Performance estimation of two-sliding mode controllers for chatter reduction in linear systems

Sliding mode control is a simple and powerful technique for the robust control of uncertain systems. However, despite theoretical promise, real systems using sliding mode controllers have a tendency to chatter at higher frequencies. Second order or two-sliding mode controllers, can be used to suppress chatter while retaining the desirable properties of a classical sliding mode controller. These more complex controllers increase the number of parameters in the system. The affect of these new parameters on system performance is unclear, and this can make it difficult to tune the controllers to meet a desired performance criteria. This study addresses the problem of estimating the performance of a system controlled by two-sliding mode controllers. Describing functions are proposed to estimate chattering amplitude and settling time, and a new method is presented, based on invariant ellipsoid sets, to predict the maximum output bound of the system. The aim is assist in producing a systematic approach for practitioners wishing to directly apply sliding mode controllers with chatter suppressing properties to real applications.