Overview The design process for fuzzy controllers that is based on the use of heuristic information from human experts has found ess in many industrial applications. Moreover, the approach to constructing fuzzy controllers via numerical input-output data is increasingly finding use. Regardless of which approach is used, however, there are certain problems that are encountered for practical control problems, including the following: (1) The design of fuzzy controllers is performed in an ad hoc manner so it is often difficult to choose at least some of the controller parameters. For example, it is sometimes difficult to know how to pick the membership functions and rule-base to meet a specific desired level of performance. (2) The fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur, or if there is noise or some type of disturbance or some other environmental effect. Hence, it may be difficult to perform the initial synthesis of the fuzzy controller, and if the plant changes while the closed-loop system is operating we may not be able to maintain adequate performance levels. As an example, we showed how our heuristic knowledge can be used to design a fuzzy controller for the rotational inverted pendulum. However, we also showed that if a bottle half-filled with water is attached to the endpoint, the performance of the fuzzy controller degraded. While we certainly could have tuned the controller for this new situation, it would not then perform as well without a b
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