25 A DSP-basd Discrt Spac ctor Modulation Dirct orqu Control of Snsorlss Induction Machins F. Khoucha, K. Marouani, A. Khloui, K. Aliouan UER Elctrotchniqu, EMP(Ex-ENIA) BP 7 Bordj-El-Bahri, Algirs, Algria Fax n : 23 2 86 32 4 Corrspondnt co-author E-mail : khoudir-marouani@udoramail.com Abstract In this papr, w prsnt a Dirct orqu Control schm of an induction motor oprating without spd snsor. h stimation of th stator flux and th rotor spd is prformd by an adaptiv obsrvr. In ordr to rduc th torqu, flux, currnt and spd rippl a Discrt Spac ctor Modulation (DSM-DC) stratgy is implmntd using a DSP-basd hardwar. o illustrat th prformancs of this control schm, xprimntal rsults ar prsntd. Indx rms Adaptiv Obsrvr, Dirct orqu Control, Induction Motor, Spac ctor Modulation. ϕˆ S ˆ - Look-up abl - Sctor N ˆϕ ˆ S Flux and orqu stimator Fig. Basic Dirct Control Schm SI IM I. INRODUCION Altrnating currnt motors ar gtting mor and mor popular for applications in industrial nvironmnts. Particularly in spd control systms, ac induction motors ar mor widly usd nowadays du to th charactristics of highr fficincy, lss inrtia, smallr volum and lowr cost. Morovr, in contrast to dc motors, induction motors can b usd for a long tim without maintnanc bcaus of thir brushlss structurs. h capabilitis to oprat at highr spds, highr torqus and largr powr ratings mak th induction motors mor attractiv than dc motors for mdium and high powr motor drivs. In rcnt yars, rsarch intrst in IM snsorlss drivs has grown significantly du to som of thir advantags, such as mchanical robustnss, simpl construction and maintnanc []. Prsnt fforts ar dvotd to improv th snsorlss opration, spcially for low spd and to dvlop robust control stratgis. h DC is on of th activly rsarchd control schm wich is basd on th dcoupld control of stator flux and torqu providing a quick and robust rspons with a simpl control construction in ac drivs. Howvr, th convntional DC stratgy using only on switching tabl at high and low spd prsnt notabl torqu, flux, currnt and spd rippl. his papr prsnts a snsorlss induction motor control schm using an adaptiv obsrvr for th stator flux and th rotor spd stimation basd on discrt spac vctor modulation (DSM-DC) switching stratgy. II. DIREC ORQUE CONROL Dirct orqu Control (DC) was proposd by M. Dpnbrock and I. akahashi. his mthod prsnts th advantag of a vry simpl control schm of stator flux and torqu by two hystrsis controllrs, which giv th input voltag of th motor by slcting th appropriat voltag vctors of th invrtr through a look-up-tabl in ordr to kp stator flux and torqu within th limits of two hystrsis bands as shown in Fig.. h application of this principl allows a dcoupld control of flux and torqu without th nd of coordinat transformations, PWM puls gnrators and currnt rgulators. Diffrnt voltag vctor slction critria can b mployd to control th torqu according to whthr th flux has to b rducd or incrasd, lading to diffrnt switching tabls. ry high dynamic prformanc can b achivd by DC, howvr, th prsnc of hystrsis controllrs lads to a variabl invrtr switching frquncy opration. In addition, th tim discrtization, du to digital implmntation, plus th limitd numbr of availabl voltag vctors is sourc of
25 2 larg currnt and torqu rippl, causing th dtrioration of th stady prformanc spcially in low spd rang. In ordr to improv th stady prformanc, diffrnt DC stratgis hav bn proposd to prform constant switching frquncy opration and to dcras th torqu rippl. In gnral, thy rquir mor complx control schms in comparison to th basic DC ons. III. FLUX AND ORQUE CONROL With rfrnc to currnt and torqu rippl, it has bn vrifid that a larg influnc is xrtd by th amplitud of th flux and th torqu hystrsis bands, and th voltag vctor slction critria. It can b notd also that a givn voltag vctor has a diffrnt ffct on th driv bhaviour at high and low spd. aking ths considrations into account, a good compromis has bn obtaind using diffrnt switching tabls at high and low spd. In gnral, th dtrmination of th switching tabls is carrid out on th basis of physical considrations concrning th ffcts dtrmind by radial and tangntial variations of th stator flux vctor on torqu and flux valus. A substantial rduction of currnt and torqu rippl could b obtaind using, at ach cycl priod, a prviw tchniqu in th calculation of th stator flux vctor variation rquird to xactly compnsat th flux and torqu rror. In ordr to apply this principl, th control systm should b abl to gnrat, at ach sampling priod, any voltag vctor. his idal bhaviour can b approximatd using a control systm abl to gnrat a numbr of voltag vctors highr than that usd in basic DC schm. hs solutions ar good for high powr applications, but ar not accptabl for mdium or low powr applications caus to th incrasd complxity of th powr circuit. I. DSM-DC CONROL SRAEGY h main ida th DSM-DC control stratgy is to forc th torqu and stator flux to approach thir rfrnc by applying in on sampling priod svral voltag vctors instad of only on voltag vctor as in basic DC. his control algorithm uss prfixd tim intrvals within a cycl priod and in this way a highr numbr of voltag spac vctors can b synthsizd with rspct to thos usd in basic DC tchniqu [4]. h incrasd numbr of voltag vctors allows th dfinition of switching tabls according to th rotor spd (Fig. 2), th flux and torqu rrors. h switching tabls ar drivd from th analysis of th quations linking th applid voltag vctor to th corrsponding torqu and flux variations. o undrstand th principl of th DSM-DC control stratgy, lt us tak, for xampl, th cas whn th stator flux is locatd in sctor, in basic DC fiv voltag vctors can b slctd (Fig. 2b) and a singl voltag vctor is applid during th whol switching priod. Whn th flux or torqu rror is big positiv or ngativ th application of singl voltag vctor during th whol switching priod assurs quick rspons. Howvr, if th rrors ar small th application of a singl voltag vctor can caus grat variation of flux or torqu and it can b sourc of rippl. With DSM-DC stratgy, 9 voltag vctors can b slctd for ach sctor, according to th rotor spd, th flux and th torqu rrors rang as is rprsntd in Fig. 2c and ABLE I. h switching priod is dividd into thr qual tim intrvals and on voltag vctor is applid at ach tim intrval. For xampl, th labl "23Z" dnots th voltag vctor which is synthsizd by using th voltag spac vctors 2, 3 and or 7, ach on applid for on third of th cycl priod. 2 - -2-4 3 555 55Z 3ZZ ZZZ 5ZZ 333 332 223 23Z 33Z 5 (a) 6 High 7 2 (a) oltag vctors obtaind by two lvl SI (b) oltag vctors slction in basic DC 56Z 556 665 3 2ZZ 5 6ZZ 22Z 66Z 222 666 Fig. 2 DSM-DC stratgy schm Sctor Sctor - (c) oltag vctors slction in DSM-DC stratgy for sctor B B (d) Fiv lvl torqu hystrsis comparator Clockwis Mdium Low (b) Countr Clockwis Mdium High 2 Sctor 6 -/2 -/6 /6 /2 () Emf rang subdivision in p.u. of th rat voltag ˆ B ω ϕ m s
25 3 ABLE I oltag vctors slction in DSM-DC stratgy for sctor and Countr Clockwis rotor spd Low mf rang C ϕ C -2-2. ADAPIE FLUX AND SPEED OBSERER In this sction w prsnt th global structur of th obsrvr undr study, which is basd on th induction motor modl writtn in stator rfrnc fram [5]. h motor modl is givn by: x& = Ax Bu y = Cx x = Whr [ ] t u 555 5ZZ ZZZ 3ZZ 333 666 6ZZ ZZZ 2ZZ 222 Mdium mf rang C ϕ C -2-2 555 ZZZ 3ZZ 33Z 333 666 ZZZ 2ZZ 22Z 222 High mf rang sctor C ϕ C -2-2 555 3ZZ 33Z 333 333 666 2ZZ 23Z 223 222 High mf rang sctor - C ϕ C -2-2 555 3ZZ 23Z 332 333 666 2ZZ 22Z 222 222 ϕ r ϕ r = [ ] t y = [ ] t v s v s () ω r : is th rotor mchanical spd. A linar stat obsrvr for th rotor flux can thn b drivd as follows by considring th mchanical spd as a constant paramtr sinc its variations ar vry slow in comparison to thos of th lctrical variabls: ( y yˆ ) xˆ & = Axˆ Bu K (2) h symbol ^ dnots an stimatd quantity. K is a gain matrix, which is usd to suitably locat th obsrvr s pols. Using Lyapounov stability thory, w can construct a mchanism to adapt th mchanical spd from th asymptotic convrgnc s condition of th stat variabls stimation rrors: ωˆ = K ( ˆ ϕ ˆ ϕ )dt K ( ˆ ϕ ˆ ϕ ) (3) s iω s r s r pω s r s r Whr K iω and s = i iˆ and s = is iˆ s. s s K pω : ar positiv gains. h voltag drop ovr th stator rsistanc at low rotor spd rducs th amplitud of th stator flux rmarkably. In ordr to improv th stimation prcision of both flux and spd variabls, w includd an adaptation mchanism of th stator rsistanc [6], which is subjct to drift du to motor hating. In th sam mannr that for th spd variabl, th stator rsistanc stimat is givn by: ( ˆ iˆ ) dt ( ˆ iˆ ) Rˆ s K ir s s s K pr s = (4) s s Fig. 3 prsnts th global adaptiv obsrvr structur. σ σ r s A= L m r σl r B = C = σl r σ σ r s L m r M σl r L s r M ω r σl r L s r ω r M ω r σl r L s M σl r L s r ω r r i s - - î s î s Induction Motor Obsrvr modl ) ϕ ) r ϕ r Adaptation Mchanism v s v s Adaptiv obsrvr ωˆ r,rˆ s Fig. 3 Global adaptiv obsrvr structur
25 4 I. EXPERIMENAL RESULS h configuration of th xprimntal systm usd to validat th proposd control algorithm is shown in Fig. 4, it is mad up of a Kw/38/5Hz squirrl cag induction motor fd by a 2-lvl IGB voltag sourc invrtr and digital signal procssor (DSP) control board. h whol control algorithm (Adaptiv spd and flux obsrvr, stator rsistanc tuning, DC algorithm and PI spd rgulator) is implmntd in a singl fixd-point MS32F24 DSP-basd dvlopmnt board from xas Instrumnts within lss than µs of tim computing. h digital control signals of th powr componnts ar gnratd by th DSP-controllr via PWM outputs. h control frquncy is about Khz. oltag and currnt variabls ar masurd by Hall-ffct snsors and sampld at th sam frquncy. A mchanical spd tachomtr is mountd on th motor s shaft only to allow comparison btwn stimatd and masurd spd. h tachomtr s signal is not usd in th closd-loop spd control. A sris of xprimntal rsults ar dpictd on figurs 5, 6 and 7, which rprsnt th prformancs of th flux and spd adaptiv obsrvr undr svral conditions in association with th DSM-DC stratgy and th stator rsistanc tuning. hy prov th ffctivnss of th adaptiv obsrvr in gnral and spcially in association with th DSM-DC stratgy, vn without th stator rsistanc tuning. h whol control algorithm was implmntd on a singl DSP-controllr board within a rasonabl computing tim, which givs rsult to a good prformanc/as of implmntation ratio. Fig. 5 shows a small rippl in th stator currnt, th stimatd torqu and th rotor spd rsponss without stator rsistanc tuning, whn th spd command is changd from 5 rpm to -5rpm. Howvr, Fig. 6 prsnt notabl torqu and spd rippl at low spd (rpm). Fig.7, shows a good torqu and spd rsponss with stator rsistanc tuning at low spd (rpm). SI Stator curnt IM Hall ffct snsors Estimatd torqu Load torqu Rfrnc and rmovd stimatd spd Dvlopmnt Softwar --- PC --- MS32F24 DSP Dvlopmnt board Control unit Digital OU Snsors Intrfac Analog IN Estimatd Spd Rfrnc Spd (a) Currnt, orqu and Spd rsponss at transint stat without stator rsistanc tuning Fig. 4 Exprimntal systm schm Rfrnc and stimatd torqu Rfrnc and stimatd Spd Stator curnt Zro spd Estimatd torqu Load torqu rmovd Rfrnc and stimatd spd (b) orqu and spd rsponss at stady stat without stator rsistanc tuning Fig.6 Currnt, orqu and Spd rsponss at ratd load (2Nm) without stator rsistanc tuning Fig.5 Currnt, orqu and Spd rsponss for spd rvrsal opration from 5rpm to -5rpm
25 5 APPENDIX Stator currnt Load torqu rmovd Rfrnc and Estimatd Spd (a) orqu and spd rsponss at transint stat with stator rsistanc tuning Induction motor data Kw Ratd powr. 283rpm Ratd spd. 22v Ratd voltag. 4.67Ω Stator rsistanc. 8Ω Rotor rsistanc..347 H Stator inductanc..374 H Rotor inductanc..366 H Mutual inductanc..3 Kg.m 2 Motor-Load inrtia # of pol pairs. Rfrnc and stimatd torqu Rfrnc and Estimatd Spd (b) orqu and spd rsponss at stady stat with stator rsistanc tuning Fig.7 Currnt, orqu and Spd rsponss with stator rsistanc tuning at low spd (rpm) and ratd load (2Nm) II. CONCLUSION his papr prsnts an induction motor driv tchniqu using th DSM-DC stratgy. Exprimntal prformanc analysis of an adaptiv stator flux and spd obsrvr with stator rsistanc tuning, prformd by a DSP controllr. h analysis focuss both on transint and static charactristics. hy prov th ffctivnss of th adaptiv obsrvr in gnral and spcially in association with th DSM-DC stratgy. With th xprimntal rsults it has bn vrifid that th DSM-DC stratgy allows th torqu, th rotor spd and th currnt rippl to b rducd in comparison to th basic DC stratgy. REFERENCES [] Gil-Su L, Dong-Hyun L, a-woong Yoon, Kyo-Bum L, Joong-Ho Song, and Ich Choy Spd and Flux Estimation for an Induction Motor, in Procdings of ICCAS22, South-Kora. [2] S. Stasi, L. Salvator, and F. Cuprtino Comparison Btwn Adaptiv Flux Obsrvr- and Extndd Kalman Filtr-Basd Algorithms for Fild Orintd Control of Induction Motor Drivs in Procdings of 999 Europan Powr Elctronics Confrnc, Lausann, Switzrland. [3] R. Bgunan and M. Ouhrouch MRAC- IFO Induction Motor Control with Simultanous locity and Rotor-Invrs im constant Estimation, IASED Intrnational Confrnc PES 23. [4] D. Casadi, G. Srra and A. ani Implmntation of Dirct orqu Control Algorithm for Induction Motors Basd on Discrt Spac ctor Modulation IEEE ransactions on Powr Elctronics, ol. 5, N 4,July 2. [5] J. Mas and J. Mlkbk Adaptiv Flux Obsrvr for Snsorlss Induction Motor Drivs with Enhancd Dynamic Prformanc in Procdings of 999 Europan Powr Elctronics Confrnc, Lausann, Switzrland. [6] Sok Ho Jon,, Kwang Kyo Oh, and Jin Young Choi Flux Obsrvr With Onlin uning of Stator and Rotor Rsistancs for Induction Motors IEEE ransactions on Industrial Elctronics, ol. 49, N 3, Jun 22. [7] K. Ohyama. G. M. Ashr and M. Summr Comparison of Pratical Prformanc and Oprating Limits of Snsorlss Induction Motor Driv using a Closd Loop Flux Obsrvr and a Full Ordr Flux Obsrvr in Procdings of 999 Europan Powr Elctronics Confrnc, Lausann, Switzrland in Procdings of 999 Europan Powr Elctronics Confrnc, Lausann, Switzrland.