Design of an extended Luenberger observer for sensorless vector control of induction machines using virtual instrument

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1 Advnce in Dt Netwo, Communiction, Compute nd Mteil Deign of n extended Luenbege obeve fo enole vecto contol of induction mchine uing vitul intument NICOLAE PARASCOIU ADRIAN OMUS Automtic, Compute, Electicl nd enegetic Engineeing Univeity of Petoni Univeittii, 6 Petoni ROMANIA ptcoiu@upet.o Abtct: - hi ppe peent the imultion of the flux nd of n induction moto oto peed etimto uing the gphicl pogmming lnguge LbView. Alo, in thi ppe it i elized tudy of the Luenbege etimto nd extended Luenbege etimto. Fo thi, it ceted vitul intument uing LbView fo the gpficl intefce nd Contol Deign nd Simultion Module fo LbView to implement the model of the induction moto nd of the Luenbege etimto in ode to elize the imultion. Key-Wo: - Luenbege etimto, ELO, vitul intument, LbView, Contol Deign nd Simultion. Intoduction Since the ely ppe, which concentted on obeve fo puely deteminitic continuou-time line time-invint ytem, obeve theoy h been extended by evel eeche to include time-vying ytem, dicete ytem, nd tochtic ytem. Sometime ll tte pce vible e not vilble fo meuement, o it i not pcticl to meue ll of them, o it i too expenive to meue ll tte pce vible. In ode to be ble to pply the tte feedbc contol to ytem, ll of it tte pce vible mut be vilble t ll time. Alo, in ome contol ytem ppliction, one i inteeted in hving infomtion bout ytem tte pce vible t ny time intnt. hu, one i fced with the poblem of etimting ytem tte pce vible. hi cn be done by contucting nothe dynmicl ytem clled the obeve o etimto, connected to the ytem unde conidetion, whoe ole i to poduce good etimte of the tte pce vible of the oiginl ytem. he theoy of obeve tted with the wo of Luenbege (964, 966, 97) o tht obeve e vey often clled Luenbege obeve. Accoding to Luenbege, ny ytem diven by the output of the given ytem cn eve n obeve fo tht ytem. wo min technique e vilble fo obeve deign. he fit one i ued fo the full-ode obeve deign nd poduce n obeve tht h the me dimenion the oiginl ytem. he econd technique exploit the nowledge of ome tte pce vible vilble though the output lgebic eqution (ytem meuement) o tht educed-ode obeve i contucted only fo etimting tte pce vible tht e not diectly obtinble fom the ytem meuement [], [4]. Poblem Fomultion he Extended Luenbege Obeve (ELO) i bed on the ue of n dptive mechnim, in which the efeence model i the induction moto nd the djutble model i Luenbege type line tte etimto. he eqution of the Luenbege line etimto e: xˆ + = Fd xˆ + Hd u+ Ld ( y C xˆ ) () whee: F, H nd L e mtixe obtined though complete dicetiztion bed on the following fomul: F = I+ A + A ;H = B + A L = L + A L B ; () ISBN:

2 Advnce in Dt Netwo, Communiction, Compute nd Mteil Fig. he Pinciple Schemtic of the ELO Etimto whee i the mpling time nd A, B nd L hve the following tuctue: ω A B = 3 b = b 3 4 ω 3 ω 4 3 ω C = (3) L = he component element of the A, B nd L mtixe e: σ L m = + ; 3 = σ σ L L σ L m Lm 4 = ; 3 = ; = ; L L σ L L L b = ; = ; = ; σ = (4) L σ R R L = ( + ) ( ); =ω ( ); m L = 3+ ( ) ; = whee: L, L, Lm e the tto, oto nd mutul inductnce; R, R e the tto nd oto eitnce nd σ i the mutul dipeion coefficient. he eqution of the Luenbege line etimto wee obtined conideing the fct tht the tuctue of the tte vecto i: xˆ () [ î ] () î() ψˆ ˆ d () ψq () = (5) Fomed by the tto cuent nd oto fluxe in the dq xe ytem nd, on the othe hnd, the input vecto i: u () = u () u ( (6) [ ] ) nd the output vecto i: y () = i () i ( (7) [ ] ) whee u nd u e the tto tenion in the dq xe ytem nd i nd i e the tto cuent in the dq xe ytem. In ce of Luenbege mtix pojection w ued fomul tht enue the popotionlity between the induction mchine elf-vlue nd the etimto bed on popotionlity coefficient. he fomul e deduced in the continuou ce obtining the L mtix, fom which, though dicetition it eult the L mtix bed on the dicetition, numbe fomul. hough uing the popotionlity, thee eult the etimto tbility no mtte wht the ω peed i. Obviouly, the popotionlity will not mintin fte dicetition, but the tbility will. he Luenbege etimto eo i given by: x~ () = x() xˆ () (8) Howeve, one my notice fom Figue, the ω peed, ued in the F, H nd L mtixe clcultion i the etimted peed obtined t the output of the dpting mechnim. he dpting mechnim i deducted though the Popov type hype-tbility condition obtining, fte the clcultion tht: ω ˆ = K [ e ˆ e ˆ i ψq ψd]dt (9) whee: K i i contnt choen o tht we hve good dynmic nd e = i î ; e = i î ; In ce of numeic implementtion of the ELO lgoithm, the (9) eltion i clculted uing one of the integl numeic evlution metho, lie the ectngle method, the tpezium method. In thi ppe in the implementtion of the dpting mechnim w ued moe complex fomul, nmely: ω= ˆ K [ e ψˆ e ψˆ ] p K i [ e ψˆ e ψˆ ]dt q q d d + (9) whee we lo ued popotionl component. he dicetition method of the integl i the tpezium method (utin) [4], [5]. ISBN:

3 Advnce in Dt Netwo, Communiction, Compute nd Mteil 3 Poblem Solution o chieve the Luenbege etimto nlyi on ue gphicl pogmming lnguge LbView nd the Contol Deign nd Simultion module. A pogm developed in LbVIEW i clled vitul intument (VI) nd it h two component the bloc digm tht epeent pogm itelf nd the font pnel tht i the intefce with ue. he Contol Deign nd Simultion module fo LbVIEW cn be ued to imulte dynmic ytem. o fcilitte model definition, thi module d function to the LbVIEW envionment tht eemble thoe found in SIMULINK. hee i lo the bility to ue m-file yntx diectly in LbVIEW though the new MthScipt node. he Contol Deign nd Simultion Module lo povide VI tht cn be ued to cete nd develop contol deign ppliction in LbVIEW. hee VI cn be ued to develop mthemticl model of dynmic ytem, nlyze the model to len bout thei dynmic chcteitic, nd cete contolle to chieve pecified dynmic chcteitic. he Contol Deign nd Simultion Module lo include numeou function tht extend the functionlity of the LbVIEW MthScipt window. hee function e ued to deign nd nlyze contolle model in text-bed envionment nd the LbVIEW MthScipt engine i ued to execute cipt peviouly witten uing he MthWo, MALAB [8]. Fo imulte in el time, we conide moto with the next pmete: P N =. W; z p = ; L =.357 H; L =.345 H; R =.385 Ω; R =.34 Ω; J =.88 N m; M = g m ; f = 5Hz. Fo bette imultion, we ceted imultion cheme fo induction moto bed on tte eqution, clled model voltge (fig.). he imultion i pefomed uing LbVIEW MthScipt fom the Contol Deign nd Simultion Module. Bed on thi model of the induction moto i implemented in the me wy the Luenbege flux etimto. Simultion cheme nd the intenl tuctue of the Luenbege etimto i hown in fig.3. Fig.3. Intenl tuctue of the Luenbege etimto With thi two model we cete the imultion model fo Luenbege obeve nd extented Luenbege obeve uing the Contol Deign nd Simultion module of LbView. In the imultion cheme of the Luenbege etimto i obeved peed etimto; the contolle ued in the peed etimto i dicete PI. Bloc digm coeponding to thee two imultion model e peented in fig.4 nd fig.5 Fig.. Simultion cheme nd the intenl tuctue of induction moto Fig.4. Simultion cheme of the Luenbege etimto ISBN:

4 Advnce in Dt Netwo, Communiction, Compute nd Mteil Fig.5. Simultion cheme of the extended Luenbege etimto he font pnel of vitul intument contni two tb tht llow you to elect one of two imultion model: Luenbege etimto o extented Luenbege Etimto. Ech tb contin the gph type indicto to diply peed, flow o cuent cht. he font pnel fo thee two ce i peented in fig.6. Fom the imultion eult we ee tht Extended Luenbege Obeve (ELO) etimto h vey good dynmic nd it cn be uccefully ued in enole vecto contol ytem type (without peed eno). High dynmic nd low volume clcultion me thi type of etimto to be the mot widely ued tody [6], [7], [8]. Fig.6. Font Pnel of the vitul intument fo Luenbege etimto nd extended Luenbege etimto ISBN:

5 Advnce in Dt Netwo, Communiction, Compute nd Mteil 4 Concluion he imultion mode cn be peently conideed the mot impotnt deign ttegy nd implementtion of n etimto o tht it nlyi though imultion without hdwe, intoduced in loop nd lo though hdwe intoduced within the imultion. Afte the imultion it i noticed tht the ELO etimto i behving vey well in ce of deceing o inceing the oto eitnce by %, poblem iing fo vlue of eitnce ping ove 5%. Regding the tbility, the ELO etimto i intenlly tble fo wide bnd of evolution up to ppoximtely. pm. Regding the enitivity nd dynmic pefomnce point of view one my y tht the ELO etimto i vey pefoming nd it cn uccefully be ued within the enole vectoed cting ytem with induction moto. Refeence: [] Bolde, I., N, Vecto contol of AC dive. CRC Pe S.A.99. [] C.Il, V.Botn, ehnici dptive de contol motoului incon: comnd vectoil f mue vitezei, Litogfi U.P.B. () [3] Hiliet M., Dengoe C., F. Auge, P. Chevel, Synthei nd nlyi of obut flux obeve fo induction mchine. IFAC Symp. on Robut Contol Deign, Pgue. () [4] LUENBERGER, D.G. An induction to obeve, IEEE n. On Automtic Contol, vol.ac.-6, no.6, pp.596-6, Decembe 97 [5] Stoicut, O., omu A, Anlyi of the Extended Luenbege Etimto uing the ezp8 development it, Intentionl Scientific Confeence MicoCAD, 9, Miolc,Ungi. [6] Ptcoiu N. Dt cquiition ytem. Vitul Intumenttion (in Romnin) Ed. Didctic i Pedgogic, Bucueti, 4 [7] omu A., Contibution o Identifiction And Contol Uing Advnced Algoithm Of he Induction Mchine With Appliction On Mining Combine. hei. Petoni. [8] * * * - LbVIEW Contol Deign Ue Mnul. Ntionl Intument Copotion, 9. ISBN: