Fractional order PI^λD^μ controller design for satisfying time and frequency domain specifications simultaneously

In order to achieve a desired control performance characterized by satisfying specifications in both frequency-domain and time-domain simultaneously, an optimal fractional order proportional integral derivative (PI^λD^μ) controller design strategy is proposed based on analytical calculation and Differential Evolution algorithm for a permanent magnet synchronous motor (PMSM) servo system in this paper. In this controller design, the frequency-domain specifications can guarantee the system stability with both gain margin and phase margin, and also the system robustness to loop gain variations. The time-domain specifications can ensure the desired step response performance with rapid rising curve, constrained overshoot, and proper power consuming. Compared with the PI^λ controller and the traditional PID controller, PI^λD^μ controller can get obvious benefits from two more degrees of freedom of the fractional orders λ and μ on satisfying multiple constraints simultaneously and achieving better servo tracking performance for the PMSM servo system. PMSM speed tracking simulations and experiments are demonstrated to show the significant advantages of using the proposed optimal PI^λD^μ controller over the optimal fractional order PI^λ controller and traditional integer order PID controller.