Input scaling factors in fuzzy control systems

The input scaling factors in a fuzzy control system are commonly used to conduct proper transformations between the real input data and the pre-specified universe of discourses of the fuzzy input variables in the system. Theoretically, they are constant parameters. However, it is noticed that, sometimes, they are also used to fine-tune the performance of the system in a similar way to the tuning of a PID controller. In this paper, the roles of the input scaling factors in a fuzzy control system are discussed. The firing of the rules in a fuzzy controller is shown with different values of the scaling factors to demonstrate the fact that the adjustment of the factors is equivalent to the re-construction of the membership functions in the rule-base. The results also suggest that such an adjustment should be done carefully if the linguistic meaning of the rule-base is to be preserved. An inverted pendulum system is used to verify the points raised