惯性传感器电容误差仿真及影响分析

Simulation Analysis of Capacitance Error in Inertial Sensors

  • 摘要: 惯性传感器是空间引力波探测的重要载荷,在惯性传感器中,精密差分电容测量是十分重要的技术。当前,质量块处于中间位置时的差分电容通常依据理想平板电容公式进行计算,然而Brandt等指出,如此计算所得的电容理论值与实际电容值存在较大偏差,这一误差可能会对静电力大小产生影响,进而干扰惯性传感器对引力波的探测。目前,国内尚未有专项研究表明惯性传感器中电容理论值与实际值之间是否存在误差,以及该误差对静电力大小的具体影响。因此,围绕电容实际值与理论值的误差的大小与产生原因、该误差如何通过反馈电路传输、该误差怎样影响静电力这三个方面,借助Creo Parametric 2.0进行建模,并运用COMSOL Multiphysics 6.0开展多物理场仿真分析。首先,构建多种结构的惯性传感器模型,并对不同模型分别实施电容仿真分析,分别得到电容仿真值。通过对比电容仿真值,剖析误差产生的原因,并通过实验对仿真结果加以验证。在电容仿真值方面,与Brandt等得出了一致的结果,即电容仿真值比电容理论值约大10%。其次,首次深入分析了电容仿真值经反馈控制电路后对反馈电压的影响,发现这一误差会使反馈电压增大10%左右。最后,对Brandt等提出的静电力修正公式进行解释与验证。计算结果表明,静电力修正值与仿真得到的静电力值误差仅约为2%。相较于原有公式20%的误差,静电力修正式所计算出的静电力与静电力仿真值更为接近。由此可见,正确运用静电力修正式能够显著提高静电力的计算精度。

     

    Abstract: Inertial sensors are important payloads for detecting gravitational waves in space, and precise differential capacitance measurement is an important technology in inertial sensors. Currently, the differential capacitance of the mass block in the middle position is usually calculated based on the ideal plate capacitance formula. However, Nico Brandt et al. pointed out that there is a significant deviation between the theoretical and actual capacitance values obtained from this calculation, which may affect the magnitude of electrostatic forces and interfere with the detection of gravitational waves by inertial sensors. At present, there is no specialized research in China that indicates whether there is an error between the theoretical and actual values of capacitance in inertial sensors, and the specific impact of this error on the magnitude of electrostatic force. Therefore, this article focuses on three aspects: the magnitude and causes of the error between the actual and theoretical values of capacitors, how this error is transmitted through feedback circuits, and how it affects electrostatic forces. Creo Parametric 2.0 is used for modeling, and COMSOL Multiphysics 6.0 is used for multi physics field simulation analysis. Firstly, construct inertial sensor models with multiple structures and conduct capacitance simulation analysis on different models separately. By comparing the capacitance simulation values of different models, analyzing the causes of errors, and verifying the simulation results through experiments. In terms of capacitance simulation values, this article has obtained consistent results with Nico Brandt et al., that is, the capacitance simulation values are about 10% larger than the theoretical capacitance values. Secondly, this article provides the first in-depth analysis of the impact of capacitor simulation values on feedback voltage after feedback control circuit, and finds that this error can increase the feedback voltage by about 10%. Finally, validate the electrostatic force correction formula proposed by Nico Brandt et al. The calculation results indicate that the error between the electrostatic force correction value and the simulated electrostatic force value is only about 2%. Compared to the original formula with a 20% error, the electrostatic force calculated by the electrostatic force correction formula is closer to the simulated value of electrostatic force. It can be seen that the correct application of the electrostatic force correction formula can significantly improve the calculation accuracy of electrostatic force.

     

/

返回文章
返回