{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T01:49:17Z","timestamp":1778636957721,"version":"3.51.4"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,6,25]],"date-time":"2018-06-25T00:00:00Z","timestamp":1529884800000},"content-version":"vor","delay-in-days":175,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61703335"],"award-info":[{"award-number":["61703335"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>This paper presents a novel fractional\u2010order PID controller tuning strategy based on Bode\u2019s optimal loop shaping which is commonly used for LTI feedback systems. Firstly, the controller parameters are achieved based on flat phase property and Bode\u2019s optimal reference model, so that the controlled system is robust to gain variations and can achieve desirable transient performance according to various control requirements. Then, robustness analysis of the controlled system is carried out to support the results. Furthermore, the parameter setting is analyzed to demonstrate the superiority of the proposed controller. At last, some simulation examples are shown to verify the accuracy and usefulness of the proposed control strategy. The proposed fractional\u2010order PID controller does not have any restriction on the controlled plant, so it can be widely applied on both integer\u2010order and fractional\u2010order systems.<\/jats:p>","DOI":"10.1155\/2018\/6570560","type":"journal-article","created":{"date-parts":[[2018,6,25]],"date-time":"2018-06-25T23:32:38Z","timestamp":1529969558000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Robust Fractional\u2010Order PID Controller Tuning Based on Bode\u2019s Optimal Loop Shaping"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3179-1004","authenticated-orcid":false,"given":"Lu","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2824-618X","authenticated-orcid":false,"given":"Shuo","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,6,25]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1515\/9783110497977"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2007.08.006"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2018.01.025"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2014.09.012"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/3273408"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2014.10.001"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2015.07.077"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1615\/CritRevBiomedEng.v32.10"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/jetcas.2013.2265797"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.07.023"},{"key":"e_1_2_9_11_2","volume-title":"PID controllers: Theory, Design and Tuning","author":"Strm K. 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