Fractional-Order Proportional Derivative Controller Synthesis and Implementation for Hard-Disk-Drive Servo System

Abstract — A fractional-order [proportional derivative] (FO-[PD]) controller is proposed for robust motion control systems. Focusing on a class of simplified models for motion control systems, a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been for the first time addressed under the same number of design parameters and the same specifications. Side-to-side fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via both simulation and experimental tests have revealed some interesting facts: 1) IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing; 2) Both FO-PD and FO-[PD] controllers outperform IO-PID controller designed in this paper; 3) FO-[PD] controller outperforms FO-PD controller more when the time constant of the motion control system increases. Extensive validation tests on our real-time experimental test-bench illustrate the same. Index Terms — Fractional calculus; fractional order controller; mo-tion control; robustness; controller tuning