Electrical Engineering

, Volume 97, Issue 2, pp 129–138 | Cite as

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

  • Yahia Laamari
  • Kheireddine ChafaaEmail author
  • Belkacem Athamena
Original Paper


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.


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


\(\alpha , \beta \)

Stator index

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

Stator (rotor) inductance


Stator voltage


Mutual inductance


Stator current

\(\sigma \)

Total leakage coefficient

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

Rotor flux


Pole pairs number

\(\Omega \)

Rotor speed


Rotor inertia

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

Stator (rotor) time constant

\(f_\mathrm{f} \)

Friction coefficient


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Yahia Laamari
    • 1
    • 2
  • Kheireddine Chafaa
    • 3
    Email author
  • Belkacem Athamena
    • 4
  1. 1.Electronics Department, Faculty of TechnologyAnnaba UniversityAnnabaAlgeria
  2. 2.Electrical Engineering LaboratoryM’Sila UniversityM’SilaAlgeria
  3. 3.Electronics Department, Faculty of TechnologyBatna UniversityBatnaAlgeria
  4. 4.Al Ain University of Science and TechnologyAl AinUAE

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