{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T23:41:49Z","timestamp":1769557309208,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T00:00:00Z","timestamp":1649894400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shenzhen Science and technology R&amp;D","award":["JCYJ20190809150603586"],"award-info":[{"award-number":["JCYJ20190809150603586"]}]},{"name":"National Key Program of China","award":["2018YFB2000103"],"award-info":[{"award-number":["2018YFB2000103"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2020-YB-022"],"award-info":[{"award-number":["2020-YB-022"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>At present, magnetic bearings are a better energy-saving choice than mechanical bearings in industrial applications. However, there are strongly coupled characteristics in magnetic bearing\u2013rotor systems with redundant structures, and uncertain disturbances in the electrical system as well as external disturbances, and these unfavorable factors degrade the performance of the system. To improve the anti-interference performance of magnetic bearing systems, this paper proposes the inverse of the current distribution matrix W\u22121 meaning that the active disturbance rejection control simulation model can be carried out without neglecting the current of each coil. Firstly, based on the working mechanism of magnetic bearings with redundant structures and the nonlinear electromagnetic force model, the current and displacement stiffness models of magnetic bearings are established, and a dynamic model of the rotor is constructed. Then, according to the dynamic model of the rotor and the mapping relationship between the current of each coil and the electromagnetic force of the magnetic bearing, we established the equivalent control loop of the magnetic bearing\u2013rotor system with redundant structures. Finally, on the basis of the active disturbance rejection control (ADRC) strategy, we designed a linear active disturbance rejection controller (LADRC) for magnetic bearings with redundant structures under the condition of no coil failure, and a corresponding simulation was carried out. The results demonstrate that compared to PID+current distribution control strategy, the LADRC+current distribution control strategy proposed in this paper is able to effectively improve the anti-interference performance of the rotors supported by magnetic bearings with redundant structures.<\/jats:p>","DOI":"10.3390\/s22083012","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T02:39:31Z","timestamp":1650335971000},"page":"3012","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Active Disturbance Rejection Control in Magnetic Bearing Rotor Systems with Redundant Structures"],"prefix":"10.3390","volume":"22","author":[{"given":"Baixin","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Mechanical & Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Hubei Maglev Engineering Technology Research Center, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7458-5345","authenticated-orcid":false,"given":"Xin","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Hubei Maglev Engineering Technology Research Center, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shao","family":"Song","sequence":"additional","affiliation":[{"name":"China Ship Development and Design Center, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huachun","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Hubei Maglev Engineering Technology Research Center, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Shenzhen Research Institute, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yefa","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Hubei Maglev Engineering Technology Research Center, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Shenzhen Research Institute, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rougang","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Hubei Maglev Engineering Technology Research Center, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Tang, J., Xu, X., and Huang, Z. (2021). Optimal design of magnetically suspended high-speed rotor in turbo-molecular pump. Vacuum, 193.","DOI":"10.1016\/j.vacuum.2021.110510"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2132","DOI":"10.1109\/TMECH.2016.2555858","article-title":"Suppression of Harmonic Current in Active\u2013Passive Magnetically Suspended CMG Using Improved Repetitive Controller","volume":"21","author":"Cui","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_3","first-page":"2284","article-title":"Multiobjective Optimization of a Combined Radial-Axial Magnetic Bearing for Magnetically Suspended Compressor","volume":"63","author":"Han","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2344","DOI":"10.1109\/TTE.2021.3079402","article-title":"A Combination 5-DOF Active Magnetic Bearing for Energy Storage Flywheels","volume":"7","author":"Li","year":"2021","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2304","DOI":"10.1109\/20.376229","article-title":"Fault tolerance of magnetic bearings by generalized bias current linearization","volume":"31","author":"Maslen","year":"1995","journal-title":"IEEE Trans. Magn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1115\/1.1303072","article-title":"Optimized realization of fault-tolerant heteropolar magnetic bearings","volume":"122","author":"Na","year":"2000","journal-title":"J. Vib. Acoust."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1115\/1.1467652","article-title":"Test and theory correlation study for a flexible rotor on fault-tolerant magnetic bearings","volume":"124","author":"Na","year":"2002","journal-title":"J. Vib. Acoust."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1109\/TMECH.2005.859830","article-title":"Design and implementation of a fault-tolerant magnetic bearing system for Turbo-Molecular Vacuum Pump","volume":"10","author":"Noh","year":"2005","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Meeker, D. (2017). A generalized unbiased control strategy for radial magnetic beatings. Actuators, 6.","DOI":"10.3390\/act6010001"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3939","DOI":"10.1109\/20.914343","article-title":"Fault tolerance of magnetic bearings with material path reluctances and fringing factors","volume":"36","author":"Na","year":"2000","journal-title":"IEEE Trans. Magn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1007\/BF02916122","article-title":"Fault tolerant control of magnetic bearings with force invariance","volume":"19","author":"Na","year":"2005","journal-title":"KSME J. Mech. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1007\/BF02915981","article-title":"Fault tolerant homopolar magnetic bearings with flux invariant control","volume":"20","author":"Na","year":"2006","journal-title":"KSME J. Mech. Sci. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xin, C., Baixin, C., Han, L., and Allen, G.M. (2020). An Accurate Linearization of Electromagnetic Force of Heteropolar Magnetic Bearings with Redundant Structures. J. Eng. Gas Turbines Power, 142.","DOI":"10.1115\/1.4046703"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Cheng, B., Cheng, X., Song, S., Deng, S., Zhou, R., Hu, Y., and Wu, H. (2021). Fault-Tolerant Control of Magnetically-Levitated Rotor with Redundant Structures Based on Improved Generalized Linearized EMFs Model. Sensors, 21.","DOI":"10.3390\/s21165404"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2454","DOI":"10.1109\/ACCESS.2020.3046668","article-title":"Design and implementation of a fault-tolerant magnetic bearing control system combined with a novel fault-diagnosis of actuators","volume":"9","author":"Cheng","year":"2020","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Meeker, D., and Maslen, E. (2020). A Parametric Solution to the Generalized Bias Linearization Problem. Actuators, 3.","DOI":"10.3390\/act9010014"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2313","DOI":"10.1177\/1077546314547101","article-title":"Static mass imbalance identification and vibration control for rotor of magnetically suspended control moment gyro with active-passive magnetic bearings","volume":"22","author":"Cui","year":"2014","journal-title":"J. Vib. Control"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhou, J., Wu, H., Wang, W., Yang, K., Hu, Y., Guo, X., and Song, C. (2022). Online unbalance compensation of a maglev rotor with two active magnetic bearings based on the LMS algorithm and the influence coefficient method. Mech. Syst. Signal Process., 166.","DOI":"10.1016\/j.ymssp.2021.108460"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6977","DOI":"10.1109\/TIA.2021.3062587","article-title":"Novel Generalised Notch Filter for Harmonic Vibration Suppression in Magnetic Bearing Systems","volume":"57","author":"Gallego","year":"2021","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4946","DOI":"10.1109\/TIE.2019.2927184","article-title":"A Second-Order Dual Mode Repetitive Control for Magnetically Suspended Rotor","volume":"67","author":"Cui","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3491","DOI":"10.1109\/TIE.2017.2752119","article-title":"Hybrid Fractional Repetitive Control for Magnetically Suspended Rotor Systems","volume":"65","author":"Cui","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7789","DOI":"10.1109\/TIE.2019.2942574","article-title":"Suppression of Harmonic Vibration in Magnetically Suspended Centrifugal Compressor Using Zero-Phase Odd-Harmonic Repetitive Controller","volume":"67","author":"Cai","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Cui, P., Du, L., Zhou, X., Li, J., Li, Y., and Wu, Y. (2021). Harmonic vibration moment suppression using hybrid repetitive control for active magnetic bearing system. J. Vib. Control.","DOI":"10.1177\/10775463211010914"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6962","DOI":"10.1109\/TIE.2016.2585545","article-title":"Harmonic current suppression of an AMB rotor system at variable rotation speed based on multiple phase-shift notch filters","volume":"63","author":"Cui","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"He, J., Peng, C., Deng, Z., and Zhu, M. (2018, January 9\u201311). Comparison of AMB-rotor system using multiple phase-shift notch filters connected in series and parallel modes for vibration control. Proceedings of the 2018 Chinese Control and Decision Conference (CCDC), Shenyang, China.","DOI":"10.1109\/CCDC.2018.8407157"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ran, S., Hu, Y., and Wu, H. (2018). Design, modeling, and robust control of the flexible rotor to pass the first bending critical speed with active magnetic bearing. Adv. Mech. Eng., 10.","DOI":"10.1177\/1687814018757536"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jin, C., Guo, K., Xu, Y., Cui, H., and Xu, L. (2019). Design of magnetic bearing control system based on active disturbance rejection theory. J. Vib. Acoust., 141.","DOI":"10.1115\/1.4040837"},{"key":"ref_28","unstructured":"Gao, Z. (2003, January 4\u20136). Scaling and bandwidth-parameterization based controller tuning. Proceedings of the 2003 American Control Conference, Denver, CO, USA."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/8\/3012\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:54:12Z","timestamp":1760136852000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/8\/3012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,14]]},"references-count":28,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["s22083012"],"URL":"https:\/\/doi.org\/10.3390\/s22083012","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,14]]}}}