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

  • Authors:

  • B. -G. HU;G. K. I. MANN;R. G. GOSINE

  • Affiliations:

  • National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academicof Sciences, P.O. Box 2728, Beijing, 100080, People's Republic of China and Also at C-CORE, Memorial University ...;Also at C-CORE, Memorial University of Newfoundland, St. Johns, Canada. and Faculty of Engineering and Applied Science Memorial University of Newfoundland, St. Johns AIB 3X5 Canada.;Also at C-CORE, Memorial University of Newfoundland, St. Johns, Canada. and Faculty of Engineering and Applied Science Memorial University of Newfoundland, St. Johns AIB 3X5 Canada.

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1998

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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 Bezier 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.