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Circuit noise is a critical factor that affects the performances of an MEMS gyroscope. Therefore, it is essential to analyze and suppress the noises in the key analog circuits, which are the main noise sources. This study presents an optimized front-end readout circuit and noise suppression methods. First, the noise analysis of the front-end readout circuit is carried out with theoretical derivation to clarify the main noise contributors. To suppress the output noise, an improved readout circuit based on the T-resistor networks is proposed, and the corresponding noise equation is derived in detail. In addition, the noise analysis of the critical circuits of the detection and control system, such as the inverting amplifiers, the first-order low-pass filters, and the first-order high-pass filters, is carried out, and the noise suppression strategy with the optimization of the resistances and is proposed. Taking the inverting amplifier as an example, the theoretical derivation is verified by measuring and comparing the output noises of different resistance schemes. In addition, the output noises of the gyroscope before and after circuit optimization are measured. Experimental results demonstrate that the output noise with the circuit optimization is reduced from 60 μV/Hz1/2 to 30 μV/Hz1/2 and the bias instability is reduced from 3.8 deg/h to 1.38 deg/h. In addition, the ARW is significantly improved from 0.035 deg/h1/2 to 0.018 deg/h1/2, which indicates that the proposed noise analysis and suppression methods are effective and feasible. [ABSTRACT FROM AUTHOR]

This paper presents the development of an analytical model of an internal vibrating ring gyroscope in a Microelectromechanical System (MEMS). The internal ring structure consists of eight semicircular beams that are attached to the externally placed anchors. This research work analyzes the vibrating ring gyroscope's in-plane displacement behavior and the resulting elliptical vibrational modes. The elliptical vibrational modes appear as pairs with the same resonance frequency due to the symmetric structure of the design. The analysis commences by conceptualizing the ring as a geometric structure with a circular shape possessing specific dimensions such as thickness, height, and radius. We construct a linear model that characterizes the vibrational dynamics of the internal vibrating ring. The analysis develops a comprehensive mathematical formulation for the radial and tangential displacements in local polar coordinates by considering the inextensional displacement of the ring structure. By utilizing the derived motion equations, we highlight the underlying relationships driving the vibrational characteristics of the MEMS' vibrating ring gyroscope. These dynamic vibrational relationships are essential in enabling the vibrating ring gyroscope's future utilization in accurate navigation and motion sensing technologies. [ABSTRACT FROM AUTHOR]

Microelectromechanical System (MEMS) gyroscopes are inertial sensors used to measure angular velocity. Due to their small size and low power consumption, MEMS devices are widely employed in consumer electronics and the automotive industry. MEMS gyroscopes typically use closed-loop control systems, which often use PID controllers with fixed parameters. These classical PID controllers require a trade-off between overshoot and rise time. However, temperature variations can cause changes in the gyroscope's parameters, which in turn affect the PID controller's performance. To address this issue, this paper proposes an adaptive PID controller that adjusts its parameters in response to temperature-induced changes in the gyroscope's characteristics, based on the error value. A closed-loop control system using the adaptive PID was developed in Simulink and compared with a classical PID controller. The results demonstrate that the adaptive PID controller effectively tracked the changes in the gyroscope's parameters, reducing overshoot by 96% while maintaining a similar rise time. During gyroscope startup, the adaptive PID controller achieves faster stabilization with a 0.036 s settling time, outperforming the 0.06 s of the conventional PID controller. [ABSTRACT FROM AUTHOR]

In this paper, a novel digital closed-loop interface circuit system of MEMS vibrating gyroscope is proposed, which includes driving, detection and quadrature circuits. Because of the high sensitivity and precision of the MEMS gyroscope, the interface circuit system is established under the condition of mode separation. The driving circuit of MEMS gyroscope adopts digital automatic gain control (AGC) to realize self-excitation closed-loop control, which makes the gyroscope system simple in structure and good in robustness. First, the working principle of the gyroscope's sensitive structure is introduced and the system simulation model of the sensitive structure is developed. Second, a Σ Δ ADC and DAC with single-bit output are designed and the feasibility of the driving circuit design is verified by the system-level model. Third, the quadrature closed-loop correction circuit is designed to reduce the coupling of the quadrature component to the gyroscope detection circuit. The simulation results show that the quadrature correction loop can effectively reduce the influence of the quadrature coupling on the detection loop of MEMS gyroscope. Finally, the system-level model of the gyroscope is established by SIMULINK, the overall system performance of the gyroscope is analyzed, and the test system of MEMS gyroscope is built by field-programmable gate array (FPGA) and application specific integrated circuit (ASIC). The experiment verifies the feasibility of the digital interface circuit design, and the zero-bias instability of the gyroscope system is 1.0∘/h. [ABSTRACT FROM AUTHOR]

Angular velocity is a very important measurement parameter for autonomous driving and industrial applications. The design of MEMS quartz gyro measurement and control circuit has always been the key to restricting the measurement angular velocity performance of gyro system. This paper introduces the application-specific integrated circuit (ASIC) design and implementation of a MEMS quartz gyro measurement and control circuit for angular velocity measurement. The designed nonlinear multiplier can use a square wave to drive the gyro's sensitive structure at the beginning of gyro start-up, thereby reducing the gyro power-up time. The drive circuit replaces the PLL with an automatic gain control unit composed of peak detection and proportional integration (PI) controller, which makes the MEMS gyro system have good robustness. First, SIMULINK is used to model and simulate the MEMS gyroscope system-level model, which illustrates the feasibility of the drive circuit design scheme. Then, the operating principle of the drive loop is analyzed, and the design of the key circuit modules of the measurement and control circuit is introduced. Finally, the performance of the gyroscope drive and detection circuit is experimentally tested, the amplitude and frequency uncertainty of the gyroscope drive circuit are evaluated, and the bias instability and nonlinearity of the gyroscope are tested, the experiment results show that the gyroscope has good performance. [ABSTRACT FROM AUTHOR]

The demodulation phase error will cause the quadrature error to be coupled to the rate output, resulting in performance deterioration of the MEMS gyroscope. To solve this problem, an in-run automatic demodulation phase error compensation method is proposed in this paper. This method applies square wave angular rate input to the gyroscope and automatically identifies the value of the demodulation phase error through the designed automatic identification algorithm. To realize in-run automatic compensation, the demodulation phase error corresponding to the temperature point is measured every 10 °C in the full-temperature environment (−40~60 °C). The relationship between temperature and demodulation phase error is fitted by a third-order polynomial. The temperature is obtained by the temperature sensor and encapsulated in the ceramic packages of the MEMS gyroscope, and the in-run automatic compensation is realized based on the fitting curve. The temperature hysteresis effect on the zero-rate output (ZRO) of the gyroscope is eliminated after compensation. The bias instability (BI) of the three gyroscopes at room temperature (25 °C) is reduced by four to eight times to 0.1°/h, while that at full-temperature environment (−40~60 °C) is reduced by three to four times to 0.1°/h after in-run compensation. [ABSTRACT FROM AUTHOR]

The recursive integral terminal sliding mode control with combined extended state observer (ESO) and adaptive Kalman filter (AKF) is proposed in this article for micromechanical system gyroscopes. To accurately estimate the unmeasured system states in the presence of measurement noises, external disturbances and system uncertainties, the special combination of ESO and AKF is proposed. The AKF is employed to deal with measurement noises and prepare necessary signals for the ESO, while the ESO constantly provides the updated estimate of the lumped disturbance for the AKF. Furthermore, a robust control scheme is designed by using the recursive integral terminal sliding mode variable. Simulation results verify that more accurate unmeasured state estimation and higher tracking accuracy are achieved under the proposed method. [ABSTRACT FROM AUTHOR]

The feedthrough effect can significantly affect the performance of MEMS gyroscopes and even lead to device failure. In order to address the inevitable problem of feedthrough capacitance caused by microfabrication process and circuit structure, two automatic feedthrough cancellation solutions are proposed based on the analysis of the feedthrough effect. Firstly, an equivalent feedthrough model is established for MEMS gyroscopes. Then, through theoretical derivation and model simulation, various influences of feedthrough effect are analysed, and the critical value of feedthrough capacitance is calculated to achieve better compensation effects. For feedthrough capacitance greater than the critical value, a feedthrough cancellation method utilizing AD5231 digital potentiometer for generating an inverse signal is designed. For the situation of feedthrough capacitance less than the critical value, a feedthrough cancellation method based on pure digital circuit calculation is proposed. The experimental results show that the method of utilizing digital potentiometer effectively reduces the feedthrough level from −17.46 dB to −32.75 dB, and the method of utilizing pure digital circuit calculation compensates the feedthrough signal of 100.04 mV to almost zero (2.44 mV) within the range of ADC sampling accuracy. These two methods can accurately and quickly suppress feedthrough signal to improve the detection performance of MEMS gyroscopes, and are expected to meet the needs of future mass production. In addition, they can be widely applied to various MEMS devices that require feedthrough cancellation. [ABSTRACT FROM AUTHOR]

Vibrational environments can cause drift or changes in Micro-Electro-Mechanical System (MEMS) gyroscope rotor parameters, potentially impacting their performance. To improve the effective use of MEMS gyroscopes, this study introduced a method for evaluating the reliability of parameter degradation under vibration. We analyzed the working principle of MEMS gyroscope rotors and investigated how vibration affects their parameters. Focusing on zero bias and scale factor as key performance indicators, we developed an accelerated degradation model using the distributional assumption method. We then collected degradation data for these parameters under various vibration conditions. Using the Copula function, we established a reliability assessment approach to evaluate the degradation of the MEMS gyroscope rotor's zero bias and scale factor under vibration, enabling the determination of reliability for these parameters. Experimental findings confirmed that increasing stress levels lead to reduced failure times and increased failure rates for MEMS gyroscope rotors, with significant changes observed in the zero bias parameter. Our evaluation method effectively characterizes changes in the reliability of the MEMS gyroscope rotor's scale factor and zero bias over time, providing valuable information for practical applications of MEMS gyroscopes. [ABSTRACT FROM AUTHOR]

Circuit noise is a critical factor that affects the performances of an MEMS gyroscope. Therefore, it is essential to analyze and suppress the noises in the key analog circuits, which are the main noise sources. This study presents an optimized front-end readout circuit and noise suppression methods. First, the noise analysis of the front-end readout circuit is carried out with theoretical derivation to clarify the main noise contributors. To suppress the output noise, an improved readout circuit based on the T-resistor networks is proposed, and the corresponding noise equation is derived in detail. In addition, the noise analysis of the critical circuits of the detection and control system, such as the inverting amplifiers, the first-order low-pass filters, and the first-order high-pass filters, is carried out, and the noise suppression strategy with the optimization of the resistances and is proposed. Taking the inverting amplifier as an example, the theoretical derivation is verified by measuring and comparing the output noises of different resistance schemes. In addition, the output noises of the gyroscope before and after circuit optimization are measured. Experimental results demonstrate that the output noise with the circuit optimization is reduced from 60 μV/Hz1/2 to 30 μV/Hz1/2 and the bias instability is reduced from 3.8 deg/h to 1.38 deg/h. In addition, the ARW is significantly improved from 0.035 deg/h1/2 to 0.018 deg/h1/2, which indicates that the proposed noise analysis and suppression methods are effective and feasible.

Impact is the most important factor affecting the reliability of Micro-Electro-Mechanical System (MEMS) gyroscopes, therefore corresponding reliability design is very essential. This paper proposes a shock-protected structure (SPS) capable of withstanding a full temperature range from −40 °C to 80 °C to enhance the shock resistance of MEMS gyroscopes. Firstly, the shock transfer functions of the gyroscope and the SPS are derived using Single Degree-of-Freedom and Two Degree-of-Freedom models. The U-folded beam stiffness and maximum positive stress are deduced to evaluate the shock resistance of the silicon beam. Subsequently, the frequency responses of acceleration of the gyroscope and the SPS are simulated and analyzed in Matlab utilizing the theoretical models. Simulation results demonstrate that when the first-order natural frequency of the SPS is approximately one-fourth of the gyroscope's resonant frequency, the impact protection effect is best, and the SPS does not affect the original performance of the gyroscope. The acceleration peak of the MEMS gyroscope is reduced by approximately 23.5 dB when equipped with the SPS in comparison to its counterpart without the SPS. The anti-shock capability of the gyroscope with the SPS is enhanced by approximately 13 times over the full-temperature range. After the shock tests under the worst case, the gyroscope without the SPS experiences a beam fracture failure, while the performance of the gyroscope with the SPS remains normal, validating the effectiveness of the SPS in improving the shock reliability of MEMS gyroscopes. [ABSTRACT FROM AUTHOR]

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In this work, a novel mechanical amplification structure for a MEMS vibratory gyroscope is proposed with the aim of improving their sensitivity. The scheme is implemented using a system of micromachined V-shaped springs as a deflection amplifying mechanism. The effectiveness of the mechanism is first demonstrated for a capacitive fully decoupled quad mass gyroscope. A proof of concept vertical-axis mechanically amplified gyroscope with an amplification factor of 365% has been designed, simulated and fabricated, and results from its evaluation are presented in this paper. Experimental results show that the natural frequency of the gyroscope is 11.67 KHz, and the full scale measurement range is up to ±400°/s with a maximum nonlinearity of 54.69 ppm. The bias stability is 44.53°/h. The experiment results show that this quad mass gyroscope's performance is a very potential new way of reaching the navigation grade in the future. [ABSTRACT FROM AUTHOR]

This paper presents the development of an analytical model of an internal vibrating ring gyroscope in a Microelectromechanical System (MEMS). The internal ring structure consists of eight semicircular beams that are attached to the externally placed anchors. This research work analyzes the vibrating ring gyroscope’s in-plane displacement behavior and the resulting elliptical vibrational modes. The elliptical vibrational modes appear as pairs with the same resonance frequency due to the symmetric structure of the design. The analysis commences by conceptualizing the ring as a geometric structure with a circular shape possessing specific dimensions such as thickness, height, and radius. We construct a linear model that characterizes the vibrational dynamics of the internal vibrating ring. The analysis develops a comprehensive mathematical formulation for the radial and tangential displacements in local polar coordinates by considering the inextensional displacement of the ring structure. By utilizing the derived motion equations, we highlight the underlying relationships driving the vibrational characteristics of the MEMS’ vibrating ring gyroscope. These dynamic vibrational relationships are essential in enabling the vibrating ring gyroscope’s future utilization in accurate navigation and motion sensing technologies.

Microelectromechanical System (MEMS) gyroscopes are inertial sensors used to measure angular velocity. Due to their small size and low power consumption, MEMS devices are widely employed in consumer electronics and the automotive industry. MEMS gyroscopes typically use closed-loop control systems, which often use PID controllers with fixed parameters. These classical PID controllers require a trade-off between overshoot and rise time. However, temperature variations can cause changes in the gyroscope’s parameters, which in turn affect the PID controller’s performance. To address this issue, this paper proposes an adaptive PID controller that adjusts its parameters in response to temperature-induced changes in the gyroscope’s characteristics, based on the error value. A closed-loop control system using the adaptive PID was developed in Simulink and compared with a classical PID controller. The results demonstrate that the adaptive PID controller effectively tracked the changes in the gyroscope’s parameters, reducing overshoot by 96% while maintaining a similar rise time. During gyroscope startup, the adaptive PID controller achieves faster stabilization with a 0.036 s settling time, outperforming the 0.06 s of the conventional PID controller.

The demodulation phase error will cause the quadrature error to be coupled to the rate output, resulting in performance deterioration of the MEMS gyroscope. To solve this problem, an in-run automatic demodulation phase error compensation method is proposed in this paper. This method applies square wave angular rate input to the gyroscope and automatically identifies the value of the demodulation phase error through the designed automatic identification algorithm. To realize in-run automatic compensation, the demodulation phase error corresponding to the temperature point is measured every 10 °C in the full-temperature environment (−40~60 °C). The relationship between temperature and demodulation phase error is fitted by a third-order polynomial. The temperature is obtained by the temperature sensor and encapsulated in the ceramic packages of the MEMS gyroscope, and the in-run automatic compensation is realized based on the fitting curve. The temperature hysteresis effect on the zero-rate output (ZRO) of the gyroscope is eliminated after compensation. The bias instability (BI) of the three gyroscopes at room temperature (25 °C) is reduced by four to eight times to 0.1°/h, while that at full-temperature environment (−40~60 °C) is reduced by three to four times to 0.1°/h after in-run compensation.

This research proposes a new fractional robust data-driven control method to control a nonlinear dynamic micro-electromechanical (MEMS) gyroscope model. The Koopman theory is used to linearize the nonlinear dynamic model of MEMS gyroscope, and the Koopman operator is obtained by using the dynamic mode decomposition (DMD) method. However, external disturbances constantly affect the MEMS gyroscope. To compensate for these perturbations, a fractional sliding mode controller (FOSMC) is applied. The FOSMC has several advantages, including high trajectory tracking performance and robustness. However, one of the drawbacks of FOSMC is generating high control inputs. To overcome this limitation, the researchers proposed a compound controller design that applies fractional proportional integral derivative (FOPID) to reduce the control efforts. The simulation results showed that the proposed compound Koopman-FOSMC and FOPID (Koopman-CFOPIDSMC) outperformed two other controllers, including FOSMC and Koopman-FOSMC, in terms of performance. Therefore, this research proposes an effective approach to control the nonlinear dynamic model of MEMS gyroscope. [ABSTRACT FROM AUTHOR]

Microelectromechanical system (MEMS) vibrating gyroscope design considerations are always intriguing due to their microscale mechanical, electrical, and material behavior. MEMS vibrating ring gyroscopes have become important inertial sensors in inertial measurement units (IMU) for navigation and sensing applications. The design of a MEMS vibrating ring gyroscope incorporates an oscillating ring structure as a proof mass, reflecting unique design challenges and possibilities. This paper presents a comprehensive design analysis of the MEMS vibrating ring gyroscope from the mechanical, electrical, and damping perspectives. The mechanical design of the MEMS vibrating ring gyroscope investigates the various frame designs of the vibrating ring structure, as well as the various beam structures, including rectangular and semicircular beam structures, which are analyzed using mathematical models and finite element analysis (FEA) simulations that provide an in-depth analysis of the stiffness and deflection of the vibrating structures. The electrical designs of the MEMS vibrating ring gyroscope are analyzed using various electrode configurations, electrostatic actuation, and capacitive detection mechanisms. The design analysis of various forms of damping, including viscous, structural, thermoelastic, and anchor damping, is discussed. The variety of design structures is investigated for MEMS vibrating ring gyroscopes' mechanical, electrical, and damping performance. [ABSTRACT FROM AUTHOR]

This article is concerned with the method of calibrating the temperature drift and random drift of Micro-Electro-Mechanical System (MEMS) gyroscope to improve the precision of MEMS gyroscope application. These methods include two steps. In the first step, the optimized BP neural network is used to establish the temperature drift error model of the MEMS gyroscope, and the B-spline method is used to improve the storage and calculation efficiency of the temperature drift calibration. In the second step, since the random drift error of a single sensor is difficult to reduce the data of multiple MEMS gyroscope sensors that have completed temperature drift calibration are fused.The error calibration evaluation indicators all use SSE (The sum of squares due to error) to compare the advantages of the proposed method.In the experimental part,the four most common MEMS chips MPU6050(including a three-axis gyroscope and accelerometer sensor) are used in the market to verify the effect of the proposed method in drift error calibration. Finally, it is proved that the data fusion of a Multi-sensor is not only significantly better than the random drift error of a single sensor. Moreover, with the increase in the number of fusion sensors, the calibration effect has a trend of gradual improvement. [ABSTRACT FROM AUTHOR]

A neural adaptive robust control method is proposed for the desired tracking of micro-electro-mechanical system (MEMS) triaxial gyroscope. In this work, input constraints and external disturbance are taken into account, and a barrier Lyapunov function (BLF) is used to ensure that the constraints are not violated and that tracking performance is achieved. In the presented control approach, RBFNNs with a non-zero parameter are employed to approximate the lumped uncertainties of the system, where the approximation precision can be modified online by the provided adaptive laws in the control strategy. All of the signals in the closed-loop system are uniformly finally bounded (UUB) thanks to the designed control mechanism, which may overcome the limitation of the finite universal approximation domain. The effectiveness of the suggested control is demonstrated by the comparison of simulation results. [ABSTRACT FROM AUTHOR]

The MEMS gyroscope is one of the basic units of inertial navigation, whose performance and accuracy is noteworthy. Because of the limitations of processing technology and other factors, the relative manufacturing error of MEMS gyroscopes is usually large. Errors directly lead to a frequency mismatch of resonant structures and consequently restrict the performance improvement of the gyroscope. This study proposes a mechanical trimming technique combining the addition and removal of gold in a ring MEMS gyroscope. Firstly, the analysis of the gyroscope dynamics and error model and trimming theory provides theoretical guidance for the trimming process. Secondly, the method of adjusting the mass is investigated, and the ablation threshold of femtosecond laser parameters on gold is analyzed, which provides the process with parameters for the trimming experiment. Finally, the frequency trimming process is conducted in three steps, including the addition of gold spheres and the removal of gold spheres and gold film, which are applicable to the trimming process at different rates of frequency split. The results shows that the proposed method can reduce the frequency split of the gyroscope from 4.36 to 0.017 Hz. [ABSTRACT FROM AUTHOR]

MEMS gyroscopes are widely applied in consumer electronics, aerospace, missile guidance, and other fields. Reliable packaging is the foundation for ensuring the survivability and performance of the sensor in harsh environments, but gas leakage models of wafer-level MEMS gyroscopes are rarely reported. This paper proposes a gas leakage model for evaluating the packaging reliability of wafer-level MEMS gyroscopes. Based on thermodynamics and hydromechanics, the relationships between the quality factor, gas molecule number, and a quality factor degradation model are derived. The mechanism of the effect of gas leakage on the quality factor is explored at wafer-level packaging. The experimental results show that the reciprocal of the quality factor is exponentially related to gas leakage time, which is in accordance with the theoretical analysis. The coefficients of determination (R2) are all greater than 0.95 by fitting the curves in Matlab R2022b. The stable values of the quality factor for drive mode and sense mode are predicted to be 6609.4 and 1205.1, respectively, and the average degradation characteristic time is 435.84 h. The gas leakage time is at least eight times the average characteristic time, namely 3486.72 h, before a stable condition is achieved in the packaging chamber of the MEMS gyroscopes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Vibrational environments can cause drift or changes in Micro-Electro-Mechanical System (MEMS) gyroscope rotor parameters, potentially impacting their performance. To improve the effective use of MEMS gyroscopes, this study introduced a method for evaluating the reliability of parameter degradation under vibration. We analyzed the working principle of MEMS gyroscope rotors and investigated how vibration affects their parameters. Focusing on zero bias and scale factor as key performance indicators, we developed an accelerated degradation model using the distributional assumption method. We then collected degradation data for these parameters under various vibration conditions. Using the Copula function, we established a reliability assessment approach to evaluate the degradation of the MEMS gyroscope rotor’s zero bias and scale factor under vibration, enabling the determination of reliability for these parameters. Experimental findings confirmed that increasing stress levels lead to reduced failure times and increased failure rates for MEMS gyroscope rotors, with significant changes observed in the zero bias parameter. Our evaluation method effectively characterizes changes in the reliability of the MEMS gyroscope rotor’s scale factor and zero bias over time, providing valuable information for practical applications of MEMS gyroscopes.

The article deals with sensor fusion and real-time calibration in a homogeneous inertial sensor array. The proposed method allows for both estimating the sensors' calibration constants (i.e., gain and bias) in real-time and automatically suppressing degraded sensors while keeping the overall precision of the estimation. The weight of the sensor is adaptively adjusted according to the RMSE concerning the weighted average of all sensors. The estimated angular velocity was compared with a reference (ground truth) value obtained using a tactical-grade fiber-optic gyroscope. We have experimented with low-cost MEMS gyroscopes, but the proposed method can be applied to basically any sensor array. [ABSTRACT FROM AUTHOR]

Long-term corrosion, construction irregularities, road pressure and other reasons lead to various defects in urban sewer pipelines. Closed-circuit television (CCTV) and quick view (QV) are currently the most commonly used techniques to detect the internal state of the pipeline, but CCTV requires a large amount of capital investment and manpower costs, while QV is faced with the use of limitations and inaccurate positioning. The inspection of urban sewerage networks has long been a challenge for the relevant management authorities to overcome. To this end, in this study, an device was assembled using a six-axis MEMS gyroscope sensor as the core component to inspect and locate the breakage point of the pipe. Specifically, a six-axis MEMS gyroscope sensor is used as the core component along with a small lithium battery and a remote control switch assembled in a highly waterproof round box, and dropped into a laboratory to simulate a sewage pipe that has external water infiltration. Then the device is recovered and the SD card on which the data is stored is removed, the data is loaded to perform the coordinate conversion process and restore the trajectory and attitude of the device along its travel. The three axis axial acceleration of the device before and after passing through the infiltration point is analyzed for anomalies, as well as changes in the roll and pitch angle fluctuations of the device. Multiple experiments demonstrated that the six-axis MEMS gyro sensor response is very sensitive, generating data and storing it through the DATALOG module. With the reading and analysis of the data, when the pipeline is broken by external water intrusion, the axial acceleration value, pitch angle and roll angle of the device will change abruptly after flowing through the infiltration point, based on the analysis of these indicators the preliminary judgment of the extent of external water infiltration and locate the location of the infiltration point, potential applications of MEMS gyroscopic sensors in the field of sewerage are believed to be vast. [ABSTRACT FROM AUTHOR]

Jump and pull-in instability are common nonlinear dynamic behaviors leading to the loss of the performance reliability and structural safety of electrostatic micro gyroscopes. To achieve a better understanding of these initial-sensitive phenomena, the dynamics of a micro gyroscope system considering the nonlinearities of the stiffness and electrostatic forces are explored from a global perspective. Static and dynamic analyses of the system are performed to estimate the threshold of the detecting voltage for static pull-in, and dynamic responses are analyzed in the driving and detecting modes for the case of primary resonance and 1:1 internal resonance. The results show that, when the driving voltage frequency is a bit higher than the natural frequency, a high amplitude of the driving AC voltage may induce the coexistence of bistable periodic responses due to saddle-node bifurcation of the periodic solution. Basins of attraction of bistable attractors provide evidence that disturbance of the initial conditions can trigger a jump between bistable attractors. Moreover, the Melnikov method is applied to discuss the condition for pull-in instability, which can be ascribed to heteroclinic bifurcation. The validity of the prediction is verified using the sequences of safe basins and unsafe zones for dynamic pull-in. It follows that pull-in instability can be caused and aggravated by the increase in the amplitude of the driving AC voltage. [ABSTRACT FROM AUTHOR]

MEMS gyroscopes are one of the core components of inertial navigation systems. The maintenance of high reliability is critical for ensuring the stable operation of the gyroscope. Considering the production cost of gyroscopes and the inconvenience of obtaining a fault dataset, in this study, a self-feedback development framework is proposed, in which a dualmass MEMS gyroscope fault diagnosis platform is designed based on MATLAB/Simulink simulation, data feature extraction, and classification prediction algorithm and real data feedback verification. The platform integrates the dualmass MEMS gyroscope Simulink structure model and the measurement and control system, and reserves various algorithm interfaces for users to independently program, which can effectively identify and classify seven kinds of signals of the gyroscope: normal, bias, blocking, drift, multiplicity, cycle and internal fault. After feature extraction, six algorithms, ELM, SVM, KNN, NB, NN, and DTA, were respectively used for classification prediction. The ELM and SVM algorithms had the best effect, and the accuracy of the test set was up to 92.86%. Finally, the ELM algorithm is used to verify the actual drift fault dataset, and all of them are successfully identified. [ABSTRACT FROM AUTHOR]

Data-driven control methods are strong tools due to their predictions for controlling the systems with a nonlinear dynamic model. In this paper, the Koopman operator is used to linearize the nonlinear dynamic model. Generating the Koopman operator is the most important part of using the Koopman theory. Dynamic mode decomposition (DMD) is used to obtain eigenfunction for producing the Koopman operator. Then, a fractional order PID (FOPID) controller is applied to control the linearized dynamic model. A swarm intelligence bat optimization algorithm is utilized to tune the FOPID controller's parameters. Simulation results on micro-electromechanical systems (MEMS) gyroscope under conventional PID controller, FOPID, Koopman-based FOPID controller (Koopman-FOPID), and Koopman-FOPID control optimized by bat algorithm (Koopman-BAFOPID) show that the proposed Koopman-BAFOPID controller has better performance in comparison with three other controllers in terms of high tracking performance, low tracking error, and low control efforts. [ABSTRACT FROM AUTHOR]

We report for the first time an implementable method to identify and suppress the driving force misalignment angle for a MEMS gyroscope working either in amplitude modulated (AM) or Lissajous frequency modulated (LFM) mode using parametric excitation. By introducing driving force misalignment angle into gyroscope dynamic equations, we illustrate that gyroscope angular rate output is affected by driving force misalignment angle and cross-axis damping jointly. We propose parametric excitation as a way to both identify and calculate the driving force misalignment angle. The identification results for a gyroscope working in both AM and LFM mode are similar, which indicates the effectiveness of the proposed identification method. Instead of using traditional amplitude control loop by adjusting the driving force, we do the automatic gain control by adjusting the parametric pump voltage so that a fixed drive voltage can be used, which also indicates fixed force coupling. Experimental results show that after suppression, the bias instability (BI) of AM mode is improved from 4.7° h−1 to 2.3° h−1 and the BI of LFM mode is improved from 1.4° h−1 to 0.9° h−1 which is the lowest result reported for LFM gyroscope. [ABSTRACT FROM AUTHOR]

As a MEMS gyroscope is susceptible to environmental interference, its performance is degraded due to random noise. Accurate and rapid analysis of random noise of MEMS gyroscope is of great significance to improve the gyroscope's performance. A PID-DAVAR adaptive algorithm is designed by combining the PID principle with DAVAR. It can adaptively adjust the length of the truncation window according to the dynamic characteristics of the gyroscope's output signal. When the output signal fluctuates drastically, the length of the truncation window becomes smaller, and the mutation characteristics of the intercepted signal are analyzed detailed and thoroughly. When the output signal fluctuates steadily, the length of the truncation window becomes larger, and the intercepted signals are analyzed swiftly and roughly. The variable length of the truncation window ensures the confidence of the variance and shortens the data processing time without losing the signal characteristics. Experimental and simulation results show that the PID-DAVAR adaptive algorithm can shorten the data processing time by 50%. The tracking error of the noise coefficients of angular random walk, bias instability, and rate random walk is about 10% on average, and the minimum error is about 4%. It can accurately and promptly present the dynamic characteristics of the MEMS gyroscope's random noise. The PID-DAVAR adaptive algorithm not only satisfies the requirement of variance confidence but also has a good signal-tracking ability. [ABSTRACT FROM AUTHOR]

This paper introduces a digital interface application-specific integrated circuit (ASIC) for a micro-electromechanical systems (MEMS) vibratory gyroscope. The driving circuit of the interface ASIC uses an automatic gain circuit (AGC) module instead of a phase-locked loop to realize a self-excited vibration, which gives the gyroscope system good robustness. In order to realize the co-simulation of the mechanically sensitive structure and interface circuit of the gyroscope, the equivalent electrical model analysis and modeling of the mechanically sensitive structure of the gyro are carried out by Verilog-A. According to the design scheme of the MEMS gyroscope interface circuit, a system-level simulation model including mechanically sensitive structure and measurement and control circuit is established by SIMULINK. A digital-to-analog converter (ADC) is designed for the digital processing and temperature compensation of the angular velocity in the MEMS gyroscope digital circuit system. Using the positive and negative diode temperature characteristics, the function of the on-chip temperature sensor is realized, and the temperature compensation and zero bias correction are carried out simultaneously. The MEMS interface ASIC is designed using a standard 0.18 μM CMOS BCD process. The experimental results show that the signal-to-noise ratio (SNR) of sigma-delta (ΣΔ) ADC is 111.56 dB. The nonlinearity of the MEMS gyroscope system is 0.03% over the full-scale range. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Angular velocity measurement is a very important measurement parameter in industrial manufacturing field and different scientific applications. The design of gyro measurement and control circuit is always the most challenging and reliable task of angular velocity measurement system. This paper introduces the design and implementation of a measurement and control circuit for digital output of gyro for angular velocity measurement. The design of measuring and controlling circuit with high precision digital output is presented. A method of on-chip scale factor and zero output compensation correction for angular velocity measurement is introduced. Peak detection and proportional integral controller are used to replace the phase-locked loop in the driving circuit, which makes the driving loop of gyro system have good robustness. A sigma-delta (ΣΔ) digital-to-analog converter is designed for digital output of angular velocity signal. Finally, the least square method is used to evaluate the nonlinearity of angular velocity measurement system according to test results, and the zero output and scale factor uncertainty of the measurement system are evaluated. [ABSTRACT FROM AUTHOR]

Impact is the most important factor affecting the reliability of Micro-Electro-Mechanical System (MEMS) gyroscopes, therefore corresponding reliability design is very essential. This paper proposes a shock-protected structure (SPS) capable of withstanding a full temperature range from −40 °C to 80 °C to enhance the shock resistance of MEMS gyroscopes. Firstly, the shock transfer functions of the gyroscope and the SPS are derived using Single Degree-of-Freedom and Two Degree-of-Freedom models. The U-folded beam stiffness and maximum positive stress are deduced to evaluate the shock resistance of the silicon beam. Subsequently, the frequency responses of acceleration of the gyroscope and the SPS are simulated and analyzed in Matlab utilizing the theoretical models. Simulation results demonstrate that when the first-order natural frequency of the SPS is approximately one-fourth of the gyroscope’s resonant frequency, the impact protection effect is best, and the SPS does not affect the original performance of the gyroscope. The acceleration peak of the MEMS gyroscope is reduced by approximately 23.5 dB when equipped with the SPS in comparison to its counterpart without the SPS. The anti-shock capability of the gyroscope with the SPS is enhanced by approximately 13 times over the full-temperature range. After the shock tests under the worst case, the gyroscope without the SPS experiences a beam fracture failure, while the performance of the gyroscope with the SPS remains normal, validating the effectiveness of the SPS in improving the shock reliability of MEMS gyroscopes.

In this work, a novel mechanical amplification structure for a MEMS vibratory gyroscope is proposed with the aim of improving their sensitivity. The scheme is implemented using a system of micromachined V-shaped springs as a deflection amplifying mechanism. The effectiveness of the mechanism is first demonstrated for a capacitive fully decoupled quad mass gyroscope. A proof of concept vertical-axis mechanically amplified gyroscope with an amplification factor of 365% has been designed, simulated and fabricated, and results from its evaluation are presented in this paper. Experimental results show that the natural frequency of the gyroscope is 11.67 KHz, and the full scale measurement range is up to ±400°/s with a maximum nonlinearity of 54.69 ppm. The bias stability is 44.53°/h. The experiment results show that this quad mass gyroscope’s performance is a very potential new way of reaching the navigation grade in the future.

Copyright of Journal of Test & Measurement Technology is the property of Publishing Center of North University of China and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The micro-electro-mechanical system (MEMS) gyroscope is a micro-mechanical gyroscope with low cost, small volume, and good reliability. The working principle of the MEMS gyroscope, which is achieved through Coriolis, is different from traditional gyroscopes. The MEMS gyroscope has been widely used in the fields of micro-inertia navigation systems, military, automotive, consumer electronics, mobile applications, robots, industrial, medical, and other fields in micro-inertia navigation systems because of its advantages of small volume, good performance, and low price. The material characteristics of the MEMS gyroscope is very significant for its data output, and the temperature determines its accuracy and limits its further application. In order to eliminate the effect of temperature, the MEMS gyroscope needs to be compensated to improve its accuracy. This study proposed an improved variational modal decomposition—extreme learning machine (VMD-ELM) algorithm based on convolutional neural networks—long short-term memory (CNN-LSTM) and particle swarm optimization—support vector machines (PSO-SVM). By establishing a temperature compensation model, the gyro temperature output signal is optimized and reconstructed, and the gyro output signal with better accuracy is obtained. The VMD algorithm separates the gyro output signal and divides the gyro output signal into low-frequency signals, mid-frequency signals, and high-frequency signals according to the different signal frequencies. Once again, the PSO-SVM model is constructed by the mid-frequency temperature signal to find the temperature error. Finally, the signal is reconstructed through the ELM neural network algorithm, and then, the gyro output signal after noise is obtained. Experimental results show that, by using the improved method, the output of the MEMS gyroscope ranging from −40 to 60 °C reduced, and the temperature drift dramatically declined. For example, the factor of quantization noise (Q) reduced from 1.2419 × 10−4 to 1.0533 × 10−6, the factor of bias instability (B) reduced from 0.0087 to 1.8772 × 10−4, and the factor of random walk of angular velocity (N) reduced from 2.0978 × 10−5 to 1.4985 × 10−6. Furthermore, the output of the MEMS gyroscope ranging from 60 to −40 °C reduced. The factor of Q reduced from 2.9808 × 10−4 to 2.4430 × 10−6, the factor of B reduced from 0.0145 to 7.2426 × 10−4, and the factor of N reduced from 4.5072 × 10−5 to 1.0523 × 10−5. The improved algorithm can be adopted to denoise the output signal of the MEMS gyroscope to improve its accuracy. [ABSTRACT FROM AUTHOR]

MEMS gyroscopes are widely applied in consumer electronics, aerospace, missile guidance, and other fields. Reliable packaging is the foundation for ensuring the survivability and performance of the sensor in harsh environments, but gas leakage models of wafer-level MEMS gyroscopes are rarely reported. This paper proposes a gas leakage model for evaluating the packaging reliability of wafer-level MEMS gyroscopes. Based on thermodynamics and hydromechanics, the relationships between the quality factor, gas molecule number, and a quality factor degradation model are derived. The mechanism of the effect of gas leakage on the quality factor is explored at wafer-level packaging. The experimental results show that the reciprocal of the quality factor is exponentially related to gas leakage time, which is in accordance with the theoretical analysis. The coefficients of determination (R2) are all greater than 0.95 by fitting the curves in Matlab R2022b. The stable values of the quality factor for drive mode and sense mode are predicted to be 6609.4 and 1205.1, respectively, and the average degradation characteristic time is 435.84 h. The gas leakage time is at least eight times the average characteristic time, namely 3486.72 h, before a stable condition is achieved in the packaging chamber of the MEMS gyroscopes.

The MEMS gyroscope is one of the basic units of inertial navigation, whose performance and accuracy is noteworthy. Because of the limitations of processing technology and other factors, the relative manufacturing error of MEMS gyroscopes is usually large. Errors directly lead to a frequency mismatch of resonant structures and consequently restrict the performance improvement of the gyroscope. This study proposes a mechanical trimming technique combining the addition and removal of gold in a ring MEMS gyroscope. Firstly, the analysis of the gyroscope dynamics and error model and trimming theory provides theoretical guidance for the trimming process. Secondly, the method of adjusting the mass is investigated, and the ablation threshold of femtosecond laser parameters on gold is analyzed, which provides the process with parameters for the trimming experiment. Finally, the frequency trimming process is conducted in three steps, including the addition of gold spheres and the removal of gold spheres and gold film, which are applicable to the trimming process at different rates of frequency split. The results shows that the proposed method can reduce the frequency split of the gyroscope from 4.36 to 0.017 Hz.

Microelectromechanical system (MEMS) vibrating gyroscope design considerations are always intriguing due to their microscale mechanical, electrical, and material behavior. MEMS vibrating ring gyroscopes have become important inertial sensors in inertial measurement units (IMU) for navigation and sensing applications. The design of a MEMS vibrating ring gyroscope incorporates an oscillating ring structure as a proof mass, reflecting unique design challenges and possibilities. This paper presents a comprehensive design analysis of the MEMS vibrating ring gyroscope from the mechanical, electrical, and damping perspectives. The mechanical design of the MEMS vibrating ring gyroscope investigates the various frame designs of the vibrating ring structure, as well as the various beam structures, including rectangular and semicircular beam structures, which are analyzed using mathematical models and finite element analysis (FEA) simulations that provide an in-depth analysis of the stiffness and deflection of the vibrating structures. The electrical designs of the MEMS vibrating ring gyroscope are analyzed using various electrode configurations, electrostatic actuation, and capacitive detection mechanisms. The design analysis of various forms of damping, including viscous, structural, thermoelastic, and anchor damping, is discussed. The variety of design structures is investigated for MEMS vibrating ring gyroscopes’ mechanical, electrical, and damping performance.

The ability to seek the accuracy of the true north direction is essential in determining the direction of the ground vehicle, sea, and air and as a reference point in the determination of Qibla direction as well. Theodolite is mainly used for surveying applications in measuring angles, including determining the direction for Muslims to perform ritual prayers, Qibla. However, transferring point-by-point from outdoor to indoor via theodolite requires many experts and is a complicated process. In this paper, we present the development of a highly accurate and compact north-finding prototype for bulk direction marking based on a Micro-Electro-Mechanical System (MEMS) gyroscope and accelerometer sensor. The system consists of two modules; a GPS-based transmitter module to obtain latitude and longitude information and a MEMS gyroscope and accelerometer-based receiver module to detect the geographic north and mark the direction. We accomplish the accuracy by implementing a 4-point static rotation method to compensate for the gyroscope bias and a digital complementary filter system to filter out drift error and fluctuations in the data. We tested the developed prototype on different geographic landscapes, weather conditions, and various building types. The field test results prove that the developed system achieves an accuracy of ±7’ 06”, verified by the Department of Survey and Mapping Malaysia.

Errors in microelectromechanical systems (MEMS) inertial measurement units (IMUs) are large, complex, nonlinear, and time varying. The traditional noise reduction and compensation methods based on traditional models are not applicable. This paper proposes a noise reduction method based on multi-layer combined deep learning for the MEMS gyroscope in the static base state. In this method, the combined model of MEMS gyroscope is constructed by Convolutional Denoising Auto-Encoder (Conv-DAE) and Multi-layer Temporal Convolutional Neural with the Attention Mechanism (MultiTCN-Attention) model. Based on the robust data processing capability of deep learning, the noise features are obtained from the past gyroscope data, and the parameter optimization of the Kalman filter (KF) by the Particle Swarm Optimization algorithm (PSO) significantly improves the filtering and noise reduction accuracy. The experimental results show that, compared with the original data, the noise standard deviation of the filtering effect of the combined model proposed in this paper decreases by 77.81% and 76.44% on the x and y axes, respectively; compared with the existing MEMS gyroscope noise compensation method based on the Autoregressive Moving Average with Kalman filter (ARMA-KF) model, the noise standard deviation of the filtering effect of the combined model proposed in this paper decreases by 44.00% and 46.66% on the x and y axes, respectively, reducing the noise impact by nearly three times. [ABSTRACT FROM AUTHOR]

Real-time, continuous, and long-term marine monitoring data benefits ocean research. This study developed a low-cost, multi-parameter, miniature wave buoy. High spatial and temporal resolution of sea surface parameters, including wind, waves, and current, can be obtained at low cost through the deployment of numerous buoys, thus forming an observation array. Tested in the laboratory water tank, the relative error of water surface slope measurement of the buoy was approximately 5.6% when the slope angle was less than 15°. For frequencies between 0.1 and 1.0 Hz, the measurement of slope spectrum was almost identical to that of the wave gauge. The buoy underestimated the slope spectrum between 1.0–1.56 Hz. A good relationship (r2 = 0.75) was obtained between wind speed at 10 m above sea surface (U10) and the low-pass-filtered mean square slope (LPMSS). After incorporating the wave age into the U10 inversion process, the root mean square error (RMSE) and BIAS were reduced to 1.15 m/s and 0.02 m/s, respectively. The 2D distribution of buoy-measured slope components was used to detect the wind direction, with an RMSE of 23.7°. The spectral tail slope steepened with increasing wind speed at low wind speeds (<7 m/s). A technical flow chart of the miniature wave buoy is proposed to observe the sea surface parameters. This miniature buoy will play an essential complementary role in the growing demand for sea state monitoring, especially in nearshore oceans. [ABSTRACT FROM AUTHOR]

In recent years, the application prospects of high-precision MEMS gyroscopes have been shown to be very broad, but the large temperature drift of MEMS gyroscopes limits their application in complex temperature environments. In response to this, we propose a method that combines mode reversal and real-time multiple regression compensation to compensate for the temperature drift of gyroscope bias. This method has strong adaptability to the environment, low computational cost, the algorithm is online in real time, and the compensation effect is good. The experimental results show that under the temperature cycle of −20~20 °C and the temperature change rate of 4 °C/min, the method proposed in this paper can reduce the zero-bias stability from about 27.8°/h to 0.4527°/h, and the zero-bias variation is reduced from 65.88°/h to 1.43°/h. This method improves the zero-bias stability of the gyroscope 61-fold and the zero-bias variation 46-fold. Further, the method can effectively suppress the zero-bias drift caused by the heating of the gyroscope during the start-up phase of the gyroscope. The zero-bias stability of the gyroscope can reach 0.0697°/h within 45 min of starting up, and the zero-bias repeatability from 0 to 5 min after startup is reduced from 0.629°/h to 0.095°/h. [ABSTRACT FROM AUTHOR]

The Micro-Electro-Mechanical System (MEMS) gyroscope has been widely used in various fields, but the output of the MEMS gyroscope has strong nonlinearity, especially in the range of tiny angular velocity. This paper proposes an adaptive Fourier series compensation method (AFCM) based on the steepest descent method and Fourier series residual correction. The proposed method improves the Fourier series fitting method according to the output characteristics of the MEMS gyroscope under tiny angular velocity. Then, the optimal weights are solved by the steepest descent method, and finally the fitting residuals are corrected by Fourier series to further improve the compensation accuracy. In order to verify the effectiveness of the proposed method, the angle velocity component of the earth's rotation is used as the input of the MEMS gyroscope to obtain the output of the MEMS gyroscope under tiny angular velocities. Experimental characterization resulted in an input angular velocity between −0.0036°/s and 0.0036°/s, compared with the original data, the polynomial compensation method, and the Fourier series compensation method, and the output nonlinearity of the MEMS gyroscope was reduced from 1150.87 ppm, 641.13 ppm, and 250.55 ppm to 68.89 ppm after AFCM compensation, respectively, which verifies the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

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.

Jump and pull-in instability are common nonlinear dynamic behaviors leading to the loss of the performance reliability and structural safety of electrostatic micro gyroscopes. To achieve a better understanding of these initial-sensitive phenomena, the dynamics of a micro gyroscope system considering the nonlinearities of the stiffness and electrostatic forces are explored from a global perspective. Static and dynamic analyses of the system are performed to estimate the threshold of the detecting voltage for static pull-in, and dynamic responses are analyzed in the driving and detecting modes for the case of primary resonance and 1:1 internal resonance. The results show that, when the driving voltage frequency is a bit higher than the natural frequency, a high amplitude of the driving AC voltage may induce the coexistence of bistable periodic responses due to saddle-node bifurcation of the periodic solution. Basins of attraction of bistable attractors provide evidence that disturbance of the initial conditions can trigger a jump between bistable attractors. Moreover, the Melnikov method is applied to discuss the condition for pull-in instability, which can be ascribed to heteroclinic bifurcation. The validity of the prediction is verified using the sequences of safe basins and unsafe zones for dynamic pull-in. It follows that pull-in instability can be caused and aggravated by the increase in the amplitude of the driving AC voltage.