Symbolic analysis and synthesis of linguistic parametrizations in fuzzy controllers

Analytical formulas for the transfer characteristic of several SISO fuzzy controllers are developed using a computer algebra system. Different formulations of the linguistic output variables and different inference methods can be compared with respect to their impact on control characteristics. The offline-defuzzyfication strategy resulting in singletons as output attributes already frequently used in practice is theoretically supported. The example of a fuzzy PI controller with two input variables show the application of the proposed method to the systematic design of fuzzy controllers