A Genetic based Fuzzy PID controller has been proposed to synchronization task of chaotic systems in which one system has been considered as "master" whilst the other system has been treated as "slave" (a perturbed system with uncertainty and disturbance). Three PID control gains p k , i k , and d k , will be updated online. An adequate adaptation mechanism is used to minimize the sliding surface error with appropriate adaptive law. Using the gradient method, coefficients of the PID controller are updated. A supervisory controller has also been used to provide the stability. The proposed method has been found with a significant performance when it was implemented on the Van Der Pol oscillator chaotic equations.

This paper presents a robust fuzzy sliding mode control scheme and the additional compensator. The additional compensator relaying on the slidingmode theory is used to improve the dynamical characteristics of the drive system. Sliding mode control method is studied for controlling DC motor because of its robustness against model uncertainties and external disturbances. In this method, using high control gain to overcome uncertainties lead to occur chattering phenomena in control law which can excite unmodeled dynamics and maybe harm the plant. In order to enhancement the sliding mode controller performance, we have used fuzzy logic. For this purpose, we have used a Fractional PID outer loop in the control law then the gains of the sliding term and Fractional PID term are tuned on-line by a fuzzy system, so the chattering is avoided and response of the system is improved against external load torque here. Presented implementation results on a DC motor confirm the above claims and demonstrate the performance improvement in this case.

A robust adaptive PID controller design motivated from the sliding mode control is proposed for a class of uncertain chaotic systems in this paper. Three PID control gains, Kp, Ki, and Kd, are adjustable parameters and will be updated online with an adequate adaptation mechanism to minimize a previously designed sliding condition. By introducing a supervisory controller, the stability of the closed-loop PID control system under with the plant uncertainty and external disturbance can be guaranteed. Finally, a well-known Vanderpol oscillator is used as an illustrative to show the efectiveness of the proposed robust a PID controller.

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