Title: Fractional order PID controller for the stabilisation of chaotic systems using Takagi-Sugeno fuzzy model

Authors: Belgacem Mecheri; Djalil Boudjehem; Badreddine Boudjehem

Addresses: Advanced Control Laboratory (Labcav), Department of Electronics and Telecommunication, Université 8 Mai 1945 Guelma, Algeria ' Advanced Control Laboratory (Labcav), Department of Electronics and Telecommunication, Université 8 Mai 1945 Guelma, Algeria ' Advanced Control Laboratory (Labcav), Department of Electronics and Telecommunication, Université 8 Mai 1945 Guelma, Algeria

Abstract: In this paper, we propose a new fractional PI^αD^β controller design to control chaotic systems. The controller design is based on the predictive control proposed by Yamamoto et al. (2001) and the fractional calculus. The parameters of the controller are determined by minimising the energy of the chaotic states using particle swarm optimisation. In order to obtain a simple model structure, we have used Takagi-Sugeno technique. A fractional PD^β and conventional predictive controllers have been also used as a comparative technique, in order to show the effectiveness of the proposed design one. The simulation results on Lorenz and Chen chaotic systems show the efficiency of the proposed fractional controller to reject disturbances and noises. These results show also that the fractional controller gives better results and overcome those of the fractional PD^β and conventional predictive controllers.

Keywords: predictive control; chaotic systems; Takagi-Sugeno fuzzy model; fractional calculus; noise perturbation rejection; particle swarm optimisation; PSO.

DOI: 10.1504/IJSCC.2021.113238

International Journal of Systems, Control and Communications, 2021 Vol.12 No.1, pp.1 - 11

Accepted: 10 Feb 2020
Published online: 25 Feb 2021 *

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