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 PIλ 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 PIλ parameters (Kp, Ki, 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

Available online: 24 Oct 2014 *

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