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Equivalent linearization of 2-way fuzzy adaptive system under nonparametric uncertainty and inconsistency

Gurkan, E
Banks, SP
Erkmen, Aydan Müşerref
Erkmen, İsmet
Our aim in this paper is to design a 2-way fuzzy adaptive controller for a flexible robot arm and to analyze the stability of this controller using describing function technique. The 2-way fuzzy adaptive system is used in order to model the nonparametric uncertainties and inconsistencies present in the nonlinear system. The use of intuitionistic fuzzy sets in the 2-way fuzzy adaptive structure makes it possible to model such uncertainties. The proposed architecture is used as a controller for a flexible-joint robot arm. In designing such a controller, we have used approximating sequences method to obtain the parameters of the 2-way fuzzy adaptive controller. The stability of the 2-way fuzzy adaptive controller is analyzed using the describing function technique. The describing functions for the 2-way fuzzy adaptive system are evaluated for the two boundaries of the uncertainty interval, which is modeled as the uncertainty width with the necessity (membership functions) at the lower bound and the possibility (1-nonmembership functions) at the upper bound. The segment lemma is used for the analysis of stability for this interval-valued describing function.