Optimal and linear sub-optimal control of second-order saturating control systems†

Abstract

Consideration is given to the problem of replacing optimum non-linear control of saturating, single variable, second-order systems by sub-optimal linear control. The performance criteria adopted are integral-square-error and integral-modulus-error, and comparisons are made of the values of these integrals under the alternative forms of control. Known results for the double integrator plant are extended to an oscillatory plant (Bushaw'a plant) and to a plant comprising an integrator and a lag. Asymptotic properties of the optimal switching curves for these plants are studied incidentally This paper is a companion to a previous paper which considers the same problem for higher-order pure integrator plants.