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This paper examines the interaction effects among stiffness coupling, system phase delay, readout demodulation phase shift, and velocity amplitude mismatch within the control process. Based on the completion of frequency difference control and demodulation phase matching, we clarify that the remaining stiffness coupling and residual system phase error are the primary factors influencing SF nonlinearity. Furthermore, SF nonlinearity is reduced through error compensation. On one hand, this paper suppresses stiffness coupling through the observation of the instantaneous frequency difference and the application of the quadrature voltage. On the other hand, system phase error is compensated by observing the amplitude control force and tuning the reference in the Phase-Locked Loops (PLLs). Subsequent simulations of these methods demonstrated a remarkable 97% reduction in SF nonlinearity within the measurement range of \u00b1500\u00b0\/s. In addition, an observed rule dictates that maintaining a sufficiently large frequency split effectively constrains the SF nonlinearity.<\/jats:p>","DOI":"10.3390\/s23249701","type":"journal-article","created":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T03:03:33Z","timestamp":1702004613000},"page":"9701","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Interactive Errors Analysis and Scale Factor Nonlinearity Reduction Methods for Lissajous Frequency Modulated MEMS Gyroscope"],"prefix":"10.3390","volume":"23","author":[{"given":"Rui","family":"Li","sequence":"first","affiliation":[{"name":"Institute of Flexible Electronics, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"},{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]},{"given":"Xiaoxu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8343-3001","authenticated-orcid":false,"given":"Kaichen","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]},{"given":"Zhennan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]},{"given":"Zhengya","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]},{"given":"Xiquan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]},{"given":"Ao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]},{"given":"Qianbo","family":"Lu","sequence":"additional","affiliation":[{"name":"Institute of Flexible Electronics, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Endean, D., Christ, K., Duffy, P., Freeman, E., Glenn, M., Gnerlich, M., Johnson, B., and Weinmann, J. 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Proceedings of the 17th International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers Eurosensors), Barcelona, Spain.","DOI":"10.1109\/Transducers.2013.6627152"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3533","DOI":"10.1109\/JSEN.2018.2810843","article-title":"Micromechanical rate integrating gyroscope with angle-dependent bias compensation using a self-precession method","volume":"18","author":"Challoner","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"085006","DOI":"10.1088\/0960-1317\/25\/8\/085006","article-title":"High Q diamond hemispherical resonators: Fabrication and energy loss mechanisms","volume":"25","author":"Bernstein","year":"2015","journal-title":"J. Micromech. Microeng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1109\/JMEMS.2021.3105128","article-title":"Radially pleated disk resonator for gyroscopic application","volume":"30","author":"Ren","year":"2021","journal-title":"J. Microelectromech. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zega, V., Comi, C., Fedeli, P., Frangi, A., Corigliano, A., Minotti, P., Langfelder, G., Falorni, L., and Tocchio, A. (2018, January 26\u201329). A dual-mass frequency-modulated (FM) pitch gyroscope: Mechanical design and modelling. Proceedings of the IEEE International Symposium on Inertial Sensors and Systems (INERTIAL), Lake Como, Italy.","DOI":"10.1109\/ISISS.2018.8358128"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.euromechsol.2018.02.005","article-title":"A new MEMS three-axial frequency-modulated (FM) gyroscope: A mechanical perspective","volume":"70","author":"Zega","year":"2018","journal-title":"Eur. J. Mech.-A\/Solids"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Izyumin, I., Kline, M., Yeh, Y.C., Eminoglu, B., and Boser, B. (2014, January 22\u201326). A 50 \u03bcW, 2.1 mdeg\/s\/Hz frequency-to-digital converter for frequency-output MEMS gyroscopes. Proceedings of the 2014\u201340th European Solid-State Circuits Conference (ESSCIRC), Venice, Italy.","DOI":"10.1109\/ESSCIRC.2014.6942106"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7386","DOI":"10.1109\/TIE.2018.2880697","article-title":"Fully Integrated, 406 \u03bcA, 5 \u00b0\/h, Full Digital Output Lissajous Frequency-Modulated Gyroscope","volume":"66","author":"Leoncini","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"19207","DOI":"10.1109\/JSEN.2022.3204431","article-title":"A Digital Control Structure for Lissajous Frequency-Modulated Mode MEMS Gyroscope","volume":"22","author":"Wang","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bestetti, M., Bonfanti, A.G., Falorni, L., Gianollo, M., Padovani, C., and Langfelder, G. (2022, January 24\u201326). Full-digital output ASIC for Lissajous Frequency Modulated MEMS Gyroscopes. Proceedings of the IEEE International Conference on Electronics, Circuits and Systems (ICECS), Glasgow, UK.","DOI":"10.1109\/ICECS202256217.2022.9971102"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5347","DOI":"10.1109\/TIE.2022.3187598","article-title":"Calibration of coupling errors for scale factor nonlinearity improvement in navigation-grade honeycomb disk resonator gyroscope","volume":"70","author":"Wang","year":"2022","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zotov, S., Prikhodko, I., Simon, B., Trusov, A., and Shkel, A. (2014, January 16\u201317). Self-calibrated MEMS gyroscope with AM\/FM operational modes, dynamic range of 180 dB and in-run bias stability of 0.1 deg\/hr. Proceedings of the DGON Inertial Sensors and Systems (ISS), Karlsruhe, Germany.","DOI":"10.1109\/InertialSensors.2014.7049406"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Sabater, A.B., and Moran, K.M. (2019, January 1\u20135). Angle random walk minimization for frequency modulated gyroscopes. Proceedings of the IEEE International Symposium on Inertial Sensors and Systems, Naples, FL, USA.","DOI":"10.1109\/ISISS.2019.8739529"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bordiga, E., Bestetti, M., and Langfelder, G. (2019, January 23\u201327). AGC-less operation of high-stability Lissajous frequency-modulated MEMS gyroscopes. Proceedings of the 20th International Conference on Solid-State Sensors, Actuators and Microsystems & Eurosensors (Transducers Eurosensors), Berlin, Germany.","DOI":"10.1109\/TRANSDUCERS.2019.8808514"},{"key":"ref_27","unstructured":"Bestetti, M., Mussi, G., Padovani, C., Donadel, A., Valzasina, C., Langfelder, G., and Bonfanti, A.G. (November, January 31). On amplitude-gain-control optimization for Lissajous frequency modulated MEMS gyroscopes. Proceedings of the IEEE Sensors, Sydney, Australia."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Alattas, K.A., Mohammadzadeh, A., Mobayen, S., Aly, A.A., Felemban, B.F., and Vu, M.T. (2021). A new data-driven control system for MEMSs gyroscopes: Dynamics estimation by type-3 fuzzy systems. Micromachines, 12.","DOI":"10.3390\/mi12111390"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1177\/1077546320988192","article-title":"Nonsingular terminal sliding mode control for micro-electro-mechanical gyroscope based on disturbance observer: Linear matrix inequality approach","volume":"28","author":"Jafari","year":"2022","journal-title":"J. Vib. Control"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1109\/TFUZZ.2021.3064704","article-title":"Fractional sliding-mode control for microgyroscope based on multilayer recurrent fuzzy neural network","volume":"30","author":"Fei","year":"2021","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"13945","DOI":"10.1109\/JSEN.2022.3181302","article-title":"In-Run Automatic Mode-Matching of Whole-Angle Micro-Hemispherical Resonator Gyroscope Based on Standing Wave Self-Precession","volume":"22","author":"Ruan","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liu, X., Qin, Z., and Li, H. (2022). Online Compensation of Phase Delay Error Based on PF Characteristic for MEMS Vibratory Gyroscopes. Micromachines, 13.","DOI":"10.3390\/mi13050647"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"19228","DOI":"10.1109\/JSEN.2022.3204631","article-title":"Identification and Correction of Phase Error for Whole-angle Micro-shell Resonator Gyroscope","volume":"22","author":"Sun","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"055002","DOI":"10.1088\/1361-6439\/acbfc6","article-title":"Identification and suppression of driving force misalignment angle for a MEMS gyroscope using parametric excitation","volume":"33","author":"Zheng","year":"2023","journal-title":"J. Micromech. Microeng."},{"key":"ref_35","unstructured":"Lynch, D.D. (1995, January 24\u201325). Vibratory gyro analysis by the method of averaging. Proceedings of the 2nd St. Petersburg Conference on Gyroscopic Technology and Navigation, St. Petersburg, Russia."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1109\/JSEN.2007.908921","article-title":"Zero-rate output and quadrature compensation in vibratory MEMS gyroscopes","volume":"7","author":"Saukoski","year":"2007","journal-title":"IEEE Sens. J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/24\/9701\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:35:12Z","timestamp":1760132112000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/24\/9701"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,8]]},"references-count":36,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["s23249701"],"URL":"https:\/\/doi.org\/10.3390\/s23249701","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,8]]}}}