This paper presents a novel multi-objective parameter optimization method based on the genetic algorithm (GA) and adaptive moment estimation (Adam) algorithm for the design of a closed-loop control system for the sense mode of a Microelectromechanical systems (MEMS) gyroscope. The proposed method can improve the immunity of the control system to fabrication tolerances and external noise. The design procedure starts by deriving a parameterized model of the closed-loop of the sense mode. The loop parameters are then optimized by the GA. Finally, the ensemble of optimized loop parameters is tested by Monte Carlo analysis to obtain a robust optimal solution. Simultaneously, the Adam-least mean square (LMS) demodulator, which is appropriate for the demodulation of very noisy signals, is also presented. Compared with the traditional method, the time consumption of the design process is reduced significantly. The digital control system is implemented by the print circuit board based on embedded Field Programmable Gate Array (FPGA). The experimental results show that the optimized control loop has achieved a better performance, the system bandwidth in open-loop and optimal closed-loop control system is about 23 Hz and 101 Hz, respectively. Compared to a non-optimized closed-loop system, the bias instability reduced from 0.0015°/s to 7.52 × 10−4°/s, the scale factor increased from 17.7 mV/(°/s) to 23 mV/(°/s) and the non-linearity of the scale factor reduced from 0.008452% to 0.006156%.

This paper presents a bias drift self-calibration method for micro-electromechanical systems (MEMS) gyroscopes based on noise-suppressed mode reversal without the modeling of bias drift signal. At first, the bias drift cancellation is accomplished by periodic switching between operation mode of two collinear gyroscopes and subtracting the bias error which is estimated by the rate outputs from a consecutive period interval; then a novel filtering algorithm based on improved complete ensemble empirical mode decomposition (improved complete ensemble empirical mode decomposition with adaptive noise-CEEMDAN) is applied to eliminate the noise in the calibrated signal. A set of intrinsic mode functions (IMFs) is obtained by the decomposition of the calibrated signal using improved CEEMDAN method, and the threshold denoising method is utilized; finally, the de-noised IMFs are reconstructed into the desired signal. To verify the proposed method, the hardware circuit with an embedded field-programmable gate array (FPGA) was implemented and applied in bias drift calibration for the two MEMS gyroscopes manufactured in our laboratory. The experimental results indicate that the proposed method is feasible, and it achieved a better performance than the typical mode reversal. The bias instability of the two gyroscopes decreased from 0.0066 ° / s and 0.0055 ° / s to 0.0011 ° / s ; and, benefiting from the threshold denoising based on improved CEEMDAN, the angle random walks decreased from 1.18 × 10 - 4 ° / s 1 / 2 and 2.04 × 10 - 4 ° / s 1 / 2 to 2.19 × 10 - 5 ° / s 1 / 2 , respectively.

The micro-fluidic inertial switch with liquid metal droplet moving under the action of acceleration has overcome the disadvantages of contact bounce, arcing and welding, as are found in the traditional inertial switch. Micro-fluidic inertial switches have no moving parts, a small contact resistance, a long service life and a large current capability. In this paper, we present a micro-fluidic inertial switch that is composed of two-stage micro-valves. This design facilitates tuning of the threshold by adjusting the mercury volume, and so provides better switching performance. Numerical simulation of an orthogonal experiment is used to identify the semi-analytical model of the switch threshold. Results show that the identified model is in accordance with simulation results. Switch prototypes are fabricated by micro-machining techniques including ICP dry etching, sputtering technology and anodic bonding. Centripetal test results show that the switch threshold can be tuned by the careful adjustment of mercury volume.

The micro-fluidic inertial switch based on liquid metal utilizes the moving mercury droplet to close the switch under the action of acceleration, which is characterized by no moving parts, small contact resistance, long service life and large current. In addition to the requirement of response time, accuracy and reliability, the micro-fluidic inertial switch needs to overcome the impact of the ambient vibration. The influence of the ambient vibration on the performance of switch is investigated by loading pulse or sinusoidal interference signals in the X, Y and Z direction. The numerical results suggest that the performance of micro-fluidic inertial switch is greatly affected by impact interference signal in X sensitive direction as compared with low frequency harmonic signal. If the impact signal with high amplitude lasts only for a short time, the wrong operation might also occur. The interference signals in insensitive direction have a relatively small impact on the performance of switch, and the impact of interference signal can be reduced by reasonable structural design. Finally, anodic bonding, deep reactive ion etching (DRIE) and sputtering technique are adopted to fabricate the micro-fluidic inertial switch. The acceleration threshold of the prototype is tested. The experiment results agree with the numerical results, which indicate that the simulation method is valid.

The switch based on electrowetting technology has the advantages of no moving part, low contact resistance, long life and adjustable acceleration threshold. The acceleration threshold of switch can be fine-tuned by adjusting the applied voltage. This paper is focused on the electrowetting properties of switch and the influence of microchannel structural parameters, applied voltage and droplet volume on acceleration threshold. In the presence of process errors of micro inertial fluidic switch and measuring errors of droplet volume, there is a deviation between test acceleration threshold and target acceleration threshold. Considering the process errors and measuring errors, worst-case analysis is used to analyze the influence of parameter tolerance on the acceleration threshold. Under worst-case condition the total acceleration threshold tolerance caused by various errors is 9.95%. The target acceleration threshold can be achieved by fine-tuning the applied voltage. The acceleration threshold trimming method of micro inertial fluidic switch is verified.

To cope with the temperature drift of sandwich capacitive micro-accelerometer,based on mechanics and thermal principle,the geometrical change of sensing structure due to the thermal expansion was analyzed.Then,in light of the geometrical change and accelerometer's closed loop op-eration mode,the output change was obtained,which implies that the output variation is less than 0?002gn per 10℃.Meanwhile,an experiment was conducted,which indicates that the output change due to the temperature is from 0?1gn to 0?2gn per 10℃.The results illustrate that the geometrical change is not a dominant reason for temperature drift.

Unlike the solid-solid contact of traditional micro acceleration switch, liquid metal can be utilized to solve the disadvantage of solid-solid contact, such as contact wear and signal bounce. Liquid-metal micro switches have demonstrated no contact bounce, low switch-on time, low contact resistance, long life, and the capability to handle large currents. So the liquid-metal micro acceleration switches have attracted researcher’s attentions increasingly. To investigate the flow characteristics of mercury droplet in micro acceleration switch, this paper establishes numerical models of micro acceleration switch by using FLUENT. The effect of contact angle, droplet volume and temperature are discussed in this paper. Based on the VOF-CSF model of FLUENT, a serial of simulations were performed. The simulation results show that the influence of contact angle and droplet volume on flow characteristics is serious, and the influence of temperature is small. As compared with theoretical analysis, simulations are in good agreement with theoretical analysis.

Microstructure curvature, or buckling, is observed in the micromachining of silicon sensors because of the doping of impurities for realizing certain electrical and mechanical processes. This behavior can be a key source of error in inertial sensors. Therefore, identifying the factors that influence the buckling value is important in designing MEMS devices. In this study, the curvature in the proof mass of an accelerometer is modeled as a multilayered solid model. Modeling is performed according to the characteristics of the solid diffusion mechanism in the bulk-dissolved wafer process (BDWP) based on the self-stopped etch technique. Moreover, the proposed multilayered solid model is established as an equivalent composite structure formed by a group of thin layers that are glued together. Each layer has a different Young's modulus value and each undergoes different volume shrinkage strain owing to boron doping in silicon. Observations of five groups of proof mass blocks of accelerometers suggest that the theoretical model is effective in determining the buckling value of a fabricated structure.

In order to truly reflect the flow characteristics of mercury droplet flow in varying-cross-section microchannel driven by inertia force, the impact of contact angle hysteresis on flow characteristics should be considered in numerical simulations. The VOF-CSF model of FLUENT software is used to study the flow characteristics of mercury droplet flow in varying-cross-section microchannel of micro fluidic inertia switch. Write the UDF of dynamic and static contact angle hysteresis,and simulate the flow characteristics in varying-section-mi-crochannel. The results show that the static contact angle and the contact angle hystersis of 10oare set in simulation, the acceleration threshold of micro fluidic inertia switch is 13. 2 gn and 16. 4 gn,respectively. The different contact angle hysteresis have an important impact on flow characteristics. The greater the contact angle hysteresis, the smaller the flow velocity of mercury droplet, and the harder mercury droplet breaks through the micro-valve and enters the reservior. Under the action of acceleration signal the contact line velocity of mercury droplet in varying-section-microchannel is lower, thus the effect of dynamic contact angle hysteresis on flow characteristics can be ignored and replaced by static contact angle hysteresis.

This paper investigates the design of a self-oscillation loop for the gyroscope system. The dynamic equations describing this system are analyzed using the method of averaging, and a criterion for selecting the circuit parameters is established based on the analysis. The validity of the criterion and the effectiveness of the control scheme are verified by the experimental results obtained from the control parameters that satisfy or violate the stability criterion. The performance of the self-oscillation loop with a z-axis gyroscope is also evaluated in light of the experimental results. The self-oscillation loop based on the auto gain control scheme effectively tracks the resonance frequency of a z-axis gyroscope. This frequency corresponds to a standard Allan variance of 0.04 Hz in 8 min at natural frequency. The output signal-to-noise ratio (SNR) is about 90 dB, and the vibratory velocity amplitude shows a deviation of 0.5% in 8 min.

Gap asymmetry in differential capacitors is the primary source of the zero bias output of force-balanced micro accelerometers. It is also used to evaluate the applicability of differential structures in MEMS manufacturing. Therefore, determining the asymmetry level has considerable significance for the design of MEMS devices. This paper proposes an experimental-theoretical method for predicting gap asymmetry in differential sensing capacitors of micro accelerometers. The method involves three processes: first, bi-directional measurement, which can sharply reduce the influence of the feedback circuit on bias output, is proposed. Experiments are then carried out on a centrifuge to obtain the input and output data of an accelerometer. Second, the analytical input-output relationship of the accelerometer with gap asymmetry and circuit error is theoretically derived. Finally, the prediction methodology combines the measurement results and analytical derivation to identify the asymmetric error of 30 accelerometers fabricated by DRIE. Results indicate that the level of asymmetry induced by fabrication uncertainty is about ±5 × 10−2, and that the absolute error is about ±0.2 µm under a 4 µm gap.

An electrostatic compensation method is proposed to realize the frequency robustness of a capacitive accelerometer by taking advantage of the electromechanical coupling characteristics, rather than mechanical structure alone. The limitations of microfabrication on structural configuration are overcome by an efficient adjustment of circuit parameters, which have equivalent contributions on the natural frequency as mechanical structures. The results of theoretical analysis and experiments indicate that this design method is practical for different microprocessing conditions, and the robustness of a mechanical structure to error can be achieved by a reasonable electrostatic compensation in electromechanical coupling microdevices. The test results have shown that the frequency deviations in more than 80% of fabricated sensors are less than 1%. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.JMM.11.4.043001]

This paper presents a robust optimal model of Micro Electro Mechanical Systems(MEMS) gyroscope and its design procedure.The proposed method adopts the sensitivity analysis considering the worst-case tolerance instead of statistical information about uncertainties.The genetic algorithm with the advantage of global optimization is employed.Sensitivity analysis shows the robust design is less sensitive to errors.Monte Carlo analysis is also performed,whose result indicates 88.35% of samples are acceptable.The gyroscope is fabricated using bonding and deep etching bulk micromachining process.

Magnetometer can be used to assist the vehicle for angular velocity measurement. The vehicle normally has the coning motion in flight application, and this would influence the interior magnetic distribution and lead to distortion in magnetometer output. In order to solve this problem, a magnetometer aided angular velocity measurement method based on real-time error compensation is put forward which considers the coning motion and magnetic deviation. It takes the advantage of the last 1 rotation cycle data of the magnetometer to compensate the output error and calculate the vehicle angular velocity. When the angular velocity is larger, the result would be more accurate. Flight experiment is carried on to verify the method, and the result shows that the angular velocity error is smaller than 1(°)/s when the angular velocity is larger than 300(°)/s.

An interpretation of the thermal drift of the bulk silicon MEMS capacitive accelerometer using multiphysics analysis is proposed in this paper. Stress, strain, electrostatics, thermal and structural interactions are simulated based on the finite element method. The thermal drift is generated by both the stiffness asymmetry of the U-springs of the structure and relative displacement caused by the mismatch in thermal expansion coefficients between the Pyrex glass substrate and heavily boron-doped silicon structure, neither of which is dispensable. Although the layout design is symmetrical, the asymmetric widths of the U-springs, which cause stiffness asymmetry, are observed by scanning electron microscopy. To achieve a fast and feasible simulation, we divide the model into two components with different configurations. During the simulation, boundary conditions are carefully set up according to the fabrication process. A series of experiments is designed to verify the result, including a temperature experiment from −40 to 100°C and DC voltage polarity experiment. To verify the conclusion, a new layout design that gradually increases the width of the U-springs without changing any other dimension is simulated, fabricated, and tested. The simulation and experiment results are compared and discussed.

The entire calibration and compensation method of a Miniature Inerial Measurement Unit(MIMU) in high dynamic and overload complicate environments was proposed. Firstly,an error model applied to the complicate application environments was established,which consists of the structure errors,installation misalignment errors and the errors of the MEMS sensors including zero output drift,temperature drift,cross-axis error,nonlinear scale factor error and acceleration effect error of gyroscope.Based on the model,the entire calibration and compensation method was proposed to calibrate 63 error coefficients without calibration of each MEMS inertial sensor separately.Then,the generalized least square algorithm was used to calibrate and calculate the error coefficients.Finally,a MIMU was developed for a flight experiment and was calibrated with this proposed method.Experimental results indicate that the positioning accuracy is improved by 1 order of magnitude.It can satisfy the high dynamic and overload requirements of the MIMU.

The introduced resonant accelerometer makes use of the equivalent electrostatic stiffness to sense the acceleration.The sensitivity can be adjusted by changing the applied sensing voltage and it is robust for the fabrication error.According to the sensing principle,the dynamic model of the single beam accelerometer is built along with the no-linear relationship of the output frequency and the displacement of all positive components.When the stiffness of the vibrating beam is much bigger than the stiffness of the fold beam,the sensitivity can effective achieve.It is the restriction for the structure design.For the differential structure,mode analysis shows it is a lower mode in plane for the work mode.Decreasing the stiffness of connected end for the double vibrating beam can reduce the disturbance error.The bulk micromachining for the resonant accelerometer can achieve high depth width ration etching.The experiment find the structure is not broken and there is the same frequency disturbance problem.FM is suggested to deal with the disturbance.Theory analysis and test provides some important conclusions for the design of the novel type resonant accelerometer.

The main advantage of a resonant accelerometer based on electrostatic stiffness over other sensing principles is it can make use of the sensing voltage to adjust the sensitivity. The dynamic model of this accelerometer is built. With the aim to achieve the resonance frequency track, a phase-locked loop(PLL) system is used to track the resonance frequency due to changing of the acceleration, the model for the control system is established and the system behavior are analyzed using an averaging method. The analysis provides a quantitative criterion for selecting the control parameters to achieve system stability, the integral control gain will critical to the system stability and stability time. Simulation results are shown to be in agreement with the all theoretical analysis.

There are some drawbacks for the resonant micro-accelerometer based on the axial fore changing, the performance is sensitive for the fabrication error and worsen for the time. The introduced resonant accelerometer makes use of the equivalent electrostatic stiffness to sense the acceleration. The sensitivity can be adjusted by changing the applied sensing voltage and it is robust for the fabrication error. The bulk micromachining for the resonant accelerometer can achieve high depth width ration etching. According to the sensing principle, built the dynamic model, adopt the closed-loop control method based on phase-locked. The simulation shows the control method can achieve steady frequency tracking and invariable amplitude vibrating, it can be used for other micro sensors. Analysis and simulation provide some important conclusions for the design of the novel type resonant accelerometer.

By analyzing the requirement of the closed-loop control for the vibratory gyroscope,the behaviour of the self-oscillation system with automatic gain control was analyzed with averaging method to achieve system stability and stable equilibrium.The theoretic analysis and experiment show that the reference voltage must be larger than a critical value;the larger the reference voltage is,the larger the signal-noise-ratio is;the system phase error will cause the resonance frequency drift and decrease the vibrating amplitude;different constants of the low pass filters result in different time to achieve the stable states.The experiment shows the frequency accuracy of the close-loop self oscillation system is about ±8ppm in 10 minutes and vibration amplitude is about 0.1% error in an hour.