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Frequency tuning of work modes in the silicon vibratory gyroscope is studied by the theoretical, numerical, and experimental methods in this paper. First, the schematic structure and simplified kinematics model of the gyroscope were presented for deducing the natural frequencies. Then, the width and length of support beams were optimized to tune wo...
Citations
... Another improved phase relation method is developed based on the virtual Coriolis force (VCF) [27,28]. In this way, an external signal for simulating the Coriolis force with the corresponding frequency and phase information was loaded to special electrodes in the sense mode to excite the vibration of the sense mode. ...
A VCF-based mode-matching micromachine-optimized tuning fork gyroscope is proposed to not only maximize the scale factor of the device, but also avoid use of an additional quadrature-nulling loop to prevent structure complexity, pick-up electrode occupation, and coupling with a mode-matching loop. In detail, a mode-matching, closed-loop system without a quadrature-nulling loop is established, and the corresponding convergence and matching error are quantitatively analyzed. The optimal straight beam of the gyro structure is then modeled to significantly reduce the quadrature coupling. The test results show that the frequency split is narrowed from 20 Hz to 0.014 Hz. The scale factor is improved 20.6 times and the bias instability (BI) is suppressed 3.28 times. The observed matching accuracy demonstrates that a mode matching system without a quadrature suppression loop is feasible and that the proposed device represents a competitive design for a mode-matching gyroscope.
... A vacuum-packaged dual-mass resonator gyroscope developing from the former structure [30] was applied in the experiment, whose structure is shown in Figure 9. The major parameters are listed in Table 1 Figure 9. ...
In this paper, an online compensation method of phase delay error based on a Phase-Frequency (P-F) characteristic has been proposed for MEMS Coriolis Vibratory Gyroscopes (CVGs). At first, the influences of phase delay were investigated in the drive and sense mode. The frequency response was acquired in the digital control system by collecting the demodulation value of drive displacement, which verified the existence and influence of the phase delay. In addition, based on the P-F characteristic, that is, when the phase shift of the nonresonant drive force through the resonator is almost 0° or 180°, the phase delay of the gyroscope is measured online by injecting a nonresonant reference signal into the drive-mode dynamics. After that, the phase delay is self-corrected by adjusting the demodulation phase angle without affecting the normal operation of the gyroscopes. The approach was validated with an MEMS dual-mass vibratory gyroscope under double-loop force-to-rebalance (in-phase FTR and quadrature FTR) closed-loop detection mode and implemented with FPGA. The measurement results showed that this scheme can detect and compensate phase delay to effectively eliminate the effect of the quadrature error. This technique reduces the zero rate output (ZRO) from -0.71°/s to -0.21°/s and bias stability (BS) from 23.30°/h to 4.49°/h, respectively. The temperature sensitivity of bias output from -20 °C to 40 °C has reached 0.003 °/s/°C.
... To mitigate this error, frequency tuning is required, and for this purpose a phenomenon called electrostatic spring softening is used to change the stiffness of the structure electronically and therefore change the frequency. This method allows the designer to reduce the mismatch and to get the optimal performance of the MEMS gyroscope [13,14]. The number of proof masses in resonant MEMS gyroscopes can affect the common mode errors and therefore the performance of the gyroscope. ...
The micro-electro-mechanical systems (MEMS)-based sensor technologies are considered to be the enabling factor for the future development of smart sensing applications, mainly due to their small size, low power consumption and relatively low cost. This paper presents a new structurally and thermally stable design of a resonant mode-matched electrostatic z-axis MEMS gyroscope considering the foundry constraints of relatively low cost and commercially available silicon-on-insulator multi-user MEMS processes (SOIMUMPs) microfabrication process. The novelty of the proposed MEMS gyroscope design lies in the implementation of two separate masses for the drive and sense axis using a unique mechanical spring configuration that allows minimizing the cross-axis coupling between the drive and sense modes. For frequency mismatch compensation between the drive and sense modes due to foundry process uncertainties and gyroscope operating temperature variations, a comb-drive-based electrostatic tuning is implemented in the proposed design. The performance of the MEMS gyroscope design is verified through a detailed coupled-field electric-structural-thermal finite element method (FEM)-based analysis.
... The vibrational amplitude greatly improves when the work frequency equals the resonant frequency. Therefore, the displacement of differential tines is maximized and the mechanical sensitivity can be effectively increased when the two work modes of the gyroscope have the same resonant frequency (i.e., they are mode matched) [12,13]. It is difficult to completely match the resonant frequencies of the two modes through structural design due to fabrication imperfections. ...
This paper presents the design and analysis of a new micro-electro-mechanical system (MEMS) tuning fork gyroscope (TFG), which can effectively improve the mechanical sensitivity of the gyroscope sense-mode by the designed leverage mechanism. A micromachined TFG with an anchored leverage mechanism is designed. The dynamics and mechanical sensitivity of the design are theoretically analyzed. The improvement rate of mechanical sensitivity (IRMS) is introduced to represent the optimization effect of the new structure compared with the conventional one. The analytical solutions illustrate that the IRMS monotonically increases with increased stiffness ratio of the power arm (SRPA) but decreases with increased stiffness ratio of the resistance arm (SRRA). Therefore, three types of gyro structures with different stiffness ratios are designed. The mechanical sensitivities increased by 79.10%, 81.33% and 68.06% by theoretical calculation. Additionally, FEM simulation demonstrates that the mechanical sensitivity of the design is in accord with theoretical results. The linearity of design is analyzed, too. Consequently, the proposed new anchored leverage mechanism TFG offers a higher displacement output of sense mode to improve the mechanical sensitivity.
... In the guidance of missiles, satellite carriers or space exploration rockets, the MEMS gyroscopes are directly utilized to realize the space attitude control and orbit control. [9][10][11][12] With the popularization and deepening of application, the requirement for higher accuracy of MEMS gyroscope is also increasing. How to further improve the mechanical sensitivity of MEMS gyroscopes to meet the urgent needs of aerospace, military defense and exclusive industrial products has become one of the research hotspots. ...
In this paper, the motion characteristics and non-ideal dynamics of a stereoscopic symmetrical quadruple hair gyroscope (SSQHG) are explored. The device description and operating principle of SSQHG are briefly interpreted. Based on a simplified mass-spring-damping model, the motion characteristics of SSQHG under different excitation methods (anti-phase drive, in-phase drive and single mass drive) are deduced, and the angular velocity mechanical sensitivity of SSQHG is subsequently calculated. The effects of electrostatic force error, mass error and stiffness error on structural dynamics are analyzed in detail. Finite element method (FEM) simulations are implemented to verify the correctness of proposed dynamic model. The simulation results show a highly consistency with theoretical analysis. Finally, the frequency response and angular velocity sensitivity experiments are performed on two fabricated prototypes. The experimental results confirm that the inevitably non-ideal errors of prototypes lead to distinct performance difference. The kinematic analysis methodology of SSQHG presented in this paper is suitable for other quadruple mass gyroscopes (QMG).
... As a miniature sensor for measuring angular velocity, MEMS gyroscopes have been widely used in military and civilian fields [1][2][3][4]. Therefore, the performance requirements of the MEMS gyroscope are also increasing [2,5,6]. When the drive mode and sense mode of the gyroscope have the same resonant frequency (mode-matching), the gyroscope can have a higher signal-to-noise ratio of the output signal without deteriorating the circuit noise. ...
... There are several post-processing frequency tuning technologies to eliminate frequency split, such as local thermal stress technology [9,10], micromachining correction technology [11,12], and electrostatic adjustment technology [1][2][3][4][5][6][7][8][13][14][15][16][17][18][19]. In [9,10], the structural stress and material parameters of the gyroscope are changed by the heat generated by loading voltage, and the resonant frequency of the gyroscope is altered to realize the mode-matching. ...
... However, these frequency tuning strategies do not work properly if the input angular velocity changed. The frequency tuning strategies that can satisfy the normal operation of the gyroscope is to introduce low-frequency oscillation signals into the sense resonator, and realize mode-matching according to the amplitude or phase characteristics of the output signals [1,6,15,19]. ...
In order to eliminate the frequency mismatch of MEMS (Microelectromechanical Systems) gyroscopes, this paper proposes a frequency tuning technology based on a quadrature modulation signal. A sinusoidal signal having a frequency greater the gyroscope operating bandwidth is applied to the quadrature stiffness correction combs, and the modulation signal containing the frequency split information is then excited at the gyroscope output. The effects of quadrature correction combs and frequency tuning combs on the resonant frequency of gyroscope are analyzed. The tuning principle based on low frequency input excitation is analyzed, and the tuning system adopting this principle is designed and simulated. The experiments are arranged to verify the theoretical analysis. The wide temperature range test (-20 ∘ C –60 ∘ C ) demonstrates the reliability of the tuning system with a maximum mismatch frequency of less than 0.3 Hz. The scale factor test and static test were carried out at three temperature conditions (−20 ∘ C, room temperature, 60 ∘ C), and the scale factor, zero-bias instability, and angle random walk are improved. Moreover, the closed-loop detection method is adopted, which improves the scale factor nonlinearity and bandwidth under the premise of maintaining the same static performances compared with the open-loop detection by tuning.
... The oscillation amplitude greatly increases when the oscillator vibrates at the resonant frequency. Therefore, the mechanical sensitivity is maximized and the signal-to-noise ratio can be effectively improved when the two modes of the gyroscope have the same resonant frequency (mode-matched) [2,3]. However, because of fabrication imperfections, it is difficult to completely match the resonant frequencies of the two modes through structural design [4]. ...
In order to solve the problem where existing mode-matching methods in microelectromechanical systems (MEMS) vibrating gyroscopes fail to meet real-time and reliability requirements, this paper presents a novel method to accomplish automatic and real-time mode-matching based on phase-shifted 45° additional force demodulation (45° AFD-RM). The phase-shifted 45° additional force signal has the same frequency as the quadrature force signal, but it is phase-shifted by 45° and applied to the sense mode. In addition, two-way phase-shifted 45° demodulations are used at the sense-mode detection output to obtain a phase metric that is independent of the Coriolis force and can reflect the mode-matching state. Then, this phase metric is used as a control variable to adaptively control the tuning voltage, so as to change the sense-mode frequency through the negative stiffness effect and ultimately achieve real-time mode-matching. Simulation and experimental results show that the proposed 45° AFD-RM method can achieve real-time matching. The mode frequency split is controlled within 0.1 Hz, and the gyroscope scale factor, zero-bias instability, and angle random walk are effectively improved.
In this paper, an improved area-varying tuning electrode with better immunility to fringe capactor is proposed, analyzed and tested, which is mainly used for frequency tuning of micromechanical gyroscopes. Based on the existing area-varying tuning electrode[23], this paper firstly analyzes the capacitance of the tuning electrode, and obtains the relationship between the capacitance and the displacement using both the analytic formula and finite element analysis, verifying that the fringe capacitance in area-varying tuning electrode decreases the tuning ability of both up-tuning electrode and down-tuning electrode. Then, parametric scanning method is used to optimize the geometry parameter of the tuning electrode, which reduces the influence of fringe capacitance and increases the tuning ability of the tuning electrode. Contrast experiments and tests are carried with gyroscope samples with tuning electrodes before and after optimizing. The tested mean value of tuning ability of the improved tuning electrode is improved by 95.7% after opimization.
In recent years, the Internet of Things (IoT) has swept through most aspects of people lives, where all objects are connected to a common network. Therefore, the security of IoT devices is naturally crucial. As for the constrained resources of IoT devices, we need to have lightweight encryption algorithms. Accordingly, the symmetric key establishment is a favourite paradigm for securing IoT. In this study, a key pre-distribution scheme (KPS) has been proposed based on the combinatorial design for IoT. The proposed KPS has been created to increase network scalability. Therefore, a combinatorial design called the unital design has been applied for the establishment of keys. In the present scheme, a kind of mapping has been proposed from the unital design to the key establishment, which yields a network with high scalability. The results indicate that the present scheme increases network scalability considerably with high resilience.
This paper presents the design and analysis of a novel dual-mass microelectromechanical systems (MEMS) resonant output gyroscope (ROG), which can effectively eliminate the influence of common-mode disturbance, such as the linear acceleration, on the gyroscope working mode by the design of dual-mass form, as well as on the frequency outputs of the double-ended tuning fork (DETF) resonators by the differential arrangement. The concept of the ROG is introduced first. Then the dynamics of the gyroscope and the force-frequency characteristics of the DETF resonator are theoretically analyzed. By establishing the distribution coefficient of force and the reasonable equivalent of the force-frequency characteristics of the DETF resonator, the accurate expression of the device sensitivity is obtained. Based on the analysis results, the leverage mechanism and the DETF resonator are designed in detail. Then the configuration of the gyroscope, a dual-mass structure, is given. Finally, the validity of the analysis and design are verified by numerical simulations.
