Intelligent Controllers for Permanent Magnet Synchronous Motor Drive Systems

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1 Intllignt Controllrs for Prmannt Magnt Synchronous Motor Driv Systms Nourddin GUERSI, Mssaoud BOUKHENAF*, Mssaoud DJEGHABA Laboratoir d Automatiqu t ds Signaux d Annaba (LASA) *Laboratoir ds Systèms Elctromécaniqus (LSELM) Univrsity BadjiMokhtar B.P ElHadjar Annaba 3, Algria gursi54@yahoo.fr Abstract: Th PMSM (Prmannt Magnt Synchronous Motor) driv systms ar oftn usd in lctrical drivs bcaus of thir simpl structurs, as of maintnanc and fficincy. Howvr, th nonlinar bhaviour which ariss mainly from motor dynamics and load charactristics and th prsnc of uncrtaintis mak thir control an xtrmly difficult task. So, th spd control stratgy should b adaptiv and robust for succssful industrial applications. To handl th control issu mor ffctivly, thr artificial intllignc control stratgis namly, fuzzy logic (FL), artificial nural ntwork (ANN) and nurofuzzy (NF) ar proposd sinc thy rquir only a rducd computation powr, whil maintaining satisfactory static and dynamic prformanc and a good insnsitivity to prturbations and paramtr uncrtaintis. Th backpropagation larning algorithm is usd for training th ANN and th NF controllrs. Th prformancs of th thr control stratgis ar invstigatd and compard in simulation. Th rsults show that th intllignt controllrs ar rliabl and highly ffctiv in th spd control of th PMSM. I. INTRODUCTION Among AC drivs, th prmannt magnt synchronous motor has bn bcoming popular du to som of its advantagous faturs []. In high prformanc variabl spd driv (HPVSD) systms th motor spd should closly follow a spcifid rfrnc trajctory rgardlss of load disturbancs, paramtr variations and modl uncrtaintis. In ordr to achiv high prformanc, fild orintd control is th most popular choic. Traditionally, ths control issus ar handld by th convntional proportionalintgral (PI) controllr and othr controllrs such as modl rfrnc adaptiv controllr, sliding mod controllr, variabl structur controllrs. Howvr, th difficultis of obtaining th xact dq axis ractanc paramtrs of th PMSM lad to cumbrsom dsign approach for ths controllrs []. Morovr, th convntional fixd gain PI controllr is vry snsitiv to stp chang of control spd, paramtr variations and load disturbancs [3]. Morovr, th prcis spd control of a PMSM driv bcoms a complx issu du to nonlinar coupling among its winding currnts and th rotor spd as wll as th nonlinarity prsnt in th lctromagntic dvlopd torqu du to magntic saturation of th rotor cor. Thus, th intllignt controllrs ar xpctd to play an incrasing rol for high prformanc PMSM driv systms. Rcntly, rsarchrs [4] hav don xtnsiv rsarch for application of fuzzy logic controllr (FLC), artificial nural ntwork (ANN) and nurofuzzy (NF) controllrs in HPVSD systms. Simplicity and lss intnsiv mathmatical dsign rquirmnts ar th main faturs of intllignt controllrs, which ar suitabl to dal with nonlinaritis and uncrtaintis of lctric motors. Howvr, ach intllignt control algorithm has its own mrits and drawbacks [3]. Thrfor, th main objctiv of this papr is to provid a usful comparison among various intllignt controllrs such as FLC, ANN and NF controllrs in trms of dsign, implmntation and prformanc aspcts for prmannt magnt synchronous motor (PMSM) drivs. As a rprsntativ of ANN, a standard Multilayr nural ntwork (MLP) is usd in this study. For th Fuzzy Logic Controllr (FLC), th nuronal implmntation allows th adjustmnt of th various mmbrship functions. For th scop of th comparison, a closd loop vctor control schm for th PMSM incorporating th intllignt controllrs is succssfully implmntd and th prformancs ar invstigatd and compard in simulation at diffrnt oprating conditions. II BACKGROUND Th arlist vctor control principls for AC prmannt magnt synchronous machins rsmbld th control of a fully compnsatd DC machin. Th ida was to control th currnt of th machin in a quadratur spac, dnotd qspac, with th magntic flux cratd by th prmannt magnts. Th torqu is thn dirctly proportional to th product of th flux linkag cratd by th magnts and th currnt. In an AC machin th rotation of th rotor dmands that th flux must rotat at a crtain frquncy. If th currnt is thn controlld in qspac with th flux, th currnt must b an AC in contrast with th DC currnt of a DC machin. Th mathmatical modlling of an AC synchronous machin is most convnintly don using a coordinat systm, which rotats synchronously with th magntic axis of th rotor, i.. with th rotor. Th xaxis of this coordinat systm is calld th dirct axis (usually dnotd as d ) and th yaxis is th quadratur axis (dnotd as q ). Th

2 magnt flux lis on th daxis and if th currnt is controlld in qspac with th magnt flux it is alignd with th qaxis. This typ of control is rfrrd to as id_control. A PMSM motor consists of prmannt magnts mountd on th rotor surfac and thr phas stator windings which hav a sinusoidal distribution and displacd by. Th stator voltag quations of a PMSM in th rotor rfrnc fram (qd fram) ar dscribd as follows: vq = Raiq Lqi q LdPwrid λmwr () vd = Raid Ldi d LqPwi r q () T =.5 P[ λmq i ( Ld Lq) idq i ] (3) wr = θ (4) w r = ( T Fwr Tm ) J (5) From quations () and (), th discrttim quation can b obtaind as follows: Lq vq( k) = Raiq( k) iq( k ) iq( k) T (6) LPwi d r d( k) λmwr Ld vd( k) = Ri s d( k) [ id( k ) id( k) ] (7) T LPwi q r q( k) T( k) = λmiq( k) P( Ld Lq) id( k) iq( k) (8) whr R : Rsistanc of th stator windings; : d and q axis a id, iq currnts; L : d and q axis inductancs; w : angular d, Lq r vlocity of th rotor; θ : Rotor angular position; λ : amplitud of th flux inducd by th prmannt m magnts of th rotor in th stator phass; T : Elctromagntic torqu; T m : Shaft mchanical torqu; P: Numbr of pol pairs; J: Combind inrtia of rotor and load; F: Combind viscous friction of rotor and load On mts primarily two mthods for implmntation of th stratgy of control which consists in maintaining th currnt id with a zro valu and to control spd and/or th position with acting on th currnt i q, i.. on th coupl dvlopd by th ngin. Th first consists in controlling th altrnating currnts circulating in th stator windings of th machin, th scond to control th Park s componnts of ths currnts [4]. III CONTROL PRINCIPLE Th machin paramtrs ar givn in Tabl. A typical closd loop vctor control schm for PMSM is shown in Fig. in which diffrnt intllignt controllrs ar usd as spd controllr. From th spd rfrnc w and masurd spd, a r rgulator calculats th st point of th torqu, i.. th valu of rfrnc of th currnt i. Th rotor position, masurd by a q position ncodr, combind with th rfrnc valus i and d i q allow to calculat, by a rvrs Park s transformation, th rfrnc valus of currnts i, i, i. Ths valus ar compard a b c with th masurd valus i to fix th control signals of a, ib, ic ach invrtr s arm. Ths signals ar obtaind ithr by rgulators with thrshold, or by analog PI rgulators whos output fds a modulator MLI [57]. Controllr Iqrf Idrf iabcrf iabc va vb vc iabc T PMSM Thta dqabc PWM Stp Tm wm Thta Figur : Vctor control with local currnt loops Pairs of pols P 4 Stator rsistanc.875 Ω Flux inducd by.75 Wb Inductanc L d 8.5 mh Inductanc L q 8.5 mh Tabl : PMSM charactristics IV PID CONTROLLER Dspit th imprssiv advancs achivd in th control nginring disciplin, PID still rmains th most common control algorithm in industrial us today. It is widly usd bcaus of its vrsatility, high rliability and as of opration [8]. A standard mthod of stting th paramtrs is through th us of ZiglrNichols' tuning ruls [9]. Ths tchniqus wr dvlopd mpirically through th simulation of a larg numbr of procss systms to provid a simpl rul. Th mthods oprat particularly wll for simpl systms and thos which xhibit a clarly dominant polpair, but for mor

3 complx systms th PID gains may b strongly coupld in a lss prdictabl way. For ths systms, adquat prformanc is oftn only achivd through manual and huristic paramtr variation. V FLC SCHEME Unlik th classical control dsign, which rquirs a plant modl for dsigning th controllr, fuzzy logic incorporats an altrnativ way which allows on to dsign a controllr using a highr lvl of abstraction without knowing th plant modl. This maks fuzzy logic controllr (FLC) vry attractiv for illdfind systms or systms with uncrtain paramtrs []. In ordr to dsign th FLC, som variabls rprsnting th dynamic prformanc of th systm, should b chosn to b fd as th inputs. In addition to th propr input signals, signal gains and fuzzy substs should b dfind. It is common to us th output rror and th rat drivativ of th output as controllr inputs [, ]. In this papr, th motor spd dviation ( Δ ω ), its drivativ ( Δ ω ) and th acclration, ar considrd as th inputs of th FLC Fig.. Aftr,, and Δ ω Δ ω, signals pass through two appropriat gains or scaling factors, and thn ar fd to th FLC. Th output ΔI q of th controllr is also scald by passing through th output gain, Fig. 3. To convrt th masurd input variabls of th FLC into suitabl linguistic variabls, svn fuzzy substs ar chosn. Th mmbrship functions of ths substs hav trapzoidal and triangular shap. Fig. 4 shows th mmbrship functions. In this papr, both inputs of th FLC hav svn substs. Thus, on fuzzy rul tabl with fortynin ruls is constructd (tabl ). Figur 5 illustrats th control surfac. Th cntr of gravity mthod is mployd. wrf Fuzzy Spd controllr d dt idrf = iqrf Park arma armb armc PMSM arma armb armc Snsor signals procssing Figur : Vctor control with fuzzy invrs modl controllr (k) = x(k) y(k)= Δω Δ(k) = (k) (k)= Δώ Figur 3: Structur of th controllr

4 Dgr of mmbrship GN MN PN EZ PP MP GP Figur 4: FLC Mmbrship functions for th input N h ar th numbrs of nurons in th input and hiddn layrs, rspctivly (Fig. 6). Assuming that th systm to b controlld can b dscribd by: y( t ) = g[ y( t),..., y( t n ), u( t),... u( t m) ] () W hav traind offlin a dirct nural ntwork modl of th systm. Thn w usd th MRAC schm (Fig. 7a) for th training of an invrs nural ntwork modl. This invrs modl gnrats th control input uˆ ( t ) : u( t) = g ˆ ˆ [ y( t ), y( t),..., y( t n ), u( t),... u( t m) ].It can b usd for controlling th systm by substituting in th xprssion of th control uˆ ( t ) th output y ( t ) at tim t by th dsird input rfrnc r(t), Fig. 7b. σ Figur 5: FLC output charactristics Th valus of th constants, mmbrship functions, fuzzy sts for th input/output variabls and th ruls usd in this work ar slctd by trial and rror to obtain th optimum driv prformanc. x x x T N i W σ σ N h T V Figur 6: Nural ntwork ρ y i Δ GN MN PN EZ PP MP GP GP EZ PP MP GP GP GP GP MP PN EZ PP MP GP GP GP PP MN PN EZ PP MP GP GP EZ GN MN PN EZ PP MP GP PN GN GN MN PN EZ PP MP MN GN GN GN MN PN EZ PP GN GN GN GN GN MN PN EZ VI Tabl : Fuzzy infrnc ruls NEURAL NETWORKS SCHEME Figur7a: MRAC schm for training th invrs controllr. Th singl output of a twolayr NN with a linar output activation function is givn by: Nh Ni ynn = vjσ wjk. ϕk θwj θv (9) j= k= whr ϕ,,ϕ Ni ar th NN inputs, σ(.) is a sigmoid activation function, w jk ar inputtohiddn layr intrconnction wights, and v j ar hiddntooutput layr intrconnction wights. θ, θ m=,, ar bias. N i and v wm r(t) Z Z Z NN Invrs modl u(t) Systm Figur7b: Schm for invrs controllr. y(t)

5 Inputs Inputmf Rul Outputmf ach rul conclusion. Th algorithm changs th valus of ω to minimiz an objctiv function E usually xprssd by th man quadratic rror (3). In this quation, th valu y ( k ) d is th dsird output valu rlatd with th condition vctor x( k) = ( x, x,, xm ). Th lmnt ŷ ( k) is th infrrd k rspons to th sam condition vctor x( k) and computd by Equation (4). VII Figur 8: NuroFuzzy ntwork. ANFIS STRUCTURE. ANFIS (AdaptivNtworkbasd Fuzzy Infrnc Systm) has provn to b an xcllnt function approximation tool [3, 4]. ANFIS implmnts a first ordr TakagiSugno (TS) fuzzy systm. Th structur of this modl is shown in Fig. 8. In this typ of modl, th condition part of a typical rul uss linguistic variabls as R ( k ): IF ( x is A and 3 x i (l) THEN () s A4 ) y = w Whr l is th rul indx and k dnots th kth numrical xampl ( x( k), x( k),, xm ( k)) y( k). Th conclusion part is rprsntd by a numrical valu which is considrd a function of systm s condition xprssd x, x,, xm in th variabls (). Ths modls ar suitabl for nuralbasdlarning tchniqus as gradint mthods to xtract th ruls [6] and gnrat modls with a rducd numbr of ruls. ω = (,,, ) () g x x x m Th nurofuzzy algorithm uss mmbrship functions of triangular typ in th prsnt study. Figur 8 illustrats th nurofuzzy schm for an xampl with two inputs ( x = x, = Δ ) and on output variabl (y =U). Th information is propagatd in thr layrs. In th first layr, th two inputs ar codifid into linguistic valus by th st of triangular mmbrship functions attributd to ach variabl. Th scond stag calculats to ach rul R its rspctiv activation dgr. In th third layr, th infrnc mchanism wights ach rul conclusion ω, initialisd by th clustrbasd algorithm, using th activation dgr computd in th scond stag. Th rror signal btwn th modl infrrd output valu ŷ and th rspctiv masurd valu (or taching valu), is usd by th gradint dscnt mthod to adjust y d Output ω E = ( yˆ ( x( k )) yd ( k )) (3) yˆ ( x( k) ) = m L l = μ A j j = m L l = j = ( l) ( x ( k) ) ω ( k) μ j A j ( x ( k )) j (4) Equation (5) stablishs adjustmnt of ach conclusion by th gradintdscnt mthod. Th symbol η is th larning rat paramtr, and i indicat th numbr of larning itrations xcutd by th algorithm. ( l) ( l) E ω ( i ) ω ( i) η ω = (5) Th NuroFuzzy Control Systm In th nurofuzzy control systm, which is basd on th fdbackrrorlarning schm, ach rul conclusion ω is modifid by th gradintdscnt mthod to minimiz th man squard rror (MSE) E. In th implmntd controllr, th nurofuzzy modl minimiss th man squard rror gnratd by th proportional controllr (P) to adjust ach rul as indicatd in quation st (6). E = ( P( y yrf )) (6) ( l) ( l) E ω ( i ) = ω ( i) η ω Fig. 9 shows th mmbrship functions. Both inputs of th NF hav svn substs. Thus, on fuzzy rul tabl with fortynin ruls is constructd (sam as tabl ). Fig. illustrats th control surfac. Dgr of mmbrship GN MN PN EZ PP MP GP Figur 9: NF Mmbrship function for th input.

6 Spd rsponss of th FLC basd driv Iq.6.4. Spd (rad/s) 8 75 d vitfuzzy Figur: NF output charactristics Figur : Spd rsponss of th FLC basd driv, with torqu disturbanc at.4s VIII SIMULATION Spd rsponss of th ANN basd driv A plant consisting of a thrphas prmannt magnt synchronous machin with sinusoidal flux distribution ratd. kw, V, 3 rpm is fd by a PWM invrtr. Th machin is modlld in th dq rotor fram Th load torqu applid to th machin's shaft is originally st to its nominal valu (3 Nm) and stps down to Nm at t=.4 s. Th PI controllr, th fuzzy controllr, th nural ntwork controllr, and th machin ar modlld by MATLAB []. Th simulatd spd rspons of th PMSM driv systm incorporating FLC is shown in Fig.. It is clar that th driv can follow th command spd without significant ovrshoot and undrshoot and zro stadystat rror. Howvr, it is found that th motor suffrs from vibration which is indicatd by th spiks in spd rspons vn at stadystat condition. For HPVSD (High Prformanc Variabl Spd Driv) applications this is not accptabl. This chattring occurs du to switching of th ruls of th FLC. Figur shows th simulatd spd rspons of th PMSM driv systm incorporating ANN controllr. It is shown that th driv rspons is similar to that of FLC but th spd rspons is fastr and th vibration of th motor is also rducd as indicatd by lss spiks. Figur 3 givs th simulatd spd rspons of th PMSM driv systms incorporating NF controllr. Clarly, it can b sn that th spd rspons is smoothr than that of ANN but littl mor sluggish. To compar th abov intllignt controllrs with a convntional PI controllr, th spd rspons, th variation of currnt I q, and torqu ar shown in Fig. 4, Fig. 5, and Fig. 6, rspctivly. Whr w can s that with th PI controllr th motor suffrs from ovrshoot and chattring. This provs that th prformanc of intllignt controllrs is mor robust whn compard to PI controllr. Spd (rad/s) Spd (rad/s) Spd (rad/s) VitNN Figur : Spd rsponss of th ANN basd driv, with torqu disturbanc at.4s Spd rsponss of th NF basd driv vitnf Figur 3: Spd rsponss of th NF basd driv, with torqu disturbanc at.4s Spd rsponss with FLC, ANN, NF, and PI Fuzzy controllr ANN controllr NF controllr PI controllr Figur 4: Spd rsponss with FL, ANN, NF, and PI controllrs, with torqu chang at.4s

7 rnc curnt Iq (A) rnc curnt Iq with FL, ANN, NF, and PI controllrs PI controllr FL controllr ANN controllr NF controllr Figur 5: Variation of rfrnc currnt I q, with FL, ANN, NF, and PI controllrs with torqu chang at.4s Torqus (N.m) Elctrical torqus with FL, ANN, NF, and PI controllrs PI controllr ANN controllr FL controllr NF controllr Figur 6a: Elctrical torqus with FL, ANN, NF, and PI controllrs. Torqus (N.m) Elctrical torqus with FL, ANN, NF, and PI controllrs PI controllr ANN controllr FL controllr NF controllr Figur 6b: Elctrical torqus (Zoom) VIV CONCLUSION This papr provids a usful comparison btwn thr diffrnt intllignt controllrs in trms of dsign, implmntation and prformanc aspcts for prmannt magnt synchronous motor (PMSM) drivs. Th prformancs of all th abov mntiond intllignt controllrs wr found to b robust as compard to convntional PI controllr. Th diffrncs btwn diffrnt intllignt controllrs ar: (a) dsign of convntional FLC is asir than ANN and NF controllrs as it is basd on simpl linguistic control ruls; (b) FLC nd a rlativly high computation as compard to ANN and NF; (c) FLC suffrs from th chattring phnomnon, which rsults in vibration of th motor; (d) Driv rspons for ANN controllr is fastr than FLC and NF; and () NF controllr provids th smoothst spd rspons of th driv. On th light of th abov comparison, th hybrid nurofuzzy controllr appars to b th bst on sinc it provids th bst prformancs. rncs [] P. C. Kraus, Analysis of Elctric Machinry. Nw York: McGrawHill, 986. [] T. H. Liu, C. M. Young, and C. H. Liu, Microprocssorbasd controllr dsign and simulation for a prmannt magnt synchronous motor driv, IEEE Trans. Ind. Elctron., vol. 35, pp , Nov [3] D. W. Novotny and R. D. Lornz, Introduction to fild orintation and high prformanc AC drivs, in Proc. IEEE/ IAS Tutorial Cours, 986. [4] Z. lbrahiin and E. Lvi. A Comparativ Analysis of Fuzzy Logic and PI Spd Control in High Prformanc AC Drivs Using Exprimntal Approach. IEEE trans. Ind. Appl.. Vol. 38. No. 5, pp I8, Spt. /Oct. [5] M N Uddin and M A Rahman. Fuzzy Logic Basd Spd Control of an IPM Synchronous Motor Driv. Journal of Advancd Computational Intllignc. vol 4 No. 3, pp 9,. [6] M A Rahman. M Nasir Uddin. and M. A. Abido. An Anificial Nural Ntwork for Onlin tuning of a Gntic Basd PI Controllr for Intrior Prmannt Magnt Synchronous Motor Driv, Powr Convrsion Confrnc (PCC). Osaka. Japan:, pp 546, April. [7] M. N Uddin. M A Abido and M. A Rahman. Dvlopmnt and Implmntation of a Hybrid Intllignt Controllr for Intrior Prmannt Magnt Synchronous Motor Driv IEEE/IAS Annual Mtinp Confrnc Rcord. Pittsburgh. USA, pp , Octobr. [8] M.A Rahman and M.A. Hoqu, OnLin Adaptiv Artificial Nural Ntwork Rasd Vctor Control of Pnnannt Magnt Svnchronous Motors. IEEE 7rans. on En.Conv. vol. 3. no 4, pp. 3 3, 998. [9] M.E Elbuluk. L long and I Husain: Nural Ntwork Basd Modl rnc Adaptiv Systms for HighPrformanc Motor Drivs and Motion Controls. IEEEtrans. on Industry Applications. Vol 38, pp , Mav/Jun. [] B Singh, V. K. Shanna and S. S Murthy, Prformanc Analysis on Adaptiv Fuzzy Logic Controllr for Switchd Rluctanc Motor Driv Systm. IEEE/IAS Ann. Mt, pp , 998. [] S Bolognani and M. Zigliono. Fuzzy Logic Control of a Switchd Rluctanc Motor driv. IEEE trans on Industry Applications. Vol.3. No 5, pp. 6368, Spt./Oct [] M.A ElSarkawi. A. A. ElSamahy and M. L. ElSvd. High Prformanc Driv of dc Brushlss Motors Using Nural Ntwwh. IEEE 7rans. on En.Com,. vol. 9. no., pp. 373,. Jun 994. [3] A. Zilouchian and M Jamshidi, Intllignt Control Systms Using Soft Computing Mthodologis. CRC. [4] P. C. Kraus, Analysis of Elctric Machinry. Nw York: McGrawHill, 986. [5] Lonhard W., Control of lctrical drivs, Springr Vrlag (985). [6] LajoiMaznc M., Villanuva C. t Hctor J., Study and implmntation of hystrsis controlld invrtr on a prmannt magnt synchronous machin, IEEE Trans. Ind. Appl. IA (985) [7] Matagn E., Nw PWM invrtr modlling mthod applid to th dsign of a currnt controllr for thr phas high prformanc PM synchronous actuator, Proc. EPE'93 Confrnc, Brighton (sptmbr993) pp [8] Astron K.J., and Hagglund T., PID Controllrs: Thory, Dsign, and Tuning, NC, USA, Rsarch Triangl Park, Instrumnt Socity of Amrica, 995. [9] Ziglr J.G., and Nichols N.B., Optimum stting for automatic controllrs, Transactions of ASME No. 64, 94, pp [] Zadh L.A., Outlin of a nw approach to th analysis of complx systms and dcision procsss, IEEE Trans. on Systms, Man and Cybrntics Vol. 3, No., 973, pp [] Lown M., Swidnbank E., and Hogg B.W., Adaptiv fuzzy logic control of a turbin gnrator systm, IEEE Trans. on Enrgy Convrsion, Vol., No. 4, 997, pp [] Talaq J., and AlBasri F., Adaptiv fuzzy gain schduling for load frquncy control, IEEE Trans. on Powr Systms, Vol. 4, No., 999, pp.455. [3] Jang, J. S., Gully N.: Fuzzy Logic toolbox Usr.s Guid. Th Mathworks Inc,. 995 [4] Jang J.S.: ANFIS: AdaptivNtworkbasd Fuzzy Infrnc Systm. IEEE Trans. On systm, Man and Cybrntics. Vol.3, No 3, May/Jun 993, pp