Computation of the Peak of Time Response in the Form of Formal Power Series

Takuya KITAMOTO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.12   pp.3240-3250
Publication Date: 2003/12/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
Keyword: 
control system,  formal power series,  peak of time response,  

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Summary: 
Suppose that we need to design a controller for the system x(t) = A x(t) + B u, u = -K x(t), y(t) = C x(t), where matrices A, B and C are given and K is the matrix to to determine. It is required to determine K so that y(t) should not exceed prescribed value (i.e., the peak of output y(t) is limited). This kind of specification, in general, difficult to satisfy, since the peak ymax of y(t) (we define ymax to be max0 t |y(t)|) is a non-trivial function of design parameter K, which can not be expressed explicitly generally. Therefore, a controller design with such specifications often requires try and error process. In this paper, we approximate ymax in the form of formal power series and give an efficient algorithm to compute the series. We also give a design example of a control system as an application of the algorithm.