{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T16:06:36Z","timestamp":1777910796890,"version":"3.51.4"},"reference-count":40,"publisher":"SAGE Publications","issue":"15","license":[{"start":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T00:00:00Z","timestamp":1674172800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p>\n                    In this paper, a practical fractional proportional\u2013integral and proportional\u2013derivative (PI\n                    <jats:sup>\u03bb<\/jats:sup>\n                    -PD\n                    <jats:sup>\u03bc<\/jats:sup>\n                    ) controller tuning method and a model reduction method are proposed for high-order systems with or without time delay. First, the Big Bang\u2013Big Crunch (BB-BC) algorithm and the time moment matching method are used to reduce the order of the high-order system function, and the approximate low-order system function is obtained. Second, the parameter region of fractional-order PI\n                    <jats:sup>\u03bb<\/jats:sup>\n                    -PD\n                    <jats:sup>\u03bc<\/jats:sup>\n                    controller is obtained according to the D partition method, and the improved weighted geometric center (WGC) method is introduced to select the special points in the stable region as the control parameters. Then, the fractional-order PI\n                    <jats:sup>\u03bb<\/jats:sup>\n                    controller is discretized by Muir method, and the fractional-order PD\n                    <jats:sup>\u03bc<\/jats:sup>\n                    controller is discretized by continued fraction expansion (CFE). Finally, the BB-BC algorithm is used to optimize the control parameters, and the parameters with better control performance are obtained. The simulation results show that the fractional PI\n                    <jats:sup>\u03bb<\/jats:sup>\n                    -PD\n                    <jats:sup>\u03bc<\/jats:sup>\n                    parameter setting method based on BB-BC algorithm can improve the control performance of the system, and the model reduction scheme based on the combination of moment matching method and BB-BC algorithm is effective in both time domain and frequency domain analysis.\n                  <\/jats:p>","DOI":"10.1177\/01423312221127742","type":"journal-article","created":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T06:23:12Z","timestamp":1674195792000},"page":"3098-3110","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Design of PI\n                    <sup>\u03bb<\/sup>\n                    -PD\n                    <sup>\u03bc<\/sup>\n                    controller for high-order systems based on model order reduction using BB-BC and time moment matching"],"prefix":"10.1177","volume":"47","author":[{"given":"Min","family":"Zheng","sequence":"first","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, China"},{"name":"Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0632-2786","authenticated-orcid":false,"given":"Peike","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haisheng","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2023,1,20]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2017.08.978"},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.buildenv.2021.108498"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2016.03.006"},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jare.2020.06.024"},{"key":"e_1_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2020.105786"},{"key":"e_1_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9445(2007)133:7(999)"},{"key":"e_1_3_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.02.052"},{"key":"e_1_3_2_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/MWSCAS.2013.6674587"},{"key":"e_1_3_2_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2005.04.005"},{"key":"e_1_3_2_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/JSEE.2012.00018"},{"key":"e_1_3_2_12_1","volume-title":"2012 IEEE symposium on robotics and applications","author":"Gong K","year":"2012","unstructured":"Gong K, Li W, Feng M, et al. 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