Synthesis of Complete Finite-Settling-Time Systems on the Basis of Integrated-Square Sampled Error and Quadratic Control Area Criterion

Abstract

Finite-settling-time systems which are nonminimal have constants which can be arbitrarily assigned. This opens up the possibility of selecting the extra system constants with a view of optimizing the system under some criterion. An approach to this problem is to minimize the intergrated-square sampled error or the quadratic control area. This paper is concerned with the problem of synthesis of nonminimal finite-settling-time systems which have no ripples after a suitable transient period has elasped under these two criteria. The treatment of these optimization problems makes use of the z transform and the modified z transform methods. By representing polynomials by vectors or matrices and making use of the linear algebraic techniques, the synthetic studies can be systematically carried out. The design equations of the optimum systems and the evaluating formulas of the minimum integrated-square sampled error and the minimum quadratic control area are derived.