Sliding Mode Control of Surface-Mount Permanent-Magnet Synchronous Motor Based on Error Model with Unknown Load

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1 JOURNAL OF SOFTWARE VOL. 6 NO. 5 MAY 0 89 Slng Moe Contol o SuaceMount PemanentMagnet Synchonous Moto Base on Eo Moel th Unknon Loa Baojun Wang Insttute o Inomaton Technology /Zhejang Insttute o Communcatons Hangzhou Zhejang P.R.Chna Emal: bjbjbj@63.com Jajun Wang Insttute o Automaton/Hangzhou Danz Unvesty Hangzhou Zhejang P.R.Chna Emal: angjajun@hu.eu.cn Abstact Suacemount pemanentmagnet synchonous moto(spmsm) has been ely apple n accuate moton contol. In ths pape the SPMSM moel s ve nto electcal magnetc subsystem an electcal mechancal subsystem. Then a novel eo moel s gven by hch the contolles can be esgne easly. In the geneal PMSM contolles esgn the unknon loa s oten neglecte. In ths pape a popotonal spee eo s use to take the place o the unknon loa thout usng loa estmaton. Base on the eo moel o the SPMSM slng moe contolles ae esgne to enhance the obustness o the SPMSM ve system. At last many smulaton esults ae gven to sho the eectveness o the popose scheme. Inex Tems Slng moe contol Suacemount pemanentmagnet synchonous moto Eo moel obustness I. INTRODUCTION In ecent yeas avancements n magnetc mateals semconucto poe evces an contol theoy have mae the SPMSM ve plays a vtally mpotant ole n accuate moton contol n the lotomeum poe ange. The esable eatues o the SPMSM ae ts compact stuctue hgh agap lux ensty hgh poe ensty hgh touetoneta ato an hgh toue capablty [3]. At pesent the eseach o SPMSM contol esgn can be ve nto thee man aspects. The st aspect s to enhance the obustness o the ve system. The secon aspect s to enhance the contol accuacy. An the th aspect s to enhance the ato o the peomance an the pce. In the SPMSM contol system to types o SPMSM moel ae oten use o the contolles esgn. One s Manuscpt eceve Decembe 6 00; evse Januay 5 0; accepte Januay 0. Coesponng autho: Jajun Wang (angjajun@hu.eu.cn). base on the eeence ame moel that otates synchonously th an electcal angula velocty [46]. The othe s base on the αβ o ab statonay eeence ame moel that keeps statc n the state eeence ame [7 8]. In the contolles esgn o both types o SPMSM moels the unknon loa toue s oten neglecte o estmate(obseve) onlne [9 0]. Ths makes the esgn o the contolles moe complex to ealze the hgh contol peomance o ve systems. So ho to pocess the unknon loa toue to enhance the obustness an accuacy o the SPMSM ve system s a vey mpotant poblem. Slng moe contol s one o the ely eseache obust contol appoaches snce t gves systems an nvaance popety to uncetantes once the system ynamcs s n the slng moe [ ]. It eatues goo obustness stubance ejecton an ast esponse contol. Slng moe contol has been ely use n the SPMSM contol esgn [ 8 ]. The oganzaton o ths pape s as ollos. Secton ntouces the eeence ame moel o the SPMSM. The moel s ve nto electcal magnetc subsystem an electcal mechancal subsystem. Base on the epate moel the eo moel s gven. In secton 3 slng moe contolles ae esgne base on the eo moel. In secton 4 smulaton esults ae shon n eent contons. Secton 5 gves the conclusons o the pape. II. ERROR MODEL OF THE SPMSM The moel o the SPMSM s gven as ollong euatons. R u = p () t L L R p u = p () t L L L 3p TL = (3) t J J 0 ACADEMY PUBLISHER o:0.4304/js

2 80 JOURNAL OF SOFTWARE VOL. 6 NO. 5 MAY 0 hee R s the state esstance L s the state nuctance p s the numbe o pole pas o the SPMSM s the pemanent magnet lux J s the moment o neta T L s the loa toue hch s assume to be unknon n ths pape s the axs stato cuent s the oto spee s the axs stato cuent u s the axs stato voltage u s the axs stato voltage. Base on the euatons o the SPMSM the moel o the SPMSM can be ve nto electcal magnetc subsystem an electcal mechancal subsystem. The electcal magnetc subsystem s gven as euaton() an the electcal mechancal subsystem s gven as euaton () an (3). The steay states o the SPMSM ae ene as u s u s stato cuent an T hee s the steay axs s the steay axs stato cuent the steay axs stato voltage us us s s the steay axs stato voltage s the eeence oto spee hch s assume to be to tmes eentable an T s the eeence electcal magnetc toue. An e ene e = e = an e =. The elaton beteen the steay u s u s an the eeence T can be gven as ollong euaton. T LpT RT = us = us = p (4) 3p 3p 3p We apply the eos e e an e as ne state vaables. In the eloente contol o the SPMSM s geneally set to zeo. Then the electcal magnetc subsystem can be tten as e R u et = e pe e p e (5) t L L 3p hee e ω e T u u ()(5) u = u u e. Then the electcal mechancal subsystem can be tten as e R p u = e e t L L L e u s T u su s (4) u s u u αβ αβ p e u a u b θ /s a b VSI 3/ Fgue The contol stuctue o the SPMSM pe e abc SPM SM T L Spee(/mn) Toue (Nm) (a) Reeence spee an pactcal spee (b) Reeence toue an pactcal toue Cuent (A) (c) Contol voltage u an u () Moto cuent an s s Jke ω T T L (e) Slng moe suace s an s () Popotonal spee eo Jke ω an T T L Fgue Smulaton esults o the st case 0 ACADEMY PUBLISHER

3 JOURNAL OF SOFTWARE VOL. 6 NO. 5 MAY 0 8 Spee(/mn) Toue (Nm) (a) Reeence spee an pactcal spee (b) Reeence toue an pactcal toue Cuent (A) (c) Contol voltage u an u () Moto cuent an s s Jke ω T T L (e) Slng moe suace s an s () Popotonal spee eo Jke ω an T T L Fgue 3 Smulaton esults o the secon case T (6) 3 t p e 3p T TL = e (7) t J J t hee u = u us. In euaton (7) the unknon loa T L s geneally neglecte. Fom the esgn o the eloente contol o the moto contol e can see that the output o the spee contolle can be seen as the eeence nput o the cuent loop. Then e can use a popotonal spee eo ke to take the place o ( T T ) / L J. No the euaton (7) can be tten as the ollong euaton. e 3p = e ke (8) t J t Fom the pactce contol e can assume the ollong contons. c e T c (9) = pee p e 3 T e pe e (0) 3p t = p hee an ae postve numbe. I the couplng paametes c an c beteen the electcal magnetc subsystem an the electcal mechancal subsystem ae assume to be stubance o each system. Then each subsystem can be seen as lnea system th out stubance comng om othe subsystem. III. SLIDING MODE CONTROL DESIGN OF SPMSM The slng moe suace o the electcal magnetc subsystem can be esgne as ollong euaton. s = e k ò e t k > 0 () The contol ule o the slng moe suace s selecte as ollong euaton. s& = m s sgn( s ) m > 0 () hee sgn(.) s sgn uncton. Then om euaton (5) () an () e can obtan u. u = Lm s L sgn( s ) Re Lke (3) The slng moe suace o the electcal mechancal subsystem can be esgne as ollong euaton. s = e k ò e t k3e& k > 0 k3 > 0 (4) The contol ule o the slng moe suace s selecte as ollong euaton. s& = m s sgn( s ) m > 0 (5) Then om euaton (6) (8) (4) an (5) e can obtan u. 0 ACADEMY PUBLISHER

4 8 JOURNAL OF SOFTWARE VOL. 6 NO. 5 MAY 0 Spee(/mn) Toue (Nm) (a) Reeence spee an pactcal spee (b) Reeence toue an pactcal toue Cuent (A) (c) Contol voltage u an u () Moto cuent an s s Jke ω T T L (e) Slng moe suace s an s () Popotonal spee eo Jke ω an T T L Fgue 4 Smulaton esults o the th case JL 3p R u kk ) e = [ms sgn( s ) ( k3 3p k3 J L 3p ( k k k3 k k3) e k3 ] (6) JL t t Fom the esgn e can see that hen the system states each slng moe suace the vaable o the eo moel also eaches zeo. The stablty poo o the SPMSM contolles s a vey easy task so t s neglecte n the pape. IV. SIMULATION RESULTS AND ANALYSIS The contol stuctue o the SPMSM ve system s gven n Fgue hee VSI pesents voltage souce nvete 3/ pesents stato abc cuent to αβ cuent. Table gves the nomal paametes o the SPMSM. An The contol paametes ae gven n Table. TABLE PARAMTER OF THE SPMSM R (W) L(mH) J ( K g m ) p (b) TABLE PARAMETERS OF THE SPMSM k k k k 3 m m In the st case smulaton the moto spee s set to be asymmetcal tangula ave hose magntue s 30/mn an euency s 0Hz. The eeence electcal magnetc toue s set to be a snusoal ave hose magntue s 0Nm an euency s 5Hz. To test the spee an toue tackng peomance e elbeately set the eeence spee an toue euency as eent euency. The smulaton esults ae gven n Fgue. In the secon case smulaton the moto spee s set to be a snusoal ave hose magntue s 30/mn an euency s 0Hz. The eeence electcal magnetc toue s set to be a snusoal ave hose magntue s 0Nm an euency s 5Hz. The smulaton esults ae gven n Fgue 3. In the th case smulaton the moto spee s set to be a snusoal ave hose magntue s 30/mn an euency s 0Hz. The eeence toue s set to be a symmetcal ectangle ave hose magntue s 5Nm an euency s 5Hz. The smulaton esults ae gven n Fgue 4. In the outh case smulaton the moto spee s set to be a symmetcal ectangle ave hose magntue s 30/mn an euency s 0Hz. The eeence electcal magnetc toue s set to be a symmetcal ectangle ave hose magntue s 5Nm an euency s 5Hz. The smulaton esults ae gven n Fgue 5. 0 ACADEMY PUBLISHER

5 JOURNAL OF SOFTWARE VOL. 6 NO. 5 MAY 0 83 Spee(/mn) Toue (Nm) (a) Reeence spee an pactcal spee (b) Reeence toue an pactcal toue Cuent (A) (c) Contol voltage u an u () Moto cuent an s s Jke ω T T L (e) Slng moe suace s an s () Popotonal spee eo Jke ω an T T L Fgue 5 Smulaton esults o the outh case Spee(/mn) Toue (Nm) (a) Spee tackng compason (b) Toue contol compason Fgue 6 Smulaton esults o the th case In the th case smulaton the stato R changes om W to 3 W an the moment o neta changes om 0.00Kgm to 0.00Kgm. Othe contons ae the same as the st case. The smulaton esults compason o the spee an toue contol th the st case ae gven n Fgue 6. In the sxth case smulaton the stato R changes om W to 3 W an the moment o neta changes om 0.00 Kgm to 0.00 Kgm. Othe contons ae the same as the secon case. The smulaton esults compason o the spee an toue contol th the secon case ae gven n Fgue 7. In the seventh case smulaton the stato R changes om W to 4 W an the moment o neta changes om 0.00 Kgm to Kgm. Othe contons ae the same as the th case. The smulaton esults compason o the spee tackng contol an toue contol th the th case ae gven n Fgue 8. In the eghth case smulaton the stato R changes om W to 4 W an the moment o neta changes om 0.00 Kgm to Kgm. Othe contons ae the same as the outh case. The smulaton esults compason o the spee an toue contol th the outh case ae gven n Fgue 9. Fom the system esgn an smulaton esults e can conclue the ollongs: () The vson o the SPMSM moel s ght an eectve o the esgn o the contolle. It can be seen as the ecentalze system hch s ely eseache an the ecentalze contol theoy can be apple to the system esgn ectly [3]. 0 ACADEMY PUBLISHER

6 84 JOURNAL OF SOFTWARE VOL. 6 NO. 5 MAY 0 Spee(/mn) Toue (Nm) (a) Spee tackng compason Fgue 7 Smulaton esults o the sxth case (b) Toue contol compason Spee(/mn) Toue (Nm) (a) Spee tackng compason (b) Toue contol compason Fgue 8 Smulaton esults o the seventh case Spee(/mn) Toue (Nm) (a) Spee tackng compason Fgue 9 Smulaton esults o the eghth case (b) Toue contol compason () The eo moel o the SPMSM s a novel ay by hch a lot o lnea contol theoy can be use. An the stablty contol theoy can be easly use o the eo moel o the SPMSM ve system ectly. (3) The popotonal spee eo can take the place o the unknon loa though the ajustment o the popotonal paametes. The smulaton esults sho that the popotonal spee eo can tackng the vaaton o eent types o the unknon loas th lttle eo. (4) The slng moe contol o the SPMSM base on the eo moel not only has goo ast spee tackng peomance but also has stong obustness to paamete vaaton an out stubances. V. CONCLUSIONS In ths pape e gve a novel eo moel o the SPMSM hch can be seen as the combnaton o to ecentalze subsystems the electcal magnetc subsystem an electcal mechancal subsystem. The popotonal spee eo s use to take the place o the unknon loa. The slng moe contol s apple to the contolles esgn o the SPMSM ve system. Smulaton esults sho that the popose scheme has goo contol peomance. It s ell knon that slng moe contol th hgh slng moe gans can cause the chatteng o the system. To enhance the contol peomance uthe eucton o the chatteng cause by hgh slng moe gans s neee n the utue. ACKNOWLEDGMENT The authos sh to thank the suppot o the Scence an Technology Depatment o Zhejang Povnce. Ths ok as suppote by a gant om 00C5096. REFERENCES [] R. J. Wa Total slngmoe contolle o PM synchonous sevo moto ve usng ecuent uzzy neual netok IEEE Tans. Contol Syst. Technol. vol.48 no.5 pp Octobe 00. [] J. Lee J. Hong K. Nam R. Otega L. Paly A. Astol Sensoless contol o suacemount pemanentmagnet synchonous motos base on a nonlnea obseve IEEE Tans. Poe Electon. vol. 5 no. pp.9097 Febuay 00. [3] F. F. M. ElSousy Hyb H base aveletneualnetok tackng contol o pemanentmagnet synchonous moto sevo ves IEEE Tans. In. Electon. vol. 57 no. 9 pp Septembe ACADEMY PUBLISHER

7 JOURNAL OF SOFTWARE VOL. 6 NO. 5 MAY 0 85 [4] Y. A. I. Mohame A hybtype vaablestuctue nstantaneous toue contol th a obust aaptve toue obseve o a hghpeomance ectve IEEE Tans. In. Electon. vol. 54 no. 5 pp Octobe 007. [5] R. Eouss M. Ouhouche Nonlnea pectve contolle o a pemanent magnet synchonous moto ve Mathematcs an Computes n Smulaton vol.8 no. pp Octobe 00. [6] S. Mat C. Chakaboty S. Sengupta Smulaton stues on moel eeence aaptve contolle base spee estmaton technue o the vecto contolle pemanent magnet synchonous moto ve Smulaton Moellng Pactce an Theoy vol.7 no.4 pp Apl 009. [7] C. Elmas O. Ustun A hyb contolle o the spee contol o a pemanent magnet synchonous moto ve Contol Engneeng Pactce vol.6 no.3 pp.6070 Mach 008. [8] Y. Feng J. Zheng X. Yu N. V. Tuong Hyb temnal slngmoe obseve esgn metho o a pemanentmagnet synchonous moto contol system IEEE Tans. In. Electon. vol. 56 no. 9 pp Septembe 009. [9] J. Guznsk H. AbuRub M. Dguet Z. Kzemnsk A. Leck Spee an loa toue obseve applcaton n hghspee tan electc ve IEEE Tans. In. Electon. vol. 57 no. pp Febuay 00. [0] A. Y. Achou B. Menl S. Bacha I. Munteanu Passvtybase cuent contolle esgn o a pemanentmagnet synchonous moto ISA Tansactons vol.48 no.3 pp May 009. [] V. I. Utkn Slng moe contol esgn pncples an applcatons to electc ves IEEE Tans. In. Electon. vol. 40 no. pp.336 Febuay 993. [] F. J. Ln H. J. Hseh P. H. Chou Tackng contol o a toaxs moton system va a ltengtype slngmoe contol th aal bass uncton netok IET Contol Theoy & Applcaton vol.4 no.4 pp Apl 00. [3] K. Kals J. Lan S. H. Zak Decentalze ynamc output eeback contol o nonlnea nteconnecte systems IEEE Tans. Autom. Contol vol. 55 no. 8 pp August 00. Baojun Wang as bon n Januay 964. He s the assocate poesso o Insttute o Inomaton Technology Zhejang Insttute o Communcatons Hangzhou Zhejang P. R. Chna. He s esponsble o the majo o netok technology o compute. Hs eseach el nclue stbute netok opeaton system automaton an contol system technology. Jajun Wang as bon n 975. He eceve the B.Sc.egee n nustal automaton om Shanong Lght Inustal Insttute Jnan Shanong P. R. Chna n 997 the M.Sc. egee n contol theoy an contol engneeng an the Ph.D. egee n poe electoncs an poe ve om Tanjn unvesty Tanjn P. R. Chna n 000 an 003. He has been assocate poesso om 005 th the Insttute o Automaton Hangzhou Danz Unvesty Hangzhou Zhejang P.R. Chna. Hs eseach nteests nclue slng moe contol backsteppng neual netoks an thes applcatons n nucton moto an pemanent magnet synchonous moto ve systems. 0 ACADEMY PUBLISHER