Observer Based Parallel IM Speed and Parameter Estimation

Transcription

1 SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 11, No. 3, Octobe 2014, UDC: : DOI: /SJEE S Obeve Baed Paallel IM Speed and Paamete Etmaton Saša Skoko 1, Dako Mačetć 1, Vean Vać 1, Đua Oo 1 Abtact: The detaled peentaton of moden algothm fo the oto peed etmaton of an nducton moto (IM) hown. The algothm nclude paallel peed and etance paamete etmaton and allow a obut haft-enole opeaton n dvee condton, ncludng full load and low peed opeaton wth a lage themal ft. The dect connecton between the njected electc gnal n the d-ax and the component of njected oto flux wee ponted at. The algothm that ha been appled n the pape ue the extacted component of the njected oto flux n the d-ax fom the obeve tate vecto and fltated meaued electcty of one moto phae. By applyng the mentoned algothm, the ytem convege towad the gven efeence. Keywod: Inducton moto, Luenbege obeve, Paamete dentfcaton. 1 Intoducton The mple contucton and upeo explotaton chaactetc have made the nducton moto vey popula n a wde ange of ndutal ve applcaton, fom the unegulated pump and compeo faclte, to moden evomechanm wth the pece egulaton of peed and poton [1, 2]. Befoe the ue of nducton moto n egulated ve, the DC moto wee ued. Howeve, the DC moto ae moe complex n the contucton, affectng both the poducton pce and the pce of ve mantenance. The uage of the nducton moto allow the educton of both ve pce, a well a the mnmzaton of electc enegy loe, geate elablty, convete volume educton, etc. Futhe advance and ve pce educton poble, though t demand the feld oented contol wth mnmum eno needed fo ve to opeate. Untl ecently, n the feld of the haft-enole ve wth an nducton moto, mple technque of etmaton ae typcally ued, uch a open-loop etmato and MRAS etmato [3]. The man pupoe of thee peed etmato the onlne calculaton of poton and the ampltude of the elected machne tate vecto, uch ae tato, oto o magnetzng flux vecto. Howeve, the open-loop machne model tate calculaton can be effected wth 1 Depatment of Powe Electonc and Dve, Faculty of Techncal Scence, Unvety of Nov Sad, Seba E-mal: aakoko78@gmal.com, dama@un.ac., veanv@un.ac., ood@un.ac. 501

2 S. Skoko, D. Mačetć, V. Vać, Đ. Oo ncoect machne equvalent ccut paamete, the nonlneaty of voltage nvete tanfe functon and the eo n the tato cuent meauement o tato voltage etmaton. A a conequence, all thoe oluton ae unelable dung the low tato voltage opeaton and have lmted peed ange fo the afe and obut opeaton (f < 1 Hz). Out of the above-gven analy, t can be concluded that the open-loop method ae not applcable n moden hgh pefomance ve wth an nducton moto. The needed mpovement n the electcal machne flux etmaton can be acheved only by ung the lnea flux obeve, whch made moe elable and obut to machne paamete change by the coectve tate feedback [4]. The lnea obeve dcued n th pape the Luenbege obeve (LO). LO ue the oto flux and the tato cuent vecto a two tate vaable and pefom the table multaneou etmaton n a wde peed ange by abtay allocatng the obeve pole [5]. The otatonal peed etmated on the ba of the dffeence between the meaued and the LO etmated tato cuent vecto. Th obeve mla to the MRAS obeve tuctue, wth the IM ued a the efeence model and the LO a the adjutable model. Howeve, the LO oto peed etmaton epeent an actvty wth a coectve feedback va the tato cuent eo, whle the MRAS etmate the oto peed n the open loop manne. In [5] hown that the Extended Luenbege obeve (ELO) can be uccefully ued n the haftenole IM ve wth the dect feld oentaton and opeatng wth low otatonal peed. In th pape, the poblte of the paallel etmaton of the tato etance and oto peed, a well a lmtaton dung the paallel etmaton of oto etance and oto peed ae hown. Baed on that analy, the autho ugget a tet gnal baed pocedue fo the etmaton of the oto etance [6, 7]. Pape [8] peent an ognal method fo the mplementaton of a enole ndect tato-flux oented contol of nducton moto ve. The popoed contol cheme n [8] ha a good pefomance wth the computatonal complexty educton obtaned by ung the analytcal elaton to detemne the LO gan matx. In pape [9] dffeent type of IM-VFD ae peented. The man focu n [9] on the enole etmaton technque whch ae beng appled to make IM-VFD moe effectve dung wde peed opeaton, ncludng vey-hgh and vey-low peed egon. In pape [10] a nonlnea adaptve contol algothm popoed fo the IM. It baed on a two tme-cale obeve that allow the on-lne dentfcaton of thee ctcal uncetan paamete,.e., load toque and moto tato and oto etance. Th pape pont out the bac equaton followng fom the uage of the njected tet gnal n the d-ax of the tato cuent, and the ynthe algothm that allow the convegence of the numecal model of a ve to the et value of the peed of otaton. 502

3 Obeve Baed Paallel IM Speed and Paamete Etmaton 2 Mathematcal Model of Inducton Machne and Contol Pncple The mathematcal model of the nducton machne cont of ytem of dffeental and algebac equaton decbng electomagnet and mechancal phenomena n a machne [11]. Fg. 1a how the nducton machne n an ognal phae doman, whee ndexe a, b and c peent tato meaue whle ndexe A, B, C peent the ndexe of oto value. The angle between the a ax and the A ax maked wth ϑ. (a) Fg. 1 (a) Thee phae nducton moto n the ognal doman, (b) Thee phae nducton moto n the dq doman. Afte the Clake and Pak tanfomaton ae appled onto the ognal phae doman model, one get the machne model n the otatng ax dq-doman, Fg. 1b: d d ud Rd dq q, (1) dt d q uq Rq dq d, (2) dt d u R ( dq ) q, (3) dt d q uq Rq ( dq ), (4) dt whee: dq electcal angle velocty of efeence axe ytem, (b) 503

4 S. Skoko, D. Mačetć, V. Vać, Đ. Oo R, R tato and oto etance, u, u tato voltage, d q u, u oto voltage, d whee: q, tato cuent, q, oto cuent, q, tato fluxe, d q, oto fluxe, q moto angula velocty. The model completed wth the algebac equaton: L L, L L, (5) d d m q q m q L L, L L. (6) m d q q m q L L Lm, L L Lm ae tato and oto elf nductance, L m mutual nductance, L, L ae tato and oto leakage nductance. Fnally, the moto toque can be calculated ung the tato cuent and flux vecto: T P( ), (8) c q d d q whee P the numbe of pole pa. The angle between the oto ax and the d-ax epeent the oto lp angle:, (9) lp whee: dq the poton of dq efeence ytem, the poton of the oto efeence ytem (Fg. 1b). In that cae, the coodnate of the oto ax and the otatng ax ytem ae connected wth the followng equaton: t (0) d t, (0) dt dq dq dq dq t. (10)

5 Obeve Baed Paallel IM Speed and Paamete Etmaton Both dect and ndect feld oentaton acheve the ndependent contol of the toque and the flux of an nducton moto. In the feld oentaton towad the oto flux, the flux ampltude contolled wth the electc cuent component paallel to the oto flux vecto o the d-ax of the otatng coodnate ytem. In the ame tme the othogonal component of the tato cuent vecto contol the toque [12, 13]. In the cae of the oto flux oentaton the followng vald:, (11) 0. (12) q The tandad ndect feld oentaton eque the oto poton data taken of the peed eno. In that cae the egulaton tuctue mut be fed wth the pope oto peed and poton etmate. In Fg. 2, the pncple cheme of the haft-enole vecto contol of an nducton moto wth the oto flux oentaton hown. Fg. 2 Pncple cheme of the vecto contolled nducton moto wth an oentaton n the decton of the oto flux. 3 Mathematcal Model of Luenbege Obeve Full ode Luenbege obeve allow the oto peed etmaton of the nducton moto. The obeve bacally epeent the etmato wth the tate vaable feedback and enable the etmaton of tate vaable and/o paamete of a nonlnea dynamc ytem n eal tme. In the cae of the nducton moto, the Luenbege obeve contucted wth the tato cuent and the oto flux vecto a tate vaable. The Luenbege obeve baed on the nducton moto model n the tatonay efeence fame, equaton (1) (6), whee dq 0. In a hotened fom, the tate pace model can be wtten a follow: d x AxBu, (13) dt y Cx, (14) 505

6 S. Skoko, D. Mačetć, V. Vać, Đ. Oo whee: x vecto of the obeve tate, u the obeve nput vecto, y the obeve output vecto, A tate matx of the obeve (Appendx A), B nput matx of the obeve, C output matx of the obeve. 506 T x, (15) The matce B and C ae defned a follow: T u u u 0 0, (16) T y. (17) T L B, C L The modfed fom of the Luenbege obeve defned wth the equaton (18) and (19) and t called the Extended Luenbege Obeve (ELO). d xˆ Ax ˆ ˆ BuG( ˆ ), (18) dt ˆ Cx. ˆ (19) The gan matx of the Luenbege obeve defned a follow: g1i g2j G G,, g3 g I J 1 0. I J G The element of the gan matx G ae defned a: g1 k 1 a11 a22, g2 k 1 a 22, 2 g3 k 1ca11 a22ck 1 a11 a22, g c k 1 a. 4 22

7 Obeve Baed Paallel IM Speed and Paamete Etmaton whee the coeffcent a11, a12, a 12, a21, a22, a 22 ae defned n Appendx F. In Fg. 3, the pncple cheme of the Extended Luenbege Obeve defned by (18) and (19) hown. Fg. 3 Pncple cheme of the Extended Luenbege Obeve. 4 Algothm Synthe fo the Rotatonal Speed Etmaton ( ˆ ) The tate pace model decbng the nducton moto and the obeve ae gven n (20) and (21). d x, dt Ax Bu Cx, (20) d xˆ ˆ ˆ ( ˆ ), ˆ ˆ dt Ax Bu G Cx. (21) Vecto n (21) maked wth ^ epeent the etmated value. The eo gnal defned a the dffeence between the actual and the etmated value e( x x ˆ). The ft ode devatve of the eo gnal defned a, d e d d ˆ x x, leadng to, dt dt dt de ( )( ˆ) ( ˆ ) ˆ ( ) Δ ˆ dt A GC x x A A x A GC e Ax. (22) 507

8 S. Skoko, D. Mačetć, V. Vać, Đ. Oo The nducton moto peed etmaton wthn the ELO can be defned ung 2 T ( ˆ ) the Lyapunov cteon functon V () e e e, whee the potve contant. Ung (22), the ft ode devatve of the cteon functon eult n the followng: dv T T T T T 2Δ dˆ e ( ) ( ) ˆ Δ Δ ˆ. dt AGC AGC e x A ee Ax (23) dt The condton of the aymptotc tablty fulflled f the um of the econd, the thd and the fouth tem n (23) equal 0 T T T 2Δ dˆ 0 xˆ ΔA ee ΔAx ˆ (24) dt The oluton of the equaton (24) expoe the method fo the nducton moto oto peed etmaton: ˆ ( ˆ ˆ e e )dt. (25) c The peed etmaton method ued by the ELO etmated oto flux vecto and the eo between the meaued and by the ELO etmated cuent vecto. LL The coeffcent c defned a c, whee λ epeent the potve Lm contant numbe. The appopate adaptve mechanm emboded n the dagam n the Fg. 4. Fg. 4 The block dagam of the adaptve mechanm fo the otatonal peed etmaton of the moto. The effectvene of the ELO peed etmaton teted ung compute mulaton and eult povded n Fg. 5. Dffeent peed pofle ae ued. Afte no load tat, the dffeent load appled n the 1 t, 2 nd and 3 d econd, 508

9 Obeve Baed Paallel IM Speed and Paamete Etmaton wth the load toque of 0.5 pu, 0.8 pu and 1 pu, epectvely, whee the nomnal toque 50 Nm. (a) Fg. 5 (a) Change of the eal and the etmated peed fo the gven tetng condton, (b) Change of the eal and the etmated peed wth a udden evee to 10 ad/ and a quck etun to 10 ad/. A eult how, the ELO capable of tackng the oto peed unde the dvee tet condton. Howeve, the gven peed etmaton algothm doe not nclude the dcepancy between the moto and the obeve paamete. If paamete ued by the obeve ae not coect, thee a devaton between the actual and the etmated moto peed, a the next et of mulaton eult how (Fg. 6). (b) (a) Fg. 6 (a) Change of the etmated and the eal moto peed fo R m = 1.2R, (b) Change of the etmated and the eal moto peed fo R m = 0.8R. 509 (b)

10 S. Skoko, D. Mačetć, V. Vać, Đ. Oo The efeent peed wa et to ω * = 10 ad/. The moto wa ft tated wthout the load, and the load wa appled n the 1 t, 2.5 th and 3.5 th econd, 0.5 pu, 0.8 pu and 1 pu, epectvely, whee the nomnal toque 50 Nm. The tato (oto) etance changed lnealy n the moto model by ±20% dung the peod. (a) Fg. 7 (a) Change of the etmated and the eal moto peed fo R m = 1.2R ; (b) Change of the etmated and the eal moto peed fo R m = 0.8R. The eult how that the change n the tato etance nfluence both the peed etmaton and the flux vecto oentaton. The oto etance change eult n the etmated peed eo a well; howeve, contay to the tato etance, t doe not nfluence the oto flux vecto oentaton [6]. 4.1 Mathematcal algothm ynthe fo the paallel etmaton R and ˆ The algothm fo the paallel etmaton of the oto peed and the moto tato etance can be contucted ung the Lyapunov functon ˆ 2 T ( R R) V () e e e. Ung the ame pocedue a befoe, the mechanm fo the paallel tato etance etmaton a follow: d Rˆ ( ˆ ˆ ) ˆ ˆ ee 1( ee ). (26) dt L Smla a the oto peed, the tato etance can be etmated by ung the ELO etmated tato cuent vecto and the eo between the actual and the etmated tato cuent vecto. The mulaton eult howng the effcency of the addtonal dentfcaton of the tato etance ae gven n Fg. 8. The algothm fo the addtonal tato etance dentfcaton wa actve dung 510 (b)

11 Obeve Baed Paallel IM Speed and Paamete Etmaton th et of compute mulaton. The tato etance n the nducton moto model lnea and t change lnealy Rm 20% R n the tme peod between 1.5 and 2. The peed et to a elatvely low value of * 10 ad and the moto loaded n the 1, 2.5 and 3.5, wth the toque of 0.5 pu, 0.8 pu and 1 pu, epectvely, whee the nomnal toque 50 Nm. (a) (b) Fg. 8 (a) Speed change of the oto,, ˆ f ( t) fo R m = 1.2R wth the coecton R ; (b) Speed change of the oto,, ˆ f ( t) fo R m = 0.8R wth the coecton R. 4.2 Mathematcal algothm ynthe fo the paallel etmaton R and ˆ Applyng the bac Lyapunov cteon functon on the oto etance 2 T ( Rˆ R) eult n the followng V ( e) e e A the eult, the fomula fo the oto tme contant ( T L R ) dentfcaton gven, 2 ( ˆ ˆ ) ( ˆ ˆ L m L m ) Tˆ L d 1 dt 511 e e. (27) The effectvene of (27) wa teted va compute mulaton and eult ae gven n Fg. 9, wth the ame load condton and peed efeence a n Fg. 8. The obtaned eult how that the ELO wth the paallel etmaton of the peed and oto tme contant cannot opeate [5, 6]. The only manne to do that to ceate the change n the oto flux vecto, whch eult n the non-zeo ght de of (27). The poblty fo the paallel peed and oto ccut paamete etmaton wll be futhe exploed n the next chapte.

12 S. Skoko, D. Mačetć, V. Vać, Đ. Oo (a) (b) Fg. 9 (a) Speed change of the oto,, ˆ f ( t) fo R m = 1.2R wth the coecton R ; (b) Speed change of the oto,, ˆ f ( t) fo R m = 0.8R wth the coecton R. 5 R (T ) Etmaton on the Ba of the Injected Tet Sgnal Steady tate equaton of the nducton moto how that t mpoble to etmate the oto peed and oto etance n paallel. That paallel etmaton poble only f non-zeo ate of the change n the oto flux vecto ceated. One manne to do that to nject the tet gnal n the d-ax. The uage of the njected gnal n the d-ax aleady an etablhed pocedue, appled n a numeou numbe of pape. In th ecton the connecton between the njected electc gnal d and the eultng flux component nvetgated ft. The non-lnea nducton moto model Lm d T d T 0 1 l dt q L m q 1 q 1 0, q 0 0 T T fed by gnal that have the teady tate value and the mall gnal devaton aound the teady tate value, a peented o o Δ, Δ, q q q o o Δ, Δ, d d d q q q o Δ. l l l 512

13 Obeve Baed Paallel IM Speed and Paamete Etmaton o whee the x dq mak the teady tate value of the gnal and the xdq epeent the mall gnal. Afte teady tate equaton ae ubtacted, the mall gnal model of the nducton moto can be contucted a follow: d 1 o o Lm (Δ ) Δ lδq Δlq Δd, (28) dt T T d 1 o o Lm (Δ q ) Δq lδ Δl Δ q. (29) dt T T The mall gnal model vald fo a gven teady tate pont, defned by o o o l, and q. The mall gnal model how how a mall gnal n the d-ax cuent component Δ d geneate the change n the moto flux n the d-ax, the mall gnal Δ. The connecton between the njected component d and defned by the followng elaton: d 1 Lm (Δ ) Δ Δd, epectvely d 1 Lm ( ) d, (30) dt T T dt T T whle d Δd and Δ. If the peodc gnal njected nto the d-ax tato cuent ( d ), d I n t 0,1dn n t the gnal ceated n the d-ax oto flux component : t LIT m o T o L 2 2 m d e L m d T LIT m LIT m LI m n t co t T 1 T 1 (31) The thd and the fouth pat of the equaton (31) ae the component of the njected flux. Dung the mulaton, the ampltude of the njected tet gnal et to 10% of the nomnal d ax tato cuent whle t fequency et to 250 Hz. The vecto dagam howng the mall gnal tato cuent and the coepondng mall gnal n the d-ax oto flux gven n Fg. 10. The uggeted oto tme contant paamete coecton algothm gven n the followng elaton: d ( ˆ L ) ˆ L ˆ m d T, o ˆ dt R d ( ˆ ˆ ) L m d. (32) dt 513

14 S. Skoko, D. Mačetć, V. Vać, Đ. Oo Fg. 10 Vecto dagam of the njected cuent and the eultng d-ax flux wth the appopate component. Fg. 10 how the njected cuent I and the coepondng njected flux, whch come fom the njected cuent, wth the appopate component n the auxlay coodnate ytem (d, q auxlay coodnate ytem of the njected cuent, x, y auxlay coodnate ytem of the coepondng njected flux). The tato electc cuent d ued n the equaton (32) can be flteed fom the meaued tato cuent, whle the ued ˆ can be flteed fom the etmated oto flux n the obeve. The oto tme contant dentfcaton method, whch can be appled n paallel wth the peed etmaton, hown n the next fgue. The block dagam of the Luenbege obeve wth the paallel algothm fo the oto etance coecton hown n Fg. 12. Matx C 1 defned n Appendx G. The effectvene of the paallel oto peed and the oto ccut paamete etmaton teted va compute mulaton, Fg. 13. The mechanm fo the addtonal dentfcaton of the oto etance and the oto tme contant actvated at 2.1 of the mulaton tme. In the tme peod , the oto etance n the moto model changed lnealy to ±20% fom t nomnal value. The moto magnetzaton undetaken and the loadng done at 1, 2.5 and 3.8, wth the load toque of 0.5 pu, 0.8 pu and 1 pu, epectvely, whee the nomnal toque 50 Nm. 514

15 Obeve Baed Paallel IM Speed and Paamete Etmaton Fg. 11 Block dagam of the coectonal algothm fo the ndependent etmaton R (T ), baed on the njected tet gnal. Fg. 12 Pncpal block dagam of the coectonal algothm ynthe fo the ndependent etmaton of the algothm R (T ) and the obeve. 515

16 S. Skoko, D. Mačetć, V. Vać, Đ. Oo (a) (b) (c) Fg. 13 (a) Change of,, ˆ f ( t) fo the cae R m = 1.2R ; (b) Change of,, ˆ f ( t) fo the cae R m = 0.8R ; (c) Change of, f ( t) fo the cae R m = ±20% R. The fnal pat how the eult of tetng the model wth the appled coecton algothm, whch opeate n paallel wth the algothm fo etmatng the oto etance. The ytem wa teted fo fou chaactetc equence. Fg. 14 and 15 how the mulaton eult wth the algothm fo the addtonal dentfcaton R (T ) mmedately actvated. In the peod between 1.5 and 2.1, the value of the etance n the moto model changed lnealy by +20%, compaed to t nomnal value. The moto magnetzaton undetaken and the loadng done at 1, 2.6 and 3.8, wth the load toque of 0.5 pu, 0.8 pu and 1 pu, epectvely, whee the nomnal toque 50 Nm. 516

17 Obeve Baed Paallel IM Speed and Paamete Etmaton (a) (b) Fg. 14 (a) Change of *,, ˆ f t fo the cae R m =1.2R (1 t equence), (b) Change of *,, ˆ f t fo the cae R m =1.2R (2 nd equence). (a) Fg. 15 (a) Change of *,, ˆ f t fo the cae R m = 1.2R (3 d equence); (b) Change of *,, ˆ f t fo the cae R m = 1.2R (4 th equence). 7 Concluon In the pape, the Luenbege obeve baed algothm fo the nducton moto peed etmaton nvetgated. It ha been hown that the bac Luenbege obeve entve to the change n both tato and oto etance paamete. In ode to dentfy the algothm that moe obut and atfactoy, the bac Luenbege obeve upgaded wth the paallel tato and oto etance dentfcaton mechanm. The pecal attenton gven to the paallel oto etance etmaton whch eque the njecton of the tet 517 (b)

18 S. Skoko, D. Mačetć, V. Vać, Đ. Oo gnal n the tato cuent n the d-ax of the oto flux. The dect lnk between the njected cuent tet gnal and the ceated mall gnal n the oto flux povded. A a eult of that connecton, the oto etance paamete coectve mechanm that can wok n paallel wth the peed etmaton uggeted. The mulaton eult pove the effectvene of the Luenbege peed obeve upgaded n that manne. Fo any condton teted, t hown that the oto paamete value wll convege towad the actual paamete value and that eo n the etmated oto peed wll be cancelled. The only awback of th algothm can be n the ntenve numec calculaton needed. One pactcal oluton fo that to epaate the oto peed and the paamete etmaton mechanm by executng the econd one wth much lowe ate. That would not affect the tackng of the low changng moto paamete, but would ave the gnfcant amount of the poceo tme. 8 Acknowledgment Th wok wa uppoted n pat by the Mnty of educaton and cence of the Republc of Seba wthn the poject III Appendce Moto paamete ued n the pape: Manuf. code: 1.ZK 132 M4, Pole 4, Powe 7.5 [kw], R =2.044[Ω], R = 1.873[Ω], L = [H], L = [H], L m = [H], J =0.021 [kgm 2 ]. 9.1 Appendx A State matx of the obeve A: 2 2 RL RL m LmR L m LL LL LL 2 2 RL RLm Lm LmR LL LL LL A. RL m R 0 L L RL m R 0 L L 518

19 Obeve Baed Paallel IM Speed and Paamete Etmaton 9.2 Appendx B State matx of the obeve  : 2 2 RL RL m LmR L m 0 ˆ 2 2 LL LL LL 2 2 RL RLm Lm LmR 0 ˆ 2 2 ˆ LL LL LL A. RL m R 0 ˆ L L RL m R 0 ˆ L L 9.3 Appendx C Matx to detemne the algothm to etmate peed ΔA Aˆ A : ˆ c ˆ ΔA c ( ˆ ) 0 0 ( ˆ ) Appendx D Matx to detemne the algothm to etmate tato etance ΔA Aˆ A : R 2 ( R ˆ R) L LL ˆ 2 ˆ ( R ) Δ R L A A A R LL

20 S. Skoko, D. Mačetć, V. Vać, Đ. Oo 9.5 Appendx E Matx to detemne the algothm to etmate oto etance ΔA Aˆ A : R 2 ( Rˆ ˆ R) Lm ( R R) L m LL LL ˆ 2 ( R ) ( ˆ R Lm R R) L m Δ ˆ LL LL A A A R ( Rˆ ) ( ˆ. R Lm R R) 0 0 L L ( Rˆ ) ( ˆ R Lm R R) 0 0 L L 9.6 Appendx F Coeffcent: a11, a12, a12, a21, a22, a 22 : RL RL L R L a, a, a, 2 2 m m m LL LL LL RL R a, a, a. m L T 9.7 Appendx G Matx C 1 : C Refeence [1] P. Va: Senole Vecto and Dect Toque Contol, Oxfod Unvety Pe, [2] B. Boe: Moden Powe Electonc and AC Dve, Pentce Hal, [3] V. Vac: Contol of Inducton Moto wthout Shaft Seno, PhD The, Unvety of Belgade, School of Electcal Engneeng, Belgade, [4] J. Holtz: Senole Contol of Inducton Machne-Wth o wthout Sgnal Injecton, IEEE Tanacton on Indutal Electonc, Vol. 53, No 1, 2006, pp

21 Obeve Baed Paallel IM Speed and Paamete Etmaton [5] H. Kubota, K. Matue, T. Nakano: DSP Baed Speed Adaptve Flux Obeve of Inducton Moto, IEEE Tanacton on Induty Applcaton, Vol. 29, No. 2, 1993, pp [6] H. Kubota, K. Matue: Speed Senole Feld-Oented Contol of Inducton Moto wth Roto Retance Adaptaton. IEEE Tanacton on Induty Applcaton, Vol. 30, No. 5, 1994, pp [7] J. Ha, S. Sul: Senole Feld-Oentaton Contol of an Inducton Machne by Hgh Fequency Sgnal Injecton, IEEE Tanacton of Induty Applcaton, Vol. 35, No. 1, 1999, pp [8] M. Joul, K. Jaay, Y. Koubaa, M. Bouak: Luenbege State Obeve fo Speed Senole ISFOC Inducton Moto Dve, Electc Powe Sytem Reeach, 2012, Vol. 89, pp [9] I. M. Alofyan, N.R.N. I: A Revew on Senole Technque fo Sutanable Relablty and Effcent Vaable Fequency Dve of Inducton Moto, Renewable and Sutanable Enegy Revew, 2013, Vol. 24, pp [10] A. Savoa, C. Veell, M. Mengon, L. Za, A. Tan, D. Caade: Adaptve flux obeve fo nducton machne wth on-lne etmaton of tato and oto etance, In Poceedng of the 15th Intenatonal Powe Electonc and Moton Contol Confeence (EPE/PEMC 12), Nov Sad, Seba, Septembe 2012, pp. LS7b LS7b [11] V. Vuckovc: Geneal theoy of electcal machne, Nauka, Belgade, (In Seban). [12] V. Vuckovc: Electcal ve. Unvety of Belgade, School of Electcal Engneeng, Belgade, (In Seban). [13] D. W. Nowotny, T. A. Lpo: Vecto Contol and Dynamc of AC Dve, Claendon Pe, Oxfod,