Adaptive robust PID controller design based on a sliding mode for uncertain haotic systems

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, K p , and K d , 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.