Fixed order controller design via parametric methods
Author(s)
Advisor
Özgüler, A. BülentDate
2003Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
In this thesis, the problem of parameterizing stabilizing fixed-order controllers
for linear time-invariant single-input single-output systems is studied. Using a
generalization of the Hermite-Biehler theorem, a new algorithm is given for the
determination of stabilizing gains for linear time-invariant systems. This algorithm
requires a test of the sign pattern of a rational function at the real roots of a
polynomial. By applying this constant gain stabilization algorithm to three subsidiary
plants, the set of all stabilizing first-order controllers can be determined.
The method given is applicable to both continuous and discrete time systems.
It is also applicable to plants with interval type uncertainty. Generalization of
this method to high-order controller is outlined. The problem of determining
all stabilizing first-order controllers that places the poles of the closed-loop system
in a desired stability region is then solved. The algorithm given relies on a
generalization of the Hermite-Biehler theorem to polynomials with complex coefficients.
Finally, the concept of local convex directions is studied. A necessary
and sufficient condition for a polynomial to be a local convex direction of another
Hurwitz stable polynomial is derived. The condition given constitutes a
generalization of Rantzer’s phase growth condition for global convex directions.
It is used to determine convex directions for certain subsets of Hurwitz stable
polynomials.
Keywords
Hermite-Biehler theoremLocal convex directions
Regional pole placement
Stabilization
Stability
First-order controllers