Optimal Fractional-Order Active Disturbance Rejection Controller Design for PMSM Speed Servo System

In this paper, a fractional-order active disturbance rejection controller (FOADRC), combining a fractional-order proportional derivative (FOPD) controller and an extended state observer (ESO), is proposed for a permanent magnet synchronous motor (PMSM) speed servo system. The global stable region in the parameter (K_p, K_d, μ)-space corresponding to the observer bandwidth ω_o can be obtained by D-decomposition method. To achieve a satisfied tracking and anti-load disturbance performance, an optimal ADRC tuning strategy is proposed. This tuning strategy is applicable to both FOADRC and integer-order active disturbance rejection controller (IOADRC). The tuning method not only meets user-specified frequency-domain indicators but also achieves a time-domain performance index. Simulation and experimental results demonstrate that the proposed FOADRC achieves better speed tracking, and more robustness to external disturbance performances than traditional IOADRC and typical Proportional-Integral-Derivative (PID) controller. For example, the J_ITAE for speed tracking of the designed FOADRC are less than 52.59% and 55.36% of the J_ITAE of IOADRC and PID controller, respectively. Besides, the J_ITAE for anti-load disturbance of the designed FOADRC are less than 17.11% and 52.50% of the J_ITAE of IOADRC and PID controller, respectively.