Silicon Micro-gyroscope Research Articles

Analysis of orthogonal signal of dual-mass micro-machined gyroscope

The dual-mass Silicon micro-machined gyroscope was processed by micro-fabrication technology. It could lead to quadrature coupling error and influence the output of the silicon micro-gyroscope. We select two commonly used gyroscope structures and analyze their quadrature coupling coefficient. Firstly, the complete dynamic model is proposed for the DMSG and the theoretical models of sensitivity and orthogonal signals are given by the dynamic model. Second, the influence of support structure on sensitivity and orthogonal signals are analyzed. The sensitivity and orthogonal signal of the two types of DMSG are derived and compared. The results show that the theoretical accuracy of the sensitivity and orthogonal signals can be improved about 50% and 30% after considering the support structure. The type-B gyroscope are insensitive to the Coriolis force (≈13% reduction) when compared to Type-A gyroscope. On the other hand the type-B gyroscope are insensitive to coupling stiffness (≈85% reduction) when compared to Type-A gyroscope. At last, the reliability of the theory is verified by simulations and experiments.

硅微陀螺仪高精度数字化相敏解调ASIC

硅微陀螺仪高精度数字化相敏解调ASIC

Establishment and analysis of coupled dynamic model for dual-mass silicon micro-gyroscope

This paper presents a coupled dynamic model for a dual-mass silicon micro-gyroscope (DMSG). It can quantitatively analyze the influence of left-right stiffness difference on the natural frequencies, modal matrix and modal coupling coefficient of the DMSG. The analytic results are verified by using the finite element method (FEM) simulation. The model shows that with the left-right stiffness difference of 1%, the modal coupling coefficient is 12% in the driving direction and 31% in the sensing direction. It also shows that in order to achieve good separation, the stiffness of base beam should be small enough in both the driving and sensing direction.

A Lever Coupling Mechanism in Dual-Mass Micro-Gyroscopes for Improving the Shock Resistance along the Driving Direction.

This paper presents the design and application of a lever coupling mechanism to improve the shock resistance of a dual-mass silicon micro-gyroscope with drive mode coupled along the driving direction without sacrificing the mechanical sensitivity. Firstly, the mechanical sensitivity and the shock response of the micro-gyroscope are theoretically analyzed. In the mechanical design, a novel lever coupling mechanism is proposed to change the modal order and to improve the frequency separation. The micro-gyroscope with the lever coupling mechanism optimizes the drive mode order, increasing the in-phase mode frequency to be much larger than the anti-phase one. Shock analysis results show that the micro-gyroscope structure with the designed lever coupling mechanism can notably reduce the magnitudes of the shock response and cut down the stress produced in the shock process compared with the traditional elastic coupled one. Simulations reveal that the shock resistance along the drive direction is greatly increased. Consequently, the lever coupling mechanism can change the gyroscope’s modal order and improve the frequency separation by structurally offering a higher stiffness difference ratio. The shock resistance along the driving direction is tremendously enhanced without loss of the mechanical sensitivity.

Analysis and design of the system of a total digital Si-gyroscope

In order to get a thorough understanding of the total digital silicon micro-gyroscope, a novel system-level model with details of both the sense and circuit is presented in this paper. Unlike the traditional structures of the digital part of the digital gyroscope, a structure with programmable delay units (PDUs) instead of DPLLs gives a brief and robust character of the whole system. And the PDUs coordinating with the FIR filter could lead to a removal of the IF filters of the sigma–delta DAC for feedback, which saves a lot of consumption. Two MASH sigma–delta ADCs are designed to convert the output of the charge–voltage converters to digital signals, which also bring a better stability. The ADCs achieve an SNR of 102.5 dB with a 10 kHz bandwidth. The stabilization of the closed drive mode has also been analyzed including how the noise caused by the quantization of the digital circuit is affecting the stabilization of both the amplitude and frequency of the driving signals. In the end, a final result of simulation of the gyroscope shows the correctness and accuracy of the whole model of the gyroscope.

Research on the non-ideal dynamics of a dual-mass silicon micro-gyroscope

This study explores the non-ideal dynamics of a dual-mass silicon micro-gyroscope (DSMG). The operating principle and description of the DSMG are interpreted. Under the in-phase, anti-phase, and single-mass excitation conditions, the motion characteristics of the drive mode and sense mode are deduced. The non-ideal dynamics of the drive and sense modes with stiffness errors are analyzed. Then, the finite element simulation of the DSMG with a stiffness error is implemented to verify the non-ideal dynamics. Simulation results demonstrate that the left and right masses share the same natural frequencies in the in-phase or anti-phase drive modes even with the existence of stiffness errors. However, a significant amplitude difference between the left and right proof masses can be observed in the in-phase and anti-phase drive modes. The harmonic response analysis proves that the in-phase drive mode is activated even under anti-phase excitation conditions. Finally, sweep frequency experiments are performed on the fabricated DSMG to verify the correctness of the theoretical analysis. Experimental results indicate that the in-phase and anti-phase modes are excited simultaneously under both the anti-phase and in-phase excitation conditions because of the stiffness errors resulting from fabrication errors. This outcome is consistent with the theoretical analysis and simulation.

Adaptive Kalman filtering based on higher-order statistical analysis for digitalized silicon microgyroscope

In order to reduce the noise level of a silicon microgyroscope (SMG) digital system, a filter based on the theory of Kalman filter algorithm is designed. The performance of a Kalman filter depends on the proper model identification and parameter estimation. The method of higher-order statistical theoretical analysis is used to obtain the statistical properties of the gyroscope random signal. By modifying the conventional Kalman filter as adaptive Kalman filter, the filtering performance is enhanced. The filter is programmed in the Field Programmable Gate Array (FPGA) soft-core of the silicon microgyroscope digital system, based on SOPC (System-on-a-Programmable-Chip) technology. The effect of the filter is evaluated by Allan variance analysis. It is shown that noise characteristics such as quantization noise and angular random walk are obviously lowered compared with the original signal. In this way, by making use of ARMA (Auto Regression Moving Average) modeling results, a method of designing adaptive Kalman filter on digitalized SMG system is implemented.

Noise Analysis of Silicon Microgyroscope's Transimpedance Amplifier Interface Circuit

The output-current of silicon microgyroscope is at the level of 10-7A. So the requirements for circuits’ SNR are very high. This paper proposes a method to improve transimpedance amplifier interface circuit’s SNR. First of all, the operating principles of silicon microgyroscope and transimpedance amplifier interface circuit are introduced. Secondly, resistor thermal noise, amplifier’s current and voltage noise are analyzed. Then noise density in a certain frequency range is calculated based on Matlab. Besides, a method to improve SNR is proposed, namely, increasing the value of DC offset resistance. Finally, simulation based on Cadence is operated to verify the method. Simulation results fit well with the theoretical analysis. That means the method to improve the SNR is feasible.

Simulation and Experimental Verification of Silicon Microgyroscope's Closed-Loop Driving Circuits Based on Cadence

The output-current of silicon microgyroscope is at the level of 10-7A, so the requirements for circuits’ SNR are very high. This paper conducts the simulation of closed-loop driving circuits in Cadence on the basis of a RLC series resonant circuit. It turns out that experimental results fit the simulation which has a great significance for improving the property of circuits. First of all, the operating principle of silicon microgyroscope is introduced. Secondly, a RLC series resonant circuit is established by measuring Q value and driving frequency. Then the overall simulation is conducted in Cadence combined with chips’ models offered by the manufacturers. Finally, the accuracy of simulation is verified by experiments. Experimental results show that, the relative error of driving sense signal’s value is 0.5%, for stability time the value is 0.6% and for driving frequency the value is 38ppm. Experimental results agree well with the simulation, which confirms simulation’s accuracy. This has a great significance for improving the property of circuits.

Silicon microgyroscope temperature prediction and control system based on BP neural network and Fuzzy-PID control method

We present a novel silicon microgyroscope (SMG) temperature prediction and control system in a narrow space. As the temperature of SMG is closely related to its drive mode frequency and driving voltage, a temperature prediction model can be established based on the BP neural network. The simulation results demonstrate that the established temperature prediction model can estimate the temperature in the range of −40 to 60 °C with an error of less than ±0.05 °C. Then, a temperature control system based on the combination of fuzzy logic controller and the increment PID control method is proposed. The simulation results prove that the Fuzzy-PID controller has a smaller steady state error, less rise time and better robustness than the PID controller. This is validated by experimental results that show the Fuzzy-PID control method can achieve high precision in keeping the SMG temperature stable at 55 °C with an error of less than 0.2 °C. The scale factor can be stabilized at 8.7 mV/°/s with a temperature coefficient of 33 ppm °C−1. ZRO (zero rate output) instability is decreased from 1.10°/s (9.5 mV) to 0.08°/s (0.7 mV) when the temperature control system is implemented over an ambient temperature range of −40 to 60 °C.

Design and Application of Quadrature Compensation Patterns in Bulk Silicon Micro-Gyroscopes

This paper focuses on the detailed design issues of a peculiar quadrature reduction method named system stiffness matrix diagonalization, whose key technology is the design and application of quadrature compensation patterns. For bulk silicon micro-gyroscopes, a complete design and application case was presented. The compensation principle was described first. In the mechanical design, four types of basic structure units were presented to obtain the basic compensation function. A novel layout design was proposed to eliminate the additional disturbing static forces and torques. Parameter optimization was carried out to maximize the available compensation capability in a limited layout area. Two types of voltage loading methods were presented. Their influences on the sense mode dynamics were analyzed. The proposed design was applied on a dual-mass silicon micro-gyroscope developed in our laboratory. The theoretical compensation capability of a quadrature equivalent angular rate no more than 412 °/s was designed. In experiments, an actual quadrature equivalent angular rate of 357 °/s was compensated successfully. The actual compensation voltages were a little larger than the theoretical ones. The correctness of the design and the theoretical analyses was verified. They can be commonly used in planar linear vibratory silicon micro-gyroscopes for quadrature compensation purpose.

Analysis and Experimental Verification on Bias Drift of Silicon Microgyroscope

There is a bias drift of silicon microgyroscope when power on which limits its application in higher precision field. This paper analyzes and validates the main cause of bias drift, combined with theoretical analysis of demodulation and experimental results, which has a great significance for improving the performance of silicon microgyroscope. First of all, operating principle of silicon microgyroscope is introduced and theoretical analysis on bias drift is made on the basis of DC output voltage of microgyroscope. Secondly, demodulated signals’ amplitude and phase are analyzed in Matlab with the experimental data. By contrasting theoretical and experimental bias drift, the accuracy of theoretical formula is verified. It turns out that, the relative error of bias drift from 2-hours value to stable value is 5.5%, it’s 6.6% for 1-hour value to stable value and for beginning it’s just 1.7%. Experimental results agrees well with the theoretical analysis, which verifies that the main cause of bias drift of silicon microgyroscope is the phase difference between Vds and Vsense. This conclusion can provide some guidance for structure design optimization and circuits improving.

Vibration Analysis of Silicon Microgyroscope Based on Simulink

To improve the anti-vibration capability of silicon mcrogyroscope, making it works well under the vibration environment, this paper analyzes the dual-mass silicon mcrogyroscope and did the following works. First of all, the operating principle, analysis parameters of silicon microgyroscope and the vibration condition are introduced. Secondly, this paper proposes a vibration analysis method base on the signal conversion between time domain and frequency domain and establishes a Simulink demodulation model according to circuits of silicon microgyroscope. Finally, we get the conclusion that under the condition of vibration, composition with the same frequency of Vds in Vsense signal is the main influence factor of bias stability by analyzing experimental data. This has a great significance for improving the anti-vibration capability and guiding the interior structure design of silicon microgyroscope.

The on-chip temperature compensation and temperature control research for the silicon micro-gyroscope

In this paper, the on-chip temperature compensation and temperature control research for the silicon micro-gyroscope are presented. The proposed micro-gyroscope architecture which integrates an on-chip temperature sensor and a serpentine micro-heater achieves the on-chip temperature compensation and the on-chip temperature control of the micro-gyroscope. We first analyze the thermodynamic steady-state temperature distribution and transient temperature response of micro-gyroscope structure. Then we simulate the temperature response of the micro-gyroscope structure by Ansys software. The Deep Dry Silicon on Glass process and wet etching process are combined for fabrication of the integrated micro-gyroscope structure. The signal measurement and control circuit based on the FPGA platform are implemented. The temperature coefficients of zero bias and scale factor are compensated with the integrated temperature sensor. Taking advantage of the drive mode resonant frequency as the temperature sensor, a high precision on-chip temperature control of micro-gyroscope is realized simultaneously. The on-chip temperature compensation and temperature control experiment of micro-gyroscope prototype is tested. Experimental results indicate that the temperature coefficients of the scale factor and zero bias decrease by 3.95 times and 3.49 times separately by on-chip temperature compensation, which optimizes significantly the temperature characteristics of the micro-gyroscope prototype. The control accuracy of drive-mode frequency reaches to 3.57 × 10?4 Hz (that is 0.123 ppm and the calculated temperature accuracy of 0.0067 °C) from 0 to 40 °C by the on-chip temperature control, which demonstrates an achievement of the precision on-chip temperature control for the micro-gyroscope.

Analysis of Impact of Driving Amplitude on Resonance Frequency of Silicon Microgyroscope

Increasing the driving amplitude could improve the sensitivity of silicon microgyroscope, which is the effective way to enhance the performance of gyroscope. However the large driving amplitude leads to the nonlinear effect. As a result, the resonance frequency is dependent with the driving amplitude, which influences the frequency stability of gyroscope. The equivalent model of driving beam is established, and the stiffness formulas of driving beam are derivated according to the large deflection theory. The linear stiffness of driving beam is 270.1N/m and the nonlinear stiffness is 3.237×108N/m3, which are 2.7% and 6.4% different from the simulative results. Harmonic balance method can be used to establish the relationship between driving amplitude and resonance frequency. The theoretical analysis results are carried out compared with the simulative analysis results. Also the impact of driving amplitude on resonance frequency is confirmed by experiment test. This paper is significant for improving the frequency stability, and provides a theoretical basis for optimizing the structure of gyroscope.

Structural Design and Simulation of a Fully Decoupled Dual-Mass Micro-Gyroscope

This paper presents the operational principle, architecture design, resonance characteristics and FEM simulation of a new fully decoupled dual-mass silicon micro-gyroscope. The drive motion and sense motion of the micro-gyroscope studied in this paper are isolated from each other, mechanical quadrature error is thus dramatically suppressed due to the minimizing of undesired coupling between the drive and sense modes. Moreover,two identical single-mass gyroscopes are adopted and coupled with coupling beams to form a dual-mass micro-gyroscope, which provides enhanced common mode rejection in a differential mode. Finally, modal and harmonic analyses are implemented by FEM software, the simulation results obtained verify the good properties of the novel micro-gyroscope.

The Simulation Analysis of Temperature Effects on System Performance of Silicon Micro-Gyroscope

The effects of temperature variation on the system performance is discussed in this paper. The temperature characteristic of the natural frequency and quality factor is analyzed theoretically firstly. Then the simulation models of the open-loop drive system, the closed-loop drive system, the closed-loop sense system and the quadrature correction system are constructed to simulate the temperature characteristic of the scale factor and zero bias. The simulation results demonstrate the relative change of the scale factor in the closed-loop drive system, that is 1.35%, almost decreases by 67 times relative to the open-loop drive system and the variation of the zero bias in the closed-loop drive system, that is 0.2789°/s, almost decreases by 364 times relative to the open-loop drive system. At the same time, the relative change of the scale factor in the closed-loop sense system, that is 0.000029%, almost decreases by 46551 times relative to the closed-loop drive system. The variation of the zero bias in the closed-loop sense system, that is 1.2×10-11°/s, almost decreases by 2.3×1010 times relative to the closed-loop drive system, which shows the proposed method is feasible and correct.

硅微陀螺仪零偏稳定性的优化

硅微陀螺仪零偏稳定性的优化

Dynamic force balancing for the sense mode of a silicon microgyroscope

This paper presents a dynamic force balancing control for the sense mode of silicon microgyroscopes based on charge injection in opposite phase to balance the charge of the Coriolis force signal, nonideal coupling error and external angular disturbance, which embeds the sense mode in a closed loop system to give it a more robust performance. This control manner can widen the bandwidth and measurement range, improve the linearity and eliminate the quadrature coupling error. Theoretical calculation of the dynamic force balancing control is considered to analyze the effect of the closed loop control strategy. Experimental results using a practical silicon microgyroscope indicated a satisfactory performance of the proposed control algorithm. Comparing with the open loop, the microgyroscope achieved a scale factor of 11.7 mV (deg s−1)−1 with a nonlinearity of 0.2%, which is improved by 3.4 times, the bias stability is increased by 5.8 times and the temperature stability of the scale factor is ameliorated by 1.7 times.

硅微陀螺仪正交耦合系数的计算及验证

Silicon microgroscope is processed usually by microfabrication technology.It could lead to a quadrature coupling error and influence the output of the silicon microgyroscope for the lower relative accuracy from the fabrication processing.To optimize the structure of the silicon microgyroscope and enhance its performance,a theoretical model of quadrature coupling coefficients for the microgyroscope was established.Firstly,energy theorem was used to infer the in-plane stiffness of driving beam to set up the stiffness matrix of the microgyroscope.Then,the theoretical analysis model of quadrature coupling coefficients was established.According to a dual-mass vibrating silicon microgyroscope developed by our research group,the theoretical calculation shows that the direct coupling coefficient and the second-order coupling coefficient are 4.74×10-5 and 8.44×10-7,respectively,and the quadrature coupling coefficient of the developed microgyroscope is 4.75×10-5,8.7% different from the simulation value.Meanwhile,the analysis indicates that the maximum value of quadrature coupling coefficient is 2.18×10-4,7.9% different from the simulation value.Finally,the calculating result is confirmed by an experiment test.It concludes that the theoretical model of quadrature coupling coefficients can provide the theory foundation and application direction for improving the properties of silicon microgyroscopes.