Disk Resonator Gyroscope Research Articles

Analysis of Parametric and Subharmonic Excitation in Push-Pull Driven Disk Resonator Gyroscopes.

For micro-electromechanical system (MEMS) resonators, once the devices are fabricated and packaged, their intrinsic quality factors (Q) will be fixed and cannot be changed, which seriously limits the further improvement of the resonator’s performance. In this paper, parametric excitation is applied in a push-pull driven disk resonator gyroscope (DRG) to improve its sensitivity by an electrical pump, causing an arbitrary increase of the “effective Q”. However, due to the differential characteristics of the push-pull driving method, the traditional parametric excitation method is not applicable. As a result, two novel methods are proposed and experimentally carried out to achieve parametric excitation in the push-pull driven DRGs, resulting in a maximum “effective Q” of 2.24 × 106 in the experiment, about a 7.6 times improvement over the intrinsic Q. Besides, subharmonic excitation is also theoretically analyzed and experimentally characterized. The stability boundary of parametric excitation, defined by a threshold voltage, is theoretically predicted and verified by related experiments. It is demonstrated that, when keeping the gyroscope’s vibration at a constant amplitude, the fundamental frequency driving voltage will decrease with the increasing of the parametric voltage and will drop to zero at its threshold value. In this case, the gyroscope operates in a generalized parametric resonance condition, which is called subharmonic excitation. The novel parametric and subharmonic excitation theories displayed in this paper are proven to be efficient and tunable dynamical methods with great potential for adjusting the quality factor flexibly, which can be used to further enhance the resonator’s performance.

0.015 Degree-Per-Hour Honeycomb Disk Resonator Gyroscope

High performance Microelectromechanical system (MEMS) gyroscopes are in great demand in the fields of precise navigation, automatic driving and precise attitude measurement. Honeycomb disk resonator gyroscope(HDRG) which works on wineglass-modes has many advantages including higher immunity to fabrication errors, better resonant mode consistency and better inner electrode arrangement, showing excellent potentials to be the next-generation MEMS gyroscope with high performance and good robustness. In this paper, a new HDRG prototype is designed based on the comprehensive optimizations of resonant structure and electrode configuration. The main structure parameters and the lumped-mass configuration are optimized systematically through the finite element simulation, while the configuration and arrangement of the inner electrodes are optimized based on the vibration amplification effect, offering systematic reference for the optimizations of other MEMS gyroscopes. The new HDRG is fabricated through a SOI fabrication technique and tested with a close-loop digital circuit. Quality factor of the optimized HDRG prototype reaches 650k, proving to be a record in silicon disk resonator gyroscopes. The bias instability of the optimized gyroscope reaches 0.015°/h under room temperature without any compensation, approaching the accuracy of navigation grade. Scale factor nonlinearity reached around 120ppm in the range of ±300°/s without compensation. The comprehensive performance is at the forefront of MEMS resonant gyroscopes.

Optimization and Fabrication of an MOEMS Gyroscope Based on a WGM Resonator.

In this paper, the characterization of a whispering gallery mode (WGM) resonator applied in a novel micro-opto-electro-mechanical system (MOEMS) gyroscope was investigated. The WGM optical transmission coupling model was analyzed and compared by adjusting key parameters, such as the cavity radius, the waveguide width, and the gap between them for silicon and silicon nitride materials in simulations, which will greatly affect the quality factor (Q) of the WGM resonator. Furthermore, the structural parameters of the disk resonant gyroscope were also optimized. Then, the fabrication process was optimized to overcome the difficulties in the realization of micro-optical devices. Finally, a gyroscope prototype with the integrated WGM resonator was verified experimentally. The scale factor and bias instability performance of the MOEMS gyroscope was 2.63 mv/°/s and 4.0339°/h, respectively.

First-Order Linear Mechatronics Model for Closed-Loop MEMS Disk Resonator Gyroscope.

In this paper, a first-order closed-loop mechatronics model of a micro-electromechanical system (MEMS) disk resonator gyroscope (DRG) with a configurable ASIC is established for closed-loop design and performance analysis. There are usually some nonlinear modules in the gyroscope mechatronics model, and it is difficult to design the closed-loop controllers using classical automatic control theory. An order-reduction method (ORM) based on the Laplace transform and inverse Laplace transform is proposed to linearize the nonlinear modules. The linearized model is proved to show good agreement with the original mechatronics model in terms of system response. The experimental verification was conducted to demonstrate the validation of this method.

Design of a novel gear-like disk resonator gyroscope with high mechanical sensitivity

The mechanical sensitivity ( $$S_{mech}$$ ) is an important performance for ring-like disk resonator gyroscope (RDRG). To provide guidelines for improving $$S_{mech}$$ , the reliable expression of $$S_{mech}$$ is derived by taking into account frequency split and difference of effective mass. The design strategy indicates the main way to improve $$S_{mech}$$ is reducing effective stiffness and frequency split. Then a novel gear-like disk resonator gyroscope (GDRG) is designed by replacing circular rings of RDRG with meander-shaped rings consisting of linear beams. Afterwards, the characteristics between RDRG and GDRG are compared. For gyroscopes fabricated ideally, GDRG has a decrease of 58.40% on effective stiffness, an increase of 49.51% on quality factor (Q) and an increase of 694.28% on $$S_{mech}$$ , comparing with RDRG. For actual fabricated gyroscopes, GDRG has much less frequency split than RDRG due to its much higher immunity to crystal orientation error and fabrication errors. Affected by these errors, effective stiffness and Q have small deviations from the values of gyroscopes fabricated ideally, $$S_{mech}$$ decreases greatly and $$S_{mech}$$ of GDRG is always much higher than that of RDRG. These results have verified GDRG can achieve high $$S_{mech}$$ due to its small effective stiffness, small frequency split and high Q. The ideas and methods described in this paper can also be applied to other similar gyroscopes.

Study of the Influence of Phase Noise on the MEMS Disk Resonator Gyroscope Interface Circuit.

In this paper, a detailed analysis of the influence of phase noise on the micro-electro-mechanical system (MEMS) disk resonator gyroscope (DRG) is presented. Firstly, a new time-varying phase noise model for the gyroscope is established, which explains how the drive loop circuit noise converts into phase noise. Different from previous works, the time-varying phase noise model in this paper is established in mechanical domain, which gain more physical insight into the origin of the phase noise in gyroscope. Furthermore, the impact of phase noise on DRG is derived, which shows how the phase noise affects angular velocity measurement. The analysis shows that, in MEMS DRG, the phase noise, together with other non-ideal factors such as direct excitation of secondary resonator, may cause a low frequency noise in the output of the gyroscope system and affect the bias stability of the gyroscope. Finally, numerical simulations and experiment tests are designed to prove the theories above.

A digital output MEMS DRG on-chip temperature compensation method based on virtual sensor

A digital output Disk Resonator Gyroscope (DRG) on-chip temperature compensation method based on virtual sensor is proposed in this paper. DRG is a combination of solid wave gyroscope and MEMS gyroscope, it has become the research emphasis of high precision gyroscope. In practical application, the ambient temperature changing will cause several problems such as the change of scale factor, zero drift and so on. To increase the environmental adaptability of DRG, the DRG temperature characteristics are analyzed, the temperature compensation models of scale factor and zero output are established in this paper. The concept of virtual temperature sensor is introduced to solve the lead or lag problem caused by integrated temperature sensor. Based on the trend of AC drive amplitude changing with temperature, the temperature measurement is converted into AC voltage amplitude measurement. The virtual temperature sensor is used to complete the on-chip temperature compensation of the DRG angular velocity output, the second-order compensation realizes the scale factor change of 40 ppm/[Formula: see text]C and zero output change of 27[Formula: see text]/h over the full temperature range varying from [Formula: see text] to 60[Formula: see text]C according to the simulation result.

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

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 to 0.0524 . Compared with the mode mismatch condition, the ARW is improved by 19.48 times.

A Digital Closed-Loop Sense MEMS Disk Resonator Gyroscope Circuit Design Based on Integrated Analog Front-end.

A digital closed-loop system design of a microelectromechanical systems (MEMS) disk resonator gyroscope (DRG) is proposed in this paper. Vibration models with non-ideal factors are provided based on the structure characteristics and operation mode of the sensing element. The DRG operates in force balance mode with four control loops. A closed self-excited loop realizes stable vibration amplitude on the basis of peak detection technology and phase control loop. Force-to-rebalance technology is employed for the closed sense loop. A high-frequency carrier loaded on an anchor weakens the effect of parasitic capacitances coupling. The signal detected by the charge amplifier is demodulated and converted into a digital output for subsequent processing. Considering compatibility with digital circuits and output precision demands, a low passband sigma-delta (ΣΔ) analog-to-digital converter (ADC) is implemented with a 111.8dB signal-to-noise ratio (SNR). The analog front-end and digital closed self-excited loop is manufactured with a standard 0.35 µm complementary metal-oxide-semiconductor (CMOS) technology. The experimental results show a bias instability of 2.1 °/h and a nonlinearity of 0.035% over the ± 400° full-scale range.

Honeycomb-Like Disk Resonator Gyroscope

In this paper, we report a novel honeycomb-like disk resonator gyroscope (HDRG) and its comprehensive test results. HDRG inherits many advantages from traditional nested-ring disk resonator such as axisymmetric structure and huge capacitive area. In addition, HDRG owns unique characteristics and potentials due to its topology structure, namely, higher immunity to fabrication errors, better resonant mode consistency and better inner electrode arrangement. This new design of HDRG is based on a tradeoff between performance parameters including quality factor, decaying time constant, effective mass, effective capacitive area, transducer sensitivity and mechanical noise. The characteristics and potentials of HDRG are investigated firstly. Afterwards, the parameter optimization and frame structure optimization of HDRG are investigated. Based on the investigation, a novel HDRG is proposed. A prototype of this design is fabricated and its overall performance is tested. Results show that the quality factor of HDRG increases from 81.1k to 171.6k and the decaying time constant increases from 1.507 s to 6.973 s. The bias instability of the gyroscope reaches 0.11 °/h at room temperature without any compensation, more than eighty times smaller than the former design, exhibiting significant performance improvement. Moreover, ranging from −40 °C to 60 °C, the temperature coefficient of scale factor is 0.188%/ °C, and the maximum variations of zero offset and bias instability over temperature are 40 °/h and 0.12 °/h respectively, showing good robustness to environment disturbance. This new gyroscope has the potential to operate steadily under variable temperature conditions, offering as a new type of MEMS gyroscope with high performance and good robustness.

A Novel High-Symmetry Cobweb-Like Disk Resonator Gyroscope

A novel cobweb-like disk resonator gyroscope (CDRG) with a very small frequency split between two degenerate modes has been designed and implemented. In comparison with the ring-like DRG (RDRG), the CDRG has fewer fabrication imperfections owing to its all-linear structure. In addition, the CDRG displays a superior nonlinear effect compared with the RDRG, and internal differential electrode excitation and detection were used to further reduce the nonlinear effect. The CDRGs and RDRGs were placed side by side on the same wafer, and the characteristics of these as-fabricated resonators were then tested. The results showed that the resonant frequencies and Q-factors of the CDRGs and RDRGs were approximately 18 kHz and nearly 100k, respectively. The smallest as-fabricated relative frequency split (29.9 ppm) of the CDRGs was about 10.8 times smaller than that (322.5 ppm) of an RDRG built side by side on the same wafer, which had the lowest relative frequency split among all current disk resonator gyros. Finally, the preliminary results for the performance of the CDRG and RDRG in the force-to-rebalance mode and mode matching are given. Under the same conditions, the maximum vibration displacement, scale factor, angular random walk, and bias instability of the CDRG were improved by 62.8%, 112%, 700%, and 314%, respectively, compared with the RDRG.

Nonlinearity Reduction in Disk Resonator Gyroscopes Based on the Vibration Amplification Effect

This article reports a novel method to reduce the electrostatic and capacitive nonlinearities in a disk resonator gyroscope (DRG) and to further improve its ultimate oscillation amplitude for performances improvement. The DRG consists of multiple rings, in the working mode, the outer rings always have larger deformation than the inner rings, which is called the vibration amplification effect (VAE). Based on this effect, we propose a method to reduce the nonlinearity in a DRG by optimizing the electrode arrangement, that is, by using the inner electrodes for driving and the outer electrodes for sensing. To verify this method, a DRG with eight layers of driving electrodes was designed and fabricated. The influence of the electrode positions on the nonlinearity of the DRG was theoretically analyzed and experimentally tested. The results show that by using the nonlinearity reduction method, the nonlinearity of the DRG can be reduced and the ultimate oscillation amplitude can be increased to 49% of the capacitive gap, which is much larger than the oscillation amplitude of traditional DRGs. Meanwhile, the sensitivity of the DRG can be improved by 100% and the angle random walk and bias instability can be reduced by 53% and 63%, respectively.

Frequency Symmetry Comparison of Cobweb-Like Disk Resonator Gyroscope With Ring-Like Disk Resonator Gyroscope

Frequency symmetry of a cobweb-like disk resonator gyroscope (CDRG) has been compared with a conventional ring-like disk resonant gyroscope (RDRG) in this letter to corroborate that linear beam structures have a better process tolerance than curved beam structures for micro-fabrication processes. The CDRG comprises multiple concentric cobweb-like rings and each is formed by 16 identical straight beams joined end-to-end. It exhibits as-fabricated symmetric vibration behavior superior to RDRGs. To compare as-fabricated structural symmetry, CDRG and RDRG are placed side-by-side on the same wafer and simulated using COMSOL. A tested frequency split as low as 0.56 Hz is achieved for CDRG, and the average relative frequency split is 79.7 ppm, which is approximately seven times smaller than that of RDRG. Additionally, a temperature characteristics test demonstrates that the as-fabricated CDRG has excellent temperature stability, and the relative frequency split varied by 2.83 ppm in the temperature ranging from -20 °C to +80 °C. The proposed concept is verified by the simulation and experimental results.

Energy Loss in a MEMS Disk Resonator Gyroscope.

Analysing and minimizing energy loss is crucial for high performance disk resonator gyroscopes (DRGs). Generally, the primary energy loss mechanism for high vacuum packaged microelectromechanical system (MEMS) resonators includes thermoelastic damping, anchor loss, and electronic damping. In this paper, the thermoelastic damping, anchor loss, and electronic damping for our DRG design are calculated by combining finite element analysis and theoretical derivation. Thermoelastic damping is the dominant energy loss mechanism and contributes over 90% of the total dissipated energy. Benefiting from a symmetrical structure, the anchor loss is low and can be neglected. However, the electronic damping determined by the testing circuit contributes 2.6%–9.6% when the bias voltage increases from 10 V to 20 V, which has a considerable impact on the total quality factor (Q). For comparison, the gyroscope is fabricated and seal-packaged with a measured maximum Q range of 141k to 132k when the bias voltage varies. In conclusion, thermoelastic damping and electronic damping essentially determine the Q of the DRG. Thus, optimizing the resonance structure and testing the circuit to reduce energy loss is prioritized for a high-performance DRG design.

Dynamic Modeling of the Multiring Disk Resonator Gyroscope.

The multiring disk resonator gyroscope (DRG) has been a candidate for high performance gyroscopes, however nowadays the finite element method (FEM) is the main method for its analysis due to its complex structure. In this paper we propose a new method to mathematically model the DRG for its vibrating modes and lumped parameters based on the component mode synthesis (CMS) method. Firstly, the natural frequencies and the associated mode shapes of the DRG are mathematically modeled and a comparison with the FEM results is conducted. It shows that the mode shapes of DRG obtained by FEM and mathematical modeling are identical and in the full ranges of geometrical parameters, natural frequency error of the simulation, and calculation results are limited in ±15%. It demonstrates the effectivity and feasibility of the mathematical modeling method. Then, based on the calculated natural frequencies and mode shapes, the lumped mass-spring model of the DRG and effects of geometry parameters on the lumped mass-spring parameters are investigated, which can be used on the design of the DRG. This mathematical modeling method can effectively improve the analyzing efficiency of the DRG and the method can also be used on the analysis of other complex multiring-type resonators.

Vibration modeling of disk resonator gyroscope by wave propagation

This paper proposes an analytical vibration model of a disk resonator gyroscope (DRG) based on the wave propagation theory, which can predict the key specifications of a DRG rapidly and accurately before fabrication, and can be employed in design optimization. This wave propagation analysis is based on the ray tracing method (RTM) which considers wave propagation and scattering in the formulation. In the RTM, wave transmission and reflection coefficients are the key issues that must be accurately predicted. A novel C-joint is proposed to predict these key coefficients between the rings and spoke with high precision and short estimated time. To verify the soundness of the proposed model, a tentative vibration model for a double-ring (the basic element of a DRG) is established by the RTM and compared with the 3D finite element (FE) model. The two models show excellent agreements in natural frequencies, trend predictions and harmonic displacements. Then, the proposed model is expanded to a multi-ring practical DRG. In addition, taking the advantage of the symmetry in the DRG, the substructuring and recursive methods are employed to reduce the computational overhead. The numerical experiments show that the proposed analytical vibration model for a DRG meets well with the 3D FE model. For instance, the differences between the calculated resonant frequencies from the 3D FE model and the analytical model are less than 3%. After fabrication, the measured average resonant frequency of the prototypes deviates 6.7% from that of the theoretical prediction.

0.04 degree-per-hour MEMS disk resonator gyroscope with high-quality factor (510\u2009k) and long decaying time constant (74.9\u2009s)

The disk resonator gyroscope is an attractive candidate for high-performance MEMS gyroscopes. This gyroscope consists of a sensor and readout electronics, and the characteristics of the sensor directly determine the performance. For the sensor, a high-quality factor and long decaying time constant are the most important characteristics required to achieve high performance. We report a disk resonator gyroscope with a measured quality factor of 510 k and decaying time constant of 74.9 s, which is a record for MEMS silicon disk resonator gyroscopes, to the best of our knowledge. To improve the quality factor of the DRG, the quality factor improvement mechanism is first analyzed, and based on this mechanism two stiffness-mass decoupled methods, i.e., spoke length distribution optimization and lumped mass configuration design, are proposed and demonstrated. A disk resonator gyroscope prototype is fabricated based on these design strategies, and the sensor itself shows an angle random walk as low as 0.001°/√h, demonstrating true potential to achieve navigation-grade performance. The gyroscope with readout electronics shows an angle random walk of 0.01°/√h and a bias instability of 0.04°/h at room temperature without compensation, revealing that the performance of the gyroscope is severely limited by the readout electronics, which should be further improved. We expect that the quality factor improvement methods can be used in the design of other MEMS gyroscopes and that the newly designed DRG can be further improved to achieve navigation-grade performances for high-end industrial, transportation, aerospace, and automotive applications.

Quality Factor Improvement in the Disk Resonator Gyroscope by Optimizing the Spoke Length Distribution

In this paper, we present a novel method to improve the quality factor in disk resonator gyroscopes (DRGs) by optimizing the spoke length distribution (SLD). As for DRGs with identical outer radius R, anchor radius r, ring width h, ring numbers n and spoke length boundaries [a, b] whereas with different SLDs, finite element simulation results show that the SLDs have a great influence on the DRGs’ resonant frequency $\text{f}_{0}$ and thermoelastic quality factor ( $\text{Q}_{\mathrm {TED}}$ ). This paper aims to find an optimized SLD to achieve the highest $\text{Q}_{\mathrm {TED}}$ of a DRG. By using the particle swarm optimization method the optimum SLD of a 9-ring DRG is obtained and the $\text{Q}_{\mathrm {TED}}$ is greatly improved. By further applying this method on the DRGs with different structural parameters, the regular rules of the optimum SLD are concluded and a simple method to get the optimized SLD for a DRG is proposed. By applying the method on the DRGs with different ring widths and ring numbers, the $\text{Q}_{\mathrm {TED}}$ of them can be improved by 25%-43%. This demonstrates that the method is effective for the $\text{Q}_{\mathrm {TED}}$ improvement. With this method, designers can easily obtain the optimized SLD in a DRG after the parameters R, r, h, and n are determined to further improve the DRG’s quality factor. [2017–0259]

Decaying Time Constant Enhanced MEMS Disk Resonator for High Precision Gyroscopic Application

This paper reports a new design strategy of adding lumped masses to the frame structure of a disk resonator gyroscope (DRG) to mitigate its figure of merit (FOM). A greatly enhanced decaying time constant τ can lead to very small FOM, which could then greatly mitigate the DRG's bias and bias drift. Additionally, this technique could also reduce the Brownian noise floor. A comprehensive investigation of the possible ways to add the lumped masses is presented, and a detailed design guideline is provided. A DRG prototype based on this design strategy is then presented and shows a τ of 38.5 s, a quality factor Q of 358 k, and a FOM of 1.9°/s. The prototype is operated in the force-to-rebalance mode, and an angle random walk of 0.012°/√h and a bias stability of 0.08°/h are demonstrated experimentally. This design strategy is suitable for use in batch fabrication of very high precision microelectromechanical systems devices such as gyroscopes.

Structural Analysis of Disk Resonance Gyroscope.

In this paper, we present two design methods to improve the performance of disk resonator gyroscope (DRG), including decreasing the frequency split and increasing the quality factor (Q). The structure parameters, which can affect the frequency split and Q value were concluded with the help of the FEM software. Meanwhile, devices with different parameters were designed, fabricated, and tested, and the experimental result was in accordance with the simulation. With the proposed methods, the DRG was selected with a high Q value and a low frequency split to satisfy the demand of high performance. The weakness and future works were pointed at last.