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

In this paper, we propose a new fractional PIαDβ 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 PDβ 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 PDβ and conventional predictive controllers.