A stable self-tuning proportional-integral-derivative controller for a class of multi-input multi-output nonlinear systems

This paper proposes a self-tuned proportional-integral-derivative (PID) controller for a class of uncertain continuous-time multi-input multi-output nonlinear dynamic systems. Within this scheme, the PID controller is employed to approximate an unknown ideal controller that can achieve control objectives. The three PID control gains are adjustable parameters and they are updated online with a stable adaptation mechanism designed to minimize the error between the unknown ideal controller and the used PID controller. The proposed approach can be regarded as a simple and effective model-free control because the mathematical model of the system is assumed unknown. The stability analysis of the closed-loop system is performed using a Lyapunov approach. It is proved that all signals in the closed-loop system are uniformly ultimately bounded and that the tracking error can be made to converge to zero in the absence of approximation errors. The effectiveness of the proposed adaptive PID control is demonstrated in simulation.