Structure Analysis of Two-dimensional Simplest Fuzzy Controllers Using Generalized Trapezoid-shaped Input Membership Function
输入采用广义梯形隶属函数的两维最简模糊控制器结构分析

Being more universal than triangular and trapezoid membership functions, the generalized trapezoid-shaped (GTS) membership function of input variables of fuzzy controllers is well defined on the basis of distilling the commonness of triangular and trapezoid membership functions. Based on obtaining the explicit analytical expressions of the type I and type II two-dimensional simplest fuzzy controllers, analytical structures of fuzzy controllers are deeply researched. It is proved that these two types of fuzzy controllers are equivalent to the variable structural combinations of nonlinear (or linear) PI controller and nonlinear (or constant) control offset. Moreover, the outputs of these fuzzy controllers are monotonically increasing, continuous, and bounded with regard to the corresponding universe of discourse. Finally, the fuzzy controller is applied to an inverted pendulum control system, of which the simulation demonstrates its effectiveness and better universality.