Model reference strategy for mismatched disturbance attenuation in relative degree one and two DSMC

Abstract

In this paper we propose a new model reference approach to reaching law based sliding mode control of discrete-time systems. The new approach significantly improves performance of the controlled plant by eliminating the persistent effect of past uncertainties on its sliding motion. It involves obtaining a desired state trajectory with the use of a reference model of the system and the reaching law approach, and then driving the state of the original plant alongside that trajectory. As a result, sliding motion of the system is not distorted by past uncertainties, and state trajectory more precisely follows the desired one. Furthermore, the proposed model reference approach allows one to apply strategies with arbitrary relative degree sliding variables to the reference model and successfully carry over the properties of these strategies to the original plant, even in the presence of non-matched uncertainties. This is an important advantage since such strategies without the reference model, despite their robustness with respect to matched disturbance, cannot typically be used when matching conditions are not satisfied. In particular, we have considered two reaching laws for the proposed model reference scheme, using relative degree one and two sliding variables, respectively. In both cases we have shown that system sliding motion is only affected by the single most recent disturbance, which results in increased robustness of the plant when compared to traditional reaching law approach.