Calibration of fuzzy control systems

Fuzzy control systems (FCS) are usually designed through linguistic control rules and the operations among the fuzzy sets that define the fuzzy controller deal with fuzzy logic. However, the configuration and tuning of this kind of system represents a problem, although the modelling of the expert knowledge seems easy. Incoherences, non-completeness or control action inconsistencies may appear when the formulation of each rule is independent. The authors present a different philosophy to analyze a FCS configuration. The control system is studied as a control function defined by its inference map. The linguistic terms, membership functions and control rules selection, determine the characteristics of this map, so it may be possible to estimate its appearance according to these factors and to use their information successfully. The contrast between the non-linearity of a FCS and its closer linear (PID) controller, allows the control engineer to study strange situations deriving from an incorrect configuration. Among the techniques to estimate this contrast, measures for singularities detection and for asymmetries, rules dispersion and entropy measurement are used