Drift and Parameter Compensated Flux Estimator for Persistent Zero Stator Frequency Operation of Sensorless Controlled Induction Motors

Transcription

1 IEEE Tranacion in Indury Applicaion, 23 aa Drif and Parameer Compenaed Flux Eimaor for Perien Zero Saor Frequency Operaion of Senorle Conrolled Inducion Moor Elecrical Machine and Drive Group Univeriy of Wupperal 4297 Wupperal Germany Joachim Holz, Fellow, IEEE, and Junao Quan Danaher Moion GmbH & Co. KG 4489 Dueeldorf Germany Abrac The performance of enorle conrolled inducion moor i poor a very low peed. The reaon are he limied accuracy of aor volage acquiiion and he preence of offe and drif componen in he acquired ignal. To overcome hee problem, a pure inegraor i employed for aor flux eimaion. The ime-variable dc offe volage i eimaed from he flux drif in a parallel aor model and ued o eliminae he offe by feedforward conrol. Reidual high-frequency diurbance are compenaed by feedback flux ampliude conrol. A linearizaion of he PWM inverer ranfer funcion and an improved aor reiance eimaion cheme furher enhance he yem performance. Experimen demonrae high dynamic performance of enorle conrol a exreme low peed and zero aor frequency. Keyword: Inducion moor, enorle peed conrol, aor flux eimaor, aor reiance eimaion, PWM inverer model, dc offe eimaion, conrol a zero aor frequency I. INTRODUCTION Vecor conrolled inducion moor drive wihou peed enor have become an aracive and commercially expanding echnology in he pa few year []. The abence of he mechanical peed enor reduce he co and he volume of he drive moor. I doe away wih he enor cable, and increae he reliabiliy of he overall yem. I i ill a problem, hough, o achieve robu enorle conrol a very low peed, paricularly in a region a and around zero aor frequency. The phyical reaon i ha all eimaion mehod, direcly or indirecly, rely on he effec of he roor induced volage, which become very mall a he aor frequency reduce, and vanihe a zero aor frequency. I ha been he ubjec of recen reearch o narrow or eliminae he region of inoperabiliy around zero aor frequency. One way oward hi goal exploi paial machine anioropie ha indicae eiher he acual roor poiion, or he field angle [2]. I require ubjecing he machine o ranien condiion o a o enable he idenificaion of he anioropic characeriic. Thi can be done by injecing a coninuou high-frequency ignal ino he aor winding [3, 4], or by exploiing he repeiive ranien exciaion caued by he wiching of he PWM inverer [5]. Thee mehod could olve he zero-frequency problem in principle, bu no wihou incurring penalie. Thee are he requiremen of addiional hardware for ignal acquiiion, and/or he high compuaional load. Under hee circumance i he rericion of uing he fundamenal model of he inducion machine exremely aracive. Thi model conider only he fundamenal paial diribuion of he flux deniy and he curren deniy wave, hu decribing he elecromagneic ubyem of he machine a a dynamic yem of econd order if complex ae variable are ued [6]. The approach end o be inaccurae a lower aor frequency a he fundamenal volage are hen low in magniude. Their fundamenal componen are difficul o eparae from he wiching harmonic, and from he offe and noie componen ha ac a diurbance in he ignal acquiiion proce. Recen reearch ha aimed a improving he eimaion accuracy of he fundamenal model for flux eimaion. The key quaniy here i he phae angle of flux linkage vecor, alo referred o a he field angle d. The field angle enable he ranformaion of he aor curren vecor ino field coordinae, hu making he elecromagneic orque and he flux of he machine independenly conrollable. Thi i a prerequiie for mainaining he abiliy of a dynamic ac drive a any peed. Eiher he aor flux linkage vecor or he roor flux linkage vecor can be ued o define a field oriened coordinae yem. Preference i given here o aor field orienaion which i impler o implemen. II. LIMITS OF STABLE OPERATION AT LOW SPEED In a enorle drive yem, he field angle, and alo he mechanical peed, are eimaed uing he aor curren vecor and he aor volage vecor a inpu variable. Their accurae acquiiion i a major concern for able operaion a very low peed. A. Inverer nonlineariy The direc meauremen of he aor volage a he machine erminal i mo accurae [7], bu hardware require-

2 men are quie ubanial. The wiched aor volage waveform require a large ignal acquiiion bandwidh, and elecric iolaion mu be mainained beween he power circui and he elecronic conrol yem. However, he proceing of he analog ignal inroduce error and offe. Uing he reference volage of he pulewidh modulaor avoid all hee problem. Thi ignal i readily available in he conrol uni, and i i free from harmonic componen. I doe no exacly repreen he aor volage, hough, a diorion are inroduced by he dead ime effec which canno be compleely eliminaed even by he mo ophiicaed compenaion raegie. Alo he PWM inverer ielf exhibi nonlinear characeriic. I i he hrehold volage of he power device ha caue diorion of he machine volage, and heir effec i paricularly pronounced a low peed when he fundamenal volage i low. The diorion componen depend on he direcion of he phae curren; heir impac on he qualiy of curren conrol and heir compenaion by a ime diplacemen of he inverer conrol ignal wa decribed by Choi e al. [8]. Eimaing he aor volage vecor for he purpoe of ae eimaion require modelling of he inverer nonlineariie. Thi reconruc he rue aor volage vecor u from he inverer conrol ignal u [9]. An adapive compenaion cheme for he inverer nonlineariy i repored in []. B. Curren acquiiion error Alo he meaured curren ignal can be in error due o unbalanced gain of he meauremen channel, a well a from dc offe and drif. Thee diurbance have heir origin in he analogue porion of he curren acquiiion channel. They caue flucuaion of he machine orque, generaing peed ocillaion of fundamenal and double fundamenal frequency [9]. Chung e al. propoe heir compenaion by cloed loop conrol on he bai of he reuling peed ocillaion. Thi mehod require precie peed meauremen which canno be ubiued by peed eimaion echnique. Moreover, he accuracy i poor under ranien condiion and hence reidual error may peri. C. Field angle eimaion DC offe and hermal drif have been ever ince idenified a major problem o accurae flux angle eimaion a very low peed. A mo common oluion i he replacemen of he aor flux inegraor by a low-pa filer. The limied dc gain of uch low-pa filer eae hi problem a long a he aor frequency i much greaer han he filer cuoff frequency. The phae angle difference beween he inegraor and he lowpa filer deermine he field angle error. The lower limi of able operaion i a abou five ime he cuoff frequency and hu inolerably high. A imple way of lowering hi boundary i limiing he peak value in aor coordinae of he eimaed aor flux componen o he flux reference magniude [2]. While uch limiing eliminae he dc offe from he flux ignal, i inroduce phae angle diorion in urn. The limi of able operaion i around a aor frequency of 2-3 Hz. A more refined way of mainaining he aor flux vecor cloe o i inended circular rajecory coni in no only clipping he peak ampliude of i orhogonal componen, bu exering a coninuou influence on he flux vecor magniude. Hu and Wu [3] propoe an adjumen of he eimaed flux vecor by cloed loop PI conrol, forcing he aor flux vecor angle o lag he vecor u i of he induced volage by p/ 2. Alhough hi would be he correc oluion in principle, he magniude of he induced volage become exremely mall a very low peed, which make dc offe and oher diurbance he dominan ignal. Anoher major drawback of hi mehod i he dynamic delay of he cloed loop conrol ued for error correcion. Thi delay generae dynamic error a ranien condiion. Poibly for hi reaon have he auhor applied heir mehod only for flux monioring, bu no for field oriened conrol in a cloed loop. Kuboa e al. propoe o eimae he dc offe uing a full order oberver [7]. They exploi he fac ha ocillaion in peed and roor flux magniude occur in he preence of dc offe. The approach i highly compuaional. I require compuing he average value wihin a fundamenal period of he eimaed roor flux componen in aionary coordinae. Thee value are ubequenly muliplied by coefficien derived from he yem marix, which in urn depend on he eimaed peed. The reul are ummed up o yield incremen of he eimaed offe volage componen. Alo Rodic e al. [4] ue he deviaion of he eimaed roor flux magniude from i reference value o build a nonlinear flux oberver. Thi oberver i conruced a a econdorder low-pa filer a low aor frequency; i conver o a fir-order low-pa filer a higher aor frequency. The experimenal reul obained wih hi mehod demonrae moderae performance. D. Saor reiance eimaion A furher ource of error in he eimaion of he aor flux angle i he mialignmen of he eimaed aor reiance wih i real value in he machine. The load dependen variaion of he winding emperaure may lead o up o ±5% error of he modelled aor reiance. Hence he aor reiance mu be coninuouly adaped o i correc value during operaion. Ha and Lee [5] propoe an idenificaion cheme which relie on he compued difference beween he real power inpu o he aor winding and he airgap power, conidering he acual load condiion a calculaed from he inananeou reacive power, he aor curren magniude, and he aor frequency. Being obained a a mall difference beween large quaniie, he eimaed aor reiance value end o be inaccurae. Mir e al. repor on a aor reiance eimaion cheme implemened in a direc orque conrol yem [6]. The conrolling variable are he aor flux magniude and he elecromagneic orque. Any given combinaion of hee variable define a cerain value of he aor curren magniude. A deviaion of he meaured curren magniude from hi value i

3 aribued o a change in aor reiance. The modelled value i hen adjued unil he wo curren coincide. I i apparen, hough, from he experimenal reul ha he eimaion of he aor reiance i fairly inaccurae. The approach of Guidi e al. [7] require modelling he inducion machine by a full order oberver. A mialignmen of he modelled aor reiance i deeced from a comparion beween he meaured and he eimaed aor curren vecor. Inroducing a linear diplacemen of he eimaed aor curren vecor increae he eniiviy of he algorihm, provided he diplacemen i adequaely choen. The experimenal reul look promiing bu migh require improved diurbance rejecion. E. The overview A a conribuion o he aforemenioned opic, hi paper decribe he deign concep of a ready-o-implemen enorle drive conrol yem for high performance a very low peed, including zero aor frequency operaion. The yem comprie a nonlinear inverer model for he eimaion of he aor volage vecor, a precie dc offe eimaor, a aor reiance adapaion cheme, and a fa compenaor for reidual diurbance like curren gain unbalance, he curren zero croing effec, and general model inaccuracie. The exac compenaion of all hee advere effec permi uing a pure inegraor for aor flux eimaion and hu provide long-erm abiliy a zero aor frequency operaion. III. MODELLING THE DRIVE SYSTEM COMPONENTS A. Saor flux eimaion Among he variou way of eablihing a machine model in erm of fundamenal variable, preference i given for reaon of impliciy o he aor model. I i derived from he aor volage equaion in aor coordinae dy u = ri + () dτ where u and i are he pace vecor repreening he aor volage and he aor curren, repecively, y i he aor flux linkage vecor, and r i he aor reiance. Time i normalized a = w R, where w R i he nominal aor frequency [6]. Equaion () erve o eimae he aor flux linkage vecor ( ) ˆ ˆ ˆ = u r i dτ (2) from he meaured or eimaed variable û = u + uz (3a) î = i + iz (3a) ˆr = r + r (3a) where u z and i z are pace vecor repreening he repecive diurbance of he aor volage and he aor curren vecor, Dr i he modelling error of he aor reiance, and ˆ mark a variable a eimaed. The ignal conen of he aor volage diurbance vecor u z in (3) i aribued o he nonlinear characeriic of he PWM inverer, he ill-defined ae of he inverer a curren zero croing, ime and ampliude dicreizaion error of he pulewidh modulaor, error due o incomplee dead ime compenaion. The diurbance vecor i z uperimpoed o he aor curren vecor repreen dc offe and drif, gain unbalance of he curren acquiiion channel, curren dicreizaion error, and reidual wiching harmonic of he fundamenal curren ignal. Apar from he inducion moor, repreened by i fundamenal model, only he imperfecion of he PWM inverer, he dc offe, and he aor reiance will be reproduced here by model or eimaor. The remaining diurbance coni of low ampliude, high-frequency ignal which enable heir eliminaion wihou employing pecific model. B. The nonlinear inverer model The forward volage of he power emiconducor can be approximaed by a fixed hrehold volage u h and a curren dependen componen r d i, where r d i he differenial reiance and i i he forward curren of he device. The reiive porion r d i of he inverer volage i a linear funcion of he device curren. The conan hrehold volage produce nonlinear volage diorion. Thee can jim j be higher in ampliude han he fundamenal ecor machine i b i a i i c ec( i ) Re Fig.. The ix poible of he ecor indicaor ec(i ); he doed line mark he raniion a which he ign of he repecive phae curren change volage a very low frequency. The deail of a nonlinear inverer model are decribed in [9]. I i demonraed here ha he effec of he hrehold volage in a paricular bridge arm depend on he direcion of he repecive phae curren, ince a conducing device i alway forward biaed. The hrehold volage componen of phae a i herefore u h.ign(i a ). Making ue of he definiion of a volage pace vecor by i hree phae volage componen [6] permi defining he hrehold volage vecor ( ), (4) 2 u h = 2 u h ign( i a ) + a u 3 h ign( i b ) + a u h ign( i c )

4 jim (a) a w =.7 u av u u where a = exp(j2p/3) i he uniy vecor roaor. Equaion (4) can be rewrien a h h where he ecor indicaor u u h i Re jim = 4 u ec( i ) (5) 3 ( ) (6) ec( i )= 2 ign( i ) + a ign( ) + a ign( ) 2 a ib i c i a uniy vecor ha mark he 6 -degree ecor in which he curren pace vecor reide. The ix dicree locaion of he ecor indicaor are hown in Fig.. The argumen of hi uniy vecor i a kind of modulo(p/3)-funcion of he curren pace vecor phae angle. Fig. 2 how he diorion ha he inverer nonlineariy impoe on he aor volage vecor when he reference volage vecor i conrolled o follow a circular rajecory. A he machine erminal, he average aor volage per modulaion cycle u av i diconinuou and exhibi rong 6h harmonic componen. I ha le fundamenal conen a mooring and more a regeneraion [9]. Neglecing he wiching harmonic, he ranfer characeriic of he PWM inverer i u av =. (b) a w Fig. 2. The effec of inverer nonlineariy a wo differen value of aor frequency. The diconinuou rajecorie u av repreen he average aor volage wihin a wiching ubcycle u h u Re u = uinv uh( i) r di (7) i The la wo erm in (7) define he conribuion of he nonlinear inverer model. Wih revered ign, hi model i inered beween he reference volage vecor and he pulewidh modulaor inpu o eablih a linear relaionhip beween u and u. The ignal flow graph Fig. 3 illurae hi. The inverer model i characerized by wo parameer, u h and r d. A mehod o idenify he hrehold volage u h i propoed in [9]. Way of adaping u h o he prevailing operaing condiion are decribed in []. Such adapaion may be oo much of refinemen for ome applicaion. The econd parameer of he inverer model Fig. 3 i he differenial reiance r d of he power device. Thi reiance i idenified a par of he eimaion cheme decribed in Secion III E. C. Offe vecor eimaion According o (2), even minor dc componen in he volage and curren ignal accumulae in he proce of inegraion o form a large offe in he eimaed aor flux linkage vecor. A oluion o hi problem exploi he fac ha he offe vecor i almo unidirecional while he derivaive vecor of he circular diplacemen roae. The ignal flow diagram Fig. 4 how he elemen of an offe volage eimaor highlighed by a haded frame. The induced volage ˆ iˆ i = r (8) erve a an inpu ignal, where û = u i he eimaed aor volage obained from he conrolling ignal of he linearized pulewidh modulaor in Fig. 3. A hown in Fig. 4, he vecor û i of he induced volage i inegraed o form a ignal ŷ. The componen of hi vecor are ubequenly limied in ampliude o he magniude value y of he aor flux reference. The rajecory of ŷ i no circular in he preence of dc offe. Since i undiurbed radiu equal y hrough he acion of he aor flux conroller, he offe componen end o drive he enire rajecory oward one of he ±y -boundarie, and a clearance appear from he repecive boundarie x u ec( i ) i o aor flux eimaor inverer model 2u h u h d u inv PWM main i ~ ~ u ˆi y i off offe eimaor e jd y ˆmin, max off D Eqn. 9 min, max off Fig. 3. Signal flow graph of a enorle drive wih compenaion of he inverer nonlineariy M 3 ~ Fig. 4. Signal flow graph howing an offe volage eimaor for high-bandwidh aor flux eimaion uing a pure inegraor

5 ŷ b y y û offd y y ŷ a max + ŷ amin ŷ a Fig. 5. Meaured rajecory of he vecor ŷ howing he effec of uncompenaed offe a he oppoed ide. Fig. 5 how an ocillographed example. I i een ha he offe make he average value of he flux componen y a and y b nonzero. In paricular, we have (y a min + y a max )/2 < and (y b min + y b max )/2 > in hi example. Hence a conribuion o he offe volage vecor û off can be eimaed from he diplacemen of he flux rajecory ŷ a ( ) ŷ bmax + ŷ bmin ˆ ˆ off = y max + y min (9) where he maximum and minimum value in (9) are hoe of he repecive componen y a and y b, and D i he ime difference beween wo zero croing of ŷ ha define a fundamenal period. Due o he nonlinear diorion of he rajecory of ŷ, he algorihm (9) i more an approximaion under he condiion hown in Fig. 5. To improve on hi, he ignal û off D i lowpa filered and fed back o he inpu of he inegraor o a o cancel he offe componen in û i. The inpu of he inegraor hen end oward zero in a quai eady-ae, which make he eimaed offe volage vecor û off equal he exiing offe in û i. The rajecory of y i exacly circular in hi iuaion which enure a precie racking of he offe volage vecor. Since offe drif i mainly a hermal effec ha change he dc offe very lowly, he repone ime of he offe eimaor i no a all criical. I i imporan o noe ha he dynamic of aor flux eimaion do no depend on he repone of he offe eimaor. D. Compenaion of reidual eimaion error The nonideal characeriic of a PWM inverer fed drive yem are manifold. An overview of he exiing imperfecion wa given in Secion III.A. Modelling or compenaing hee effec o improve he performance a zero aor frequency ju uncover new inufficiencie ha go unnoiced before. An example are he phenomena ha occur when he fundamenal componen of he phae curren revere heir direcion. The exac poin of zero croing i ill defined in he i α, i β.5.5 i α i β m 2 m Fig. 6. Meaured aor curren waveform o illurae he zero croing effec preence of wiching harmonic. When a paricular phae curren revere, he volage error caued by he dead-ime effec change i ign and hu counerac he endency of hi curren o flow in he inended direcion. The iuaion i even more complex a he uperimpoed wiching harmonic eablih repeiive change beween poiive and negaive curren flow a illuraed in Fig. 6. Dead-ime error compenaion cheme fail o operae properly. Exac volage conrol by he pulewidh modulaor i impaired by an addiional effec: The repecive bridge arm i compleely open-circuied when he curren i very low, and conrol of he correponding phae volage i lo. I i hen he induced volage of he machine ha appear emporarily a hi phae erminal. Eimaing he exac aor volage vecor from he command value of he pulewidh modulaor become difficul. The aforemenioned effec produce diorion of he eimaed flux vecor ignal ha are dominaed by muliple of ix harmonic. Oher imperfecion are dicued in Secion II. I i indeed ˆi y i u hf off x k noie compenaor ŷ min, max e jd e jd off D min, max i α Eqn. 9 off Fig. 7. Signal flow graph of a fully compenaed aor flux eimaor. The lower porion how he eimaor of Fig. 4. y

6 ŷ b û hfa û hfb.. û hfa û hfb Fig. 8. Meaured componen of he high-frequency diurbance almo impoible o model or eimae all hee deficiencie. However, wih he dc offe accuraely idenified, he remaining diurbance exhibi higher, mo of hem much higher frequencie han he fundamenal frequency. An efficien way o minimize heir impac on he eimaed flux vecor i adjuing he radial componen of ŷ cloe o i reference value y by fa proporional cloed loop conrol. Thi leave he angenial componen he field angle unaffeced and hu doe no inerfere wih he correc operaion of he eimaor. Moreover, a angenial error conver o a radial error afer a quarer revoluion of he flux vecor and i hen eliminaed. The noie compenaor hown in Fig. 7 generae he highfrequency ignal u hf o erve hi purpoe. The ocillogram Fig. 8 how ha he componen of u hf, alhough very mall, exhibi dominan 6h-order harmonic a prediced, and oher high-frequency noie in addiion. To e he dc offe eimaion cheme, offe volage of 25 mv were added o he repecive inpu of he A/D converer for he a- and b-componen of he aor curren ignal. The drive yem wa hen ared from a compleely deenergized condiion, wih he peed reference e o..5 Hz. The ocillogram Fig. 9 how ha he yem ar from arbirary iniial value of he flux componen and field angle eimae. The machine i hen energized by building an iniial flux vecor in he a-axi. Correc eimaion become p p ŷ a û offa 2 3 ŷ b ŷ a û offa Fig. 9. Sarup proce wih a high dc offe inenionally inroduced; haded porion enlarged on he righ 8 ŷ b 2 3 ŷ b (b) flux vecor componen (a) circular flux vecor rajecory howing phae angle error i α, i β (c) ocillaion in curren and peed caued by field angle error Fig.. Ocillogram wih 25 mv dc offe inenionally inroduced, howing ha he noie compenaor conrol only he ampliude of he aor flux vecor, (a). Field angle error peri a een in (b). Conequence are heavy orque and peed ripple, (c). effecive a.5 afer aring. The high-frequency compenaor fir ai he aor flux eimaor o eablih find he correc iniial condiion, and hen he eimaed offe componen û off a ar building up. The race of ŷ a indicae ha he rajecory ŷ gradually cener in he origin. The haded porion of hi proce i enlarged in he righ-hand ide of Fig. 9, howing ha iniial error in field angle are no compleely avoided in hi exreme condiion. Oher han aumed in [9], he noie compenaor doe no compenae all offe effec. I correc only he radial flux componen while leaving he angenial componen unaffeced. While a mooh circular flux rajecory can be alo obained in he preence of dc offe wih he dc offe eimaor diconneced, Fig. (a), he remaining phae angle error hown in Fig. (b) end o deabilize he conrol. Fig. (c) how ha a endency exi o execue ocillaion. One would rarely encouner uch large offe in a pracical yem. Once idenified, he offe volage vecor can be ored in a nonvolaile memory o provide favorable condiion a any nex ar. Fig. 6 how an example. E. Eimaion of he aor reiance Correc modelling of he aor reiance i of paramoun imporance for enorle conrol a very low peed. The mehod propoed here exploi he well defined relaionhip beween he field oriened componen of he aor curren a conan flux. Thi condiion make he aor curren vecor ŷ b

7 i r = con. eniive region i d i y i d e jd reference model i 2 +y ll x 2 2 N i d D k Di d adapive conroller k = l + σl Fig.. Loci of he aor curren vecor a aor field orienaion wih he aor reiance a a parameer move on a defined rajecory, he Heyland circle, a he load varie. The locaion and he ize of he Heyland circle are independen of he aor frequency. However, he value of he aor reiance doe have an influence boh on he diameer and he origin of he Heyland circle. Fig. how ha, for a given value of he orque curren componen, he field curren componen i d varie a a funcion of r. To exploi he effec, an analyi ar from he machine equaion in a aor flux oriened reference frame, hence y = y d = y. The following equaion hold, [2], τ r dy dτ di + y = ωτσ r r li q + τσ d r l + li dτ d (a) diq = ωτ r r( y σli d)+ τσ r l + li dτ q (b) where τ r i he roor ime conan, l i he aor inducance, ω r i he roor (lip) frequency, and σ = l m 2 /l l r i he oal leakage coefficien. Equaion () implifie a eadyae, d/d =, y = ωτσli r r q + li d (a) li q= ωτ r r( y σli d) (b) Thee equaion permi eliminaing he roor frequency w r, y i lσl d = + i l + σl ( l + σl) y 2 (2) The reul indicae ha he d-axi curren ha a defined magniude a any given exciaion and load, expreed by y and i, provided ha correc aor field orienaion exi. Equaion (2) doe no depend on he aor reiance. I can herefore erve a a reference model o generae he value of in he MRAS yem hown in Fig. 2. The adjuable model i he aor flux eimaor Fig. 7 by virue of i unable aor reiance, (2). Since he correc value of u and i have already been e in hi model, any error in y i caued by an incorrec value of he modelled aor reiance. Adjuing can herefore erve o aify (2). The machine parameer l and l a funcion of he load are deermined by elf-commiioning. The convergence of hi approach i proved in he following. If a aor reiance error Dr = r exi, a volage error Dr i i creaed. Thi build an error in he aor flux Fig. 2. Saor reiance eimaion by model reference adapive conrol; he adjuable model i he aor flux eimaor in Fig. 7, being manipulaed by he he adapive conroller in he upper righ. N: Numeraor, D: Denominaor vecor, which i compued from (2), oberving û = u a dicued before. Dy = y = Dr idτ (3) Equaion (2) i rewrien a y 2 ( l + σl) idy + lσli 2 = (4) becoming nonzero in he preence of a aor reiance error 2 2 ( l + σl) id + lσli = ε (5) The difference beween (5) and (4) i ( ) ŷ 2 y 2 l + σl iddy ε (6) which can be wrien wih reference o (3) a ( ) = ε = ( ŷ 2 y 2 ) r idτ ( l + σl) i d (7) I i now aumed ha undiurbed volage and curren ignal are ued for aor flux eimaion, which he offe compenaion cheme enure. A nonzero error e can be hen only caued by a aor reiance error Dr. Uing he approximaion y 2 ŷ 2 2y Dy and referring o (3), equaion (7).5 p p 2 (a) 2 4 (b) 2 4 Fig. 3. Sep change of he aor reiance; (a) a noload and zero aor frequency wih ubequen nominal orque ep, (b) a 3% raed load

8 demonrae ha e if Dr. Alhough he noaion r i ued for he reiance ha i eimaed by hi cheme, he idenified quaniy i in fac r + r d ince he differenial reiance r d of he power device appear in erie wih he aor winding reiance r. To e he idenificaion cheme, he aor reiance were increaed o 25% of heir nominal value in a ep fahion. The ocillogram Fig. 3(a) how he repone a no-load and zero aor frequency, aring a =. A nominal orque load i α i α, i β.2 (a) ŷ b ŷ b 2 3 ŷ b 2 4 (a) circular flux vecor rajecory 2 min 2 4 Fig. 4. Fa aor reiance idenificaion when operaing a very low peed afer a ranien from high peed; (a) acceleraion of he cold machine (b) deceleraion of he heaed machine (c) aor curren waveform and eimaed peed Fig. 5. Seady-ae performance a low peed (33 rpm). A comparion wih he waveform in Fig. demonrae he improvemen achieved by offe eimaion. (b) i α (b) flux vecor componen wihou phae angle error i α, i β.5.5. ŷ i α ep i ubequenly applied a = 2, producing he deired fa and well damped repone. Thi indicae ha he correc reiance value wa idenified. Fig. 3(b) how he repone o a ep change of he aor reiance, applied a =, while operaing a very low peed, w =..5 Hz, and 3% raed load. The eimaed field angle i in error during he ranien phae, a indicaed by he emporary increae of. The machine wa no fully loaded during hi experimen ince a higher load han 3% raed may caue a ranien inabiliy a hi very low peed. Such condiion i unrealiic, hough, ince variaion of he aor reiance are inherenly owed o low hermal effec. The eniiviy again aor reiance mimach reduce a he peed increae, and conequenly alo he effecivene of reiance idenificaion cheme in general. An accurae value of he aor reiance can only be idenified if he peed i low. I i a hard e heaing a machine up a high peed wih he aor reiance changing, and hen reurning o dynamic conrol a very low peed. Thi underline he imporance of a fa idenificaion cheme. The repone ime in Fig. 3(b) i only 28 m. Such fa reacion enable able low-peed conrol following deceleraion from high peed wih he aor reiance iniially ill idenified, hough a minor limiing of he peed gradien i ill required. Fig. 4 how an example. I i an advanage of he idenificaion mehod ha i relie on he meaured aor curren and hence i no affeced by he inheren inaccuracie of aor volage aquiiion a low peed. However, Fig. how ha i doe require a minimum orque curren of abou 5% R o make he effec of r on i d apparen, where he ubcrip R denoe a raed value. The mehod decribed in [9] i herefore preferred a ligh load, bu i ue mu be inhibied a very low peed a i become inaccurae. IV. SYSTEM PERFORMANCE The effecivene of he offe eimaor i illuraed by he ocillogram Fig. 5. The waveform of he aor flux componen in Fig. 5(b) appear perfecly inuoidal a oppoed o hoe in Fig. (b). Boh ocillogram were recorded i β ŷ 2p Fig. 6. Sar-up of he deenergized drive yem for operaion a.5 raed peed (.25 Hz)

9 i α,i β ŷ b 2p w 2p Fig. 7. Zero peed operaion wih he load reducing in ep from 3% nominal orque o no-load; w indicaed on op ŷ b Fig. 8. Long-erm zero peed operaion followed by a nominal orque ep i α,β ŷ b 2p. ŷ b Fig. 9. Load rejecion repone wih a 2% orque ep applied a zero peed p p Fig. 2. Raed orque ep applied a w =.3 wih ubequen operaion a regeneraion wih 25 mv offe inenionally added o he curren ignal i a and i b. The aor curren are inuoidal in Fig. 5(c), producing a conan orque a indicaed by he ignal. The ignal of he eimaed peed i moohened, alhough no ideally, which i owed o he low frequency of operaion (.23 raed peed, or.4 Hz). The ocillogram Fig. 6 how a ar-up proce of he deenergized drive yem wih ubequen operaion a.3 raed peed (.5 Hz). The recorded variable aume arbirary value in he very beginning while he ae of he drive yem i no ye fully idenified. In Fig. 7, he peed reference i e o zero while he load i reduced in ep from 2% nominal orque. Sable zero aor frequency operaion i finally reached a no-load. Fig. 8 demonrae ha he field angle i correcly eimaed wihou drif, even during an exended ime of zero aor frequency operaion. The ubequen repone o a orque ep of raed magniude demonrae ha full dynamic conrollabiliy i mainained. The ime expanion of uch proce wih a orque ep of 2% nominal magniude applied i hown in Fig. 9. Accurae zero peed operaion i reumed afer a hor unavoidable ranien. Finally, Fig. 2 how he repone o a poiive orque ep diurbance of raed magniude applied during peed conrolled operaion a.3% raed peed. The drive operae in he regeneraion mode afer he ep. A endency o deabilize a regeneraion ha been oberved a hi very low peed. V. SUMMARY A precie and robu enorle conrol yem for inducion machine i baed on a refined aor flux idenificaion cheme. A dc offe volage eimaor and a noie compenaor are ued o generae undiurbed volage and curren ignal a he inpu o he aor flux eimaor. The abence of offe and drif permi uing a pure inegraor o derive he aor flux linkage vecor from he vecor of he induced volage. The mehod hu eliminae all exiing bandwidh rericion for flux eimaion. I enable mooh operaion a very low peed and longerm abiliy a zero aor frequency while mainaining full dynamic conrollabiliy. Accurae dynamic orque conrol i achieved by a fa aor reiance eimaion cheme. The correcion of ill-defined reiance value accumulaed in he unobervable high-peed region i demonraed while reenering he low peed region in a ranien proce..

10 VI. REFERENCES. K. Rajahekara, A. Kawamura, and K. Maue, (Edior), Senorle Conrol of AC Moor, IEEE Pre Book, J. Holz, Senorle Poiion Conrol of Inducion Moor an Emerging Technology, IEEE Tran. Indurial Elecronic, Vol. 45, No. 6, Nov/Dec. 998, pp M. W. Degner, R. D. Lorenz, Uing Muliple Saliencie for he Eimaion of Flux, Poiion and Velociy in AC Machine, IEEE Tran. Indury Appl., Vol. 34, No. 5, Sep/Oc 998, pp N. Teke, G. M. Aher, M. Summer, and K. J. Bradley, Suppreion of Sauraion Saliency Effec for he Senorle Poiion Conrol Inducion Moor Drive under Loaded Condiion, IEEE Tran. Indury Appl., Vol. 47, No. 5, Oc 2, pp J. Holz and H. Pan, Eliminaion of Sauraion Effec in Senorle Poiion Conrolled Inducion Moor, IEEE Indury Appl. Soc. Ann. Meeing, Chicago, Oc. 3-8, J. Holz, The Repreenaion of AC Machine Dynamic by Complex Signal Flow Graph, IEEE Tran. Indurial Elecronic, Vol. 42, No. 3, June 995, pp H. Kuboa, Y, Kaaoka, H. Oha and K. Maue, Senorle Vecor Conrolled Inducion Machine Drive wih Fa Saor Volage Offe Compenaion, IEEE Indury Appl. Soc. Ann. Meeing, Phoenix AZ, Oc J.-W. Choi and S.-K. Sul, Inverer Oupu Volage Synhei uing Novel Dead Time Compenaion, IEEE Tran. Power Elecronic, Vol., No. 2, April 996, pp J. Holz and J. Quan, Senorle Vecor Conrol of Inducion Moor a Very Low Speed uing a Nonlinear Inverer Model and Parameer Idenificaion, IEEE Tran. Indury Appl., Vol. 38, July/Aug. 22. Th. Frenzke, F. Hoffman, and H. G. Langer, Speed Senorle Conrol of Tracion Drive Experience on Vehicle, 8h Europ. Conf. Power Elecr. and Appl. EPE, Lauanne, 999, on CD ROM.. D.-W. Chung and S.-K. Sul, Analyi and Compenaion of Curren Meauremen Error in Vecor-Conrolled AC Moor Drive, IEEE Tran. Ind. Appl., Vol. 34, No. 2, March/April 998, pp J. Holz, Senorle Conrol of Inducion Moor, Proceeding of he IEEE, Vol. 9, No. 8, Aug J. Hu and B. Wu, New Inegraion Algorihm for Eimaing Moor Flux over a Wide Speed Range. IEEE Tran. Power Elecronic, Vol. 3, No. 5, 998, pp M. Rodic and K. Jezernik, An Analyi of Speed Senorle Torque and Flux Conroller for Inducion Moor, IEEE Power Elecronc Speciali Conf., PESC, Galway/Ireland, 2, on CD ROM. 5. I.-J. Ha and S.-H. Lee, An Online Idenificaion Mehod for boh Saor and Roor Reiance of Inducion Moor wihou Roaional Tranducer, IEEE Tran. Ind. Elecronic, Vol. 47, No. 4, Aug. 2, pp S. Mir, E. Elbuluk and D. S. Zinger, PI and Fuzzy Eimaor for Tuning he Saor Reiance in Direc Torque Conrol of Inducion Machine, IEEE Tran. Power Elecronic, Vol. 3, No. 3. March 998, pp G. Guidi and H. Umida, A Senorle Inducion Moor Drive for Low Speed Applicaion uing a Novel Saor Reiance Eimaion Mehod, IEEE Ind. Appl. Soc. Ann. Meeing, Phoenix AZ, Oc. 999.