As a mathematical model to represent the dynamics of a plant to be controlled, the T‐S fuzzy model is widely used in the control system design. In order to facilitate controller design, it sometimes needs suitable coordinate transformations of the T‐S fuzzy model. Subsequently, some questions arise: (1) can local systems in different fuzzy rules perform different coordinate transformations? if yes, then (2) is the transformed T‐S fuzzy model equivalent to its original one? In answering these questions, this paper at first gives a brief review on the T‐S fuzzy model to catch the real meaning of local systems in the context of the whole system expressed by the T‐S fuzzy model. Then, bearing controller design in mind it discusses the equivalence between pre‐ and transformed systems in various types of T‐S fuzzy models. Finally, in order to share the benefits from the results discussed in this paper, a controller design based on an affine T‐S fuzzy model is provided. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

中文翻译：

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关于TS模糊模型坐标转换的一些问题

作为代表要控制的工厂动态的数学模型，TS模糊模型已广泛用于控制系统设计中。为了简化控制器设计，有时需要对TS模糊模型进行适当的坐标转换。随后，出现了一些问题：（1）不同模糊规则的局部系统可以执行不同的坐标转换吗？如果是，则（2）变换后的TS模糊模型是否等于其原始模型？在回答这些问题时，本文首先简要回顾一下TS模糊模型，以在TS模糊模型所表示的整个系统的背景下捕捉局部系统的实际含义。然后，考虑到控制器的设计，它讨论了各种类型的TS模糊模型中预变换系统和变换系统之间的等效性。最后，为了从本文讨论的结果中共享收益，提供了基于仿射TS模糊模型的控制器设计。©2020日本电气工程师学会。由John Wiley＆Sons，Inc.发布