Studies on the Synthesis of Complete Finite-Settling-Time Systems under the Minimum Integrated-Square Sampled Error and the Minimum Quadratic Control Area Criteria

Abstract

Finite-settling-time systems which are non-minimal have some constants which can be arbitrarily assigned. This opens up the possibility of selecting extra system constants with a view to optimizing the system under some criterion. An approach to this problem is to minimize the integrated-square sampled error, and another is to minimize the quadratic control area. This paper is concerned with the problem of the synthesis of non-minimal finite-settling-time systems, which have no ripples between sampling instants, under these two criteria. The treatment of these optimization problems makes use of the z transform and the modified z transform methods respectively. By representing polynomials by vectors or matrices, and by making use of the linear algebra techniques, these two synthetic studies are carried out in a systematic manner. Fundamental design equations of the optimum system, and evaluating formulas of the minimum integrated-square sampled error and the minimum quadratic control area are derived.