Equivalence between Fuzzy PID Controllers and Conventional PID Controllers

This paper proposes the equivalence between fuzzy Proportional-Integral-Derivative (PID) controllers and conventional PID controllers. A well-designed conventional PID controller, with the help of the proposed method, can be rapidly transformed to an equivalent fuzzy logic controller (FLC) by observing and defining the operating ranges of the input/output of the controller. Furthermore, the knowledge base of the proposed equivalent fuzzy PID controller is represented as a cube fuzzy associative memory (FAM), instead of a combination of PD-type and PI-type FLCs in most research. Simulation results show the feasibility of the proposed technique, both in continuous and discrete time. Since the design techniques of conventional linear PID controllers have matured, they can act as preliminary expert knowledge for nonlinear FLCs designs. Based on the proposed equivalence relationship, the designer can further tune the membership functions of fuzzy variables in the control rules to exhibit the nonlinearity of a FLC and yield more satisfactory system responses in an efficient way.

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