Sensorless Speed and Position Control of Induction Motor Drives

Transcription

1 IECON Roanoke VA, 3 Senole Spee an Poition Contol of Inuction oto Dive aaa Joachim Holtz, Fellow, IEEE Electical achine an Dive Goup, Univeity of Wuppetal 497 Wuppetal Gemany Abtact Contolle inuction moto ive without mechanical pee eno at the moto haft have the attaction of low cot an high eliability. To eplace the eno, the infomation on the oto pee i extacte fom meaue tato voltage an cuent at the moto teminal. Vecto contolle ive equie etimating the magnitue an patial oientation of the funamental magnetic flux wave in the tato o in the oto. Open loop etimato o cloe loop obeve ae ue fo thi pupoe. They iffe with epect to accuacy, obutne, an enitivity againt moel paamete vaiation. Dynamic pefomance an teay-tate pee accuacy in the low pee ange can be achieve by exploiting aniotopic effect of the machine.. INTRODUCTION AC ive bae on full igital contol have eache the tatu of a matue technology. The wol maket volume i about, million US$ with an annual gowth ate of 5%. Ongoing eeach ha concentate on the elimination of the pee eno at the machine haft without eteioating the ynamic pefomance of the ive contol ytem []. Spee etimation i an iue of paticula inteet with inuction moto ive whee the mechanical pee of the oto i geneally iffeent fom the pee of the evolving magnetic fiel. The avantage of pee enole inuction moto ive ae euce hawae complexity an lowe cot, euce ize of the ive machine, elimination of the eno cable, bette noie immunity, inceae eliability an le maintenance equiement. The opeation in hotile envionment motly equie a moto without pee eno. A vaiety of iffeent olution fo enole ac ive have been popoe in the pat few yea. Thei meit an limit ae eviewe bae on a uvey of the elate liteatue. the comman ignal a hown in Fig.. The v/f chaacteitic enue that the tato flux i maintaine at it nominal value. A peet minimum value of the tato voltage account fo the eitive tato voltage op. Since v/f -contolle ive opeate puely a feefowa ytem, the mechanical pee may w iffe fom the efeence pee w. A loa cuent epenent lip compenation cheme can be employe to euce the pee eo. Contant volt-pe-hetz contol enue obutne at the expene of euce ynamic pefomance, which i aequate fo application like pump an fan ive, an fo low-cot ive. Thee contibute a ubtantial hae of the maket fo enole ac ive. 3. ROTOR FIELD ORIENTATION 3. oel efeence aaptive ytem The moel efeence appoach (RAS) make ue of the eunancy of two machine moel of iffeent tuctue that etimate the ame tate vaiable on the bai of iffeent et of input vaiable []. The tato moel in the uppe potion of Fig. eve a a efeence moel, the oto moel in the lowe potion a the ajutable moel. It tuning ignal i obtaine though a popotional-integal (PI) contolle fom a cala eo ignal e, compute fom the phae iplacement between the two etimate flux vecto, ŷ S an ŷ R. A the eo ignal e get minimize by the PI contolle, the tuning ignal appoache the actual pee of the moto. The tato moel ue a elay element intea of an integato to eliminate an accumulation of the ift eo. An banwith limite at the input of the oto moel enue equivalence of the two moel.. CONSTANT VOLTS-PER-HERTZ CONTROL To avoi the excitation at the eigenfequencie of inuction machine, a gaient limite euce the banwith of w Fig. gaient limite t g v/f cuve u u ag( u ) Contant volt-pe-hetz contol PW ac main cuent limite 3 u u Fig. ˆ t t tato moel l t l m t jt oto moel k S R e oel efeence aaptive ytem fo pee etimation

2 i w i Fig. 3 i -contolle pee contolle i w l + w l i i -contolle q kq A fiel tato cooinate u w main k 3 k t' B k = k y k = l h t y Feefowa of tato voltage, oto flux oientation u u q PW 3. Feefowa contol of tato voltage Okuyama [3] eive the commane tato voltage fom a teay-tate machine moel a the baic efeence ignal. Thei component in oto fiel cooinate ae make by the hae fame in Fig. 3. It i thu the machine which, though it moel, let the invete uplicate the actual teminal voltage. Thi poce can be chaacteize a elf-contol. A upeimpoe i -contolle compenate fo the paamete inaccuacy of the teay-tate moel, while an -contolle enue the coect alignment of the oto fiel angle with the oto flux vecto. Tanient eviation fom the coect fiel alignment ae eliminate by the aitional coection ignal A an B [, 3]. Toque ie time of thi cheme i epote aoun 5 m; pee accuacy i within ± % above 3% ate pee an ± pm at 45 pm [3]. 3.3 Roto fiel oientation with impove tato moel A enole oto fiel oientation cheme bae on the tato moel i ecibe by Ohtani [4]. The uppe potion of Fig. 4 how the claical tuctue in which the contolle y w w flux contolle pee contolle i -contolle q N fiel tato cooinate i (S) D l m t CR-PW main y etimato Fig. 4 Senole pee contol bae on iect -etimation; oto fiel oientation y y u 3 u u D N x +y t t y (S) Fig. 5 Roto flux etimato fo the tuctue in Fig. 4 fo pee an oto flux geneate the cuent efeence vecto in fiel cooinate. Thi ignal i tanfome to tato cooinate an pocee by a et of fat cuent contolle CR PW. A poible mialignment of the efeence fame i etecte a the iffeence of the meaue q-axi cuent fom it efeence value. Thi eo ignal fee a PI contolle, the output of which i the etimate mechanical pee. It i ae to an etimate value of the oto fequency, compute fom the efeence value an y. The integation of pouce the fiel angle. The tato moel i ue to etimate the oto flux vecto y. The ban-limite integation by mean of a fit-oe elay entail a evee lo of gain in the etimate flux component y at low tato fequency, an a lage fiel angle eo. Thi tenency i compenate by an ae flux component y, obtaine fom the efeence value ŷ (S) in tato cooinate. The latte component ominate the eulting flux vecto ŷ at low fequency, eplacing it by it efeence value y in a mooth tanition. Thi eult in ŷ y at low fequency, which eactivate the oto flux contolle in effect. Howeve, the fiel angle a the agument of the oto flux vecto i till une contol though the pee contolle an the -contolle, although the accuacy of euce. Fiel oientation i finally lot at vey low tato fequency. Only the fequency of the tato cuent i then contolle. The cuent ae foce into the machine without efeence to the oto fiel. Thi povie obutne an cetain tability, although not ynamic pefomance. A the pee inceae fom a vey low value, oto flux etimation become moe accuate an cloe loop oto flux contol i eume. The coect value of the fiel angle i eajute a the q-axi cuent, obtaine fom the y -etimato Fig. 5, now elate to the coect oto flux vecto. The - contolle then ajut the etimate pee, an in conequence alo the fiel angle, fo a ealignment of the efeence fame with the oto fiel. At 8 pm, pee accuacy i epote to be within ± 3 pm. Toque accuacy at 8 pm i about ±.3 pu. at. pu. efeence toque, impoving ignificantly a the toque inceae. inimum paamete enitivity exit at τ = τ [4]. 3.4 Aaptive Obeve The accuacy of the open loop etimation moel ecibe t u i y t ' u

3 u tato k t t' î l m oto t jt le, thu ajuting the -input to the oto moel. The phae angle of ŷ, which i the etimate oto fiel angle, then appoximate the tue fiel angle that exit in the machine. The coect pee etimate i eache when the cuent eo, an hence the toque eo T e euce to zeo. The contol cheme i epote to opeate at a minimum pee of.34 p.u. o 5 pm [5]. eo compenato G ( w) ˆ D G ( w) ˆ D DT e pee aaptation Fig. 6 Nonlinea obeve; the moel of the inuction moto i hown in the uppe potion in the peviou chapte euce a the mechanical pee euce. The limit of acceptable pefomance epen on how peciely the moel paamete can be matche to the coeponing paamete in the actual machine. It i paticulaly at lowe pee that paamete eo have ignificant influence on the teay-tate an ynamic pefomance of the ive ytem. The obutne againt paamete mimatch an ignal noie can be impove by employing cloe loop obeve to etimate the tate vaiable, an the ytem paamete Full oe nonlinea obeve A full oe obeve can be contucte fom the machine moel, hown in the uppe potion of Fig. 6. The moel output the etimate value î an ŷ of the tato cuent vecto an the oto flux linkage vecto, epectively. Aing an eo compenato to the moel etablihe the obeve. The eo vecto compute fom the moel cuent an the meaue machine cuent i = î. It i ue to geneate coecting input to the electomagnetic ubytem that epeent the tato an the oto in the machine moel. Kubota et al. [5] elect the complex gain facto G () an G () uch that the two complex eigenvalue of the obeve λ, ob = k. λ, mach, whee λ, mach ae the machine eigenvalue, an k > i a eal contant. The value of k > cale the obeve by pole-placement to be ynamically fate than the machine. Given the nonlineaity of the ytem, the eulting complex gain G () an G () in Fig. mut epen on the etimate angula mechanical pee, [5]. The oto fiel angle i eive fom the component of the etimate oto flux linkage vecto ŷ. The pee ignal i equie to aapt the oto tuctue of the obeve to the mechanical pee of the machine. The ignal i obtaine though a PI-contolle fom the cuent eo. In fact, the tem ŷ z epeent the toque eo T e caue by the cuent eo. If a moel toque eo exit, the etimate pee ignal get coecte by the PI contol- 4. STATOR FIELD ORIENTATION Contol at tato fiel oientation i pefee in combination with the tato moel. Thi moel iectly etimate the tato flux vecto. Uing the tato flux vecto to efine the cooinate ytem i then a taightfowa appoach. A fat cuent contol ytem ene the tato cuent vecto a focing function, making the electomagnetic ubytem of the machine behave like a complex fit-oe ytem. It i only chaacteize by the ynamic of the oto wining. Othe than oto fiel oientation, tato fiel oientation oe not inheently povie ecouple contol of toque an flux. In the ignal flow gaph Fig. 7, the toque comman exet an uneie influence on the tato flux. Xu et al [6] popoe a ecoupling aangement, hown in the left of Fig. 7, to eliminate the co-coupling between the q-axi cuent an the tato flux. The intenal influence of i cancelle by the extenal ecoupling ignal, povie that the etimate ignal an paamete match the actual machine ata. The ecoupling ignal epen on the oto fequency w. An etimate value i theefoe equie. It i obtaine fom the etimato Fig. 8, which alo upplie the emaining unknown ytem vaiable. The tato flux linkage vecto i etimate by the appoximate tato moel. The angula velocity of the evolving fiel i then etemine fom the tato flux linkage vecto. Although i compute fom the etimate value ŷ, it value i obtaine at goo accuacy. The eaon i that the uncetaintie in ŷ ae owe to mino offet an ift component in meaue cuent an voltage ignal. Thee itubance exet little influence on the angula velocity at which the pace vecto ŷ otate. The tato fiel angle i obtaine a the integal of the etimate tato fequency. The angula mechanical velocity of the oto i compute a =, whee i eive fom the tato cuent vecto in tato fiel cooinate an fom ŷ uing the conition fo tato fiel oienta- flux comman w t ' toque comman t' i t' machine Fig. 7 achine contol at tato flux oientation uing a ynamic feefowa ecouple l m T e T L t t ' t m y w w

4 u ˆ t t y jw y ˆ (F) t tato flux etimato i l w -etimato l N x +y x t' D t D N Fig. 8 Etimato fo tato flux, tato fiel angle, mechanical pee an oto fequency tion []. The ignal flow gaph of a enole ive with tato fiel oientation i hown in Fig PERFORANCE AT VERY LOW SPEED 5. Stato eitance The impotant infomation on the fiel angle an the mechanical pee i conveye by the inuce voltage of the tato wining, inepenent of the epective metho that i ue fo enole contol. The inuce voltage u i = u i not iectly acceible by meauement. It mut be etimate, eithe iectly fom the iffeence of the two voltage pace vecto tem u an, o iniectly when an obeve i employe. In the uppe pee ange above a few Hz tato fequency, the eitive voltage i mall a compae with the tato voltage u of the machine, an the etimation of u i i pefome with goo accuacy. Even the tempeatue-epenent vaiation of the tato eitance ae negligible at highe pee. If opeate at fequencie above the citical low pee ange, a enole ac ive pefom a goo a a vecto contolle ive with a haft eno; even paing though zeo pee in a quick tanition i not a poblem. A the tato fequency euce at lowe pee, the tato w y Fig. 9 pee contolle flux contolle fiel tato (F) cooinate cuent contolle u (S) ecoupling ignal (F) ej ac main PW moel Stato flux oiente contol without pee eno (S) u 3 u voltage euce almot in iect popotion, while the eitive voltage maintain it magnitue; it become the ignificant tem at low pee. It i paticulaly the tato eitance that etemine the etimation accuacy of the tato flux vecto. A coect initial value of the tato eitance i eaily ientifie by conucting a c tet uing initialization [7]. Conieable vaiation of the eitance take place when the machine tempeatue change at vaying loa. Thee nee to be tacke to maintain the ytem table at low pee. 5. Nonlineaity of the PW invete At low pee, alo the voltage itotion intouce by the nonlinea behavio of the PW invete become ignificant. They ae caue by the fowa voltage of the powe evice. Thi voltage can be moele by an aveage thehol voltage u th, an an aveage iffeential eitance. The iffeential eitance appea in eie with the machine wining; it value i theefoe ae to the tato eitance of the machine moel. Othe than thi, the influence of the thehol voltage i nonlinea which equie a pecific invete moel. Repeenting the evice fowa voltage, the polaity of the thehol voltage u th i uniquely etemine by the iection of cuent flow. Diffeence in magnitue between the fowa voltage of an active evice an a ecovey ioe ae mino an can be neglecte. The thehol voltage i then contant. The contibution of the thee phae component pemit efining a thehol u jim u u u th Re Fig. Voltage itotion ue to the nonlineaity of the invete voltage vecto u th. Thi vecto ha a contant magnitue, while it phae angle change by +6º o 6º wheneve one of the phae cuent change it ign. The tato voltage vecto u = u u th theefoe follow a itote an icontinuou tajectoy, even when the efeence ignal u of the pulewith moulato ecibe a cicula tajectoy. Fig. how an example at motoing opeation. The funamental amplitue of u i then le than it efeence value u; it i lage at egeneation. The voltage tajectoy exhibit tong ixth hamonic component. Since the thehol voltage oe not vay with tato fequency a the tato voltage oe, the itotion ae moe ponounce when the tato fequency, an hence alo the tato voltage, ae low. The latte may even excee the commane voltage in magnitue, which then make coect flux etimation an table opeation of the ive impoible. The invete voltage vecto u th i moelle by the tuctue in Fig.. It phae angle epen on the polaitie of the thee phae cuent, of which only ix poible combination exit. Thee contol the ecto inicato ec( ), which locate the cuent pace vecto in one paticula 6º-ecto of the

5 u ec( ) to tato flux etimato u inv invete moel u th u th ˆ ac main PW u comp Fig. Compenation of the invete nonlineaity 3 complex plane. The magnitue of u th i u th fo fomal eaon []. The eitive voltage op of the powe evice epen on the iffeential eitance. The eulting compenation ignal u comp account fo the linea an nonlinea voltage op in the invete. ˆ y Fig. ˆ i offet etimato ac off x e j ac itubance etimato Sŷq, u off T t min, t max ŷ min, max Offet-compenate tato flux etimato k t u y off 5.3 Stato flux etimation Uing a compenate invete make the contolling efeence voltage vecto u an unitote an accuate etimate û of the funamental tato voltage vecto. Thi enable an accuate etimation of the tato flux linkage vecto even at vey low tato fequency. A ignal flow gaph of a tato flux etimato i hown in Fig.. The uppe potion of Fig. how that the tato flux vecto i obtaine by integating the inuce voltage û i = û ˆ, [8]. Uing a pue integato avoi the etimation eo an banwith limitation aociate with a low pa filte. The metho neceaily incopoate the ientification of a time-vaying vecto û off that epeent offet an ift voltage. Thee ae unavoiable when analog cicuit ae involve, a in tato cuent acquiition that povie the ignal. The offet voltage etimato i hown in the lowe potion of Fig.. It integate the inuce voltage û i in a econ, paallel flux etimation channel. The minimum an the maximum value pe funamental peio T of the eulting ignal ŷ, occuing at the epective time intant t min an t max, ae ubequently ae, epaately fo thei epective -axi an the q-axi component, to fom the component of the c offet vecto û off T. It i appaent that the offet of a inuoial ignal i zeo if it minimum an maximum value um up to zeo. The offet vecto i lowpa-filtee an then fe back to the input of the lowe flux integato in Fig.. It input i foce to zeo in a teay tate, which i poof that û off epeent the c component of û i. The inuce voltage i futhe contaminate by hamonic component,. Thee ae intouce by eo in the acquiition of the funamental cuent component, [], by incomplete compenation of the ea time effect [9], an by paamete eo of the nonlinea invete moel. The hamonic of û i ae etecte by the ac itubance etimato hown in the cente of Fig.. The etimato imply compute the intantaneou iffeence in amplitue between the etimate tato flux vecto ŷ an it efeence ignal y. Popotional contol by a gain contant k i ue fo fat cancellation of the hamonic component. The etimate fiel angle i obtaine a the agument of the tato flux vecto ŷ, an the etimate pee a the eivative of the fiel angle. 5.4 Stato eitance aaptation An impotant meaue to impove the low-pee pefomance i the accuate on-line aaptation of the tato eitance, which i the mot elevant paamete in enole contol. Kubota et al [] ue the obeve tuctue Fig. 6 to etemine the component Dº / of the eo vecto D in the iection of the tato cuent vecto, which i popotional to the eviation of the moel paamete ˆ fom the actual tato eitance. The ientification elay of thi metho i epote a.4. A fate algoithm elie on the othogonal elationhip in teay-tate between the tato flux vecto an the inuce voltage [8]. The vecto iagam Fig. 3 illutate the pinciple. The pace vecto ignal ae pocee in a ynchonou efeence xy-fame C, aligne with the tato cuent vecto. The elation = (u x u ix )/i x i eaily veifie, whee u ix =u i.in (g ). To facilitate the coect etimation of, the vecto u i of the inuce voltage, obtaine a the eivative of the tato flux vecto ŷ, mut not epen on the tato eitance. The eaon i that i the vaiable to etimate. The etimate tato flux i theefoe eive fom the intantaneou eactive powe, efine a q = u z, which notation ecibe the z-component of the vecto pouct of the tato voltage an tato cuent vecto. The etimate tato eitance value i then ue a an input ignal ˆ to the tato flux etimato Fig.. It ajut it paamete though a lowpa filte. The filte time contant T f = w R t f i about m. The ientification elay of thi metho i about 35 m [8].

6 y g jim i ˆ Fig. 3 Vecto iagam illutating the etimation of the tato eitance; S mak the tationay efeence fame (a,b), an C mak the cuent efeence fame (x,y) 5.5 Low pee pefomance achieve by impove moel The ocillogam Fig. 4 how the epone to loa tep change of ate magnitue while the pee i maintaine contant at 5 pm. Thi coepon to opeating at a tato fequency of.6 Hz (w =.3) uing the no-loa inteval. Fig. 5 emontate peitent opeation at zeo tato fequency. A loa tep of % ate magnitue emontate that coect fiel oientation wa maintaine. 6. SENSORLESS CONTROL THROUGH SIGNAL INJECTION Signal injection metho exploit machine popetie that ae not epouce by the funamental machine moel ecibe in Section 3 an 4. The injecte ignal excite the. i β i α, i β i α t Fig. 4 Contant pee opeation at 5 pm (f = w /p = ±.6 Hz, w = ±.3), with loa tep change of ate magnitue,ŷ a,ŷ b p t Fig. 5 Peitent opeation at zeo tato fequency, followe by a loa tep of % ate magnitue u u y g C x ŷ a ŷ b Re. iq S machine at a much highe fequency than that of the funamental fiel. The eulting high-fequency cuent geneate flux linkage that cloe though the leakage path in the tato an the oto, leaving the mutual flux linkage with the funamental wave almot unaffecte. The high-fequency effect can be theefoe coniee upeimpoe to, an inepenent of, the funamental behavio of the machine. High-fequency ignal injection i ue to etect aniotopic popetie of the machine. 6. Aniotopie of an inuction machine A magnetic aniotopy can be caue by atuation of the leakage path though the funamental fiel. The patial oientation of the aniotopy i then coelate with the fiel angle, which quantity can be ientifie by poceing the epone of the machine to the injecte ignal. Othe aniotopic tuctue ae the icete oto ba in a cage oto. A oto may be alo cutom eigne o a to exhibit peioic vaiation within a funamental pole pitch of local magnetic o electical chaacteitic, fo example the imenion of the oto lot. Detecting uch aniotopy eve to ientify the oto poition angle, the change of which efine the haft pee. The cae of a atuation-inuce aniotopy i coniee fit. The funamental fiel atuate the tato an oto ion in the egion of highe flux enity, thee poucing highe magnetic eitivity of the local leakage path. A tanient excitation by an injecte voltage u t change the leakage fluxe in the iection of the focing voltage vecto, u t = y t /t. The tanient cuent change accoingly. Given the highe magnetic eitance in the atuate egion, the local leakage path equie moe magnetizing cuent than the neighboing zone of le funamental flux enity. The pace vecto i t of the tanient cuent theefoe incline in pace towa the atuate egion a een fom the leakage flux vecto y t. The leakage inuctance i theefoe not contant in a atuate machine. It vaie with the angula iplacement between the leakage flux vecto y t an the funamental flux vecto. The cala leakage l inuctance in the tato equation u t = l i t /t of an iotopic machine convet into a tanient inuctance teno l when an aniotopy exit. The tato equation become u t = l i t /t. The teno l eflect only the funamental component of the patial atuation function. It ecibe the phyical phenomenon that the eivative i t /t of the tanient tato cuent ha a iffeent iection in pace than the voltage vecto u t that oiginate the excitation. Thee i geneally moe than one aniotopy peent in an inuction moto. The exiting aniotopie have iffeent patial oientation, uch a the actual angula poition of the funamental fiel, the poition of the oto ba within a oto ba pitch, an, if applicable, the angula poition within a funamental pole pai of a cutom eigne oto. ultiple aniotopie make the tanient inuctance teno moe involve. Fig. 6 i a viualization of the invee inuctance teno l that ecibe the iection of a tanient cuent change a a function of the exciting voltage: i t /t = l u t. It iplaye ove one electical evolution of an

7 A/V jim Re l Fig. 6 The invee inuctance teno l, ecibing atuation an oto ba aniotopie unloae inuction machine. The quai-cicle ae caue by the oto ba aniotopy; thei numbe coepon to the numbe of oto ba pe pole pitch. They iplace along anothe, low-fequency tajectoy une the influence of the atuation aniotopy. Thei hape vay, changing fom a vetical ellipe though almot a cicle to a hoizontal ellipe. Thi i owe to the changing magnetic atuation of the leakage path a the funamental fiel otate. The epone to an injecte high-fequency ignal neceaily eflect all aniotopie, fiel epenent an oto poition epenent. While intening to extact infomation on one paticula aniotopy, the othe aniotopie act a itubance. 6. Signal injection The injecte ignal may be peioic, ceating eithe a highfequency evolving fiel, o an altenating fiel in a pecific, peetemine patial iection. Such ignal can be efee to a caie, being peioic at the caie fequency with epect to pace, o time. The caie ignal, motly ceate by aitional component of the tato voltage, get moulate by the actual oientation in pace of the machine aniotopie. The caie fequency component ae ubequently extacte fom the machine cuent. They ae emoulate an pocee to etieve the eie infomation. Intea of injecting a peioic caie, the high-fequency content of the witche wavefom in a PW contolle ive ytem can be exploite fo the ame pupoe. The witching of the invete pouce a pepetual excitation of the tanient leakage fiel []. Thei itibution in pace i govene by the aniotopie of the machine. eauing an poceing of aequate voltage o cuent ignal pemit ientifying thei patial oientation. 6.3 Injection of a evolving caie A polyphae caie otating at fequency w c i geneate by the voltage pace vecto u c = u c exp(jw c t). Thi ignal i ae to the contolling voltage of the pulewith moulato, thu ceating the tanient excitation of the machine. The moulation by the machine aniotopie eflect in a pace vecto i c of caie fequency w c, foming pat of the meaue tato cuent vecto. It i epaate by a filte fom the funamental cuent of lowe fequency, an fom the witching hamonic of highe fequencie. The epaate pace vecto i c conit of a poitive equence component i p, an a numbe of component i nj that otate at the angula velocity ω c + ω j, i.e. in negative iection. Of i u =.7% i =.% i =.69% lot w c w c + w max i.8.5 w i = w c + N p w max i = 7.% p Fig. 7 eaue pectal cuent component fom an unexcite machine having two aniotopie, opeate in a pee ange w =... w max = p. Hz (meauement ata taken fom []) the latte component, one paticula mut be epaate to extact the angula oientation ω j t of the electe aniotopy. The othe act a itubance. Rotating at the fequency of the caie ignal, the cuent vecto i c follow in fact elliptic tajectoie. Thi i owe to the exitence of it poitive equence an negative equence component. Thee ae a many ellipe upeimpoe a aniotopie exit. The axi atio of a atuation ellipe i l q /l, a cloe to unity value that ange between.9 an.96 [, 3]. It i theefoe ifficult to ientify the angula inclination of the ellipe an thu etemine the angula oientation of the aniotopy. The chaacteizing component i n i vey mall, being upeimpoe by the lage poitive equence cuent vecto i p, an contaminate by the effect of othe aniotopie an itubance. Finally, all thee ignal ae buie une the much lage funamental cuent, an une the witching hamonic. To give an example, the cuent amplitue i p /i R an i n / R fom [], efee to the ate funamental cuent R ae hown in Fig. 7. The value ae meaue fom an inuction machine at zeo funamental excitation, i =, uch a to avoi atuation geneating an aitional aniotopy. Howeve, the oto ha an engineee aniotopy of l q /l =.9. Thee ae thee categoie of negative equence cuent: The cuent i at fequency w c + w i caue by the engineee oto aniotopy. It hamonic pectum pea between w c an w c + w max when the machine pee w vaie between an w max, whee w max = p. Hz i an aume maximum value in Fig. 7. Thi fequency component caie the pee infomation; it magnitue i =. R i extemely low. The cuent lot at fequency w c + N/p w i caue by the icete oto lot; it exten ove the fequency ange w c to w c + N/p w max, whee N i the numbe of oto lot an p i the numbe of pole pai. The cuent i u at fequency w c oiginate fom wining aymmetie, an fom gain unbalance in the tato cu- w c w

8 ent acquiition cicuit. Thi itubance i in vey cloe pectal poximity to the pee-elate component i ; both convege to the ame fequency at w =. Alo, i u > i in thi example. If thi machine wa fully fluxe an loae, anothe negative equence cuent at woul appea at fequency w c + w. Alo thi component ha an extemely low pectal itance (w w) fom the component i, whee w w i the lip fequency. The itibution of the ignificant negative equence pecta in Fig. 7 inicate that it i extemely ifficult to epaate thee ignal by filteing [4]. 6.4 Spee an poition etimation bae on aniotopie Degne an Loenz [] ue a ynamic moel of the mechanical ubytem of the ive moto a pat of a cloe phaelocke loop (PLL) fo pectal epaation. A ignal flow gaph of the pee an oto poition etimato i hown in Fig. 8. The caie geneate pace vecto i c i tanfome to a +w c - efeence fame in which i p how a a complex contant. It contibution i nullifie though the feeback action of an integato. The emaining ignal i n contain all negative equence component. It i tanfome to the w c -efeence fame. Thi tanfomation hift the fequency oigin in Fig. 7 to w c ; the negative equence component then appea a low-value poitive equence ignal. The unbalance itubance at fequency zeo i compenate by an etimate vecto î u = i u exp(jĵ u ), an the itubance geneate by oto lotting by an etimate vecto î lot. What emain i the cuent vecto î = î exp j(t + ĵ ), epeenting the oto aniotopy a a econ hamonic. Thi ignal caie the impotant infomation, ince wt = J i twice the oto poition angle; ĵ i a phae iplacement intouce by ignal filteing. The mechanical ytem moel in the uppe ight of Fig. 8 eceive an acceleation toque ignal, fome a the iffeence between the electomagnetic toque T el an the loa toque TˆL, both being epeente by thei etimate value. The feefowa ignal TˆL eve to impove the etimation ynamic. It i obtaine by a epaate loa moel. The etimate angula velocity of the oto i the integal of the acceleation toque, whee τ m i the nomalize mechanical time contant. Integating yiel the etimate oto poition angle Ĵ. The etimate angle ϑˆ contol two aniotopy moel. The uppe moel in Fig. 8 fom pat of the PLL. It compute the phae angle component t = Ĵ of the negative equence cuent vecto î, while it magnitue î an phae iplacement ĵ ae intouce a peetemine contant paamete. A commane by the compute phae angle eo e = i î z, the PID contolle foce the eulting pace vecto î to align with it efeence vecto i, thu etablihing Ĵ J a eie. The aniotopy moel thu tato coo. w c eve to impe on the etimate cuent vecto î the ame oto poition epenent vaiation that the eal machine, though it inheent aniotopy, foce on the negative equence cuent component i. The oto lot elate cuent vecto î lot i etimate by the aniotopy moel in the lowe potion of Fig. 3 in a imila fahion. The vecto î lot i ue to compenate the uneie itubance lot that fom pat of i n. The atuation-inuce aniotopy i not moelle in thi appoach, which limit it application to unatuate machine. Anothe poblem i the nonlineaity of the PW invete which caue itotion of the machine cuent. Thee geneate aitional negative equence cuent component that ten to fail the opeation of the poition etimato [5]. A geneal ifficulty of all evolving caie injection metho i the exteme low ignal-to-noie atio which i le than 3 in the example of Fig. 7. Thi call fo pecial effot to enue that the low-level ignal ae ufficiently epouce when oing the analog-to-igital conveion of the meaue cuent [6]. The nonlineaity of the PW invete, commonly known a ea-time effect, pouce itotion of the pulewith moulation wheneve one of the phae cuent change it ign. With the high-fequency caie ignal upeimpoe to the moulato input, the tato cuent ae foce to multiple zeo coing when the funamental phae cuent ae cloe to zeo. The effect caue evee cuent itotion that the etablihe metho fo ea-time compenation cannot hanle. Being time-icete event, the cuent itotion ae ifficult to compenate in a fequency omain metho. An offline ientification metho wa popoe by Teke [5]. The compenation i one hee uing et of time-vaiable pofile ove one electical evolution, one pofile fo evey opeating point in tem of loa an excitation level, an epaately fo the epective - an the q-component. Cuent publication on evolving caie metho how that numeou ie effect equie the ignal poceing tuctue to get moe an moe involve, while the epenence on pa- + w c -cooinate t f t w c i n w c -cooinate ˆ e i u ˆ jj u Fig. 8 Spee an oto poition etimato uing a PLL to ientify the epone to an injecte evolving caie e i iˆ lot PID Tˆ L K, T i, T jˆ jˆ lot N p mechanical ubytem t m moel of built-in aliency lot effect moel Ĵ

9 amete o on pecific off-line commiioning poceue peit. 6.5 Injection of an altenating caie Revolving caie can the whole cicumfeential pofile of all aniotopie that exit in a machine. Thi eve to etemine the chaacteitic of only one paticula aniotopy. The ubequent poceing tep fully ientify it patial oientation without uing a-pioi knowlege. An altenative cla of metho elie on injecting not a otating, but altenating caie in a pecific, though time-vaiable patial iection. The iection i electe in an eucate gue to achieve maximum enitivity in locating the tagete aniotopy. It i an avantage of thee metho that aleay exiting knowlege i jut upate by acquiing an incemental eo pe ampling peio. u c cowt j q fiel angle etimato Z y Z x LPF i c ( X) u c t N u m 6.6 Balance of quaatue impeance The appoach of Ha an Sul [7] aim at ientifying a fiel angle while the machine opeate at low o zeo pee. Accoing to the vecto iagam Fig. 9, an altenating highfequency ac caie ignal of amplitue u c i ae to the - axi component of the contol input of the pulewith moulato. The voltage ignal excite the machine in the iection of the etimate -axi. Thi iection may have an angula iplacement g = fom the tue -axi, the location of which i appoximately known fom the ientification in a peviou cycle. The injecte voltage a an ac component i c to the funamental tato cuent of the machine, epeente in Fig. 9 by the pace vecto. Owing to the aniotopic machine impeance, the high-fequency ac cuent i c evelop at a patial iplacement g with epect to the tue fiel axi of the machine. When the machine i opeate in atuate conition, it impeance Z c at caie fequency w c i a function of the cicumfeential angle a in fiel cooinate. The impeance ha a maximum value Z in the -axi, an a minimum value Z q in the q-axi. The ientification of the -axi i bae on the aumption of a ymmetic chaacteitic Z c (+a) = Z c ( a). An othogonal xy-cooinate ytem i intouce in Fig. 8, having it eal axi iplace by π/4 with epect to the etimate -axi. It iplacement with the tue -axi i then (π/4 g). The ientification poceue i illutate in the ignal flow gaph Fig., howing the cuent contol ytem an the geneation of the ac caie in it uppe potion. The hae fame in the lowe potion highlight the fiel angle etimato. Hee, the meaue tato cuent i banpa-filtee to epaate the ac caie cuent i c. The cuent i c an alo the excitation ignal u c co w c t ae tanfome to xy-cooinate, an then convete to complex vecto that have the epective m amplitue an coneve the phae angle. The complex highfequency impeance Z c i fome which i a function of the tanfomation angle π/4; een fom the fiel oiente cooinate ytem in Fig. 9, the tanfomation angle i (π/4 g). Fo eaon of ymmety, the eal an imaginay component Z x an Z y woul be equal if accuate fiel alignment, g =, exite. A nonzeo eo angle g make Z x inceae, an Z y eceae. Hence an eo ignal e = Z y (g) Z x (g) can be contucte which ajut the etimate fiel angle to an impove value by mean of a PI contolle. Fig. how that thi angle i ue fo cooinate tanfomation. In a conition of accuate fiel alignment,, fom which g follow. It i ocumente in [7] that the iffeence between the impeance value Z an Z q i mall when the machine i fully atuate. The euce eo enitivity then equie a high amplitue of the injecte ignal. 6.7 Evaluation of elliptic cuent tajectoie The caie injection metho ecibe o fa uffe fom cetain awback. We have the poo ignal-to-noie atio an the paamete epenence of the evolving caie metho, an the low enitivity of the quaatue impeance metho. u c D u c q= BPF m p 4 PW main ( X) i c 3 Fig. Signal flow gaph of a fiel angle etimation cheme bae on impeance meauement in quaatue axe j y g p 4 +g x p 4 g Fig. 9 Vecto iagam howing the injecte ac caie i c in iffeent efeence fame; F: fiel oiente fame, S: tationay fame S F ( S) i c

10 Linke [8] ue an altenating ac caie injecte in the etimate iection of the -axi to extact a atuation aniotopy ignal at high ignal-to-noie atio. An altenating caie voltage can be ecompoe into two ientical component that otate in oppoe patial iection. The aociate cuent tajectoie aume elliptic hape une the influence of exiting aniotopie []. The patial oientation of thee ellipe eviate fom the tue fiel axi a a function of the eo angle g = between the tue an the etimate fiel axi. The ignal flow gaph Fig. illutate the fiel angle etimation cheme. The banpa filtee caie-fequency cuent i c i otate by w c t + which make it poitive equence component i p a complex c value. A lowpa filte uppee all accompanying ac component like negative equence cuent an witching hamonic. The imaginay pat of i p i in g, which i popotional to the eo angle g = fo mall eo value. Thi ignal i ample at about khz. It fee an I-contolle to ceate the etimate fiel angle in a cloe loop. In oing o, efeence i mae to the injecte caie ignal to buil the tanfomation tem w c t +. A the acquie ignal i a c value in pinciple, the ampling fequency can be choen inepenently fom the caie fequency. Thi enue goo an ynamically fat alignment with the fiel axi without the nee of chooing a high caie fequency. Alo the ynamic of the pee an toque contol ytem i not impaie a the caie ignal oe not appea in the toque builing q-cuent component. Theefoe, the meaue q-cuent nee not be lowpa filtee, a i equie when a otating caie i ue. Accoing to Fig., uch filte i only povie fo the component i in the excitation axi. The metho yiel a ignal of high ignal-to-noie atio, pemitting opeation at low caie level. A -ma caie cuent wa foun ufficient fo fiel angle etimation in a -kw ive ytem. w c t LPF i x u c u c w c t + u BPF pee-inepenent value. The influence of the atuation-inuce aniotopy can be uppee by patial filte []. Roto poition acquiition i poible at ampling ate of eveal khz [3]. The patial eolution an the ignal-to-noie atio ae vey high. Thi pemit implementing pecie incemental poitioning ytem fo high ynamic pefomance. Howeve, the incemental poition i lot at highe pee when the fequency of the poition ignal become highe than twice the ampling fequency. Othe than continuou caie injection metho, which ae fequency omain metho, PW excitation contitute a equence of non-peioic time-icete event, an hence equie time-omain metho fo ignal poceing. The abence of pectal filte enable a fate ynamic epone. The ocillogam Fig. 3 how a poitioning cycle that equie maximum ynamic at % ate toque. The high magnetic atuation uing the acceleation inteval tempoaily euce the amplitue of the poition ignal; the poiac main ( ) i c x t ip fiel angle etimato PW 3 Fig. Signal flow gaph of a fiel angle etimation cheme bae on injecting an altenating caie 6.8 High-fequency excitation by PW witching The witching of a PW invete ubject the machine to epetitive tanient excitation. The eulting change i t /t of the tanient machine cuent ae influence by the aniotopie of the machine, chaacteize by the tanient inuctance teno l. The tanient cuent eivative i epaate fom the funamental component by taking the aociate zeo equence voltage l i t /t fom a wye-connecte tato wining [9]. Thi voltage i popotional to the chaacteitic component of the aniotopy ignal in that paticula phae axi in which a witching ha occue. Recontucting the complete patial oientation of an aniotopy equie theefoe the evaluation of a minimum of two witching event in iffeent phae axe. The witching intant mut be execute within a vey hot time inteval, uch that the angula oientation of the aniotopy emain almot unchange. The acquie axi component of the aniotopy ignal compoe a oto poition vecto p(j N ). The angle J N inicate the angula poition of the oto within one oto ba pitch. The ocillogam Fig. how a full evolution of p(j N ). Thi emphaize the high patial eolution that thi metho povie. Alo notewothy i the high level of the acquie ignal, which i aoun 35 V. A full mechanical evolution i pefome when J N /N incement by p whee N i the numbe of oto ba. The aniotopy ignal ae obtaine by intantaneou ampling a jim 4 V p J N t Re Fig. Tajectoy of the oto poition vecto p(j N ) within one oto ba pitch

11 J p α p β p/ 4V 4V m..4.6 t Fig. 3 Senole poition contol howing moto haft iplacement of ±9º at % ate tanient toque; tace fom top: haft poition angle J, poition ignal p α an p β ; contant value inicate zeo pee. tion accuacy emain unaffecte, a the elevant infomation i containe in the phae angle. 7. SUARY AND PERFORANCE COPARISON A lage vaiety of enole contolle ac ive cheme ae ue in inutial application. Open loop contol ytem maintain the tato voltage-to-fequency atio at a peetemine level to etablih the eie machine flux. They ae paticulaly obut at vey low an vey high pee, but atify only low o moeate ynamic equiement. Small loa epenent pee eviation can be compenate incopoating a pee o oto fequency etimato. High-pefomance vecto contol cheme equie a flux vecto etimato to ientify the patial location of the magnetic fiel. Fiel oiente contol tabilize the tenency of inuction moto to ocillate at tanient, which enable fat contol of toque an pee. The obutne of a enole ac ive can be impove by aequate contol tuctue an by paamete ientification technique. Depening on the epective metho, enole contol can be achieve ove a bae pee ange of : to :5 at vey goo ynamic pefomance. It i a paticula attaction of the funamental moel that un on a imple hawae platfom. Alo table an peitent opeation at zeo tato fequency can be achieve with thee moel, povie that all ive ytem component ae peciely moelle an thei paamete coectly aapte. Accuate pee etimation in the vey low pee egion, howeve, i ifficult ince the funamental moel become unobevable. Impove low pee pefomance can be achieve by exploiting the aniotopic popetie of inuction moto. The patial oientation of the aniotopie ae elate to the fiel angle, an to the mechanical oto poition. Thee can be ientifie eithe by injecting high-fequency caie ignal into the tato wining an poce the epone of the machine, o by making ue of the tanient that a PW invete geneate. Thee metho have ecently emege. They bea geat pomie fo the evelopment of univeally applicable enole ac moto ive. 8. REFERENCES. J. Holtz, Senole Contol of Inuction oto, Poceeing of the IEEE, Vol. 9, No. 8, Aug., pp C. Schaue, Aaptive Spee Ientification fo Vecto Contol of Inuction oto without Rotational Tanuce, IEEE In. Appl. Soc. Ann. eeting, San Diego Ca 989, pp T. Okuyama, N. Fujimoto, T. atui, an Y. Kubota, A High Pefomance Spee Contol Scheme fo Inuction oto without Spee an Voltage Seno, IEEE In. Appl. Soc. Ann. eeting, Denve Co. 986, pp T. Ohtani, N. Takaa, an K. Tanaka, Vecto Contol of Inuction oto without Shaft Encoe, IEEE Tan. In. Appl., Vol. 8, No., Jan/Feb. 99, pp H. Kubota, K. atue, an T. Nakano, DSP Bae Spee Aaptive Flux Obeve of Inuction oto, IEEE Tan. In. Appl., Vol. 9, No., Ap/a. 993, pp X. Xu an D. W. Novotny, Implementation of Diect Stato Flux Oiente Contol on a Veatile DSP Bae Sytem, IEEE Tan. In. Appl., Vol. 9, No., Ap/a. 99, pp J. Holtz an A. Khambakone, Vecto Contolle Inuction oto Dive with a Self-Commiioning Scheme, IEEE Tan. In. Elect., 99, pp J. Holtz an J. Quan, Senole Vecto Contol of Inuction oto at Vey Low Spee uing a Nonlinea Invete oel an Paamete Ientification, IEEE Tan. In. Appl., Vol. 39, No. 4, J. Holtz, Pulewith oulation fo Electonic Powe Convete, Poceeing of the IEEE, Vol. 8, No. 8, Aug. 994, pp H. Kubota an K. atue, Spee Senole Fiel Oiente Contol of Inuction oto with Roto Reitance Aaptation, IEEE Tan. In. Appl., Vol. 3, No. 5, Sept/Oct. 994, pp J. Holtz, On the Spatial Popagation of Tanient agnetic Fiel in AC achine, IEEE Tan. In. Appl., Vol. 3, No. 4, July/ Aug. 996, pp W. Degne an R. D. Loenz, Uing ultiple Saliencie fo the Etimation of Flux, Poition an Velocity in AC achine, IEEE Tan. In. Appl., Vol. 34, No. 5, Sept/Oct. 998, pp J. Holtz, Senole Poition Contol of Inuction oto an Emeging Technology, IEEE Tan. In. Elect., Vol. 45, No. 6, Nov/Dec. 998, pp N. Teke, G.. Ahe,. Sumne, an K. J. Baley, Suppeion of Satuation Saliency Effect fo the Senole Poition Contol of Inuction oto Dive une loae Conition, IEEE Tan. In. Elect., Vol. 47, No. 5, Sep/Oct., pp N. Teke, G.. Ahe, K. J. Baley, an. Sumne, Analyi an Suppeion of Invete Clamping Saliency in Senole Poition Contolle of Inuction oto Dive, IEEE In. Appl. Soc. Ann. eeting, Chicago, Sept. 3 - Oct. 4,. 6. F. Biz, A. Diez, an. W. Degne, Dynamic Opeation of Caie-Signal-Injection-Bae Senole Diect Fiel-Oiente AC Dive, IEEE Tan. In. Appl., Vol. 36, No. 5, Sept/Oct., pp J.-I. Ha an S.-K. Sul, Senole Fiel-Oiente Contol of an Inuction achine by High-Fequency Signal Injection, IEEE Tan. In. Appl., Vol. 35, No., Jan/Feb. 999, pp Linke, R. Kennel, an J. Holtz, Senole Spee an Poition Contol of Pemanent agnet Synchonou achine, IECON, 8th Annual Conf. of the IEEE Inutial Electonic Society, Sevilla/Spain,. 9. J. Jiang, Senole Fiel Oiente Contol of Inuction oto at Zeo Stato Fequency, Ph.-D. Dietation (in Geman), Wuppetal, J. Holtz an H. Pan, Elimination of Satuation Effect in Senole Poition Contolle Inuction oto, IEEE In. Appl. Soc. Ann. eeting, Pittbugh, Oct. 3-8,.