{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T01:02:04Z","timestamp":1772326924259,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,20]],"date-time":"2016-10-20T00:00:00Z","timestamp":1476921600000},"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":["No.61374207"],"award-info":[{"award-number":["No.61374207"]}],"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":["No.91436107"],"award-info":[{"award-number":["No.91436107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A micromachined gyroscope in which a high-speed spinning rotor is suspended electrostatically in a vacuum cavity usually functions as a dual-axis angular rate sensor. An inherent coupling error between the two sensing axes exists owing to the angular motion of the spinning rotor being controlled by a torque-rebalance loop. In this paper, a decoupling compensation method is proposed and investigated experimentally based on an electrostatically suspended micromachined gyroscope. In order to eliminate the negative spring effect inherent in the gyroscope dynamics, a stiffness compensation scheme was utilized in design of the decoupled rebalance loop to ensure loop stability and increase suspension stiffness. The experimental results show an overall stiffness increase of 30.3% after compensation. A decoupling method comprised of inner- and outer-loop decoupling compensators is proposed to minimize the cross-axis coupling error. The inner-loop decoupling compensator aims to attenuate the angular position coupling. The experimental frequency response shows a position coupling attenuation by 14.36 dB at 1 Hz. Moreover, the cross-axis coupling between the two angular rate output signals can be attenuated theoretically from \u221256.2 dB down to \u2212102 dB by further appending the outer-loop decoupling compensator. The proposed dual-loop decoupling compensation algorithm could be applied to other dual-axis spinning-rotor gyroscopes with various suspension solutions.<\/jats:p>","DOI":"10.3390\/s16101747","type":"journal-article","created":{"date-parts":[[2016,10,20]],"date-time":"2016-10-20T10:15:49Z","timestamp":1476958549000},"page":"1747","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Decoupling Control of Micromachined Spinning-Rotor Gyroscope with Electrostatic Suspension"],"prefix":"10.3390","volume":"16","author":[{"given":"Boqian","family":"Sun","sequence":"first","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shunyue","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haixia","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoxia","family":"He","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.3390\/s140101394","article-title":"The development of micromachined gyroscope structure and circuitry technology","volume":"14","author":"Xia","year":"2014","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113001","DOI":"10.1088\/0960-1317\/19\/11\/113001","article-title":"The development of micro-gyroscope technology","volume":"19","author":"Liu","year":"2009","journal-title":"J. Micromech. Microeng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1109\/7.102707","article-title":"Theory of operation of a two-axis-rate gyro","volume":"26","author":"Robert","year":"1990","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.asr.2006.09.020","article-title":"Precision electrostatic suspension system for the Gravity Probe B relativity mission\u2019s science gyroscopes","volume":"39","author":"Bencze","year":"2007","journal-title":"Adv. Space Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.sna.2004.08.030","article-title":"Nonlinear compensation of active electrostatic bearings supporting a spherical rotor","volume":"119","author":"Han","year":"2005","journal-title":"Sens. Actuators A Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.sna.2014.09.017","article-title":"3D micro-machined inductive contactless suspension: Testing and modeling","volume":"220","author":"Lu","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"085027","DOI":"10.1088\/0960-1317\/21\/8\/085027","article-title":"Performance of an active electric bearing for rotary micromotors","volume":"21","author":"Han","year":"2011","journal-title":"J. Micromech. Microeng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.sna.2006.03.002","article-title":"The study of an electromagnetic levitating micromotor for application in a rotating gyroscope","volume":"132","author":"Zhang","year":"2006","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2011.08.003","article-title":"Design and characterization of MEMS micromotor supported on low friction liquid bearing","volume":"177","author":"Chan","year":"2012","journal-title":"Sens. Actuators A Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/JMEMS.2004.824900","article-title":"A self-acting gas thrust bearing for high-speed microrotors","volume":"13","author":"Wong","year":"2004","journal-title":"J. Microelectromech. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1049\/mnl.2013.0660","article-title":"Optimized geometry model for liquid-suspended miniature gyroscope","volume":"9","author":"Zhang","year":"2014","journal-title":"Micro Nano Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"012001","DOI":"10.1088\/1742-6596\/187\/1\/012001","article-title":"Micro \/nano electro mechanical systems for practical applications","volume":"187","author":"Esashi","year":"2009","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_13","first-page":"317","article-title":"The basic research for the new compass system using latest MEMS","volume":"4","author":"Fukuda","year":"2010","journal-title":"Int. J. Mar. Navig. Saf. Sea Transp."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.1143\/JJAP.42.2468","article-title":"Electrostatically levitated ring-shaped rotational-gyro accelerometer","volume":"42","author":"Murakoshi","year":"2003","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dillard, B., Trent, V., Greene, M., and Taylor, E. (2011). Radiation effects on multiple DOF MEMS inertial sensors. Nanophoton. Macrophoton. Space Environ. V, 8164.","DOI":"10.1117\/12.892799"},{"key":"ref_16","unstructured":"Nakamura, S. (November, January 31). MEMS inertial sensor toward high accuracy and multi-axis sensing. Proceedings of the 4th IEEE Conference on Sensors, Irvine, CA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1243\/09544062JMES665","article-title":"Design and fabrication of a micromachined electrostatically suspended gyroscope","volume":"222","author":"Damrongsak","year":"2008","journal-title":"Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1049\/el.2011.1554","article-title":"Hybrid microfabrication and 5-DOF levitation of micromachined electrostatically suspended gyroscope","volume":"47","author":"Cui","year":"2011","journal-title":"Electron. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4336","DOI":"10.1109\/TIE.2016.2544252","article-title":"Rotation control and characterization of high-speed variable-capacitance micromotor supported on electrostatic bearing","volume":"63","author":"Sun","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"115034","DOI":"10.1088\/0960-1317\/20\/11\/115034","article-title":"Experimental study of a variable-capacitance micromotor with electrostatic suspension","volume":"20","author":"Han","year":"2010","journal-title":"J. Micromech. Microeng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"105032","DOI":"10.1088\/0960-1317\/22\/10\/105032","article-title":"Micromachined electrostatically suspended gyroscope with a spinning ring-shaped rotor","volume":"22","author":"Han","year":"2012","journal-title":"J. Micromech. Microeng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2176","DOI":"10.3390\/s130202176","article-title":"A micro dynamically tuned gyroscope with adjustable static capacitance","volume":"13","author":"Xia","year":"2013","journal-title":"Sensors"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ellis, C.D., and Wilamowski, B.M. (2008). Fabrication and control of an electrostatically levitated rotating gyro. Micro (MEMS) Nanotechnol. Sp. Def. Secur. II, 6959.","DOI":"10.1117\/12.783861"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3519","DOI":"10.1109\/TIM.2009.2018006","article-title":"Capacitive sensor interface for an electrostatically levitated micromotor","volume":"58","author":"Han","year":"2009","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"S11","DOI":"10.1088\/0960-1317\/13\/4\/302","article-title":"Electronic interface design for an electrically floating micro-disc","volume":"13","author":"Giindila","year":"2003","journal-title":"J. Micromech. Microeng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Watanabe, T., and Terasawa, T. (2010, January 12\u201315). An all-digital TAD-OFDM detection for sensor using TAD-digital synchronous detection. Proceedings of the 17th IEEE ICECS, Athens, Greece.","DOI":"10.1109\/ICECS.2010.5724630"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kraft, M., and Damrongsak, B. (2010, January 1\u20134). Micromachined gyroscopes based on a rotating mechanically unconstrained proof mass. Proceedings of the 2010 IEEE Sensors, Waikoloa, HI, USA.","DOI":"10.1109\/ICSENS.2010.5690984"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ma, G., Chen, W., Xiao, Q., Zhang, W., Cui, F., and Li, K. (2009, January 5\u20138). Single-neuron spinning control system for a non-silicon micro machined rotational gyro. Proceedings of the 4th IEEE International Conference on Nano\/Micro Engineered and Molecular Systems, Shenzhen, China.","DOI":"10.1109\/NEMS.2009.5068578"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3901\/CJME.2009.01.001","article-title":"Modeling and analysis of a micromotor with an electrostatically levitated rotor","volume":"22","author":"Han","year":"2009","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.isatra.2009.11.003","article-title":"Compact H\u221e robust rebalance loop controller design for a micromachined electrostatically suspended gyroscope","volume":"49","author":"Ma","year":"2010","journal-title":"ISA Trans."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7001","DOI":"10.1109\/JSEN.2015.2469715","article-title":"Static behavior of closed-loop micromachined levitated two-axis rate gyroscope","volume":"15","author":"Poletkin","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Torti, R.P., Gondhalekar, V., Tran, H., Selfors, B., Bart, S., and Maxwell, B. (1994). Electrostatically suspended and sensed micromechanical rate gyroscope. Sens. Imaging Vis. Control Guid. Aerosp. Veh., 2220.","DOI":"10.1117\/12.179613"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/10\/1747\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:33:34Z","timestamp":1760211214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/10\/1747"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,20]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,10]]}},"alternative-id":["s16101747"],"URL":"https:\/\/doi.org\/10.3390\/s16101747","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,20]]}}}