Optimal Control Design for Variable Structure Systems with Fixed Order Compensators

This paper addresses the design of fixed order dynamic compensators for variable structure control applied to a linear multivariable plant. The variable structure control law considered in this paper is a function of the outputs and the compensator states. A methodology is developed to design the sliding surface and the parameter matrices of the compensator simultaneously so that a specific performance criterion is minimized. The problem is formulated in such a way that well-known design techniques for optimal linear fixed order compensation can be applied directly. An example is given to illustrate how the sliding surface and the compensator parameters are selected using the procedures described.