Sain Debdoot, Mohan B M
Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, 721302, India.
ISA Trans. 2021 Apr;110:319-327. doi: 10.1016/j.isatra.2020.10.048. Epub 2020 Oct 18.
Though Center of Gravity (CoG) defuzzification is a well-known and long-standing method in the history of fuzzy systems, because of its computational complexity, its use in the field of modeling of fuzzy controllers is almost nil. From literature, it appears that modeling of fuzzy Proportional Integral Derivative (FPID) controllers is rarely attempted using CoG defuzzification. In fact, none of the FPID controller models are obtained using both two-dimensional input space and CoG defuzzification. The available mathematical models of fuzzy Proportional Integral (FPI) and fuzzy Proportional Derivative (FPD) controllers using two-dimensional input space and CoG defuzzification were due to Arun and Mohan (2017). In this paper, the authors make an attempt to model and design an FPID controller using two-dimensional input space and CoG defuzzification. The incremental control effort produced by the newly developed FPID controller is found by combining the individual control efforts produced by incremental FPI and incremental FPD controllers. The incremental FPI and incremental FPD controller structures are unveiled using two-dimensional input space, CoG defuzzification, Min t-norm, Max t-conorm, and Larsen Product (LP) inference. The applicability and usefulness of the newly obtained FPID controller are depicted with simulation and real-time experimentation.
尽管重心（CoG）去模糊化是模糊系统历史上一种广为人知且由来已久的方法，但由于其计算复杂性，它在模糊控制器建模领域的应用几乎为零。从文献来看，似乎很少有人尝试使用CoG去模糊化来对模糊比例积分微分（FPID）控制器进行建模。事实上，没有任何一个FPID控制器模型是通过二维输入空间和CoG去模糊化两者结合得到的。使用二维输入空间和CoG去模糊化的模糊比例积分（FPI）和模糊比例微分（FPD）控制器的现有数学模型是由Arun和Mohan（2017年）提出的。在本文中，作者尝试使用二维输入空间和CoG去模糊化对FPID控制器进行建模和设计。通过将增量FPI和增量FPD控制器产生的个体控制作用相结合，得出新开发的FPID控制器产生的增量控制作用。使用二维输入空间、CoG去模糊化、最小t - 范数、最大t - 余范数和拉森积（LP）推理揭示了增量FPI和增量FPD控制器的结构。通过仿真和实时实验描述了新得到的FPID控制器的适用性和实用性。
