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

Takuya KITAMOTO

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 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 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.

• Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.12 pp.3240-3250
• Publication Date: 2003/12/01
• Type of Manuscript: PAPER
• Category: Systems and Control

Authors

Takuya KITAMOTO

Keyword

control system,  formal power series,  peak of time response