Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
A Solution Method for Pole Placement and Stability Radius Enlargement Problem
Keishi KAWABATATakehiro MORI
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2008 Volume 21 Issue 5 Pages 151-158


This paper presents a robust controller design method for linear time-invariant SISO systems based on an optimization approach. The task is to enlarge real stability radius to counter plant parameter perturbations by using extra degree of freedom of the controller parameters in the pole placement scheme. The formula for the real stability radius is known as an infimum of a certain function and that makes its gradients discontinuous. It is shown that by some manipulations, the considered problem can be converted to a nonlinear optimization problem, to which a gradient-based optimization method becomes applicable. The case of complex stability radius is also considered, which is less sharp as a robust stability index than the real counterpart, but has a much simpler form. Numerical examples for both cases are presented to show that they actually work, and some comparisons are discussed, leading to a suggestion on the effective uses of these two stability radius computation methods.

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