POLITECHNIKA WARSZAWSKA

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5. Speed estimation of induction motor a) isα usα usβ isβ αβ isx rs _ usx esx 1 Amplitude Ψsx = Ψs T Limiter N usy esy _ isy xy rs ÷ esy ω s = sin γ s Ψsx cos ∫ γ s b) + T dΨ sx = 1 N esx Ψsx = Ψ dt s + ω s c y LPF + ωc s + ω c Limiter Fig. 5.3. Improved stator flux estimator in polar coordinates: a) stator flux estimator with amplitude limiter, b) amplitude limiter 5.2.2.1. Luenberger Observer Luenberger observer (LO) is of the deterministic type and basically is applicable to linear time-invariant deterministic systems. The extended Luenberger observer (ELO) is applicable to nonlinear time-varying deterministic system. x& = Ax + Bu i s = Cx s (5.8) where 103
5. Speed estimation of induction motor x = [ i u s s = [ u ψ ] sα r = [ i ⎡A11 A12 ⎤ A = ⎢ ⎥ ⎣A21 A22 ⎦ ⎡1 0⎤ C = [ I 0], I = ⎢ ⎥ ⎣0 1⎦ T , i s T usβ ] sα T isβ ] , ψ r = [ ψ rα ψ ] rβ T (5.9) u s B Induction Motor i s ^ i s + - I/s + C + + ^ ω m A ^ ψ r ∧ ∧ ∧ ω m (r s ,T r ) Adaptive scheme Fig.5.4. Block diagram of adaptive flux and speed observer K Based on a Lyapunov function V T = e e + ( ˆ ωm −ωm ) / c (5.10) where c is positive factor, and applying the conventional procedure of pole placement technique, the gain matrix K can be calculated as follows: ⎡k K = −⎢ ⎣k 1 3 I + k I + k 2 4 J⎤ ⎥, J⎦ ⎡0 J = ⎢ ⎣1 −1⎤ 0 ⎥ ⎦ (5.11) 104
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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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