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

总结了应用最为广泛的三角形和梯形隶属函数的共同特点, 明确定义了一种将以上两种隶属函数作为特例的广义梯形 (Generalized trapezoid-shaped, GTS) 隶属函数, 推导了输入变量采用 GTS 隶属函数的 I 类和 II 类两维最简模糊控制器的解析式. 基于此, 深入研究了模糊控制器的解析结构, 并证明了这两类模糊控制器等价于一种变结构的非线性 (或线性) PI 控制器与相应的非线性 (或定常) 控制偏置之和, 并且在其输入论域上是单调递增、连续且有界的. 最后, 将该类控制器应用于倒立摆控制系统, 通过仿真证明了其有效性, 同时揭示了此类控制器是一种更一般化的模糊控制器.

Structure Analysis of Two-dimensional Simplest Fuzzy Controllers Using Generalized Trapezoid-shaped Input Membership Function

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.