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.

重心去模糊化虽然是模糊系统历史上众所周知且长期存在的方法，但由于其计算复杂性，其在模糊控制器建模领域的应用几乎为零。从文献来看，似乎很少使用CoG去模糊来对模糊比例积分微分（FPID）控制器进行建模。实际上，使用二维输入空间和CoG去模糊化都无法获得FPID控制器模型。使用二维输入空间和CoG去模糊的模糊比例积分（FPI）和模糊比例微分（FPD）控制器的可用数学模型归功于Arun和Mohan（2017）。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控制器产生的各个控制工作结合起来，可以找到新开发的FPID控制器产生的增量控制工作。增量FPI和增量FPD控制器结构使用二维输入空间，CoG反模糊，Min t-范数，Max t-conorm和Larsen乘积（LP）推论来揭示。通过仿真和实时实验描述了新获得的FPID控制器的适用性和实用性。Max t-conorm和Larsen乘积（LP）推论。通过仿真和实时实验描述了新获得的FPID控制器的适用性和实用性。Max t-conorm和Larsen乘积（LP）推论。通过仿真和实时实验描述了新获得的FPID控制器的适用性和实用性。