{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:26:26Z","timestamp":1760171186191,"version":"3.38.0"},"reference-count":28,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2020,12,20]],"date-time":"2020-12-20T00:00:00Z","timestamp":1608422400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100012166","name":"national key research and development program of china","doi-asserted-by":"publisher","award":["2018YFB0905500"],"award-info":[{"award-number":["2018YFB0905500"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"national key research and development program of china","doi-asserted-by":"publisher","award":["2018YFB0905503"],"award-info":[{"award-number":["2018YFB0905503"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Key Fund for Equipment Pre-research of China under Grant","award":["61407210206"],"award-info":[{"award-number":["61407210206"]}]}],"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":[[2021,8]]},"abstract":"<jats:p> Vernier-gimballing magnetically suspended flywheel is often used for attitude control and interference suppression of spacecrafts. Due to the special structure of the conical magnetic bearing, the radial component generated by the axial magnetic force and the change of the magnetic air gap will cause the nonlinearity of stiffness and disturbance. That will lead to not only poor stability of the suspension control system but also unsatisfactory tracking accuracy of the rotor position. To solve the nonlinear problem of the system, this article proposes a proportional\u2013integral\u2013derivative neural network control scheme. First, the rotor model considering the nonlinear variation of disturbance and stiffness parameters is established. Then, the weight of neural network is adjusted by the gradient descent method online to ensure the accurate output of magnetic force. Finally, the convergence analysis is carried out based on the Lyapunov stability theory. Compared with the general proportional\u2013integral\u2013derivative control and the radial basis function neural network control, the simulation results demonstrate that the proposed method has the highest tracking accuracy and excellent performance in improving stability. The experimental results prove the correctness of the theoretical analysis and the validity of the proposed method. <\/jats:p>","DOI":"10.1177\/0959651820977572","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T07:03:39Z","timestamp":1608534219000},"page":"1100-1112","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["PIDNN control for Vernier-gimballing magnetically suspended flywheel under nonlinear change of stiffness and disturbance"],"prefix":"10.1177","volume":"235","author":[{"given":"Jiqiang","family":"Tang","sequence":"first","affiliation":[{"name":"School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9395-7551","authenticated-orcid":false,"given":"Mengyue","family":"Ning","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing, China"}]},{"given":"Xu","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0422-4530","authenticated-orcid":false,"given":"Tongkun","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Optoelectronics 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 Optoelectronics Engineering, Beihang University, Beijing, China"}]}],"member":"179","published-online":{"date-parts":[[2020,12,20]]},"reference":[{"key":"bibr1-0959651820977572","doi-asserted-by":"publisher","DOI":"10.2514\/1.55984"},{"key":"bibr2-0959651820977572","doi-asserted-by":"publisher","DOI":"10.2514\/1.G002925"},{"key":"bibr3-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.mee.2006.01.248"},{"key":"bibr4-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2005.12.002"},{"key":"bibr5-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1109\/TMAG.2009.2022178"},{"key":"bibr6-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2015.04.008"},{"key":"bibr7-0959651820977572","unstructured":"Fang J, Sun J, Fan Y. Magnetically suspended inertial momentum wheel technology. Beijing, China: National Defense Industry Press, 2012, pp.6\u201312."},{"key":"bibr8-0959651820977572","doi-asserted-by":"publisher","DOI":"10.2514\/1.32092"},{"key":"bibr9-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2005.05.004"},{"key":"bibr10-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2015.05.011"},{"key":"bibr11-0959651820977572","doi-asserted-by":"publisher","DOI":"10.2514\/1.G001258"},{"volume-title":"Proceedings of the ASME international mechanical engineering congress and exposition","author":"Farmakopoulos MG","key":"bibr12-0959651820977572"},{"key":"bibr13-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2005.859824"},{"key":"bibr14-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2016.2636213"},{"first-page":"3942","volume-title":"Proceedings of the 42nd IEEE international conference on decision and control","author":"Sivrioglu S","key":"bibr15-0959651820977572"},{"key":"bibr16-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2010.0237"},{"key":"bibr17-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2009.2018433"},{"key":"bibr18-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2012.11.002"},{"key":"bibr19-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2016.04.022"},{"key":"bibr20-0959651820977572","unstructured":"Combrinck A. Adaptive control of an active magnetic bearing flywheel system using neural networks. MS Thesis, North-West University, Kirkland, WA, 2010."},{"key":"bibr21-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1177\/0959651818813625"},{"key":"bibr22-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126618500652"},{"key":"bibr23-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2018.12.036"},{"key":"bibr24-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2020.2987912"},{"journal-title":"Design method and experimental research of high load ratio and low power magnetic bearing for inertial actuator","year":"2014","author":"Wang C","key":"bibr25-0959651820977572"},{"key":"bibr26-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2014.03.009"},{"key":"bibr27-0959651820977572","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2018.07.036"},{"key":"bibr28-0959651820977572","unstructured":"Shu H. PID neural network and its control system. 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