Mohan B M, Patel A V
Dept. of Electr. Eng., Indian Inst. of Technol., Kharagpur.
IEEE Trans Syst Man Cybern B Cybern. 2002;32(2):239-48. doi: 10.1109/3477.990881.
This paper deals with simplest fuzzy PD controllers which employ only two fuzzy sets on the universe of discourse of each input variable, and three fuzzy sets on the universe of discourse of output variable. First, analytical structures of the simplest fuzzy PD controllers are derived via triangular membership functions for fuzzification, intersection T-norm, Lukasiewicz OR and Zadeh (1965) OR T-conorms, Mamdani's minimum, Larsen's product and drastic product inference methods, and center of area method for defuzzification. Properties of such fuzzy PD controllers are investigated. Based on these properties a comparative study is made on fuzzy controllers derived, and also on the fuzzy controllers and their counterpart-conventional linear PD controller. Finally, sufficient conditions for bounded-input bounded-output stability of fuzzy PD control systems are established using the well known small gain theorem.
本文研究了最简单的模糊PD控制器，该控制器在每个输入变量的论域上仅采用两个模糊集，在输出变量的论域上采用三个模糊集。首先，通过用于模糊化的三角隶属函数、交T范数、卢卡西维茨或运算和扎德（1965）或运算T余范数、Mamdani极小值、Larsen乘积和剧烈乘积推理方法以及用于去模糊化的面积中心法，推导了最简单模糊PD控制器的解析结构。研究了此类模糊PD控制器的特性。基于这些特性，对所推导的模糊控制器以及模糊控制器与其对应的传统线性PD控制器进行了比较研究。最后，利用著名的小增益定理建立了模糊PD控制系统有界输入有界输出稳定性的充分条件。
