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Modeling and Analysis of Mamdani Two-Term Controllers Using Non-Uniformly Distributed Multiple Fuzzy Sets and CoA/CoG Defuzzification
IETE Technical Review ( IF 2.4 ) Pub Date : 2021-06-02 , DOI: 10.1080/02564602.2021.1933628
Manoranjan Praharaj 1 , B. M. Mohan 1
Affiliation  

While fuzzy controllers with multiple fuzzy sets and non-uniformly distributed membership functions have the potential to provide better system performance, from the literature, it appears to the authors that till now, no one has found exact mathematical models of fuzzy PI/PD controllers with non-uniformly distributed multiple fuzzy sets and Center of Area (CoA) defuzzification. To bridge this gap, in this paper, analytical structures of the general Mamdani type fuzzy PI/PD controllers are presented using unequally distributed multiple fuzzy sets, Minimum (Min) t-norm, Maximum (Max) s-norm, Larsen Product (LP) inference, and CoA defuzzification. For the purpose of comparison, analytical structures of the controllers are also obtained using Center of Sums (CoS) defuzzification. Properties of the newly obtained controllers are analyzed and compared. Since digital computers are often used for simulation, a rough estimate of the computational complexities and memory requirements are provided. To show the applicability of the newly developed controllers, a nonlinear DC series motor and a nonlinear plant with dead-time are considered. The effectiveness of the proposed controllers is finally shown through a detailed system performance comparison. 



中文翻译:

使用非均匀分布的多重模糊集和 CoA/CoG 去模糊化的 Mamdani 两项控制器的建模和分析

虽然具有多个模糊集和非均匀分布隶属函数的模糊控制器有可能提供更好的系统性能,但从文献来看,在作者看来,到目前为止,还没有人找到精确的模糊 PI/PD 控制器的数学模型非均匀分布的多个模糊集和区域中心(CoA)去模糊化。为了弥补这一差距,在本文中,一般 Mamdani 型模糊 PI/PD 控制器的分析结构使用不均匀分布的多个模糊集、最小 (Min) t-范数、最大 (Max) s-范数、Larsen Product (LP ) 推理和 CoA 去模糊化。为了比较,控制器的分析结构也使用和中心(CoS)去模糊化获得。对新获得的控制器的性能进行了分析和比较。由于数字计算机通常用于模拟,因此提供了计算复杂性和内存需求的粗略估计。为了展示新开发的控制器的适用性,考虑了非线性直流串联电动机和具有死区时间的非线性设备。最终通过详细的系统性能比较显示了所提出控制器的有效性。 

更新日期:2021-06-02
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