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Particle swarm optimization of an extended Kalman filter for speed and rotor flux estimation of an induction motor drive


A novel method based on a combination of the extended Kalman filter with particle swarm optimization (PSO) to estimate the speed and rotor flux of an induction motor drive is presented. The proposed method will be performed in two steps. As a first step, the covariance matrices of state noise and measurement noise will be optimized in an off-line manner by the PSO algorithm. As a second step, the optimal values of the above covariance matrices are injected in our speed–rotor flux estimation loop (on-line). Computer simulations of the speed and rotor flux estimation have been performed to investigate the effectiveness of the proposed method. Simulations and comparison with genetic algorithms show that the results are very encouraging and achieve good performances.

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\(\alpha , \beta \) :

Stator index

\(L_\mathrm{s} (L_\mathrm{r} )\) :

Stator (rotor) inductance

\(u\) :

Stator voltage

\(L_\mathrm{m}\) :

Mutual inductance

\(i_\mathrm{s}\) :

Stator current

\(\sigma \) :

Total leakage coefficient

\(\Phi _\mathrm{r}\) :

Rotor flux

\(p\) :

Pole pairs number

\(\Omega \) :

Rotor speed

\(J\) :

Rotor inertia

\(T_\mathrm{s} (T_\mathrm{r} )\) :

Stator (rotor) time constant

\(f_\mathrm{f} \) :

Friction coefficient


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Correspondence to Kheireddine Chafaa.

Appendix: Motor parameters

Appendix: Motor parameters

The ratings of the three phase 50 Hz, 1.5 kW, 220/380 V, 4 poles, 1420 rpm squirrel cage induction motor are

$$\begin{aligned}&R_\mathrm{s} =4.85~\Omega ,R_\mathrm{r} =3.805~\Omega ,\, L_\mathrm{s} =0.274~\mathrm{H},\, L_\mathrm{r} =0.274~\mathrm{H} \\&L_\mathrm{m} =0.258~\mathrm{H} , \quad J=0.031 \mathrm{kg}\,\mathrm{m}^{2},\quad f_\mathrm{f} =0.008\,\mathrm{N}\,\mathrm{m/rad/s} \end{aligned}$$

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Laamari, Y., Chafaa, K. & Athamena, B. Particle swarm optimization of an extended Kalman filter for speed and rotor flux estimation of an induction motor drive. Electr Eng 97, 129–138 (2015).

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  • Induction motors
  • Speed estimation
  • Stochastic state observer
  • Extended Kalman filter
  • Particle swarm optimization