Linear control of saturating control systems†

Abstract

The problem is considered of replacing optimum non-linear control of saturating, single-variable systems by sub-optimal linear control. Both the optimal and sub-optimal controllers are designed to minimize the integral-square-error of the systems in response to a step input, and a comparison is made of the values of this integral using the two forms of control. The values of the integral are obtained to high accuracy using numerical minimization techniques. Consideration is also given to the stability of the systems under the linear controller.