Oscillation design of sampling proportional–derivative sliding-mode systems for linear plants with hysteresis

Abstract

This article deals with the self-sustained oscillation appearing in the sliding-mode system. The oscillation provides considerable robust performance and, meanwhile, leads to detrimental effects such as the reduced control precision, mechanical wear, and resonance. A graphical method is introduced to design the sliding-mode controller with proportional–derivative terms. The method indicates how to determine the proportional–derivative coefficients and the desired oscillation frequency and amplitude for the stability of systems. The analysis shows that the zero-order holder plays an important role in the robustness of systems which can be improved by shorter sampling periods. The influences of the hysteresis on the oscillations are also discussed, and a method of tuning the coefficients of proportional–derivative terms is used to compensate the hysteresis. The first simulation shows the design processes of the graphical method in a specific system, and the second simulation confirms the validity of the method of hysteresis compensation. The design process is also demonstrated via the experiment on an inverted pendulum.