采用非线性规则和不均匀分布的输入输出隶属函数时典型模糊控制器的结构分析

Structure Analysis of Typical Fuzzy Controllers with Nonlinear Rules and Unevenly Distributed Membership Functions for Input and Output Variables

针对两输入 (e,Δe)一输出 (Δu)的典型模糊控制器 ,其输入变量采用三角形、全交迭、对称、不均匀分布的隶属函数 ,输出变量采用对称、不均匀分布的单点隶属函数 ,当采用非线性控制规则和Sum Product推理方法时 ,推导了输出的解析表达式 ,分析了其结构特性和极限特性 ,证明了此类模糊控制器具有通用逼近性 。

A class of typical fuzzy controllers with two inputs and one output is defined in terms of nonlinear control rules, unevenly distributed input and output membership functions, Sum Product reasoning method, and weighted mean method for defuzzification. It is proved that the output of the controller is a combination of a global two dimensional multilevel relay and a local nonlinear controller. On this basis, the structure characteristics and limit characteristics of the typical fuzzy controllers are studied, the universal approximation capability of the typical fuzzy controllers is constructively proved. Finally, the local stability of typical fuzzy control systems is also discussed.