Stabilization of Unstable Fixed Points of Chaotic Fractional Order Systems by a State Fractional PI Controller

This paper presents a new method to control chaos in fractional order systems based on the fractional control theory. The proposed controller is a fractional PI (PIα) controller and can locally stabilize unstable equilibrium points of a class of chaotic fractional order systems. Using the ideas available in the chaos control methods such as Ott-Grebogi-Yorke (OGY), this local stabilization can be extended to the global stabilization. The controller has simple structure and its parameters can be determined by pole placement technique. To illustrate its capability, the proposed controller is applied to control chaos in the fractional order unified system. Numerical simulations confirm the ability of the controller to reject external constant disturbances as well as its robustness against the variation of system parameters.