Fractional Order PID Controller for the Stabilization of Chaotic Systems Using Takagi-Sugeno Fuzzy Model

Belgacem Mecherihttp://orcid.org/0000-0001-6245-7581, Djalil Boudjehemhttp://orcid.org/0000-0001-6245-7581, and Badreddine Boudjehemhttp://orcid.org/0000-0001-6245-7581 

Volum 12, Issue 01 Pages 1-11, 2021

International Journal of Systems, Control and Communications




In this paper we propose a new way to construct a fractional controller of the form PI^{alpha}D^{beta} for controlling chaotic systems. The proposed controller design is based on the predictive control proposed by Yamamoto and fractional calculus.rnThe parameters of the controller are determined by minimizing the error of the states' energy using particle swarm optimization. In order to obtain a simple model structure we have used Takagi Sugeno technique to model chaotic systems.rnThe obtained results using the proposed controller are compared with those obtained using fractional $PD^beta$ and conventional predictive controllers. The simulation results on Lorenz and Chen chaotic systems show the efficiency of the proposed fractional controller to reject disturbance and noise injected into system. These results show also that the fractional controller gives better results and overcome those of fractional PD^{beta} and conventional predictive controllers.


Predictive Control; Chaotic Systems; Takagi Sugeno Fuzzy Model; Fractional Calculus; Noise Perturbation Rejection; Particle swarm optimization.