In this paper, a systematic design and high accuracy implementation of fractional order proportional integral (FOPI) controller is proposed for a permanent magnet synchronous motor (PMSM) speed system, and the numerical implementation performance of the fractional order operator is evaluated with comprehensive investigation using different implementation methods. Three commonly used numerical implementation methods of fractional operators are investigated and compared in this paper. Futhermore, for the impulse response invariant method, the effects of different discretization orders on the system control performance are compared. The simulation results show that the high accuracy numerical implementation method of the designed high-order FOPI controller has improved performance over normal accuracy fractional order operation implementation.

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