A study on discrete sliding mode control: robustness analysis and experimental investigation

In this paper a discrete-time Sliding-Mode (SM) based controller design method is presented. The controller is designed for a general SISO system with nonlinearity and external disturbance. Closed-Loop behavior of the general system with the proposed control and Lyapunov stability is shown. It will be shown that application of the proposed controller forces the state trajectory to be within an O(Ts 2 ). The proposed controller is applied to a stage driven by a piezo drive that is known to suffer from hysteresis nonlinearity. Structure of proposed SMC controller is proven to offer chattering-free motion and rejection of the disturbances represented by hysteresis and the time variation of the piezo drive parameters. As a separate idea to enhance the accuracy of the closed loop system a combination of disturbance rejection method and the SMC controller is explored. The disturbance observer is constructed using a second order lumped parameter model of the Piezo-Stage and is based on SMC framework. Closed-loop experiments are presented using PID controller with disturbance compensation and Sliding-Mode Controller with and without disturbance compensation for the purpose of comparison.