Synthesis of Finite-Settling-Time Systems under Integrated-Square Error Criterion

Abstract

Finite-settling-time systems which are nonminimal have some constants which can be assigned arbitrarily. Though these systems have not the shortest settling-time such as minimal systems have, this opens up the possibility of selecting the extra system constants with a view of optimizing the system under the integrated-square error criterion. In this paper a general procedure is discussed to synthesize such nonminimal finite-settling-time systems under this criterion without considering hidden oscillations. The fundamental formulas determining the optimum type of overall pulse transfer functions and calculating the minimum value of the integrated-square error are obtained. It is also shown that the case of more than two inputs can be reducd to that of one input. In examples, suggestion is given of determining the length of the settling-time.