Contents I. Introduction
PID controllers have found extensive industrial applications due to their simplicity in structure, ease of design and inexpensive maintenance, low cost, and effectiveness for most linear systems [1]–[5]. However, when using a PID control, it is difficult to achieve efficient control of time variable and nonlinear plants of control performance, since dynamic equations for most controlled plants are tightly coupled and can be highly uncertain and nonlinear (e.g., due to load changes). Thus, such controllers post additional difficulties to the stabilization control design and, especially, the tracking control design. In order to overcome these kinds of difficulties in the design of a PID controller, various schemes have been developed in the last decades, among which a successful approach is fuzzy logic control with tuning capability. Over the last decade, tracking control theory has been well developed and provides a precise solution in robust stabilization and disturbance rejection. Since the PID controller has only three parameters to be specified, conventional constrained optimization techniques cannot be employed to obtain a closed form tracking solution. In recent years, fuzzy system with tracking performance have been proposed with the adaptive control for unknown nonlinear systems. From the universal approxi-mation, fuzzy system can approximate any nonlinear function over a compact set, where the influence of disturbance and uncertainty can be attenuated to a desired value. Tuning three PID control parameters to achieve the optimal control is a desirable option for control engineers. Since design techniques for dynamical systems are closely related to their stability, robustness, and performance properties, this technique including the adaptation capability provides good results to the trajectory tracking problem with good-fitting data by using a small amount of the fuzzy inference mechanisms.
