{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T21:38:22Z","timestamp":1775165902472,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T00:00:00Z","timestamp":1566172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shandong Provincial Natural Science Foundation, China","award":["ZR2018BEE020"],"award-info":[{"award-number":["ZR2018BEE020"]}]},{"name":"Applied Basic Research Program of Science and Technology of Qingdao","award":["19-6-1-18-jch"],"award-info":[{"award-number":["19-6-1-18-jch"]}]},{"name":"A Project of Shandong Province Higher Educational Science and Technology Program","award":["J18KA018"],"award-info":[{"award-number":["J18KA018"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51704174"],"award-info":[{"award-number":["51704174"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Taishan Scholar Program of Shandong","award":["ts201712054"],"award-info":[{"award-number":["ts201712054"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The environment in space provides favorable conditions for space missions. However, low frequency vibration poses a great challenge to high sensitivity equipment, resulting in performance degradation of sensitive systems. Due to the ever-increasing requirements to protect sensitive payloads, there is a pressing need for micro-vibration suppression. This paper deals with the modeling and control of a maglev vibration isolation system. A high-precision nonlinear dynamic model with six degrees of freedom was derived, which contains the mathematical model of Lorentz actuators and umbilical cables. Regarding the system performance, a double closed-loop control strategy was proposed, and a sliding mode control algorithm was adopted to improve the vibration isolation performance. A simulation program of the system was developed in a MATLAB environment. A vibration isolation performance in the frequency range of 0.01\u2013100 Hz and a tracking performance below 0.01 Hz were obtained. In order to verify the nonlinear dynamic model and the isolation performance, a principle prototype of the maglev isolation system equipped with accelerometers and position sensors was developed for the experiments. By comparing the simulation results and the experiment results, the nonlinear dynamic model of the maglev vibration isolation system was verified and the control strategy of the system was proved to be highly effective.<\/jats:p>","DOI":"10.3390\/s19163608","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T11:22:38Z","timestamp":1566213758000},"page":"3608","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Modeling and Control of a Six Degrees of Freedom Maglev Vibration Isolation System"],"prefix":"10.3390","volume":"19","author":[{"given":"Qianqian","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}]},{"given":"Ning","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}]},{"given":"Sifang","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6102-9355","authenticated-orcid":false,"given":"Hongbo","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}]},{"given":"Bilong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,19]]},"reference":[{"key":"ref_1","first-page":"304","article-title":"Active disturbance rejection control for microgravity active vibration isolation system in space station","volume":"46","author":"Jia","year":"2017","journal-title":"Inf. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1016\/0094-5765(90)90119-6","article-title":"A new approach to controller design for microgravity isolation systems","volume":"21","author":"Sinha","year":"1990","journal-title":"Acta Astronaut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"20053","DOI":"10.3390\/s150820053","article-title":"Measurement model and precision analysis of accelerometers for maglev vibration isolation platforms","volume":"15","author":"Wu","year":"2015","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2383","DOI":"10.1121\/1.4777693","article-title":"Flight performance of the International Space Station active rack isolation system","volume":"114","author":"Bushnell","year":"2003","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"586","DOI":"10.2514\/2.3631","article-title":"Survey of active vibration isolation systems for microgravity applications","volume":"37","author":"Grodsinsky","year":"2000","journal-title":"J. Spacecr. Rocket."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1016\/j.conengprac.2005.04.016","article-title":"On active acceleration control of vibration isolation systems","volume":"14","author":"Zhu","year":"2006","journal-title":"Control Eng. Pract."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1752","DOI":"10.2514\/1.J057914","article-title":"Dynamic analysis of umbilical cables for maglev vibration isolation systems","volume":"57","author":"Wu","year":"2019","journal-title":"AIAA J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"35106","DOI":"10.1063\/1.3298605","article-title":"Design and control of six degree-of-freedom active vibration isolation table","volume":"81","author":"Hong","year":"2010","journal-title":"Rev. Sci. Instrum."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.vacuum.2006.02.018","article-title":"Offset scatter reduction of spinning rotor gauges by vibration isolation","volume":"81","author":"Bock","year":"2006","journal-title":"Vacuum"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.sna.2012.11.001","article-title":"Dynamic modeling and adaptive vibration control study for giant magnetostrictive actuators","volume":"190","author":"Zhang","year":"2013","journal-title":"Sens. Actuators A Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12206-012-0915-4","article-title":"Modelling and testing of a dielectic electro-active polymer (DEAP) actuator for active vibration control","volume":"27","author":"Berardi","year":"2013","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1007\/s12555-014-0428-2","article-title":"Adaptive wavelet neural network controller for active suppression control of a diaphragm-type pneumatic vibration isolator","volume":"15","author":"Chen","year":"2017","journal-title":"Int. J. Control Autom."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.jsv.2006.07.050","article-title":"A six-axis single-stage active vibration isolator based on Stewart platform","volume":"300","author":"Preumont","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.mechmachtheory.2015.06.008","article-title":"Dynamic modeling and robust nonlinear control of a six-DOF active micro-vibration isolation manipulator with parameter uncertainties","volume":"92","author":"Ying","year":"2015","journal-title":"Mech. Mach. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jsv.2016.07.021","article-title":"Investigation on active vibration isolation of a Stewart platform with piezoelectric actuators","volume":"383","author":"Wang","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.jsv.2015.07.013","article-title":"Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation","volume":"358","author":"Zhu","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1063\/1.4764002","article-title":"Design and optimization of voice coil actuator for six degree of freedom active vibration isolation system using Halbach magnet array","volume":"83","author":"Kim","year":"2012","journal-title":"Rev. Sci. Instrum."},{"key":"ref_18","unstructured":"Muller, T., Hurlebaus, S., Stobener, U., and Gaul, L. (February, January 31). Modeling and control of an active vibration isolation. Proceedings of the International Modal Analysis Conference IMAC, Orlando, FL, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3042","DOI":"10.1016\/j.ymssp.2007.04.003","article-title":"Control concepts for an active vibration isolation system","volume":"21","author":"Kerber","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","first-page":"43","article-title":"Iterative SISO feedback design for an active vibration isolation system","volume":"2005","author":"Zenga","year":"2005","journal-title":"Traineesh. Rep."},{"key":"ref_21","unstructured":"Hampton, R., Tryggvason, B., Decarufel, J., Townsend, M.A., and Wagar, W.O. (1997). The Microgravity Vibration Isolation Mount: A Dynamic Model for Optimal Controller Design."},{"key":"ref_22","unstructured":"Kim, Y.K., and Whorton, M.S. (2001). Equations of Motion for the g-LIMIT Microgravity Vibration Isolation System."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1007\/s11071-014-1242-3","article-title":"Dynamics and control of a parallel mechanism for active vibration isolation in space station","volume":"76","author":"Liu","year":"2014","journal-title":"Nonlinear Dynam."},{"key":"ref_24","first-page":"49","article-title":"An active magnetic suspension for space-based micro-gravity vibration isolation","volume":"8","author":"Fenn","year":"1990","journal-title":"Act. Noise Vib. Control"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1177\/1077546317714939","article-title":"Study on structural optimization design and cascade PID control of maglev actuator for active vibration isolation system","volume":"24","author":"Hu","year":"2018","journal-title":"J. Vib. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"434","DOI":"10.4028\/www.scientific.net\/AMM.390.434","article-title":"Nonlinearity of maglev actuator and adaptive vibration control using improved FxLMS algorithm","volume":"390","author":"Li","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_27","unstructured":"Yang, B.J., Calise, A., Craig, J., and Whorton, M. (2013). Adaptive Control for a Microgravity Vibration Isolation System, Cambridge University Press."},{"key":"ref_28","unstructured":"Hampton, R.D., Knospe, C., Grodsinsky, C., Allaire, P.E., and Lewis, D.W. (1992). Microgravity Vibration Isolation: Optimal Preview and Feedback Control."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xie, L., Qiu, Z., and Zhang, X. (2019). Development of a 3-PRR precision tracking system with full closed-loop measurement and control. Sensors, 19.","DOI":"10.3390\/s19081756"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3608\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:12:15Z","timestamp":1760188335000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3608"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,19]]},"references-count":29,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["s19163608"],"URL":"https:\/\/doi.org\/10.3390\/s19163608","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,19]]}}}