Online parameter tracking in PMSM-control schemes with and without encoder

Transcription

1 Onlin paramr racking in PMSM-conrol schms wih an wihou ncor Dipl.-Ing. Simon Fursängr, Univrsiä Sign, Prof. Dr.-Ing. Mario Pacas, Univrsiä Sign, Absrac Th ncorlss opraion bas on funamnal wav mols of h PMSM ruirs h knowlg of h machin paramrs o nsur an accura simaion of h roor posiion. As h saor rsisanc an prmann roor flux ar mpraur pnn, hs valus n o b aap o nsur a goo prformanc of h riv. In his papr, an onlin paramr racking mho for h PMSM is inrouc, which is abl o inify h mpraur pnn paramrs in high ynamic applicaions wih coninuously changing sp an oru. I works in boh mos of opraion wih as wll as wihou mchanical angl ncor. 1 Inroucion In h las cas, innsiv rsarch was carri ou on h vlopmn of conrol schms for h prmann magn synchronous machin (PMSM) wihou mchanical angl ncor. Common argumns for h us of snsorlss conrol schms ar h rucion of coss u o h liminaion of h snsor an h associa uipmn (.g. cabl, inrfac car, insallaion, c.) an h rliabiliy improvmn u o h inpnnc of an ncor. Howvr, hr ar applicaions wih spcial ruirmns of ynamics or accuracy of h riv sysm ha mak h uilizaion of an ncor manaory in h rgular opraion bu ha can ak avanag of a snsorlss conrol schm for mrgncy opraions in cas of snsor failurs: If a failur is c, h riv can kp running in h ncorlss opraion mo unil h nx rgular inspcion. If ncssary h ynamic of h riv can b ruc or h mrgncy mo can a las allow a conroll sop avoiing furhr amags in h machin or h procss. I is wll known, ha all snsorlss conrol schms, hos ha us signal injcion o c h roor posiion [2]-[3] or spcially h so-call funamnal wav mols [1] n h xac knowlg of h machin paramrs, lik saor rsisanc, prmann flux an inucancs o guaran a propr opraion. Any iscrpancy bwn h mol an h ral machin las o crasing prformanc of h riv sysm an can vn rsul in insabiliy of h conrol. Th inucancs pn mainly on h corrsponing currn bu o no show any pnnc of h mpraur. Whil inucancs can b masur a sansill an o no n o b aap onlin, his procur canno b appli o h saor rsisanc an prmann flux u o hir srong mpraur pnncy. For PMSM in inusrial applicaions h mpraur ris in ra opraion can rach 1K. Th corrsponing chang in h rsisanc of h coppr wining will b almos 4% ( α =.39% / K ). On h ohr han h prmann flux of h PMSM will cras wih incrasing mpraur, pning of h us magn marial. For NFB-magns h magniu of h prmann flux can suffr a cras of up o 12%. Th ffc of paramr variaions in h accuracy of h sima roor posiion pns on h acual opraing poin an h machin siz (variaions of h saor rsisanc ar gnrally mor crucial in smallr machins wih rlaivly high rsisanc valus). In gnral, mols of h machin ha o no compnsa h variaions of h paramrs u o mpraur changs la o wors or vn insabl bhavior. Thus, o nsur h propr opraion of h PMSM h mol paramrs n o b rack onlin. In aiion o h mhos which us a hrmal mol of h machin o allow a rough simaion of h saor rsisanc, som procings ar scrib in h liraur, which ar abl o inify h changs of machin paramrs onlin: In [4] h prmann flux is masur onlin in orr o sima h roor mpraur. Y, his approach works only wih mchanical angular ncor. In [5] a mho is scrib, which as an AC-componn o h rfrnc of h flux gnraing componn of h saor currn in orr o inify h paramrs. Howvr, his mho can only Cu ISBN VDE VERLAG GMBH Brlin Offnbach 12

2 work in say sa coniions an is hrfor no suiabl for high ynamic applicaions wih coninuous changing sp an oru. Svral ohr mhos [6]-[8] can inify h saor rsisanc unr h assumpion ha h prmann flux is known an os no chang. As sa abov, i is obvious ha his assumpion is no vali for high mpraur variaions in h machin. In [9] h saor rsisanc is masur onc a sansill wih signal injcion an h chang of h prmann flux is compnsa onlin uring h normal opraion. A furhr mho is scrib in [1], which allows an aapaion of h saor rsisanc in h low sp rgion an an aapaion of h prmann flux a highr sps. Y, a coninuous paramr racking is no possibl. Furhrmor, h mnion mhos [5]-[1] wr valia wih low powr PMSM an c-link volags of mainly 15V or 28V. This is suiabl for crain applicaions bu no in sanar inusry applicaions wih 56V c-link volags. I is worh o mnion ha h inificaion of h saor rsisanc is mor crucial wih highr c-link volags an highr powr machins as h small volag rop of h saor rsisanc is masur rla o h swich c-link volag. Th following chaprs scrib a nw mho for h inificaion of h saor rsisanc as wll as of h prmann flux in high ynamic applicaions wih coninuous changing sp an oru. Th prsn conrol schm for h ajusmn of h machin paramrs is bas on h saor uaions of h PMSM in h --rfrnc fram. 2 Conrol srucur Th implmn conrol srucur is pic in Fig. 1. I is bas on h wll known fil orin conrol wih ncor an has aiionally a runan snsorlss roor posiion simaion bas on h proposal of [1]. Th a im compnsaion block is ssnial for a goo prformanc of h snsorlss conrol as wll as for h paramr inificaion. I liminas h nonlinariy of h invrr moul, spcially h volag rror caus by h invrr a im [1]. Th conrol srucur can b swich onlin from conrol wih ncor o snsorlss opraion by closing h conrol loop ihr wih h masur or wih sima valus of h posiion angl an angular vlociy. i Currn Conrollr u u jφ u α u β 2 3 u U u V u W Daim Compnsaion D U D V D W i φ i -jφ i α i β 2 3 i U i V u φ PMSM i u u Machinmol Roorposiionsimaion φ φ m m i Paramr racking Fig. 1. Conrol srucur Wih h implmn mahmaical machin mol h volags u an u can b calcula, mol, mol on h basis of h saor currn i = i + j i an h angular vlociy. ISBN VDE VERLAG GMBH Brlin Offnbach 121

3 Th volag rrors u an u can b obain by subracing h mol volags from h volag rfrncs u an u. Ths valus ar ncssary for h implmn snsorlss conrol as wll as for h paramr inificaion. i u = u u = u R i L + L i, mol s i u = u u = u R i L L i Ψ, mol s In h acual conrol mho h mol is ihr f by h masur valus ( i = i, = ) or h m m sima valus ( i = i, = ) pning on h way of calculaing h --componns of h saor currn. In h firs cas h ransformaion of h masur currns o h --rfrnc fram is prform by using h masur roor posiion angl, in h scon h sima angl is uiliz. In h opraion wih angular ncor h volag rrors u an u ar zro if h mol paramrs xacly corrspon o h ral ons an h machin asymmris can b nglc. Thus, any iffrncs in h valus of h volag rrors rsul from wrong mol paramrs, as i is shown in (3) an (4), whr R = R R, Ψ = Ψ Ψ an L = L L. S S, mol S, machin, mol, machin,mol, machin Hnc, h volag rrors can b us o ajus h mol paramrs as i is shown in h nx paragraph. i (3) u = R i L + L i s i u = R i L L i Ψ (4) s In ncorlss opraion h calcula volag rrors can b us by h Roor posiion simaion - block in Fig. 1 o sima h acual roor posiion as ail scrib in [1]. In his opraion h volag rrors pn on h angl rror ϕ = ϕ ϕ an angular vlociy rror = (5-6). For small angl rrors ( sin( ϕ) ϕ, cos( ϕ) 1 ). u = Ψ sin ϕ Ψ ϕ ( cos ) u = Ψ ϕ Ψ ϕ h uaions can b simplifi by approximaing h rigonomric rms (5) (6) Accoring o [1] h roor posiion can b sima bas on h wo volag rrors by using h conrol srucur pic in Fig. 2. This simaion of h roor posiion works proprly if h paramrs of h mol fi o hir physical valus, ohrwis h volag rrors inclu rms caus by paramr variaions an cras h prformanc of h snsorlss conrol [1]: i u Ψ ϕ R i L + L i s i u Ψ R i L L i Ψ s In ncorlss mo of opraion (7) (8) as wll as in opraion mo wih ncor (3) (4), h wo volag rrors pn on h variaions of h paramrs. Howvr, wihou angular ncor h volag rror u canno b us for h paramr inificaion bcaus i pns no only on h u u k p - 1 Ψ T s Fig. 2. Roor posiion simaion + φ (1) (2) (7) (8) ISBN VDE VERLAG GMBH Brlin Offnbach 122

4 variaions of h paramrs bu also on h angl rror ϕ. A coupling of boh pars, paramr variaions an angl rror, is no possibl. This rsricion os no apply o h volag rror u ha only pns on h angular vlociy rror whos avrag valu is zro as long as h snsorlss conrol is sabl. Thrfor, h volag rror u can b us for paramr racking vn in h snsorlss opraion. 3 Paramr Tracking To achiv h onlin paramr racking, h ffc of ach paramr rror on h volag rror has o b xamin. I is obvious ha h volag rror uaions (3) (4) ar unr-rmin. In h opraion mo wih ncor hr ar wo uaions wih four unknown machin paramrs; in h ncorlss opraion mo (7) (8) h problm is vn wors sinc h volag rror u canno b us o inify h paramrs. Thus, som simplificaions ar ncssary in orr o coupl h ffcs on h four unknown variabls. Firs of all, h rivaiv rms in (3) (4) an (7) (8) can b nglc as hir avrag valus ar zro an h ynamic of h paramr racking will xhibi a slow bhaviour u o h larg hrmal im consan of h machin. Furhrmor, h uaion sysm can b simplifi by sparaing h bas sp rang from h fil wakning ara. In h bas sp rang, h flux gnraing currn i is zro. So h uaions (3) an (4) can b simplifi as follows: u L i u R i Ψ s (9) (1) whr h volag rror uaion u is only vali in h opraion wih angular ncor. As can b sn in (9), h valu of h inucanc L can ircly b sima by h volag rror u. Howvr, h inucancs of h machin ar mpraur inpnn an an onlin paramr racking is no ncssary. In h cas of h inucancs L an L i is rasonabl o masur hm onc a sansill [1]. For h rminaion of h saor rsisanc an h prmann link flux, h volag rror uaion in axis ns o b coupl: For highr sps h impac of h flux rror incrass whil h impac of h rsisanc rror incrass wih highr currn. For h coupling of boh paramrs h srucur in Fig. 3 is propos, which uilizs wo wigh I-conrollr o aap h paramrs R an S Ψ so ha h valu of h volag rror u bcoms zro. Th coupling of h wo paramrs is achiv by iffrn wighing facors in ach channl: By muliplying h volag rror u wih h saor currn h gain in his loop is high for highr currn valus whras i is ruc in a scon sp for highr angular vlociy (Fig. 3). Accoring o his, h aapaion of h saor rsisanc convrgs mos uickly in opraion poins wih high currn an low sp. Th mchanism for h aapaion of h prmann flux bhavs vic vrsa so ha boh paramrs convrg o hir corrc valus if h machin runs frunly unr a las wo iffrn opraing poins (.g. consan sp bu changing oru or vic vrsa). In ynamic applicaions h sp as wll as h oru is changing consisnly. Thus, h coniion for h paramr simaion is fulfill. u X X / N...1% % % % >75% / N i i...1% 1...5% % >15% x1 x1/2 x1/4 x1/8 x1/16 x1 x1/2 x1/4 x1/8 x1/16 Fig. 3. Dcoupling of h volag rror K I,R s K I,Ψ s R S Ψ ISBN VDE VERLAG GMBH Brlin Offnbach 123

5 4 Exprimnal Rsuls To valia h inrouc onlin paramr racking mho, a PMSM was conroll wih a profil of changing sp rfrnc an loa oru which is pic in Fig. 5 o mula a procss wih high ynamics. Th Nominal Valus of h machin can b sn in Tabl 1. Ra oru 7.8Nm Ra currn 5.1A Ra volag 36V Ra sp 3min -1 Ra powr 2.45kW Pol pairs 3 Saor rsisanc 1.2Ω Prmann link flux 25mVs DC-Link volag 56V PWM fruncy 8kHz Tmpraur- Snsor Drivingmachin.9m Loamachin Tabl 1: Nominal valus a 2 C Fig. 4. Mchanical sup n/n N 5% -5% 2s 4s 6s 8s Ψ /Ψ 2 M/M N 2% 98% 96% 3min 6min 9min 12min 15min - 2s 4s 6s 8s R s /R 2 15% -2% 13% Fig. 5. Prioical sp rfrnc an loa oru Th machin was rivn unil is mpraur rach h say sa. For his purpos h machin cas mpraur was masur an h prmann flux as wll as h saor rsisanc hav bn inifi wih h propos onlin paramr racking mho in h opraion wih mchanical snsor an in ncorlss opraion. Fig. 6 shows h inifi paramrs in snsorlss opraion. A h bginning an a h n of h masurmn, h saor rsisanc was also masur ircly in orr o compar h inifi paramrs wih h physical ons. Th paramr inificaion wih ncor, which is lss challnging han wihou ncor, las o h sam rsuls. 11% 9% T 12 C 8 C 4 C C masur valus 3min 6min 9min 12min 15min 3min 6min 9min 12min 15min Fig. 6. Inifi machin paramrs an masur cas mpraur ISBN VDE VERLAG GMBH Brlin Offnbach 124

6 Evn if h mol iniial paramrs ar s wrong, h racking mho convrgs o h physical valus. Fig. 7 shows how h inifi paramrs convrg in h opraion wih ncor if h mol paramrs ar chang o purposly wrong valus. Bcaus of h larg hrmal im consan of h machin, h ynamic of h paramr racking mho is chosn vry slow o incras h robusnss agains isurbing ffcs. Furhr masurmns wih a iffrn Machin (.51kW, 1Nm) confirm h robusnss of h onlin paramr racking mho. 5 Conclusion A mho for h onlin paramr racking is propos in his papr. I allows h inificaion an aapaion of h mpraur pnn paramrs of h PMSM for h opraion wih an wihou angular ncor. Th mho works vry rliabl in applicaions wih sp an loa variaions bu ns a las wo frunly changing opraion poins. Exprimnal rsuls valia h corrc funcion of h propos schm. Ψ /Ψ 2 12% 11% 9% paramrs chang o wrong valus R s /R 2 15% 13% 11% 9% 7% 5% 2min 4min 6min paramrs inifi corrcly 2min 4min 6min Fig. 7. Bhavior of h racking mho by sing h paramrs purposly wrong 6 Rfrncs [1] Barinbrg, V.; Göz, F.: Vrbssrs Spannungs-Moll zur snsorlosn Ansurung von Anribn mi prmannrrgn Synchronmoorn, SPS IPC Drivs 28 [2] Schröl, M.; Simzbrgr, C.: "Snsorlss conrol of PM synchronous moors using a priciv currn conrollr wih ingra INFORM an EMF valuaion", Powr Elcronics an Moion Conrol Confrnc, 28. EPE-PEMC h, pp , 1-3 Sp. 28 [3] Link, M.; Knnl, R.; Holz, J.: "Snsorlss sp an posiion conrol of synchronous machins using alrnaing carrir injcion", Elcric Machins an Drivs Confrnc, 23. IEMDC'3. IEEE Inrnaional, vol.2, pp vol. 2, 1-4 Jun 23 [4] Spch, Anras; Bockr, Joachim: "Obsrvr for h roor mpraur of IPMSM", Powr Elcronics an Moion Conrol Confrnc (EPE/PEMC), 21 14h Inrnaional, pp.t [5] L, K.; Jung D.; Ha, I.: An Onlin Inificaion Mho for Boh Saor Rsisanc an Back- EMF Cofficin of PMSMs Wihou Roaional Transucrs, IEEE Transacions on Inusrial Elcronics, vol. 51, pp , April 24 [6] Inou, Y.; Kawaguchi, Y.; Morimoo, S.; Sanaa, M.: "Prformanc improvmn of snsorlss IPMSM rivs in low-sp rgion using onlin paramr inificaion", Enrgy Convrsion Congrss an Exposiion, 29, pp , 2-24 Sp. 29 [7] Morau, S.; Kahoul, R.; Louis, J.-P.: "Paramrs simaion of prmann magn synchronous machin wihou aing xra-signal as inpu xciaion", Inusrial Elcronics, 24 IEEE Inrnaional Symposium on, vol.1, pp vol. 1, 4-7 May 24 [8] Nahi Mobarakh, B.; Miboy-Tabar, F.; Sargos, F.M.: "On-lin inificaion of PMSM lcrical paramrs bas on coupling conrol", Inusry Applicaions Confrnc, 21. Thiry-Sixh IAS Annual Ming. Confrnc Rcor of h 21 IEEE, vol.1, pp [9] Morimoo, S.; Sanaa, M.; Taka, Y.: "Mchanical snsorlss rivs of IPMSM wih onlin paramr inificaion", Inusry Applicaions Confrnc, 25. Fourih IAS Annual Ming. Confrnc Rcor of h 25, vol.1, pp , 2-6 Oc. 25 [1] Fukumoo, T.; Haman, H.; Hayashi, Y.: "Prformanc Improvmn of h IPMSM Posiion Snsorlss Vcor Conrol Sysm by h On-lin Moor Paramr Error Compnsaion an h Pracical Da-im Compnsaion", Powr Convrsion Confrnc - Nagoya, 27. PCC '7, pp , 2-5 April 27 ISBN VDE VERLAG GMBH Brlin Offnbach 125