硅微陀螺的温度特性研究
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摘要
硅微陀螺是组成惯性导航系统的关键器件之一。由于硅材料是一种热敏材料,温度变化导致的各种误差对硅微陀螺的各项性能指标影响很大。当环境温度变化时,硅微陀螺的谐振频率和品质因数会发生改变,会对陀螺的标度因数和零偏造成一定的影响,从而影响到陀螺的输出精度和性能。因此,很有必要研究陀螺的温度特性,建立合适的温度模型,对温度误差进行补偿。本文的主要研究内容和工作如下:
1.分析了硅微陀螺的各种误差来源,推导了硅微陀螺的运动方程,得到了影响硅微陀螺振动位移和结构灵敏度的主要因素。温度的变化会使谐振频率发生偏移、品质因数发生改变,会对原有的各种误差进一步放大,从而影响硅微陀螺的输出精度。
2.通过理论分析推导和试验验证,从理论和试验两个方面研究了温度对谐振频率、品质因数、真空度、输出增益以及标度因数的影响。建立了谐振频率、品质因数、输出增益以及标度因数的温度模型。
3.分析了硅微陀螺的零偏产生机理。由于静电力不平衡误差和各种加工误差,会导致微陀螺发生模态耦合,从而产生正交误差。正交误差对硅微陀螺输出影响很大,必须采取措施加以消除。由于电路误差的存在,不可能完全消除正交误差的影响,使其成为了硅微陀螺零偏的主要来源。
4.建立了硅微陀螺在不同温度变化条件下的零偏误差补偿模型。通过温度试验,分别建立了全温区、自然温升和小温变范围的温度误差补偿模型,并进行了仿真补偿验证。基于LabWindows/CVI编程语言开发了硅微陀螺温度补偿测控软件,并通过硬件实现了零偏的实时估计和补偿,最后对常温启动和全温区零偏进行了温度补偿验证。采用温度补偿可以有效改善硅微陀螺零偏的温度灵敏度,提高陀螺的零偏稳定性。
5.建立了硅微陀螺随机漂移误差的时间序列分析模型。在利用多分辨率分析提取随机漂移趋势项的基础上,建立了随机漂移的时间序列分析模型,并重点分析了ARMA模型参数估计问题,最后结合卡尔曼滤波方程,实现了漂移模型的具体应用,有效提高了硅微陀螺的使用精度。
Silicon micromachined gyroscopes are the most key components of inertial navigation systems. The temperature error will bring great influence on various performance index on account of the sensitivity of silicon material. The resonant frequency will generate excursion and mechanical quality factor will change due to temperatue variation which cause the variation of the scale factor and zero bias, so the output precision and performance reduce obviously.Consequently, it is necessary to carry out research on the temperature characteristics of gyroscopes, set up appropriate temperature model, and take compensation methods to temperature error.The main content and work of this thesis are given as follows:
1. Analyse the source of temperature error and ratiocinate the motion equations. It indicates that resont frequency and quality factor are the main factors which influence the motion displacement and sructure sensitivity. The resonant frequency will generate excursion and quality factor will change with temperatue variation, which will magnify the original error, and it will bring great influence on the output precision.
2. Research on the effect of temperature on quality factor, vacuum degree, output gain and scale factor theoretically and experimentally.Set up the temperature model among temperature to resonant frequency, quality factor, vacuum degree, output gain and scale factor.
3. Analyse the mechanism of zero bias. Drive mode will have coupled with sense mode of the gyroscope on account of different structure fabrication errors, which also caused electrostatic force not balanced. Gyroscope will generate zero bias without out angular velocity. Mode coupling can caused quadrature error, which has great influence on gyroscope output.The method of phase demodulation can eliminate quadrature error.The quadrature error is one of the main source of zero bias.
4. Set up the zero bias error compensation model of gyroscope at different temperature change condition respectively. The temperature error compensation model is set up at the range of whole temperature, nature temperature rise and small temperature variation experimentally, and take emulate compensation certification. Develop temperature compensation measurement and control software based on LabWindows/CVI program language, and realize the zero bias estimation and compensation timely by circuit hardware.At last, take compensation certification at normal temperature startup condition and whole temperature range. The temperature coefficient and zero bias stability is improved obviously after temperature compensation.
5. Set up the Autoregressive Moving-Average model. According to multi-resolution analysis theory, the arithmetic of gyroscope random drift trend is put forward which is applied to time-series analysis. Give emphasis to analyse the parameter estimation of ARMA model.Lastly, construct the kalman filter equation, and its application precision in practical system will be further improved.
1.分析了硅微陀螺的各种误差来源,推导了硅微陀螺的运动方程,得到了影响硅微陀螺振动位移和结构灵敏度的主要因素。温度的变化会使谐振频率发生偏移、品质因数发生改变,会对原有的各种误差进一步放大,从而影响硅微陀螺的输出精度。
2.通过理论分析推导和试验验证,从理论和试验两个方面研究了温度对谐振频率、品质因数、真空度、输出增益以及标度因数的影响。建立了谐振频率、品质因数、输出增益以及标度因数的温度模型。
3.分析了硅微陀螺的零偏产生机理。由于静电力不平衡误差和各种加工误差,会导致微陀螺发生模态耦合,从而产生正交误差。正交误差对硅微陀螺输出影响很大,必须采取措施加以消除。由于电路误差的存在,不可能完全消除正交误差的影响,使其成为了硅微陀螺零偏的主要来源。
4.建立了硅微陀螺在不同温度变化条件下的零偏误差补偿模型。通过温度试验,分别建立了全温区、自然温升和小温变范围的温度误差补偿模型,并进行了仿真补偿验证。基于LabWindows/CVI编程语言开发了硅微陀螺温度补偿测控软件,并通过硬件实现了零偏的实时估计和补偿,最后对常温启动和全温区零偏进行了温度补偿验证。采用温度补偿可以有效改善硅微陀螺零偏的温度灵敏度,提高陀螺的零偏稳定性。
5.建立了硅微陀螺随机漂移误差的时间序列分析模型。在利用多分辨率分析提取随机漂移趋势项的基础上,建立了随机漂移的时间序列分析模型,并重点分析了ARMA模型参数估计问题,最后结合卡尔曼滤波方程,实现了漂移模型的具体应用,有效提高了硅微陀螺的使用精度。
Silicon micromachined gyroscopes are the most key components of inertial navigation systems. The temperature error will bring great influence on various performance index on account of the sensitivity of silicon material. The resonant frequency will generate excursion and mechanical quality factor will change due to temperatue variation which cause the variation of the scale factor and zero bias, so the output precision and performance reduce obviously.Consequently, it is necessary to carry out research on the temperature characteristics of gyroscopes, set up appropriate temperature model, and take compensation methods to temperature error.The main content and work of this thesis are given as follows:
1. Analyse the source of temperature error and ratiocinate the motion equations. It indicates that resont frequency and quality factor are the main factors which influence the motion displacement and sructure sensitivity. The resonant frequency will generate excursion and quality factor will change with temperatue variation, which will magnify the original error, and it will bring great influence on the output precision.
2. Research on the effect of temperature on quality factor, vacuum degree, output gain and scale factor theoretically and experimentally.Set up the temperature model among temperature to resonant frequency, quality factor, vacuum degree, output gain and scale factor.
3. Analyse the mechanism of zero bias. Drive mode will have coupled with sense mode of the gyroscope on account of different structure fabrication errors, which also caused electrostatic force not balanced. Gyroscope will generate zero bias without out angular velocity. Mode coupling can caused quadrature error, which has great influence on gyroscope output.The method of phase demodulation can eliminate quadrature error.The quadrature error is one of the main source of zero bias.
4. Set up the zero bias error compensation model of gyroscope at different temperature change condition respectively. The temperature error compensation model is set up at the range of whole temperature, nature temperature rise and small temperature variation experimentally, and take emulate compensation certification. Develop temperature compensation measurement and control software based on LabWindows/CVI program language, and realize the zero bias estimation and compensation timely by circuit hardware.At last, take compensation certification at normal temperature startup condition and whole temperature range. The temperature coefficient and zero bias stability is improved obviously after temperature compensation.
5. Set up the Autoregressive Moving-Average model. According to multi-resolution analysis theory, the arithmetic of gyroscope random drift trend is put forward which is applied to time-series analysis. Give emphasis to analyse the parameter estimation of ARMA model.Lastly, construct the kalman filter equation, and its application precision in practical system will be further improved.
引文
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[2]文炜.基于MEMS技术的惯性测量器件及系统的发展现状和应用[J].飞航导弹,2006(9):56-59
[3] P. Greiff, B. Boxenhorn, T. King, L. Niles. Silicon monolithic micromechanical gyroscope [C]. Proceedings of International Conference on Solid-State Sensors and Actuators, 1991: 966-968
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[5] A. Kourepenis, J. Borenstein, J. Connelly, R. Elliott. Performance of MEMS Inertial Sensors [C]. Proceedings of IEEE Position Location and Navigation Symposium, 1998: 1-8
[6] C. Acar and A. Shkel. Inherently Robust Micromachined Gyroscopes with 2-DOF Sense-Mode Oscillator [J]. Journal of Microelectromechanical Systems, 2006, 15 (2): 380-387
[7] Michael I.Ferguson, Didier Keymeulen, et al. Effect of Temperature on MEMS Vibratory Rate Gyroscope. Proceedings of theIEEE Aerospace Conference, Big Sky, Montana, March 2005:1-5.
[8] Tony K. Tang, Roman C. Gutierrez, Christopher B. Stell,et al. A Packaged Silicon MEMS Vibratory Gyroscope for Microspacecraft [J]. IEEE.1996:500-505
[9] Farrokh Ayazi.A HARPSS polysilicon vibrating gyroscopeprocess. Journal of Microelectromechanicsl Systems,2001,10(2):169-179
[10]李新刚,袁建平.微机械陀螺的发展现状[J].力学进展,2003,33(3):289-302.
[11] Kirill Shcheglov, Christopher Evans, Roman Gutierrez, et al. Temperature dependent Characteristics of the JPL Silicon MEMS Gyroscope[J].IEEE,2000: 403-411
[12] M A.Hopcroft, M.Agarval, et al.Temperature Compensation of a MEMS Resonator using Quality Factor as a thermometer[C].MEMS2006, Istanbul, Turkey, 22-26 January 2006:222-226
[13] Renata Melamud, Bongsang Kim,et al. Composite Flexural-mode resonator with controllable turnover temperature[C], MEMS 2007, Kobe, Japan, 21-25 January 2007:199-202
[14] Wan-Thai Hsu, John R.Clark,et al. Mechanically Temperature-Compensated Flexural-Mode Micromechanical[C].IEDM 2000,2000,399-402
[15] Wan-Thai Hsu, Clark T.-C.Nguyen. Stiffness-compensated temperature-insensitive micromechanical resonators[J].IEEE, 2002:731-735
[16]赵小宁,李县洛,雷宝权.激光微陀螺零偏温度补偿研究[J].中国惯性技术学报, 2004,12(3):55-57
[17]张鹏飞,龙兴武.二频机抖激光微陀螺小范围温度漂移补偿模型的研究[J].激光杂志, 2006, 27(2):44-45
[18]葛文涛,陈明刚,张伟.激光捷联惯性导航系统温度误差建模及补偿[J].中国惯性技术学报, 2007,15(3):290-293
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