{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T21:54:55Z","timestamp":1775858095680,"version":"3.50.1"},"reference-count":68,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61876041"],"award-info":[{"award-number":["61876041"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hong Kong RGC","award":["CityU 11207823"],"award-info":[{"award-number":["CityU 11207823"]}]},{"name":"Hong Kong RGC","award":["CityU 11203321"],"award-info":[{"award-number":["CityU 11203321"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Automat. Contr."],"published-print":{"date-parts":[[2025,1]]},"DOI":"10.1109\/tac.2024.3417717","type":"journal-article","created":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T18:28:59Z","timestamp":1718994539000},"page":"34-49","source":"Crossref","is-referenced-by-count":25,"title":["Maximization of Gain\/Phase Margins by PID Control"],"prefix":"10.1109","volume":"70","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8513-5577","authenticated-orcid":false,"given":"Qi","family":"Mao","sequence":"first","affiliation":[{"name":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2219-7732","authenticated-orcid":false,"given":"Yong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7330-3040","authenticated-orcid":false,"given":"Jianqi","family":"Chen","sequence":"additional","affiliation":[{"name":"Center for Advanced Control and Smart Operations (CACSO), Nanjing University, Suzhou, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3171-1887","authenticated-orcid":false,"given":"Jie","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, City University of Hong Kong, Hong Kong, SAR, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0012-5447","authenticated-orcid":false,"given":"Tryphon T.","family":"Georgiou","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1080\/00207178008922838"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0093318"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1080\/00207178208932897"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1985.1103805"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(86)90038-5"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(86)90122-2"},{"key":"ref7","volume-title":"Feedback Control Theory","author":"Doyle","year":"2013"},{"key":"ref8","volume-title":"Network Analysis and Feedback Amplifier Design","author":"Bode","year":"1945"},{"key":"ref9","volume-title":"Synthesis of Feedback Systems","author":"Horowitz","year":"1963"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1115\/1.4019264"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(86)90115-9"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.1989.70439"},{"key":"ref13","volume-title":"PID Controllers: Theory, Design, and Tuning","volume":"2","author":"strm","year":"1995"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/87.508897"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2003.1240451"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2004.01.002"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2006.876913"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2008.11.021"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1115\/1.3653115"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1977.1101470"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1978.1101812"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1981.1102603"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/9.388685"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1987.1104675"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/9.1310"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.1988.194633"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2016.2621438"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2019.108790"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/9.983352"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2018.2853567"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3059155"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00257-6"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2013.06.001"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2017.08.1166"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/LCSYS.2019.2915306"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2020.3030876"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2017.2695981"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109185"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2014.07.002"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2022.3154347"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.cels.2016.01.004"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1321-1"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2122132119"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-29640-7"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/ICCD.2015.7357079"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1109\/MysuruCon55714.2022.9972504"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(94)00130-B"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2003.08.005"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1093\/nsr\/nwx048"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1946-08668-1"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/003"},{"key":"ref52","volume-title":"Nonlinear Programming","author":"Bertsekas","year":"2016"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0793-1"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1109\/CDC45484.2021.9683241"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.900824"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2016.2584007"},{"key":"ref57","volume-title":"Modern Control Systems","author":"Richard","year":"2010"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/9.718613"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1109\/9.863595"},{"key":"ref60","first-page":"13","article-title":"Sums of arctangents and some formulas of Ramanujan","volume":"10","author":"Boros","year":"2005","journal-title":"SCIENTIA Ser. A: Math. Sci."},{"key":"ref61","article-title":"Classical stability margins by PID control","author":"Mao","year":"2023"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2014.02.020"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1016\/S0959-1524(02)00017-3"},{"key":"ref64","volume-title":"Adv. PID Control","volume":"461","author":"strm","year":"2006"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2023.110974"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12678-3"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.2307\/3109807"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2016.2645758"}],"container-title":["IEEE Transactions on Automatic Control"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/9\/10818614\/10568309.pdf?arnumber=10568309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T19:58:41Z","timestamp":1735675121000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10568309\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":68,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/tac.2024.3417717","relation":{},"ISSN":["0018-9286","1558-2523","2334-3303"],"issn-type":[{"value":"0018-9286","type":"print"},{"value":"1558-2523","type":"electronic"},{"value":"2334-3303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]}}}