Structure Analysis of Simplest Fuzzy Controllers Using Generalized Trapezoid Shaped Input Membership Functions
Meng Xian-yao · Mohu xitong yu shuxue · 2008
The Generalized Trapezoid Shaped (GTS) membership functions, more universal than any other linear ones, of input variables of fuzzy controllers are well defined on the basis of distilling the commonness of triangular and trapezoid fuzzy sets. Based on obtaining the explicit analytical expression of the two-dimensional simplest fuzzy controller with the input space using Consistent GTS(CGTS) fuzzy partition, analytical structure of CGTS fuzzy controller is deeply researched and it is proved that the fuzzy controller is equivalent to be variable structure combinations of linear PI controller and constant control offset. Moreover, the output of the fuzzy controller is monotone increasing, continuous and bounded with regard to the corresponding universe of discourse. Simultaneously, the better universality of this type of fuzzy controller is revealed.