{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:07:07Z","timestamp":1787029627622,"version":"build-2736575974"},"reference-count":44,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2023,11,9]],"date-time":"2023-11-09T00:00:00Z","timestamp":1699488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52005478"],"award-info":[{"award-number":["52005478"]}]},{"name":"National Natural Science Foundation of China","award":["2022215"],"award-info":[{"award-number":["2022215"]}]},{"name":"Youth Innovation Promotion Association, Chinese Academy of Sciences","award":["52005478"],"award-info":[{"award-number":["52005478"]}]},{"name":"Youth Innovation Promotion Association, Chinese Academy of Sciences","award":["2022215"],"award-info":[{"award-number":["2022215"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents an interval type-2 fuzzy proportional\u2013integral\u2013derivative (IT2F-PID) controller that is designed using a new disassembled gradational optimization (D-GO) method. A PID controller is first optimized using the D-GO method and then connected to a type-1 fuzzy logic system (T1-FLS). The parameters of the T1-FLS are optimized, and the T1-FLS is blurred into the interval type-2 fuzzy logic system (IT2-FLS). Finally, the IT2F-PID controller is formed. The proposed method is compared with the concurrent and general optimization methods. The simulation results show that the D-GO method reduces the optimization time by over 90% compared with the general method, and decreases the integral-of-time-absolute-error (ITAE) by 30%. Beyond that, compared with the concurrent optimization method, the D-GO method reduces time by over 25%, and the ITAE value by about 95%. In the normal case, model uncertainty, target uncertainty, and external disturbance, the control ability of the IT2F-PID controller designed using the D-GO method is verified via simulations using a nonlinear forced closed-loop system. The results show that the overshoot is reduced by 80% and the fluctuation is reduced by 67% compared with a traditional PID controller and an IT2F-PID controller built using the general method.<\/jats:p>","DOI":"10.3390\/s23229067","type":"journal-article","created":{"date-parts":[[2023,11,9]],"date-time":"2023-11-09T10:19:27Z","timestamp":1699525167000},"page":"9067","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Interval Type-2 Fuzzy PID Controller Using Disassembled Gradational Optimization"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7715-5227","authenticated-orcid":false,"given":"Yongzhi","family":"Chu","sequence":"first","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, No. 3888, Dong Nanhu Road, Changchun 130033, China"},{"name":"Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"CAS Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hasiaoqier","family":"Han","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, No. 3888, Dong Nanhu Road, Changchun 130033, China"},{"name":"Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianjiao","family":"Ma","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, No. 3888, Dong Nanhu Road, Changchun 130033, China"},{"name":"Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingchao","family":"Zhu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, No. 3888, Dong Nanhu Road, Changchun 130033, China"},{"name":"Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhongcan","family":"Li","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, No. 3888, Dong Nanhu Road, Changchun 130033, China"},{"name":"Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4120-2448","authenticated-orcid":false,"given":"Zhenbang","family":"Xu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, No. 3888, Dong Nanhu Road, Changchun 130033, China"},{"name":"Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingwen","family":"Wu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, No. 3888, Dong Nanhu Road, Changchun 130033, China"},{"name":"Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"CAS Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0959-1524(02)00062-8","article-title":"Simple analytic rules for model reduction and PID controller tuning","volume":"13","author":"Skogestad","year":"2003","journal-title":"J. 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