An adaptive PID controller

This paper proposes an adaptive proportional-integral-derivative (PID) controller which integrates the fuzzy sets with the Cerebella Model Articulation Controller (CMAC). Three gain parameters of PID controller, constructed by three fuzzy CMAC (FCMAC) models, are real-time modified in the sense of adaptation to solve the tracking control problem of a class of nonlinear systems. The proposed PID controller is first used to approximate an ideal control, and then based on the estimated approximation error bound an appended controller is designed to assure the system stability. Both controllers are derived from the Lyapunov stability analysis, so that the system tracking ability and the error convergence can be guaranteed in the closed-loop control system. Finally, we apply the proposed control scheme to two nonlinear systems to show the satisfactory performances.