POLITECHNIKA WARSZAWSKA

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Table 5.2. Basic open loop speed estimators 5. Speed estimation of induction motor Method 1 Based on rotor flux vector estimation (Eq. 5.1) 2 Based on stator flux vector estimation (Eq. 5.2) 3 Based on voltage induced by rotor flux –rotor EMF (Eq. 5.3) 4 Based on voltage induced by stator flux –stator EMF (Eq. 5.4) 5 Based on vector and scalar product (Eq. 5.5) 6 Based on torque current estimation (Eqs. 5.6, 5.7) Parameter sensitivity r s , σx s , T r , x M r s , σx s , T r , x s r s , σx s , T r , xM xr r s , σx s , T r , x s r s , σx s , T r , x M r s , σx s , xM xr Remarques Higher accuracy when flux is calculated in polar coordinates Higher accuracy when flux is calculated in polar coordinates Two integrations are eliminated Two integrations are eliminated Valid only for waveform with harmonics Only for Field oriented Control Schemes Note that four important parameters influence the accuracy of open loop estimators: stator resistance r s , stator transient reactance σx s , stator reactance x s and rotor time constant T r . These parameters convary due to temperature (r s , r r ), saturation (x M , x s , x r ) and skin effect (r r ). In low speed region, the accuracy of the open loop estimation is reduced, and in particular, parameter deviations from their actual values have great influence on the steady state and transient performance of the drive system, which uses an open loop estimator. Higher accuracy is achieved if the stator flux is calculated by a scheme, which avoids using of pure integrators (Fig. 5.2.). This leads to improved schemes working with polar coordinates ψ = ψ , γ ] (Fig. 5.3.). It is important, that in the s [ s s case of rotor field-oriented system stator flux must be recalculated to the rotor flux. Finally, it should be noted that the robustness against parameter mismatch and noise (in the measured signals) can be considerably improved by using closed loop observers. 101
5. Speed estimation of induction motor a) isα usα rs _ 1 ∫ Ψsα isβ usβ rs _ T N 1 T N ∫ Ψsβ b) isα usα usβ isβ αβ isx rs _ usx esx 1 Ψsx = Ψs T N ∫ usy esy _ isy xy rs ÷ esy ω s = sin γ s Ψsx cos ∫ γ s Fig. 5.2. Stator flux vector estimators: a) Stator flux estimator in cartesian coordinates b) Stator flux estimator in polar coordinates 5.2.2. Closed loop estimators – observers Having an open loop estimator of a dynamic system state variables, by introducing a correction term involving the estimation error, one obtains a closed loop estimator which is referred to as an observer. If the plant is considered to be deterministic, then the observer is deterministic observer, otherwise it is a stochastic observer. The most popular observers are Luenberger and Kalman types. 102
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POLITECHNIKA WARSZAWSKA WARSAW UNIV
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Contents 1. Introduction 4 2. Mathe
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1. Introduction 1. INTRODUCTION The
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1. Introduction In the author’s o
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2. Mathematical description of indu
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3. Basics of Artificial Neural Netw
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4. ANN based Current Controllers (C
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7. Simulation and experimental resu
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8. Conclusions 8. CONCLUSIONS The r
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References REFERENCES Books and Ove
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References [34] D. Schauder, and R.
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References [66] A. Tripathi and P.
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References [97] J. W. Kolar, H. Ert
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References [129] M. P. Kazmierkowsk
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A1. Description of the simulation p
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A2. Laboratory setup A2. Laboratory
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A2. Laboratory setup A2.3. dSpace D
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A2. Laboratory setup Offset calibra
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A2. Laboratory setup consists of an
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A3. Motor parameters A3. MOTOR PARA
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A4. Notation - u s - stator voltage
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POLITECHNIKA WARSZAWSKA

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