A method for suppressing zero bias error of silicon micro-resonant accelerometer

Abstract

The invention discloses a method for suppressing the zero bias error of a silicon micro-resonant accelerometer. The method uses an incremental continuous timestamp counting method based on sliding average to measure the resonant frequency signal, establishes a zero bias drift compensation model, and online compensates for the zero bias drift caused by temperature drift to suppress the zero bias error. The incremental continuous timestamp counting method cancels the preset gate. When the rising edge of the signal to be measured is detected, the FPGA samples to obtain a new timestamp event, obtains a new data point, replaces and discards the old data point, and uses RAM to execute the update demand of the frequency sample point data to be measured. The zero bias drift compensation model is respectively completed by a variable temperature hysteresis experiment and a full temperature calibration experiment to model the zero bias term and the scale factor term. The zero bias term is obtained by a two-variable model based on a BP neural network, and the scale factor term is obtained by a single-variable model based on a polynomial. The method can improve the zero bias performance of the silicon micro-resonant accelerometer.

Description

Technical Field

[0001] The invention belongs to the technical field of micro-inertial systems, and in particular relates to a method for suppressing zero bias errors of a silicon micro-resonant accelerometer. Background Art

[0002] Silicon micro-resonant accelerometer is a MEMS sensor with potential high-precision characteristics. This type of accelerometer converts the input acceleration signal into a frequency signal. It has the characteristics of strong anti-interference and quasi-digital output. It is widely used in inertial navigation, gravity measurement and other fields. Due to the detection mechanism of the resonator force-frequency characteristics, the resonator composed of the resonant beam is very sensitive to stress, which leads to a large influence of temperature on zero bias drift: on the one hand, the Young's modulus of silicon material has a temperature coefficient, which directly causes the resonant frequency to change with temperature; on the other hand, during the bonding and gluing process, the mismatch of the thermal expansion coefficients of silicon, glass and ceramic substrates introduces thermal stress, which in turn causes the drift of the resonant frequency of the sensitive structure.

[0003] In order to solve the zero bias drift problem caused by temperature in resonant accelerometers, two resonators symmetrically arranged in the sensitive axis direction are usually used for differential design in the sensitive structure to suppress the zero bias drift error caused by temperature. However, the accuracy of its mechanical structure is easily limited by processing technology, packaging technology and manufacturing errors, which leads to asymmetric temperature coefficients of the two resonator frequencies. The common mode error caused by temperature cannot be completely eliminated, and ultimately the zero bias output of the accelerometer will drift with temperature. In addition, with the continuous improvement of the accuracy of silicon micro-resonant accelerometers, higher requirements are put forward for the measurement noise of the resonant frequency in the engineering application of resonant beam accelerometers. Summary of the invention

[0004] The present invention is aimed at the zero bias error problem of accelerometers in the prior art under different situations such as normal temperature, constant temperature, and variable temperature, and provides a method for suppressing the zero bias error of a silicon micro-resonant accelerometer. The incremental continuous timestamp counting method based on sliding average is used to complete the frequency measurement of the resonant frequency signal, and a zero bias drift compensation model is established. The zero bias drift caused by temperature drift is compensated online, and the compensated acceleration signal is converted into a digital signal output, so as to realize the zero bias error suppression of the silicon micro-resonant accelerometer; the incremental continuous timestamp counting method based on sliding average is specifically as follows: The prefabricated gate in the continuous timestamp counting method is cancelled. When the rising edge of the square wave signal to be measured is detected, the FPGA samples to obtain a new timestamp event, obtains a new data point, replaces and discards the original old data point, and uses RAM resources to execute the update requirements of the frequency sample point data to be measured; the zero bias term and the scale factor term that change with the temperature factor are modeled through the variable temperature hysteresis experiment and the full temperature calibration experiment, and the zero bias drift is compensated online; among them, the zero bias term is obtained by a dual variable prediction model based on the BP neural network, and the scale factor term is obtained by a single prediction model based on a polynomial. This method can improve the zero bias performance of the silicon micro-resonant accelerometer, compensate for the zero bias drift caused by the temperature factor in real time, and avoid the disadvantage that the traditional single temperature variable compensation method cannot suppress the variable temperature hysteresis error.

[0005] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present invention is: a method for suppressing the zero bias error of a silicon micro-resonant accelerometer, using an incremental continuous timestamp counting method based on sliding average to complete the frequency measurement of the resonant frequency signal, establishing a zero bias drift compensation model, performing online compensation for the zero bias drift, and converting the compensated acceleration signal into a digital signal output, thereby realizing the zero bias error suppression of the silicon micro-resonant accelerometer;

[0006] The incremental continuous timestamp counting method based on sliding average is specifically as follows: the prefabricated gate in the continuous timestamp counting method is cancelled, and when the rising edge of the square wave signal to be measured is detected, the FPGA samples to obtain a new timestamp event, obtains a new data point, replaces and discards the original old data point, and uses RAM resources to execute the update requirements of the frequency sample point data to be measured;

[0007] The zero bias drift compensation model is specifically as follows: the zero bias term and the scale factor term that change with the temperature factor are modeled through the variable temperature hysteresis experiment and the full temperature calibration experiment, and the zero bias drift is compensated online; the zero bias term is obtained by using the temperature and temperature change rate dual variable prediction model based on the BP neural network, and the scale factor term is obtained by using the single temperature prediction model based on the polynomial.

[0008] As an improvement of the present invention, in the incremental continuous timestamp counting method based on sliding average, according to the demand for updating the sample point data, the slope of the m sample point fitting line after the incremental algorithm is optimized based on FPGA is calculated. The implementation is as follows:

[0009]

[0010] Among them, C3 and C4 are the update coefficients after the rising edge of the frequency to be measured is enabled.

[0011] As another improvement of the present invention, the zero bias drift compensation model is calculated as follows:

[0012]

[0013] Among them, △f is the output frequency difference, T is the temperature, △T is the temperature change rate, △f0(T,△T) is the zero bias term dual variable prediction model, K(T) is the scale factor term single variable prediction model, and a(△f,T,△T) is the acceleration after compensation.

[0014] As another improvement of the present invention, the zero bias term dual variable prediction model: utilizes the variation trend of the zero bias output frequency difference of the accelerometer with the temperature and the temperature change rate, takes the temperature and the temperature change rate as the independent variable input, and outputs the zero bias term as the dependent variable based on the BP neural network, and constructs a dual variable compensation prediction model based on the BP neural network;

[0015] The scale factor single variable prediction model utilizes the variation trend of the accelerometer scale factor with temperature, uses the least square method to fit the scale factor of the accelerometer prototype through temperature, and constructs a polynomial-based single temperature variable compensation prediction model.

[0016] As another improvement of the present invention, a method for suppressing zero bias error of a silicon micro-resonant accelerometer comprises the following steps:

[0017] S1, resonant frequency signal generation: using a closed-loop control loop to drive the resonator, the closed-loop control loop at least uses automatic gain control and phase-locked loop technology to track the resonant frequency signal of the resonator in real time and output two resonant frequency signals;

[0018] S2, frequency measurement: the frequency of the dual-path resonant frequency signal of the resonant accelerometer is measured by using an incremental continuous timestamp counting method based on sliding average;

[0019] S3, full-temperature modeling experiment: a full-temperature modeling experiment is performed on the silicon micro-resonant accelerometer prototype, wherein the hysteresis temperature change experiment is used for zero bias term modeling, and the full-temperature calibration experiment is used for scale factor term modeling; the resonator output frequency data is obtained according to step S2, and the temperature and temperature change rate data of the accelerometer prototype are recorded;

[0020] S4, establishing a prediction model for zero bias term and scale factor term: according to the zero bias term and scale factor term obtained in step S3, establishing a zero bias term bivariate prediction model and a scale factor term univariate prediction model, wherein the zero bias bivariate prediction model is based on data fitting of a BP neural network, and the scale factor term univariate model is based on data fitting of a polynomial;

[0021] S5, establishing a zero bias drift compensation model: according to the zero bias term and the scale factor term obtained in step S4, a zero bias drift compensation model is established, and the output of the model is an acceleration signal a(△f,T,△T):

[0022]

[0023] S6, signal output: convert the compensated acceleration signal into a digital signal output and transmit it to the host computer through the serial port to achieve zero bias error suppression of the silicon micro-resonant accelerometer.

[0024] As a further improvement of the present invention, in the full-temperature modeling experiment of S3, the temperature of the accelerometer prototype is measured by encapsulating it in the same packaging tube shell as the accelerometer prototype, and the temperature range of the full-temperature test is -40°C to 60°C.

[0025] Compared with the prior art, the present invention has the following technical advantages and effects:

[0026] (1) The present invention proposes an incremental continuous timestamp frequency measurement method based on sliding average, which uses incremental counting to replace incremental counting, reduces FPGA memory resources and suppresses the random noise at the frequency measurement end of the resonant accelerometer to a certain extent, thereby improving the frequency measurement accuracy of the accelerometer.

[0027] (2) The present invention proposes a zero bias drift compensation model for a silicon micro-resonant accelerometer, introduces a temperature change rate into the zero bias term to suppress the hysteresis error, and uses a BP neural network to complete a zero bias term compensation model based on multivariate nonlinearity of temperature and temperature change rate, thereby effectively suppressing the zero bias drift under normal temperature, constant temperature, and variable temperature scenarios.

[0028] (3) The method of the present invention avoids the shortcoming that the single temperature variable drift compensation model under the traditional thermal balance temperature compensation method is difficult to solve the variable temperature hysteresis error, and improves the temperature performance of the silicon micro-resonant accelerometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A flowchart of the steps of a method for suppressing zero bias error of a silicon micro-resonant accelerometer according to the present invention;

[0030] Figure 2It is an overall block diagram of the system implementation of the present invention;

[0031] Figure 3 It is the principle block diagram of the continuous timestamp counting method;

[0032] Figure 4 This is a flow chart of initializing the incremental coefficients of the present invention;

[0033] Figure 5 This is a data update flow chart of the incremental coefficient of the present invention. DETAILED DESCRIPTION

[0034] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0035] Example 1

[0036] A method for suppressing zero bias error of a silicon micro-resonant accelerometer, such as Figure 1 As shown, the following steps are included:

[0037] S1, resonant frequency signal generation: a closed-loop control loop is used to drive the resonator to generate two resonant frequency signals. The closed-loop drive control loop adopts automatic gain control and phase-locked loop technology to track the resonant frequency signal of the resonator in real time and output two resonant frequency signals;

[0038] S2, frequency measurement: the frequency of the dual-path resonant frequency signal of the resonant accelerometer is measured by using an incremental continuous timestamp counting method based on sliding average;

[0039] The overall block diagram of the system implementation of the present invention is as follows Figure 2 As shown. The zero-bias error suppression measurement and control system of silicon micro-resonant accelerometer consists of four main parts: silicon micro-resonant accelerometer head structure, analog circuit part, FPGA digital system part and data transmission part. The function of the analog circuit is mainly to detect the comb capacitance and convert it into a voltage signal, and then realize amplitude control and phase control through automatic gain control and phase-locked loop respectively. The two signals are coupled by AC and DC to provide a driving signal for the resonator inside the accelerometer head. The digital part based on FPGA mainly completes the incremental continuous timestamp frequency measurement based on sliding average, temperature and temperature change rate measurement, zero-bias drift compensation and serial port data transmission. The data transmission part sends the measured two-way frequency, temperature, temperature change rate and acceleration signal after online compensation to the host computer through the RS485 bus, which is convenient for the subsequent evaluation of the zero-bias drift compensation effect.

[0040] In the original continuous time stamp frequency measurement method, the measured signal and the actual gate time are synchronized, so the actual gate time T in the measurement is realgate is the period of the signal to be measured Tclk An integer multiple of n, that is, satisfying T realgate =n·T real When the first timestamp in the gate ends, the corresponding count value N of the signal to be tested will be recorded. x1 and clock signal count value N s1 , and then the frequency value of the signal to be measured is obtained according to the corresponding calculation formula. The measurement principle block diagram is as follows Figure 3 As shown. In a gate time T realgate In the process, n timestamps will be obtained, and the N timestamps corresponding to these n timestamps will be x and N s The values ​​are recorded, and when the entire counting cycle is over, a certain mathematical method is used to process the recorded data. In an ideal situation without counting errors, the n sets of data points (N x(i) ,N s(i) ), where i = 1, 2, ..., n, that is, all these points are on the same straight line, and l can be represented by a linear function:

[0041] N s =a ideal ·N x +b ideal (1)

[0042] In the above formula, a ideal is the slope of the line l, b ideal is the intercept of the straight line l. Combined with the reference clock frequency f clk , we can calculate the actual frequency value f real for:

[0043]

[0044] In the actual measurement process, since the measured signal and the clock signal are asynchronous signals, that is, the rising edge of the clock signal does not completely coincide with the rising edge of the measured signal, the clock count value N s(i) There is a ±1 error, which is also called quantization noise. In order to improve the estimation accuracy of the slope of the straight line l, it is necessary to make full use of n data points for straight line fitting. In univariate linear regression analysis, the least squares method is the most commonly used data processing method. Its principle is to find the best function matching of the data by minimizing the sum of squares of errors. In the i-th measurement cycle, a set of data (N x(i) ,N s(i) ), where N x(i) is the accumulated count value of the signal counting register to be tested corresponding to the i-th timestamp, N s(i) is the accumulated count value of the clock signal counting register. x(i) The horizontal coordinate mapped to the rectangular coordinate system, N s(i)Mapped to the vertical axis. In the actual gate time, the measured signal count value N x Linear monotonically increasing, and the sampling point intervals follow a uniform distribution. After traversing n sets of data points, the fitting straight line obtained by the univariate linear regression equation should be:

[0045] N s =a·N x +b+ε (3)

[0046] In the above formula, a is the slope of the fitted line, and ε is the quantization error of each timestamp. Under normal circumstances, its mean is zero and it obeys the normal distribution. Then the i-th group of actual data points (N x(i) ,N s(i) ) is:

[0047] △N s(i) =N s(i) -(a·N x(i) +b) (4)

[0048] The residual sum of squares of n groups of actual data is calculated as:

[0049]

[0050] According to statistical knowledge, in parameter estimation, the least squares estimate is a linear unbiased estimate with the smallest variance. The above formula is used to obtain partial derivatives of the slope a and the intercept b:

[0051]

[0052] After the above formula is rearranged, the slope of the straight line estimated by the least squares method is:

[0053]

[0054] Find the slope of the fitted line Combined with the reference clock frequency f clk , the measured frequency value f can be calculated x :

[0055]

[0056] Formula (8) is the calculation formula of the original continuous timestamp frequency measurement method. This method combines the idea of ​​linear regression and makes full use of all data points in the counting process, making the frequency measurement accuracy better than the traditional counting method. However, since the rising edge of the measured signal does not completely coincide with the rising edge of the clock signal, there is a ±1 counting error of the clock signal.

[0057] In order to suppress the increase of the frequency measurement deterministic error caused by the increase of sampling rate in the continuous time stamp frequency measurement method, the frequency measurement sampling rate f sampele , the frequency of the signal to be measured freal With clock frequency f clk The continuous timestamp frequency measurement method obtains the frequency measurement accuracy by fitting the slope of the linear regression line, but it is limited by the gate time T. realgate The influence of sampling rate f sampele Increasing will lead to a decrease in the cycle count value m of the signal to be measured, and the accuracy of the slope of the univariate linear regression fitting line will decrease accordingly.

[0058] Therefore, the present invention proposes to cancel the gate time limit. When the measured frequency freal and the crystal oscillator main frequency fclk are constant, the frequency measurement error of the continuous timestamp is only related to the period count value m of the measured signal. At the same time, under the condition that the period count value m of the measured signal is not reduced, the idea of ​​sliding average is considered to improve the continuous timestamp frequency measurement method.

[0059] In the sliding average, the frequency value at each moment is calculated from the past (m-1) groups of data points (N x(k) ,N s(k) ), where k = 1, 2, ..., m-1, and the current m-th group of data points (N x(m) ,N s(m) ) A total of m sample points are used for linear fitting under univariate linear regression. When the m+1th group of data points is valid, it will replace the original 1st group of data points. When the m+2th group of data points is valid, it will replace the original 2nd group of data points, and so on.

[0060] Based on the continuous timestamp improved by the sliding average idea, by performing continuous straight line fitting under the sliding average of m sample points, the rising edge of the frequency signal to be measured can be used as the enable signal to update the slope of the straight line to be fitted, and then the resonant frequency of the accelerometer output can be calculated according to the main control clock frequency of the FPGA.

[0061] By canceling the preset gate, the frequency to be measured f real and the crystal oscillator main frequency f clk Under certain conditions, the frequency measurement error is linked to the period count value m of the signal to be measured, and the sampling rate f is suppressed. sample The impact brought by this is to achieve zero-bias noise suppression at the frequency measurement end. However, due to the cancellation of the gate, the sample data point (N x(k) ,N s(k) ) will always be in an infinitely accumulated incrementing state, which will eventually cause the register width of the corresponding counter inside the FPGA to overflow, thus severely limiting the effective working time of the frequency measurement module. In order to optimize register resources and frequency measurement working time, the incremental algorithm is used to eliminate the problem of infinite progressive iteration of register counts.

[0062] In this embodiment, the incremental data point update parameters are shown in Table 1.

[0063] Table 1 Incremental data point parameters optimized based on incremental algorithm

[0064] parameter The first data point The second data point … The mth data point <![CDATA[Count N of the signal to be measured x > <![CDATA[x1]]> <![CDATA[x2]]> … <![CDATA[x m <!-- 5 -->]]> <![CDATA[Clock signal count N s > <![CDATA[y1]]> <![CDATA[y2]]> … <![CDATA[y m ]]> <![CDATA[Increment of the signal to be measured ΔN x > <![CDATA[Δx1(x1)]]> <![CDATA[Δx2(x2-x1)]]> … <![CDATA[Δx m (x m -x m-1 )]]> <![CDATA[Clock signal increment ΔN s > <![CDATA[Δy1(y1)]]> <![CDATA[Δy2(y2-y1)]]> … <![CDATA[Δx m (x m -x m-1 )]]>

[0065] From this, we can get the conversion relationship between the count value N and the increment value △N:

[0066]

[0067] The formula for the slope of the known least squares fitting line is:

[0068]

[0069] Then according to formula (9), we can get:

[0070]

[0071] Similarly, formula (9) can be calculated to obtain:

[0072]

[0073] Because the count value of the signal to be measured satisfies x i =i, we have:

[0074]

[0075] include:

[0076]

[0077] According to the dual-port incremental RAM write address update timing diagram, the signal to be tested adopts incremental counting changes, that is, the count value of the signal to be tested satisfies x i =i, so we can get △x i =x i+1 -x i =(i+1)-i=1, that is, the increment △x to be measured is always a constant value of 1, and formula (14) can be simplified as:

[0078]

[0079] Similarly, formula (11) can be further simplified as:

[0080]

[0081] Substituting equation (15) and equation (16) into the denominator B2 of equation (10), we can obtain:

[0082]

[0083] According to formula (17), the denominator B2 is only related to the number m of sample points of the straight line to be fitted. Next, substitute formula (12), formula (13), and formula (16) into the numerator B1 of formula (10), and we can get:

[0084]

[0085] In summary, the expression of the slope of the fitting line can be rewritten as follows after combining the numerator B1 and the denominator B2 using the incremental algorithm:

[0086]

[0087] Find the slope of the fitted line Then, combined with the reference clock frequency f clk , the frequency value to be measured of the silicon micro-resonant accelerometer can be obtained.

[0088] Therefore, the slope of the m sample points fitted straight line after the incremental algorithm is implemented based on FPGA to optimize hardware resources is The implementation is rewritten as follows:

[0089]

[0090] Among them, △y is the incremental count value of the frequency to be measured, and C3 and C4 are the update coefficients after the rising edge of the frequency to be measured is enabled.

[0091] In this embodiment, the initialization update parameters of the incremental continuous timestamp frequency measurement method are as follows: Figure 4 As shown in the figure, before the number of sample points to be fitted reaches m, it is still in the power-on initialization state, and the RAM will store all incremental data of this stage. Until the number of sample points to be fitted reaches m, the state machine will enter the second stage of sample point update and replacement; in the first stage, the original coefficient formula corresponding to the first sample point to be fitted before the update is stored:

[0092]

[0093] Further, when the RAM memory initializes m incremental data points, it will enter the second stage. In this stage, when the new (m+1)th incremental data △y m+1 After the update, the original incremental data △y1 will be replaced, and the update coefficient of the corresponding incremental algorithm should be as follows: Figure 5 shown.

[0094]

[0095] The incremental continuous timestamp counting method based on sliding average of the present invention cancels the preset gate in the counting method principle, uses sliding average to suppress the random noise of frequency measurement based on the continuous timestamp frequency measurement principle, and uses incremental counting to replace incremental counting, thereby reducing the occupied resources of FPGA memory and solving the problem of limited working time of continuous timestamp under incremental counting. It suppresses the random noise of the frequency measurement end of the resonant accelerometer to a certain extent, and effectively improves the frequency measurement accuracy of the accelerometer.

[0096] S3, full-temperature modeling experiment: a full-temperature modeling experiment is performed on the silicon micro-resonant accelerometer prototype, wherein the hysteresis temperature change experiment is used for zero bias term modeling, and the full-temperature calibration experiment is used for scale factor term modeling; the resonator output frequency data is obtained according to step S2, and the temperature and temperature change rate data of the accelerometer prototype are recorded; the full-temperature calibration experiment steps for scale factor term modeling are as follows: the rotation angle λ of the test turntable is set to 90° and 270° in turn, corresponding to the accelerometer +1g, -1g four position point input, taking the temperature range of -40℃~60℃ as an example, a constant temperature change rate is set, and the following processes are repeated respectively:

[0097] (1) Set the temperature of the incubator to -40°C and power on the accelerometer prototype without sampling.

[0098] (2) After the incubator sensor reaches -40°C, continue to keep the temperature for 1 hour, and then start collecting data after the temperature is maintained;

[0099] (3) Raise the temperature of the incubator from -40°C to 60°C at a specified temperature change rate and keep it at 60°C for 1 hour;

[0100] (4) Turn off the power of the accelerometer prototype and save the frequency data and temperature data.

[0101] The steps of the hysteresis temperature change experiment for zero bias modeling are as follows: Taking the temperature range of -40℃ to 60℃ as an example, set a constant temperature change rate and conduct a full-temperature hysteresis experiment on the accelerometer at the +0g position:

[0102] (1) First, fix the accelerometer on a single-axis temperature-controlled turntable so that the acceleration sensitive direction is horizontal to the ground;

[0103] (2) Set the temperature of the temperature control box to 60°C and keep it at 60°C for 1 hour;

[0104] (3) One minute after the accelerometer is powered on, it starts collecting temperature and frequency data;

[0105] (4) Cool the incubator from 60°C to -40°C at a specified temperature change rate and keep it at -40°C for 1 hour;

[0106] (5) Raise the temperature of the incubator from -40°C to 60°C at a specified temperature change rate and keep it at 60°C for 1 hour;

[0107] (6) Turn off the power of the accelerometer prototype and save the frequency data, temperature and temperature change rate data.

[0108] In the full-temperature modeling experiment, the temperature of the accelerometer prototype is measured by a RTD-based temperature sensor encapsulated in the same package tube shell as the accelerometer prototype; the temperature range of the full-temperature test is -40°C to 60°C.

[0109] S4, establishment of prediction model for zero bias term and scale factor term: after obtaining sufficient experimental data, use temperature T and temperature change rate △T through a suitable regression prediction model to fit the changing trend of scale factor K(T) and zero bias △f0(T,△T).

[0110] According to the model of the zero bias term changing with temperature T and temperature change rate △T obtained in step S3, it is recorded as △f0(T,△T), and the model establishment method is based on the data fitting of the BP neural network, wherein the data fitting of the prediction model under the dual input of temperature and temperature change rate under the BP neural network is based on the data fitting of the prediction model, and the neural network toolbox provided by MATLAB is used to complete the training of the neural network, with temperature and temperature change rate as independent variables, and the frequency difference output of the accelerometer prototype as the dependent variable, and the hidden layer nodes of the neural network are set to 10, and the Levenberg-Marquardt algorithm is used for recursive training. 80% of the training data is used to construct the BP neural network, 10% of the verification data is used to supervise the effectiveness of the training during the training process, and 10% of the test data is used to test the effect of the trained model; according to the model of the scaling factor term changing with temperature T in step S3, it is recorded as K(T), and the model establishment method is based on polynomial data fitting.

[0111] For the zero bias term, under a fixed acceleration input of +0g, a hysteresis temperature change experiment is performed to obtain the variation trend of the zero bias output frequency difference of the accelerometer with temperature and temperature change rate. A BP neural network is used to input temperature and temperature change rate as independent variables, and the frequency difference output of the accelerometer prototype, that is, the zero bias term, is used as the dependent variable output to complete the dual variable compensation prediction model based on the BP neural network. For the scale factor term, under a fixed acceleration input of ±1g, a full-temperature calibration experiment is performed to obtain the variation trend of the accelerometer scale factor with temperature. The least squares method is used to fit the scale factor of the accelerometer prototype through temperature to complete the single temperature variable compensation prediction model based on the polynomial.

[0112] S5, establishment of zero bias drift compensation model: Substitute the zero bias △f0(T,△T) and scale factor K(T) obtained in step 4 into the zero bias drift compensation model, and the output after acceleration compensation is:

[0113]

[0114] In the static mathematical model of the accelerometer, its zero bias and scale factor are only related to temperature-related factors and have nothing to do with the acceleration input; when the acceleration input is a constant, the zero bias △f0 and the scale factor K can both be expressed as functions related to temperature; based on the zero bias term and the scale factor term, the zero bias drift is compensated online; the zero bias term, under a fixed acceleration input of +0g, utilizes the variation trend of the accelerometer zero bias output frequency difference with temperature and temperature change rate to complete a temperature and temperature change rate dual variable compensation prediction model based on a neural network; the scale factor term, under a fixed acceleration input of ±1g, utilizes the variation trend of the accelerometer output frequency difference with temperature to complete a polynomial-based single temperature compensation prediction model of the scale factor term K.

[0115] S6, signal output: convert the compensated acceleration signal into a digital signal output and transmit it to the host computer through the serial port to achieve zero bias error suppression of the silicon micro-resonant accelerometer.

[0116] In summary, the method of the present invention uses an incremental continuous timestamp counting method based on sliding average to complete the frequency measurement of the resonant frequency signal, suppressing the frequency noise at the frequency measurement end; conducting a full-temperature modeling experiment on the accelerometer prototype, measuring the temperature and temperature change rate of the sensitive structure in real time through a temperature sensor, and recording the resonant frequency, temperature and temperature change rate related data; establishing a prediction model for the zero bias term and scale factor term of the accelerometer output frequency difference with temperature and temperature change rate, suppressing the zero bias error caused by temperature drift; converting the compensated acceleration signal into a digital signal output, and realizing the zero bias error suppression of the silicon micro-resonant accelerometer in real time and accurately. This method can improve the zero bias performance of the silicon micro-resonant accelerometer, compensate for the zero bias drift caused by temperature factors in real time, and avoid the disadvantage that the traditional single temperature variable compensation method cannot suppress the variable temperature hysteresis error.

[0117] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope of the claims of the present invention.

Claims

1. A method for suppressing zero bias error of a silicon micro-resonant accelerometer, characterized in that: The incremental continuous timestamp counting method based on sliding average is used to measure the frequency of the resonant frequency signal, a zero bias drift compensation model is established, the zero bias drift is compensated online, and the compensated acceleration signal is converted into a digital signal output to achieve zero bias error suppression of the silicon micro-resonant accelerometer. The incremental continuous timestamp counting method based on sliding average is specifically as follows: the prefabricated gate in the continuous timestamp counting method is cancelled, and when the rising edge of the square wave signal to be measured is detected, the FPGA samples to obtain a new timestamp event, obtains a new data point, replaces and discards the original old data point, and uses RAM resources to execute the update requirements of the sample point data of the frequency to be measured; in the incremental continuous timestamp counting method based on sliding average, according to the requirements of updating the sample point data, the slope of the fitted straight line of the m sample points after the incremental algorithm is implemented based on FPGA to optimize the hardware resources is The implementation is as follows: Among them, C3 and C4 are the update coefficients after the rising edge of the frequency to be measured is enabled; The zero bias drift compensation model: the zero bias term and the scale factor term that change with the temperature factor are modeled by the variable temperature hysteresis experiment and the full temperature calibration experiment respectively, and the zero bias drift is compensated online; wherein, the zero bias term is obtained by a two-variable prediction model based on the BP neural network, and the scale factor term is obtained by a single prediction model based on a polynomial; the calculation method of the zero bias drift compensation model is: Wherein, △f is the output frequency difference, T is the temperature, △T is the temperature change rate, △f0(T,△T) is the zero bias term dual variable prediction model, K(T) is the scale factor term single variable prediction model, and a(△f,T,△T) is the acceleration after compensation; The zero bias term dual variable prediction model: utilizes the variation trend of the zero bias output frequency difference of the accelerometer with the temperature and the temperature change rate, takes the temperature and the temperature change rate as the independent variable input, and the zero bias term as the dependent variable output, to construct a dual variable compensation prediction model based on the BP neural network; The scale factor single variable prediction model utilizes the variation trend of the accelerometer scale factor with temperature, uses the least square method to fit the scale factor of the accelerometer prototype through temperature, and constructs a polynomial-based single temperature variable compensation prediction model.

2. The method for suppressing zero bias error of a silicon micro-resonant accelerometer according to claim 1, characterized in that: The steps include: S1, resonant frequency signal generation: using a closed-loop control loop to drive the resonator, the closed-loop control loop at least uses automatic gain control and phase-locked loop technology to track the resonant frequency signal of the resonator in real time and output two resonant frequency signals; S2, frequency measurement: the frequency of the dual-path resonant frequency signal of the resonant accelerometer is measured by using an incremental continuous timestamp counting method based on sliding average; S3, full-temperature modeling experiment: a full-temperature modeling experiment is performed on the silicon micro-resonant accelerometer prototype, wherein the hysteresis temperature change experiment is used for zero bias term modeling, and the full-temperature calibration experiment is used for scale factor term modeling; the resonator output frequency data is obtained according to step S2, and the temperature and temperature change rate data of the accelerometer prototype are recorded; S4, establishing a prediction model for zero bias term and scale factor term: according to the zero bias term and scale factor term obtained in step S3, establishing a zero bias term dual variable prediction model and a scale factor term univariate prediction model, wherein the zero bias term dual variable prediction model is based on data fitting of a BP neural network, and the scale factor term univariate model is based on data fitting of a polynomial; S5, establishing a zero bias drift compensation model: according to the zero bias term and the scale factor term obtained in step S4, a zero bias drift compensation model is established, and the output of the model is an acceleration signal a(△f,T,△T): S6, signal output: convert the compensated acceleration signal into a digital signal output and transmit it to the host computer through the serial port to achieve zero bias error suppression of the silicon micro-resonant accelerometer.

3. The method for suppressing zero bias error of a silicon micro-resonant accelerometer according to claim 2, characterized in that: In the full-temperature modeling experiment of S3, the temperature of the accelerometer prototype is measured by a RTD-based temperature sensor encapsulated in the same package tube shell as the accelerometer prototype; the temperature range of the full-temperature test is -40°C to 60°C.

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