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

Abstract

We consider stabilizing �rst-order systems with time delay. e set of all stabilizing proportional-integral PI controllers are determined using an extension of the Hermite-Biehler theorem. e time delay is approximated by a second-order Padé approximation. For uncertain plants, with interval type uncertainty, robust stabilizing PI controllers are determined.

New Versions of the Hermite Bieler Theorem in Stability Contexts

“…That led to tremendous interest in the latter which also provided elementary derivations of Routh's algorithm for determining the Hurwitz stability of a real polynomial. A version of the Hermite-Bieler theorem was used to determine the set of all stabilizing proportionalintegral PI controllers [1]. Using similar approaches, results on the stability of fractional order polynomials are obtained [7].…”

Lead-lag Controller Design for Time Delay Systems Using Genetic Algorithms

“…Time delay inherently exists in many physical systems such as chemical, mechanical and hydraulic systems [3], [22] and [24]. Therefore, it is natural that the above line of research was extended to time delay systems, see [1], [2], [8], [9], [10], [11], [13], [14], [28] and [33]. This paper aims at proposing a method to design stabilizing lead-lag controllers for time delay systems.…”