A new method for the computation of all stabilizing controllers of a given order

Abstract

A new method is given for computing the set of all stabilizing controllers of a given order for linear, time invariant, scalar plants. The method is based on a generalized Hermite-Biehler theorem and the successive application of a modified constant gain stabilizing algorithm to subsidiary plants. It is applicable to both continuous and discrete time systems. © 2005 Taylor & Francis Ltd

Stabilizing First-Order Controllers With Desired Stability Region

“…In [18], an alternative method that take advantage of the fact that ψ λ (s) is a real polynomial was given. Fig.…”

“…An exact solution to stabilizing discrete-time systems by firstorder controllers was given in [16]. Using extensions of the Hermite-Biehler theorem the set of all stabilizing firstorder controllers were determined in [17,18]. In this paper, we give a method to determine the set of all first-order controllers that place the poles of the closed-loop system in the region S. Once this set is determined, it is more convenient to search, among such controllers, those that satisfy other performance criteria imposed on the unit step response.…”

Stabilizing PID Controllers for a Class of Time Delay Systems

“…Computational methods for determining the set of all stabilizing controllers, of a given order and structure, for linear time invariant delay free systems are reported in the literature (Saadaoui & Ozguler, 2005;Silva, 2005). In this line of research, the main objective is to compute the stabilizing regions in the parameter space of simple controllers since stabilization is a first and essential step in any design problem.…”

PI Controller Design for Time Delay Systems Using an Extension of the Hermite-Biehler Theorem

“…In [5], the Hermite-Biehler theorem is used to determine analytically the set of stabilizing gains , , and of a PID controller by replacing the time delay by a �rst-order Padé approximation. In fact, extensions of the HermiteBiehler theorem were effectively used to determine the set of all stabilizing controllers of a given order and a given structure for systems without delay, see [1,6,7].…”