Abstract
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.
Highlights
Proportional-Integral-Derivative (PID) controllers are widely used in industrial process control.The three-mode controller contains a proportional, an integral, and a derivative term
A conventional PID controller design for P(s) with K P = 1.2, K I = 0.36, and K D = 1, which was simulated by Simulink is shown in Figure 4, and the PID controller can simultaneously improve system responses in rise time, settling time, steady-state error, and overshoot
The derived equivalence equation is straightforward, so a well-designed conventional PID controller can be transformed to an equivalent fuzzy logic controller (FLC) by defining the input/output operating ranges and following the Sugeno-style inference
Summary
Proportional-Integral-Derivative (PID) controllers are widely used in industrial process control. The three-mode controller contains a proportional, an integral, and a derivative term. The popularity of a PID controller can be attributed to its good performance and functional simplicity, which allows engineers to operate it in a simple and straightforward manner. For simplicity of the controller design, a PI or PD controller are popular for practical applications. A PI controller can add damping to a system and reduce steady-state error, but yields penalized rise time and settling time. A PD controller adds damping and reliably predicts and reduces large overshoots, but does not improve the steady-state error. For complete design considerations, a PID controller should be employed to obtain a desirable system response in settling time, steady-state error, and overshoot
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