Abstract
Appropriate Footprints of Uncertainty (FOUs) are crucial to the ability of Interval Type-2 (IT2) Fuzzy PI Controllers (FPICs) to deal with system uncertainty; hence how to quickly and accurately determine the right FOUs is important to the designer. In this research, the effects of increasing the difference between two FOUs of IT2 FPICs, on computing the firing intervals, on switch points of KM type-reducer and on close-form solution of output, are studied. It is proven that as the difference between two FOUs increases: around the convergence point, the control laws gradually become fewer; the number of combinations of switch points is gradually decreasing (the output form of the KM type-reducer will no longer change); the variable gain of IT2 FPIC Kp decreases monotonously, and Ki increases monotonously in input space. A guideline for designing FOUs is provided, as the difference increases. The position control experiments and simulations are carried out, in order to illustrate the presented findings.
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This work was supported in part by the National Key R&D Program of China [Grant Numbers 2017YFB1104800]; the National Natural Science Foundation of China [Grant Numbers 51975590].
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [CZ], [HZ], [ZL], [XJ], [ST] and [JD]. The first draft of the manuscript was written by [CZ] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Zhang, C., Zhou, H., Li, Z. et al. Analysis of the difference between footprints of uncertainty for interval type-2 fuzzy PI controllers. Soft Comput 26, 9993–10005 (2022). https://doi.org/10.1007/s00500-022-07386-0
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DOI: https://doi.org/10.1007/s00500-022-07386-0