Backlash Vibration Suppression Control of Torsional System by Novel Fractional Order PID^k Controller

Abstract

This paper proposes a novel fractional order PID^k controller for torsional system’s backlash vibration suppression control, in which the order k of D controller can not only be integer but also be any real number. Various methods have been proposed for two-inertia system’s speed control, but the control systems designed by these methods may not be able to suppress the vibration caused by gear backlash. In order to improve control system’s robustness against the backlash, several methods have been proposed. However their design processes are very complicated. Clear and straightforward design concept is required in practical applications. As a novel approach, in this paper the D controller’s order is expanded to include any real number. Robust PID^k controller against backlash is designed by adjusting the order k directly. An approximation method based on Short Memory Principle is also introduced to realize the discrete D^k controller. Design process and experimental results demonstrate straightforward robust control design through the novel FOC approach, the PID^k control system’s better robustness against backlash non-linearity and good approximation of the realization method.