Capacitance displacement sensing zero offset calibration and compensation method

Abstract

The invention provides a capacitance displacement sensing zero offset calibration and compensation method, which comprises the following steps of: adding a compensation signal and a calibration signal into a servo control system of electrostatic suspension capacitive inertial measurement equipment, and calibrating and compensating the capacitance displacement sensing zero offset in a closed-loop state. The method comprises the following steps: by utilizing a nonlinear effect caused by capacitance displacement sensing zero offset, actively applying a calibration signal modulated by a sine carrier trapezoidal wave to a test mass block, analyzing a quadratic term nonlinear response of an output signal of a measurement system controller, and calculating to obtain a capacitance displacement sensing zero offset value according to the nonlinear response; and a compensation signal corresponding to the zero-bias anti-phase value is directly applied to the input end of the system controller, so that the zero-bias compensation of the capacitance displacement sensor is realized. By using the method, the capacitance displacement sensing zero offset generated by a system full link can be calibrated and compensated in a closed-loop state.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of measurement, in particular to a method for calibrating and compensating zero offset of capacitive displacement sensing. BACKGROUND

[0002] Precise measurement devices such as space gravitational wave detection inertial sensors, satellite gravity measurement electrostatic suspension accelerometers, etc. all work based on the principle of capacitive displacement differential detection. Capacitive displacement sensing is the core function of capacitive inertial sensors and accelerometers, and is an important prerequisite for realizing high-precision identification of test mass displacement and attitude, and then realizing high-precision acceleration measurement.

[0003] The calibration and compensation of capacitive displacement sensing zero offset at home and abroad mainly uses the nominal reference capacitor in an open loop state to carry out research on electronic parameters, such as Xiaotian Yang's research in "Analysis and Compensation of Sensing Offset of Capacitive Displacement Sensor" (see Chengrui Wang, Ming Hu, et al. Sensing offset analysis and compensation of a capacitive displacement transducer for space inertial sensors, Measurement Science and Technology, Vol. 36(015115) 2025), and Li Gan's research in "Front-End Modeling and Symmetry Adjustment Method" (see Li Gan, Davor Mance, Peter Zweifel, et al. LTP IS FEE Sensing Channel: Front-End Modeling and Symmetry Adjustment Method, IEEE Sensors Journal, Vol. 12(5), 2012).

[0004] However, there is currently no method for calibrating the capacitive displacement sensing zero offset generated by the whole link of the system in a closed loop state, and the calibration method proposed in the present application is implemented in a closed loop state to comprehensively affect the capacitive displacement sensing zero offset caused by electrode manufacturing defects, transmission lines, electronic symmetry defects, etc. the whole link. SUMMARY

[0005] Therefore, the application provides a method for calibrating and compensating for zero offset of a capacitive displacement sensor of an electrostatic suspension capacitive inertial measurement device.

[0006] The method for calibrating and compensating for zero offset of a capacitive displacement sensor provided by the application specifically comprises the following steps.

[0007] A method for calibrating and compensating for zero offset of a capacitive displacement sensor adds a compensation signal V of and a calibration signal V s to a servo control system of an electrostatic suspension capacitive inertial measurement device; the calibration and compensation for zero offset of the capacitive displacement sensor are performed in a closed loop state of the servo control system; the method comprises the following steps.

[0008] The method utilizes nonlinear effects caused by zero offset of the capacitive displacement sensor, actively applies a sinusoidal carrier triangle wave modulated calibration signal V s to the proof mass, analyzes quadratic nonlinear response of an output signal of a measurement system controller, calculates a zero offset value of the capacitive displacement sensor from the nonlinear response, and directly applies a compensation signal V of corresponding to an inverse value of the zero offset to an input end of the system controller to realize compensation for the zero offset of the capacitive displacement sensor.

[0009] Preferably, the method comprises the following steps.

[0010] Step 1: superimposes the sinusoidal carrier triangle wave modulated calibration signal V s on a control output V c of the servo control system, forms a feedback driving signal V f through a driving amplifier, and applies the feedback driving signal to an electrode to generate a modulating force on the proof mass.

[0011] Step 2: performs Fourier transform on the control output V c of the system controller to obtain an amplitude spectrum, extracts an amplitude at a modulating triangle wave frequency f s in the amplitude spectrum as a nonlinear response compensation amplitude ΔV cs .

[0012] Step 3: calculates a quadratic nonlinear coefficient K2 based on the nonlinear response compensation amplitude ΔV cs .

[0013] Step 4: According to the measurement formula of acceleration generated by electrostatic force, the corresponding relationship between the quadratic non-linear coefficient in the measurement formula and the zero offset x of the capacitive displacement sensor in the test mass is determined; and according to the quadratic non-linear coefficient K2 and the corresponding relationship, the zero offset x of the capacitive displacement sensor is determined.

[0014] Step 5: A compensation signal V of that offsets the zero offset x of the capacitive displacement sensor is generated and applied to the input end of the system controller to realize compensation of the zero offset x of the capacitive displacement sensor.

[0015] Preferably, the parameters of the calibration signal V s are set as follows:

[0016] The frequency f e of the sinusoidal carrier is much higher than the closed-loop bandwidth f0 of the servo control system, and f e ≥10f0.

[0017] The frequency f s of the modulated trapezoidal wave is within the measurement bandwidth of the servo control system, and f0≥10f s .

[0018] The amplitude V e of the sinusoidal carrier is set to half of the measurement and control range of the servo control system.

[0019] Preferably, the calibration signal V s is constructed as follows:

[0020]

[0021] where t is time, i represents the i-th calibration signal period, i=0,1,2,…,T s is the calibration signal period, is twice the period of the modulated trapezoidal wave, ΔT is the gradient rise and fall time of the modulated trapezoidal wave, V e is the amplitude of the sinusoidal carrier, f e is the frequency of the sinusoidal carrier.

[0022] Preferably, the quadratic non-linear coefficient K2 is calculated based on the non-linear response compensation amplitude ΔV cs as follows:

[0023]

[0024] where G P is the acceleration generated by a unit feedback voltage applied to the electrode; G a is the feedback amplification circuit gain of the driving amplification module; V e is the amplitude of the sinusoidal carrier in the calibration signal V s .

[0025] Preferably, the determining the capacitive displacement sensor zero offset x according to the quadratic nonlinearity coefficient K2 and the corresponding relationship is specifically:

[0026]

[0027] Wherein, m is the mass of the test mass, d is the average distance of the electrodes, A is the electrode area, and ε is the dielectric constant.

[0028] Preferably, the generating the compensation signal V of for offsetting the capacitive displacement sensor zero offset x is: of = -K d x, wherein K d is the capacitive displacement sensor gain.

[0029] Preferably, as time goes on, the calibration signal V s changes, the quadratic nonlinearity coefficient K2 and the capacitive displacement sensor zero offset x are updated, and a new compensation signal V of is calculated and input into the system controller; until the capacitive displacement sensor zero offset x is reduced to a set acceptable range.

[0030] Preferably, the determination that the capacitive displacement sensor zero offset x is reduced to a set acceptable range is that: the maximum feedback voltage V f-max corresponding to the maximum range of the system is multiplied by the quadratic nonlinearity coefficient K2, and it is determined whether the product is less than or equal to the measurement resolution.

[0031] Preferably, in order to ensure the resolution of the nonlinear response compensation amplitude ΔV cs extracted from the amplitude spectrum, the calibration signal is applied to the servo control system and runs for no less than 10 cycles, and then the Fourier transform is performed on the control output V c .

[0032] Advantages:

[0033] (1) The capacitive displacement sensor zero offset calibration method proposed in the present application is based on the calibration of the quadratic nonlinearity coefficient caused by the zero offset, and then the capacitive displacement sensor zero offset is calculated through the relationship between the capacitive displacement sensor zero offset and the quadratic nonlinearity coefficient, and a displacement sensor value equal in amplitude and opposite in phase to the capacitive displacement sensor zero offset is applied to the input end of the controller, so as to realize the compensation and influence elimination of the system capacitive zero offset, and improve the measurement linearity and precision of the capacitive inertial measurement device.

[0034] (2) The present application is implemented in a closed state, which avoids the difference between the capacitive displacement sensor zero offset determined in an open loop state and the actual closed loop operation, and further improves the measurement linearity and precision of the capacitive inertial measurement device.

[0035] (3) The application does not need to change the structure of the servo control system of the capacitive inertial measurement device, only needs to add two superimposed signals V of and V s , and combines simple calculation, so that the compensation and influence elimination of the capacitive displacement sensor zero offset are realized, which is simple and has good real-time performance.

[0036] (4) The application designs a sinusoidal carrier trapezoidal wave modulated calibration signal, which can make the nonlinear response sinusoidal carrier signal of the capacitive inertial measurement device due to the sensing zero offset, and reflect the trapezoidal wave modulation frequency in the control output signal. The trapezoidal wave modulation can effectively reduce the system overshoot and harmonic influence caused by the sudden change of the sine wave amplitude, and provides an effective method for analyzing the nonlinearity and sensing zero offset of the capacitive inertial measurement device of the inertial measurement device.

[0037] (5) In the case of nonlinear system measurement, the quadratic nonlinear coefficient calculated according to the linearity is an approximate value. The application reduces the quadratic nonlinear coefficient and the capacitive sensing zero offset to an acceptable range through multiple iterations, thereby improving the measurement linearity and precision of the capacitive inertial measurement device. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 It is a principle block diagram of the capacitive displacement sensor zero offset calibration and compensation method of the application;

[0039] Figure 2 It is a schematic diagram of the calibration signal of the application;

[0040] Figure 3 It is a schematic diagram of the calibration signal generated in the example of the application;

[0041] Figure 4 It is a schematic diagram of the control output signal of the system controller in the example of the application; (a) is the control output signal, and (b) is a partial enlarged view of the control output signal;

[0042] Figure 5 It is an amplitude spectrum obtained by FFT transformation of the output signal of the system controller in the example of the application. DETAILED DESCRIPTION

[0043] The application will be described in detail below in combination with the drawings and examples.

[0044] The problem to be solved by the application is that the capacitive displacement sensor zero offset of the capacitive inertial measurement device such as an inertial sensor and an electrostatic suspension accelerometer is small and difficult to calibrate the whole link system, and the application provides a basis for digital compensation of the capacitive displacement sensor zero offset, thereby improving the recognition and control accuracy of the test quality position and attitude, and improving the measurement linearity and precision of the capacitive inertial measurement device.

[0045] First, the principle on which the present application is based is analyzed.

[0046] Affected by sensor electrode manufacturing defects, symmetry defects of capacitive displacement sensing electronics parameters, etc., the capacitive displacement sensing zero offset is caused, and the capacitive displacement detection value cannot accurately reflect the actual position and attitude of the test mass, causing the nonlinearity of acceleration measurement, directly affecting the measurement accuracy. The following formula (1) is the general measurement formula under the accelerometer mode, where the third term on the right side of the equation is the quadratic nonlinearity term. It can be seen that the quadratic nonlinearity coefficient is directly related to the distance x of the test mass from the electrode center. For an accelerometer, the position of the test mass in the electrode is ultimately determined by the reference "zero point" of the control input under servo control. When the capacitive displacement sensor has a zero offset when providing a reference input to the controller, the test mass will deviate from the center of the electrode after servo control, thereby generating a non-linear measurement term.

[0047]

[0048] where a e is the acceleration generated by the electrostatic force; ε is the dielectric constant, m is the mass of the test mass, d is the average distance between the electrodes, A is the electrode area; V P is the DC bias voltage applied to the test mass, V drms is the effective value of the AC detection carrier voltage applied to the test mass, V f is the feedback drive voltage signal applied to the electrode after the control output of the system controller is driven and amplified; x is the capacitive displacement sensing zero offset in the test mass, i.e. the distance of the test mass from the center of the electrode; is the acceleration generated by the unit feedback drive voltage, i.e. the physical feedback gain of the accelerometer; is the acceleration measurement bias value caused by the sensing zero offset; is the quadratic nonlinearity coefficient.

[0049] For satellite gravity measurement, gravitational wave detection and other application fields, the measurement uncertainty of the device is usually required to be better than 10 -5 The capacitive displacement sensing zero offset needs to be controlled at the nm level. As mentioned earlier, the capacitive displacement sensing zero offset is affected by electrode manufacturing defects and electronic parameter symmetry defects, and cannot be accurately detected and controlled in the part state, so it needs to be calibrated and compensated at the whole machine level. Since the capacitive displacement sensing zero offset x directly affects the quadratic nonlinearity coefficient, the quadratic nonlinearity coefficient can be calibrated, and then the capacitive displacement sensing zero offset x can be calculated from the expression of the quadratic nonlinearity coefficient:

[0050]

[0051] Equation (2) gives the expression for the zero bias x of the capacitive displacement sensing and the nonlinear coefficient K2 of the quadratic term. The dielectric constant ε, electrode area A, mass m of the test mass block, and average electrode spacing d are all known constants or can be tested with high precision. Therefore, the zero bias of the capacitive displacement sensing can be obtained by calibrating the nonlinear coefficient of the quadratic term and then compensated at the input of the controller.

[0052] The calibration principle for the nonlinear quadratic term is as follows: When a signal with a frequency much higher than the system control bandwidth is applied to the inspection quality through control, a DC disturbance will be generated on the inspection quality due to the nonlinearity of the system, as shown in the first term on the right side of equation (3) below. The second term, the harmonic term, has a frequency much higher than the response frequency of the inspection quality and will not appear in the system's measurement control signal. Since the DC disturbance term breaks the force balance of the inspection quality, a disturbance compensation signal needs to be generated in the control signal to maintain the balance of the inspection quality. The quadratic nonlinear coefficient can be obtained by analyzing the disturbance compensation signal in the control signal. In actual implementation, in order to improve the identification of the DC disturbance compensation signal, the high-frequency sine signal is further modulated using a low-frequency trapezoidal wave with a frequency within the measurement bandwidth, thereby modulating the original DC disturbance compensation signal into a single-frequency signal within the measurement bandwidth, which is beneficial to improve the calibration accuracy through spectrum analysis.

[0053]

[0054] Among them, a s G is the acceleration of the disturbance generated by the calibration signal on the inspection mass block. a To drive the gain of the feedback amplifier circuit; V e f is the amplitude of the sinusoidal carrier wave; e The frequency of the sinusoidal carrier wave.

[0055] Based on the above analysis, the present invention provides a calibration and compensation method for zero bias in capacitive displacement sensing. This method utilizes the nonlinear effect caused by the zero bias in capacitive displacement sensing, and applies a calibration signal V modulated by a sinusoidal carrier trapezoidal wave to the test mass block. s The nonlinear response of the quadratic term of the output signal of the measurement system controller is analyzed. The zero bias value of the capacitive displacement sensing is calculated from the nonlinear response, and the compensation signal V corresponding to the zero bias inverse value is directly applied to the input of the system controller. of This enables compensation for zero bias in capacitive displacement sensing.

[0056] The following is combined Figure 1 The implementation process of the calibration and compensation method for zero bias of capacitive displacement sensing in the embodiments of the present invention is described in detail.

[0057] Figure 1It is a schematic diagram of the servo control system of the electrostatic suspension capacitive inertial measurement device. The difference between the present application and the prior art is that the present application adds a compensation signal V of and a calibration signal V s in the servo control system of the electrostatic suspension capacitive inertial measurement device; and provides a calibration and compensation scheme, which can calibrate and compensate the zero offset of the capacitive displacement sensor in the closed loop state of the servo control system. The closed loop calibration and compensation method specifically comprises the following steps:

[0058] Step 1, based on the control output signal V c of the system controller of the servo control system, superimpose a sinusoidal carrier sawtooth wave modulation signal, denoted as a calibration signal V s ; V s is applied to the electrode through a drive amplifier as a quadratic term coefficient calibration excitation signal.

[0059] As shown in Figure 1 , superimpose a sinusoidal carrier sawtooth wave modulation calibration signal V s on the control output signal V c of the system controller in the stable control state of the system, and the waveform of the calibration signal V s is as shown in Figure 2 . The calibration signal V s is composed of a carrier and a modulation wave; the carrier is a sine wave with a frequency much higher than the closed loop bandwidth of the system, but a direct current term response can be generated due to the nonlinearity of the system; the modulation wave is a sawtooth wave with a frequency within the system measurement frequency band, which can modulate the direct current term generated by the calibration signal to the frequency, which is easy to extract in the amplitude spectrum.

[0060] The frequency f e of the sinusoidal carrier should be much higher than the closed loop bandwidth f0 of the system, and f e ≥10f0, and the frequency f s of the modulation sawtooth wave should be within the system measurement bandwidth, and f0≥10f s . In order to ensure that the nonlinear response of the test quality is strong enough and improve the signal-to-noise ratio of the measurement, the amplitude of the sinusoidal carrier signal should be large enough, and at the same time, in order to ensure the stability of the system during excitation, the amplitude V e of the sinusoidal carrier is set to about half of the measurement and control range of the servo control system.

[0061] Referring to Figure 2 , the setting feature of the calibration signal V s is that the signal period T s , the amplitude of the sinusoidal carrier is V e , and the sinusoidal carrier is modulated by the sawtooth wave, the duty cycle of the sawtooth wave is about 0.5(T s / 2), and the rising edge and falling edge time of the sawtooth wave is ΔT, which is generally less than T s / 8.

[0062] A mathematical expression of the calibration signal is shown in equation (3) to make the test mass produce a nonlinear response related to the capacitive displacement sensing zero offset x:

[0063]

[0064] where t is time, i represents the i-th calibration signal period, i = 0, 1, 2, …, T s is the period of the calibration signal, is twice the period of the modulated trapezoidal wave, AT is the gradient rise and fall time of the modulated trapezoidal wave, V e is the amplitude of the sinusoidal carrier, f e is the frequency of the sinusoidal carrier.

[0065] Step 2, Fourier transform spectrum analysis is performed on the control output V c of the system controller to extract the amplitude at the modulated trapezoidal wave frequency f s from the amplitude spectrum as the nonlinear response compensation amplitude V cs .

[0066] In order to ensure the resolution of the nonlinear response compensation amplitude AV cs extracted from the amplitude spectrum, the above calibration signal is applied to the servo control system and run for no less than 10 periods, then Fourier transform is performed on the control output signal V c of the system controller to analyze the amplitude-frequency response of the system, and the nonlinear response compensation amplitude V s of the system at the trapezoidal wave modulation frequency f cs is extracted from the amplitude-frequency graph.

[0067] Step 3, the quadratic nonlinear coefficient K2 of the foregoing is calculated based on the nonlinear response compensation amplitude AV cs .

[0068] In this step, the compensation amplitude generated by the calibration signal passing through the nonlinear response of the system at the output of the system controller satisfies the force balance relationship of the test mass: Accordingly, the quadratic nonlinear coefficient is calculated according to the following formula:

[0069]

[0070] where G P is the physical feedback gain of the accelerometer, i.e. the acceleration generated by a unit feedback voltage applied to the electrode; G a is the drive feedback amplifier gain, i.e. the amplification multiple between the control output V c of the system controller and the voltage V f applied to the electrode, i.e. V f / Vc .

[0071] Step 4, the previous analysis process determines the corresponding relationship between the quadratic nonlinearity coefficient in the measurement formula and the capacitance displacement sensor zero offset x in the test mass according to the measurement formula of the acceleration generated by the electrostatic force; here, the capacitance displacement sensor zero offset value x is calculated according to the quadratic nonlinearity coefficient K2 and the corresponding relationship.

[0072] According to the relationship between the quadratic nonlinearity coefficient K2 and the capacitance displacement sensor zero offset x given by formula (1), the capacitance displacement sensor zero offset value x expression is:

[0073]

[0074] Where m is the mass of the test mass, d i The average distance of the electrodes corresponding to the calibration direction i, A i is the electrode area of the calibration direction i, and ε is the dielectric constant.

[0075] Step 5, a compensation signal V of that offsets the capacitance displacement sensor zero offset x is generated and applied to the input end of the system controller to achieve compensation of the capacitance displacement sensor zero offset x.

[0076] In order to offset the influence of the capacitance displacement sensor zero offset x, an x displacement signal corresponding sensor voltage signal needs to be generated to the input end of the system controller, so the compensation voltage to the controller input end is calculated by the following formula: V of = -K d x, where K d is the capacitance displacement sensor gain.

[0077] Step 6, repeat steps 1-5 above until the capacitance displacement sensor zero offset x is reduced to an acceptable range.

[0078] In the case of nonlinearity in system measurement, the quadratic nonlinearity coefficient calculated in step 3 according to linearity is an approximate value, so steps 1-5 need to be repeated to reduce the quadratic nonlinearity coefficient and the capacitance sensor zero offset to an acceptable range through multiple iterations.

[0079] In a preferred scheme, the judgment basis for entering the acceptable range above is usually calculated according to the third term on the right side of formula (1) to determine that the influence of the quadratic nonlinearity coefficient K2 caused by the capacitance displacement sensor zero offset x does not exceed the measurement resolution requirement when the feedback control voltage V f reaches the maximum. Specifically, the maximum value of the feedback voltage V f-max corresponding to the maximum range of the system is multiplied by the quadratic nonlinearity coefficient K2 to determine whether the product is less than or equal to the measurement resolution rate. If so, it is determined that it has entered the acceptable range.

[0080] Example

[0081] This example is directed to the present solution, which is verified by a specific setting scene.

[0082] Setting scene: a mass of the accelerometer's proof mass m = 20 g, electrode area A = 1.9 cm 2 , electrode average d = 80 pm, bias voltage V P = 7 V, corresponding to the physical gain G p = 1.84 x 10 -4 m / s 2 / V, capacitive displacement sensing gain k d = 6.3 x 10 5 V / m, drive feedback amplifier circuit gain G a = 2, system closed-loop bandwidth is 2.4 Hz, and the capacitive displacement sensor has a zero offset of 3.2 pm. The following is the digital simulation calibration process:

[0083] Step 1: superimpose a frequency f e = 200 Hz sine carrier f s = 0.05 Hz calibration signal modulated by a trapezoidal wave with a duty cycle of 0.6, i.e. a period of 12 s, and a trapezoidal wave rise and fall time AT of 2 s, a sine wave amplitude V e = 1 V, and the calibration signal is as shown in Figure 3 .

[0084] Step 2: calibrate 50 cycles, a total of 1000 s, and the system controller output signal is as shown in 4, the compensation signal amplitude is calculated as AV cs = 5.68 mV, and the duration of each calibration cycle is about 6 s, and the duty cycle is about 0.3, excluding the adjustment time before and after. The FFT transform of the control output signal is shown in Figure 5 , and the amplitude at the main frequency 0.05 Hz is 3.41 mV. For the square wave compensation signal AV cs , the amplitude of the amplitude spectrum is 0.588 times the time domain amplitude, and the amplitude calculated from this relationship is 5.68 mV x 0.588 = 3.34 mV, which is very close to the amplitude of the main frequency of the amplitude spectrum, and can be used as the basis for analysis and calculation. The error is mainly caused by the test duration frequency resolution, harmonics, etc.

[0085] Step 3: take the controller output time domain compensation value AV cs = 5.68 mV as the basis, and calculate the quadratic nonlinearity coefficient according to the formula : K2 = -1 x 10 -6 m / s 2 / V 2 .

[0086] Step 4: using the quadratic non-linear coefficient K2 value calculated in the previous step, according to the formula The capacitance displacement sensor zero offset value is calculated as x = 3.1 μm, which is very close to the set capacitance sensor zero offset, indicating the effectiveness of the method.

[0087] Step 5: calculate the compensation voltage needed to be applied to the control input from the capacitance displacement sensor zero offset x:

[0088] V of = -K d x = 6.3 x 10 -5 V / m x 3.1 x 10 -5 m = -1.953 V.

[0089] In this example, the capacitance displacement sensor zero offset x has already entered the acceptable range, and does not need to be further adjusted.

[0090] The above specific embodiments only describe the design principles of the present application, and the shapes and names of the components in the description can be different and are not limited. Therefore, those skilled in the art of the present application can modify or equivalently replace the technical solutions described in the foregoing embodiments; and these modifications and replacements do not deviate from the purpose and technical solutions of the present application, and should all belong to the protection scope of the present application.

Claims

1. A method for calibrating and compensating for zero bias in capacitive displacement sensing, characterized in that, Add a compensation signal V to the servo control system of the electrostatic levitation capacitive inertial measurement equipment. of and calibration signal V s Calibration and compensation of capacitive displacement sensing zero bias are performed in the closed-loop state of the servo control system; this method includes: Utilizing the nonlinear effect caused by the zero bias of capacitive displacement sensing, a calibration signal V modulated by a sinusoidal carrier trapezoidal wave is actively applied to the test mass block. s The nonlinear response of the quadratic term of the output signal of the measurement system controller is analyzed. The zero bias value of the capacitive displacement sensing is calculated from the nonlinear response, and the compensation signal V corresponding to the zero bias inverse value is directly applied to the input of the system controller. of This enables compensation for zero bias in capacitive displacement sensing.

2. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 1, characterized in that, The method includes the following steps: Step 1: In the control output V of the servo control system c The calibration signal V is superimposed with a sinusoidal carrier trapezoidal wave modulation. s After being driven and amplified, a feedback drive signal V is formed. f The force applied to the electrode generates a modulation force on the test mass block; Step 2: Control output V of the system controller c Perform a Fourier transform to obtain the amplitude spectrum, and extract the amplitude spectrum located at the modulation trapezoidal wave frequency f. s The amplitude at that point is used as the nonlinear response compensation amplitude ΔV cs ; Step 3: Compensate for the amplitude ΔV based on the nonlinear response. cs Calculate the nonlinear coefficient K2 of the quadratic term; Step 4: Based on the measurement formula for acceleration generated by electrostatic force, the correspondence between the quadratic nonlinear coefficient in the measurement formula and the zero bias x of the capacitive displacement sensing in the test mass block was determined; based on the quadratic nonlinear coefficient K2 and the aforementioned correspondence, the zero bias x of the capacitive displacement sensing was determined. Step 5: Generate a compensation signal V to cancel the zero bias x of the capacitive displacement sensing. of It is applied to the input of the system controller to achieve compensation for zero bias x of capacitive displacement sensing.

3. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 2, characterized in that, The calibration signal V s The parameters are set as follows: The frequency f of the sinusoidal carrier e The closed-loop bandwidth f0 of the servo control system is much higher than that of the servo control system. e ≥10f0; The frequency f of the modulated trapezoidal wave s Within the measurement bandwidth of the servo control system, f0 ≥ 10f s ; The amplitude V of the sinusoidal carrier wave e Set to half of the measurement and control range of the servo control system.

4. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 3, characterized in that, The calibration signal V s The structure is as follows: Where t is time, and i represents the i-th calibration signal period, i = 0, 1, 2, ..., T s To calibrate the signal period, it is twice the period of the modulated trapezoidal wave, where ΔT is the rise and fall time of the gradient side of the modulated trapezoidal wave, and V... e f is the amplitude of the sinusoidal carrier wave. e The frequency of the sinusoidal carrier wave.

5. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 2, characterized in that, The compensation amplitude ΔV based on the nonlinear response cs The nonlinear coefficient K2 of the quadratic term is calculated as follows: Among them, G P The acceleration generated by the unit feedback voltage applied to the electrode; G a To drive the feedback amplifier circuit gain of the amplifier module; V e For calibration signal V s The amplitude of the sinusoidal carrier wave in the equation.

6. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 2, characterized in that, The determination of the zero bias x of the capacitive displacement sensing based on the quadratic nonlinear coefficient K2 and the corresponding relationship is specifically as follows: Where m is the mass of the test mass block, d is the average distance between the electrodes, A is the electrode area, and ε is the dielectric constant.

7. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 2, characterized in that, The compensation signal V that generates the zero bias x of the capacitive displacement sensing is used to cancel it out. of For: V of =-K d x, where K d This represents the gain of the capacitive displacement sensing.

8. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 2, characterized in that, Over time, the calibration signal V s Changes are made, the nonlinear coefficients of the quadratic term K2 and the zero bias of the capacitive displacement sensor x are updated, and a new compensation signal V is calculated. of Input to the system controller; until the capacitive displacement sensing zero bias x decreases to the set acceptable range.

9. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 8, characterized in that, The method for determining whether the voltage has decreased to a set acceptable range is as follows: the feedback voltage V corresponding to the system's maximum range is... f-max Multiply the maximum value by the quadratic term nonlinear coefficient K2, and determine whether the product is less than or equal to the measurement resolution. If it is, it is determined to be within the acceptable range.

10. The method for calibrating and compensating zero bias in capacitive displacement sensing as described in claim 2, characterized in that, To ensure the extraction of the nonlinear response compensation amplitude ΔV from the amplitude spectrum cs To achieve the desired resolution, the calibration signal is applied to the servo control system and run for at least 10 cycles, then the control output V is adjusted. c Perform a Fourier transform.

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