Design of Indirect Adaptive Fuzzy Control (IAFC) for Nonlinear Hysteretic Systems

Nonlinear hysteretic phenomena occur in many physical systems, such as electronic throttle and solenoid valves in automobiles, piezoelectric sensors, and many other mechanical actuators. In order to handle the nonlinear properties of hysteretic systems, an indirect adaptive fuzzy controller (IAFC) is proposed in this paper. However, it is a hard task to directly identify unknown hysteretic effects. Firstly, to overcome this problem, a hysteretic function is employed to construct the nonlinear properties of backlashlike hysteretic systems. Then the existence of an indirect adaptive controller (IAFC) is derived in this paper. Unlike the existing fuzzy control methods, our proposed IAFC can deal with different kinds of hysteretic problems with adaptive and control laws. Based on the learning algorithm, the adaptive and control laws not only can be derived but the stability of the closed- loop system can also be guaranteed by the Lyapunov stability criterion. Finally, MATLAB software is used for simulations, and the results show that our proposed IAFC can effectively handle the nonlinear properties in some unknown hysteretic systems.