Study of a Three-Parameter Fractional Order PID Controller and its Optimal Tuning Method

In this paper, a simplified fractional order PI
^λ
D
^μ
controller with only three pending parameters is proposed by building the relationships between the controller parameters. An estimation model of the optimal relationship coefficient between the controller parameters is built in order to guarantee good dynamic performance of the control system. Then the optimal three-parameter PI
^λ
D
^μ
controller can be tuned analytically according to the estimated relationship coefficient. The three-parameter PI
^λ
D
^μ
controller is applied to the permanent magnet synchronous motor (PMSM) speed control. Motor speed control simulations are performed and then the robustness, step response performance and anti-load disturbance performance of the three-parameter PI
^λ
D
^μ
control system are verified.