静电刚度谐振式微加速度计相关技术研究
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摘要
谐振式微加速度计是基于MEMS制作技术的、具有稳定性好和准数字的频率信号输出等优点的新型微加速度计。论文系统地研究了静电刚度谐振式微加速度计原理、制作、信号处理、测试方法等相关理论和技术,并对制作的样机进行了测试。
论文的主要研究工作可概括如下:
介绍了微机械加速度计的需求概况,总结对比了各种类型微加速度计的特点,分析了微机械谐振式加速度计国内外研制现状,归纳了研制中存在的问题。提出了静电刚度谐振式微加速度计的研究思路、内容和方法。
介绍了平板电容存在静电负刚度的原理,并分析了如何将静电负刚度应用于谐振式微加速度计的设计中,根据静电刚度谐振式微加速度计的动力学原理,确定了结构参数和加载电压对灵敏度的影响,得到了量程、灵敏度和结构稳定性相互制约的关系。分析了频率差分双端固支音叉梁的动力学原理,提出通过减小音叉梁固定连接端刚度的方法来抑制面内低阶模态的干扰,并进行了有限元仿真验证,为合理设计音叉梁结构提供了依据。分析了静电驱动力对加速度计分辨率和输出频率稳定度的影响,确定了闭环驱动控制的要求。
介绍了键合后深刻蚀体硅工艺过程,对设计的静电刚度谐振式微加速度计表芯进行了流片。对制造的微结构进行了几何尺寸的光学静态测量,确定了微结构谐振频率的范围。利用激光频闪干涉测量技术和计算机视觉技术相结合方法,对挑选好的裸片进行了开环特性动态测试,发现了同频干扰现象。针对微机械谐振式电容传感器中普遍存在的同频干扰问题,分析了干扰来源,提出从微结构版图布局及结构差分设计、频率调制解调等几个方面的干扰抑制方法,为了验证方法的有效性和普适性,针对相同工艺制造的具有相同测控要求的微机械谐振陀螺进行了实验研究,成功利用高频方波调制、模拟开关解调方法实现了微机械陀螺开环特性的测量,真空圆形储能焊封装下驱动模态对应的谐振频率为13.552kHz,品质因数Q约为1800。
根据静电驱动的微机械谐振传感器闭环恒幅驱动的共性要求,确定了振动幅度的自动增益控制方案,鉴于真空封装下微机械谐振传感器系统的高阶弱非线性,提出采用近似平均法求解系统的平衡点及线性化后分析系统的稳定条件。建立了多种条件下以静电刚度谐振式微加速度计为例的微机械谐振传感器的闭环线性反馈的自激驱动分析模型,理论分析和实验测试表明,只有直流参考电压大于起振临界条件,系统才能从不稳定平衡点过渡到稳定平衡点;系统相位偏离相位平衡条件将导致驱动力频率发生变化,太大的偏差系统将不能起振;调节滤波器的时间常数可以改变动态起振时间;当谐振频率和品质因数变化时,自动增益控制环在没有PI控制器下无法实现恒幅驱动。在PI控制器作用下,稳态振幅只与直流参考电压大小有关,但PI控制器的参数需要满足约束条件,不同的参数对应不同的动态性能,稳态值不受影响。鉴于加速度计表芯制造进度的滞后,前期采用微机械谐振陀螺对上述理论分析结论进行了实验验证,利用自激原理成功实现了陀螺的稳定起振,10分钟内频率最大偏离稳态值为0.04Hz,输出信噪比达到80dB,实验结果与理论分析结论相吻合。
在微机械谐振传感器的结构封装品质因数较小时,分析了在幅度开环控制下,单一的锁相环控制下的系统行为,理论分析和仿真表明,要实现稳定的闭环频率跟踪,积分控制器需要满足约束条件;在谐振频率变化条件下,不能实现恒幅驱动。在加入幅度自动增益控制环后,幅度控制环和频率跟踪环相互耦合;有PI控制器可以实现恒幅驱动和稳定的频率跟踪,但PI控制器参数的选择需要满足稳定条件,参数还影响系统的动态性能。
对制造的静电刚度谐振式微加速度计利用前述频率调制解调方法进行了开环测试,测得在直流驱动电压为15V,交流电压峰-峰值5V条件下,检测端固定电容大约为0.4pF,测试结果与有限元分析相一致,变化电容大约为3.1fF。谐振频率约为35.746kHz,品质因数约为1400,再次验证了该干扰抑制方法的有效性。利用前述自激驱动方法成功实现了静电刚度谐振式微加速度计的稳定谐振,在闭环翻转测试中,在检测端加载1V直流电压时,灵敏度为18Hz/g;加载5V直流电压时,灵敏度为58Hz/g,闭环谐振频率10分钟内最大偏差0.2Hz,分辨率约为3.5mg。
最后,总结了研究内容和得出的一些有益结论,提出了进一步研究的设想。
The resonant-type accelerometer has the highest resolution and accuracy during all kinds of accelerometers, but the system is also very complex. It has many advantages: wide dynamic range, the quasi-digital output signal, and the inherent continuous self-test capability. In this thesis, the theory and technology about a novel resonant accelerometers designing, fabricating, signal processing and closed-loop control were researched systematically; and based on these, the principial resonant accelerometer system were made and tested.
The main contents of this thesis include the following issues:
The general study situation of the micro resonant accelerometers was reviewed, and the difficult for fabrication good performance this type sensor system were also concluded. Researching methods and contents of resonant accelerometers based on electrostatic stiffness were presented.
Principle of the electrostatic negative stiffness effective for parallel plate capacitance was introduced, how to use this effective to design a novel type resonant accelerometer was also discussed, dynamic principle of resonant accelerometer based on electrostatic stiffness was analyzed, concluded the relationship among the sensivitity, sensing voltage and structure parameters. The measurement range, sensivitity, structure stability are coupled. Dynamic for double ended tuning fork was analyzed, the method to decrease the disturbance of lower mode vibration was presented and verified by FEM. Influence of vibration amplitude for frequency stability and resolution was introduced and constructed the requirement of closed-loop control circuit.
After introduction the bulk-silicon fabrication technology, the design resonant accelerometer was fabricated. Structure parameter was tested by optical microscope and resonance frequency was computed again. Same frequency disturbance was found during the open loop measurement, disturbed source was analyzed and some method was adopted to eliminate the disturbance. For a vacuum packaged MEMS gyrocope, high frequency square wave was used to achieve the frequency modulation and an analog switch for un-modulation. Resonance frequency is 13.552kHz and Q factor is about 1800 tested by these method.
According to closed-loop control requirement for resonant sensors, auto gain control (AGC) strategy was introduced. Due to little nolinearity of the whole closed-loop system, averaging method was used to analyze behavior of the system. Some self-oscillation analytical models with different parameters was constructed and analyzed. Theory and experiment show that the reference DC voltage must large enough to satisfy the critical condition, phase balance error will cause the frequency of driving voltage is different from resonance frequency, the micro-sensors can not vibrating when phase error is too large. The time to achieve stable vibrating amplitude is concern to the parameters of low pass filter. When Q factor and resonance frequency is variable, AGC method can not achieve constant vibrating amplitude without PI controller. The vibrating amplitude is only related to reference voltage when there is a PI controller in AGC loop. But parameters of PI controller are important for transition performance and they should satisfy the restriction. The maximal measurement error for closed-loop resonance frequency during 10 minutes is 0.04Hz and SNR is about 80dB for forenamed gyroscope driving by self-oscillation method.
When Q factor is smaller, the behavior of resonant accelerometer drived by a single PLL was analyzed. Theory and simulation result show that the integral control gain is critical to closed-loop resonance frequency. This control method can not achieve constant vibration amplitude as resonance frequency is variable. Vibration amplitude and resonace frequency are coupled for the whole system. When there is a PI contoller in auto gain control loop, the stable vibrational amplitude is only influenced by reference DC voltage, but the controller parameters should satisfy system stable condition, it is important to transient performance.
Based on introducation the micro fabricating technology and signal processing method, the whole resonant accelerometer system was fabricated and tested, static capacitance in detecting end is about 0.4pF, the corresponding variational capacitance is about 3.1fF with DC driving voltage is 15V, AC voltage is 5V. Measurement result is nearly the same as FEM. Resonance frequency is about 35.746kHz, Q factor is about 1400. When sensing voltage is 1V, sensitivity is 18Hz/g, sensing voltage is 5V, sensitivity is 58Hz/g, the maximal error for closed-loop resonance frequency during 10 minutes is 0.2Hz and the resolution is about 3.5mg.
Finally, the major content and contribution of the work were summarized, and the future researches were also brought out.
论文的主要研究工作可概括如下:
介绍了微机械加速度计的需求概况,总结对比了各种类型微加速度计的特点,分析了微机械谐振式加速度计国内外研制现状,归纳了研制中存在的问题。提出了静电刚度谐振式微加速度计的研究思路、内容和方法。
介绍了平板电容存在静电负刚度的原理,并分析了如何将静电负刚度应用于谐振式微加速度计的设计中,根据静电刚度谐振式微加速度计的动力学原理,确定了结构参数和加载电压对灵敏度的影响,得到了量程、灵敏度和结构稳定性相互制约的关系。分析了频率差分双端固支音叉梁的动力学原理,提出通过减小音叉梁固定连接端刚度的方法来抑制面内低阶模态的干扰,并进行了有限元仿真验证,为合理设计音叉梁结构提供了依据。分析了静电驱动力对加速度计分辨率和输出频率稳定度的影响,确定了闭环驱动控制的要求。
介绍了键合后深刻蚀体硅工艺过程,对设计的静电刚度谐振式微加速度计表芯进行了流片。对制造的微结构进行了几何尺寸的光学静态测量,确定了微结构谐振频率的范围。利用激光频闪干涉测量技术和计算机视觉技术相结合方法,对挑选好的裸片进行了开环特性动态测试,发现了同频干扰现象。针对微机械谐振式电容传感器中普遍存在的同频干扰问题,分析了干扰来源,提出从微结构版图布局及结构差分设计、频率调制解调等几个方面的干扰抑制方法,为了验证方法的有效性和普适性,针对相同工艺制造的具有相同测控要求的微机械谐振陀螺进行了实验研究,成功利用高频方波调制、模拟开关解调方法实现了微机械陀螺开环特性的测量,真空圆形储能焊封装下驱动模态对应的谐振频率为13.552kHz,品质因数Q约为1800。
根据静电驱动的微机械谐振传感器闭环恒幅驱动的共性要求,确定了振动幅度的自动增益控制方案,鉴于真空封装下微机械谐振传感器系统的高阶弱非线性,提出采用近似平均法求解系统的平衡点及线性化后分析系统的稳定条件。建立了多种条件下以静电刚度谐振式微加速度计为例的微机械谐振传感器的闭环线性反馈的自激驱动分析模型,理论分析和实验测试表明,只有直流参考电压大于起振临界条件,系统才能从不稳定平衡点过渡到稳定平衡点;系统相位偏离相位平衡条件将导致驱动力频率发生变化,太大的偏差系统将不能起振;调节滤波器的时间常数可以改变动态起振时间;当谐振频率和品质因数变化时,自动增益控制环在没有PI控制器下无法实现恒幅驱动。在PI控制器作用下,稳态振幅只与直流参考电压大小有关,但PI控制器的参数需要满足约束条件,不同的参数对应不同的动态性能,稳态值不受影响。鉴于加速度计表芯制造进度的滞后,前期采用微机械谐振陀螺对上述理论分析结论进行了实验验证,利用自激原理成功实现了陀螺的稳定起振,10分钟内频率最大偏离稳态值为0.04Hz,输出信噪比达到80dB,实验结果与理论分析结论相吻合。
在微机械谐振传感器的结构封装品质因数较小时,分析了在幅度开环控制下,单一的锁相环控制下的系统行为,理论分析和仿真表明,要实现稳定的闭环频率跟踪,积分控制器需要满足约束条件;在谐振频率变化条件下,不能实现恒幅驱动。在加入幅度自动增益控制环后,幅度控制环和频率跟踪环相互耦合;有PI控制器可以实现恒幅驱动和稳定的频率跟踪,但PI控制器参数的选择需要满足稳定条件,参数还影响系统的动态性能。
对制造的静电刚度谐振式微加速度计利用前述频率调制解调方法进行了开环测试,测得在直流驱动电压为15V,交流电压峰-峰值5V条件下,检测端固定电容大约为0.4pF,测试结果与有限元分析相一致,变化电容大约为3.1fF。谐振频率约为35.746kHz,品质因数约为1400,再次验证了该干扰抑制方法的有效性。利用前述自激驱动方法成功实现了静电刚度谐振式微加速度计的稳定谐振,在闭环翻转测试中,在检测端加载1V直流电压时,灵敏度为18Hz/g;加载5V直流电压时,灵敏度为58Hz/g,闭环谐振频率10分钟内最大偏差0.2Hz,分辨率约为3.5mg。
最后,总结了研究内容和得出的一些有益结论,提出了进一步研究的设想。
The resonant-type accelerometer has the highest resolution and accuracy during all kinds of accelerometers, but the system is also very complex. It has many advantages: wide dynamic range, the quasi-digital output signal, and the inherent continuous self-test capability. In this thesis, the theory and technology about a novel resonant accelerometers designing, fabricating, signal processing and closed-loop control were researched systematically; and based on these, the principial resonant accelerometer system were made and tested.
The main contents of this thesis include the following issues:
The general study situation of the micro resonant accelerometers was reviewed, and the difficult for fabrication good performance this type sensor system were also concluded. Researching methods and contents of resonant accelerometers based on electrostatic stiffness were presented.
Principle of the electrostatic negative stiffness effective for parallel plate capacitance was introduced, how to use this effective to design a novel type resonant accelerometer was also discussed, dynamic principle of resonant accelerometer based on electrostatic stiffness was analyzed, concluded the relationship among the sensivitity, sensing voltage and structure parameters. The measurement range, sensivitity, structure stability are coupled. Dynamic for double ended tuning fork was analyzed, the method to decrease the disturbance of lower mode vibration was presented and verified by FEM. Influence of vibration amplitude for frequency stability and resolution was introduced and constructed the requirement of closed-loop control circuit.
After introduction the bulk-silicon fabrication technology, the design resonant accelerometer was fabricated. Structure parameter was tested by optical microscope and resonance frequency was computed again. Same frequency disturbance was found during the open loop measurement, disturbed source was analyzed and some method was adopted to eliminate the disturbance. For a vacuum packaged MEMS gyrocope, high frequency square wave was used to achieve the frequency modulation and an analog switch for un-modulation. Resonance frequency is 13.552kHz and Q factor is about 1800 tested by these method.
According to closed-loop control requirement for resonant sensors, auto gain control (AGC) strategy was introduced. Due to little nolinearity of the whole closed-loop system, averaging method was used to analyze behavior of the system. Some self-oscillation analytical models with different parameters was constructed and analyzed. Theory and experiment show that the reference DC voltage must large enough to satisfy the critical condition, phase balance error will cause the frequency of driving voltage is different from resonance frequency, the micro-sensors can not vibrating when phase error is too large. The time to achieve stable vibrating amplitude is concern to the parameters of low pass filter. When Q factor and resonance frequency is variable, AGC method can not achieve constant vibrating amplitude without PI controller. The vibrating amplitude is only related to reference voltage when there is a PI controller in AGC loop. But parameters of PI controller are important for transition performance and they should satisfy the restriction. The maximal measurement error for closed-loop resonance frequency during 10 minutes is 0.04Hz and SNR is about 80dB for forenamed gyroscope driving by self-oscillation method.
When Q factor is smaller, the behavior of resonant accelerometer drived by a single PLL was analyzed. Theory and simulation result show that the integral control gain is critical to closed-loop resonance frequency. This control method can not achieve constant vibration amplitude as resonance frequency is variable. Vibration amplitude and resonace frequency are coupled for the whole system. When there is a PI contoller in auto gain control loop, the stable vibrational amplitude is only influenced by reference DC voltage, but the controller parameters should satisfy system stable condition, it is important to transient performance.
Based on introducation the micro fabricating technology and signal processing method, the whole resonant accelerometer system was fabricated and tested, static capacitance in detecting end is about 0.4pF, the corresponding variational capacitance is about 3.1fF with DC driving voltage is 15V, AC voltage is 5V. Measurement result is nearly the same as FEM. Resonance frequency is about 35.746kHz, Q factor is about 1400. When sensing voltage is 1V, sensitivity is 18Hz/g, sensing voltage is 5V, sensitivity is 58Hz/g, the maximal error for closed-loop resonance frequency during 10 minutes is 0.2Hz and the resolution is about 3.5mg.
Finally, the major content and contribution of the work were summarized, and the future researches were also brought out.
引文
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