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| Derivation and analysis on the analytical structure of interval type-2 fuzzy controller with two nonlinear fuzzy sets for each input variable |
| Bin-bin Lei, Xue-chao Duan, Hong Bao, Qian Xu |
| MOE Key Laboratory of Electronic Equipment Structure Design, Xidian University, Xi'an 710071, China; Xinjiang Observatory, National Astronomical Observatories, Chinese Academy of Sciences, Urumqi 830011, China |
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Abstract Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical structure of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a type-2 fuzzy controller functions and lay a foundation for more rigorous system analysis and design. In this study, we derive and analyze the analytical structure of an interval type-2 fuzzy controller that uses the following identical elements: two nonlinear interval type-2 input fuzzy sets for each variable, four interval type-2 singleton output fuzzy sets, a Zadeh AND operator, and the Karnik-Mendel type reducer. Through dividing the input space of the interval type-2 fuzzy controller into 15 partitions, the input-output relationship for each local region is derived. Our derivation shows explicitly that the controller is approximately equivalent to a nonlinear proportional integral or proportional differential controller with variable gains. Furthermore, by comparing with the analytical structure of its type-1 counterpart, potential advantages of the interval type-2 fuzzy controller are analyzed. Finally, the reliability of the analysis results and the effectiveness of the interval type-2 fuzzy controller are verified by a simulation and an experiment.
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Received: 23 February 2016
Published: 06 June 2016
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每个输入具有两个非线性模糊集合的区间二型模糊控制器解析结构的推导与分析
题目：每个输入具有两个非线性模糊集合的区间二型模糊控制器解析结构的推导与分析
目的：针对具有非线性模糊集合的区间二型模糊控制器内部工作原理未知的问题，提出内部解析结构的推导方法，同时分析区间二型模糊控制器的特点和优势，为模糊控制器的系统设计提供理论指导。
创新点：首先，将区间二型模糊控制器的解析结构推导推广到了具有非线性模糊集合和扎德AND算子的区间二型模糊控制器。其次，分析了区间二型模糊控制器优于对应一型模糊控制器的原因。最后，通过结构分析为区间二型模糊控制器的不确定迹参数的调整提供了理论依据。
方法：首先，根据区间二型模糊控制器Karnik-Mendel降型方法的特点将整个模糊输入空间划分为若干分区（图6）。其次，在得到的每一个分区上，推导区间二型模糊控制器具体的输入输出函数表达式（式（31）、式（A8）‐（A21））。同时，证明了文中具有非线性模糊集合的区间二型模糊集合近似等效为具有变增益的非线性PI或PD控制器。然后，在得到的解析结构的基础上，从理论上分析了文中的区间二型模糊控制器的参数变化对控制性能的影响以及在超调量和上升时间方面优于对应一型模糊控制器的原因。最后，通过仿真实例和实验验证了上述理论分析的正确性和文中区间二型模糊控制器的有效性。
结论：文中提出的具有非线性模糊集合的区间二型模糊集合近似等效为具有变增益的非线性PI或PD控制器。
关键词：
区间二型模糊控制器,
解析结构,
Karnik-Mendel降型
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