Disk Resonator Gyroscope Research Articles

Research on Energy Dissipation Mechanism of Cobweb-like Disk Resonator Gyroscope.

The micro disk resonator gyroscope is a micro-mechanical device with potential for navigation-grade applications, where the performance is significantly influenced by the quality factor, which is determined by various energy dissipation mechanisms within the micro resonant structure. To enhance the quality factor, these gyroscopes are typically enclosed in high-vacuum packaging. This paper investigates a wafer-level high-vacuum-packaged (<0.1 Pa) cobweb-like disk resonator gyroscope, presenting a systematic and comprehensive theoretical analysis of the energy dissipation mechanisms, including air damping, thermoelastic damping, anchor loss, and other factors. Air damping is analyzed using both a continuous fluid model and an energy transfer model. The analysis results are validated through quality factor testing on batch samples and temperature characteristic testing on individual samples. The theoretical results obtained using the energy transfer model closely match the experimental measurements, with a maximum error in the temperature coefficient of less than 2%. The findings indicate that air damping and thermoelastic damping are the predominant energy dissipation mechanisms in the cobweb-like disk resonant gyroscope under high-vacuum conditions. Consequently, optimizing the resonator to minimize thermoelastic and air damping is crucial for designing high-performance gyroscopes.

Machine learning-driven discovery of high-performance MEMS disk resonator gyroscope structural topologies

The design of the microelectromechanical system (MEMS) disc resonator gyroscope (DRG) structural topology is crucial for its physical properties and performance. However, creating novel high-performance MEMS DRGs has long been viewed as a formidable challenge owing to their enormous design space, the complexity of microscale physical effects, and time-consuming finite element analysis (FEA). Here, we introduce a new machine learning-driven approach to discover high-performance DRG topologies. We represent the DRG topology as pixelated binary matrices and formulate the design task as a path-planning problem. This path-planning problem is solved via deep reinforcement learning (DRL). In addition, we develop a convolutional neural network-based surrogate model to replace the expensive FEA to provide reward signals for DRL training. Benefiting from the computational efficiency of neural networks, our approach achieves a significant acceleration ratio of 4.03 × 105 compared with FEA, reducing each DRL training run to only 426.5 s. Through 8000 training runs, we discovered 7120 novel structural topologies that achieve navigation-grade precision. Many of these surpass traditional designs in performance by several orders of magnitude, revealing innovative solutions previously unconceived by humans.

An automatic Q-factor matching method for eliminating 77% of the ZRO of a MEMS vibratory gyroscope in rate mode

Mismatching quality factors (Q-factors) is one of the main factors causing zero-rate output (ZRO) in degenerate (DE) Micro-Electro-Mechanical Systems (MEMS) vibratory gyroscopes. To eliminate the ZRO of the DE MEMS gyroscope, this study introduces a method for real-time identification and automatic matching of Q-factors in rate mode. By leveraging the vibration characteristics of the DE MEMS vibratory gyroscope in rate mode, dedicated online test methods are designed to determine the Q-factors for both the drive and sense modes, enabling online identification of the Q-factor mismatching. Furthermore, an automatic Q-factor matching system is designed utilizing the mechanical-thermal dissipation mechanism of the resistive damper. The effectiveness of this proposed method is validated through simulations and experiments conducted on a MEMS disk resonator gyroscope (DRG). The results show a measurement error within 4% for Q-factor identification, and automatic Q-factor matching effectively reduces the ZRO by 77%. Employing this automatic Q-factor matching method successfully reduces the ZRO that is caused by the mismatching of Q-factors in the MEMS DRG from 0.11°/s to 0.025°/s and improves the bias instability (BI) from 0.40°/s to 0.19°/s.

Temperature drift suppression for micro‐electro‐mechanical system gyroscope based on vibrational‐displacement control with harmonic amplitude ratio

AbstractMicro‐electro‐mechanical system gyroscope detection output is susceptible to drift due to ambient temperature variations. Furthermore, the drive‐mode vibration amplitude is affected by the signal pickup circuit and structural parameters, which significantly influence the temperature drift of the bias and scale factor (SF). This study proposes a vibration amplitude control method based on harmonic amplitude sideband‐ratio (SBR), namely SBR‐AGC, which characterizes the vibration amplitude using the harmonic amplitude ratio of the vibrational electrical signal. The constancy of vibration amplitude is maintained via closed‐loop control to suppress bias and SF temperature drift. The experimental results on cobweb‐like disk resonator gyroscope reveal that the temperature coefficient of bias in the SBR‐AGC mode lies within −20 to 60°C and decreases by 36%, and the temperature coefficient of the SF lies within −10 to 50°C and decreases by 49.7%. Therefore, the environmental adaptability of the gyroscope is effectively improved.

Removal of the rate table: MEMS gyrocompass with virtual maytagging

High-performance micro-electro-mechanical system (MEMS) gyrocompasses for north-finding systems have been very popular for decades. In this paper, a MEMS north-finding system (NFS) based on virtual maytagging (VM) is presented for the first time. In stark contrast to previous schemes of MEMS-based NFSs (e.g., carouseling, maytagging) and the abandoning rate table, we developed a honeycomb disk resonator gyroscope (HDRG) and two commercial accelerometers for azimuth detection. Instead of the physical rotation of the integrated turntable in traditional NFSs, the vibratory working modes of the HDRG are rotated periodically with electronic control to reduce the uncertainty in the azimuth. After systematically analyzing the principle of NFSs with VM, we designed tests to verify the practicability at the sensor level. A bias instability of 0.0078°/h can be obtained during one day with VM in an HDRG. We also implemented comparative north-finding experiments to further check our strategy at the system level. The accuracy in the azimuth can reach 0.204° for 5 min at 28.2° latitude with VM and 0.172° with maytagging. The results show that without any mechanical turning parts, VM technology makes it possible to develop high-precision handheld MEMS NFSs.

A Low-Noise Interface ASIC for MEMS Disk Resonator Gyroscope.

This paper proposes a low-noise interface application-specific integrated circuit (ASIC) for a microelectromechanical systems (MEMS) disk resonator gyroscope (DRG) which operates in force-to-rebalance (FTR) mode. The ASIC employs an analog closed-loop control scheme which incorporates a self-excited drive loop, a rate loop and a quadrature loop. A ΣΔ modulator and a digital filter are also contained in the design to digitize the analog output besides the control loops. The clocks for the modulator and digital circuits are both generated by the self-clocking circuit, which avoids the requirement of additional quartz crystal. A system-level noise model is established to determine the contribution of each noise source in order to reduce the noise at the output. A noise optimization solution suitable for chip integration is proposed based on system-level analysis, which can effectively avoid the effects of the 1/f noise of the PI amplifier and the white noise of the feedback element. A performance of 0.0075°/√h angle random walk (ARW) and 0.038°/h bias instability (BI) is achieved using the proposed noise optimization method. The ASIC is fabricated in a 0.35 μm process with a die area of 4.4 mm × 4.5 mm and power consumption of 50 mW.

Calibration of Coupling Errors for Scale Factor Nonlinearity Improvement in Navigation-Grade Honeycomb Disk Resonator Gyroscope

With the performance of micromechanical gyroscopes approaching navigation grade, the scale factor nonlinearity is gradually becoming the limitation for high-performance applications such as the satellite attitude measurement. Coupling errors caused by parasitic capacitance are the major sources of scale factor nonlinearity but are usually neglected. In this paper, the parasitic-capacitance coupling errors are introduced into the traditional gyroscope model and the scale factor nonlinearity induced by the coupling errors has been analyzed theoretically. The analysis indicates that two parasitic-capacitance couples from sense excitation signal to drive or sense detection signal are the dominant causes of scale factor nonlinearity. Two measurements (i.e. the amplitude of driving excitation signal and axis tuning voltage) are used to realize the calibration of coupling errors with the least square method. The experiment is also carried out to verify this novel calibration method on a navigation-grade honeycomb disk resonator gyroscope. The experimental results demonstrate that the coupling errors has decreased by 87.5 and 44.5 times respectively after the error compensation and that the scale factor nonlinearity has been improved from 244.8ppm to 29.00ppm. Furthermore, this calibration method can be applied to other resonator gyroscopes with the similar structure and control scheme.

Bias Thermal Stability Improvement of Mode-Matching MEMS Gyroscope Using Mode Deflection

This letter presents a novel strategy to eliminate the bias drift by using mode deflection. The bias of a mode-match gyroscope is mainly caused by the asymmetrical damping and its azimuth. Mode deflection is a method to deflect the drive mode to the direction of damping axis through the circuit configuration, thereby nulling the damping azimuth. After deflection, the bias is not sensitive to the drift of damping and its stability will be greatly improved. Experiments performed on a honeycomb disk resonator gyroscope have demonstrated the effect of this method. The compensation method yields a navigation-grade performance with the bias instability of 0.014°/h. The bias variation overall temperature range from −40°C to 60°C is improved from 73.6°/h to 1.15°/h and the RMS of the bias is 0.26°/h. [2022-0167]

An In-Run Automatic Mode-Matching Method With Amplitude Correction and Phase Compensation for MEMS Disk Resonator Gyroscope

An In-Run Automatic Mode-Matching Method With Amplitude Correction and Phase Compensation for MEMS Disk Resonator Gyroscope

Scale Factor Self-Calibration of MEMS Gyroscopes Based on the High-Order Harmonic Extraction in Nonlinear Detection

This article presents a novel self-calibration method to improve the scale factor (SF) stability by the synchronous control on the first-order and third-order harmonic components of nonlinear detection. On the conventional scheme of a drive loop, the readout amplitude of the first-order harmonic component is controlled at a constant value. However, the actual vibration amplitude of drive-mode motion would drift due to the change of circuit gains between the readout amplitude and actual amplitude, thereby resulting in the deterioration of the SF stability. The third-order harmonic component of nonlinear detection shares the same circuit with the vibration signal, indicating that its readout amplitude can track the change in circuit gains in real time. Therefore, this new approach replaces the original fixed reference with the varying readout amplitude of the third-order harmonic component to eliminate the drive-mode vibration error and eventually calibrate the drift of SF. Experiments performed on a honeycomb disk resonator gyroscope (HDRG) have demonstrated the feasibility of the calibration method. The calibration based on the harmonic extraction yields a short-term SF repeatability of 24.9 ppm and a long-term SF repeatability of 30.8 ppm. Allan deviation analysis of the calibrated SF demonstrates a 3.5-ppm precision upon an average of 200 s. The temperature sensitivity of the SF is reduced from 717.3 ppm/°C to 5.02 ppm/°C and the SF repeatability is improved from 15643 ppm to 94.9 ppm over the temperature range of −30 °C to 30 °C.

A Mode-Matched DRG Realized by Monolithic Integrated Interface Circuit Design

This article proposes a novel design method for the mode-matched disk resonator gyroscope (DRG) realized by the monolithic integrated interface circuit. The mode-mismatched dynamics model of DRG is simplified by introducing the analysis method of “slow” dynamics, the effect of mode mismatching is quantified, and the automatic mode-matched interface circuit is designed based on the analysis of the simplified model. The force-rebalance loop is designed based on a self-clock circuit that releases the chip from the dependence on external clocks, avoids the design of multipliers, analog-to-digital converters (ADCs), and digital-to-analog converters (DACs), and improves the integration of the chip. The highly integrated automatic mode-matching loop is realized by the designing of a quadrature loop and stiffness tuning loop on the basics of the mode-matching theory. The design method is applied to develop a monolithic integrated interface chip of DRG with an area of 4.2 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times4.3$ </tex-math></inline-formula> mm and power consumption of 90 mW. The DRG integrated circuit achieves the bias instability (BI) of 0.38°/h and the angle random walk (ARW) of 0.0354°/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd \text{h}$ </tex-math></inline-formula> within a full scale of ±300°/s, which provides a highly integrated circuit design scheme for DRG’s extensive application.

A mode order optimized disk resonator gyroscope considering thermoelastic damping

Mode properties and thermoelastic damping (TED) are crucial for the disk resonator gyroscope (DRG). Most of the DRG structure designs do not involve the mode order adjustment and the compatibility design of mode order optimization and quality factor is more lacking. In this paper, a novel mode order optimized DRG is designed and its mode properties and TED are investigated. Parametric studies are conducted to explore the DRG performance which is closely related to structure shapes and dimensions. The parametric study of the proposed DRG indicates that the operation mode being the first order and having a low frequency, the large frequency difference between the operation mode and parasitic modes and the high thermoelastic quality factor are compatible by selecting appropriate structural dimensions. To further improve the quality factor, masses and slots are applied in the proposed DRG respectively. The results show that TED can be effectively reduced with reasonable mass or slot configurations and meanwhile the DRG maintains favorable mode properties due to the strong stability of mode order optimization of the proposed DRG. In general, the research finding in this paper can be a useful reference for other micromachined gyroscope designs.

Virtual Rotating MEMS Gyrocompassing With Honeycomb Disk Resonator Gyroscope

High performance north-finding systems (NFSs) based on Micro-Electro-Mechanical System (MEMS) gyroscopes are widely concerned over decades. This letter proposes a novel strategy for MEMS gyrocompassing, exploiting the measurements of a honeycomb disk resonator gyroscope (HDRG). Completely different from previous MEMS gyrocompassing approaches for drift reduction of MEMS gyroscopes (e.g., carouseling, maytagging), without any mechanical turning parts, the virtual rotating framework is greatly conducive to the compactness and reliability of NFSs. The experimental results show that the true north can be found with the accuracy of 0.48° for 5 minutes averaging time at 28° latitude, proving the possibility of eliminating the need for physical rotation of MEMS gyroscopes.

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

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).

Effect of Quadrature Control Mode on ZRO Drift of MEMS Gyroscope and Online Compensation Method.

The quadrature coupling error is an important factor that affects the detection output of microelectromechanical system (MEMS) gyroscopes. In this study, two quadrature error control methods, quadrature force-to-rebalance control (Mode I) and quadrature stiffness control (Mode II) were analyzed. We obtained the main factors affecting the zero-rate output (ZRO) under force-to-rebalance (FTR) closed-loop detection. The analysis results showed that the circuit phase delay in Mode I caused the quadrature channel to leak into the in-phase channel. However, in Mode II, the quadrature coupling stiffness was corrected in real time, which effectively improved the stability of the ZRO. The changes in the vibration displacement and Q-factor were the main factors for the ZRO drift in Mode II. Therefore, we propose an online compensation method for ZRO drift based on multiparameter fusion. The experimental results on a cobweb-like disk resonator gyroscope (CDRG) with a 340 k Q-factor showed that the bias instability (BI) of Mode II was significantly better than that of Mode I. After online compensation, the BI reached 0.23°/h, and the bias repeatability reached 3.15°/h at room temperature.

An In-Run Automatic Mode-Matching Method for N = 3 MEMS Disk Resonator Gyroscope

This paper demonstrates an in-run automatic mode-matching method for a Micro-Electro-Mechanical systems (MEMS) disk resonator gyroscope (DRG) operating in the n = 3 wineglass mode. In proposed method, two sideband signals whose frequencies are located at both sides of the drive mode symmetrically, are used to excite the gyroscope, and the response of the gyroscope in the Coriolis force channel is demodulated to obtain the indicator of the frequency split for mode-matching. The input angle rate can still be measured when the proposed mode-matching loop works normally. However, due to the asymmetry of the amplitude of the double-sideband response of the sense mode, there is a tuning error, which leads to a shift of the matching frequency. To eliminate the tuning error and achieve perfect mode-matching, a novel compensation method for the amplitude correction is proposed. The theories of electrostatic tuning of the MEMS DRG, the proposed mode-matching method and the compensation method are analyzed and introduced. The simulation results show that this method can achieve in-run automatic closed-loop mode matching for gyroscopes, and the compensation method can effectively eliminate the tuning error and reduce the frequency split from ~0.5 Hz to < 0.01 Hz. The experimental results show that the bias instability (BI) and the angle random walk (ARW) is improved by 5.8 times and 1.7 times, respectively, under mode-matching. After the tuning error is eliminated with compensation method, the BI and ARW are further reduced to 1.36 °/h and 0.1562 °/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd \text{h}$ </tex-math></inline-formula> , respectively.

A Quick Start Method for MEMS Disk Resonant Gyroscope.

High-precision disk resonator gyroscope has a high quality factor in order to improve the performance of the gyroscope, as the high quality factor can lead to a long starting time. In this paper, a control system of the driving loop of the disk MEMS resonant gyroscope with the quick start is designed. The control system has functions of quick frequency locking and fast step response. Coarse-precision mode transition system is designed for quick frequency locking. A large-small mode transition system is designed for fast step response. The correctness of the design is verified by circuit test. The test results show that the start-up time is reduced by over 80% compared with the traditional control loop.

A Wafer-Level Vacuum Packaged MEMS Disk Resonator Gyroscope With 0.42°/h Bias Instability Within ±300°/s Full Scale

This article reports a MEMS disk resonator gyroscope (DRG) with superior overall performance in terms of bias instability, measurement range, and size. Specifically, a fully filled electrodes MEMS DRG is proposed to improve sensing capacitance to 23.66 pF and drive capacitance to 6.14 pF. The DRG is fabricated using a wafer-level vacuum-package process and is controlled and sensed by a configurable ASIC, enabling a small footprint. The DRG achieves an angle random walk of 0.05°/√h and bias instability of 0.42°/h within a full scale of ±300°/s, making it a very promising solution for angular measurement in high-end industrial applications.

Bandwidth and noise analysis of high-Q MEMS gyroscope under force rebalance closed-loop control

The force-to-rebalance (FTR) closed-loop detection method is commonly used to expand the bandwidth (BW) for micro-electro-mechanical system (MEMS) gyroscopes with low-frequency split and high-quality factors. However, the relationship between the BW and output noise is often incompatible; thus, reducing the detection accuracy of the gyroscope. This paper presents an analysis of the BW and noise spectra under modulation-demodulation FTR gyroscopes. The expressions for the BW and the noise-equivalent rate (NER) spectrum are derived to explore the effects of the loop gain on the BW and NER. It is demonstrated that the gain of the amplifier circuit is maximally transferred to the vibration displacement signal conversion part, which can reduce the output noise without affecting the BW. The simulation and experimental results on the Cobweb-like disk resonator gyroscope show that the derived expressions of BW and NER are correct, and the noise optimization method is effective, which provides an idea for the realization of a high-precision MEMS gyroscope.

A Rate-Integrating Honeycomb Disk Resonator Gyroscope With 0.038°/h Bias Instability and °7000°/s Measurement Range

This letter presents a high performance rate-integrating honeycomb disk resonator gyroscope (HDRG). High Q factor resonator and symmetric vibration detection gain are the key to high performance rate-integrating gyroscope. By stiffness-mass decoupling design, HDRG can achieve high Q factor of about 600k and decay time of over 44s. A compensation method is applied to suppress the rate-dependent angular drift caused by the asymmetry circular distribution of detection gains. Finally, the rate-integrating HDRG shows an excellent bias instability of 0.038°/h, 1.05ppm scale factor nonlinearity, wide measurement range of over ±7000°/s and a threshold value of about ±0.0001°/s, which is the best performance in the reported rate-integrating MEMS gyroscopes.