Control Curve Design for Nonlinear (or Fuzzy) Proportional Actions Using Spline-based Functions

Abstract

This work explores a novel approach fora systematic design of a nonlinear mapping system typicallyfor nonlinear, or fuzzy, PID control applications. The paper investigates a nonlinear design of proportionalactions using spline-based functions. Specifically, the controller uses Bézier curves to formthe nonlinear mapping in order to emulate fuzzy PID systems. While other researchers have addressed the fuzzy systemsfor approximations of given functions, we believethat, in general control problems, these approximationsshould be considered in dealing with the properties of unknowncontrol actions. Proportional action is selected asa 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.