Designing Discrete-Time Sliding Mode Controller With Mismatched Disturbances Compensation

The main objective of this article is to explore the issue of how to improve the performance of discrete-time sliding mode control (DSMC) law for a class of discrete-time dynamic systems with both matched and mismatched disturbances. By using tools from mismatched disturbance compensation technique, a new kind of discrete-time sliding surface is constructed and subsequently utilized in designing the desirable DSMC laws. Specifically, two different types of DSMC laws, i.e., the equivalent-control-based DSMC law and the reaching-law-based DSMC law, are respectively constructed based upon the developed sliding surface. Rigorous analysis on stability of the corresponding closed-loop system is performed where it is shown that the mismatched disturbances could be successfully attenuated from the output channel in steady state. The effectiveness of the analytic result is supported by the experimental studies as well as numerical simulations.