Impact of Observability and Multi-objective Optimization on the Performance of Extended Kalman Filter for DTC of AC Machines

  • Ibrahim Mohd Alsofyani
  • Nik Rumzi Nik Idris
  • Kyo-Beum LeeEmail author
Original Article


It is well known that the selection of extended Kalman filter (EKF) covariance elements has a considerable bearing on the effectiveness of EKF performance. The observability at very low frequency is also an essential property for the selection of EKF elements. This paper investigates the optimization of the EKF covariance elements when zero frequency is included in the training profile for direct torque control (DTC) of induction motor. In addition, the paper studies the optimization of EKF by speed and torque fitness functions using a non-dominated sorting genetic algorithm-II at zero and high speeds under stable flux regulation. For this purpose, DTC with constant switching frequency controller which has the capability of establishing continuous flux rotation regardless of speed variation is used. The optimized results of EKF for both DTC motor drives and speed and torque cost functions are verified experimentally.


DTC Extended Kalman filter Instructions Induction motor Multi-objective optimization NSGA II 

List of Symbols


System matrix


Input matrix


Direct torque control


Extended Kalman filter


Field oriented control


Induction motor


Stator current space vector


Kalman filter

ls, lr

Stator and rotor self inductances

Rs, Rr

Stator and rotor resistances


Control-input vector


Stator voltage space vectors


State space vector


\(\sigma = 1 - L_{m}^{2} /(L_{s} L_{r} )\)

\(\omega _{r}\)

Rotor speed

\(l_{\sigma }\)

\(l_{\sigma } = l_{s} - l_{m}^{2} /l_{r}\)

\(\psi_{s} , \psi_{r}\)

Stator and rotor flux linkage space vectors



This research was supported by a Grant (no. 20172020108970) from the Korea Institute of Energy Technology Evaluation and Planning (KETEP) that was funded by the Ministry of Trade, Industry and Energy (MOTIE).


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Copyright information

© The Korean Institute of Electrical Engineers 2019

Authors and Affiliations

  • Ibrahim Mohd Alsofyani
    • 1
  • Nik Rumzi Nik Idris
    • 2
  • Kyo-Beum Lee
    • 1
    Email author
  1. 1.Department of Electrical and Computer EngineeringAjou UniversitySuwonKorea
  2. 2.Faculty of Electrical EngineeringUniversiti Teknologi MalaysiaJohor BahruMalaysia

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