SENSORLESS SPEED CONTROL SYSTEMS BASED ON ADAPTIVE OBSERVERS LUENBERGER AND GOPINATH

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1 Annal of the Univeity of Caiova, Electical Engineeing eie, No. 32, 2008; ISSN SENSORLESS SPEED CONTROL SYSTEMS BASED ON ADAPTIVE OBSERVERS LUENBERGER AND GOPINATH Maiu-Auelian PICIU, Lauenţiu ALBOTEANU Faculty fo Engineeing in Electomechanic, Envionment and Indutial Infomatic, Univeity of Caiova 107, Decebal Bl., , Caiova, Tel , Fax , Abtact Thi pape develop a high dynamic and obut enole contol ytem fo dive baed on adaptive obeve, Luenbege and Gopinath obeve, and alo compaiion between them. The intantaneou peed i accuately etimated by an extended Luenbege and Gopinath obeve. Extenive imulation eult with the popoed contol tuctue, applied to a aynchonou moto dive, pove high-dynamic pefomance in wide peed ange. Keywod: Induction moto dive, enole, adaptive obeve, peed contol. 1. INTRODUCTION The enole contol i an impotant goal in indutial application to obtain a good pefomance pe pice indice [1]. Induction moto dive have been thooughly tudied in the pat few decade and many vecto contol tategie have been popoed, anging fom low cot to high pefomance application. Speed etimation i an iue of paticula inteet with induction moto dive whee the mechanical peed of the oto i geneally diffeent fom the peed of the evolving magnetic field. The advantage of peed enole induction moto dive ae educed hadwae complexity and lowe cot, educed ize of the dive machine, bette immunity, elimination of the eno cable, inceaed eliability and le maintenance equiement. The induction moto i howeve elatively difficult to contol compaed to othe type of electical moto. Fo high pefomance contol, field oiented contol i the mot widely ued contol tategy. Thi tategy equie infomation of the flux in moto, howeve the voltage and cuent model obeve ae nomally ued to obtain thi infomation. Geneally, uing the induction moto tate equation, the flux and peed can be calculated fom the tato voltage and cuent value [2]. The flux i etimated o obeved fom the tato voltage equation and the peed i obtained uing the etimate flux and the oto equation. The main objective of thi pape i to analyze andevaluate two of optimum ued flux obeve (Luenbege and Gopinath) in electical dive ytem without enole, and alo thei compaion. The analyi i done by ue of moden contol theoy and by extenive teting. The teting i done with a Matlab/Simulink model fo two of them. 2. THE MACHINE AND ADAPTIVE OBSERVERS The accuacy of the open loop etimation model decibed in liteatue educe mechanical peed. The limit of acceptable pefomance depend on how peciely the model paamete can be matched to the coeponding paamete in the eal moto. It i paticulaly at lowe peed that paamete eo have ignificant influence on the teady-tate and dynamic pefomance of the dive ytem. The obutne againt paamete mimatch and ignal noie can be impoved by employing cloed loop obeve to etimate the vaiable, and the ytem paamete The machine equation A otating coodinate ytem i choen ta etabilih voltage equation of induction moto. Thi coodinate ytem otate at an angula tato velocity ω k, whee the value of ω k i left unpecified to be a geneal a poible. When a pecific olution of the ytem equation i ought, the coodinate ytem mut be defined fit. The tato voltage equation in the geneal k- coodinate ytem i : dψ u = i + jωkψ + (1) In the oto, ω i the angula mechanical velocity of the oto, and hence the oto voltage equation i: dψ 0 = i + + j( ω ω ψ (2) k ) Equation (1) and (2) epeent the electomagnetic ubytem of the machine a a econd ode dynamic ytem by two tate equation, howeve, in tem of fou tate vaiable: i, i, ψ, ψ. 124

2 Annal of the Univeity of Caiova, Electical Engineeing eie, No. 32, 2008; ISSN The equation of the mechanical ubytem i : dω τm = Te T (3) L whee τ m i the mechanical time contant, T e i the electomagnetic toque and T L i the load toque. T e i computed fom the z-component of the vecto poduct of two tae vaiable: Te = ψ i z = ψ αiβ ψ βi α (4) whee ψ = ψ α + jψ and β i = i α + ji β ae the elected tate vaiable. Figue 1: Induction moto ignal; tate vaiable: oto flux vecto, tato cuent vecto; ynchonou coodinate epeentation 2.2. The Luenbege obeve The Luenbege obeve can be contucted fom the tato voltage moto equation (1), the tationay coodinate ytem i choen, fo that: ω k = 0, τ ' di k 1 σ + i = (1 jωτ ) ψ u στ + (5a) σ τ dψ + ψ = jωτ ψ + l i (5b) m Thee equation epeent the machine model and they ae viualized in the uppe poition of Figue 2. The model output i etimated angula mechanical peed ωˆ. Adding an eo compenato to the model etablihe the obeve. The eo vecto computed fom the model cuent and the meaued moto cuent i i ˆ = i i, and i ued to geneate coecting input to the electomagnetic ubytem that epeent the tato and the oto in the moto model. The equation of the nonlinea obeve ae then etablihed in accodance with (5): ' dˆ i k 1 τ ˆ σ + i = (1 jωτ ) ψˆ + u G( ωˆ ) i (6) στ σ dψˆ τ + ψˆ = jωτ ˆ ψ + lh i G( ωˆ ) i (7) Kubota and al. [3] elect the complex gain facto G (ωˆ ) and G (ωˆ ) uch that the two complex eigenvalue of the obeve λ 1,2ob =λ 1,2mach, whee λ 1,2mach ae the machine eigenvalue, and k>1 i a eal contant. Given the nonlineaity of the ytem, the eulting complex gain G (ωˆ ) and G (ωˆ ) in figue 2 depend on the etimated angula mechanical peed ωˆ, [3] The Gopinath obeve In ode to evaluate the effect of the voltage meauing cheme and whethe a flux obeve i able o not to compenate fo the voltage eo, a educed ode Gopinath tato flux obeve wa implemented. The obeve wa contucted a a combination between a flux imulato and a feedback of coection of a pedictive etimated eo, Figue 3. Figue 2: Full ode nonlinea Luenbege obeve Figue 3: The Gopinath obeve baed on induction moto tate model dψˆ + ( a = ( a ga ga 11 ) i 12 ) ψˆ gu + di + g, (8) 125

3 Annal of the Univeity of Caiova, Electical Engineeing eie, No. 32, 2008; ISSN whee g i Gopinath obeve gate. The coefficient ae obtained fom expoue of pole on eal axi in complex plane (x =-α, y =β= 0): /l α + ωβ σl l g a = 1 (9a) 2 2 ( /l ) ω l + m whee = 0 g ωα / l β b = (9b) 2 2 ( / l ) + ω lm 2 β, = k ( / ) + ω l σl l 2 α,( k > 0). The tato cuent etimated i given by follow equation : dˆ i 1 = σl ' u i + jω ψˆ l jω σ l ˆ i l (10) 3. SENSORLESS SPEED CONTROL SYSTEMS 3.1.Model efeence adaptive ytem baed on Luenbege obeve To complete a enole contol ytem, a Luenbege etimato fo the ytem i etablihed. Figue 4 how the ignal flow gaph. The oto flux linkage vecto i etimated uing equation of machine. The angula mechanical velocity of the oto i calculate by geneal equation (3). The oto field angle i deived with efeence fom the component of the etimated oto flux linkage vecto. The ignal ωˆ i equied to adapt the oto tuctue of the obeve to the mechanical peed of machine. The phae angle of ˆψ, that define the etimated oto field angle, then appoximate the tue field angle that pevail in the machine. The coect peed etimate i eached when the phae angle of the cuent eo i, and hence the toque eo T e educe to zeo. The contol cheme i epoted to opeate at minimum peed 50 pm [3]. Figue 4: Speed and cuent contol ytem fo Luenbege obeve 3.2.Model efeence adaptive ytem baed on Gopinah obeve Figue 5 how the ignal flow gaph of Gopinath obeve and it enole contol ytem who i like ytem baed on Luenbege obeve a contuction. The othene i who mechanical peed i computation; in the fit cae a vecto poduct between the eo vecto, computed fom the model cuent and the meaued machine cuent, and the etimated oto field (in fact, the tem ψˆ i who epeent the toque eo T e ). Figue 5: Speed and cuent contol ytem fo Gopinath obeve 126

4 Annal of the Univeity of Caiova, Electical Engineeing eie, No. 32, 2008; ISSN The econd cae i (Gopinath cae) vecto poduct between the tato cuent etimated and the oto field etimated The model of enole peed contol ytem with Luenbege and Gopinath obeve Figue 6 peente the cheme of contol peed tating fom cheme 4 and 5. The teting i done with a Matlab/Simulink model which wa ued to evaluate the both peed evolution, eal and etimate peed. Figue 6: The Simulink model of peed and cuent contol ytem without invete Figue 7: The Simulink model of peed and cuent contol ytem with invete Figue 7 i imilaly with 6, but it i contain the invete of voltage. Both of cheme contain the following block: PI peed contolle with echewal atuation by technical anti wind-up 127

5 Annal of the Univeity of Caiova, Electical Engineeing eie, No. 32, 2008; ISSN (PI_Speed) and flux contolle with eo annulment (PI_XiRt) MA_N - aynchonou moto without atuation OBS_Luenbege and OBS_Gopinath full ode nonlinea obeve fo etimate the intantaneou peed and flux P3HTg voltage invete with peciption cuent The load toque T L i conideed to be pactical contant. The electomagnetic toque of the induction moto i calculated in evey ampled peiod baed on the tato voltage and cuent. Figue 9: The wavefom of the efeence, eal and etimate peed obtained fom Gopinath obeve 4. SIMULATION RESULTS The theoetical idea ae well uppoted by digital imulation. The dive ytem pefomance ae teted at tep peed efeence at low peed 10 ad/ and at high peed of 100 ad/ (Figue8 )fo the Luenbege obeve and (Figue 9) fo Gopinath obeve, both of them fo cheme without invete. Figue 10: The efeence, eal and etimate peed obtained fom Gopinath and Luenbege obeve at low peed fo anging peed Figue 8: The wavefom of the efeence, eal and etimate peed obtained fom Luenbege obeve 128

6 Annal of the Univeity of Caiova, Electical Engineeing eie, No. 32, 2008; ISSN CONCLUSIONS Figue 11: The efeence, eal and etimate peed obtained fom Gopinath and Luenbege obeve at high peed fo anging peed Both obeve peented in the pape can etimate the peed in an electical dive ytem. The value of the peed etimated on-line can be ued by the contol of the electical dive ytem in low peed ange. Fo both obeve the dive ytem mut be endowed an acquiition ytem fo the electical vaiable, which help to calculate the electomagnetic toque of the electical moto, who i baed on the geneally equation of motion the ame in evey dive ytem fo any kind of electical moto. The etimation pefomance of both obeve ae compaable. Fo the obeve peented in thi pape the dive paamete wee conideed contant. The main featue ae the following: The intantaneou peed i etimated by an extended Luenbege and Gopinath obeve. To obtain a high-dynamic cuent enole contol, a cuent to voltage feedfowad decoupling and a dynamic coection to educe the electic time contant ae applied. Moeove, an accuate dynamic limitation of the eal electomagnetic toque i obtained. Extenive imulation eult uing a aynchonou moto dive pove highdynamic pefomance and obutne of the popoed contol tuctue in dspace envionment. Refeence Figue 12: The efeence, eal and etimate peed obtained fom Gopinath, Luenbege obeve and Invete with the anging peed [1] OHNISHI, K. MATSUI N., HORI, Y. Etimation identification, and enole contol in motion, contol ytem, Poceeding of IEEE, 82, 8, pp , Aug [2] H. Tajima and Y. Hoi, Speed Senole Field- Oientation Contol of the Iduction Machine, IEEE Tanaction on Induty Application, vol. 29, no. 1, pp , Jan./Feb [3] H. Kubota, K. Matue and T. Nakano, DSP Baed Speed Adaptive Flux Obeve of Induction Moto, IEEE Tanaction on Induty Application, vol. 29, no. 2, Ap/Ma. 1993, pp [4] ANDREESCU, G.D., RABINOVICI, R., Cuent enole contol of dc moto by toque and peed obeve, Poc 8 th Euopean Conf. on Powe Electonic and Application EPE 99, Lauanne, Switzeland, CDROM, 086.pdf, pp. 1-8, Sept