Fuzzy controller structure transformation

In the application of Fuzzy Control in technical processes one is faced with the task to design controller with more than two input variables and a different number of partitioning sets. However, for complete rule based systems the number of rules raises drastically with the number of input variables. Hence, reduction of the structure is necessary leading to hierarchical control. In our paper the transformation of a high-dimensional controller to a cascaded two-dimensional controller is demonstrated. There are two restrictions to be fulfilled, as well. First, the rule basis of the transformed structure must be consistent with the high dimensional one. Second, the output signal value of the controller must be consistent with the high dimensional controller. The paper gives the results of investigations regarding the conditions for fulfillment of the restrictions formulated above. For this, it is necessary to define dominant and non-dominant input variables as well as virtual variables. The number of sets for the virtual variables will be discussed. The cascaded controller will be described by two-dimensional characteristic fields which are suited for the interpretation.