There are several methods for modelling nonlinear systems. A main distinction can be made between global and local models. In this chapter we concentrate on approximation of a nonlinear system by a set of local linear models. Each local model is valid for a certain range of operating conditions and an interpolative scheduling mechanism combines the outputs of the local models into a continuous global output. Such a model structure can be conveniently represented by means of fuzzy If-Then rules.
Using membership functions, the antecedent of the rule defines a fuzzy region in the product space of the antecedent variables in which the rule is valid. The antecedent variables must convey information about the process operating conditions. The consequent of the rule is typically a local linear regression model. The overlap of the antecedent membership functions of different rules provides a smooth interpolation of the rules' consequents. Construction of a rule-based fuzzy model requires identification of the antecedent and consequent structure, of the membership functions for different operating regions and estimation of the consequent regression parameters. While the latter task can be solved using linear estimation techniques, the construction of the membership functions is a nonlinear optimisation problem. Several existing constructive techniques are reviewed in this chapter and a method based on fuzzy clustering is described in more detail. The presented approach does not require any prior knowledge about the operating regimes and also an appropriate number of rules can be determined automatically. If a sufficiently rich identification data set covering the operating ranges of interest is not available, the rules obtained from data can be combined with prior knowledge transformed into the membership functions for the relevant operating regions and the local models. The models provided by the user can also be nonlinear (semi)mechanistic models based on first principles. Examples are provided to illustrate the basic concepts of the described fuzzy modelling and identification techniques.