Title: A fractional computational algorithm for designing advanced feedback controllers of dynamical nonlinear systems

Authors: Ammar Soukkou; Salah Leulmi

Addresses: Department of Electronics, Faculty of Science and Technology, Jijel University, P.O. Box 98, Ouled Aissa, Jijel 18000, Algeria ' Department of Electric Power Engineering, Faculty of Technology, Electric Power Systems Laboratory, University of August 20th, 1955, Skikda, Algeria

Abstract: This paper contributes a new alternative for the designing of a simple and efficient controller extracted from a partially complex approach for controlling complex dynamical systems. The developed adjustable form of fractional-order proportional-integral (A2Fo-PI) controller with optimal structure and parameters represents a powerful and simple approach to provide a reasonable tradeoff between computational overhead, storage space and numerical accuracy in the modelling and control of dynamical nonlinear systems. The multiobjective genetic learning algorithm with chaotic mutation, adopted in this work, can be visualised as a combination of structural and parametric genes of a controller orchestrated in a hierarchical fashion and is applied to select an optimal knowledge base, which characterises the developed controller, and satisfies various contradictory design specifications such as simplicity, accuracy, stability and robustness. Good simulation results have been obtained in regulation of the activated sludge process (ASP) in a highly disturbed environment and with transient behaviour, showing the efficiency of the proposed design and demonstrating that the proposed A2Fo-PI offers encouraging advantages and has better performances.

Keywords: fractional-order control; multiobjective optimisation; activated sludge process; fractional calculus; controller design; advanced control; feedback control; dynamical systems; nonlinear systems; genetic algorithms; chaotic mutation; simulation.

DOI: 10.1504/IJMIC.2016.078327

International Journal of Modelling, Identification and Control, 2016 Vol.26 No.2, pp.90 - 109

Received: 09 Feb 2015
Accepted: 18 Aug 2015
Published online: 15 Aug 2016 *

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