A method and system for evaluating charge measurement errors based on finite element simulation

Abstract

This invention provides a method and system for evaluating charge measurement error based on finite element simulation, belonging to the field of precision measurement. The method includes: establishing a geometric model for charge measurement based on the sensitive probe of a Tianqin inertial sensor in finite element simulation software; applying a vacuum domain and an infinite element domain outside the sensitive probe of the Tianqin inertial sensor; selecting a physical field interface; and setting materials and meshes; outputting electrostatic force on the test mass through simulation by setting different boundary conditions and combining the Maxwell stress tensor principle; performing post-processing on the output electrostatic force to convert it into a charge measurement value; and evaluating the charge measurement error based on the actual charge value and the charge measurement value using two indicators: average relative error and relative standard deviation, thereby quantifying the impact of different factors on the charge measurement error. This invention can quantitatively evaluate the impact of different factors on the charge measurement error by simulating the residual charge on the test mass.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement, and more specifically, relates to a method and system for evaluating charge measurement errors based on finite element simulation. Background Technology

[0002] In precision measurement, sensitive elements are typically insulated to isolate them from external interference such as electrical and thermal noise. For example, in the European Space Agency's LISA space gravitational wave detection program, the sensitive probe of the inertial sensor is a typical isolated conductor. However, because an isolated conductor has no electrical connection to surrounding objects, free charges in space will adhere to it, leading to charge accumulation. Although the amount of accumulated charge is small, the electrostatic force generated by the accumulated charge can interfere with the instrument's measurement results, thus requiring charge management on the isolated conductor.

[0003] To meet the requirement that the total noise of the inertial sensor in the millihertz frequency band is better than 10, in gravitational wave detection... -15 m / s 2 / Hz 1 / 2 In terms of magnitude, the current mainstream charge management scheme first measures the charge value on the inspection mass using electrostatic modulation, and then uses ultraviolet light to generate photocurrent to control the charge on the inspection mass below the required value. Therefore, high-precision charge measurement is the foundation of charge management. The mainstream inspection mass charge measurement methods are all based on electrostatic modulation. The measurement accuracy of this method depends on the electrostatic model, which is based on the ideal interaction between the inspection mass charge and the plate voltage, without considering the influence of actual interference factors on the electrostatic force. However, the actual electrostatic force is affected by factors such as the complex structure of the inertial sensor, the distribution of the inspection mass charge, the plate voltage, and the position of the inspection mass, leading to charge measurement errors. Currently, research on measurement errors is lacking, and theoretical research suffers from problems such as simple models and unclear parameters; ground experiments have limited degrees of freedom; and on-orbit experiments are costly. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a method and system for evaluating charge measurement error based on finite element simulation, which aims to fill the gap in existing research on charge measurement error and address the problem that theoretical research suffers from simple models and unclear parameters.

[0005] To achieve the above objectives, the present invention provides a method for evaluating charge measurement errors based on finite element simulation, comprising the following steps:

[0006] Step 1: In the finite element simulation software, establish a geometric structure model for charge measurement based on the sensitive probe of the Tianqin inertial sensor. Apply a vacuum domain and an infinite element domain outside the sensitive probe of the Tianqin inertial sensor, select the physical field interface, and set the material and mesh. In the geometric structure model, set the potential on the isolated conductor, and calculate the residual charge value on the isolated conductor as the actual charge value based on the relationship between the residual charge and the potential of the isolated conductor.

[0007] Step 2: By setting different boundary conditions and combining the Maxwell stress tensor principle, the electrostatic force on the mass is verified through simulation output;

[0008] Step 3: Perform post-processing on the output electrostatic force to convert the electrostatic force into a charge measurement value;

[0009] Step 4: Based on the actual charge value and the charge measurement value, evaluate the charge measurement error using two indicators: average relative error and relative standard deviation, and then quantify the impact of different factors on the charge measurement error.

[0010] More preferably, the electrostatic force is:

[0011]

[0012] in, for The unit vector in the direction of the outward normal to the surface. For Maxwell's stress tensor; It is a unit surface element.

[0013] More preferably, step four specifically includes the following steps:

[0014] The electrostatic force is multiplied by a sinusoidal voltage with the same frequency and phase as the modulation voltage for orthogonal demodulation; where, in the geometric model, the voltage of the four plates on the x-axis is the modulation voltage that causes the isolated conductor to translate.

[0015] After orthogonal demodulation, a moving average filter is performed to obtain the electrostatic force amplitude at the modulation frequency;

[0016] The charge measurement value is calculated by multiplying the electrostatic force amplitude at the modulation frequency by the gain coefficient.

[0017] More preferably, the gain coefficient is:

[0018]

[0019] The charge measurement value is:

[0020] Q TM,est =H q *F 1ω

[0021] Among them, Hq α is the gain coefficient; α is the geometry factor, which represents the ratio between the actual capacitance gradient caused by geometric edge effects and the theoretical capacitance gradient based on a parallel-plate capacitor; C tot V represents the total capacitance of the sensitive probe of the Tianqin inertial sensor. MOD For the modulation voltage amplitude; C x To test the capacitance of the plates in the x-direction when the mass is at its center position; x represents the offset of the mass in the x-direction; F 1ω Let ω be the amplitude of the electrostatic force at the modulation frequency ω.

[0022] More preferably, the relative standard deviation represents the fluctuation of the charge measurement value, and its specific expression is as follows:

[0023]

[0024] Where σ is the variance of the charge measurement; Q TM The average value of the charge measurements;

[0025] The average relative error is:

[0026]

[0027] Where n is the amount of data for the charge measurement; Q TM,est This is a charge measurement; Q TM This represents the actual charge value.

[0028] On the other hand, the present invention provides a system for evaluating charge measurement errors based on finite element simulation, comprising:

[0029] The geometric structure model construction module is used to establish a geometric structure model for charge measurement based on the sensitive probe of the Tianqin inertial sensor in finite element simulation software. It applies a vacuum domain and an infinite element domain outside the sensitive probe of the Tianqin inertial sensor, selects the physical field interface, and sets the material and mesh. Among them, the potential on the isolated conductor is set in the geometric structure model, and the residual charge value on the isolated conductor is calculated as the actual charge value.

[0030] The electrostatic force simulation module is used to build modules based on geometric structure models. By setting different boundary conditions and combining the Maxwell stress tensor principle, it can verify the electrostatic force on the mass through simulation output.

[0031] The charge measurement module is used to perform post-processing on the output electrostatic force, converting the electrostatic force into charge measurement values.

[0032] The electrical measurement error assessment module is used to evaluate the charge measurement error based on the actual charge value and the charge measurement value, using two indicators: average relative error and relative standard deviation. This allows for a quantitative assessment of the impact of different factors on the charge measurement error.

[0033] More preferably, the electrostatic force is:

[0034]

[0035] in, for The unit vector in the direction of the outward normal to the surface. For Maxwell's stress tensor; It is a unit surface element.

[0036] More preferably, the charge measurement acquisition module includes an orthogonal demodulation unit, an electrostatic force amplitude calculation unit, and a charge measurement calculation unit;

[0037] The orthogonal demodulation unit is used to perform orthogonal demodulation by multiplying the electrostatic force with a sinusoidal voltage of the same frequency and phase as the modulation voltage; wherein, in the geometric structure model, the voltage of the four plates on the x-axis is the modulation voltage that causes the isolated conductor to translate.

[0038] The electrostatic force amplitude calculation unit is used to obtain the electrostatic force amplitude at the modulation frequency by performing a moving average filter after quadrature demodulation.

[0039] The charge measurement calculation unit is used to multiply the electrostatic force amplitude at the modulation frequency by the gain coefficient to calculate the charge measurement value.

[0040] More preferably, the gain coefficient is:

[0041]

[0042] The charge measurement value is:

[0043] Q TM,est =H q *F 1ω

[0044] Among them, H q α is the gain coefficient; α is the geometry factor, which represents the ratio between the actual capacitance gradient caused by geometric edge effects and the theoretical capacitance gradient based on a parallel-plate capacitor; C tot V represents the total capacitance of the sensitive probe of the Tianqin inertial sensor. MOD For the modulation voltage amplitude; C x To test the capacitance of the plates in the x-direction when the mass is at its center position; x represents the offset of the mass in the x-direction; F 1ω Let ω be the amplitude of the electrostatic force at the modulation frequency ω.

[0045] More preferably, the relative standard deviation represents the fluctuation of the charge measurement value, and its specific expression is as follows:

[0046]

[0047] Where σ is the variance of the charge measurement; The average value of the charge measurements;

[0048] The average relative error is:

[0049]

[0050] Where n is the amount of data for the charge measurement; Q TM,est This is a charge measurement; Q TM This represents the actual charge value.

[0051] In summary, compared with the prior art, the above-described technical solutions conceived by this invention have the following advantages:

[0052] Beneficial effects:

[0053] This invention provides a method and system for evaluating charge measurement errors based on finite element simulation. The method involves establishing a geometric model of the charge measurement based on the sensitive probe of a Tianqin inertial sensor in finite element simulation software. The influence of different factors on charge measurement can be simulated by changing the boundary conditions. For example, the influence of non-ideal modulation voltage can be simulated by changing the modulation voltage on the plates. Using Maxwell's stress tensor principle, the electrostatic force on the test mass is output through simulation. The output electrostatic force is post-processed to convert it into a charge measurement value. The data sources for the actual charge value and the charge measurement value are not limited by practical applications. Only the residual charge on the test mass needs to be set in the simulation model to obtain the actual charge value, thus allowing for a quantitative evaluation of the influence of different factors on charge measurement errors. More specifically, a simulation geometry is established based on the sensitive probe of the Tianqin inertial sensor in finite element simulation software; a suitable physics interface is selected, and the parameters and network of the simulation geometry are set. The simulation settings of the boundary conditions refer to the actual charge measurement. Corresponding modulation voltages are applied to the four plates along the x-axis, while the other frames and plates are grounded. The potential on the isolated conductor is set to V. TM V TM =Q TM / C tot ; where Q TM The residual charge value on the isolated conductor is calculated. The electrostatic force on the isolated conductor over a long period of time is calculated using transient simulation. The electrostatic force output calculated by simulation is obtained by orthogonal demodulation and moving average filtering of the electrostatic force in MATLAB to obtain the electrostatic force amplitude at the modulation frequency. Multiplying the amplitude by the measurement gain coefficient yields the charge value. The orthogonal demodulation uses a sinusoidal voltage with the same frequency and phase as the modulation voltage. The moving average filtering selects an appropriate number of cycles based on the amount of data. Finally, the charge measurement error is evaluated by two indicators: relative error and relative standard error of the mean.

[0054] This invention provides a method and system for evaluating charge measurement errors based on finite element simulation. In the finite element simulation software, a geometric model of charge measurement can be established based on the sensitive probe of the Tianqin inertial sensor, which can take into account complex geometric problems. Moreover, bidirectional coupling of electrostatic force and displacement can be achieved through the multiphysics coupling interface in COMSOL. Attached Figure Description

[0055] Figure 1 This is a flowchart of a method for evaluating charge measurement error based on finite element simulation provided in an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the method for evaluating charge measurement error based on finite element simulation provided in this embodiment of the invention;

[0057] Figure 3 This is a schematic diagram of the geometric structure for charge measurement provided in an embodiment of the present invention; Figure 3 1-12 are control plates; 13-18 are injection plates; 19 is for quality inspection; 20 is the plate frame.

[0058] Figure 4 This is a bar graph showing the charge measurement error caused by the geometric structure of the charge measurement provided in the embodiment of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0060] like Figure 1 and Figure 2 As shown, this invention provides a method for evaluating charge measurement error based on finite element simulation, comprising the following steps:

[0061] A geometric structural model for charge measurement was established based on the sensitive probe of the Tianqin inertial sensor. The model was then divided into a network, and material parameters were attached to the structure.

[0062] Set boundary conditions, change the influence of boundary condition simulation factors on charge measurement, and perform long-term simulation to output the electrostatic force on the quality inspection.

[0063] The output electrostatic force is post-processed to convert the electrostatic force into a charge measurement value;

[0064] Charge measurement error is evaluated using two indicators: mean relative error and relative standard deviation.

[0065] To make the problem description clearer, the mathematical expression is given below:

[0066] Basic settings are configured in the finite element simulation software. A geometric model for charge measurement is established based on the inertial sensor's sensitive probe. The inertial sensor's sensitive probe includes one inspection mass and 18 electrode plates, as shown in the attached diagram. Figure 3 As shown in the figure. Figures 1-12 represent 12 control plates used to monitor the displacement of the inspection mass and control its position at the center; figures 13-18 represent 6 injection plates used to apply AC modulation signals for capacitive displacement sensing to the inspection mass. To simulate the vacuum environment around the sensitive probe of the inertial sensor, a vacuum domain and an infinite element domain are applied outside the probe. Two physical field interfaces are selected: electrostatics and global ordinary differential equations and differential algebraic equations. The material of the sensitive probe region is set to gold, the surrounding infinite element domain is set to vacuum, and finally, the mesh is set to a physical field control mesh with ultra-fine mesh cell size.

[0067] During simulation modeling, the "terminal" interface in the physics field is used to set the boundary conditions for each part according to the charge measurement principle. The potential on the inspection mass is set to V. TM V TM =Q TM / C tot , where Q TM C represents the residual charge on an isolated conductor. tot The total capacitance of the inertial sensor's sensitive probe is given; the voltages of the four plates along the x-axis are set according to the following formula, and the other 14 plates and plate frames are grounded using terminals.

[0068]

[0069] Among them, V MOD f is the modulation voltage amplitude; MOD To modulate the voltage frequency;

[0070] The electrostatic force on the inspection mass, calculated using Maxwell's stress tensor principle, is:

[0071]

[0072] in, for The unit vector in the direction of the outward normal to the surface. For Maxwell's stress tensor; Unit surface area;

[0073] The electrostatic force is multiplied by a sinusoidal voltage of the same frequency and phase as the modulation voltage for quadrature demodulation, i.e.:

[0074]

[0075] Where F represents the sum-frequency signal and difference-frequency signal obtained after orthogonal demodulation of the electrostatic force;

[0076] After orthogonal demodulation, a moving average filter is performed to obtain the electrostatic force amplitude at the modulation frequency. The moving average filter is selected for four periods based on the amount of data, but is not limited to four periods.

[0077]

[0078] Among them, F 1ω t0 represents the electrostatic force amplitude; t0 is the start time of the moving average filter, which is typically 0.

[0079] After obtaining the electrostatic force amplitude at the modulation frequency, the charge measurement value is calculated by multiplying it by the gain coefficient. The gain coefficient is derived from calculations based on a theoretical model.

[0080] The gain coefficient is as follows:

[0081]

[0082] Among them, H q α is the gain coefficient; α is the geometry factor, which means the ratio between the actual capacitance gradient caused by the edge effect of the geometry and the theoretical capacitance gradient based on the parallel plate capacitor. In the post-processing, two cases are considered: one is to consider the capacitance gradient given by the theoretical model based on the parallel plate capacitor, i.e., α = 1; the other is to give the capacitance gradient value based on the finite element simulation and correct the capacitance gradient, i.e., α = 1.46.

[0083] C x To test the capacitance of the plates in the x-direction when the mass is at its center position; x is the offset of the mass in the x-direction.

[0084] The charge measurement value is:

[0085] Q TM,est =H q *F 1ω

[0086] The average relative error is given by comparing the actual charge value set in the simulation, i.e.:

[0087]

[0088] Where n is the amount of data for the charge measurement;

[0089] In addition, the relative standard deviation of the mean represents the fluctuation of the charge measurement value, that is:

[0090]

[0091] Where σ is the variance of the charge measurement; QTM This represents the average value of the charge measurements.

[0092] σ is the variance of the charge measurement; The average value of the charge measurements;

[0093] On the other hand, the present invention provides a system for evaluating charge measurement errors based on finite element simulation, comprising:

[0094] The geometric structure model construction module is used to establish a geometric structure model for charge measurement based on the sensitive probe of the Tianqin inertial sensor in finite element simulation software. It applies a vacuum domain and an infinite element domain outside the sensitive probe of the Tianqin inertial sensor, selects the physical field interface, and sets the material and mesh. In particular, it sets the potential on the isolated conductor in the geometric structure model, and calculates the residual charge value on the isolated conductor as the actual charge value based on the relationship between the residual charge and the potential of the isolated conductor.

[0095] The electrostatic force simulation module is used to build modules based on geometric structure models. By setting different boundary conditions and combining the Maxwell stress tensor principle, it can verify the electrostatic force on the mass through simulation output.

[0096] The charge measurement module is used to perform post-processing on the output electrostatic force, converting the electrostatic force into charge measurement values.

[0097] The electrical measurement error assessment module is used to evaluate the charge measurement error based on the actual charge value and the charge measurement value, using two indicators: average relative error and relative standard deviation. This allows for a quantitative assessment of the impact of different factors on the charge measurement error.

[0098] More preferably, the electrostatic force is:

[0099]

[0100] in, for The unit vector in the direction of the outward normal to the surface. For Maxwell's stress tensor; Unit surface area;

[0101] More preferably, the charge measurement acquisition module includes an orthogonal demodulation unit, an electrostatic force amplitude calculation unit, and a charge measurement calculation unit;

[0102] The orthogonal demodulation unit is used to perform orthogonal demodulation by multiplying the electrostatic force with a sinusoidal voltage of the same frequency and phase as the modulation voltage; wherein, in the geometric structure model, the voltage of the four plates on the x-axis is the modulation voltage that causes the isolated conductor to translate.

[0103] The electrostatic force amplitude calculation unit is used to obtain the electrostatic force amplitude at the modulation frequency by performing a moving average filter after quadrature demodulation.

[0104] The charge measurement calculation unit is used to multiply the electrostatic force amplitude at the modulation frequency by the gain coefficient to calculate the charge measurement value.

[0105] More preferably, the gain coefficient is:

[0106]

[0107] The charge measurement value is:

[0108] Q TM,est =H q *F 1ω

[0109] Among them, H q α is the gain coefficient; α is the geometry factor, which represents the ratio between the actual capacitance gradient caused by geometric edge effects and the theoretical capacitance gradient based on a parallel-plate capacitor; C tot V is the total capacitance of the inertial sensor's sensitive probe. MOD For the modulation voltage amplitude; C x To test the capacitance of the plates in the x-direction when the mass is at its center position; x represents the offset of the mass in the x-direction; F 1ω This represents the amplitude of the electrostatic force.

[0110] More preferably, the relative standard deviation represents the fluctuation of the charge measurement value, and its specific expression is as follows:

[0111]

[0112] Where σ is the equation for the charge measurement value; The average value of the charge measurements;

[0113] The average relative error is:

[0114]

[0115] Where n is the amount of data for the charge measurement; Q TM,est This is a charge measurement; Q TM This represents the actual charge value.

[0116] To further illustrate the method for evaluating charge measurement error based on finite element simulation in the embodiments of the present invention, it is now described in detail below with reference to the accompanying drawings and specific examples:

[0117] In the finite element simulation software, a simulation geometry was established based on the sensitive probe of the Tianqin inertial sensor. A suitable physics interface was selected, and the parameters and network of the simulation geometry were set. The boundary conditions were set with reference to actual charge measurements. Corresponding modulation voltages were applied to the four plates along the x-axis, while the rest of the frame and plates were grounded. The potential on the isolated conductor was set to V. TM V TM =Q TM / C tot ; where Q TM This represents the residual charge value on an isolated conductor. The transient calculation of the long-term electrostatic force on the isolated conductor is used. The simulated electrostatic force output is then subjected to orthogonal demodulation and moving average filtering using MATLAB to obtain the electrostatic force amplitude at the modulation frequency. Multiplying this amplitude by the measurement gain coefficient yields the charge value. The orthogonal demodulation involves multiplying the signal by a sinusoidal voltage with the same frequency and phase as the modulation voltage. The moving average filtering uses an appropriate number of cycles depending on the amount of data. Figure 4 As shown, the charge measurement error is finally evaluated using two indicators: relative error and relative standard error of the mean.

[0118] In summary, compared with the prior art, the present invention has the following advantages:

[0119] This invention provides a method for evaluating charge measurement error based on finite element simulation. The method involves establishing a geometric model of the charge measurement based on the sensitive probe of a Tianqin inertial sensor within finite element simulation software. By setting boundary conditions, factors influencing charge measurement are identified. The electrostatic force on the test mass is output through simulation using the Maxwell stress tensor principle. The output electrostatic force is then post-processed to convert it into a charge measurement value. The data sources for both the actual charge value and the charge measurement value are not limited by practical applications. Specifically, by simply setting the residual charge on the test mass in the simulation model, the actual charge value can be obtained, allowing for a quantitative assessment of the impact of different factors on charge measurement error.

[0120] This invention provides a method and system for evaluating charge measurement errors based on finite element simulation. In the finite element simulation software, a geometric model of charge measurement can be established based on the sensitive probe of the Tianqin inertial sensor, which can take into account complex geometric problems. Moreover, bidirectional coupling of electrostatic force and displacement can be achieved through the multiphysics coupling interface in COMSOL.

[0121] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for evaluating charge measurement error based on finite element simulation, characterized in that, Includes the following steps: Step 1: In the finite element simulation software, establish a geometric structure model for charge measurement based on the sensitive probe of the Tianqin inertial sensor. Apply a vacuum domain and an infinite element domain outside the geometric structure model, select the physical field interface, and set the material and mesh. In the geometric structure model, set the potential on the isolated conductor, and calculate the residual charge value on the isolated conductor as the actual charge value based on the relationship between the residual charge and the potential of the isolated conductor. Step 2: By setting different boundary conditions and combining the Maxwell stress tensor principle, the electrostatic force on the mass is verified through simulation output; Step 3: Perform post-processing on the output electrostatic force to convert the electrostatic force into a charge measurement value; Step 4: Based on the actual charge value and the charge measurement value, evaluate the charge measurement error using two indicators: average relative error and relative standard deviation, and then quantify the impact of different factors on the charge measurement error. The electrostatic force is: in, for The unit vector in the direction of the outward normal to the surface. For Maxwell's stress tensor; Unit element; Step four specifically includes the following steps: The electrostatic force is multiplied by a sinusoidal voltage with the same frequency and phase as the modulation voltage for orthogonal demodulation; where, in the geometric model, the voltage of the four plates on the x-axis is the modulation voltage that causes the isolated conductor to translate. After orthogonal demodulation, a moving average filter is performed to obtain the electrostatic force amplitude at the modulation frequency; The charge measurement value is calculated by multiplying the electrostatic force amplitude at the modulation frequency by the gain coefficient. The gain coefficient is: The charge measurement value is: in, This is the gain coefficient; The geometric structure factor is the ratio between the actual capacitance gradient caused by the edge effect of the geometric structure and the theoretical capacitance gradient based on the parallel plate capacitor. The total capacitance of the sensitive probe of the Tianqin inertial sensor; The amplitude of the modulated voltage; To check if the quality is in the center position The capacitance of the directional plates; To inspect quality The offset caused by the direction; For electrostatic force at modulation frequency The amplitude at that point.

2. The method according to claim 1, characterized in that, The relative standard deviation represents the fluctuation of charge measurement values, and its specific expression is: in, The variance of the charge measurement values; The average value of the charge measurements; The average relative error is: in, n The amount of data for charge measurement; This is a charge measurement value; This represents the actual charge value.

3. A system for evaluating charge measurement error based on finite element simulation, characterized in that, include: The geometric structure model construction module is used to establish a geometric structure model for charge measurement based on the sensitive probe of the Tianqin inertial sensor in finite element simulation software. It applies a vacuum domain and an infinite element domain outside the sensitive probe of the Tianqin inertial sensor, selects the physical field interface, and sets the material and mesh. In particular, it sets the potential on the isolated conductor in the geometric structure model, and calculates the residual charge value on the isolated conductor as the actual charge value based on the relationship between the residual charge and the potential of the isolated conductor. The electrostatic force simulation module is used to build modules based on geometric structure models. By setting different boundary conditions and combining the Maxwell stress tensor principle, it can verify the electrostatic force on the mass through simulation output. The charge measurement module is used to perform post-processing on the output electrostatic force, converting the electrostatic force into charge measurement values. The electrical measurement error assessment module is used to assess the charge measurement error based on the actual charge value and the measured charge value, using two indicators: average relative error and relative standard deviation, and then to quantify the impact of different factors on the charge measurement error. The electrostatic force is: in, for The unit vector in the direction of the outward normal to the surface. For Maxwell's stress tensor; Unit element; The charge measurement value acquisition module includes an orthogonal demodulation unit, an electrostatic force amplitude calculation unit, and a charge measurement value calculation unit; The orthogonal demodulation unit is used to perform orthogonal demodulation by multiplying the electrostatic force with a sinusoidal voltage of the same frequency and phase as the modulation voltage; wherein, in the geometric structure model, the voltage of the four plates on the x-axis is the modulation voltage that causes the isolated conductor to translate. The electrostatic force amplitude calculation unit is used to obtain the electrostatic force amplitude at the modulation frequency by performing a moving average filter after quadrature demodulation. The charge measurement calculation unit is used to multiply the electrostatic force amplitude at the modulation frequency by the gain coefficient to calculate the charge measurement value. The gain coefficient is: The charge measurement value is: in, This is the gain coefficient; The geometric structure factor is the ratio between the actual capacitance gradient caused by the edge effect of the geometric structure and the theoretical capacitance gradient based on the parallel plate capacitor. The total capacitance of the sensitive probe of the Tianqin inertial sensor; The amplitude of the modulated voltage; To check if the quality is in the center position The capacitance of the directional plates; To inspect quality The offset caused by the direction; For electrostatic force at modulation frequency The amplitude at that point.

4. The system according to claim 3, characterized in that, The relative standard deviation represents the fluctuation of charge measurement values, and its specific expression is: in, The variance of the charge measurement values; The average value of the charge measurements; The average relative error is: in, n The amount of data for charge measurement; This is a charge measurement value; This represents the actual charge value.

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