On digital high-gain and sliding-mode control

Abstract

This paper is on the analysis and design of sampled-data high-gain control and sliding-mode control systems. In continuous high-gain control, it is usually true that the higher the gains, the more effective the system uncertainties may be suppressed. When implemented digitally, however, there are limits to the feedback gains without causing instability.This paper analyses high-gain,sampled-data,systems utilizing the results of the singular perturbation theory. The system can be decomposed into fast and slow subsystems under high gain feedback. It is shown how the fast subsystem goes unstable when the gains get high enough due to the sampling effect. With reasonable approximations, a set of simple stability criteria is derived relating the feedback gains to the sampling period and other factors. It is also shown that control chattering, which is typical in variable structure systems with sliding mode, also happens in high-gain control systems when the gains exceed or are close to the critical values. Moreover, since the behaviour of a variable structure system with sliding mode is very close to that of a high-gain system, the design issue of a digital slidingmode control system is also explored in this paper. From the similarity between the two control techniques, the stability criteria for high-gain systems are shown to be applicable to the design of digital sliding mode control in order to guarantee stability and avoid chattering.