Improved Adaptive Flux Observer of an Induction Motor with Stator Resistance Adaptation

Transcription

1 Taek BENIOUD, Abdelhafid OARI Univeity of Science and Technology of Oan (), () Ipoved Adaptive Flux Obeve of an Induction oto with Stato Reitance Adaptation Abtact. In thi pape, an ipoved chee of adaptive flux obeve of induction oto i popoed. Thi adaptive obeve i ued with fieldoiented contol of induction achine. It i baed on uing induction oto odel with the etiation of the load toque beide the etiation of the tato eitance. The obutne of thi obeve with epect to the vaiation of the tato eitance. The pefoance of the popoed adaptive obeve wee copaed to thoe of the claical one via nueical iulation. The obtained eult how the effectivene of the popoed chee. Stezczenie. Zapoponowano ulepzony adaptacyjny yte obewatoa tuienia w ilniku indukcyjny. Bazuje on na odelu w któy okeśla ię oent obciążenia i ezytancję tojana. jet poponowane dla pola zoientowanych kontoli indukowanie azyny. (Ulepzony obewato tuienia w ilniku indukcyjny z poiae ezytancji tojana) Keywod: induction oto, adaptive flux obeve, diect field-oiented contol. Słowa kluczowe: obewato tuiena, ilnik indukcyjny. Intoduction At the peent tie, the diect field oiented contol (FOC) technique i widepead ued in high pefoance induction oto (I) dive [], []. It allow, by ean of coodinate tanfoation, to epaate the electoagnetic toque contol fo the oto flux one, and, hence to anage induction oto a dc oto. Such contol ethod need the knowledge of the oto flux, which i not diectly eauable. In ode to avoid expenive eno, oto flux obeve ae coonly ued [3]. Given that the effectivene of the contol tategy i baed on ight oto flux detection, the dive pefoance i tictly connected to thee of the oto flux obeve [4]. Theefoe, the pefoance of the obeve, in te of tability, accuacy and obutne, citically influence thoe of the dive. In thi wok, we popoe to ipove the obutne and pefoance of the adaptive flux obeve of induction oto, uing the etiation of the load toque a an added input fo the adaptive obeve. The etiation of the load toque will give bet etiation of the oto flux, becaue the adaptive obeve will have oe iilaity to the eal odel of the induction oto. Thi pape i oganied a follow. In Section II, the tate odel of I i peented. Section III peent the ipoved adaptive flux obeve. In Section IV, the effectivene of the popoed chee i dicued via iulation eult. Section V peent the final eak. Diect Field Oiented Contol oden contol technique often equie a tate-pace odel []. K id iq d p Kq ud T i d K id iq p Kd q uq i T q () d i d d ( p ) q T T q i q ( p ) d q T T p f p ( d iq q id ) T J J J The tate-pace epeentation of the I depend on the choice of the efeence fae (, ) o (d,q) and on the tate vaiable elected fo the electic equation. We wite the equation in the fae (d, q) becaue it i the ot geneal and ot coplex olution, the fae (, ) being only it one paticula cae. The I atheatical odel [, 3, 6, 7, 8] in pace vecto notation, etablihed in d-q coodinate yte otating at ynchonou peed i given by the Eq (). Whee (), R R, K The atix epeentation of the tate odel of I i [9, ]: (3) x A x B u, y C x Hee A i the oto paaete atix, B i the input atix C the output atix, and Y i the output vecto. The tate vaiable ae the two coponent of tato cuent, (i d, i q ) the two coponent of the oto flux ( d, q ), and the electical oto peed. The vecto input u i epeented by the tato voltage v d, v q and the load toque T which can be conideed a the thid input of the I. We have theefoe: (4) u u u T d q Thee ae any categoie of vecto contol tategie. We ae inteeted in thi tudy to the o-called DFOC. We have hown in Eq (), that the electoagnetic toque expeion, in the dynaic egie, peent a coupling between tato cuent and oto flux. The ain objective of the vecto contol of i, to independently contol the toque and the flux. Thi i done by uing a d-q otating efeence fae ynchonouly with the oto flux pace vecto. The d- axi i aligned with the oto flux pace vecto. Unde thi condition we have: d and. The toque equation becoe: () T p i e d q q PRZEGĄD EEKTROTECHNICZNY (Electical Review), ISSN 33-97, R. 87 NR 9a/ 3

2 It i ight to adjut the flux while acting on the coponent i d of the tato cuent and to adjut the toque while acting on the i q coponent. We have two vaiable of action then a in the cae of a DC achine. Cobining equation () and (), we obtain the following d and q-axi tato cuent : (6) T i d, T iq l whee T i the oto contant ; T, and ae l R utual inductance and leeping pulation. Uing Eq (), we obtain the voltage equation []: u R i p i d d q u R i i (7) q q d Thee equation ae function of oe tuctual electic paaete of the I (R, R,,, ), which ae in eality appoxiate value. We will coe back theeafte to the influence of the bad knowledge of ot inteet paaete (T = /R ) on the contol of the achine [3]. The oto flux aplitude can be obtained by olving Eq. (), and it patial poition i given by: (8) i q w dt T Ipoved Adaptive Flux Obeve a. Adaptive flux obeve The adaptive tate obeve [9,, ], which etiate the oto flux, i given by the following equation: whee e ˆ i iˆ i i i, i e Fo Eq (3), we can find the following adaptive chee fo oto eitance etiation. (4) ˆ R ( e ˆ ˆ i ii ei ii) Rˆ Theefoe, the following popotional and integal adaptive chee i ued pactically in ode to ipove the epone of the oto eitance etiation. () Rˆ K p ( e iˆ e iˆ ) K ˆ ( e i e iˆ ) i i i i i i i i i whee K p, K ae abitay poitive gain. i The oto eitance i ade popotional to the tato eitance which i identified adaptively, becaue both eitance change with the opeating tepeatue. (6) R no, no R Rˆ R no no Rˆ R noinal value of oto and tato eitance. b. Popoed Adaptive flux obeve In thi wok, we popoe to add the etiation of the load toque T to the chee of the adaptive flux obeve ˆ given by Eq (9). A it i hown in Fig., the etiation of the load toque (peented in dotted line) i ealied by the poduct of the eo e (between the eal and the etiated peed of the I) with an appopiated gain (7) Tˆ with e ˆ K e K : (9) x ˆ Aˆ( Rˆ ) xˆ B u G( i iˆ ), yˆ C x ˆ whee ean the etiated value and G i the obeve gain atix which i choen to allow tability of (9). Thi adaptive obeve give the etiation of the oto flux uing the etiation of the tato cuent i and the ˆ adjutent of the value of oto eitance. The input vecto of thi obeve i copoed by the two tato voltage: u () d u u q In ode to deive the adaptive chee, yapunov theoe i utilized. Fo Eq (3), the eo of the tato cuent i decibed by the following equation [, 3]: () e ( A G C) e A xˆ R whee e x xˆ and A Aˆ A X I X X Now, we define the following yapunov function candidate [8] () V e e T R i a poitive contant. The tie deivative of V becoe: T R (3) ( ) ˆ ˆ R V e A G C e e ˆ i i eii R u Tˆ B G Induction oto Fig.. Schee of ipoved adaptive flux obeve  Rˆ Ipoved Adaptive flux obeve The etiated load toque T will be the thid input of the ˆ tate obeve of oto flux. The equation of the new popoed adaptive tate obeve i: ud (8) x ˆ ˆ ( ˆ AR) ˆ u ˆ xb q Gi ( i ), yˆ C xˆ Tˆ C i ˆ î R etiat ˆ K - e i - ˆ e 36 PRZEGĄD EEKTROTECHNICZNY (Electical Review), ISSN 33-97, R. 87 NR 9a/

3 Siulation eult Siulation, uing ATAB Softwae Package, have been caied out to how the effectivene of the popoed obeve. Diect field oiented contol with the popoed adaptive flux obeve i illutated by a copute iulation hown in the block diaga of Fig. 3. Claical Popotional-Integal contolle ae ued fo peed, flux and tato cuent loop. The apling tie of iulation i et to. The I paaete ued in iulation ae given in Table I. The efeence tajectoie of peed, flux, and tato cuent ae given in Fig. 3. Flux efeence i et to it ated value of Wb. Speed [ad/] Flux [Wb] Toque [N] Fig.. Refeence tajectoie Tie [] Thi benchak how that the load toque appea at the low peed (.7 ad/ec), and the load toque i vaied at.3 fo to N. Thu we have a poitive toque fo both cae; fo poitive peed and a negative peed. We tudy enitivity to tato eitance ditubance fo an inceae of % on the tato eitance R. Table. The paaete of the induction oto Paate Notation Value Roto eitance R 3.8 Ω Stato eitance R 4.8 Ω utual inductance.8 H Stato inductance.74 H Roto inductance.74 H Roto inetia J.3 Kg/ Pole pai p Vicou fiction coef f.8 N ec ad - echanical powe P ax KW Noinal voltage V n V Noinal cuent I n 3. A Noinal peed Ω n N Fit, we ue the popoed adaptive flux obeve given by equation (4), aociated to the diect oiented contol of I, with the inceae of % in the value of the tato eitance R. The inceae in tato eitance i ade in fo of ap at the tie t =. Secondly, we ue a claic obeve (without the adaptation of the tato eitance) with the ae inceae of the tato eitance at the ae tie (t = ). Fig. 4 how that peed tack pefectly the efeence without ovetaking. The dop in peed afte the application o the eliination of the load toque i alot zeo. The contol tategy allow keeping the ae egulation pefoance depite the change of the value of the tato eitance. Figue how high pefoance of the tacking of the flux. The deied flux eain contant in the I to atify the objective of the field-oiented contol. Figue 6 how, good pefoance of obevation of the electoagnetic toque; we note liited peak afte application of load toque. A hown in Fig. 7, the dive toque follow the load toque when the peed i contant. Duing an inceae o deceae in the peed, a diffeence of.3 N appea between the two toque. Speed eo tacking [ad/] Tie [] Fig.3. Speed eo tacking (ipoved adaptive obeve) Roto flux coection eo [Wb] Tie [] Fig.4. Roto flux eo tacking (ipoved adaptive obeve) Toque etiation [N] Tie [] Fig.. Obevation eo of E toque (ipoved obeve) Toque [N] eal toque load toque Tie [] Fig.6. oto and load toque (ipoved adaptive obeve) PRZEGĄD EEKTROTECHNICZNY (Electical Review), ISSN 33-97, R. 87 NR 9a/ 37

4 Fig.7. Scheatic diaga of Diect field oiented contol of I with ipoved adaptive flux obeve Figue 8 how, a high pefoance of etiation of the oto flux uing the popoed adaptive obeve; the obevation eo of flux i alot zeo. Figue 9 illutate a good etiation of the value of the tato eitance with apidity and peciion, we note a conideable dop to the tat of the contol. Roto flux etiation eo [Wb] Speed eo tacking [ad/] Tie [] Fig.. Speed eo tacking (claical obeve) Tie [] Fig.8. Obevation eo of the oto flux (ipoved adaptive obeve) Figue how that peed tack pefectly the efeence without ovetaking. The dop in peed afte the application o the eliination of the load toque i alot zeo. In Figue. how high pefoance of the tacking of the flux. The deied flux eain contant in the I Stato eitance etiation [Oh] R R et Roto flux coection eo [Wb] Tie [] Fig.. Roto flux coection eo (claical obeve) Figue how a good tacking of the electoagnetic toque. Figue 3 how a bad etiation pefoance of etiation of the flux with conideable etiation eo when we hace vaiation in the value of the tato eitance (afte t= ) Tie [] Fig.9. Obevation of the oto eitance (ipoved adaptive obeve) 38 PRZEGĄD EEKTROTECHNICZNY (Electical Review), ISSN 33-97, R. 87 NR 9a/

5 Toque [N] Tie [] Fig.. oto and load toque (claical obeve) Roto flux Roto etiation flux eo [Wb]. -. eal toque load toque Tie [] Fig.3. Roto flux etiation eo (claical obeve) Concluion In thi pape, we peented a new chee of adaptive flux obeve of induction oto, baed on the coection of the value of the tato eitance and the etiation of the load toque. The etiation of the toque i baed on the ue of the eo between eal and etiated peed of induction oto, thi will have to ipove the pefoance of the adaptive flux obeve. The eult how that the popoed adaptive obeve offe bette pefoance while tacking the peed and the flux, even in peence of tato eitance vaiation. Futue wok concen eal tue ipleentation of the popoed chee to validate thee theoetical eult. REFERENCES [] J.P. Caon, J.P. Hautie. (99): odeling and Contol of Induction achine. Technip Edition []. A. Ouhouche and C. Volat. (): Siulation of a Diect Field-Oiented Contolle fo an Induction oto Uing atlab/ Siulink. Poceeding of the IASTED Intenational Confeence odelling and Siulation - Pittbugh, Pennylvania, USA. [3]. Alai. (): Senitivity analyi in iultaneou tate/ paaete etiation fo induction oto. Int. J. of Contol, vol. 7, n, pp [4]. Alexandu, R. Bojoi, G. Gheladi, S..Tenconi. (): An AC oto cloed loop pefoance with diffeent oto flux obeve. CFA Annal, Vol III, pp.-3. [] T. Van Raue J.. Dion,. Dugad and J..Thoa (994): Applied nonlinea contol of an induction oto uing digital ignal poceing. IEEE Tan. Cont. Syt. Technol, Vol., No. 4, pp J. [6] Soltani, Y.Abdolaleki and. Hajian. (): Adaptive fuzzy liding-ode contol of peed enole univeal field oiented induction oto dive. Ianian Jounal of Science & Techno-logy, Tanaction B, Engineeing, Vol. 9, No. B4. [7] A. Bouhenna, A. anoui,. Chenafa, A. Belaidi. (8): Feedback Gain Deign ethod fo the Full-Ode Flux Obeve in Senole Contol of Induction oto. Int. J. of Copute, Counication & Contol, IJCCC, Vol. III, No., pp [8] A. anoui,. Chenafa, A. Bouhenna and E. Etien. (4): Powefull nonlinea obeve aociated with field-oiented contol of an induction oto. Int. J. Appl. ath. Coput. Sci, Vol. 4, No., 9. [9] F. Khoucha, K. aouani, A. Kheloui, K. Aliouane. (4): A DSP-baed Dicete Space Vecto odulation Diect Toque Contol of Senole Induction achine. NORPIE, Nodic Wokhop on Powe and Indutial Electonic, Tondhei, Noway. [] H. Kubota and K. atue. (994): Speed enole fieldoiented contol of induction oto with oto eitance adaptation. IEEE Tan. Ind. Appl., vol. 3, no., pp [] T. Pana and C. Ruu. (): Speed and oto flux etiation in peed enole contol of induction oto. The annal of "Dunaea Dejo" Univeity of Galati Facicle III, ISSN - 44X. Electothecnic, Electonic, Autoatic Contol, Infoatic. [] G. C. Veghee. and S.R. Sande. (988): Obeve fo flux etiation in induction achine. IEEE Tan. Ind. Electon., Vol. 3, No., pp [3]. O. Sonnaillon, G Biheie, Citian De Angelo, G. Gacía and J. Solona. (4): State etiation in electic oto dive with a educed nube of eno. In Poc. VI Intenational Confeence of Indutial application (INDUSCON), code COE_3, Joinville, Bazil. Autho:. Beniloud Taek, Univeity of Science and Technology of Oan, Depateent of Electotechnic, BP, El- naoua, Oan Ageia. E-ail: taek_b4@yahoo.f; d Oai. Abdelhafud, Univeity of Science and Technology of Oan,Depateent of Autoatic, BP, El-naoua, Oan Ageia. E-ail: oai@univ-uto.dz. PRZEGĄD EEKTROTECHNICZNY (Electical Review), ISSN 33-97, R. 87 NR 9a/ 39