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SPECIAL SECTION PAPERS

Impact of Synchronization in Micromechanical Gyroscopes

[+] Author and Article Information
Martial Defoort

Department of Mechanical and
Aerospace Engineering,
University of California, Davis,
1 Shields Avenue,
Davis, CA 95616
e-mail: mjdefoort@ucdavis.edu

Parsa Taheri-Tehrani

Department of Mechanical and
Aerospace Engineering,
University of California, Davis,
1 Shields Avenue,
Davis, CA 95616
e-mail: ptaheri@ucdavis.edu

Sarah H. Nitzan

Department of Mechanical and
Aerospace Engineering,
University of California, Davis,
1 Shields Avenue,
Davis, CA 95616
e-mail: sarah.nitzan@gmail.com

David A. Horsley

Department of Mechanical and
Aerospace Engineering,
University of California, Davis,
1 Shields Avenue,
Davis, CA 95616
e-mail: dahorsley@ucdavis.edu

1Corresponding authors.

2Present address: Invensense, 1745 Technology Drive #200, San Jose, CA 95110.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 3, 2016; final manuscript received February 17, 2017; published online May 30, 2017. Assoc. Editor: Slava Krylov.

J. Vib. Acoust 139(4), 040906 (May 30, 2017) (7 pages) Paper No: VIB-16-1575; doi: 10.1115/1.4036397 History: Received December 03, 2016; Revised February 17, 2017

In this paper, we study the occurrence of synchronization between the two degenerate resonance modes of a microdisk resonator gyroscope. Recently, schemes involving the simultaneous actuation of the two vibration modes of the gyroscope have been implemented as a promising new method to increase their performance. However, this strategy might result in synchronization between the two modes, which would maintain frequency mode-matching but also may produce problems, such as degrading stability and sensitivity. Here, we demonstrate for the first time synchronization between the degenerate modes of a microgyroscope and show that synchronization arising from mutual coupling dramatically reduces frequency instability at the cost of increased amplitude instability. We present an alternative synchronization scheme that suppresses this drawback while still taking advantage of a passive frequency mode-match operation.

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Figures

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Fig. 1

Schematic of the DRG and shape of the two modes X and Y used to probe Coriolis force and study the synchronization process

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Fig. 2

Setup for implementation of synchronization between the X mode and an external tone

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Fig. 3

Experimental results of the frequency of the X mode fX as the frequency of the external tone fe is swept upward and downward (as suggested by the arrows), here in the nonlinear regime. fX follows fe within the synchronization range, which increases quadratically with the amplitude of X, as presented in the inset (data points: experimental results and line: prediction from Eq.(4)).

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Fig. 4

Allan deviation of fX with and without synchronization. At 100 s averaging time, the Allan deviation is reduced by 3 orders of magnitude in the synchronization regime.

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Fig. 5

Frequency response as a function of time. X (top) and HM (bottom) fluctuate with the same trend when driven as free oscillators. X was driven with a nonlinearity of 2.5 Hz to observe stable synchronization. When the external tone is switched on (dashed area) with a force Fe=0.1 FX, X gets synchronized to it and response at the reference's frequency, while the HM response demonstrates that the mechanism at the origin of the fluctuations is not affected. The transitions between the two regimes (typically 1 s) have been removed for clarity. Inset: comsol simulation of X and HM.

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Fig. 6

Setup for the mutual synchronization of the X and Y modes through natural mode coupling (curved arrows)

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Fig. 7

Allan deviation of the frequency difference between X and Y (fX − fY) in the mutual synchronization regime. Inset: fluctuations of the resonance frequencies of X and Y in the time domain.

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Fig. 8

Y response upon applied constant rate with and without synchronization. Top: rate of 20 deg/s for 9 s. Bottom: rate of 40 deg/s for 4.5 s. Note that for the synchronization case, the constant driving amplitude has been subtracted.

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Fig. 9

Amplitude and frequency response as a function of time, as synchronization is turned on (dashed area) and off. When X is synchronized to the external oscillator, its amplitude (top) fluctuates with the same trend as the frequency of HM (bottom). The transitions between the two regimes (typically 1 s) have been removed for clarity. Inset: comsol simulation of X and HM.

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Fig. 10

Typical phase spaces resulting from the two synchronization setups presented (left: X synchronized with an external tone in the nonlinear regime and right: synchronization between X and Y in the linear limit, both graphs using the same scales) and compared with the nonsynchronized scenario. These plots reveal that the frequency fluctuations vanish in the synchronization regime at the cost of greater amplitude noise.

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Fig. 11

Allan deviation of the zero rate output of the gyroscope with and without mutual synchronization. As the frequency fluctuations are converted into amplitude fluctuations, the performance of the gyroscope decreases.

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Fig. 12

Alternative setup for the implementation of synchronization in a gyroscope. The drive mode X is synchronized to Y by means of a feedback loop, while Y remains a free-running oscillator. The amplitude fluctuations induced by synchronization only affect X and can be recovered by a PID, enabling to use Y as the sense mode of the gyroscope.

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Fig. 13

Allan deviation of the zero rate output of the gyroscope, comparing mutual and one-way synchronization. The Allan deviation of the nonsynchronized mode's amplitude is displayed as a reference of the limit reachable by the one-way synchronization scheme.

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