Browsing by Subject "First-order controllers"

Now showing 1 - 3 of 3

Open Access
Fixed order controller design via parametric methods
(2003) Saadaoui, Karim
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.
Open Access
On the set of all stabilizing first-order controllers
(IEEE, 2003) Saadaoui, Karim; Özgüler, Arif Bülent
A computational method is given for determining the set of all stabilizing proper first-order controllers for finite dimensional, linear, time invariant, scalar plants. The method is based on a generalized Hermite-Biehler theorem.
Open Access
Stabilizing first-order controllers with desired stability region
(ACTA Press, 2009) Saadaoui, K.; Özgüler, A. B.
In this paper, we determine the set of all stabilizing first-order controllers that place the poles of the closed-loop system in a desired stability region. The solution is based on a generalization of the Hermite-Biehler theorem applicable to polynomials with complex coefficients and the application of a modified stabilizing gain algorithm to three subsidiary plants. The method given is also applicable to PID controllers.