Sliding mode control of a class of uncertain dynamic systems using linear matrix inequality approach

Abstract

Over the year, many researchers have considered the problem of stabilizing the uncertain systems. In variable structure control (VSC) system, the controller structure around the plant is intentionally changed by using a viable high-speed switching feedback control to obtain a desired plant behavior or response. In this project, the problem of designing a variable structure control (VSC) law for uncertain system is considered. Using LMI approach, a design method of a linear sliding surface which is linear to the state is developed. A sufficient condition for the existence of linear sliding surface is given in term of LMIs and an explicit formula of linear sliding surfaces guaranteeing the quadratic stability of the reducedorder equivalent system dynamics restricted to the sliding surfaces is derived. The sliding mode controller is then applied to an Electrohydraulic servo system. The simulation works were performed using MATLAB/SIMULINK software. A comparison with Pole Placement method shows that the sliding mode controller designed using LMI method produce a better performance responses.