Adaptive Robust PID Controller Design Based on a Sliding Mode for Uncertain Chaotic Systems


Yaghoub Heidari - Department of Electrical, Nour Branch, Islamic Azad University, Nour, Iran Rashin Nimaeeb Rad - Department of Mathematics, Nour Branch, Islamic Azad University, Nour, Iran


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, \(K_p, K_i\), 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.