Design of optimal sampled data linear regulator

Abstract

Optimal Sampled-data control for linear time invariant processes with quadratic cost criteria are determined through the application of the discrete minimum principle. In order to apply the discrete minimum principle. both continuous system's state equations and integral performance indices are discretized. An extensive work is done to find an analytical expression for the dependance of the optimal control on the sampling period. Thus the effect of changing the sampling time upon the closed loop system's performance is investigated. Based on the theory cited above original numerical methods and a computer program have been developed, to compute optimum sampling period and the matrix of optimum feedback gains. Then for various linear time invariant processes numerical results are obtained for the sampling period and the optimal control and, the associated costs are evaluated. Additionally the trajectories of the states, and the controls are plotted within the time interval of interest.