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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.E86A
No.12
pp.32403250 Publication Date: 2003/12/01 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: PAPER Category: Systems and Control Keyword: control system, formal power series, peak of time response,
Full Text: PDF>>
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 y_{max} of y(t) (we define y_{max} to be max_{0 t} y(t)) is a nontrivial 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 y_{max} 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.

