Title: Robust fractional controller for interval first order system with time delay

Authors: Sami Hafsi; Rihem Farkh; Kaouther Laabidi

Addresses: Faculté des sciences de Tunis, Universite de Tunis El Manar, LR-11-ES20 Analyse, Conception et Commande des Systémes, 1002, Tunis, Tunisia ' Faculté des sciences de Tunis, Universite de Tunis El Manar, LR-11-ES20 Analyse, Conception et Commande des Systémes, 1002, Tunis, Tunisia ' Faculté des sciences de Tunis, Universite de Tunis El Manar, LR-11-ES20 Analyse, Conception et Commande des Systémes, 1002, Tunis, Tunisia

Abstract: In this paper, a new method is proposed to define the parameters of fractional order PI^λ controller that stabilise an uncertain first order system with time delay. In fact, based on an extension version of Hermite-Biehler theorem and Pontryagin theorem the complete set stabilising PI^λ parameters (K_p, K_i, λ) is determined. The closed-loop characteristic equation of the system is a fractional order quasi-polynomial with interval uncertainty structure which is decomposed into several vertex. In the complex plane the value set of the vertex is a convex polygon. Simulation results are given to show the effectiveness of the proposed method.

Keywords: fractional-order control; robust control; fractional order PI controllers; first order delay system; Hermite-Biehler theorem; Pontryagin theorem; time delay; interval uncertainty; simulation.

DOI: 10.1504/IJAAC.2014.065450

International Journal of Automation and Control, 2014 Vol.8 No.4, pp.339 - 361

Received: 02 Oct 2013
Accepted: 29 Mar 2014
Published online: 31 Oct 2014 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article