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Fuzzy Control and Identification by John H. Lilly

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CHAPTER 5

MODELING AND CONTROL METHODS USEFUL FOR FUZZY CONTROL

Basic fuzzy control, unlike most control methods, is not based on a mathematical model of the process being controlled. This is one of the strengths of fuzzy control. However, more advanced fuzzy control methods, such as some types of parallel distributed compensation and fuzzy adaptive control, as well as fuzzy system identification, do require at least an assumption of some particular structure of the model. Some methods assume continuous-time linear or nonlinear state-space model structures while others assume discrete-time state space or input–output difference equation model structures.

We emphasize that a particular dynamic system can be modeled with any of these model structures, as will be demonstrated below. The particular structure used depends on the one required by the control or identification method. Therefore, we give a brief summary of several well-known model structures for dynamic systems.

5.1 CONTINUOUS-TIME MODEL FORMS

The four most common methods for describing continuous-time dynamic systems are the transfer function (for time-invariant linear systems), the impulse response (for time-varying or time-invariant linear systems), the input–output ordinary differential equation (for any type of continuous-time system), and the state-space description (for any type of system). Of these, only the linear or nonlinear time-invariant state-space descriptions are useful for fuzzy identification and control. ...

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