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2 Robut Shaping Indiect Field Oiented Contol fo Induction Moto 59 4 X Robut Shaping Indiect Field Oiented Contol fo Induction Moto M. Bouhnife, C. aouci and A. Chaibet aboatoie Coande et Sytèe, ESACA, ue Victo Hugo, 9 3 evalloi-peet, Fance {bouhnife, claouci, achaibet}@etaca.f. Intoduction Ove the pat yea, than to the yteatic ue of digital icopoceo in induty, we have een a vey ignificant developent in the egulation contol of the aynchonou achine. he latte i widely ued in induty fo it diveity of ue and it ability to withtand geat vaiation in it noinal egie. Cuently, eveal type of contol ae popoed. Nonlinea contol uch a lineaization input-output (Benchaib & Edwad, ) (Chan et al., 99) (De uca & Ulivi, 989) (Maina & Valigi, 99), the contol eulting fo the theoy of paivity (Niclaon et al., 997) (Godee, 996) which geneally equie the eaueent of all yte tate (cuent and flu). A the flu of the oto cannot be eaued, a geat pat of the liteatue i devoted to the contol poble coupled with a nonlinea flu obeve (Kanellaopoulo et al., 99). Othe contol uing only the eit etun (oto peed and tato cuent) wee developed eulting in contol of the paive type (Abdel Fattah & opao, 3), othe contol uing the technique of bactepping o the technique deived fo the oientation of the flu field (Peeada et al., 999) (Baabone et al., 3). he paaete of uch contol ut be elected in ode to enue total tability fo a given noinal unning and noinal value of the paaete. hu, diffeent obut contol with paaete uncetaintie, uch a the dicontinuou o adaptive contol, wee developed (Maina et al., 998). hee technique adapt the contol to the vaiation of eitance and the load couple. A contol which i vey coon in induty i the indiect field oiented contol (FOC) baed on the oientation of the field of oto flu. hi contol allow the decoupling of peed and flu, and we obtain linea diffeential equation iila to the D.C. achine. he egulation i caied out finally by iple contolle PI (cf Fig. ). Howeve, the decoupling obeved i only ayptotic. he behaviou of the tanient egie and the total tability of the yte eain a ajo poble. In addition, the odification of paaete uch a oto eitance o eitive toque deteioate the quality of decoupling. In thi pape, we popoe a diaga of H egulation, lined to the field oiented contol allowing a coect tanient egie and good obutne againt paaete vaiation to be

3 6 Mechatonic Syte, Siulation, Modelling and Contol enued. hi Pape i divided into eveal pat: he fit one decibe the odel of the aynchonou achine, uing the auption of Pa. In the econd pat, we peent the field oiented contol pinciple, a well a egulation iulation, uing PI. he thid pat i devoted to the poble of the H contol and the loop haping deign pocedue appoach oiginally popoed in (McFalane et al., 988) and futhe developed in (McFalane & Glove, 988) and (McFalane & Glove, 989) which incopoate the chaacteitic of both loop haping and H deign. Specifically, we ae ue of the ocalled noalized copie facto H obut tabilization poble which ha been olved in (Glove & McFalane, 988) (Glove & McFalane, 989) and i equivalent to the gap etic obutne optiization a in (McFalane & Glove, 99). he deign technique ha two ain tage: ) loop haping i ued to hape the noinal plant ingula value to give deied open-loop popetie at fequencie of high and low loop gain; ) the noalized copie facto H poble entioned above i ued to obutly tabilize thi haped plant. Finally, the lat pat how how to integate the loop haping deign pocedue into the field oiented contol with the uenbege obeve and popoe iulation eult.. Matheatical odel of aynchonou achine We ue oe iplifying auption and Pa tanfoation. he tato cuent I, I ), ( d q the oto flu ) and the otation peed w ae conideed a tate vaiable. he odel ( d, q of the aynchonou achine in the efeence ae d, q elated to the otating field i given in the fo:. X f ( ) BU () X ) ( Id, I q, d, q, w i the tate vecto. U v d v q ) (, i the contol vecto. di d R R I I p dt d q d di q I R R I p dt d q d d d I w dt d d gl q d q I w q gl d q dt d C C dt J e f v q d v q q ()

4 Robut Shaping Indiect Field Oiented Contol fo Induction Moto 6 w C gl e w w, p( I q d, w I d d, dt ), q R w pw d q (3) Whee J i the oent of inetia., and ae epectively oto inductance, tato inductance and utual inductance. R and R ae epectively the eitance of the oto and of the tato, P i the nube of pole pai of the achine, i the fiction coefficient and i Blondel dipeion coefficient. f 3. Indiect field oiented contol he ai of thi ethod of fequency contol (Slipway Fequency Contol) conit in not uing the flu oto aplitude but iply it poition calculated accoding to the efeence vaiable (Peeada et al., 999) (Blache, 97). hi ethod doe not ue a flu eno (phyical eno o dynaic odel) but need the oto peed eno. Fig. how an eaple of an applied indiect field contol with a type PI egulation on the aynchonou achine fed by an invete contolled by the tiangulo-inuoidal tategy with fou bipola caie. 3. Field oiented contol he FOC (Field Oiented Contol) i an aithetic bloc which ha two input ( and C ) e and geneate the five vaiable of the invete ( V, V, w, I d, I q ). It i defined by leading the tatic egie fo which the oto flu and the electoagnetic couple ae aintained contant equal to thei efeence value. If we do not tae into account the vaiation of the diect cuent and the quaing coponent, the equation of thi bloc ae deduced in the following way: d q id Ce iq p Riq vd Rid iq vq Riq id (4) hi ethod conit to contol the diect coponent I d and the quaing I q tato cuent in ode to obtain the electoagnetic couple and the flu deied in the achine.

5 6 Mechatonic Syte, Siulation, Modelling and Contol Invete MAS v a v b v c Pa - v q v d - p S i Ce FOC Fig.. Indiect field contol of aynchonou achine 3. Siulation of field oiented contol he bet-nown invete up to now ae the two level invete. Howeve, oe application uch a electic taction equie thee-phae aynchonou vaiato functioning at vey high powe and/o peed. hee two level invete ae liited in tenion (,4V) and powe (MVA). o inceae powe and tenion, we ue a ultilevel invete. In ou wo, the ultilevel invete ued i contolled by the tiangulo-inuoidal tategy with fou bipola caie (Bouhnife, 7). Fig. how the eult of the indiect field contol of an aynchonou achine fed by thi invete. he decoupling i aintained and the peed follow the efeence vey well and i not affected by the application of a eitive toque. In the net ection, we will eplain biefly the pinciple of the H contol and how it can be integated into the indiect field contol. 4. Robut contol 4. H Contol Fo given P() and >, the H - Stabilize the loop yte in Fig. 3 intenally. - Maintain the no ( P, K) F tandad poble i to find K() which: with F (P, K) defined a the tanfe function of eit Z accoding to entie W. 4. H Copie factoization appoach An appoach wa developed by McFalane and Glove (McFalane & Glove, 988) (McFalane & Glove, 989) tating fo the concept of the copie factoization of a tanfe ati. hi appoach peent an inteeting popetie and it ipleentation ue taditional notion of autoatic.

6 Robut Shaping Indiect Field Oiented Contol fo Induction Moto 63 W Z P() F (p,k) U K Y Fig. 3. Poble H tandad t() t() t() t() t() t() Fig.. Siulation of the indiect field contol of aynchonou achine 4.3 Robut contolle deign uing noalized copie facto We define the noinal odel of the yte to be contolled fo the copie facto on the ~ ~ left: G M N. hen the uncetaintie of the odel ae taen into conideation o that (ee Fig. 4) G ~ ~ M ~ G ( M ~ ) ( N ) (5) N M N K N ~ ~ M Fig. 4. Copie facto tabilization poble

7 64 Mechatonic Syte, Siulation, Modelling and Contol whee G ~ i a left copie factoization (CF) of G, and, ae unnown and table tanfe function epeenting the uncetainty. We can then define a faily of odel a follow: Whee ~ ~ ~ G ( M ) ( N ) : ( ) (6) M N a epeent the agin of aiu tability. he obut tability poble i thu to find the geatet value of a, o that all the odel belonging to can be tabilized by the ae coecto K. he poble of obut tability H aount to finding in and K() tabilizing G() o that: M N M a N I ( I K G) K ( I G) in a (7) Howeve, McFalane and Glove (McFalane & Glove, 99) howed that the inial value of i given by: in up( XY) (8) a whee indicate the geatet eigenvalue of XY, oeove fo any a, a contolle up tabilizing all the odel belonging to i given by: whee A, B and C ae tate atice of the yte defined by the function G and X, Y ae the poitive definite atice and the olution of the Ricatti equation : A X XA XB AY YA YC BX C CY BB C (9) 4.4 oop-haping deign pocedue Contay to the appoach of Glove-Doyle, no weight function can be intoduced into the poble. he adjutent of the pefoance i obtained by affecting an open odelling (loop-haping) poce befoe calculating the coecto. he deign pocedue i a follow: W () W efeence K ( ) W () G G a () W () G W Fig. 5. he loop-haping deign pocedue K() We add to the ati G() of the yte to be contolled a pe-copenato W and/o a pot-copenato W, the ingula value of the noinal plant ae haped to give a deied open-loop hape. he noinal plant G() and haping function W and W ae cobined in

8 Robut Shaping Indiect Field Oiented Contol fo Induction Moto 65 ode to ipove the pefoance of the yte o that G W GW a (ee Fig.5). In the onovaiable cae, thi tep i caied out by contolling the gain and the phae of G a ( jw) in the Bode plan. Fo copie factoization of G a (), we apply the peviou eult to calculate a, and then yntheie a tabilizing contolle K enuing a value of lightly lowe than a : I ( I K W G W ) ( I W G W ) K () he final feedbac contolle i obtained by cobining the H contolle K with the haping function W and W o that Ga() = WGW. (See Fig.5). 5. Robut contol of the aynchonou achine When the efeence i diected we have the electoagnetic couple can be witten in the fo: and. In thi cae, the epeion of d q C e p idiq, () hi equation iplifie the odel of the aynchonou achine a follow: did ( ( R ( ) R ) id i dt diq ( id ( R ( ) R ) i dt d R R id dt d p f p iq C dt J J J R iq q q R vd ) v ) By uing the tanfo of aplace, we can wite that: l p l Ce I d, Ce I q, (3) l l J f he equation (3) how that we can act independently on oto flu and the electoagnetic couple by ean of coponent I d and I q epectively of the tato cuent. he goal conit in contolling the diect coponent I d and in quaing coponent I of the tato cuent in ode to obtain the electoagnetic couple and the q flu deied in the achine. We can epeent ou yte by cobining equation (3) and (3) in two ub-yte with the tanfe function decibed below, See (Bouhnife, 7) fo detail: q ()

9 66 Mechatonic Syte, Siulation, Modelling and Contol G flu J Gvitee (4) J In ode to enue a high gain in low fequencie and a low gain in high fequencie, we add the weight function fo flu and peed epectively o that. ( 5).5 ( ) W W (5) f 5. oop haping contolle he calculation of the flu contolle by MAAB oftwae give: a.7756 (6) he calculation of the peed contolle by MAAB oftwae give: a.6998 (7) K () Invete MAS K () + - W () va vb vc Pa - vq vd K () + w () Ce FOC - K () Fig. 6. Robut contol of aynchonou oto 5. Siulation of the obut contol o illutate the pefoance of the H contol, we iulated a no-load tat with application of the load (noinal load C=N) at t =.5Sec to t =.5Sec. hen the achine i ubjected to an inveion of the intuction between ad/ec at t 3 =3Sec (Fig.7). he peed egulation peent bette pefoance with epect to the puuit and the ejection of the ditubance. We note that the cuent i liited to acceptable aiu value. he decoupling i aintained and the peed follow the efeence well and i not affected by the application of a eitive toque. 6. uenbege obeve We apply the uenbege obeve ethod fo the etiation of the oto flu coponent (Olawa-Kowala, 989). he odel of the efeence achine lined to the tato field i

10 Robut Shaping Indiect Field Oiented Contol fo Induction Moto 67 linea in the electoagnetic tate. he two tato cuent coponent ae eauable. We will conide the a output of the odel: C y Bu A (8) with: i i i i y y y v v u u u 4 3,, (9) and:,, c B p p p p A () Fig. 7. Siulation eult of obut contol of aynchonou oto Fo the obevation of the tate 3 and 4 we ue the following uenbege obeve: Hu y Fz z ˆ ˆ () he dienion of the vecto and atice which appeaed in thi elation ae: (,). (,), (,), 3,), ( H F z ()

11 68 Mechatonic Syte, Siulation, Modelling and Contol Vecto Z i elated to the initial tate vecto by the tanfoation ati : Z= (3) o deteine the elation between the atice of yte A,B and C and the atice of the obeve F, K and H, the equation of eo i calculated ( e zˆ ) : e zˆ Fzˆ y Hu A Bu Fzˆ C Hu A Bu F( e ) C Hu A Bu Fe ( F C A) ( H B) u (4) o give the equation of eo the fo: e Fe (5) We ut chec the elation: A F H B KC (6) he eo dynaic (5) i decibed by the eigenvalue of the tate ati of obeve F. We ipoe to thi ati the following fo: F diag, ) (7) ( In ode to tabilize the eo dynaic, λ and λ ut be negative. With thi choice of F, the eplicit equation of the obeve ae given by: z z z z y y y y h u h u h u h u (8) We ipoe to the tanfoation ati the following fo: t t (9) t t he eleent of the, K ati and H ae obtained fo the equation (5):

12 Robut Shaping Indiect Field Oiented Contol fo Induction Moto 69 t t h h p p p p p ( ). t ( ). t t t p h h t t t t p p ( ). t ( ). t (3) Fo equation (3), we obtain the oiginal tate in the fo: 3. 4 thu oto flu : 3 4 z z t t t t (3) (3) 6. Siulation eult he eult of iulation how that the uenbege obeve give an eo tend to zeo and the flu obeved follow vey well the eal flu of the achine and ha a bette obutne a egad paaetic vaiation (vaiation of oto eitance). he eult of iulation of obut contol ae peent in (Fig. 9) and we note clealy that decoupling i aintained and the peed follow the efeence well and i not affected by the application of a eitive toque. 7. Concluion In thi pape, we have tudied the obutne of H contol applied to an induction oto and by uing the uenbege obeve fo the obevation of oto flu. he obtained eult howed the obutne of the vaiable flu and peed againt etenal ditubance and uncetaintie of odelling. hi ethod enabled u to enue a good obutne/tability copoie a well a atifactoy pefoance. he ue of the uenbege obeve enable u to avoid the ue of the diect ethod of eaueent weaening the echanical engineeing of the yte.

13 7 Mechatonic Syte, Siulation, Modelling and Contol (a) (b) Fig. 8. uenbege obeve (a) with no vaiation of R and (b) with inceae of R % Fig. 9. Robut contol with uenbege obeve 8. Refeence Benchaib, A. & Edwad, C. (). Nonlinea liding ode contol of an induction oto. Intenational Jounal of Adaptive Contol and Signal Poceing, Vol.4, No.-3., (Ma ) page nube (-)

14 Robut Shaping Indiect Field Oiented Contol fo Induction Moto 7 Chan, C. C., eung, W. S. & Ng, C.W. (99). Adaptive decoupling contol of induction oto dive. IEEE anaction on Induty Electonic, Vol.37, No., (Feb. 99) page nube( 4 47) De uca, A. & Ulivi, G. (989). Deign of an eact nonlinea contolle fo induction oto. IEEE anaction on Autoatic Contol, Vol. 34, No., (Dec 989) page nube (34 37) Maina, R. & Valigi, P. (99). Nonlinea contol of induction oto: a iulation tudy. Euopean Contol Confeence, pp. 57-6, Genoble, -5 July, Fance Niclaon, P.J. Otega, R. & Epinoa-Peez, G. (997). Paivity baed contol of a cla of Blondel-Pa tanfoable electic achine. IEEE anaction on Autoatic Contol, Vol.4, No.5, (May 997) page nube (69-647) Godee,.U. (996). Paivity baed ethod fo contol of induction oto. Ph.D. hei, Univeity of Pittbugh, 996 Kanellaopoulo, I. Kein, P.. & Diilveto, F. (99). Nonlinea flu obeve baed contol of induction oto, Aeican Contol Confeence, pp.7 74, Chicago, (June 99). USA Abdel Fattah, H. A. & opao, K. A. (3). Paivity baed toque and flu tacing fo induction oto with agnetic atuation. Auotatica, Vol.39, No., (Decebe 3), page nube (3-3) Peeada, S. onielli, A. & Moici, R. (999).High-pefoance indiect field-oiented output-feedbac contol of induction oto, Autoatica, Vol.35, No.6, (June 999) page nube (33-48) Baabone, O. Gaido, A.J. & Maeda, F.J. (3). A enole obut vecto contol of induction oto dive. IEEE Intenational Confeence on Eeging echnologie and Factoy Autoation, ibon, (Septebe 3). Potugal Maina, R Peeada, S & oei, P. (998).Adaptive output feedbac contol of cuent-fed induction oto with uncetain oto eitance, Autoatica, Vol. 34, No. 5, (Oct 998) page nube (67-64), ISSN 5-98 McFalane, D. Glove, K. & Noton, M. (988). Robut tabilization of a fleible pace platfo: an H copie facto appoach, Intenational Confeence on Contol, pp (677-68), ISBN , Ofod, UK, Apil 988. McFalane, D. & Glove, K. (988). An H deign pocedue uing obut tabilization of noalized copie facto, IEEE Confeence on Deciion and Contol, pp ( ), INSPEC , Autin, X, USA, Decebe 988. McFalane, D & Glove, K. (989). Robut contolle deign uing noalied copie facto plant deciption, lectue Note in Contol and infoation Science, Spinge Velag, (38), Belin, Geany Glove, K. & McFalane, D. (988). Robut tabilization of noalized copie facto: An eplicit H olution, IEEE Intenational Aeican Contol Confeence, pp(84 847), Atlanta, Ga, USA, June 988. Glove, K. & McFalane, D. (989). Robut tabilization of noalized copie facto plant deciption with H bounded uncetainly, IEEE anaction on Autoatic Contol, Vol. 34, No.8, (Aug.989) page nube (8-83) McFalane, D. & Glove, K. (99). A loop haping deign pocedue uing H ynthei, IEEE anaction on Autoatic Contol, Vol. 37, No.6, (June 99) page nube ( )

15 7 Mechatonic Syte, Siulation, Modelling and Contol Blache, F. (97). he pinciple of field oientation a applied to the new tanveto cloed-loop contol yte fo otating-field achine, Sieen Review, Vol.34, pp ( 7 ), Mai 97. Bouhnife, M. (7). Coande obute d une achine aynchone alientée pa un à onduleu ulti-niveau, Revue Intenationale en Génie électique, Vol, No.6, (Novebe Decebe 7) page nube (77-749). Olawa-Kowala, M. (989). Application of etended luenbege obeve fo flu and oto tie contant etiation in induction oto dive. IEE Contol heoy and Application, Vol.36, No.6, (Nov 989) page nube (34 33), ISSN:

16 Mechatonic Syte Siulation Modeling and Contol Edited by Annalia Milella Donato Di Paola and Gazia Cicielli ISBN Had cove, 98 page Publihe Inech Publihed online, Mach, Publihed in pint edition Mach, hi boo collect fifteen elevant pape in the field of echatonic yte. Mechatonic, the ynegitic blend of echanic, electonic, and copute cience, integate the bet deign pactice with the ot advanced technologie to ealize high-quality poduct, guaanteeing at the ae tie a ubtantial eduction in developent tie and cot. opic coveed in thi boo include iulation, odelling and contol of electoechanical achine, achine coponent, and echatonic vehicle. New oftwae tool, integated developent envionent, and yteatic deign ethod ae alo intoduced. he edito ae eteely gateful to all the autho fo thei valuable contibution. he boo begin with eight chapte elated to odelling and contol of electoechanical achine and achine coponent. Chapte 9 peent a nonlinea odel fo the contol of a thee-dof helicopte. A helicopte odel and a contol ethod of the odel ae alo peented and validated epeientally in Chapte. Chapte intoduce a plana laboatoy tetbed fo the iulation of autonoou poiity anoeuve of a uniquely contol actuato configued pacecaft. Integated ethod of iulation and Real-ie contol aiing at ipoving the efficiency of an iteative deign poce of contol yte ae peented in Chapte. Reliability analyi ethod fo an ebedded Open Souce Softwae (OSS) ae dicued in Chapte 3. A new pecification technique fo the conceptual deign of elf-optiizing echatonic yte i peented in Chapte 4. Chapte 5 povide a geneal oveview of deign pecificitie including echanical and contol conideation fo ico-echatonic tuctue. It alo peent an eaple of a new optial ynthei ethod to deign topology and aociated obut contol ethodologie fo onolithic copliant icotuctue. How to efeence In ode to coectly efeence thi cholaly wo, feel fee to copy and pate the following: M. Bouhnife, C. aouci and A. Chaibet (). Robut Shaping Indiect Field Oiented Contol fo Induction Moto, Mechatonic Syte Siulation Modeling and Contol, Annalia Milella Donato Di Paola and Gazia Cicielli (Ed.), ISBN: , Inech, Available fo: Inech Euope Univeity Capu SeP Ri Inech China Unit 45, Office Bloc, Hotel Equatoial Shanghai

17 Slava Kautzea 83/A 5 Rijea, Coatia Phone: +385 (5) Fa: +385 (5) No.65, Yan An Road (Wet), Shanghai, 4, China Phone: Fa:

18 he Autho(). icenee IntechOpen. hi chapte i ditibuted unde the te of the Ceative Coon Attibution-NonCoecial- ShaeAlie-3. icene, which peit ue, ditibution and epoduction fo non-coecial pupoe, povided the oiginal i popely cited and deivative wo building on thi content ae ditibuted unde the ae licene.