Global robust optimal sliding mode control for a class of uncertain linear systems

Abstract

The problem of robustifying optimal Linear Quadratic Regulator (LQR) is considered for a class of uncertain linear systems. First, an optimal controller is designed for the nominal system and an integral sliding surface is constructed. The ideal sliding motion can minimize a given quadratic performance index, and the reaching phase, which is inherent in conventional sliding mode control, is completely eliminated. Then the sliding mode control law is synthesized to guarantee the reachability of the specified sliding surface. The system dynamics is global robust to uncertainties which satisfy matching conditions. Finally, the proposed global robust optimal sliding mode controller (GROSMC) is applied to an electrical servo drive system. Simulation results show that the GROSMC has both optimal performance and robustness to parameter variations and external load disturbances, which are superior to the traditional LQR.