A Robust Sensorless Direct Torque Control of Induction Motor Based on MRAS and Extended Kalman Filter

Transcription

1 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed Naceu ABDELKRIM Reeach Unit of Modelling, Analyi and Contol of Sytem - MACS, National Engineeing School of Gabe - ENIG, Zig 69 Gabe- Tuniia meaoudi.mutapha@yahoo.f, laaad.bita@enig.nu.tn Abtact In thi pape, the claical Diect Toque Contol (DTC) of Induction Moto (IM) uing an open loop pue integation uffe fom the well-known poblem of integation epecially in the low peed opeation ange i detailed. To tackle thi poblem, the IM vaiable and paamete etimation i pefomed uing a ecuive non-linea obeve known a EKF. Thi obeve i ued to etimate the tato cuent, the oto flux linkage, the oto peed and the tato eitance. The main dawback of the EKF in thi cae i that the load dynamic ha to be known which i not uually poible. Theefoe, a new method baed on the Model Refeence Adaptive Sytem (MRAS) i ued to etimate the oto peed. The two diffeent nonlinea obeve applied to enole DTC of IM, ae dicued and compaed to each othe. The oto peed etimation in DTC technique i affected by paamete vaiation epecially the tato eitance due to tempeatue paticulaly at low peed. Theefoe, it i neceay to compenate thi paamete vaiation in enole induction moto dive uing an online adaptation of the contol algoithm by the etimated tato eitance. A imulation wok lead to the elected eult to uppot the tudy finding. Keywod Induction moto dive; Diect Toque Contol; Senole; Paamete etimation; Model Refeence Adaptive Sytem; Extended Kalman Filte. 35

2 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM Intoduction In ecent yea ignificant advance have been made on the enole contol of IM. One of the mot well-known method ued fo contol of AC dive i the Diect Toque Contol (DTC) developed by Takahahi in 1984 [1]. DTC of IM i known to have a imple contol tuctue with compaable pefomance to that of the field-oiented contol (FOC) technique developed by Blachke in 197 []. Unlike FOC method, DTC technique equie utilization of hyteei band compaato intead of flux and toque contolle [3-4]. To eplace the coodinate tanfomation and pule width modulation (PWM) ignal geneato of FOC, DTC ue look-up table to elect the witching pocedue baed on the invete tate [5]. Diect toque contol (DTC) of induction moto (IM) equie an accuate knowledge of the magnitude and angula poition of the contolled flux. In DTC, the flux i conventionally obtained fom the tato voltage model, uing the meaued tato voltage and cuent. Thi method, utilize open loop pue integation uffeing fom the well known poblem of integation effect in digital ytem, epecially at low peed opeation ange [6]. In the lat decade, many eeache have been caied on the deign of enole contol cheme of the IM. Mot method ae baically baed on the Model Refeence Adaptive Sytem cheme (MRAS) [7-8]. In [9] the autho ued a eactive-powe-baed-efeence model deived fom (Gacia-Coeda and Robenten, 1999) in both motoing and geneation mode but one of the diadvantage of thi algoithm i it enitivity to detuning in the tato and oto inductance. The baic MRAS algoithm i vey imple but it geatet dawback i the enitivity to uncetaintie in the moto paamete. An othe method baed on the Extended Kalman Filte (EKF) algoithm i ued [1-1]. The EKF i a tochatic tate obeve whee nonlinea equation ae lineaized in evey ampling peiod. An inteeting featue of the EKF i it ability to etimate imultaneouly the tate and the paamete of a dynamic poce. Thi i geneally ueful fo both the contol and the diagnoi of the poce. In [1] the autho ued the EKF algoithm to imultaneouly etimate vaiable and paamete of the IM in healthy cae and unde diffeent IM fault. [7-13] ued the Luenbege Obeve fo tate etimation of IM. The Extended Luenbege Obeve (ELO) i a deteminitic obeve which alo lineaize the equation in evey ampling peiod. Thee i othe type of method fo tate etimation that i baed on the intelligent technique i ued in 36

3 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p the ecent yea by many autho [ ]. Fuzzy logic and neual netwok ha been a ubject of gowing inteet in ecent yea. Neual netwok and fuzzy logic algoithm ae quite heavy fo baic micopoceo. In addition, eveal pape povide enole contol of IM that ae baed on the vaiable tuctue technique [17-18] and the High Gain Obeve (HGO) [19] that i a poweful obeve that can etimate imultaneouly vaiable and paamete of a lage cla of nonlinea ytem and doen t equie a high pefomance poceo fo eal time implementation. DTC impove the induction machine contolle dynamic pefomance and educe the influence of the paamete vaiation duing the opeation []. The pue integation method ued in the claical DTC of IM uffe fom the well known poblem of integation epecially at low peed opeation ange i eplaced in thi wok by the EKF. Thi obeve i ued to etimate the tato cuent, the oto flux linkage, the oto peed and the tato eitance. The peed etimation i affected by paamete vaiation epecially the tato eitance due to tempeatue ie paticulaly at low peed [1]. Theefoe, it i adequate to compenate thi paamete vaiation in enole induction moto dive uing an online adaptation of the contol cheme by the etimated tato eitance uing the EKF. The majo dawback of the peed etimation uing the EKF i the condition that the load dynamic i to be known. To ovecome thi poblem, a novel peed etimato i ued baed on the MRAS tategy. The two diffeent nonlinea obeve applied to enole DTC of IM, ae dicued and compaed to each othe in the ame opeation condition. Diect Toque Contol Pinciple Induction Moto Model The IM model expeed in the tationay efeence fame can be witten in pace vecto notation a: Voltage Equation: dψ (.1a) v = Ri + dt 37

4 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM dψ (.1b) v = = Ri + jωψ dt Flux Equation: ψ = Li + Lmi (.a) ψ = Li + Lmi (.b) Mechanical Equation: dω J + fvω = Te Tl dt 3 Te = p i j ( ψ ) (.3a) (.3b) Subtituting (.a) and (.b) into (.3b), yield 3 Lm Te = p ψ jψ σ LL ( ) whee v, v ae the tato and oto voltage epectively, i, i ae the tato and oto cuent, ψ, ψ (.4) ae the tato and oto fluxe, ω i the oto peed, R, R ae the tato and oto eitance, L, L ae the tato and oto elf inductance, L m i the mutual inductance, σ i the leakage coefficient with σ = 1 L m /( L L ), p i the pole-pai numbe, J i the moto inetia and f v i the vicou fiction coefficient. Uing the α-β coodinate ytem and epaating the machine vaiable into thei eal and imaginay pat, the time-vaying tate pace model of the induction moto i obtained fom (.1a) to (.3b) and i given by equation (.5a) and (.5b): 1 (.5a) γi α ωiβ + ψ α 1 σ LT i σ L α 1 i ωi + α γiβ ψ β β 1 σ LT v = α ψ + σ L α + 1 v Ri α ψ α β ψ β Ri β + ψ β ω 1 3 p p f v ( ψ ) αiβ ψβi α Tl ω J J J 38

5 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p iα 1 iβ i α = 1 ψ α iβ ψ β ω (.5b) 1 R R whee γ = + σ L L Flux and Toque Etimation In the conventional DTC cheme, the tato flux i gotten fom (.6), which i deived fom (.1a) uing only the meaued tato voltage and cuent. ˆ ψ = v R i dt (.6) ( ) Uing equation (.1a) the tato flux expeion i: dψ = V Ri dt If Ri dψ = V dt (.7) (.8) The appoximation of the voltage dop in the tato eitance i ealitic, excepting at low peed ang when the (R.i ) tem mut be conideed. ψ t+ t = ψ t + V t (.9) ( ) ( ). If a equence of null voltage i applied, we note that the vaiation of the tato flux module i alway negative and popotional to voltage dop (R.i ), a hown by equation (.1). dψ dt = R. i (.1) At aveage and high peed, the tem (R.i ) can be neglected and theefoe the tato flux vaiation i null fo a null voltage vecto. 39

6 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM dψ dt = (.11) The electomagnetic toque i calculated by (.1), which i deived fom (.3b). ˆ 3 T = ˆ ˆ e p i i ( βψ α αψ β ) (.1) The expeion of the electomagnetic toque a function of the tato flux i the following: * T =.Im. e KT ψ ψ (.13) K T i a contant depending on the moto paamete. K T 3pL = m ( σ LL) Uing the complex notation of the tato flux and the oto fluxe we get: = i, =. i ψ = ψ, θ = ψ. (.14) ψ [ ψ θ ] ψ and [ ] e θ e θ The electomagnetic toque can be expeed with the following manne: T = K. ψ. ψ in( ρ ) (.15) e T whee ρ = ( θ θ ) i the angle between the tato and oto fluxe vecto. Knowing that the tato flux i maintained in the hyteei band, one can uppoe that it follow it efeence " and the expeion (.15) become: * e = T.. in ( ) T K ψ ψ ρ (.16) Contol algoithm DTC equie accuate knowledge of the amplitude and angula poition of the contolled flux (with epect to the tationay tato axi) in addition to the angula velocity fo the toque contol pupoe [-3]. ψˆ = ψˆ + ψ ˆ α β (.17a) 4

7 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p ˆ θ ψ ψˆ 1 β = tan ψˆ α (.17b) ( ψ ) V ( I ψ,it ) V D,IT 3 e e 3 ( ψ ) V D,DT 5 e ( ψ ) V I,DT 6 e D ψ : Deceaeψ e e I ψ : Inceaeψ DT : Deceae T IT : Inceae T e e Figue 1. Secto fo tato flux plane. Thick vecto in each ecto ae vecto ued to inceae o deceae flux in counte clock wie diection The voltage ouce invete can be modeled a hown in figue 1, whee S a, S b, S c ae the witching tate. Eight output voltage vecto V to V 7 {, 1, 11, 1, 11, 1, 11, 111} ae obtained fo diffeent witch combination. Hence, V and V 7 ae zeo voltage vecto. Fom the invete witching we get: v = V S S 3 v ( ) α a b S c = V 3 ( S S ) β b c (.18a) (.18b) Table 1 peent the output voltage vecto which ae elected to change the toque angle. Thi i done baed on the intantaneou toque equiement, enuing the eo between ˆ * ψ and ψ to be within a toleance band δ ψ. The objective of DTC i to maintain the electomagnetic toque and the tato flux module within a defined band of toleance, i.e. the hyteei band ued in thi wok ae δ Te =.1 and δ ψ =.1. 41

8 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM The witching patten of the VSI i elected baed on the output of a pai of hyteei a vaiable tuctue contolle fo both toque and tato flux. In ode to adjut the electomagnetic toque and the tato flux linkage, the Takahahi DTC algoithm chooe the tato voltage pace vecto that poduce the deied change [4-5]: If ψ i unde the hyteei band, the DTC algoithm chooe the voltage vecto that inceae the tato flux. If ψ i ove the hyteei band, it chooe the voltage vecto that deceae the tato flux. When ψ i inide the hyteei band, the null voltage vecto ae choen. Table 1. The claic witching table Secto (S i : i =1 to 6) τ ψ τ Te S 1 S S 3 S 4 S 5 S 6 1 V V 3 V 4 V 5 V 6 V 1 1 V 7 V V 7 V V 7 V -1 V 6 V 1 V V 3 V 4 V 5 1 V 3 V 4 V 5 V 6 V 1 V V V 7 V V 7 V V 7-1 V 5 V 6 V 1 V V 3 V 4 Whee, τ ψ: the output of the flux hyteei and τ Te: the output of the toque hyteei To implify the witching table, we uppoed that the output of the toque egulato take only two tate, a that of the flux hown in table. Thi mean aying that the condition of peevation of the toque i aely ued (When the toque efeence i inide the hyteei band), which i ealitic epecially when we wok in dicet cae. Table. The modified witching table Secto (S i : i =1 to 6) τ ψ τ Te S 1 S S 3 S 4 S 5 S 6 1 V V 3 V 4 V 5 V 6 V 1 1 V 6 V 1 V V 3 V 4 V 5 1 V 3 V 4 V 5 V 6 V 1 V V 5 V 6 V 1 V V 3 V 4 4

9 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p Extended Kalman Filte The Kalman filte KF i a pecial kind of obeve, which povide optimal filteing of noie in meauement and inide the ytem if the covaiance matice of thee noie ae known. The poce and the meauement noie ae both aumed to be Gauian with a zeo mean. The element of thei covaiance matice (Q and R) eve a deign paamete fo the convegence of the algoithm [1]. Fo nonlinea poblem, the KF i not tictly applicable ince lineaity play an impotant ole in it deivation and pefomance a an optimal filte. The EKF attempt to ovecome thi difficulty by uing a lineaized appoximation whee the lineaization i pefomed about the cuent tate etimate [15]. In addition, the KF ha the ability to poduce etimate of tate that ae not meauable. Thi featue i paticulaly impotant fo etimation poblem aociated with the quiel cage IM a the oto quantitie ae not diectly acceible. If a imultaneou etimate of the machine paamete, let ay tato eitance, i needed then it i defined a an auxiliay tate vaiable. A new tate vecto containing the oiginal tate and the paamete i then etablihed. In thi cae, the nonlineaity of the ytem inceae. Theefoe, the Extended Kalman Filte (EKF) i moe convenient uitable than the KF. Let u now ee the ecuive fom of the EKF a in [1-15]. Pediction: xˆ(( k+ 1) / k = F( k). xˆ( k/ k) + G( k). u( k ) (3.1) T P(( k+ 1)/ k) = F( k). P( k/ k). F ( k) + Q (3.) Coection: [ ] xˆ(( k+ 1) /( k+ 1)) = xˆ(( k+ 1) / k) + K( k+ 1) y( k+ 1) H( k+ 1). xˆ(( k+ 1) / k ) (3.3) T K( k+ 1) = P(( k+ 1)/ k). H ( k+ 1). H( k). P(( k+ 1)/ k). H ( k) + R T 1 (3.4) P(( k+ 1) /( k+ 1)) = P(( k+ 1) / k) K( k+ 1). H( k+ 1). P(( k+ 1) / k ) (3.5) whee the etimation covaiance eo i: T { ˆ ˆ } Pk ( / k) = E ( xk ( ) xk ( ))( xk ( ) xk ( )) (3.6) 43

10 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM K i the Kalman gain matix. ((k+1)/k) denote a pediction at time (k+1) baed on data up to and including k. (3.) and (3.5) fom the well-known Riccati equation. Figue. The geneal diagam of the Extended Kalman Filte Equation (.5a)-(.5b) define a continuou model, but a etimation i to be implemented on a digital poceo, the IM continuou model mut be witten in a dicete fom. By applying the Eule fomula a dicete time-vaying non-linea model i obtained: A = e AT I + AT. (3.7) d T Aξ B = e. Bdξ BT. d (3.8) The dicete time vaying nonlinea tochatic model of the induction moto ha the following fom: x( k+ 1) = F( k) x( k) + G( k) u( k ) (3.9) yk ( ) = Hk ( ). xk ( ) (3.1) whee x(k), u(k) and y(k) ae epectively the tate vecto, the input vecto and the output vecto which ae defined a fellow: ( ) ( ) ( ) ψ ( ) ψ ( ) ω ( ) ( ) T x k = i k i k k k k R k α β α β (3.11) T ( ) = ( ) ( ) ( ) α β, y( k) i α ( k) i β ( k) u k v k v k T k l T = (3.1) The poce and the meauement noie vecto ae andom vaiable and chaacteized by: 44

11 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p { } { T } E w( k) =, E w( k) w( j) = Qδ ; Q (3.13) { } { T } kj E v( k) =, E v( k) v( j) = Rδ ; R (3.14) kj The initial tate x() i chaacteized by: T { ()} =, {( () )( () ) } E x x E x x x x = P (3.15) MRAS Baed Roto Speed Etimation The MRAS technique i ued in enole IM dive, at a fit time, by Schaude [6]. Since thi, it ha been a topic of many publication [8-9]. The MRAS i impotant ince it lead to elatively eay to implement ytem with high peed of adaptation fo a wide ange of application. The baic cheme of the paallel MRAS configuation i given in figue 3. The cheme conit of two model; efeence and adjutable one and an adaptation mechanim. The block efeence model epeent the actual ytem having unknown paamete value. The block adjutable model ha the ame tuctue of the efeence one, but with adjutable paamete intead of the unknown one. The block adaptation mechanim etimate the unknown paamete uing the eo between the efeence and the adjutable model and update the adjutable model with the etimated paamete until atifactoy pefomance i achieved. Uing a popotional plu integal (PI) obeve, the IM peed obeve equation i given by (4.1) [7]: ( β α α β) K ( β α α β ) = + t KP I ˆ ω ε ψˆ ε ψˆ ε ψˆ ε ψ ˆ dt (4.1) Thi expeion depend on the unknown oto flux component (ψ α and ψ β ). Theefoe, thee two vaiable ae added to the tate vecto and etimated uing the EKF. Stability of thi obeve and convegence of etimation have been poven in eveal pape [7-9]. 45

12 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM Figue 3. Schema of the oto peed etimation baed on MRAS tuctue Figue 4. Diect Toque Contol bloc diagam of a enole IM dive. Simulation Reult The efficiency of the popoed contol cheme ha been veified uing MATLAB/SIMULINK oftwae package. Moto paamete ued in imulation ae given in Table 3. 46

13 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p Toque T e, T l (Nm) 15 1 Electomagnetic toque 5 load toque Time () Figue 5. The electomagnetic and load toque. Stato flux Magnitude (Wb) Real and etimated flux magnitude 1.15 Zoom Time () Figue 6. The tato flux magnitude 1.5 ψ β (Wb) 1.5 ψ β (Wb) ψ α (Wb) -1.5 (a) ψ α (Wb) -1.5 (b) Figue 7. Stato flux linkage tajectoie duing tating and teady tate, (a) with compenation of the tato eitance vaiation effect, (b) without compenation of the tato eitance vaiation effect. 47

14 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM Stato cuent i α (A) Stato cuent i β (A) 1-1 (a) (b) Real and etimated value Time () Real and etimated value Time () Figue 8. The actual and etimated tato cuent Stato flux ψ α (Wb) Stato flux ψ β (Wb) (a) (b) Real and etimated value Time () Real and etimated value Time () Figue 9. The actual and etimated tato flux linkage 48

15 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p Roto peed (ad/) Roto peed (ad/) Real and etimated peed Refeence peed (a) Time () Real and etimated peed Refeence peed -5 (b) Time () Figue 1. The actual and etimated peed (a) uing the EKF, (b) uing the MRAS Stato eitance (Ohm) Stato eitance (Ohm) 4 3 Real and etimated value (a) Time () Real and etimated value Zoom (b) Time () Figue 11. The actual and etimated tato eitance, (a) Abupt vaiation, (b) Smooth vaiation 49

16 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM Table 3. Moto Data Rated powe 3 kw Rated peed 144 pm fequency 5 Hz p R.3 Ω R 1.55 Ω L = L.61 H M.49 H J.76 kg.m The ipple affecting both electomagnetic toque epone Fig. 5 and flux epone Fig. 6 i due to the ue of hyteei contolle. In Fig. 7 (b) it can be een the effect of the tato eitance vaiation due to tempeatue. Afte.6 and due to the tato eitance inceae, the tato flux linkage tajectoy i deceaed. By contat, Fig. 7 (a) how that the tato flux tajectoy i kept contant in peence of tato eitance vaiation and thi i due to the online adaptation of the contol algoithm by the obeved tato eitance uing the EKF. The eal and etimated tate vaiable uing the EKF ae given epectively in Fig. 8 to Fig. 11. It i clealy hown that the etimated vaiable ae in cloe ageement with the eal one. Roto peed (ad/) Real and etimated peed - Refeence peed (a) Time () Roto peed (ad/) (b) - Real and etimated peed Refeence peed Time () Figue 1. The actual and etimated peed at low peed ange, (a) uing the EKF, (b) uing the MRAS 5

17 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p Etimation eo (ad/) Etimation eo (ad/) (a) Time () (b) Time () Figue 13. Roto peed etimation eo, (a) uing the EKF, (b) uing the MRAS Stato flux poition ( ) Time () Figue 14. Evolution of the tato flux poition 6 Secteu Time () Figue 15. Secto ucceion duing the IM contol uing the DTC tategy 51

18 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM Toque T e, T l (Nm) Time () Figue 16. The electomagnetic and load toque fo vaied taget Dicuion Paamete vaiation effect In ode to tet the enitivity of the DTC of the IM to the paamete vaiation, the nominal and the etimated tato eitance ae initially et equal, and then at.6 the tato eitance i changed to 1.5 time the nominal eitance. The eult ae hown in Fig. 11 (a) and (b). Fig. 11 (a) how the tacking of the tato eitance (fo a mooth change). Fig. 11 (b) alo how the tacking of the tato eitance vaiation. In thi lat cae, the tato eitance value i changed abuptly: tepped-up by 5 % of it initial value. It i clealy hown that the etimated tato eitance convege afte le than 1 m to the nominal value with a tiny eo. Thi eult demontate that even if the tato eitance change abuptly, the EKF till give a good etimate of thi majo paamete. Meauement noie effect To highlight the obutne of the obeve, white Gauian noie with vaiance of 1 - ae imultaneouly added to the meaued tato voltage and cuent. Fig. 9 how the eal and etimated α and β component of the tato fluxe. The eal and etimated oto peed ae given in Fig. 1 (a) uing the EKF and Fig. 1 (b) uing MRAS. It clealy appea that the EKF and the MRAS have the popety of noie ejection. The on line etimation of the IM tate and paamete i teted by many eeache and i poved to give atifactoy eult. The mot ued technique to etimate thee tate and paamete ae pointed to the EKF. 5

19 Leonado Jounal of Science ISSN Iue 1, Januay-June 8 p Accoding to the KF theoy, R (meauement eo covaiance matix) and Q (poce eo covaiance matix) have to be obtained by conideing the tochatic popetie of the coeponding noie [1]. Howeve, ince thee ae uually not known, in mot cae, the covaiance matix element ae ued a weighting facto o tuning paamete. In thi tudy, tuning the initial value of P and Q i done by tial and eo to achieve a apid initial convegence and the deied tanient and teady tate behavio of the etimated tate and paamete [6]. Steady tate and tanient behavio To compae the pefomance of the two peed obeve EKF and MRAS, it i ight to tudy thei behavio at tat-up and at teady tate egion. Fig. 1 (a) and (b) how epectively, the actual and etimated peed at tating uing the EKF and the MRAS technique. The peed etimation eo given by the two obeve i negligible, but the eo with the MRAS i lightly highe. The etimated oto peed uing the EKF and the MRAS ae in cloe ageement with the eal one. Opeation at low peed egion Since, the MRAS peed etimation ued hee i baed on the popotional plu integal (PI) obeve, the well-known pue integation poblem at low peed egion i encounteed in thi wok. It i concluded that tate obevation pefomance of the EKF i quite atifactoy whee ove all peed egion and lightly bette than MRAS. Fo the invetigation of the dive behavio at both low and zeo peed, the efeence peed i initially et to ad/, at.4 it i changed to ad/, and then at 1.5 the et point i changed to - ad/. Fig. 1 (a) and (b) how that, the etimated and eal peed ae in cloe ageement with each othe in both the fowad and evee diection. The evolution of the tato flux poition and the ecto ucceion duing the IM DTC contol at low peed egion and unde vaiou load condition ae given epectively by Fig. 14 and Fig. 15. Opeation unde vaiou load condition Unlike the EKF which ue the mechanical equation and equie an accuate knowledge of the load toque fo peed etimation, the MRAS obeve i deived uing the 53

20 A Robut Senole Diect Toque Contol of Induction Moto Baed on MRAS and Extended Kalman Filte Mutapha MESSAOUDI, Habib KRAIEM, Mouna BEN HAMED, Laaad SBITA and Mohamed N. ABDELKRIM diffeence between the output of two dynamic model, the efeence and the adjutable model and the eo vecto i diven to zeo tough an adaptive law. The load toque impact on the peed etimation i tudied unde diffeent level of load vaiation. The efeence toque i initially et to Nm, at.6 it i changed to 5 Nm, to the ated value at 1 and at 1.4 it i kept again to Nm. Then at 1.6 the et point i changed to -1 Nm. Fig. 16 how imultaneouly the efeence and the electomagnetic toque. Fig. 1 (a) and (b) pove the obutne of the EKF and MRAS to the load toque vaiation. Concluion In thi pape, the well-known claical DTC of IM i detailed and modified to impove it pefomance, and a compaion between two nonlinea obeve, the EKF and the MRAS i peented. The two obeve ae tudied and compaed in the ame opeating condition, in ode to extact thei advantage and dawback. Simulation eult how that both obeve have the popety of noie ejection and they ae obut againt paamete and load vaiation. The tate obevation pefomance of the EKF i quite atifactoy and lightly bette. But, thi type of obeve equie an accuate knowledge of the load toque and need moe computational time due to heavy matice manipulation. By contat, the MRAS tategy doen t need the load toque to be known and it i much eaie to implement. In a futue fellow up wok, the popoed cheme i to be implemented on a DSP baed on the 16 bit floating point aithmetic Texa Intument TMS3C31 poceo. Refeence 1. Takahahi I., Noguchi T., A New Quick-Repone and High-Efficiency Contol Stategy fo an Induction Moto. IEEE Tan. Ind. Applicat., 1986, (5), p Blachke F., The Pinciple of Field Oientation a Applied to the New Tankvecto Cloe-Loop Contol Sytem fo Rotating-Field Machine. Siemen Review, 197, l(34), p

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