{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T22:16:33Z","timestamp":1767651393801,"version":"3.38.0"},"reference-count":24,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2018,11,23]],"date-time":"2018-11-23T00:00:00Z","timestamp":1542931200000},"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":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:p> Vernier-gimballing magnetically suspended flywheel with conical hybrid magnetic bearing can produce gyro moment by tilting the rotational rotor around a certain radial direction. When rotor is tilted, the nonlinear variation of conical magnetic bearing\u2019s displacement stiffness and the coupling interference can result in not only poor stability of suspension control system but also precision\u2019s degradation of gyro moment. To solve these two problems, the forces acting on tilted rotor are analyzed, and furthermore, a nonlinear model considering variation of displacement stiffness is constructed accordingly, then a radial basis function neural network is utilized to estimate the nonlinear variation of displacement stiffness and disturbance, and the adaptive controller with nonlinear variation compensation is presented based on the Lyapunov stability theory. Compared with cross-feedback method in tilting control and proportional\u2013integral\u2013derivative method in translation control, simulation researches are done, and the results indicate that the presented control method does well in estimating nonlinear variation and has better performances on suspension control when rotor is tilted. <\/jats:p>","DOI":"10.1177\/0959651818813625","type":"journal-article","created":{"date-parts":[[2018,11,24]],"date-time":"2018-11-24T06:01:03Z","timestamp":1543039263000},"page":"1017-1029","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["Adaptive neural network control for rotor\u2019s stable suspension of Vernier-gimballing magnetically suspended flywheel"],"prefix":"10.1177","volume":"233","author":[{"given":"Jiqiang","family":"Tang","sequence":"first","affiliation":[{"name":"School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1768-4608","authenticated-orcid":false,"given":"Xiaofeng","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8835-6674","authenticated-orcid":false,"given":"Ying","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing, China"}]},{"given":"Xu","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing, China"}]}],"member":"179","published-online":{"date-parts":[[2018,11,23]]},"reference":[{"key":"bibr1-0959651818813625","doi-asserted-by":"publisher","DOI":"10.1109\/62.707557"},{"volume-title":"Studies on the attitude determination and control system of high precision three-axis stabilized satellite","year":"2002","author":"Qian Y.","key":"bibr2-0959651818813625"},{"key":"bibr3-0959651818813625","doi-asserted-by":"publisher","DOI":"10.4283\/JMAG.2013.18.4.432"},{"key":"bibr4-0959651818813625","first-page":"1","volume":"680","author":"Xie Y","year":"2001","journal-title":"Inst Space Astronaut Sci Rep"},{"key":"bibr5-0959651818813625","doi-asserted-by":"publisher","DOI":"10.1063\/1.1452673"},{"key":"bibr6-0959651818813625","doi-asserted-by":"crossref","unstructured":"Schweitzer G, Maslen EH. 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