Design of Discrete-Time Sliding Mode Control With Disturbance Compensator-Based Switching Function

Abstract

In this brief, a new disturbance compensator based switching function is proposed for disturbed discrete-time systems. A sliding mode controller is developed based on this switching function. A high order disturbance compensator is embedded in the new switching function to achieve accurate disturbance rejection. Rigorous analysis on system dynamics of the corresponding closed-loop system is performed where it is shown that the proposed switching function is invariant to disturbances and has the ability to achieve the ideal quasi-sliding mode (QSM). In other words, the proposed method enables the convergence of the system trajectory and keeps it on the sliding surface independent of disturbances, which is rarely achieved in the discrete-time sliding mode control (DSMC). Moreover, the presented method is capable of delivering a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ) control accuracy of the system states, which is much higher than most previous methods. Simulation results on a MAGnetic LEViation system illustrate the main characteristics and performance of the proposed method.