Discrete-time sliding mode control

Project members: G. Monsees, J.M.A. Scherpen

Sliding mode control is a well known robust control algorithm for linear as well as nonlinear systems. Continuous-time sliding mode control has been extensively studied and has been used in various applications. Much less is known of discrete-time sliding mode controllers. In practice it is often assumed that the sampling frequency is sufficiently high to assume that the closed-loop system is continuous-time. Another possibility is to design the sliding mode controller in discrete-time, based on a discrete-time model of the sampled system under control.

State-based, discrete-time, sliding mode control has received quite some attention over the last decade. The main problem encountered in discrete-time sliding mode control, as opposed to continuous-time sliding mode control, is the limited switching speed. Where the switching frequency in continuous-time is assumed to be infinite, in discrete-time it is limited by the sampling frequency. Therefore (perfect) sliding mode can not be attained in discrete-time. Instead, the best achievable result is to steer the closed-loop system within a small boundary region around the switching surface called the quasi sliding mode band. As opposed to discrete-time state-based sliding mode control, discrete-time output-based sliding mode has received little attention. Research in this area has been focused on a transfer function approach so far.

Our research has been focused on the design of an output-based discrete-time sliding mode controller based on a linear state-space representation of the system. Using this method, the design of the output-based controller can be applied easily to MIMO (multiple input multiple output) as well. Further improvements are made by the use of disturbance estimation and reduced order state observation. It is also shown that the derived controller can be applied to the problem of target tracking, possibly in conjunction with a feedforward controller. Simulation studies demonstrate the applicability of the developed control theory.