Microscale Vibratory Rate Sensors
Vibratory rate "gyros" exploit two resonant modes for measuring the sensor's angular rate of rotation. The greatest sensitivity is achieved when the resonant modes have degenerate frequencies since this configuration provides the greatest signaltoratio with respect to intrinsic (mechanicalthermal noise) and extrinsic (electronic) noise sources. One way to achieve degeneracy is to design an axisymmetric resonator the hemisperical resonator gyro, or "wine glass" gyro, is one such example. In this program we design planar, axisymmetric resonators that are fabricated using DRIE. Small fabrication errors, however, detune the modes of interest and thereby degrade sensor performance. We are pioneering postfab techniques, and algorithms to guide the process, to drive the modal frequencies to degeneracy. We are also developing approaches to further isolate the modes from case vibration since this can be a sourse of spurious rate measurements. Past projects have developed model identification algorithms for extracting sensor mass and stiffness matrix parameters from MIMO frequency response data, efficient methods for electrostatically tuning the resonator modal frequencies, and the design and fabrication of a control and signal processing ASIC that was integrated with a prototype gyro from the Jet Propulsion Lab.
Noise Analysis A closedform expression has been developed to predict the rateequivalent power spectrum as a function of resonator quality factor, resonant frequency, detuning frequency, closedloop bandwidth, and the intensities of mechanicalthermal and electrical noise sources (data at right). The standard deviation of the integrated rate reveals angle white noise created by electrical pickoff noise. 

Resonator Design & Mass Perturbation Planar resonator designs are explored to facilitate postfabrication point mass perturbation. The design shown at right has 96 locations where gold film ablation or micro deposition techniques locally modify the resonator. Mass perturbation does not adversely effect resonator quality factor and can be used to "tune" the resonant frequencies of two similar modes and further isolate the modes from vibration. 

Tuning Algorithms Waferlevel tuning of resonators using point mass perturbations has been demonstratd for both the n=2 and n=3 modal pairs. The tuning process involves a systematic test procedure in which empirical sensitivites are identified for each resonator and used to guide the mass perturbations at selected locations on the resonator. No electrostatic tuning is used in these examples. 

ASIC for Gyro Signal Processing & Prior Work Our group was the first to create a digital ASIC that implements the sensor filtering and control architecture in a low power chip. The ASIC was integrated with a sensor prototype from JPL. We have also performed extensive analysis on the nonlinear control loops used for sensor excitation, and created system identifcation algorithms for extracting mass, damping and stiffness matrices associated with the corioliscoupled resonator modes. 

Relevant Publications
Kim, DJ., Behbahani, A., M'Closkey, R.T., Stupar, P., and DeNatale, J., "Waferscale etch process for precision frequency tuning of MEMS gyros", 2015 IEEE Intl. Symp. Inertial Sensors and Systems, pp. 12, March 2015
Ge, H., Kim, DJ., and M'Closkey, R.T., "Simultaneous exploitation of the fundamental and higher order wineglass modes in a vibratory gyro", 2015 IEEE Intl. Symp. Inertial Sensors and Systems, pp. 14, March 2015
Schwartz, D., Kim, DJ., Stupar, P., DeNatale, J., and M'Closkey, R.T., "Modal parameter tuning of an axisymmetric resonator via mass perturbation", J. Microelectromech. Syst., Vol. 24, No. 3, pp. 545555, June 2015
Kanik, M., Bordeenithikasem, P., Kim, DJ., Selden, N., Desai, A., M’Closkey, R.T., and Schroers, J., "Metallic Glass Hemispherical Shell Resonators", J. Microelectromech. Syst., Vol. 24, No. 1, pp. 1928, Feb. 2015
Kim, D. and M'Closkey, R.T., "A MEM Vibratory Gyro with ModeMatching Achieved by Resonator Mass Loading", Proc. 2014 Position, Location and Navigation Symp. (PLANS), IEEE/ION, Monterey, CA, pp. 499503, May 2014
Lorentz, T., Kim, D. and M'Closkey, R.T., "A Novel Technique for Extracting Parametric Models from MEM Resonator Test Data", Proc. 1st IEEE Intl. Symp. Inertial Sens. Syst., Laguna Beach, pp. 117120, Feb. 2014
Kanik, M., Bordeenithikasem, P., Schroers, J., Kim, D., and M'Closkey, R.T., "Microscale ThreeDimensional Hemispherical Shell Resonators Fabricated from Metallic Glass", Proc. 1st IEEE Intl. Symp. Inertial Sens. Syst., Laguna Beach, pp. 912, Feb. 2014
Kim, DJ. and M'Closkey, R.T., "Spectral Analysis of Vibratory Gyro Noise", IEEE Sensors J., Vol. 13, N. 11, pp. 43614374, Nov. 2013
Kim, D. and M'Closkey, R.T., "Noise Analysis of Closed–Loop Vibratory Rate Gyros", Proc. 2012 American Control Conf., Montreal, pp. 9297, June 2012
Schwartz, D., Kim, D. and M'Closkey, R.T., "A ModelBased Approach to MultiModal Mass Tuning of a MicroScale Resonator", Proc. 2012 American Control Conf., Montreal, pp. 98103, June 2012
Kim, D. and M'Closkey, R.T., "Dissecting Tuned MEMS Vibratory Gyros", Feedback Control of MEMS to Atoms, Gorman, J.J. and Shapiro, B. (Eds.), New York: Springer, 211266, Oct. 2011
Schwartz, D. and M'Closkey, R.T., "Decoupling of a Disk Resonator from Linear Acceleration via Mass Matrix Perturbation", J. Dyn. Sys., Meas., and Cont., Trans. ASME, Vol. 134, No. 2, pp. 133, Mar. 2012
Schwartz, D., Kim, D. and M'Closkey, R.T., "Frequency Tuning of a Disk Resonator Gyro Via Mass Matrix Perturbation", J. Dyn. Sys., Meas., and Cont., Trans. ASME, Vol. 131, No. 6, pp. 1  12, Nov. 2009
Schwartz, D., Kim, D.J., M'Closkey, R.T., "Frequency tuning of a disk resonator gyro via mass matrix perturbation", Proc. 2008 American Control Conference, Seattle, USA: IEEE, 37403745, June 2008
Kubena, R.L., Stratton, F.P., Chang, D.T., Joyce, R.J., Hsu, T.Y., Lim, M.K., and M'Closkey, R.T., "Next Generation Quartz Oscillators and Filters for VHFUHF Systems", IEEE Microwave Symp. Digest, San Francisco, 668671, June 2006
Kim, D.J., and M'Closkey, R.T., "A Systematic Method for Tuning the Dynamics of Electrostatically Actuated Vibratory Gyros", IEEE Trans. Control Syst Technol., Vol 14, No. 1, pp. 69  81, Jan. 2006
Kubena, R.L., Chang, D.T., Stratton, F.P., Joyce, R.J., Hsu, T.Y., Lim, M.K., and M'Closkey, R.T., "Arrays of highQ high stability ultrahighfrequency resonators for chemical/biological sensors", J. Vac Sci Technol. B., Vol. 23, No. 6, pp. 2979  2983, Dec. 2005
Kim, D.J. and M'Closkey, R.T., "RealTime Tuning of MEMS Gyro Dynamics", Proc. 2005 American Control Conf., Portland, Vol. 5, 35983603, June 2005
Kubena, R.L., Stratton, F.P., Chang, D.T., Joyce, R.J., Hsu, T.Y., Lim, M.K., and M'Closkey, R.T., "MEMSBased Quartz Oscillators and Filters for onChip Integration", IEEE Intl. Frequency Control Symp. Exhib., Piscataway, NJ, USA, 122127, 2005
Chen, YC, M'Closkey, RT, Tran, T A., and Blaes, B, "A Control and Signal Processing Integrated Circuit for the JPLBoeing Micromachined Gyroscopes,", IEEE Trans. Control Syst. Technol., Vol. 13, No. 2, pp. 286  300, Mar. 2005
M'Closkey, R.T. and Challoner A.D., "Modeling, Identification, and Control of MicroSensor Prototypes", Proc. 2004 American Control Conf., Boston, Vol. 1, 924, June 2004
Chen, Y.C., Hui, J., and M'Closkey, R., "Closedloop Identification of a MicroSensor", Proc. 42nd IEEE Conf. on Decision Control, Maui, Vol. 3, pp. 26322637, Dec. 2003
Yong, Y.K., Vig, J., Ballato, A., Kubena, R., and M'Closkey, R., "Frequencytemperature analysis of MEMS ATcut quartz resonators", Proc. 2003 IEEE Intl. Freq. Control Symp., Tampa, 1095  1099 , May 2003
Lim, M., M'Closkey, R.T., Kirby, D., Kubena, R., Vig, J.R., Ballato, A., and Yong, Y.K., "3D Modeling of HighQ Quartz Resonators for VHFUHF Applications", Proc. 2003 IEEE Intl. Freq. Control Symp., Tampa, pp. 823  828, May 2003
Chen, Y.C., M'Closkey, R.T., Tran, T., and Blaes, B., "Integration of a signal processing and control ASIC with the JPL microgyroscope", Proc. ASME IMECE, New Orleans, Nov. 2002
M'Closkey, R.T., Vakakis, A., and Gutierrez, R., "Mode Localization Induced by a Nonlinear Control Loop", Nonlinear Dynamics, Vol. 25, pp. 221  236, July 2001
M'Closkey, R.T., Gibson, S., and Hui, J., "System Identification of a MEMS Gyroscope", J. Dyn. Sys., Meas., and Cont., Trans. ASME, Vol. 123, pp. 201  210, June 2001
Grayver, E. and M'Closkey, R.T., "Automatic Gain Control ASIC for MEMS Gyro Applications", Proc. 2001 American Control Conf., Arlington, VA, Vol. 2, 1219  1222, June 2001
M'Closkey, R.T., Gibson, S., and Hui, J., "Modal Parameter Identification of a MEMS Gyroscope",Proc. 2000 American Control Conf., Chicago, IL, Vol. 3, 16991704, June 2000
M'Closkey, R.T. and Vakakis, A., "Analysis of a Microsensor Automatic Gain Control Loop", Proc.1999 American Control Conf., San Diego, CA, Vol. 5, 33073311, June 1999
M'Closkey, R.T., Gibson, S., and Hui, J., "InputOutput Dynamics of the JPL Microgyroscope", Proc. 37th IEEE Conf. Decision and Control, Tampa, FL, Vol. 4, 43284333, Dec. 1998
M'Closkey, R.T., Gibson, S., and Hui, J.K., "Model Identification of the JPL Microgyroscope", Proc. ASME Dynamic Systems and Control Division, Anaheim, DCS64, pp. 801805, Nov. 1998