New smooth approximation of variable structure systems with application to tracking control

Abstract

This paper presents an exponential-type continuous control law that approximates relay-type discontinuous control law in the conventional variable structure control to an arbitrary extent of accuracy by simply adjusting a parameter. This continuous control law allows us to apply a high control authority to obtain a fast response and alleviate chattering at the same time. An exposition is also given to show how to apply the new control law to tracking control problem. Some numerical examples are included to illustrate the proposed method.