Adaptive robust PID controller design based on a sliding mode for uncertain chaotic 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, 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 Duffing–Holmes chaotic system is used as an illustrative to show the effectiveness of the proposed robust adaptive PID controller.