function of th IPMSM Srvo Driv An FOC IPMSM srvo driv, including spd control loop, currnt rgulators, voltag dcoupling, and coordinat transformation, is shown in Figur. In this figur, i a, i b, and i c rprsnt th thr phas currnts; v d and v q rprsnt th d axis and q axis stator voltags; i d and i q rprsnt th d axis and q axis stator currnts; ~ rm rprsnts th mchanical rotor spd; P dnots th numbr of pol pairs; v a and v b rprsnt th voltag componnts of th IPMSM in th stationary fram; i a and i b rprsnt th currnt componnts of th IPMSM in th stationary fram; th suprscript * rprsnts th rfrnc valu; and t () is th spd-tracking rror. Sinc th magntic flux m m gnratd from th prmannt magnt of th rotor is fixd in rlation to th rotor shaft position i rm, th flux position i r can b dtrmind by th shaft-position snsor. Using th FOC mchanism, with id 0, th lctromagntic torqu T is proportional to i q [3]. In addition, two WFNNs ar proposd to tun th PI spd controllr onlin, whr th inputs of th WFNN ar th spd-tracking rror and its drivativ. Th outputs T K P and T K I ar th onlin incrmntal valus of th proportional and intgral gains, rspctivly. Th spd control modl of th IPMSM srvo driv systm is shown in Figur (a). Th quation of th PI controllr in th tim domain is * iq KPt () KI # () t dt, () From xprimntation, it was found that th proposd intllignt control approach can guarant th optimal bandwidth at diffrnt spd commands. whr K P and K I ar th proportional and intgral gains, rspctivly. By using th Laplac trans form, th transfr function of th PI controllr is shown as ts i G() s K P ts, i () whr t i K P / K I. To dsign th spd controllr using pol-zro cancllation, all of th dlay tims of th spd control loop ar combind into an ffctiv dlay tim t R D as follows [5]: tr D tid tfd tsd, (3) whr t ID is th dlay tim of th currnt control loop TI (), s t FD is th first-ordr dlay of th spd filtr, and t SD is th dlay tim owing to th calculation of th spd control loop. Thn, th spd control modl of th IPMSM driv systm can b simplifid to Figur (b). Morovr, th modl of th invrtr usd in th motor srvo driv can b simplifid and rprsntd by a first-ordr systm with a gain and a phas dlay [5] as KT G() s t s, RD whr K T is a torqu constant. In addition, th controlld plant of th motor driv systm can b rprsntd as Kq G3() s Js B ts, q (5) whr J is th inrtia constant, B is th damping cofficint, Kq / B, and tq J/ B. Th opn-loop transfr function of th systm is Gs () G() s G() s G3() s ts i KT Kq K P a ts k $ t s $ i RD ts q KPKTKq( tis ) ts( t s )( ts ). i RD q Th PI controllr of th spd control loop is dsignd by using pol-zro cancllation, i.., ti tq. Thn, th closdloop transfr function of th spd control can b rprsntd as KPKTKq Gc() s ts( tr s ) KPK K KPKTKq tt i RDs tis KPKK T q Ωn, s pωns Ωn i D T q whr th undampd natural frquncy is dnotd by Ωn KPKTKq/ titrd KIKK T q/ tr D and also p ti/ 4KPKKt T q RD / 4KIKKt T q R D. Th rsulting closdloop transfr function is a standard scond-ordr transfr function. (4) (6) (7) 30 IEEE Systms, Man, & Cybrntics Magazin Octobr 08

4 0-V ac ω rm ω rm K P K I S i q i d 0 Currnt Rgulators and Voltag Dcoupling v d v q dq αβ v α v β SVPWM Switching Signals PWM VSI 3 V K P, K I θ r i q i d αβ dq i α i β abc αβ i a i b i c P d dt θ rm Encodr IPMSM Torqu Mtr ė Two WFNN WFNNs K I K P Gar Rducr Magntic Powdr Brak Figur. A block diagram of an IPMSM srvo driv systm. VSI: voltag sourc invrtr; SVPWM: spac vctor PWM. ω rm K P K I s st SD T I (s) K T T L J s B ω rm st FD (a) T L ω rm K P K I s K T t ΣD s J s B G (s) G (s) G 3 (s) ω rm (b) Figur. A schmatic modl of an IPMSM srvo driv systm: a (a) spd control loop and (b) simplifid spd control loop. Octobr 08 IEEE Systms, Man, & Cybrntics Magazin 3

5 Dynamic Prformanc Analysis of th IPMSM Srvo Driv Systm According to (7), th closd-loop frquncy charactristic of th motor srvo driv is xprssd in th following: ~ rm ^ Xh Gc ^ Xh ) ~ rm ^ Xh Xn ^ Xh pxn ^ Xh X zb^xh MB ^Xh n Th cutoff frquncy Ω b is dfind as follows: 7- _ Ωb ΩniA 7p_ Ωb ΩniA, Thn, on can obtain th following rlationship among Ω b, Ω n, and p: (8) (9) 4 Ωb Ωn - p - 4p 4p. (0) Sinc th undampd natural frquncy Ω n is proportional to K I, from (0), th cutoff frquncy Ω b is also proportional to K I. That is to say, incrasing K I rsults in a ris in th cutoff frquncy Ω b. On th othr hand, th ffct of p can b ignord owing to its valu bing smallr than on. A Two-Input, Two-Output WFNN A four-layr WFNN with two inputs and on output, which uss th first drivativ of a Gaussian function as its mmbrship function, is shown in Figur 3. Th proposd WFNN compriss an input (th i layr), a mmbrship (th layr), a rul (th k layr), and an output (th o layr). y (k) In th input layr, th nod input and th nod output ar rprsntd as nt i( N) x, y i i f ( nt i i( N)) nt i( N), i,, () whr x i and y i dnot th input and output of th ith nod in this layr, N rprsnts th Nth itration, and x and x dnot th tracking rror and its drivativ o. Morovr, in th mmbrship layr, ach nod prforms a wavlt from its mothr wavlt. Th nod input and th nod output ar dnotd as xi - a nt( N) b, () y( N) hnt ( ( N)),,, 3, (3) hx ( ) - xxp(. 05x ), (4) whr a and b dnot th paramtrs of translation and dilation of th associatd wavlt mmbrship function, and x i and y ar th input and output of th th nod of th ith input. By proprly choosing th paramtrs in th first drivativ of th Gaussian function, it posssss th univrsal approximation proprty [4]. Furthrmor, in th rul layr, ach nod k is dnotd by P, which multiplis th input signals and outputs th rsult of th product. For th kth rul nod, % ntk( N) ~ kx( N) yk( N) f k 3^ntk( N) h ntk( N), k,..., 9, (5) 3 whr x rprsnts th th input to th nod of layr 3, 3 ~ k rprsnts th connctd wights btwn th mmbrship layr and th rul layr and is assumd to b unity, and k is th numbr of ruls with complt rul connction if ach input nod has th sam linguistic variabls. In addition, in th output layr, th nod input and th nod output ar dnotd as ω 4 kl Output Layr o nto( N) ~ koxk, yo( N) fo 4^nto( N) h nto( N), o, k (6) Π Π Π Π Π Π Π Π Π ω k 3 Figur 3. A WFNN with th first drivativ of a Gaussian mmbrship function.. Rul Layr k Mmbrship Layr Input Layr i 4 whr x k rprsnts th kth input to th nod of layr 4, 4 and th connctd wight ~ ko rprsnts th output action strngth of th oth output associatd with th kth rul. In this study, th suprvisd gradint dcnt tchniqu is adoptd to driv th onlin algorithm of th WFNN. An rror function E is dfind as * E ( ~ rm - ~ rm). (7) In th proposd WFNN, th connctd wights of th output layr and th translation and dilation of th wavlt mmbrship functions ar traind onlin. Th dtaild drivation of th onlin larning algorithms basd on th 3 IEEE Systms, Man, & Cybrntics Magazin Octobr 08

6 back-propagation mthod is similar to [9] and is omittd in this study. In addition, th onlin larning algorithms using varid larning-rat paramtrs can guarant th convrgnc of th tracking rror by using th convrgnc analysis of a discrt-typ Lyapunov function. In th convrgnc analysis, th nrgy function E shown in (7) is rprsntd as a discrt-typ Lyapunov function. Th rsulting larning-rat paramtr of th connctd wights of th output layr h ~ is EN ( ) h~, EN ( ) y() k 4< c 4 m 0 y() k f F ~ k k (8) whr f 0 is a positiv constant. Additionally, th rsultd larning-rat paramtrs of th translation and dilation of th wavlt mmbrship function h a and h b ar as follows: ha 4< hb 4< EN ( ) EN ( ) y() k nt d y() k nt a EN ( ) EN ( ) y() k nt d y() k nt b, n f0f. n f0f (9) Dsign and Exprimntation Th spcifications of th IPMSM ar thr-phas 945 W 6.87 A.5 N m 4,000 r/min. Th insulatd-gat bipolar transistor voltag sourc invrtr with a switching frquncy of 0 khz is controlld by using SVPWM tchnology through th voltag vctors v * a Tabl. Th paramtrs of th IPMSM srvo driv. Itms Quantitis Itms Quantitis B 0.06 N m/(rad/s) KT N m/a Kq 8.4 (rad/s)/n m tq 0.05 s J N m/(rad/s ) trd 0.00 s and v * b, as shown in Figur. Morovr, th tst platform of th IPMSM srvo driv systm compriss a torqu mtr, gar rducr, and magntic powdr brak. In addition, th implmntation of th control algorithms for th IPMSM srvo driv systm is basd on a TMS30F b floating-point DSP with 0 MHz. Th nominal valu of th gains of th spd controllr using th paramtrs of th IPMSM srvo driv systm, which ar shown in Tabl, via th pol-zro cancllation tchniqu ar K P 0. and KI. Th simulation cutoff frquncy Ω b of th spd control loop of th IPMSM srvo driv systm is. Hz, as shown in Figur 4(a). Th xprimntal frquncy rspons of th spd control loop of th IPMSM srvo driv systm is shown in Figur 4(b), with th cutoff frquncy Ω b of 0.4 Hz, which is obtaind by using an Agilnt A dynamic signal analyzr. Owing to th uncrtaintis, including th damping of th IPMSM srvo driv, th bandwidth of th xprimntal frquncy rspons is smallr than th simulation frquncy rspons. Sinc using th proposd WFNNs to tun th gains of th PI spd controllr onlin maks th polzro cancllation fail, th closd-loop transfr function cannot b rprsntd as a standard scond-ordr transfr function. Thus, a third-ordr transfr function, Magnitud (db) Phas ( ) Magnitud (db) 0.4 Hz. Hz Hz Frquncy 0,000 Hz Hz Frquncy 00 Hz (a) (b) Figur 4. Th tst rsults of a nominal dsignd IPMSM srvo driv systm: th (a) simulation frquncy rspons and (b) xprimntal frquncy rspons. Octobr 08 IEEE Systms, Man, & Cybrntics Magazin 33

7 considring th paramtrs of th IPMSM srvo driv, rsults as follows: Gc() s KPKTKts q i KPKK T q 3 ttt i q RDs ti( TRD tq) s ti( KPKK T q ) s KPKK T q K P 7. K s 7. K P I. K K s K K s ( 7. K K K P 3 P P P K ) s 7. K P I I I I (0) In th xprimntation, th sampling rats ar 0. ms for th currnt control loop and ms for th spd control loop. Th xcution or comput tim of th C program in th TMS30F b floatingpoint DSP can b obtaind by th clock tool of th Txas Instrumnts Cod Composr Studio vrsion 5 program diting intrfac. Th total opration cycls and total xcution tim for th WFNNs and FOC ar,670 and 0.05 ms, rspctivly. As a rsult, th total xcution tim of th proposd onlin autotuning tchniqus using WFNNs is still lss than ms, which is th sampling intrval of th spd control loop. Morovr, th sarching mchanism for th proposd onlin autotuning tchniqu using WFNNs is basd on th ris tim of diffrnt spd commands. According to th diffrnt ris tims of 0.4, 0.3, and 0. s, a largr tracking rror and its drivativ will rsult in largr incrmntal valus of K P and K I. And th undampd natural frquncy Ω n will incras accordingly. Furthrmor, according to (0), Ω n is th main factor that is rlatd to th 3-dB bandwidth. Thrfor, th bandwidth of th spd control loop will b incrasd accordingly to achiv th optimal bandwidth for diffrnt ris tims and to avoid ovrdsign of th bandwidth. In addition, in this study, th dlay tims of th currnt control loop, spd filtr, and spd control loop ar dsignd to b 0.000, 0.00, and 0.00 s, rspctivly. All of th dlay tims of th spd control loop can b combind into an ffctiv dlay tim t R D, as shown in (3) and Tabl. Additionally, th paramtrs of th PI currnt controllrs ar tund by trial and rror to achiv th bst transint and stady-stat control prformanc, considring th stability rquirmnt. Th chosn paramtrs of th PI currnt controllrs ar Ki P 9 and Ki I, 000, whr K i P and K i I rprsnt th proportional and intgral gains of th PI currnt controllrs, rspctivly. Using th outputs of a standard scond-ordr transfr function with ris tims of 0.4, 0.3, and 0. s as thr conscutiv spd commands from,000 to 3,000 r/min at a no-load condition, th spd rsponss of th IPMSM srvo driv systm ar shown in Figur 5(a). Th currnt command i * q and spd-tracking rror ar shown in Figur 5(b). Th outputs of th WFNNs T K P and T K I and th rsulting PI spd controllr gains ar shown in Figur 5(c). Furthrmor, th simulation frquncy rsponss of th spd control loop of th IPMSM srvo driv systm ar shown in Figur 5(d) (f) and ar obtaind by using (0) with th stady-stat gains of th PI spd controllr at th rspctiv spd command. In addition, th xprimntal frquncy rsponss of th spd control loop of th IPMSM srvo driv systm ar shown in Figurs 5(g) (i) and ar also obtaind by using an Agilnt A dynamic signal analyzr with th stady-stat gains of th PI spd controllr at th rspctiv spd command. From th simulation frquncy rsponss shown in Figur 5(d) (f), th cutoff frquncis Ω b ar 3., 6.8, and 9.7 Hz, rspctivly. Additionally, from th xprimntation frquncy r - sponss shown in Figur 5(g) (i), th cutoff frquncis Ω b ar 0.9, 4.3, and 8.3 Hz, rspctivly. Thrfor, th proposd onlin autotuning tchniqus us ing WFNNs can achiv th optimal bandwidth for th IPMSM srvo driv according to th ris tim of diffrnt spd commands. Using th outputs of a standard scond-ordr transfr function with ris tims of 0.4, 0.3, and 0. s as thr conscutiv spd commands from,000 to 3,000 r/min at a -N m load condition, th spd rsponss of th IPMSM srvo driv systm ar shown in Figur 6(a), th spdtracking rror and currnt command i * q ar dtaild in Th proposd onlin autotuning tchniqus using WFNNs can achiv th optimal bandwidth for th IPMSM srvo driv according to th ris tim of diffrnt spd commands at diffrnt load conditions. Figur 6(b), and th outputs of th WFNNs T K P and T K I and th rsulting PI spd controllr gains ar shown in Figur 6(c). Compard with th stady-stat gains of th PI spd controllr at a no-load condition, th gains ar incrasd for th -N m load condition to achiv th sam ris tim. Furthrmor, th simulation frquncy rsponss of th spd control loop of th IPMSM srvo driv systm ar includd in Figur 6(d) (f) and ar obtaind by using (0) with th stady-stat gains of th PI spd controllr at th rspctiv spd command. In addition, th xprimntal frquncy rsponss of th spd control loop of th IPMSM srvo driv systm ar shown in Figur 6(g) (i), with th stady-stat gains of 34 IEEE Systms, Man, & Cybrntics Magazin Octobr 08

8 ω rm 3,000 r/min ω rm,997 r/min K I 0 5 s 0.005/0.005// t r 0.4 s t r 0.3 s t r 0. s ω rm,000 r/min 5 s 0 A i q.8 A K P 0 K I.034 K I.077 K I.9 0 r/min K I K 500 r/min P 0.3 K P 0.77 K P s 4 A /300 r/min K P (a) (b) (c) Phas ( ) Magnitud (db) 3. Hz Hz Frquncy 0,000 Hz (d) () (f) Magnitud (db) Phas ( ) Magnitud (db) Magnitud (db) 6.8 Hz Hz Frquncy 0,000 Hz 9.7 Hz Phas ( ) Hz Frquncy 0,000 Hz 0.9 Hz 4.3 Hz 8.3 Hz Magnitud (db) Magnitud (db) Hz Frquncy 00 Hz Hz Frquncy 00 Hz (g) (h) (i) Hz Frquncy 00 Hz Figur 5. Th tst rsults of th onlin autotuning of a PI spd controllr of an IPMSM srvo driv systm at no load: th (a) spd rspons at conscutiv spd commands, (b) currnt command and tracking rror, (c) outputs of th WFNNs and th rsulting PI spd controllr gains, (d) simulation frquncy rspons at a ris tim of 0.4 s, () simulation frquncy rspons at a ris tim of 0.3 s, (f) simulation frquncy rspons at a ris tim of 0. s, (g) xprimntal frquncy rspons at a ris tim of 0.4 s, (h) xprimntal frquncy rspons at a ris tim of 0.3 s, and (i) xprimntal frquncy rspons at a ris tim of 0. s. I/O: input-output. Octobr 08 IEEE Systms, Man, & Cybrntics Magazin 35

9 ω rm 3,000 r/min ω rm,995 r/min K I 0 5 s 0.005/0.005// t r 0.4 s t r 0.3 s t r 0. s ω rm,000 r/min 0 A i q 3.98 A K P 0 5 s K I.0 K I.09 K I.6 0 r/min K I K 500 r/min 5 s P 0.3 K P 0.9 K P A /300 r/min K P (a) (b) (c) Phas ( ) Magnitud (db) 4.4 Hz Hz Frquncy 0,000 Hz (d) () (f) Magnitud (db) Phas ( ) Magnitud (db) Magnitud (db) 7.6 Hz Hz Frquncy 0,000 Hz 3.7 Hz Phas ( ) Hz Frquncy 0,000 Hz.4 Hz 5.8 Hz 30.8 Hz Magnitud (db) Magnitud (db) Hz Frquncy 00 Hz Hz Frquncy 00 Hz (g) (h) (i) Hz Frquncy 00 Hz Figur 6. Th tst rsults of th onlin autotuning of a PI spd controllr of an IPMSM srvo driv systm at a -N m load: th (a) spd rspons at conscutiv spd commands, (b) currnt command and tracking rror, (c) outputs of th WFNNs and th rsulting PI spd controllr gains, (d) simulation frquncy rspons at a ris tim of 0.4 s, () simulation frquncy rspons at a ris tim of 0.3 s, (f) simulation frquncy rspons at a ris tim of 0. s, (g) xprimntal frquncy rspons at a ris tim of 0.4 s, (h) xprimntal frquncy rspons at a ris tim of 0.3 s, and (i) xprimntal frquncy rspons at a ris tim of 0. s. 36 IEEE Systms, Man, & Cybrntics Magazin Octobr 08

10 th PI spd controllr at th rspctiv spd command. From th simulation frquncy rsponss in Figur 6(d) (f), th cutoff frquncis Ω b ar 4.4, 7.6, and 3.7 Hz, rspctivly. Additionally, from th xprimntation frquncy rsponss displayd in Figur 6(g) (i), th cutoff frquncis Ω b ar.4, 5.8, and 30.8 Hz, rspctivly, which shows that th proposd onlin autotuning tchniqus using WFNNs can achiv th optimal bandwidth for th IPMSM srvo driv according to th ris tim of diffrnt spd com - mands at diffrnt load conditions. Conclusion An intllignt autotuning schm for th PI spd controllr using two two-input, on-output, four-layr WFNNs was succssfully dvlopd and implmntd in this study to achiv th optimal bandwidth of an FOC IPMSM srvo driv. Th proposd intllignt autotuning schm was dvlopd to sarch th optimal bandwidth of srvo motor drivs without using th information of plant paramtrs and th charactristics of srvo motor drivs. From th xprimntal rsults, th gains of th PI spd controllr of th IPMSM srvo driv wr tund automatically to achiv th rquird optimal bandwidth according to th ris tim of diffrnt spd commands at diffrnt load conditions. Acknowldgmnt This work was supportd by th National Scinc Council, Taiwan, through grant MOST 04--E MY3. About th Authors Faa-Jng Lin (linf@.ncu.du.tw) arnd his B.S. and M.S. dgrs in lctrical nginring from th National Chng Kung Univrsity, Tainan, Taiwan, and his Ph.D. dgr in lctrical nginring from th National Tsing Hua Univrsity, Hsinchu City, Taiwan, in 983, 985, and 993, rspctivly. Currntly, h is th chair profssor in th Dpartmnt of Elctrical Enginring at th National Cntral Univrsity, Taoyuan, Taiwan. H is an Institution of Enginring and Tchnology fllow, and h is a Fllow of th IEEE. Shih-Gang Chn (csg388@gmail.com) arnd his B.S. dgr in lctrical nginring from Yuan Z Univrsity, Taoyuan, Taiwan. H arnd his M.S. dgr in lctrical nginring from th National Cntral Univrsity, Taoyuan, Taiwan, in 06 and is currntly working toward his Ph.D. dgr. Wi-An Yu (yusky53@gmail.com) arnd his B.S. dgr in lctrical nginring from th National Taiwan Ocan Univrsity, Klung, Taiwan. H is currntly working toward his M.S. dgr in lctrical nginring at th Th gains of th PI spd controllr of th IPMSM srvo driv wr tund automatically to achiv th rquird optimal bandwidth. National Cntral Univrsity, Taoyuan, Taiwan. Hsiao-Ts Chou (cht674@ gmail.com) arnd his B.S. dgr in lctrical nginring from th National Chin-Yi Univrsity of Tchnology, Taichung, Taiwan. H is currntly working toward his M.S. dgr in lctrical nginring at th National Cntral Univrsity, Taoyuan, Taiwan. Rfrncs [] J. Lmmns, P. Vanassch, and J. Drisn, PMSM driv currnt and voltag limiting as a constraint optimal control problm, IEEE J. Emrg. 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