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Derivation and structural analysis of a three-input interval type-2 TS fuzzy PID controller

  • Fuzzy systems and their mathematics
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Abstract

Showing superior performance in many areas, interval type-2 (IT2) fuzzy control has received wide acceptability in the last few years. The improved performance is mainly by virtue of the footprint of uncertainty (FoU) underlying the IT2 fuzzy sets. But the design of IT2 fuzzy controllers remains a challenging task since the FoU increases the computational complexity. We propose in this paper a simplified structure of a novel three-input IT2 Takagi–Sugeno (TS) fuzzy PID controller, a parallel combination of fuzzy PI and fuzzy PD controllers having two inputs, respectively. A novel TS rule base is presented which incorporates uncertainty in both input IT2 fuzzy sets and the rule consequent parameters. The rule base consists of two rules that are logically connected with algebraic product (AP) triangular norm and bounded sum (BS) triangular co-norm. AP and BS operators enable the simplification of the input plane, which in turn reduces the complexity of the controller structure. The effect of FoU on the controller structure is fully investigated. Further, we present the simulation studies on magnetic levitation (MagLev) and cart-pole systems to demonstrate the applicability of the proposed fuzzy PID controller.

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Acknowledgements

This research was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2018R1A5A1025137) and in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2021R1I1A3040696).

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Authors and Affiliations

  1. Department of Electronics & Communication Engineering, Indian Institute of Information Technology (IIIT) Kota, Rajasthan, India

    Ritu Raj

  2. Department of Electrical Engineering, Indian Institute of Technology (IIT) Kharagpur, West Bengal, India

    B. M. Mohan

  3. School of Architecture and Civil Engineering, Kyungpook National University, Daegu, 41566, Republic of Korea

    Dong-Eun Lee

  4. School of Electronics Engineering, Kyungpook National University, Daegu, 41566, Republic of Korea

    Jung-Min Yang

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  1. Ritu Raj
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  2. B. M. Mohan
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Correspondence to Jung-Min Yang.

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Raj, R., Mohan, B.M., Lee, DE. et al. Derivation and structural analysis of a three-input interval type-2 TS fuzzy PID controller. Soft Comput 26, 589–603 (2022). https://doi.org/10.1007/s00500-021-06601-8

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