Finite dimensional variable structure control design for distributed delay systems

Abstract

A general design method for the variable structure control of distributed time-delay systems is studied in this paper. The proposed switching function and variable structure controller are of finite dimension. The basic idea is to construct a finite dimensional system which contains all the unstable poles of the original time-delay system and hence those unstable poles of the time delay system will be absorbed by the developed variable structure controller. The proposed method is applied to the stabilization of combustion in a liquid monopropellant rocket motor and satisfactory results are obtained by simulation study. Simulation results show that the developed variable structure controller can still stabilize the combustion when the two key parameters, pressure exponent and maximal time lag r, change from their nominal value down to 0.0 and 0.1 respectively. By this result, we can somewhat overestimate the two parameters to obtain a reliable controller for the rocket motor control systems.