The gyroscope with high axial symmetry and dual differential configuration effectively suppresses common-mode disturbances, such as environmental vibrations, serving as a critical strategy for developing high-precision micro-electromechanical systems (MEMS) gyroscopes. This article proposes a highly symmetric eight-mass structure with linear actuation. The structure exhibits a resonance mode similar to the 2 theta vibrational mode of a disk structure but with a larger proof mass. By incorporating a decoupling frame and a linear capacitive design, the system enables large-amplitude displacement actuation and detection, thereby reducing mechanical thermal noise. In order to overcome the problem of optimizing the order of multiple interference modes caused by multiple masses, this study uses the Lagrangian multibody dynamics method to establish an eight-degree-of-freedom dynamic model of the eight-mass structure and calculates the modal order of the resonator. The theoretical resonance frequencies, calculated based on structural parameters, show a deviation of only 3.95% compared with finite element simulations. Using this approach, the frequency difference between the operational mode and parasitic modes reaches 3.45 kHz, effectively preventing interference from parasitic modes. To address quadrature errors caused by stiffness coupling, this article proposes a linear quadratic regulator (LQR) closed-loop quadrature suppression scheme incorporating electrostatic stiffness. The LQR-based feedback mechanism enables high-precision adjustment of electrostatic stiffness while ensuring system stability. Furthermore, an MEMS gyroscope control circuit designed for modal matching and force balancing was developed. Experimental results demonstrate that the proposed eight-mass MEMS gyroscope achieves a scale factor of 147.4 LSB/degrees/s, a scale factor nonlinearity of 268 ppm, a bias instability of 0.681 degrees/h, and an angle random walk of 0.0623 degrees/ root h.

With the rapid advancement of error correction technologies such as closed-loop quadrature control and mode matching, the performance and accuracy of Micro-Electro-Mechanical Systems (MEMS) Quadruple Mass Gyroscopes (QMGs) have been significantly enhanced. However, internal signal cross-coupling and aliasing within the gyroscope system severely restrict further breakthroughs in room-temperature bias performance, presenting a critical technical bottleneck. Initiating from the closed-loop control architecture of the MEMS QMG, this study establishes a comprehensive bias cross-coupling model across the drive, quadrature, and force-rebalance loops. The distinct influences of internal coupled signals—such as the drive-mode excitation signal, drive-mode frequency signal, and quadrature suppression voltage—on bias drift are rigorously analyzed. By jointly evaluating the mechanical resonator, control circuitry, and environmental temperature, the critical significance of the rate of change of the quadrature suppression voltage on QMG bias drift is unveiled. Consequently, an innovative bias compensation methodology is proposed by incorporating this rate of change into a multi-parameter fusion framework. Experimental results demonstrate that within a full-scale range of ±200 (°)/s, the room-temperature bias instability (BI) of the QMG is drastically reduced from 0.163 (°)/h to 0.0194 (°)/h, representing an 8.4-fold performance improvement. The angle random walk (ARW) increased from 0.0075 (°)/√h to 0.0088 (°)/√h. Under thermal cycling tests spanning from −40 °C to 50 °C, the bias fluctuation range is suppressed from 0.3 (°)/s to 0.045 (°)/s, and the BI decreases from 1.89 (°)/h to 0.683 (°)/h, yielding a 2.7-fold enhancement in thermal robustness. Additionally, the method avoids degrading the gyroscope's threshold, ensuring the MEMS QMG consistently sustains an angular rate detection resolution of 0.0001 (°)/s. These findings conclusively validate the effectiveness and robustness of the proposed method for high-reliability applications.

During intervals without absolute position updates, a long-endurance marine rotational inertial navigation system accumulates quasi-periodic position error and secular longitude drift. Direct spectral processing is affected by vessel motion, whereas velocity-aided damping can transfer velocity-log disturbances into the navigation solution. A trajectory-discrepancy signal is constructed from the inertial position solution and a velocity-derived auxiliary trajectory. A normal time-frequency transform reconstructs selected Schuler and Earth-rate components, and a Kalman filter estimates the equivalent gyroscope biases associated with the residual longitude trend. Finite-window harmonic analysis evaluates identifiability of the selected components. Finite-horizon observability of the error-state model is assessed along the evaluation trajectories using piecewise-constant-system calculations, and a reduced information-matrix analysis evaluates separation of the north and up equivalent gyroscope biases. Over two non-overlapping 744~h segments, the method achieves total-position root-mean-square errors of 0.14 and 0.38~nmi. Comparisons with four conventional navigation solutions are conducted over these two segments. Ablation, bootstrap, perturbation, and parameter-sensitivity tests are conducted over two non-overlapping windows. The results show suppression of quasi-periodic error and accumulated longitude drift and quantify sensitivity to the evaluated input and parameter variations.

Constructing a stiffness-mass model for the multi-ring resonator (MRR) is vital to the performance analysis of disk resonator gyroscopes (DRGs). However, FEM is computationally expensive, while existing analytical methods involve intricate derivations without traceable parameter-property correlations. This study first proposes a dynamic eigencurve to characterize the intrinsic effective stiffness/mass distribution pattern of the multi-ring bending mode, thus enabling the development of a fast and accurate dynamic modeling method. The eigencurve is obtained by normalizing the effective stiffness/mass contributed by each component of the MRR as well as their geometric positions, and exhibits remarkable consistency across different designs. Upon incorporation of the structural parameters into the normalization factor functions developed via goodness-of-fit analysis and linear superposition of dynamic variables, the eigencurve denormalized by these factors can be rapidly converted into the effective stiffness/mass distribution curve for a given MRR configuration. By integrating this denormalized curve, an explicit mapping model between the multi-ring structure and its dynamic properties is systematically derived. The proposed model deviates by less than 10.6% from FEM results with extremely high computational efficiency. Furthermore, a PSO algorithm based on this model is applied to optimize MRR modal distribution, revealing that an anchor-to-outer radius ratio exceeding 0.69 is essential to achieve a low operational mode frequency with large separation from interference modes. This study provides a simple and effective analytical framework for typical multi-ring architectures, facilitating the extension of modeling methodologies to complex multi-ring variants, and also offers optimization strategies for the design of high-performance DRG.

Offshore lifting operations are highly sensitive to vessel heave motion and the heave compensation system is essential for ensuring operational safety and extending the weather window. A novel portable integrated hybrid active-passive heave compensator (PI-HAHC) is developed, which adopts the dual-piston accumulator to combine the passive and active heave compensation system. The simplified dynamic model of PI-HAHC is given and a numerical model based on the AMESim platform is established. The mechanical parameters of the device are optimized based on the particle swarm optimization algorithm and the numerical simulations are performed to evaluate the performance under different sea states. Different control strategies are implemented to investigate the effect of active heave compensation. The experimental tests are conducted to validate the dynamic performance and compensation efficiency of the proposed PI-HAHC system, with heave compensation efficiency reaching up to 98.38% in the prototype experiments.

Mode-matching effectively enhances the signal-to-noise ratio of MEMS gyroscopes but considerably narrows the mechanical bandwidth. Force-to-rebalance (FTR) closed-loop control extends the operational bandwidth yet is constrained by the system phase margin. Traditional pole-zero cancellation compensation enables bandwidth extension while maintaining phase margin, but severely deteriorates noise performance, leaving the bandwidth-noise trade-off unresolved. This paper first analytically characterizes the noise behavior of the single-pair pole-zero compensated FTR system, identifying that channel gain is the key factor of this trade-off. A new strategy is then proposed that exploits the previously overlooked interaction between the compensator pole and the PI zero, introducing the frequency ratio λ as an explicit design variable. Analysis reveals that configuring λ > 1 reduces the channel gain required to achieve the target bandwidth, and a quantitative selection criterion for λ is established under simultaneous bandwidth, stability, and noise constraints. Following the proposed selection criterion, experimental results on the same hardware platform demonstrate that at 100 Hz closed-loop bandwidth, ARW is improved from 0.0789 °/√h to 0.0186 °/√h and BI from 0.252 °/h to 0.093 °/h, with a dynamic range of ±200 °/s and scale factor nonlinearity of 259.688 ppm.

This article examines the mechanism of electrical feedthrough in MEMS disk resonant gyroscopes. Such error signals ultimately degrade the performance of MEMS gyroscopes. To address these issues, this work proposes a multifrequency modulation (MFM) feedthrough suppression scheme. In this approach, the drive mode is excited via parametric modulation at twice the resonant frequency, force to rebalance (FRB) feedback in the sense mode is implemented using a half-frequency signal, and quadrature error is suppressed by applying a dc electrostatic negative-stiffness voltage, thereby effectively isolating the feedthrough signal from the sensing signal in the frequency domain. Experimental results demonstrate that this method increases the closed-loop scale factor of the MEMS disk gyroscope to 236 838 LSB/degrees/s, a 33.2-fold improvement, while reducing the bias instability to 0.159 degrees/h, an 8.6-fold improvement.

The merge of droplet microfluidics with single‐molecule homogeneous immunoassay (SiMHoI) provides a transformative tool for biomedical diagnosis with high sensitivity, simplified workflow and reduced reagent consumption. Existing droplet‐based SiMHoIs use polymerase chain reaction for single‐molecular protein signal amplification; and thus, suffer from the intrinsic deficiencies of intensive instrument dependence, high background interference, and redundant reaction time. To tackle these limitations, an enzymatic recycling (ER) reaction is introduced into the microdroplets as an isothermal amplification mechanism. This approach utilizes antibody‐ or aptamer‐labeled nucleic acid probes to capture trace amounts of targets confined in the microdroplets at a single‐ or sub‐single‐molecule level. Single‐target fluorescence signal is then amplified via an in‐droplet ER reaction with molecular beacons. This strategy eliminates the reliance on thermal cycling, and achieves selective droplet illumination within 20 min. The self‐noise suppression mechanism of the in‐droplet ER reaction enhances the positive‐to‐negative ratio nearly 20‐fold compared to the bulk‐phase reaction and reduce the detection limit to 10⁻¹⁸ m . Clinical validation with human serum specimens shows excellent consistency with flow cytometry ( P > 0.05). The isothermal signal amplification approach proposed here upgrades current droplet‐based molecular diagnostic platforms, and enables an engineering solution for detection of ultra‐low‐abundance biomarkers at preclinical stage.

This paper proposed a fast phase error identification method for MEMS gyroscopes to reduce zero rate output (ZRO) drift. The method applies a sinusoidal disturbance signal to the quadrature suppression electrode of the MEMS gyroscope. The phase error is identified using a designed forgetting factor recursive least squares (FFRLS) algorithm based on the outputs of the quadrature suppression loop (QSL) and the force rebalanced (FRB) loop. Compared with previously methods, this approach enables real-time phase error identification during gyroscope operation. The identified phase error can be directly used for ZRO compensation. The identification accuracy and effectiveness of the method were analyzed through simulations. Experimental results indicate that the identified phase error is -14.1026 deg. After compensation, the gyroscope's bias instability was reduced by a factor of 3.5, reaching 0.0965 degrees/h.

This paper presents the results of a micro-electro-mechanical systems (MEMS) frequency-modulated accelerometer (FMA) with a +/- 50 g dynamic range demonstrating a bias and scale factor stability of 12.65 mu g and 1.9 ppm respectively over an operational temperature range of -40 degrees C to 60 degrees C. The device utilizes advanced MEMS fabrication techniques, low-stress packaging, optimized MEMS structure to achieve exceptional performance. At room temperature, its Allan deviation for measurements reveals a bias instability of 89 ng, while the maximum scale factor nonlinearity within +/- 50 g is less than 50 ppm. These confirm that the device meets the navigation-grade performance, offering both high stability and wide range.

With the introduction of technologies such as structural optimization and error correction, the performance of the MEMS quad-mass gyroscope (QMG) has significantly improved, while noise has gradually become a critical factor limiting its performance. For ease of analysis, this paper categorizes noise into two types: noise at the signal detection end and noise at the excitation end. Firstly, a closed-loop noise model for QMG is established, and the effects of these two types of noise on the dynamic and static performance of QMG are investigated. Additionally, the correlation between structural parameters and noise transmission is analyzed, and the dual impact of DC Bias Voltage optimization on improving QMG performance is explored. Based on the above analysis, a force-to-rebalance (FTR) dual-loop control method incorporating SID and normalized least mean squares (NLMS) is proposed and applied to the MEMS QMG, where SID and NLMS are respectively employed to mitigate the influence of detection-end and drive-end noise on the bias performance. Compared to the traditional method, the proposed approach reduces the bias instability (BI) of the MEMS QMG from 0.407°/h to 0.024°/h and the angular random walk (ARW) from 0.137°/√h to 0.006°/√h, achieving improvements of 16.96 times and 22.83 times, respectively. Furthermore, the system achieves a threshold of 0.0001°/s.

This letter proposes a wafer-level vacuum-packaged micro - electro - mechanical systems (MEMS) quadruple mass gyroscope (QMG) based on the classical QMG architecture. The design incorporates several innovations to enhance performance in open-loop and mode-split operation modes. The proposed QMG employs variable-area comb electrodes to improve driving electrostatic nonlinearities and sensing nonlinearities. Quadrature errors are reduced through electrostatic negative stiffness using quadrature electrodes on proof masses. Wafer-level vacuum packaging achieves a high drive mode Q-factor of 1.06 million, enabling a low ac driving voltage of 4.7 mV, thereby effectively suppressing the feedthrough interference. The use of numerous sensing combs and a frequency and damping regulator reduces the sense mode Q-factor to 0.11 million, enhancing environmental interference resistance. In addition, the numerous sensing combs further enhance the open-loop scale factor. Leveraging these innovative designs, the QMG achieves a bias instability of 0.54 degrees/h at a frequency split of 70 Hz, an angle random walkof 0.55 degrees/root h, a dynamic range of +/- 300 degrees/s, and a theoretical bandwidth of 37.8 Hz. These characteristics demonstrate that the proposed QMG achieves satisfactory performance in frequency-split and open-loop modes.

In differential MEMS resonant sensors, a pair of resonators are interconnected with other structural components while sharing a common substrate. This leads to mutual coupling of vibration energy between resonators, interfering with their frequency outputs and affecting the sensor's static performance. This paper aims to model and analyze the vibration coupling phenomena in differential common-based MEMS resonators (DCMR). A mechanical model of the DCMR structure was established and refined through finite element simulation analysis. Theoretical calculations yielded vibration coupling curves for two typical silicon resonant accelerometer (SRA) structures containing DCMR: SRA-V1 and SRA-V2, with coupling stiffness values of 2.361 × 10-4 N/m and 1.370 × 10-2 N/m, respectively. An experimental test system was constructed to characterize the vibration coupling behavior. The results provided coupling amplitude-frequency characteristic curves and coupling stiffness values (7.073 × 10-4 N/m and 1.068 × 10-2 N/m for SRA-V1 and SRA-V2, respectively) that validated the theoretical analysis and computational model. This novel approach enables effective evaluation of coupling intensity between 5resonators and provides a theoretical foundation for optimizing device structural designs.

The abnormal expression of microRNA (miRNA) is closely related to the occurrence and progression of diverse cancers. Accurate diagnosis of early-stage cancers via low-cost Point-of-Care Testing (POCT) remains highly desirable but challenging. Herein, a dual-colorimetric amplification biosensor has been developed for the simultaneous detection of two tumor-associated miRNAs. It enables the sensitive and accurate diagnosis of cancers without the requirement for complex procedures and expensive detection instruments. Specifically, the target miR-10b can initiate the Catalytic Hairpin Assembly (CHA) reaction between gold nanoparticles (GNPs) and magnetic beads (MBs), thereby leading to the coupling of GNPs onto MBs. Meanwhile, miR-21 can activate the Hybridization Chain Reaction (HCR) on MBs. After magnetic separation, the color of the supernatant changes from red to pale, and the G-quadruplex/hemin DNAzyme would form on the MBs sediment, which can further catalyze the colorless ABTS/H2O2 to green. Based on this, the concentrations of miR-10b and miR-21 could be visualized simultaneously. Under optimal conditions, the constructed biosensor demonstrates the feasibility, accuracy, and selectivity towards target miRNAs in both buffer solutions and real serum samples. The proposed strategy may offer a novel path for the precise diagnosis of cancers in POCT.

MEMS lumped mass gyroscopes, widely used in industrial applications, have not yet reached the navigation grade. This article proposes a novel MEMS quadruple mass gyroscope (QMG) that exhibits superior overall performance in terms of bias instability (BI), angle random walk (ARW), size, and robustness. This superior overall performance is achieved via a dual-umbrella-like driving architecture (DULDA). Specifically, the DULDA is used to enhance the driving displacement by 80% and the effective mass by 180% without increasing the layout area. The DULDA also allows a single driving frame to drive four proof masses for anti-phase motion simultaneously. In addition, the DULDA, combined with a coupling mechanism for the sensing mode, positions the two operating modes in the first two orders and yields a frequency split of 5.49 kHz between the operating mode and the parasitic mode. The QMG is fabricated using MEMS processes and features wafer-level vacuum packaging, with structural layer dimensions of only 3.9 x 3.1 mm. Without any compensation, the proposed QMG achieves a BI of 0.26 degrees/h and an ARW of 0.02 degrees/root h within a full scale of +/- 150 degrees/s, making a 90% reduction in BI and a 150% decrease in ARW compared with a QMG without the DULDA. Consequently, the proposed QMG, with its advanced driving architecture, offers a promising solution for angular measurement in high-end industrial applications.

In this article, we propose a linear equivalent step-control strategy for the traveling-wave micromotor rotating platform, utilizing a microelectromechanical system (MEMS) three-ring capacitive angular position sensor. Designed for practical applications, the strategy incorporates a simplified online angle demodulation process that satisfies step-control requirements. In addition, we developed a more robust method for identifying the absolute zero position feature based on abrupt changes in the inner ring peak-to-valley values. A control strategy based on linear equivalent angle demodulation, which requires fewer computational resources, is presented, along with a step-angle refinement technique to enhance resolution. Experimental results indicate that the current control strategy can effectively locate the zero position of the traveling-wave micromotor rotating platform under fluctuation, achieving a step-angle precision of 0.216 degrees and an angular position repeatability (APR) of 0.237 degrees, with no cumulative error. Our study marks the first successful implementation of a multiposition step control combining the traveling-wave micromotor and the MEMS three-ring capacitive angular position sensor in practical applications, providing a promising solution for its use in various fields.

In this work, a room-temperature-stabilized disk resonator gyroscope (RTDRG) using a thermoelectric cooler (TEC) is proposed. Unlike the conventional oven-based temperature control method, the proposed system leverages the bidirectional heating/cooling capability of TECs to maintain the operating temperature of the gyroscope at ambient conditions. This approach significantly reduces start-up time while enhancing the gyroscope's Q-factor. A prototype RTDRG system was experimentally validated across an extreme temperature range from -40 degrees C to +60 degrees C using a thermal chamber turntable. Experimental results indicate that the RTDRG can be stably controlled at 25 degrees C. Comparative analyses reveal substantial performance enhancements under TEC regulation: 90-fold improvement in resonant frequency stability versus temperature, 52-fold increase in Q-factor stability, and 18-fold reduction in temperature-dependent bias drift. Residual drift observed in the system is attributed to unequal thermal resistances from the TEC to the disk resonator gyroscope (DRG) and temperature detector. In future work, the resonant frequency or Q-factor of the DRG will be considered as a temperature-sensitive parameter to develop a higher-precision temperature closed-loop control system.

Microelectromechanical systems (MEMS) gyroscopes have stringent requirements in terms of control accuracy and system stability. The traditional PI control is widely used in the closed-loop drive loop of MEMS gyroscopes, but the parameters need to be finely tuned to achieve optimal performance. In order to simplify the complexity of parameter tuning and improve the stability and anti-interference ability of the system, a MEMS gyroscope driving closed-loop system based on Linear Active Disturbance Rejection Control (LADRC) is proposed in this paper. The demodulated output signals with the same reference amplitude are inputted to the LADRC controller to predict the tracking total perturbation, and the control signals are generated to drive the system. Simulation results show that the phase margin of the system is significantly improved by using the LADRC controller approach, the stabilisation time is improved by a factor of 7.5 and the phase margin is improved by a factor of 45°. Simulation results show that the LADRC control contributes to the stability of the control system compared to the PI controlled approach. The simulation further verifies that a wide range of changes in the parameters of the LADRC controller does not affect the system stability, but improves the system's anti-interference capability.

In this paper, we propose a novel three-ring capacitive angular position sensor with an absolute zero position feature based on microelectromechanical system (MEMS) technology. The sensor utilizes an inner absolute zero position detection ring to provide easily analyzable zero position information within a 15 degrees angular range. The sensor also incorporates an outer precise angular position detection ring to offer high-precision measurements. The excitation-coupling electrode ring provides a carrier signal and enables noncontact measurement between the stator and the rotor. To validate the design, we fabricated a sensor with a sensing structure outer diameter of 21.3 mm and a thickness of less than 1 mm, and we then tested the sensor with a traveling wave micromotor rotating platform. Experimental results show that the sensor achieved an angular resolution of 0.003 degrees and an online detection accuracy of 0.029 degrees for angular position. The abrupt change in the voltage amplitude caused by the absolute zero position feature exhibited good repeatability and periodicity, and this feature helped the micromotor successfully achieve zero self-calibration with a precision of 0.73 degrees. Our results validate the practicality of the absolute zero position and break through the bottleneck of current MEMS-based capacitive angular position sensors that can only detect angular increments.

The micro hemispherical resonant gyroscope (MHRG) combines the advantages of MEMS gyroscopes and hemisphere resonant gyroscopes, making it widely used in high-precision navigation and control fields. However, due to its high quality factor (Q) and low-frequency splitting characteristics, the control system exhibits narrow bandwidth, which leads to significant energy coupling during the startup phase, making high-precision closed-loop control prone to failure. To address this, this paper proposes a segmented displacement startup approach, where different reference levels are set to reduce feedthrough energy and achieve rapid energy suppression within each segment, enabling stable startup with small PI control parameters. Experimental results show that the bias instability is 0.047 degrees/h, which is a 72% improvement compared to the straight startup approach.