An Automatic Building Approach To Special Takagi‐Sugeno Fuzzy Network For Unknown Plant Modeling And Stable Control

Abstract

ABSTRACTIn previous studies, several stable controller design methods for plants represented by a special Takagi‐Sugeno fuzzy network (STSFN) have been proposed. In these studies, the STSFN is, however, derived directly from the mathematical function of the controlled plant. For an unknown plant, there is a problem if STSFN cannot model the plant successfully. In order to address this problem, we have derived a learning algorithm for the construction of STSFN from input‐output training data. Based upon the constructed STSFN, existing stable controller design methods can then be applied to an unknown plant. To verify this, stable fuzzy controller design by parallel distributed compensation (PDC) method is adopted. In PDC method, the precondition parts of the designed fuzzy controllers share the same fuzzy rule numbers and fuzzy sets as the STSFN. To reduce the controller rule number, the precondition part of the constructed STSFN is partitioned in a flexible way. Also, similarity measure together with merging operation between each neighboring fuzzy set are performed in each input dimension to eliminate the redundant fuzzy sets. The consequent parts in STSFN are designed by correlation measure to select only the significant input terms to participate in each rule's consequence and reduce the network parameters. Simulation results in the cart‐pole balancing system have shown that with the proposed STSFN building approach, we are able to model the controlled plant with high accuracy and, in addition, can design a stable fuzzy controller with small parameter number.