Analysis and design of fuzzy PID control systems

The describing function (DF) approach is employed to analyze the stability of a fuzzy PID control system. The fuzzy PID controller is composed of the memory component due to its integral action and the dynamic component due to its derivative action. Its DF is amplitude- and frequency dependent which is different from that of static nonlinear controllers. Two algorithms are developed to calculate the DF. A stability criterion is presented to predict the closed-loop stability approximately. The design of fuzzy PID controllers is briefly discussed based on this criterion. Numerical simulations are also carried out.<
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