Fuzzy Adaptive Model Following Speed Control for Vector Controlled Permanent Magnet Synchronous Motor

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1 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Fuzzy Aatv Mol Followng S Control for Vctor Controll Prannt Magnt Synchronous Motor Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES Intllgnt Control & Elctrcal Powr Systs aboratory (ICEPS). Faculty of ngnr scncs. Dartnt of lctrcal ngnrng, Djllal abs Unvrsty, S Bl Abbs, Algra E-al: aroufl@yahoo.fr Abstract In ths ar a hybr controllr cobnng a lnar ol followng controllr (MFC) an fuzzy logc control (FC) for s vctor controll rannt agnt synchronous otor (PMSM) s scrb on ths stuy. Th FC s ntrouc at th aatv chans lvl. Frst, an MFC syst s sgn to allow th lant stats to b controll to follow th stats rouc by a rfrnc ol. In th nonal contons, th ol followng s rfct an th aatv chans bas on th fuzzy logc s l. Sconly, whn aratr varatons or xtrnal sturbancs occur, an augnt sgnal wll b gnrat by FC chans to rsrv th sr ol followng control rforanc. Th ffctvnss an robustnss of th roos controllr s onstrat by so sulaton rsults. Kywors PMSM, Flux Ornt Control, FC, MFC an Aatv Mol Rfrnc Syst htt://ljt.acacrct.org 19

2 Fuzzy Aatv Mol Followng S Control For Vctor Controll Prannt Magnt Synchronous Motor Introucton Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES Wth th vlont of th tchnology of owr lctroncs control, rar arth agntc atrals an otor sgn, PMSM gt w alcatons n any control systs [1,2].Thy ar rfct bcaus th control syst s usually lss colx thn that of fl ornt nucton otor rvs. In tycal PMSM rvs, classcal PI controllrs hav bn us togthr wth vctor control tho for s control. Howvr, th rforancs n havly on th otor aratrs [3] whch ar t varyng u to tratur rs an changs n otor rv oratng contons. Thus, t s srabl to hav a robust controllr for th rv syst to ruc aratr snstvty [4]. Aatv control s an ffcnt tchnu for alng wth larg aratr varatons. Th control nut s sgn to rv th controll lant to track th rsons rouc by th rfrnc ol [5,7]. Varous control algorths vlo rur th syst stats, thus thy ar not asy to lnt [6]. To ovrco ths robl an to nhanc th flxblty of changng control algorth, a FC s us to lnt th aataton chans. Th an avantag of FC rss n th fact that no athatcal olng s rur for th sgn of th controllr. Th FC uss a control ruls st that s bas ssntally on th knowlg of th syst bhavor an th xrnc of th control ngnr. It has bn ont out that fuzzy controllrs can rov hgh rforanc wth ruc sgn an lntaton colxty [7]. Thn, n th roos hybr controllr frst MFC s sgn to allow th lant outut to b controll to follow th rfrnc ol outut [8,9]. In th nonal contons, th ol followng s rfct. But whn aratrs varatons or xtrnal sturbanc occur, an augnt sgnal wll b gnrat autoatcally by th FC aatv chans whch uss th rror btwn lant outut an th rfrnc ol outut as nut. Th FC aatv chans outut s a to MFC syst [9,10] n orr to rsrv th sr ol followng control rforanc. Unr th roos control Sulnk sch th coulng control of toru an rct currnt n th fl ornt chans s guarant an th robust control rforanc s obtan by th roos hybr controllr. Ths ar rsnts a thortcal stuy on an aatv FC for vctor controll PMSM rv usng ol rfrnc aatv aroach. In th roos controllr, FC s us to lnt th aataton chans. 20

3 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Frstly, th ol uncrtanty of th PMSM s analyz, an thn vctor control tchnu s rsnt an al to rv th otor f by PWM voltag sourc nvrtr. Sconly, th MFC law s ntrouc for s vctor controll PMSM, thn FC rncl s roos for th aataton chans an ts alcaton to th s control of aatv ol followng controllr. In orr to slfy th ralzaton, th controllr s sgn on th bass of th orr-ruc ol of th PMSM syst. Fnally, th control rforanc of th hybr controllr s valuat by sulaton unr Matlab/Sulnk softwar for ffrnt oratng contons. Th rsults show that ths tho can control th PMSM syst wth uncrtanty an aratr varatons or ffctvly. Control of PMSM Mathatcal Mol of th PMSM Th lctrcal an chancal uatons of th PMSM n th rotor () rfrnc fra ar as follows: ) ( ) ( ) ( b a t I R v t R v f f r s r s φ φ φ φ ω ω (1) Th chancal uaton can b wrttn as: ] ) ( [ 2 3 ) / ( f r r r C J f T C t φ ω ω (2) Whr s th stator rsstanc, ( ) ar stator nuctancs n fra (,), s R, r ω s th rotor s, ( φ φ, ) ar stator flux, s th rotor flux, ( ar f φ ),v ( ), ( v an

4 Fuzzy Aatv Mol Followng S Control For Vctor Controll Prannt Magnt Synchronous Motor Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES rsctvly stator currnts an stator voltags n th fra (,), s th lctroagntc C toru, T s th loa toru. J an ar th rotor ont nrta an th frcton coffcnt. f r Currnt Controllr an Dcoulng Consaton If a voltag sourc PWM nvrtr s us, th stator currnts n to b controll to track th coan currnts. As can b sn fro (1), th ynacs of th stator currnts wth stator voltags as nut ar coul an nonlnar. Howvr, f th stator voltags coans ar gvn n th for v v u u u u _ co (3) _ co Whr th fs consaton ar u u _ co _ co ωr ω ( r + φ ) f Thn th stator currnts ynacs ruc to v v R s R I s + + t t (4) Snc th currnt ynacs n (4) ar lnar an coul, PI controllrs can b us for currnt trackng v v k k P P ( ( _ rf _ rf ) + k ) + k I I ( ( _ rf _ rf ) t ) t (5) Fgur 1 shows th block agra of th coulng syst 22

5 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Fgur 1. Dcoulng syst wth f consaton Vctor Control of th PMSM Th objctv of th vctor control of PMSM s to allow th otor to b controll just lk a saratly xct DC otor. So, th rct axs s algn wth rannt agnt flux lnkag has an th rct currnt follows s forc to b zro. Thn 1(b) can b wrttn as φ φ f φ (6) An th lctroagntc toru s C kt kt 3 φ (7) f 2 Not that th lctroagntc toru uaton s slar to that of DC otor Pw Invrtr Puls Wth Moulaton (PWM) tchnu s us to gnrat th rur voltag or currnt to f th otor or has sgnals. Ths tho s ncrasngly us for AC rvs wth th conton that th haronc currnt s sall as larg as ossbl. Gnrally, th PWM schs gnrat th swtchng oston attrns by coarng th thr-has snusoal 23

6 Fuzzy Aatv Mol Followng S Control For Vctor Controll Prannt Magnt Synchronous Motor Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES wav fors wth a trangular carrr. Th nvrtr ol s rrsnt by th rlatonsh btwn outut has voltags ( va, vb, vc ) an th control logc sgnals ( s1, s2, s3 ) as follows: v v v a b c V s c s s (8) Whr V c : rctf voltag, s ( 1,2,3) [0 1] : logc sgnals MFC for Vctor Controll PMSM MFC Thory Suos that th lant an th chosn rfrnc ol ar xrss as [3-5] x& y x& y A C A C x x x x + B u + B u (9) (10) n Whr x R, x R, u R, u R, y R, y R, an A, B, C, A, B, C an A, B ) ar stablzabl an s a stabl atrx. ( A n ar constant atrcs of arorat nsons. Th ars (A, B ) Th objctv s to fn th control nut u such that th lant stats can track thos of th rfrnc ol. Thn th rsultng y wll fllow y autoatcally. For asy lntaton, th control nut u s chosn to b u k x + k 0 + k u (11) l x u 24

7 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Whr 0 y y s th rror btwn th syst outut an th ol outut. Dfn th rror vctor x x (12) Thn fro (9), (10) an (11), w can obtan th followng uaton: & ( A B k C ) + A A B k x ( B B k ) u (13) ( x ) + u Euato n (13) shows that f A, B, k x, k, ku ar chosn to lt -( A B kc ) b a Hurwtz atrx an (14) - k B A A ) x + ( (15) + - ku B B (16) + Whr B ( B B ) T 1 T B s th lft suo nvrs atrx of B, thn th rror syst of (13) wll b asytotcally stabl an th outut of th controll lant wll follow that of th rfrnc ol. MRAFC for PMSM Th lnar ol followng control syst roos abov can la to rfct ol followng charactrstcs only whn th lant s nvarant. Thus, an aataton sgnalu a s a to th control law (11). Th a sgnal s gnrat fro th aatv fuzzy controllr chans an t s nclu to th MFC syst to ruc th ol followng rror u to th uncrtants n th lant. A block agra of th roos hybr controllr s shown n fgur 2 25

8 Fuzzy Aatv Mol Followng S Control For Vctor Controll Prannt Magnt Synchronous Motor Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES Fgur 2. Proos aatv fuzzy controllr wth MFC Th rror btwn th ol outut ω r an th actual s ωr an ts chang ar calculat vry salng ro as ω r ωr Δ ( k) ( k 1) (17) Th rror an th chang n rror Δ wll b rocss by th fuzzy rul bas aataton syst to rouc a corrcton tr u whch s a to th MFC outut u. Th hybr controllr outut s thus of so that th clos loo syst bhavs lk th rfrnc ol. Th control sgnal s a su of two trs a l u u + u (18) l a Whr u k ω + k ω k (19) l u rf r + u a s th fuzzy aatv chans outut 26

onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr 2008. 19-33 Prncl of FC Th sgn of FC os not rurs athatcal ollng.

9 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Prncl of FC Th sgn of FC os not rurs athatcal ollng. Th forulaton of th control ruls s bas on th knowlg of th PMSM rv an th xrnc of th control ngnr. Fuzzy ogc Controllr Structur Th FC has thr functonal blocks as shown n fgur 3 Fgur 3. FC ntrnal structur In th fuzzfcaton block, th nuts an outut crs varabls ar convrt nto fuzzy varabls, an u usng th trangular an th trazoal brsh functons shown n fgur 4 (a) Fgur 4. (a) Mbrsh functons (b) Control surfac 27

10 Fuzzy Aatv Mol Followng S Control For Vctor Controll Prannt Magnt Synchronous Motor Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES Each unvrs of scours s v nto thr fuzzy sts: Ngatv (N), Zro (Z) an Postv (P). Th fuzzy varabl an rouc th fuzzfcaton block ar thn rocss by an nfrnc chans that xcuts a st of control ruls contan n (3x3) tabl as shown n tabl 1. Tabl 1 Fuzzy control ruls for u Th fuzzy ruls ar xrss unr th IF-THEN for. Th crs outut of th FC s obtan by usng Max-Mn nfrnc algorth an th cntr of gravty fuzzfcaton aroach. FC Dsgn Th fuzzy controllr bhavour ns on th brsh functons, thr strbuton an th ruls that nflunc th fuzzy varabl n th syst. Thr s no foral tho to trn accuratly th aratrs of th controllr. Tunng th FC s an tratv rocss rurng tral svral cobnatons of brsh functons an control ruls. Th ajustnt can b on by obsrvng th rsons of th syst rgulator an ofyng th fuzzy sts n th unvrss of scours of th nut varabls ( an & ) an outut varabl (u& ) untl satsfactory rsons s obtan. Th control surfac 4 (b), a thr nsonal grahc showng th outut varabl corrsonng to all cobnatons of valus of th nuts can b us to facltat th FC tunng. Th nubr of ruls can b ruc n orr to otz th nfrnc ngn xcuton s. In ths ar, a tral an rror aroach s us to trn an ajust th wghtng factorsc ( 1,2,3) [6, 8]. 28

11 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Mol Rfrnc Aatv Fuzzy ogc Controllr Th rfrnc ol s us to scfy th sr rforanc that satsfs sgn scfcatons. A fuzzy logc aataton loo s a n aralll to th MFC fback loo [8-10]. In th nonal cas, th ol followng s rfct an th fuzzy controllr aataton loo s l. Whn aratr chang an aataton sgnal rouc by aataton chans wll b a to th outut sgnal of th MFC to rsrv th sr ol followng control rforanc [8-10]. Fgur 5 shows a Sulnk block agra of th roos hybr controllr for vctor control PMSM. Th rfrnc ol chosn s frst orr transfr functon wth t constant st at 0.7s. Fgur 5. Sulnk ol of roos hybr controllr for vctor controll Sulaton Rsults Th control rforanc of th roos sch n fgur 5 s valuat by sulaton usng Matlab/Sulnk softwar. Th aratrs of th PMSM ar as follows: 1.4H 4 J C 10N 2.8H 3 1.1*10 kg. R 0.6Ω 2 φ f 0.12wb f r 1.4*10 I 20A n 3 N / ra. s 1 In orr to val th aatv control law tho for a w oratng oan, w us th rfrnc rofls shown n fgur 6 as coan nut. Th robustnss s valuat by usng ncrasng nrta (3*J), stator rsstanc augnt +50% an varaton loa 10N. 29

12 Fuzzy Aatv Mol Followng S Control For Vctor Controll Prannt Magnt Synchronous Motor Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES Fgur 6.:Rfrnc rofl nuts Fgur 7: S rsonss for vctor control of PMSM (a) an (b) MFC, (c) hybr controllr Th sulaton rsults wthout an wth th roos controllr n th abov thr cass ar shown n fg.7. Whn th ont of nrta ncrass (3*J) th MFC rsons bcos oscllatory. Whovr, th robust control rforanc of th hybr controllr n th coan trackng s obvous. 30

13 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Fgur 8. Rsonss of MRAFC for vctor control of PMSM unr abrutly st loa varaton Fgur 9. Rsonss of MRAFC for vctor control of PMSM unr abrutly st loa varaton, ncrasng nrta 3*J Fgur 10. Rsonss of MRAFC for vctor controll PMSM unr abrutly st loa varaton, augnt nrta 3*J, an ncrasng stator rsstanc +50% 31

14 Fuzzy Aatv Mol Followng S Control For Vctor Controll Prannt Magnt Synchronous Motor Ablkar MEROUFE, Ah MASSOUM, Bagha BEABES Fg.8, 9 an 10 show th robustnss of th s rsons n th cas of xtrnal an ntrnal sturbancs. Th syst outut tracks vry closly th rfrnc ol vn wth ncrasng nrta, augnt stator rsstanc an loa varatons. Th rsults rov th ffctvnss of th fuzzy aatv chans facng to th ffrnt rturbatons. Concluson A hybr controllr cobnng th avantags of fuzzy logc control an ol rfrnc aatv control for s vctor controll PMSM f by voltag sourc nvrtr has bn roos n ths ar. Th roos controllr s nsnstv to th xtrnal an ntrnal syst aratr varatons an ths rovs ts robustnss. Th rsults obtan show that Th coulng s antan unr ntrnal an xtrnal sturbancs. Th cobnaton of MFC an FC rt to ovo th robl of flux orntaton an th uncrtants n th ol rrsntatvly Ths stratgy of control gvs a stabl syst wth a satsfactory rforanc thr wth or wthout loa varaton. Th roos sch s ffctv only urng transnts snc th aratrs of th s MFC controllr ar not ugra by th aataton chans. Th sulaton rsults hav bn confr th ffcncy of th roos aataton sch n antanng goo rforanc unr xtrnal an ntrnal sturbancs. Rfrncs 1. P. Pllay, R. Krshnan, Alcaton charactrstcs of rannt agnt synchronous an brushlss DC otors for srvo rvs, (Procal styl), IEEE Trans. In. Alcatons, Vol.27,, c/oct Dlanguo Xu, Yang Gao: An aroach to toru rl consaton for hgh rforanc rannt agnt synchronous otor srvo syst, 35 th annual IEEE, Powr lctroncs scalsts confrnc, Auchn, Grany,

15 onaro Elctronc Journal of Practcs an Tchnologs Issu 13, July-Dcbr Yng Shch Kong, an Pn Gng Huang: Hgh rforanc oston controllr for rannt agnt synchronous otor rvs bas on TM5320F2818 DSP, Proc. Of th 2004 IEEE Int. Conf. on Control alcatons. Tor, Tawan, St.2-4, Chang-Mng aw, Kuc-Hsang Chao an Paa-Jng n: A scrt aatv fl ornt nucton otor rv, IEEE Trans. On Powr Elctroncs, Vol. 7, N o 2,, Arl Sny R. Bows, an Jan : Nw robust aatv control algorth for hgh rforanc Ac rv, IEEE Trans. Elctroncs, Vol. 47, N o 2, Arl u Mngj, a Zhongn, Chng Xng, an Ouyang Mnggao: Aatv oston srvo control of rannt agnt synchronous otor, Procng of th 2004 Arcan control confrnc Boston, Jun 30- July 2, D. I. K, J. W., an S. K: Control of rannt agnt ac srvo otors va fuzzy rasonng,ieee/ias 92 Inustry Alcatons Socty Annual Mtng Confrnc Rcor Octobr 1992, 8. Faa-Jng n: Fuzzy aatv ol followng oston control for ultra sonc otor, IEEE Trans. On Powr Elctroncs, Vol. 12, N o 2,, March Faa-Jng n,ho-mng Su, an Hong-Pong Chn: Inucton otor srvo rv wth aatv rotor t constant staton, IEEE Trans. On Arosac an Elctronc systs, Vol. 34, N o 1, January Faa-Jng n, an aw C.M: Rfrnc ol slcton an aatv control for nucton otor rvs, IEEE Trans., AC-38,

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