An adaptive fuzzy PID control for a class of SISO uncertain nonlinear systems

In this work we propose an adaptive PID control law to deal with a class of single input single output (SISO) uncertain nonlinear systems. In fact, a fuzzy system is used for approximating the PID control gains. The fuzzy system parameters are adjusted online using a robust adaptation law based on the Gradient method and augmented by the so-called “e-modification” term, in order to minimize the error between the fuzzy PID controller and the unknown ideal controller. The stability of the closed-loop system is proven analytically using the Lyapunov approach. A simulation example is presented to illustrate the performance of the proposed scheme.