Design of Continuous and Discrete Optimal Control Systems with Prescribed Transient Response

Abstract

The performance index matrices for the optimal control problem are to be chosen so that the closed-loop system would have a prescribed transient response. Two algorithms are developed, the direct algorithm which is based directly on the sensitivity of the closed-loop poles with respect to changes in these matrices, and the associated matrix algorithm which is based on the sensitivity of this special matrix eigenvalues to performance matrix changes. While in the first algorithm one has to solve simultaneously two matrix equations, it is sufficient in the second to solve only one much simpler equation. By applying the direct algorithm to both discrete and continuous cases, it is found that even with R(the control performance index matrix) equal I, the discrete case involves a great deal of computation. On the other hand the associated matrix algorithm yields similar equation for both continuous and discrete cases. The paper also includes a thorough discussion of the existence and uniqueness of both algorithms and for both discrete and continuous control systems.