{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T15:57:49Z","timestamp":1772726269467,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T00:00:00Z","timestamp":1536278400000},"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":["61434003"],"award-info":[{"award-number":["61434003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In order to solve the problem where existing mode-matching methods in microelectromechanical systems (MEMS) vibrating gyroscopes fail to meet real-time and reliability requirements, this paper presents a novel method to accomplish automatic and real-time mode-matching based on phase-shifted 45\u00b0 additional force demodulation (45\u00b0 AFD-RM). The phase-shifted 45\u00b0 additional force signal has the same frequency as the quadrature force signal, but it is phase-shifted by 45\u00b0 and applied to the sense mode. In addition, two-way phase-shifted 45\u00b0 demodulations are used at the sense-mode detection output to obtain a phase metric that is independent of the Coriolis force and can reflect the mode-matching state. Then, this phase metric is used as a control variable to adaptively control the tuning voltage, so as to change the sense-mode frequency through the negative stiffness effect and ultimately achieve real-time mode-matching. Simulation and experimental results show that the proposed 45\u00b0 AFD-RM method can achieve real-time matching. The mode frequency split is controlled within 0.1 Hz, and the gyroscope scale factor, zero-bias instability, and angle random walk are effectively improved.<\/jats:p>","DOI":"10.3390\/s18093001","type":"journal-article","created":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T11:47:41Z","timestamp":1536320861000},"page":"3001","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["MEMS Gyroscope Automatic Real-Time Mode-Matching Method Based on Phase-Shifted 45\u00b0 Additional Force Demodulation"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3761-6848","authenticated-orcid":false,"given":"Feng","family":"Bu","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1614-9606","authenticated-orcid":false,"given":"Dacheng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heming","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengmeng","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1007\/s00542-015-2645-x","article-title":"Research development of silicon MEMS gyroscopes: A review","volume":"21","author":"Guo","year":"2015","journal-title":"Microsyst. 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