{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T01:51:15Z","timestamp":1772761875588,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T00:00:00Z","timestamp":1734998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62173208"],"award-info":[{"award-number":["62173208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["tsqn202103061"],"award-info":[{"award-number":["tsqn202103061"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2019KJN036"],"award-info":[{"award-number":["2019KJN036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSTC 113-2221-E-006-145-MY2"],"award-info":[{"award-number":["NSTC 113-2221-E-006-145-MY2"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Taishan Scholar Project of Shandong Province of China","award":["62173208"],"award-info":[{"award-number":["62173208"]}]},{"name":"Taishan Scholar Project of Shandong Province of China","award":["tsqn202103061"],"award-info":[{"award-number":["tsqn202103061"]}]},{"name":"Taishan Scholar Project of Shandong Province of China","award":["2019KJN036"],"award-info":[{"award-number":["2019KJN036"]}]},{"name":"Taishan Scholar Project of Shandong Province of China","award":["NSTC 113-2221-E-006-145-MY2"],"award-info":[{"award-number":["NSTC 113-2221-E-006-145-MY2"]}]},{"name":"Shandong Qingchuang Science and Technology Program of Universities","award":["62173208"],"award-info":[{"award-number":["62173208"]}]},{"name":"Shandong Qingchuang Science and Technology Program of Universities","award":["tsqn202103061"],"award-info":[{"award-number":["tsqn202103061"]}]},{"name":"Shandong Qingchuang Science and Technology Program of Universities","award":["2019KJN036"],"award-info":[{"award-number":["2019KJN036"]}]},{"name":"Shandong Qingchuang Science and Technology Program of Universities","award":["NSTC 113-2221-E-006-145-MY2"],"award-info":[{"award-number":["NSTC 113-2221-E-006-145-MY2"]}]},{"name":"National Science and Technology Council (NSTC), Taiwan","award":["62173208"],"award-info":[{"award-number":["62173208"]}]},{"name":"National Science and Technology Council (NSTC), Taiwan","award":["tsqn202103061"],"award-info":[{"award-number":["tsqn202103061"]}]},{"name":"National Science and Technology Council (NSTC), Taiwan","award":["2019KJN036"],"award-info":[{"award-number":["2019KJN036"]}]},{"name":"National Science and Technology Council (NSTC), Taiwan","award":["NSTC 113-2221-E-006-145-MY2"],"award-info":[{"award-number":["NSTC 113-2221-E-006-145-MY2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetry is widely present in science and daily life. And the internal structure of surface-mounted permanent magnet synchronous motors (PMSMs) has good symmetry. This article is dedicated to studying the tracking problem of PMSMs with adaptive and backstepping control methods. The research objective of this study is to design new adaptive controllers Uq and Ud, which enable the state of the motor position servo system to asymptotically and stably track the given signals of the system. They can suppress the impact of changes in B, J, and TL and can also enhance the robustness of the system. (i) The strongly coupled current and speed, variation of parameters over time, and nonlinearity of motor torque objectively pose significant challenges in the design of adaptive tracking controllers for PMSMs. (ii) Adaptive control technology and backstepping control methods are used for designing controllers for the PMSMs. (iii) After rigorous reasoning, an intelligent adaptive tracking control strategy for the PMSMs has been derived, which is for the direct axis current and the angle. (iv) The new adaptive tracking controllers are superior to existing controllers in that they can strongly suppress the disturbance of system parameters J, TL, and B, make the system state asymptotically stable, and achieve good tracking performance for the given signals. The results of the simulation indicate the validity of the designed control strategy.<\/jats:p>","DOI":"10.3390\/sym17010002","type":"journal-article","created":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T09:00:57Z","timestamp":1735030857000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Adaptive Control Design of Permanent Magnet Synchronous Motor Systems with Uncertainties"],"prefix":"10.3390","volume":"17","author":[{"given":"Yutang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics Science, Liaocheng University, Liaocheng 252000, China"}]},{"given":"Jiaojiao","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Automation, Qufu Normal University, Qufu 273165, China"}]},{"given":"Zong-Yao","family":"Sun","sequence":"additional","affiliation":[{"name":"Institute of Automation, Qufu Normal University, Qufu 273165, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2254-723X","authenticated-orcid":false,"given":"Chih-Chiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan 70101, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103256","DOI":"10.1016\/j.mechatronics.2024.103256","article-title":"Magnetic equivalent circuit modeling of a permanent magnet linear synchronous motor composed of curved segments","volume":"104","author":"Fuchs","year":"2024","journal-title":"Mechatronics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102989","DOI":"10.1016\/j.simpat.2024.102989","article-title":"Electromagnetic torque modeling and validation for a permanent magnet spherical motor based on XGBoost","volume":"136","author":"Guo","year":"2024","journal-title":"Simul. 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