A method and system for compensating scale nonlinearity error of a hemispherical resonator gyro

Abstract

The application relates to the technical field of hemispherical resonator gyroscopes, and provides a hemispherical resonator gyroscope scale nonlinearity error compensation method and system, which comprises the following steps: installing a hemispherical resonator gyroscope on a turntable, the input shaft of the hemispherical resonator gyroscope coincides with the rotating shaft of the turntable, controlling the turntable to rotate at two speeds with equal values and opposite directions respectively, recording the resonator gyroscope mode angle output by the hemispherical resonator gyroscope, based on the flat plate capacitance detection principle of the hemispherical resonator gyroscope, deducing an error model by combining the complete Taylor expansion, the Fourier series expansion and the binomial theorem with the relationship between the precession angular velocity and the mode angle of the hemispherical resonator gyroscope, performing multiple linear fitting according to the resonator gyroscope mode angle and the error model, solving the scale nonlinearity term according to the identifiable parameters of the nonlinearity error, and performing feedback compensation according to the scale nonlinearity term. The application can estimate the scale nonlinearity error and perform feedback compensation, thereby improving the output precision of the hemispherical resonator gyroscope.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hemispherical resonator gyroscopes, and in particular to a hemispherical resonator gyroscope scale nonlinearity error compensation method and system. BACKGROUND

[0002] The hemispherical resonator gyroscope is a solid-state high-precision gyroscope based on the Coriolis vibration effect, and is one of the core devices in the field of inertial navigation. Its core advantages are no mechanical moving parts, high reliability, long service life, and strong anti-interference capability. It has a wide application prospect in the field of inertial technology engineering. The principle of vibration signal detection of the hemispherical resonator gyroscope is to convert the vibration displacement signal to a voltage signal through a flat plate capacitor, which is called flat plate capacitor detection. The hemispherical shell and the detection electrode form a capacitor. When the resonator vibrates, the distance between the two electrode plates changes with the vibration of the resonator, causing the capacitance value of the capacitor to change, thereby causing the voltage to change. The vibration position of the resonator can be obtained according to the voltage change, and then the input detection and accurate control of the gyroscope can be performed.

[0003] At present, due to the limitations of manufacturing process defects, the resonator is not uniform in processing, and there is uneven processing between the resonator and the detection electrode, thereby causing scale nonlinearity error, which affects the output precision of the gyroscope. The existing method mainly compensates for the linear scale error, and does not systematically consider the nonlinearity error caused by the nonlinearity of the capacitor, multiple frequency harmonics and other factors. After compensation, the precision still cannot meet the demand of high-end applications. The parameter identification precision is low. The existing calibration method often relies on data analysis of a single angular velocity input, which is easily affected by noise and transient interference terms, and cannot accurately identify the nonlinearity term coefficient. Some high-precision compensation schemes need to rely on complex hardware circuits or a large amount of calibration data, which has the problems of high cost and long calibration period, and is difficult to be popularized in engineering. SUMMARY

[0004] The present application aims to at least solve one of the technical problems in the related art. To this end, the present application provides a hemispherical resonator gyroscope scale nonlinearity error compensation method and system, which can estimate the scale nonlinearity error and perform feedback compensation, thereby improving the output precision of the hemispherical resonator gyroscope.

[0005] The present application provides a hemispherical resonator gyroscope scale nonlinearity error compensation method, comprising:

[0006] S1: mounting the hemispherical resonator gyroscope on a turntable, wherein the input shaft of the hemispherical resonator gyroscope coincides with the rotating shaft of the turntable;

[0007] S2: controlling the turntable to rotate at two speeds with equal values and opposite directions respectively, and recording the resonator mode angle output by the hemispherical resonator gyroscope;

[0008] S3: Based on the principle of plate capacitance detection using a hemispherical resonant gyroscope, an error model is derived by combining the relationship between the precession angular velocity and mode angle of the hemispherical resonant gyroscope through complete Taylor expansion, Fourier series expansion, and binomial theorem. The calculation expression of the error model is as follows:

[0009]

[0010] in, The precession angular velocity of the resonant gyroscope mode. The Bryan coefficient, The axial damping of the harmonic oscillator is uneven. The angle between the damping axis and the electrode axis. The mode angle of the resonant gyroscope. Input angular velocity from the outside. The nonlinear error coefficient of the first sine term. The nonlinear error coefficient of the first cosine term. The nonlinear error coefficient of the second sine term. The nonlinear error coefficient of the second cosine term. For the first Nonlinear error coefficient, For the first sine or the first Cosine;

[0011] S4: Based on the resonant gyroscope mode angle and error model obtained in step S2, perform multivariate linear fitting to obtain identifiable parameters of nonlinear error;

[0012] S5: Solve for the scaling nonlinear term based on the identifiable parameters of the nonlinear error, and perform feedback compensation based on the scaling nonlinear term.

[0013] Furthermore, step S4 includes:

[0014] S41: Move the turntable... When the hemispherical resonant gyroscope rotates, the mode angle of the resonant gyroscope output is substituted into the error model to obtain the first error model;

[0015] S42: Perform multiple linear regression fitting on the first error model to obtain the first fitting model, solve the first fitting model, and obtain the identifiable parameters of the first nonlinear error;

[0016] S43: Move the turntable... When the hemispherical resonant gyroscope rotates, the mode angle of the resonant gyroscope output is substituted into the error model to obtain the second error model;

[0017] S44: Perform multiple linear regression fitting on the second error model to obtain the second fitting model, solve the second fitting model, and obtain the identifiable parameters of the second nonlinear error;

[0018] The identifiable parameters of the non-linear error include the identifiable parameters of the first non-linear error and the identifiable parameters of the second non-linear error.

[0019] Further, the scale non-linear term is solved in combination with the first error model, the first fitting model, the second error model, the second fitting model, the identifiable parameters of the first non-linear error and the identifiable parameters of the second non-linear error.

[0020] Further, the relationship between the precession angular velocity of the hemispherical resonator gyro and the mode angle is:

[0021]

[0022] wherein, is the mode precession angular velocity of the resonator gyro, is the Bryan coefficient, is the external input angular velocity, is the non-uniform axial damping of the resonator, is the included angle between the damping axis and the electrode axis, is the mode angle of the resonator gyro.

[0023] Further, the identifiable parameters of the non-linear error are solved by the least square method.

[0024] Further, in the S2 step, the rotary table is controlled to rotate at two speeds with equal values and opposite directions respectively, and continuous data covering N resonator mode periods are recorded to eliminate the influence of noise in the data samples.

[0025] Further, the fundamental source of the non-linear error in the scale of the hemispherical resonator gyro is the non-linear error between the voltage and the vibration.

[0026] The application also provides a hemispherical resonator gyro scale non-linear error compensation system for executing the above-mentioned hemispherical resonator gyro scale non-linear error compensation method, which comprises:

[0027] An installation module is configured to install the hemispherical resonator gyro on the rotary table, and the input shaft of the hemispherical resonator gyro coincides with the rotary shaft of the rotary table.

[0028] A data acquisition module is configured to control the rotary table to rotate at two speeds with equal values and opposite directions respectively, and record the resonator gyro mode angle output by the hemispherical resonator gyro.

[0029] A model derivation module is configured to derive an error model based on the flat plate capacitance detection principle of the hemispherical resonator gyro, by combining the relationship between the precession angular velocity and the mode angle of the hemispherical resonator gyro through complete Taylor expansion, Fourier series expansion and binomial theorem.

[0030] a fitting module, which performs multiple linear fitting according to the mode angle of the resonant gyroscope obtained in the S2 step and the error model, to obtain identifiable parameters of the nonlinear error;

[0031] a feedback compensation module, which solves a scale nonlinear term according to the identifiable parameters of the nonlinear error and performs feedback compensation according to the scale nonlinear term.

[0032] The above one or more technical solutions in the embodiments of the present application have at least one of the following technical effects:

[0033] The present application significantly improves the output precision of the gyroscope, solves the precision restriction problem caused by manufacturing process defects such as uneven processing of the resonator and uneven gap between electrodes, and makes the output precision of the gyroscope meet the stringent requirements of high-end inertial measurement, navigation control and other scenes.

[0034] The present application performs deep modeling based on the core detection principle of the hemispherical resonator gyroscope, performs complete Taylor expansion on the capacitance expression, retains the small nonlinear terms, combines the Fourier series expansion and the binomial theorem, and accurately reveals that the nonlinear relationship between the voltage vibration displacement is the root cause of the scale nonlinear error; comprehensively covers the multi-order harmonic nonlinearities caused by capacitance detection, and takes into account the influence of the uneven process defects of the resonator axial damping, realizes the error root quantity and full error type coverage, provides a solid theoretical support for accurate compensation, and avoids the problem of treating the symptoms but not the root cause of the traditional compensation method.

[0035] The present application effectively eliminates the noise influence in the data sample by controlling the rotation of the turntable at two different speeds and recording long enough data, establishes an error model based on the data of two rotations, accurately identifies the scale nonlinear term coefficient through parameter fitting and model combination, avoids the identification deviation caused by single data acquisition, ensures the accuracy of the error parameters, and provides a reliable basis for subsequent compensation.

[0036] The compensation process of the present application is based on the output data and inherent parameters of the gyroscope, does not need to modify the hardware of the gyroscope, can be directly applied to various hemispherical resonator gyroscopes based on flat plate capacitance detection, has strong compatibility, wide application range, and the high-precision hemispherical resonator gyroscope after compensation can meet the wide application requirements in the field of inertial technology engineering.

[0037] Additional aspects and advantages of the present application will be in part apparent and in part pointed out hereinafter. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to make the technical solutions in the present application or prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are some embodiments of the present application, and all other embodiments obtained by those of ordinary skill in the art without any creative work on the premise of the accompanying drawings are within the protection scope of the present application.

[0039] Figure 1 is a flowchart of a scale nonlinearity error compensation method of a hemispherical resonator gyroscope provided by the present application.

[0040] Figure 2 is a schematic diagram of a hemispherical resonator gyroscope vibration signal detection principle provided by the present application.

[0041] Figure 3 is a schematic diagram of a scale nonlinearity error of a hemispherical resonator gyroscope before compensation provided by the present application.

[0042] Figure 4 is a schematic diagram of a scale nonlinearity error of a hemispherical resonator gyroscope after compensation provided by the present application.

[0043] Figure 5 is a structural schematic diagram of a scale nonlinearity error compensation system of a hemispherical resonator gyroscope provided by the present application.

[0044] Reference signs:

[0045] 101, installation module; 102, data acquisition module; 103, model derivation module; 104, fitting module; 105, feedback compensation module. DETAILED DESCRIPTION

[0046] In order to make the technical solutions in the present application or prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are some embodiments of the present application, and all other embodiments obtained by those of ordinary skill in the art without any creative work on the premise of the accompanying drawings are within the protection scope of the present application. The following embodiments are used to illustrate the present application, but cannot be used to limit the scope of the present application.

[0047] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the embodiments of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples without contradiction.

[0048] The following will be described in combination with Figures 1 to 5 A scale nonlinearity error compensation method and system of a hemispherical resonator gyroscope are described.

[0049] As Figure 1 shown, a scale nonlinearity error compensation method of a hemispherical resonator gyroscope comprises:

[0050] S1: mounting the hemispherical resonator gyroscope on a turntable, the input shaft of the hemispherical resonator gyroscope coincides with the rotating shaft of the turntable;

[0051] By coinciding the input shaft of the hemispherical resonator gyroscope with the rotating shaft of the turntable, it can be ensured that the hemispherical resonator gyroscope only detects the pure target angular velocity provided by the turntable, and the collected data can truly reflect the correlation between the scale nonlinearity error of the gyroscope itself and the input angular velocity without additional interference terms.

[0052] S2: controlling the turntable to rotate at two speeds with equal values and opposite directions respectively, and recording the resonator mode angle output by the hemispherical resonator gyroscope;

[0053] The turntable is controlled to rotate at two speeds with equal values and opposite directions respectively, and continuous data covering N resonator mode periods are recorded to eliminate the influence of noise in the data samples.

[0054] By creating comparable and separable data conditions through symmetric input, the complex multi-parameter error model is converted into a solvable equation set, the target error and interference error can be accurately separated, and the error coefficients are determined.

[0055] Recording continuous data covering N resonator mode periods can obtain long enough data, and the influence of noise in the data samples can be eliminated by statistics.

[0056] S3: based on the flat plate capacitance detection principle of the hemispherical resonator gyroscope, the error model is derived by combining the relationship between the precession angular velocity and the mode angle of the hemispherical resonator gyroscope through complete Taylor expansion, Fourier series expansion and binomial theorem.

[0057] The error model includes a scaling nonlinearity error term, axial damping unevenness of the harmonic oscillator, an angle-related error term between the damping axis and the electrode axis, and a multi-harmonic nonlinearity error term.

[0058] The principle of hemispherical resonant gyroscope vibration signal detection is as follows: Figure 2 As shown, the vibration displacement signal is converted into a voltage signal through a parallel plate capacitor. The resonator hemispherical shell and the detection electrode form a capacitor. When the resonator vibrates, the distance between the two plates changes with the vibration of the resonator, causing the capacitance value to change, which in turn causes the voltage to change.

[0059] When there is no vibration, the gap between the resonator and the detection electrode is The parallel-plate capacitor formed by the detection electrode and the resonator has no current output, and the amplifier input resistance... The voltage on it is 0. To detect the voltage across the resistor.

[0060] When the harmonic oscillator vibrates, the magnitude of the parallel plate capacitance is:

[0061]

[0062] in, It is a parallel plate capacitor. The relative permittivity, The vacuum permittivity, For the area of ​​the flat plate, This represents the gap between the resonator and the detection electrode when the resonator is not vibrating. for The vibration displacement at any given moment;

[0063] In some specific embodiments of the present invention , .

[0064] Can exist Taylor expansion, the computational expression is:

[0065]

[0066] set up , To determine the amplitude of the harmonic oscillation, the current is... The equation of motion for a hemispherical harmonic gyroscope is expressed as follows:

[0067]

[0068] in, For charge quantity, To detect the DC voltage across the resistor, Angular frequency; Figure 2In, To detect the AC voltage on the resistor.

[0069] The output voltage after the amplifier is:

[0070]

[0071] where, is the input resistance of the amplifier.

[0072] From the above formula, it can be seen that there is a linear relationship between the voltage detected by the capacitor and the vibration displacement.

[0073] The relationship between the precession angular velocity of the hemispherical resonator gyroscope and the mode angle is:

[0074]

[0075] where, is the mode precession angular velocity of the resonator gyroscope, is the Bryan coefficient, is the input angular velocity from the outside world, is the non-uniformity of the axial damping of the resonator, is the included angle between the damping axis and the electrode axis, is the mode angle of the resonator gyroscope.

[0076] Equation (2) When the Taylor expansion is performed at , small quantities are ignored, and the complete Taylor expansion is:

[0077]

[0078] where, is the capacitance of the plate when it is at the equilibrium position, is the normalized amplitude of the vibration displacement, is the summation order of the power series;

[0079] The Fourier series expansion of is:

[0080]

[0081] where, is the imaginary unit;

[0082] Combining the binomial theorem:

[0083]

[0084] where, is the first added term of the binomial, is the second added term of the binomial, is the binomial coefficient, is the factorial symbol, is the index variable, is the order of summation of the power series;

[0085] After the Taylor series expansion of the capacitance expression, the power series is replaced by the sine and cosine functions, and the capacitance expression is rearranged, which shows that:

[0086]

[0087] where, is the coefficient of the cosine component of the double frequency, is the coefficient of the cosine component of the double frequency; The Fourier series of the variable capacitance is:

[0088]

[0089] Definition:

[0090]

[0091] where, is the amplitude of the zeroth harmonic,

[0092] is the amplitude of the odd harmonics, is the amplitude of the even harmonics, then:

[0093] In particular,

[0094]

[0095] where, is the amplitude of the first harmonic;

[0096] In particular,

[0097] where, is the amplitude of the second harmonic, is the amplitude of the third harmonic;

[0098] Thus, when the parallel plate capacitor is used to detect sinusoidal motion, the capacitance change function contains an infinite number of harmonics of the driving frequency, is the amplitude of the harmonic, in particular,

[0099]

[0100] When the non-linear error is not considered, the voltage and vibration are linearly related, and the calculation expression is:

[0101] ​​​

[0102] where, is the amplitude constant of output voltage;

[0103] Considering nonlinear error,

[0104]

[0105] where, is the output voltage considering nonlinear error;

[0106] There is nonlinear error between voltage and vibration, which is the fundamental source of nonlinear error in the scale of hemispherical resonator gyroscope.

[0107] Corresponding to the vibration amplitude, the antinode point and the node point satisfy:

[0108]

[0109] where, is the antinode point, is the node point, is the vibration amplitude of the resonator.

[0110] Combining equation (17) and equation (18), it is obvious that the scale has nonlinear error of the term;

[0111] Equation (5) can be optimized as:

[0112]

[0113] where, is the precession angular velocity of the resonator gyroscope mode, is the Bryan coefficient, is the non-uniform axial damping of the resonator, is the included angle between the damping axis and the electrode axis, is the mode angle of the resonator gyroscope, is the input angular velocity from the outside, is the first sine term nonlinear error coefficient, is the first cosine term nonlinear error coefficient, is the second sine term nonlinear error coefficient, is the second cosine term nonlinear error coefficient, is the nonlinear error coefficient, is the sine or cosine.

[0114] Equation (19) is the error model.

[0115] For example:

[0116]

[0117] S4: According to the resonant gyro mode angle and the error model, a multi-element linear fitting is performed to obtain identifiable parameters of the nonlinear error;

[0118] S41: The turntable is rotated at The resonant gyro mode angle of the hemispherical resonant gyro output when the turntable is rotated at

[0119]

[0120] wherein, is the resonant gyro mode angle speed of the hemispherical resonant gyro output when the turntable is rotated at

[0121] S42: A multi-element linear regression fitting is performed on the first error model to obtain a first fitting model, and the first fitting model is solved to obtain identifiable parameters of the first nonlinear error;

[0122] The least square method is used to perform a multi-element linear regression fitting on formula (21) to obtain a first fitting model, and the calculation expression is:

[0123]

[0124] wherein, is the first constant term identifiable parameter, is the first 2 times frequency cosine term identifiable parameter, is the first 4 times frequency cosine term identifiable parameter, is the first 2 times frequency sine term identifiable parameter, is the first 4 times frequency sine term identifiable parameter;

[0125] The identifiable parameters of the first nonlinear error are fitted by the least square method, and the identifiable parameters of the first nonlinear error include .

[0126] S43: The resonant gyro mode angle of the hemispherical resonant gyro output when the turntable is rotated at is substituted into the error model to obtain a second error model, and the calculation expression is:

[0127]

[0128] wherein, is the resonant gyro mode angle speed of the hemispherical resonant gyro output when the turntable is rotated at

[0129] ​​​S44: performing multiple linear regression fitting on the second error model to obtain a second fitting model, and solving the second fitting model to obtain identifiable parameters of the second nonlinear error;

[0130] The multiple linear regression fitting is performed on the formula (23) to obtain a second fitting model, and the calculation expression is:

[0131]

[0132] wherein, is a second constant term identifiable parameter, is a second 2 times frequency cosine term identifiable parameter, is a second 4 times frequency cosine term identifiable parameter, is a second 2 times frequency sine term identifiable parameter, is a second 4 times frequency sine term identifiable parameter;

[0133] The identifiable parameters of the second nonlinear error are fitted by the least square method, and the identifiable parameters of the second nonlinear error include .

[0134] S5: identifying the scale nonlinear term according to the identifiable parameters, and performing feedback compensation according to the scale nonlinear term;

[0135] The scale nonlinear term is solved in combination with the first error model, the first fitting model, the second error model, the second fitting model, and the identifiable parameters of the first nonlinear error and the identifiable parameters of the second nonlinear error;

[0136] In combination with the formula (21), the formula (22), the formula (23), and the formula (24), the following can be obtained:

[0137]

[0138] The scale nonlinear term includes , , , .

[0139] The scale nonlinear term is input into the model of the formula (20) to perform compensation, and the gyro scale nonlinear error after the compensation meets the accuracy requirement.

[0140] As shown in Figure 3 , the scale nonlinear error before the compensation has a great fluctuation amplitude, the error in the initial stage is even close to 1000ppm, and the error subsequently fluctuates around 580ppm for a long time, and the error at 165.8s is still 577.1ppm, and the overall stability is poor and the error magnitude is high.

[0141] As shown in Figure 4As shown, the compensation error amplitude is greatly narrowed, and the fluctuation is smaller and smaller over time. The scale nonlinearity error is only 1.18ppm at 178.8s. The scale nonlinearity error after compensation is better than 2ppm. The accuracy and stability are greatly improved.

[0142] As shown in the drawings, Figure 5 A scale nonlinearity error compensation system of a hemispherical resonator gyroscope is used to execute the scale nonlinearity error compensation method of the hemispherical resonator gyroscope, and comprises:

[0143] The installation module 101 installs the hemispherical resonator gyroscope on a turntable, and the input shaft of the hemispherical resonator gyroscope coincides with the rotating shaft of the turntable;

[0144] The data acquisition module 102 controls the turntable to rotate at two speeds with equal values and opposite directions respectively, and records the resonator mode angle output by the hemispherical resonator gyroscope;

[0145] The model derivation module 103 derives the error model based on the flat plate capacitance detection principle of the hemispherical resonator gyroscope, through complete Taylor expansion, Fourier series expansion, and binomial theorem in combination with the relationship between the precession angular velocity and the mode angle of the hemispherical resonator gyroscope;

[0146] The fitting module 104 performs multivariate linear fitting according to the resonator mode angle obtained in the S2 step and the error model, to obtain identifiable parameters of the nonlinearity error;

[0147] The feedback compensation module 105 solves the scale nonlinearity term according to the identifiable parameters of the nonlinearity error, and performs feedback compensation according to the scale nonlinearity term.

[0148] Through the cooperative work of the above modules, the present application expands the deep modeling based on the core detection principle of the hemispherical resonator gyroscope, accurately reveals that the nonlinearity relationship of the voltage vibration displacement is the fundamental source of the scale nonlinearity error by performing complete Taylor expansion on the capacitance expression, retaining the nonlinearity small quantity term, combining the Fourier series expansion and the binomial theorem, comprehensively covers the multi-order harmonic nonlinearity caused by the capacitance detection, and takes into account the influence of the process defects of the axial damping of the resonator, significantly improves the output accuracy of the gyroscope, solves the accuracy restriction problem caused by the manufacturing process defects such as uneven processing of the resonator and uneven gap between the electrodes, makes the output accuracy of the gyroscope meet the strict requirements of high-end inertial measurement, navigation control and other scenes, realizes the error root source quantization and full error type coverage, provides a solid theoretical support for accurate compensation, and avoids the problem of treating the symptoms but not the root cause in the traditional compensation method.

[0149] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for compensating for nonlinear scaling errors in a hemispherical resonant gyroscope, characterized in that, include: S1: The hemispherical resonant gyroscope is mounted on the turntable, and the input axis of the hemispherical resonant gyroscope coincides with the rotation axis of the turntable; S2: Control the turntable to rotate at two speeds with equal values ​​but opposite directions, and record the mode angle of the resonant gyroscope output by the hemispherical resonant gyroscope; S3: Based on the principle of plate capacitance detection using a hemispherical resonant gyroscope, an error model is derived by combining the relationship between the precession angular velocity and mode angle of the hemispherical resonant gyroscope through complete Taylor expansion, Fourier series expansion, and binomial theorem. The calculation expression of the error model is as follows: in, The precession angular velocity of the resonant gyroscope mode. The Bryan coefficient, The axial damping of the harmonic oscillator is uneven. The angle between the damping axis and the electrode axis. The mode angle of the resonant gyroscope. Input angular velocity from the outside. The nonlinear error coefficient of the first sine term. The nonlinear error coefficient of the first cosine term. The nonlinear error coefficient of the second sine term. The nonlinear error coefficient of the second cosine term. For the first Nonlinear error coefficient, For the first sine or the first Cosine; S4: Based on the resonant gyroscope mode angle and error model obtained in step S2, perform multivariate linear fitting to obtain identifiable parameters of nonlinear error; S5: Solve for the scaling nonlinear term based on the identifiable parameters of the nonlinear error, and perform feedback compensation based on the scaling nonlinear term.

2. The method for compensating for nonlinear scaling errors in a hemispherical resonant gyroscope according to claim 1, characterized in that, Step S4 includes: S41: Move the turntable... When the hemispherical resonant gyroscope rotates, the mode angle of the resonant gyroscope output is substituted into the error model to obtain the first error model; S42: Perform multiple linear regression fitting on the first error model to obtain the first fitting model, solve the first fitting model, and obtain the identifiable parameters of the first nonlinear error; S43: Move the turntable... When the hemispherical resonant gyroscope rotates, the mode angle of the resonant gyroscope output is substituted into the error model to obtain the second error model; S44: Perform multiple linear regression fitting on the second error model to obtain the second fitting model, solve the second fitting model, and obtain the identifiable parameters of the second nonlinear error; The identifiable parameters of the nonlinear error include identifiable parameters of the first nonlinear error and identifiable parameters of the second nonlinear error.

3. The method for compensating for nonlinear scaling errors of a hemispherical resonant gyroscope according to claim 2, characterized in that, The scaling nonlinear term is solved by combining the first error model, the first fitting model, the second error model, the second fitting model, and the identifiable parameters of the first nonlinear error and the second nonlinear error.

4. The method for compensating for nonlinear scaling errors of a hemispherical resonant gyroscope according to claim 1, characterized in that, The relationship between the precession angular velocity and the mode angle of a hemispherical resonant gyroscope is as follows: in, The precession angular velocity of the resonant gyroscope mode. The Bryan coefficient, Input angular velocity from the outside. The axial damping of the harmonic oscillator is uneven. The angle between the damping axis and the electrode axis. This is the mode angle of the resonant gyroscope.

5. The method for compensating for nonlinear scaling errors of a hemispherical resonant gyroscope according to claim 1, characterized in that, The identifiable parameters of the nonlinear error are solved using the least squares method.

6. The method for compensating for nonlinear scaling errors of a hemispherical resonant gyroscope according to claim 1, characterized in that, In step S2, the turntable is controlled to rotate at two speeds that are equal in value but opposite in direction, and continuous data covering N harmonic oscillator mode cycles is recorded to eliminate the influence of noise in the data samples.

7. The method for compensating for nonlinear scaling errors of a hemispherical resonant gyroscope according to claim 1, characterized in that, The fundamental source of nonlinear error in the scaling of a hemispherical resonant gyroscope is the nonlinear error between voltage and vibration.

8. A scaling nonlinearity compensation system for a hemispherical resonant gyroscope, characterized in that, To perform a hemispherical resonant gyroscope scaling nonlinearity error compensation method as described in any one of claims 1 to 7, comprising: The mounting module mounts the hemispherical resonant gyroscope onto a turntable, wherein the input axis of the hemispherical resonant gyroscope coincides with the rotation axis of the turntable. The data acquisition module controls the turntable to rotate at two speeds that are equal in value but opposite in direction, and records the mode angle of the resonant gyroscope output by the hemispherical resonant gyroscope. The model derivation module is based on the plate capacitance detection principle of the hemispherical resonant gyroscope. It derives the error model by combining the relationship between the precession angular velocity and the mode angle of the hemispherical resonant gyroscope with complete Taylor expansion, Fourier series expansion and binomial theorem. The fitting module performs multivariate linear fitting based on the resonant gyroscope mode angle and error model obtained in step S2 to obtain identifiable parameters of nonlinear error. The feedback compensation module solves for the scaling nonlinear term based on the identifiable parameters of the nonlinear error, and performs feedback compensation based on the scaling nonlinear term.

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