{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T00:15:22Z","timestamp":1792800922964,"version":"4.5.0"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,7]],"date-time":"2018-06-07T00:00:00Z","timestamp":1528329600000},"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":["10772011"],"award-info":[{"award-number":["10772011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The high-precision speed control of gimbal servo systems is the key to generating high-precision torque for control moment gyroscopes (CMGs) in spacecrafts. However, the control performance of gimbal servo systems may be degraded significantly by disturbances, especially a dynamic imbalance disturbance with the same frequency as the high-speed rotor. For assembled CMGs, it is very difficult to measure the rotor imbalance directly by using a dynamic balancing machine. In this paper, a gimbal disturbance observer is proposed to estimate the dynamic imbalance of the rotor assembled in the CMG. First, a third-order dynamical system is established to describe the disturbance dynamics of the gimbal servo system, in which the rotor dynamic imbalance torque along the gimbal axis and the other disturbances are modeled to be periodic and bounded, respectively. Then, the gimbal disturbance observer is designed for the third-order dynamical system by using the total disturbance as a virtual measurement. Since the virtual measurement is derived from the inverse dynamics of the gimbal servo system, the information of the rotor dynamic imbalance can be obtained indirectly only using the measurements of gimbal speed and three-phase currents. Semi-physical experimental results demonstrate the effectiveness of the observer by using a CMG simulator.<\/jats:p>","DOI":"10.3390\/s18061873","type":"journal-article","created":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T03:13:18Z","timestamp":1528427598000},"page":"1873","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Indirect Measurement of Rotor Dynamic Imbalance for Control Moment Gyroscopes via Gimbal Disturbance Observer"],"prefix":"10.3390","volume":"18","author":[{"given":"Liya","family":"Huang","sequence":"first","affiliation":[{"name":"School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7746-4589","authenticated-orcid":false,"given":"Zhong","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xu, X.B., Chen, S., and Liu, J.H. (2017). Elimination of harmonic force and torque in active magnetic bearing systems with repetitive control and notch filters. Sensors, 17.","DOI":"10.3390\/s17040763"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9129","DOI":"10.3390\/s120709129","article-title":"Performance testing of a magnetically suspended double gimbal control moment Gyro based on the single axis air bearing table","volume":"12","author":"Cui","year":"2012","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.ast.2016.04.022","article-title":"Adaptive neural network-based satellite attitude control in the presence of CMG uncertainty","volume":"54","author":"Mackunis","year":"2016","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/TAC.2008.2008324","article-title":"Controllability of spacecraft attitude using control moment Gyroscopes","volume":"54","author":"Bhat","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Heiberg, C.J. (2000, January 14\u201317). A practical approach to modeling single-gimbal control momentum Gyroscopes in agile spacecraft. Proceedings of the AIAA Guidance, Navigation, and Control Conference, Denver, CO, USA.","DOI":"10.2514\/6.2000-4545"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.2514\/1.49410","article-title":"Feedback control with nominal inputs for satellites using control moment Gyros","volume":"34","author":"Kusuda","year":"2011","journal-title":"J. Guid. Control Dyn."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Heiherg, C.J., Bailey, D., and Wie, B. (1997, January 11\u201313). Precision pointing control of agile spacecraft using single gimbal control Gyroscopes. Proceedings of the AIAA Guidance, Navigation, and Control Conference, New Orleans, LA, USA.","DOI":"10.2514\/6.1997-3757"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1061\/(ASCE)AS.1943-5525.0000156","article-title":"Vibration isolation platform for control moment Gyroscopes on satellites","volume":"25","author":"Zhang","year":"2012","journal-title":"J. Aerosp. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3135","DOI":"10.1109\/TMECH.2015.2394456","article-title":"High precision disturbance compensation for a three-axis Gyro-stabilized camera mount","volume":"20","author":"Li","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lu, M., Hu, Y.W., Wang, Y.G., Li, G., Wu, D.Y., and Zhang, J.Y. (2015, January 7\u201311). High precision control design for SGCMG gimbal servo system. Proceedings of the IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Busan, Korea.","DOI":"10.1109\/AIM.2015.7222586"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/j.ymssp.2016.05.033","article-title":"Frequency-varying synchronous micro-vibration suppression for a MSFW with application of small-gain theorem","volume":"82","author":"Peng","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.2514\/1.A33198","article-title":"Performance analysis of a flywheel microvibration isolation platform for spacecraft","volume":"52","author":"Wei","year":"2015","journal-title":"J. Spacecr. Rockets"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1719","DOI":"10.2514\/1.J053885","article-title":"Analysis and optimization of microvibration isolation for multiple flywheel systems of spacecraft","volume":"54","author":"Luo","year":"2016","journal-title":"AIAA J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.actaastro.2016.01.007","article-title":"Design and analysis of a moment control unit for agile satellite with high attitude stability requirement","volume":"122","author":"Zhang","year":"2016","journal-title":"Acta Astronaut."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1109\/TAES.2013.120543","article-title":"Disturbance characteristics analysis of CMG due to imbalance and installation Errors","volume":"50","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jsv.2015.12.029","article-title":"Feedforward compensation control of rotor imbalance for high-speed magnetically suspended centrifugal compressors using a novel adaptive notch filter","volume":"366","author":"Zheng","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4496","DOI":"10.1016\/j.jsv.2013.03.034","article-title":"Dynamic modeling and observation of micro-vibrations generated by a Single Gimbal Control Moment Gyro","volume":"332","author":"Luo","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1177\/1077546313490005","article-title":"Studies on vibration isolation for a multiple flywheel system in variable configurations","volume":"21","author":"Luo","year":"2013","journal-title":"J. Vib.Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1109\/TAES.2017.2670798","article-title":"Vibration control for rapid attitude stabilization of spacecraft","volume":"53","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1016\/S1000-9361(11)60430-5","article-title":"Analysis and testing of microvibration produced by momentum wheel assemblies","volume":"25","author":"Zhou","year":"2012","journal-title":"Chin. J. Aeronaut."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF02953618","article-title":"Theoretical and experimental motion analysis of self-compensating dynamic balancer","volume":"9","author":"Lee","year":"1995","journal-title":"KSME J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1016\/j.cja.2014.08.001","article-title":"A new vibration mechanism of balancing machine for satellite-borne spinning rotors","volume":"27","author":"Wang","year":"2014","journal-title":"Chin. J. Aeronaut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1109\/TMECH.2015.2495225","article-title":"Field dynamic balancing for rigid rotor-AMB system in a magnetically suspended flywheel","volume":"21","author":"Liu","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"16000","DOI":"10.3390\/s131216000","article-title":"Field balancing of magnetically levitated rotors without trial weights","volume":"13","author":"Fang","year":"2013","journal-title":"Sensors"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"21876","DOI":"10.3390\/s150921876","article-title":"Field balancing and harmonic vibration suppression in rigid AMB-rotor system with rotor imbalances and sensor runout","volume":"15","author":"Xu","year":"2015","journal-title":"Sensors"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.jsv.2016.04.005","article-title":"Automatic balancing of AMB systems using plural notch filter and adaptive synchronous compensation","volume":"374","author":"Xu","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2753","DOI":"10.1109\/TPEL.2014.2352366","article-title":"Mismatched disturbance rejection control for voltage-controlled active magnetic bearing via state-space disturbance observer","volume":"30","author":"Peng","year":"2015","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_28","unstructured":"Noshadi, A., Shi, J., Lee, W.S., Shi, P., and Kalam, A. (2015, January 5\u20136). Repetitive disturbance observer-based control for an active magnetic bearing system. Proceedings of the 2015 5th Australian Control Conference (AUCC), Gold Coast, Australia."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"031010","DOI":"10.1115\/1.3085886","article-title":"Vibration control and unbalance estimation of a nonlinear rotor system using disturbance observer","volume":"131","author":"Inoue","year":"2009","journal-title":"J. Vib. Acoust."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"740498","DOI":"10.1155\/2014\/740498","article-title":"On stability of open-loop operation without rotor information for brushless DC motors","volume":"2014","author":"Wu","year":"2014","journal-title":"Math. Probl. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1873\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:07:47Z","timestamp":1760195267000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1873"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,7]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["s18061873"],"URL":"https:\/\/doi.org\/10.3390\/s18061873","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,7]]}}}