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TECHNICAL PAPERS

Stability and Resolution Analysis of a Phase-Locked Loop Natural Frequency Tracking System for MEMS Fatigue Testing

[+] Author and Article Information
X. Sun, R. Horowitz, K. Komvopoulos

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Dyn. Sys., Meas., Control 124(4), 599-605 (Dec 16, 2002) (7 pages) doi:10.1115/1.1514658 History: Received August 01, 2001; Revised March 01, 2002; Online December 16, 2002
Copyright © 2002 by ASME
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References

Komvopoulos, K., 2001, “Microelectromechanical Structures for Multiaxial Fatigue Testing,” Advances in Fracture Research, Proc. of 10th Int. Congress on Fracture, Elsevier, Honolulu, HI, Paper No. ICF100217OR.
Markus, K. W., Koester, D. A., Cowen, A., Mahadevan, R., Dhuler, V. R., Roberson, D., and Smith, L., 1995, “MEMS Infrastructure: The Multi-User MEMS Processes (MUMPs),” Proc. of SPIE: Micromachining and Microfabrication Process Technology, International Society for Optical Engineering, Austin, TX, 2639 , pp. 54–63.
Connally,  J. A., and Brown,  S. B., 1993, “Micromechanical Fatigue Testing,” Exp. Mech., 33(2), pp. 81–90.
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Hale, J. K., 1980, Ordinary Differential Equations, 2nd Edition, Krieger, Huntington, NY, pp. 175–212.
M’Closkey, R. T., and Vakakis, A., 1999, “Analysis of a Microsensor Automatic Gain Control Loop,” Proc. of American Control Conf., San Diego, CA, pp. 3307–3311.
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Park, S., 2000, “Adaptive Control Strategies for MEMS Gyroscopes,” Ph.D. dissertation, Univ. of California at Berkeley.

Figures

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Scanning electron microscopy image of a polycrystalline silicon MEMS resonator used for fatigue testing.
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Block diagram of a phase-locked loop.
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Block diagram of the natural frequency tracking system for a MEMS resonator.
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The excitation frequency tracks the natural frequency when KI=20<23.4=KI0.
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The excitation frequency tracks the natural frequency when KI=10<23.4=KI0.
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The excitation frequency oscillates about the natural frequency when KI=25>23.4=KI0.
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The excitation frequency tracks the decay of the resonator natural frequency (KI=10).
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The response of the excitation frequency for a cubic nonlinear resonator with 1% cubic force (KI=0.1):a) Overall response, and b) detail at steady state.
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The response of the excitation frequency for a cubic nonlinear resonator with 5% cubic force (KI=0.1).
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The excitation frequency tracks the natural frequency under the presence of Brownian and capacitive position sensing noise (KI=20).

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