Chapter List

6.1 Introduction

The sliding mode control approach [1, 2] is based on keeping exactly a properly chosen constraint by means of high frequency switching of the control. The approach exploits the main features of the sliding mode: its insensitivity to external and internal disturbances, ultimate accuracy and finite-time transient. However, the use of standard sliding modes has some restrictions. If the task is to keep an output variable ? at zero, the standard sliding mode can be implemented only when the relative degree of ? is 1. In other words, the control has to appear explicitly in the first total derivative . Also, high frequency control switching leads to the so-called chattering effect which is exhibited by high frequency vibration of the controlled plant and can be dangerous in some applications.

A number of methods were proposed to overcome these difficulties. In particular, high gain control with saturation approximates the sign-function and diminishes the chattering; while on-line estimation of the so-called equivalent control [1] is used to reduce the discontinuous-control component [3], the sliding-sector method [4] is suitable to control disturbed linear time-invariant systems. Yet, the most comprehensive approach seems to be the...