Electrostatic compensation of structural imperfections in dynamically amplified dual-mass gyroscope

Efimovskaya, Alexandra; Lin, Yuqing; Wang, Danmeng; Shkel, Andrei M.

doi:10.1016/j.sna.2018.03.001

Cited by 35 publications

(7 citation statements)

References 15 publications

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“…Anti-angle term (coupling term) of frequency matrix can be eliminated by using γ 12 alone in Equation (16), which means that the voltage difference applied to the quadrature control electrodes can electrostatically correct the quadrature coupling so that the two modal principal axes of the working mode are aligned with each corresponding excitation electrode. Besides, it can also be seen from Equations (20) and (21) that in order to achieve mode-matching, the quadrature error of the DRG must be restrained first. Otherwise, the frequency split cannot be eliminated.…”

Section: Electrostatic Stiffness Tuning Theorymentioning

confidence: 99%

“…Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 • /h to 2.8331 • /h, and the Angle Random Walk (ARW) decreases from 1.0208 • / √ h to 0.0524 • / √ h. Compared with the mode mismatch condition, the ARW is improved by 19.48 times.Micromachines 2020, 11, 210 2 of 22 Therefore, the mode-matching technology improves the bias stability and mechanical sensitivity of MEMS gyroscopes by eliminating the frequency split between the driving mode and the sensing mode, which has attracted significant attention from researchers [19][20][21]. Furthermore, some frequency modification techniques are proposed.…”

mentioning

confidence: 99%

“…Micromachines 2020, 11, 210 2 of 22 Therefore, the mode-matching technology improves the bias stability and mechanical sensitivity of MEMS gyroscopes by eliminating the frequency split between the driving mode and the sensing mode, which has attracted significant attention from researchers [19][20][21]. Furthermore, some frequency modification techniques are proposed.…”

mentioning

confidence: 99%

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Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force

et al. 2020

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An automatic mode-matching method for MEMS (Micro-electromechanical Systems) disk resonator gyroscopes (DRGs) based on virtual Coriolis force is presented in this paper. For this mode-matching method, the additional tuning electrodes are not required to be designed, which simplifies the structure design. By using the quadratic relationship between the driving voltage and the electrostatic force, the virtual Coriolis force is obtained by applying an AC voltage whose frequency is half of the driving mode resonant frequency to the sense electrode. The phase difference between the virtual Coriolis force and the sense output signal is used for mode-matching. The structural characteristics and electrode distribution of the DRG are briefly introduced. Moreover, the mode-matching theories of the DRG are studied in detail. The scheme of the mode-matching control system is proposed. Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 • /h to 2.8331 • /h, and the Angle Random Walk (ARW) decreases from 1.0208 • / √ h to 0.0524 • / √ h. Compared with the mode mismatch condition, the ARW is improved by 19.48 times.Micromachines 2020, 11, 210 2 of 22 Therefore, the mode-matching technology improves the bias stability and mechanical sensitivity of MEMS gyroscopes by eliminating the frequency split between the driving mode and the sensing mode, which has attracted significant attention from researchers [19][20][21]. Furthermore, some frequency modification techniques are proposed. Laser finishing, ion beam milling, and selective deposition mass loading reduce frequency split [22,23]. However, these methods are often used to change the dynamic characteristics of the sensor permanently, and this type of tuning is inflexible and time-consuming. The tuning control is limited and can only be achieved offline.Electrostatic tuning is usually used for mode-matching, which can provide more flexibility and real-time realization [24][25][26][27][28][29]. The mode-matching process based on phase-locked loop (PLL) takes advantage of the phase delay of 90 • between the quadrature input and output of the sensing mode. This feature is used in [27] to achieve mode-matching and to adjust the tuning voltage using PLL technology. The amplitude-frequency characteristic refers to the maximum amplitude of the quadrature response signal during mode-matching [28]. However, in these methods, the signal from the Coriolis demodulation channel is used to control the frequency tuning voltage. Therefore, the angular velocity can only be measured if the tuning voltage is fixed, and the matching loop is disconnected after mode-matching. Thus, these methods cannot achieve real-time mode-matching. However, in practical applications, the frequency split of the vibratory mode changes with changes in environmental parameters [29]. Therefore, such one-time matching methods a...

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Section: Electrostatic Stiffness Tuning Theorymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force

et al. 2020

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“…Honeycomb-like disk resonator gyroscopes (HDRGs) [14] and cobweb-like disk resonator gyroscopes (CDRGs) [15] have achieved good results in reducing frequency split. Electrostatic tuning is a widely used method to reduce frequency split in DRGs because of its simple implementation and wide applicability [16][17][18][19]. However, this method requires a high tuning voltage when the frequency split is large, and it is difficult to control the magnitude of large voltages with high precision [20].…”

Section: Introductionmentioning

confidence: 99%

Development of a Novel Gear-like Disk Resonator Applied in Gyroscope

Zhang

Feng

et al. 2022

Applied Sciences

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This paper proposes a novel gear-like disk resonator (GDR). The design, fabrication, and characterization of GDR are presented. In comparison with a ring-like disk resonator (RDR), a GDR replaces the circular rings with meander-shaped rings consisting of linear beams. The finite element method (FEM) is implemented, and the simulation results show that the GDR has a much lower frequency and effective stiffness, higher quality factor (Q), and better immunity to crystal orientation error. Affected by high Q and small frequency splits, the mechanical sensitivity (Smech) is shown to increase greatly. GDR and RDR with the same structure parameters are built side-by-side on the same wafer, and prototypes are fabricated through the SOI fabrication technique. The frequency response test and ring-down test are implemented using a readout circuit under a vacuum condition (5 Pa) at room temperature. The frequency split (9.1 Hz) of the GDR is about 2.8 times smaller than that (25.8 Hz) of the RDR without electrostatic tuning. Compared with the RDR, the Q (19.2 k) and decay time constant (0.59 s) of the GDR are improved by 145% and 236%, respectively. The experimental results show great promise for the GDR being used as a gear-like disk resonator gyroscope (GDRG).

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“…The fourth harmonic error mainly causes the frequency split of the n = 2 mode and is a primary error source of the gyroscope. There are several ways to reduce the fourth harmonic error, such as electrostatic trimming [ 19 , 20 , 21 ], mechanical trimming [ 22 , 23 , 24 ], femtosecond laser trimming [ 25 ], chemical trimming [ 26 , 27 ], and ion beam trimming [ 28 , 29 ]. The electrostatic trimming requires extra voltages which makes the circuit more complicated and may introduce new noise and errors.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Estimating and Balancing the Second Harmonic Error of Cylindrical Fused Silica Resonators

et al. 2021

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The cylindrical resonator gyroscope (CRG) is a type of Coriolis vibratory gyroscope which measures the angular velocity or angle through the precession of the elastic wave of the cylindrical resonator. The cylindrical fused silica resonator is an essential component of the CRG, the symmetry of which determines the bias drift and vibration stability of the gyroscope. The manufacturing errors breaking the symmetry of the resonator are usually described by Fourier series, and most studies are only focusing on analyzing and reducing the fourth harmonic error, the main error source of bias drift. The second harmonic error also is one of the obstacles for CRG towards high precision. Therefore, this paper provides a chemical method to evaluate and balance the second harmonic error of cylindrical fused silica resonators. The relation between the frequency split of the n = 1 mode and the second harmonic error of the resonator is obtained. Simulations are performed to analyze the effects of the first three harmonic errors on the frequency splits. The relation between the location of the low-frequency axis of n = 1 mode and the heavy axis of the second harmonic error is also analyzed by simulation. Chemical balancing experiments on two fused silica resonators demonstrate the feasibility of this balancing procedure, and show good consistency with theoretical and simulation analysis. The second harmonic error of the two resonators is reduced by 86.6% and 79.8%, respectively.

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Electrostatic compensation of structural imperfections in dynamically amplified dual-mass gyroscope

Cited by 35 publications

References 15 publications

Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force

Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force

Development of a Novel Gear-like Disk Resonator Applied in Gyroscope

A Novel Method for Estimating and Balancing the Second Harmonic Error of Cylindrical Fused Silica Resonators

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