Extended Torque-Speed Region Sensor-Less Control of Interior Permanent Magnet Synchronous Motors

Transcription

1 Extn oru-sp Rgon Snsor-Lss Control of Intror Prmannt agnt Synchronous otors arco ursn 1, Alssa Scafat 1, Alssanro Gurrro 1, Robrto Ptrlla 1 Dpartmnt of Elctrcal an Informaton Engnrng, Unrsty of L'Aula Poggo Roo, L Aula, Italy Dpartmnt of Elctrcal, anagmnt an chancal Engnrng, Unrsty of Un Va ll Scnz, Un, Italy Abstract - In ths papr a snsor-lss sp controllr for an Intror Prmannt agnt synchronous motor s prsnt. It allows to fully xplot th toru-sp charactrstc of th motor, also n th flux-waknng rgon. It s bas on th stmaton of a gnralz back-ef spac ctor by mans of a Lunbrgr stat an sturbanc obsrr. h stmat rotor-magnt poston an sp ar thn mploy ns an optms ctor control schm of rct an uaratur motor currnts trajctors. st rsults ar prsnt, n orr to rfy th prformanc an monstrat th ffctnss of th propos soluton. I. INRODUCION h so-call Intror Prmannt agnt (IP) synchronous motor (bul wth magnts splac ns th rotor boy) rprsnts an attract soluton for mrgng applcatons, such as lctrc hcls an omstc applancs. Lk th mor popular Surfac Prmannt agnt (SP) synchronous motors (bult wth magnts splac on th rotor surfac), th IP motors ar charactrz by th absnc of rotor losss, that calls for cool rotor an ncrasng ffcncy, an th hgh toru s. wght rato. Atonal faturs ar th robustnss of th rotor structur, mchancally sut to hgh sp opraton, an th prsnc of magntc salncy, that s th rct axs nuctanc s substantally ffrnt from th uaratur axs nuctanc, whr th axs s usually slct to b algn wth th P flux axs accorng to th ualnt Park mol of th synchronous machn. hs charactrstc s partcularly sut for xtnng th toru/sp opratng rgon by propr fl waknng control tchnus, [1]; an, also, t allows th applcaton of som spcfc approachs to poston an sp tcton ( slf-snsng or snsor-lss control), such as njcton of hgh fruncy oltag or currnts nstgatng th rotor salncy, []. Dspt of ths, IP motors ar stll far from a larg ffuson, on of th rasons bng crtanly th ffcult mplmntaton of a controllr abl to fully xplot ts pcularts, a task strctly rlat to th spcfc motor sgn, [3]. In fact, th salncy gs rs to ut strong non-lnar opratng charactrstcs, oftn ncras by saturaton an mutual axs ntracton ( crosscouplngs ). hn, to tak aantag of th motor faturs, th controllr must ft th motor charactrstcs as clos as possbl an all or th opratng rang. In ths papr a snsor-lss sp controllr for an ntror prmannt magnt synchronous motor s prsnt. It allows to fully xplot th toru-sp charactrstc of th motor, also n th flux-waknng rgon. It s bas on th stmaton of a gnralz back-ef spac ctor by mans of a Lunbrgr stat an sturbanc obsrr, an allows an unf approach both for surfac an ntror P motors. h stmat rotormagnt poston an sp ar thn mploy ns an optmz ctor control schm of rct an uaratur motor currnts trajctors. st rsults ar prsnt, usng an xprmntal st-up bas on th S 30F81 Dgtal Sgnal Controllr (DSC), n orr to rfy th prformanc an monstrat th ffctnss of th propos soluton. II. FICIIOUS PERANEN-AGNE FLUX ODEL An IP synchronous motor hang symmtrcal wyconnct stator phass wth solat nutral conncton an snusoal back-ef s consr. Nglctng saturaton an cross-couplngs ffcts, th Park -mol of th machn s: ψ = R s = R + pψ + ωψ s = L ψ = L + pψ ωψ + ψˆ whr,,,, ψ, ar th componnts of oltag, currnt an flux lnkag of th ualnt -crcuts, th rspct L, synchronous nuctancs, R s th wnng rsstanc, ψˆ th prmannt magnt flux lnkag, ω th rotor lctrcal sp, an p = /t. otor lctromagntc toru can b calculat as: 3 m = PP[ ψˆ + ΔL ] whr PP s th numbr of pol pars, an L = L L. (1) ()

2 By substtutng fluxs xprssons nto oltag uatons, th oltag mol s obtan: = R s = R s + L p + L p + pψˆ + ωl ωl + ωψˆ whr synchronous nuctancs ar assum to b constant an prmannt magnt flux lnkag s consr as a tm aryng functon. Prous uaton can b mathmatcally manpulat n orr to obtan an xprsson that s formally ualnt to that of a SP, by fnng th fcttous prmannt-magnt flux as llustrat n Fg. 1, [4]: r (3) ψˆ = ψˆ + ΔL. (4) S β s Δ L r ψ Fg. 1 Fcttous prmannt-magnt flux rprsntaton. Prmannt magnt flux lnkag ψˆ calculat from (4) can b substtut nto () an (3) gng rspctly: = R s = R s N 3 m = pψˆ + L p + L p + pψˆ + ωl ψ r ω ωl + ωψˆ hs rlatons show that IP motor can b consr ualnt to SP hang L as synchronous nuctanc an th prmannt magnt flux rplac by th fcttous on. Euaton (6) can b consr a gnrals oltag mol for both IP an SP, whr propr sgnfcanc of th prmannt magnt flux lnkag s assum. If matrx form s consr an th transformaton from th rotor-fx to th stator-fx αβ ualnt crcuts s prform, th followng rlaton s obtan: whr: + α s (5) (6) αβ = Rsαβ + Lpαβ αβ (7) = = ˆ + Δ ( ) ) cos αβ pψ p ( ψ αβ L t (8) sn rprsnts th spac ctor of th back-ef rlat to th fcttous prmannt magnt flux (n th followng rfrr as gnralz back-ef), whch concs wth th usual back- EF whn an sotropous motor s consr: = ˆ cos ΔL 0 : αβ pψ p ψ αβ sn By assumng a stay-stat conton for th rct axs currnt ( p = 0 ), th componnts of th gnralz back-ef can b wrttn: α β ( r ) ( ) ω ω( k + ΔL ) ( k + ΔL ) cos sn bng k th usual back-ef constant. By ths assumpton th spac ctor of th gnralz back-ef s 90 grs splac wth rspct to th P flux (s Fg. 1), an ts ampltu = β + α = ω + ( k ΔL ) pns on motor sp an rct currnt. ol (7) can b arrang nto canoncal stat form: p [ A] + [ B] [ B] (9) (10) = (11) [ α β whr th currnt componnts =, ] ar stat arabls, th oltags [ α, β [ α, β = ] ar known nputs, th gnralz back- EFs = ] act as sturbancs, an th systm paramtrs matrcs ar x whr [ I] R R L s [ A] = [] I, [ B] [] I s th unt matrx. 1 = (1) L III. BACK-EF OBSERVER ol (11) can b manpulat amng at th lopmnt of a ynamcal stat an sturbanc obsrr for th stmaton of th gnralz back-ef componnts (9), whch contan n fact th rotor-magnt poston nformaton, n for motor control. h gnralz back-ef sturbanc can b mol through a fcttous ynamcs, such that: p = 0 (13) Hraftr, from (11) an (13), th followng 4 th orr ynamcal systm s obtan: ~ ~ p x = [ A] x + [ B] u (14) whr [ α, β, α, β x = ] s th stat an sturbanc ctor, [ β u = α, ] ar th nputs an

3 [ A] [ B] [] [] 0 0 [ A] ~ =, [ B] [] [ B] ~ = (15) 0 ar systm paramtrs matrcs. ol (15) s suppos to b lnar an tm-narant. Hnc, a Lunbrgr stat obsrr can b bul as follows: [ A] xˆ + [ B] u + [ K] ( ˆ ) xˆ = (16) whr x ˆ = ˆ, ˆ, ˆ, ˆ ] s th ctor of stmat uantts 4x an [ ] [ α β α β K R s a gan matrx. h Lunbrgr obsrr stmats th gnralz back-ef (an currnts) componnts from th masurmnt of th motor phas oltags an currnts; t uss th currnt stmaton rror (.. th ffrnc btwn th masur an th stmat on) as corrcton fback. Accorng to (9), upon th stmaton of th back-ef componnts, th magnt axs poston s obtan by a rrs trgonomtrc formula such as: = arccos ˆ + β ˆ α ˆ β (17) hs approach las to calculat th stmat sp as th rat of th stmat poston, Fg.. ωˆ α β /t Lunbrgr Obsrr ˆα arccos ˆ β Fg.. Snsor-lss stratgy IV. EXENDED ORQUE-SPEED CONROL OF HE IP OOR hs scton brfly rcalls som hnts about th toru-sp opraton of an IP, an how t can b optmz by propr currnt ctor control stratgy. A. IP opraton n th Park currnts plan Nglctng th rsst rop at hgh sp opraton, th suar alu of th stay-stat oltag ampltu of th IP s gn by: = + ω ( ψ + ψ) (18) Hraftr, th constant oltag ( ), toru ( m ) an currnt ( ) loc n th Park currnts plan can b foun as follows: ω ( L + ψˆ ) + ( ξ L ) α β (19) Fg. 3 Constant toru, oltag an currnt loc n th Park currnts plan. m ( 1 ξ) = ψˆ + L (0) = + (1) whr th salncy rato ξ = L L s ntrouc. h constant loc ar rprsnt n Fg. 3, thy ar known as oltag llps, toru hyprbola, an currnt crcl rspctly. At rat conton thy shar a pont whch s th rat opratng pont of th IP motor (pont B); accorng to (19), for ncrasng sp (an fx rat oltag) on has a famly of oltag lmt llpss whch conrgs to thr cntr gn by ( ψˆ L, 0 ), (pont C): n that pont th sp s thortcally nfnt an th toru s zro. wo mor curs can b raft n orr to aluat th control stratgy of an IP, [1]: a) th maxmum toru-to-currnt rato cur, whch s th locus of th ponts closst to th orgn or ach constant toru hyprbola; an b) th maxmum toru-tooltag rato cur, whch s th locus of th ponts at maxmum toru or ach oltag llps (ths last bul wth fx rat oltag an ncrasng sp). hs curs ar rprsnt n Fg. 4. Dpnng on th motor sgn th maxmum toru-tooltag rato cur can b ntrnal or xtrnal to th rat currnt crcl: of cours, only n th frst cas an optmzaton s possbl mong or that trajctory. B. Optmum Control From th analyss of th charactrstcs curs rcall n th prous scton, th trajctory of optmum opraton of an IP n th Park currnts plan can b thought as rprsnt n Fg. 4, [5]: a) whn th sp s blow th rat alu ( constant toru rgon) thr s no problm for th oltag lmt, th opraton

4 must l or th maxmum/toru/to/currnt rato locus (maxmum toru s ach at pont B); b) abo th rat sp ( flux waknng rgon), th opratng zon s lmt by th oltag lmt llpss (collapsng towar thr cntr at ncrasng sp) an th rat currnt crcl: maxmum toru opraton ls on th ntrscton of ths curs (from pont B to P); c) whn th maxmum toru/to/oltag rato locus s attan (pont P), maxmum toru s possbl or that locus (from pont P to R); onc th stay stat sp s rach (n pont R), opraton ls on th oltag lmt llps tll to satsfy th rur toru wth mnmum currnt (pont Q). Such scrpton gs an a of th complxty of th currnt control for an IP. Dffrntly from th SP motor, whr th -currnt st pont s always st to zro (an th -currnt on s smply proportonal to th toru), n cas of th IP both th currnts n to b comman accorng to th toru/sp opratng pont. oltags ( α, β ), known by th controllr, ar mploy nsta of thr masurmnts. m sgn Gnralz Fg. 5 Propos snsor-lss ctor control schm for th IP. V. EXPERIENAL RESULS h xprmntal systm s shown n Fg. 6. It nclus th IP motor an th rspct brak, a gnral purpos oltag sourc nrtr (upp wth IGB powr swtchs), a control moul wth mb S 30F81 DSP. An host PC, lnk to th control moul by th sral ntrfac, s mploy both to run th softwar lopmnt nronmnt an for ral-tm sttng of control paramtrs an st-ponts. h control moul nclus a DAC conrtr, whch allows ral-tm osclloscop splay of th arabls comput by th gtal controllr. h nrtr s oprat at 10kHz PW fruncy. an ata of Fg. 4 Optmum trajctory an opratng ponts n th Park currnts plan. C. Implmntaton h optmum control stratgy can b mplmnt through thr ctor-control charactrstcs ( F t, F, F ) accorng to th schm shown n Fg. 5. hs charactrstcs wll pro th st ponts of th currnts (, ) as functons of th toru comman ( m ) an th opratng sp, that s = F ( m, ω), = F ( m, ω), whr th alu of th sp wll affct th control charactrstcs n th flux waknng rgon only. oror, n orr to assur that th comman opratng pont s attanabl, a propr lmtaton of th toru rfrnc wth th sp s ncssary, whch corrspons to th maxmum toru s. sp cur ach by optmum control, m Lm = F t (ω). h back-ef obsrr pros stmat rotor-magnt poston ( ) an sp ( ωˆ ) for currnt ctor control, sp control loop, an currnt trajctors gnraton. In orr to smplfy th mplmntaton, th comman alus of th fng Fg. 6 Exprmntal systm. ABLE I IP OOR RAED VALUES AND PARAEERS Numbr of pols pars 3 Sp (rpm) 000 oru (Nm) 5 (max 17.5) Currnt (A) 5 (max 17.5) L (mh) L (mh) Rs (ohm) 1.5 back-ef constant (V/Krpm) 64

5 1.04V = 1pu ω ωˆ, (a) Δ 100mV = 0.05pu (c), 1.04V = 1pu (b) Δ () Fg. 7 otor start-up from stanstll to 3000 rpm: (a) actual & stmat sp, poston rror (b) actual & stmat poston, currnt, poston rror (c) currnts an thr rfrncs () trajctory of th currnts rfrncs th IP motor ar rport n abl I. Both stay stat an transnt opraton ar nstgat n orr to rfy th prformanc of th propos snsor-lss approach both n th constant toru an flux-waknng rgons. Rsults ar prsnt n pr unts alus, assumng th rat sp/currnt/oltag as bas alus, an π as bas poston. Fg. 7 shows a motor start-up wth th targt sp locat at 3000 rpm n th flux waknng rgon, wth 1.5 Nm loa toru. Accorng to th optmum control stratgy, th transnt currnt ar gnrat to acclrat at maxmum toru capablty both n th constant toru (mong on th maxmum/toru/ to/currnt rato cur) an n th flux waknng rgon (mong on th rat currnt crcl). h snsor-lss algorthm s oprat off-ln n orr to aluat th conrgnc proprts. h stmat poston conrgs to th actual on ns th frst lctrcal pro, an mantans a goo trackng or th whol tst. h pak alu of th poston stmaton rror ( Δ = ) s lmt to fw grs, t s slghtly largr urng th transnt pro, an rucs whn stay-stat s rach. h strong aratons of th currnt, followng optmal trajctory urng transnt, o not affct th poston stmaton; hnc, th assumpton of p = 0 n computaton of th gnralz back-ef obsrr, can b accpt. Followng fgurs rfr to snsor-lss opraton at ffrnt stay-stat contons. Fg. 9 shows th stmat an actual poston at 3000 rpm, 1.5 Nm. h obsrr confrms th goo Δ Fg. 8 Stay-stat opraton at 3000 rpm, 1.5 Nm loa: actual & stmat poston, poston rror, currnt

6 Fg. 9 Stay-stat opraton at 110 rpm, 1.5 Nm loa: actual & stmat αβ currnts β, îβ ˆ, ˆ α α, îα β Fg. 10 Stay-stat opraton at 100 rpm, 1.5 Nm loa: (up) actual & stmat poston (own) stmat αβ gnralz back-efs prformanc at hgh-sp opraton, as xpct for a back- EF bas approach. Fg. 9 shows th stmat an actual αβ currnts, at mum sp (110 rpm), 1.5 Nm, monstratng th goo bhaour n trm of currnt obsraton, obtan by propr sttng of th rspct gan matrx. Fg. 10 rfrs to low sp opraton at 100 rpm, 1.5 Nm. As xpct by a back-ef bas approach, th prformanc rucs u to th lack of accuracy n oltag nputs an paramtr scrpancs: th stmat αβ componnts bcom stort, an th poston stmaton trorats accorngly. Fnally, abl II shows som ncat alus of th poston stmaton rror at ffrnt sp an loang contons, comput as th arag of th pak alus or th cycl. Exprmnts monstrat that th poston rror s strongly (but not lnarly) affct by th obsrr gans. Hnc, n orr to ach mnmum rror, gan alus ar ajust by a propr mappng accorng to th toru/sp opratng contons. ABLE II POSIION ESIAION ERRORS sp (rpm) no-loa 1.5 Nm VI. CONCLUSION In ths papr a snsor-lss sp control of an ntror prmannt magnt synchronous motor s prsnt. h mtho s bas on th stmaton of a gnralz back-ef spac ctor by mans of a Lunbrgr stat an sturbanc obsrr, an allows an unf approach both for surfac an ntror P motors. h snsor-lss tchnu can b mplmnt n softwar, t rurs th knowlg of th motor currnts an oltags only, an allows mplmntaton through a stanar gtal sgnal controllr an th sam harwar n for usual ctor control. Exprmntal tsts confrm th ffctnss of th propos soluton n a larg sp rang, nclung flux waknng, an ts compatblty wth optmum toru-sp control stratgs. In cas of ry-low sp (lss than 5 Hz), or stan-stll opraton, th mtho looss ts prformanc: som spcfc procurs, such as njcton of hgh fruncy oltags or currnts nstgatng th rotor salncy, can b us to orcom th problm. REFERENCES [1] J.. Km, S. K. Sul, Sp Control of Intror Prmannt agnt Synchronous otor Dr for th Flux Waknng Opraton, IEEE rans. on In. Appl., ol. 33, pp , Jan./Fb [] F. Paraslt, R. Ptrlla,. ursn, Sp Snsorlss Control of an Intror P Synchronous otor, n Conf. Rc. of th 00 IEEE-Inustry Applcatons Socty Annual tng (IAS 00), CD-Rom, Pttsburgh, Octobr 00. [3] S. R. acnn,.. Jahns, Control chnus for Impro Hghsp Prformanc of Intror P Synchronous otor Drs, IEEE rans. on In. Appl., pp , [4] S. Koonlaboon, S. Sangwongwanch, Snsorlss Control of Intror Prmannt-agnt Synchronous otors Bas on a Fcttous Prmannt- agnt Flux ol, Proc. of th IEEE-IAS Annual mtng, CD-Rom, Kowloon, Hong Kong, Oct. -6, 005. [5]. ursn, A. Scott, D. D Antono, E. Chrcozz Fast Prototypng of Vctor Controllrs for Intror P Synchronous otors, n Proc. of th Int. Conf. on Elctrcal achns (ICE 006), CD-Rom, Chana (Crt), Sptmbr 006. [6]. ursn, R. Ptrlla, A. Scafat Sp an Poston Estmaton for P Synchronous otor usng slf-compnsat Back-EF Obsrrs, n Proc. of th IEEE Inustral Elctroncs Socty (IECON-006), CD Rom, Pars, No. 7-10, 006.