Control curve design for nonlinear (or fuzzy) proportional actions using spline-based functions

This work explores a novel approach for a systematic design of a nonlinear mapping system typically for nonlinear, or fuzzy, PID control applications. The paper investigates a non-Linear design of proportional actions using spline-based functions. Specifically, the controller uses Bezier curves to form the nonlinear mapping in order to emulate fuzzy PID systems. While other researchers have addressed the fuzzy systems for approximations of given functions, we believe that, in general control problems, these approximations should be considered in dealing with the properties of unknown control actions. Proportional action is selected as a basic function for nonlinear control curve designs. The reasons for this selection are discussed. Specific heuristic properties for the proportional action are defined based on the intuitions in general PID controller applications. The new controller is designed to be compatible with these properties. The nonlinearity variation index is used as a process-independent measure for evaluation of different designs. The system has been shown to improve the conventional fuzzy PID controllers on three aspects. These include a high degree of transparency with respect to nonlinear tuning parameters, versatility to cover various nonlinear functions, and simplicity of nonlinear mapping expressions. (C) 1998 Elsevier Science Ltd. All rights reserved.