SENSORLESS VECTOR-CONTROLLED INDUCTION MOTOR DRIVE SYSTEM WITH ROTOR RESISTANCE ESTIMATION USING PARALLEL PROCESSING WITH FLOATING POINT DSP

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1 Wokshop on ELECTRICAL MACHINES' PARAMETERS Technical Univesity of Cluj-Napoca, 26 th of May 2001 SENSORLESS VECTOR-CONTROLLED INDUCTION MOTOR DRIVE SYSTEM WITH ROTOR RESISTANCE ESTIMATION USING PARALLEL PROCESSING WITH FLOATING POINT DSP Teodo Pana Technical Univesity of Cluj-Napoca, Dept. of Electical Dives and Robots, 3400, Cluj-Napoca, P.O. Box 1-99, ROMANIA Fax: ; E- Abstact The pape deals with the aspects elated to simultaneous oto speed estimation and oto esistance identification in field-oiented induction moto systems using only the induction moto model. A statistical based computing algoithm is poposed in ode to avoid the division by zeo. Thee basic algoithms have been consideed in ode to establish the optimum solution. The study of the speed and oto esistance estimato has been pefomed togethe with a Gopinath flux obseve. Hence, the oto flux, oto speed and esistance have been estimated using only the electical feedback magnitudes of the moto: the stato voltages and cuents. The estimated oto esistance is applied to the input of the flux obseve and voltage compensato blocks. In ode to evaluate the pefomances of the poposed method, a multipocesso based simulation, using floating point DSP, has been pefomed. 1. INTRODUCTION This pape deals with the aspects elated to simultaneous oto speed estimation and oto esistance identification in field-oiented induction moto systems, which allows speed and oto esistance estimation using only the induction moto model. Hence, the contol of the induction moto could be achieved without the use of special estimation stategies, such as Kalman filtes, Fuzzy estimatos, neual netwoks etc. A statistical based computing algoithm is poposed in ode to avoid the division by zeo. Thee basic algoithms have been consideed in ode to establish the optimum solution. The study of the speed and oto esistance estimato has been pefomed togethe with a Gopinath flux obseve. Hence, the oto flux, oto speed and esistance have been estimated using only the electical feedback magnitudes of the moto: the stato voltages and cuents. Two cases have been consideed: the sensoless vecto contol without oto esistance feedback loop (based on the immunity of the Gopinath flux obseve to the vaiation of the oto esistance) and the vecto contol with oto esistance feedback loop. The esults pove the simplicity and the pefomance of the estimato based only on the electomagnetic phenomena inside the moto. 2. THE SPEED AND ROTOR RESISTANCE PRINCIPLE As it is aleady known, the most difficult aspects concening the implementation of the electical dive systems based on the field-oientation theoy, ae in elation with oto flux components, speed and oto esistance estimation. It has been aleady poved that simultaneous identification of the oto esistance and the oto speed is possible only when the oto flux is time-vaiant [12]. If the model of the induction moto is consideed, the oto speed and oto esistance can be expessed as follows: ψdψ d + ψ qψ q R = d d q q iqψ d idψ q ω = d d q q ( i ψ + i ψ ) ( i ψ + i ψ ) Fom the oto equation of the induction moto, the modulus vaiation of the oto flux phaso is deduced: d 2 Rid ωψ q ψ = 2[ ψ d ψ q ] = dt Riq + ω ψ d = 2R [ ψ d id + ψ qiq ] o (1) (2) 81

2 Wokshop on ELECTRICAL MACHINES' PARAMETERS Technical Univesity of Cluj-Napoca, 26 th of May 2001 d 2 ψ 2 [ ] T = R ψ [ i ] (3) dt As equation (2) shows, if the modulus of the oto flux is kept constant, the following elation esults: ψ d id + ψqiq = 0 (4) At this point, some peliminay conclusions might be consideed: - if the modulus of the oto flux is kept stictly constant, the denominatos in expessions fom (1) ae always zeo; consequently, in ode to estimate the oto speed and esistance, the oto flux must be time-vaiant [12]. This comes in contadiction with the basic pinciple of the vecto contol of induction moto; - even if the oto flux is time vaiant, the shape of the denominato is wavy and hence division by zeo peiodically appeas in the computation of the estimated magnitudes fom (1). 3. THE STATISTIC ALGORITHMS The difficulties in implementing elations (1) on digital computing devices deive fom the dividing by zeo opeation. It has also to be pointed out two moe aspects that make this opeation moe complicated: - the ichness of the oto speed signal, especially at low values; - the speed pofiles, that vay fom one application to anothe, including the fequency and duation of speed vaiations. Thee types of identification algoithms wee taken into consideation [4]: - The Least Squae Method (LS); - The Recusive Least Squae Method (RLS); - The Fixed Tace Method. Ψ ^ FLUX OBSERVER u s i s ω ^ R ^ SPEED AND ROTOR RESISTANCE ESTIMATIOR Fig. 1. The speed and oto esistance estimation assembly. Taking into account the easons enumeated above, and also the simulation esults, we conside that only the Fixed Tace Method could be applied fo the speed and oto esistance estimation. It is, in fact, an impoved vesion of the ecusive least squae one, based on the following ecusive expessions: whee θˆ [ m] = θˆ [ m 1] P [ m] λ + = λ + P P[ m 1] x[ m] P[ m 1 ]( x( m) P[ m 1] [ m 1] ( x( m) ) 2 ) 2 ( θˆ [ m 1] x[ m] y[ m] ) y[ m] θ ˆ[ m ] = (6) x[ m] (5) 82

3 Wokshop on ELECTRICAL MACHINES' PARAMETERS Technical Univesity of Cluj-Napoca, 26 th of May 2001 Ψ ω ω ^ K./. sin λ i sd λ i sq λ cosλ Voltage compensato ω ^ R u sd λ u sq λ Speed and esistance est. -1 T.A. u sd u sq -1 T.S. PWM Invete Ψ ^ Flux analyze Ψ ^ d Ψ ^ q Flux Obseve i sd i sq T.S. I.M. DSP TMS320C4x PC 486 Fig. 2. The field-oiented induction moto dive system. Hee θ could be eithe R o ω fom (1). λ is the fogetting facto of the exponential window. As λ is constant in the RLS method, it is vaiable in the fixed tace one, in accodance with the vaiation of the estimated value and is given by the following expession: 1 λ = (7) 1+ γ ( x[ m] ) 2 The vaiable fogetting facto is obtained by fixing the tace of the gain matix P: ( P[ m] ) = t ( P[ 0 ]) = γ > 0 t (8) The ecusive fom fo the fixed tace algoithm used in the estimation is expessed by the following elation: θ ˆ [ m] θ ˆ[ m 1] [ 0] x[ m] [ 0] ( x[ m] P = P ) 2 θ ( ˆ[ m ] x[ m] y[ m] ) 4. THE FIELD-ORIENTED INDUCTION MOTOR DRIVE SYSTEM The analytical stuctue of the oto flux -speed and esistance estimation assembly in Fig. 1. Fom the Fig. 1 one can notice that the outputs of each estimato is at the same time input fo the othe one. With othe wods the two estimatos have embedded feedback loops. The speed and oto esistance estimato was fist simulated as a component block of the field-oiented induction moto dive shown in Fig. 2. Only the stato cuents and voltages of the induction moto have been consideed as feedback magnitudes. The Gopinath educed ode flux obseve (pesented in detail in [2] and [3]) was used to estimate the oto flux components [2,3]. The influence of the poles allocation of the flux obseve was also taken into consideation, though the k coefficient. The poles allocation of the flux obseve was designed in ode to obtain duplicate poles on the eal axis, which guaantees the flux estimation with unity damping facto [2,3]. The pole allocation is pefomed eal time, accoding to the instantaneous oto speed and oto esistance, estimated by the poposed speed and oto esistance estimato. Accoding to α and β, the gain coefficients ga and gb ae calculated. In Fig. 2 the field-oiented induction moto dive system is pesented. The estimated oto esistance is also used in the computation of the voltage commands, by the voltage compensation block. It has been aleady poved that the modulus of the oto flux must be time-vaiant in ode to keep the denominato of elations (1) at nonzeo values. Some authos conside that the ipples caused by the nonsinusoidal PWM voltage supply could avoid the pemanent division by zeo [5]. Good esults have been epoted also using a low fequency sinusoidal signal summed to the constant flux efeence one [7,8]. The simulations poved that using the vaiation of the oto flux modulus with 5%, satisfactoy esults have been obtained. In ode to test the pefomances of the poposed sensoless dive system, a eal time simulation using (9) 83

4 Wokshop on ELECTRICAL MACHINES' PARAMETERS Technical Univesity of Cluj-Napoca, 26 th of May 2001 a multi- pocesso compute assembly, based on a floating point digital signal pocesso (TMS320C31) has been pefomed, as shown in Fig. 3 a and b. PC HOST Compute PWM & IM Model Digital input Digital output N/A TMS320C4X Boad Contol & Estimation Algoithms Analog input Analog output A/N a). PC HOST Compute PWM & IM Model SYSTEM BUS DSP EXTERNAL BUS TMS320C4X Boad Contol & Estimation Algoithms b). Fig. 3. The stuctue of the bi-pocesso eal-time simulation assembly. Fig. 3a shows the stuctue with analogic feed-back loop, while Fig. 3b shows the stuctue which uses the online eal-time dialogue between the DSP boad and the host compute, pefomed at the beginning and at the end of each sample time. Consequently, the vecto-contol algoithm, as well as the flux, oto speed and oto esistance estimation ones have been implemented on a TMS320C31 based netwok, using C pogamming language. At this stage, in ode to simulate as close as possible the eal woking conditions, the model of the induction moto has been implemented on the host compute. In case of TMS320C31 DSP family, the pocesso intecommunication takes place simultaneous with the tasks execution. An initial deviation of 0.3Ω between the seconday esistance as paametes fo the flux estimato and voltage compensato and the eal oto esistance of the moto (1.47Ω) has been consideed. A simple time about 150 micoseconds has been used. Fig. 4 shows the estimated magnitudes when the field-oiented system has been excited with a evesal efeence input. It has to be pointed out the influence of the k paamete of the flux obseve on the pefomance of the whole system. In fact k contols the compensation of the flux estimation eo, caused by the deviation of the oto esistance with the tempeatue [2,3]. This ate could now be minimized (by choosing a small k), because of the estimation of the instantaneous oto esistance. 84

5 Wokshop on ELECTRICAL MACHINES' PARAMETERS Technical Univesity of Cluj-Napoca, 26 th of May 2001 Fig. 4. Expeimental esults using implementation of the contol algoithm on TMS320C31 floating point DSP. 85

6 Wokshop on ELECTRICAL MACHINES' PARAMETERS Technical Univesity of Cluj-Napoca, 26 th of May CONCLUSIONS The esults which have been obtained using the simultaneous oto speed estimation and oto esistance identification encouaged us in futhe eseach. It also can be concluded that the only eliable statistical algoithm in ode to avoid the division by zeo is the fixed tace method. This algoithm assues the best esults in both apid and slow speed vaiations and also the smallest estimation eos fo both oto speed and esistance. As Fig. 4 shows, the pefomances of the dive system ae influenced by the amplitude and the fequency of the supeimposed sinusoidal component of the oto flux efeence input. This could be subject also fo futhe eseach. 6. REFERENCES [1] Saoj Biswas, Heny Sendaula, Thomas Cao, "Self Tunning Vecto Contol fo Induction Motos" Poceedings of IECON'89 Annual Confeence of IEEE Industial Electonics Society, Philadelphia, USA, 1989, pp [2] Y. Hoi, V. Cotte and Y. Kaya. A Novel, "Induction Machine Flux Obseve and its Application to a High Pefomance AC Dive System" 10th IFAC Wold Congess, 1987, Pegamon Pess, 1987, pp ,. [3] Y. Hoi, and T. Umeno, "Robust Flux Obseve Based Field Oientation (FOFO) Contolle: Its Theoetical Development on the Complex Numbe System and Implementation Using DSP" Poceedings of the 11th IFAC Wold Congess, Tallinn, 1990, pp [4] Yoichi. Hoi, "Robust and Adaptive Contol of a Sevomoto using Low Pecision Shaft Encode" Poceedings of IEEE IECON'93 Confeence,, Hawaii, 1993, pp [5] T. Kanmachi, I. Takahashi, "Senso-less Speed Contol of An Induction Moto with No Influence of Seconday Resistance Vaiation" Poc. of IEEE IAS Annual Meeting, 1994, pp [6] Apad Kelemen and Maia Imecs, "Vecto Contol of Induction Machines Dives" OMIKK Publishe, Budapest, [7] Kubota, H., Matsuse, K., and Nakano, T, "DSP-Based Speed Adaptive Flux Obseve of Induction Moto" IEEE Tansactions on Industy Applications, Vol. 29, No.2, pp [8] Kubota H., Matsuse, K., and Nakano, T, "New Adaptive Flux Obseve of Induction Moto fo Wide Speed Range Moto Dives" Conf. Rec , IEEE IECON'90, 1990, pp [9] T. Pana and Y. Hoi, "A MATLAB Toolbox fo Field-Oiented Induction Moto Systems Design" Poc. of 1994 Japan USA Symphosium on Flexible Automation, Kobe, Japan, 1994, pp [10] T. Pana, Y. Hoi, "Simultaneous Speed Estimation and Roto Flux Identification fo Sensoless Induction Moto Dives," Japan Industy Applications Society Confeence, JIASC'94, 1994, Ehimae, Japan, 1994, pp [11] Teodo Pana, Model Based Speed and Roto Resistance Estimation fo Sensoless Vecto-Contolled Induction Moto Dives Using Floating Point DSP, Poc. of th Intenational Wokshop on Advanced Motion Contol, Mie, Japan, 1996, pp [12] Shinji Shinnaka, "A Unified Analysis on Simultaneous Identification of Velocity and Roto esistance of Induction Motos" The Tansactions of The Institute of Electical Enginees of Japan, Vol 113-D, No.12, 1993, pp