{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:34:59Z","timestamp":1760243699693,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2013,11,19]],"date-time":"2013-11-19T00:00:00Z","timestamp":1384819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To investigate the drive-mode resonance frequency of a micromachined vibratory gyroscope (MVG), one needs to measure it accurately and efficiently. The conventional approach to measure the resonant frequency is by performing a sweep frequency test and spectrum analysis. The method is time-consuming and inconvenient because of the requirements of many test points, a lot of data storage and off-line analyses. In this paper, we propose two novel measurement methods, the search method and track method, respectively. The former is based on the magnitude-frequency characteristics of the drive mode, utilizing a one-dimensional search technique. The latter is based on the phase-frequency characteristics, applying a feedback control loop. Their performances in precision, noise resistivity and efficiency are analyzed through detailed simulations. A test system is implemented based on a field programmable gate array (FPGA) and experiments are carried out. By comparing with the common approach, feasibility and superiorities of the proposed methods are validated. In particular, significant efficiency improvements are achieved whereby the conventional frequency method consumes nearly 5,000 s to finish a measurement, while only 5 s is needed for the track method and 1 s for the search method.<\/jats:p>","DOI":"10.3390\/s131115770","type":"journal-article","created":{"date-parts":[[2013,11,19]],"date-time":"2013-11-19T12:33:03Z","timestamp":1384864383000},"page":"15770-15784","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Two Novel Measurements for the Drive-Mode Resonant Frequency of a Micromachined Vibratory Gyroscope"],"prefix":"10.3390","volume":"13","author":[{"given":"Ancheng","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoping","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Luo","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingming","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofeng","family":"He","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kanghua","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Automation, National University of Defense Technology,  Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1109\/5.704269","article-title":"Micromachined inertial sensors","volume":"86","author":"Yazdi","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_2","first-page":"55","article-title":"Inertial sensor technology trends","volume":"86","author":"Baibour","year":"2001","journal-title":"Sens. J. IEEE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","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_4","doi-asserted-by":"crossref","first-page":"5952","DOI":"10.3390\/s90805952","article-title":"Oscillation control algorithms for resonant sensors with applications to vibratory gyroscopes","volume":"9","author":"Park","year":"2009","journal-title":"Sensors"},{"key":"ref_5","unstructured":"Saukoski, M. (2008). System and Circuit Design for a Capacitive MEMS Gyroscope, Helsinki University of Technology."},{"key":"ref_6","unstructured":"Poreddy, S.R. (2004). Design and Dynamic Analysis of MEMS Gyroscopes, University of Missouri-Columbia."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Lobur, M., and Holovatyy, A. (2007, January 23\u201326). Research of Influence of Materials Properties on Resonance Frequencies of Micromechanical Tuning Fork Gyroscope. Lviv-Polyana, Ukraine.","DOI":"10.1109\/MEMSTECH.2007.4283440"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1088\/0957-0233\/1\/12\/015","article-title":"Measurement of Young's modulus and internal stress in silicon microresonators using a resonant frequency technique","volume":"1","author":"Zhang","year":"1990","journal-title":"Meas. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1016\/0924-4247(91)87075-E","article-title":"Temperature dependence of resonant frequency in all-fibre optically addressed silicon microresonator sensors","volume":"25\u201327","author":"Walsh","year":"1991","journal-title":"Sens. Actuators A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"296","DOI":"10.3390\/s110100296","article-title":"Effect of axial force on the performance of micromachined vibratory rate gyroscopes","volume":"11","author":"Hou","year":"2011","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1115\/1.1369360","article-title":"System identification of a MEMS gyroscope","volume":"123","author":"Gibson","year":"2001","journal-title":"J. Dyn. Sys. Meas. Cont."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1049\/el:19820697","article-title":"Digital method of sweep frequency generation","volume":"18","author":"Hill","year":"1982","journal-title":"Electron. Lett."},{"key":"ref_13","first-page":"1117","article-title":"Research on temperature characteristic of mode frequency of silicom micro-gyroscope","volume":"22","author":"Man","year":"2009","journal-title":"Chin. J. Sens. Actuators"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1530","DOI":"10.1088\/0960-1317\/14\/11\/014","article-title":"A study on resonant frequency and Q factor tunings for MEMS vibratory gyroscopes","volume":"14","author":"Jeong","year":"2004","journal-title":"J. Micromech. Microeng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0957-0233\/23\/8\/085107","article-title":"Methods for the robust measurement of the resonant frequency and quality factor of significantly damped resonating devices","volume":"23","author":"Niedermayer","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1857","DOI":"10.1007\/978-1-4614-4981-2_203","article-title":"The design and implementation of interface electronics for silicon micromechanical gyroscopes","volume":"238","author":"Wang","year":"2014","journal-title":"Lect. Notes Electr. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0960-1317\/19\/12\/125015","article-title":"Transient response and stability of the AGC-PI closed-loop controlled MEMS vibratory gyroscopes","volume":"19","author":"Cui","year":"2009","journal-title":"J. Micromech. Microeng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1088\/0960-1317\/13\/5\/318","article-title":"A study on wafer level vacuum packaging for MEMS devices","volume":"13","author":"Lee","year":"2003","journal-title":"J. Micromech. Microeng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/0097-8485(77)85016-X","article-title":"Feasibility of a one-dimensional search system","volume":"1","author":"Ritter","year":"1977","journal-title":"Comput. Chem."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/TAU.1971.1162151","article-title":"A digital frequency synthesizer","volume":"19","author":"Tierney","year":"1971","journal-title":"IEEE Trans. Audio Electroacoust."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1115\/1.1514658","article-title":"Stability and resolution analysis of a phase-locked loop natural frequency tracking system for MEMS fatigue testing","volume":"124","author":"Sun","year":"2002","journal-title":"J. Dyn. Syst. Meas. 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