A method for performance parameter identification and electrostatic adjustment of a micro-hemispherical resonant gyroscope

Abstract

A method for identifying the performance parameters of a micro-hemispherical resonant gyroscope and performing electrostatic adjustment, relating to the field of micro-hemispherical resonant gyroscopes. The present invention aims to address the problems of complex operation, low adjustment efficiency, and low adjustment accuracy in current electrostatic adjustment methods. The present invention comprises the following steps: obtaining an amplitude-frequency characteristic curve of a micro-hemispherical resonant structure; using the amplitude-frequency characteristic curve to perform a test to obtain the circular frequency mismatch Δω and the quality factor Q of the micro-hemispherical resonant structure; and using the excitation frequency f corresponding to the two peaks on the amplitude-frequency characteristic curve obtained in step 2. x 、f y The corresponding circular frequency ω x 、ω y The method selects a direct-term tuning electrode and obtains the relationship between the direct-term tuning voltage and frequency splitting. A nonlinear optimization method is used to fit the relationship between the direct-term tuning voltage and frequency splitting to identify gyroscope performance parameters. The gyroscope performance parameters are then used to determine the coupled-term tuning electrode and its optimal tuning voltage. This invention is used to achieve high-precision electrostatic tuning of a micro-hemispherical resonant gyroscope.

Description

Technical Field

[0001] The present invention relates to the field of micro-hemispherical resonant gyroscopes, and in particular to a method for identifying performance parameters of a micro-hemispherical resonant gyroscope and performing electrostatic adjustment. Background Art

[0002] The micro-hemispherical resonant gyroscope is a new type of MEMS gyroscope. It is processed using MEMS based on the traditional hemispherical resonant gyroscope. Therefore, it inherits the advantages of the traditional hemispherical resonant gyroscope, such as large dynamic range, high precision, long life and good impact resistance. At the same time, it has the technical advantages of miniaturization, low cost and low power consumption of MEMS technology. It is currently the MEMS gyroscope with the highest precision and the best development prospects, and has very important military value.

[0003] A micro-hemispherical resonant gyroscope (MHRG) utilizes a micro-hemispherical resonant structure to sense changes in external angular rate. When the resonant structure is in a second-order vibration state, the presence of an external angular rate causes the Coriolis force to act on the resonant structure, causing a standing wave to rotate at a constant rate in the direction opposite to the external angular rate. By measuring the rotation angle of the standing wave, the angle of rotation of the carrier relative to the inertial space can be determined. Ideally, the circumferential vibration frequency of the MHRG is uniform. However, factors such as the inconsistent softening of the fused quartz during high-temperature blowtorch molding, unstable blowtorch airflow, and loose fit between the fused quartz and the graphite mold can cause dimensional and symmetry errors in the resonant structure, resulting in inconsistent circumferential vibration frequencies of the MHRG, known as frequency distortion. Frequency distortion can cause orthogonal drift in the gyroscope, limiting its accuracy. Therefore, electrostatic trimming is essential for the assembled MHRG to suppress orthogonal drift.

[0004] Currently, frequency adjustment methods primarily include mechanical adjustment and electrostatic adjustment. While mechanical adjustment permanently reduces the gyroscope's frequency distortion, it also reduces the quality factor of the resonant structure, thereby affecting its vibration performance. Electrostatic adjustment does not affect the quality factor of the resonant structure and allows operation of the assembled gyroscope. However, existing electrostatic adjustment methods are complex to operate and have low adjustment efficiency, failing to meet the demand for high-precision electrostatic adjustment. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems of complex operation, low adjustment efficiency and low adjustment precision in the current electrostatic adjustment method, and to propose a method for identifying the performance parameters of a micro-hemispherical resonant gyroscope and performing electrostatic adjustment.

[0006] A method for identifying performance parameters of a micro-hemispherical resonant gyroscope and performing electrostatic adjustment is as follows:

[0007] Step 1: Fix the micro-hemispherical resonant gyroscope on the test circuit, connect the electrode signal interface to the test circuit, perform a modal test on the micro-hemispherical resonant structure, and obtain an amplitude-frequency characteristic curve of the micro-hemispherical resonant structure;

[0008] Step 2: Use the amplitude-frequency characteristic curve to test and obtain the circular frequency mismatch of the micro-hemispherical resonant structure Δω=ω x -ω y and quality factor Q;

[0009] Among them, ω x 、ω y They are f x 、f y The corresponding circular frequency is in rad / s; f x 、f y are the excitation frequencies corresponding to the two peaks on the amplitude-frequency characteristic curve, in Hz;

[0010] Step 3: Use the ω obtained in step 2 x 、ω y , select the direct term trimming electrode and obtain the relationship between the direct term trimming voltage and frequency splitting;

[0011] Step 4: Using a nonlinear optimization method, fit the relationship between the direct term adjustment voltage and the frequency splitting obtained in step 3 to identify the gyro performance parameters;

[0012] The gyro performance parameters include: the gyro's rigid axis azimuth angle θ ω , electrostatic adjustment coefficient υ and direct optimal adjustment voltage U diropt ;

[0013] Step 5: Use the gyro performance parameters to obtain the coupling term adjustment electrode and its optimal adjustment voltage U cropt ;

[0014] Step 6: Use the direct term obtained in step 3 to adjust the electrode, the gyro performance parameters obtained in step 4, and the direct term to adjust the optimal adjustment voltage U diropt , Step 5 obtains the coupling term adjustment electrode and its optimal adjustment voltage U cropt Realize electrostatic adjustment of micro-hemispherical resonant gyroscope.

[0015] The beneficial effects of the present invention are:

[0016] 1. This invention proposes a method for identifying and electrostatically tuning the performance parameters of a micro-hemispherical resonant gyroscope. Based on the identification equation for gyro electrostatic tuning, a nonlinear optimization method is used to simultaneously identify the gyro's rigid axis azimuth and electrode tuning coefficients. Ultimately, the optimal tuning voltage applied by the gyro's tuning electrodes is determined, achieving high-precision electrostatic tuning of the gyroscope. This method overcomes the problems of existing electrostatic tuning, such as complex operation, low tuning efficiency, low tuning accuracy, and the inability to accurately identify performance parameters after the gyroscope is assembled.

[0017] 2. The present invention significantly improves the efficiency of electrostatic adjustment and the accuracy of rigid axis azimuth angle identification. During the test, there is no need to use a laser vibrometer. Only the measurement and control module needs to be used to test the gyroscope. It does not rely on external detection equipment such as a laser vibrometer. Therefore, the present invention has strong adaptability and wide application. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Flowchart of the present invention;

[0019] Figure 2 This is a curve diagram of the fitting results of the direct term adjustment voltage and frequency decomposition. DETAILED DESCRIPTION

[0020] Specific implementation method 1: Figure 1 As shown, the specific process of the method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope in this embodiment is as follows:

[0021] Step 1: Fix the micro-hemispherical resonant gyroscope on the test circuit, connect the electrode signal interface to the test circuit, perform a modal test on the micro-hemispherical resonant structure, and obtain an amplitude-frequency characteristic curve of the micro-hemispherical resonant structure;

[0022] Step 2: Use the amplitude-frequency characteristic curve to test and obtain the circular frequency mismatch of the micro-hemispherical resonant structure Δω=ω x -ω y And the quality factor Q:

[0023] Step 2.1 The relationship between the quality factor Q of the resonant structure and the amplitude-frequency characteristics can be explained by a first-order model, specifically:

[0024] Get the amplitude ν of the particle velocity in steady-state vibration m :

[0025]

[0026] f=ω / (2π)

[0027] f0=ω0 / (2π)

[0028] Where f0 is the natural frequency of vibration, f is the excitation frequency, ω0 and ω are the circular frequencies corresponding to f0 and f, in rad / s, f0 and f are in Hz, δ is the damping coefficient of the system, and p is the amplitude of the excitation force;

[0029] When ω=ω0, that is, f=f0, the amplitude of velocity vibration reaches the maximum, v m The maximum value of is expressed as:

[0030]

[0031] Step 22: Based on the amplitude-frequency characteristic curve of the micro-hemispherical resonant structure obtained in step 1 and the (v m ) max Get the quality factor Q:

[0032]

[0033]

[0034]

[0035]

[0036] Among them, f1 and f2 are the amplitude-frequency characteristic curves of v m Pick The horizontal axis at the time of , BW = f2-f1 is the passband width of the spectrum;

[0037] Step 2 and 3: Obtain the excitation frequency f corresponding to the two peaks on the amplitude-frequency characteristic curve according to the amplitude-frequency characteristic curve of the micro-hemispherical resonant structure. x 、f y The corresponding radian value ω x 、ω y The circular frequency mismatch Δω of the resonant structure is:

[0038] Δω=ω x -ω y =2πΔf

[0039] Δf=f x -f y

[0040] The frequency decomposition of the resonant structure is the difference between the two natural frequencies on the amplitude-frequency characteristic curve, that is, Δf = f x -f y , Δω is the circular frequency mismatch, f x 、f y are the excitation frequencies corresponding to the two peaks on the amplitude-frequency characteristic curve, in Hz, and ω x =2πf x ωy =2πf y f x 、f y The corresponding circular frequency is in rad / s.

[0041] Step 3: Use the excitation frequency f corresponding to the two peaks on the amplitude-frequency characteristic curve obtained in step 2 x 、f y The corresponding radian value ω x 、ω y , select the direct term trim electrode and obtain the relationship between the direct term trim voltage and frequency splitting:

[0042] Step 3.1. Obtain the vibration form of the standing wave during the electrostatic adjustment process:

[0043] First, obtain the vibration distribution of the radial displacement standing wave of the resonant structure under electrostatic excitation when there is no frequency splitting in the resonant structure:

[0044] w(θ,t)=A0cos2(θ-θ0)cosω0t

[0045] Where A0 is the initial amplitude, ω0 is the vibration frequency, θ0 is the position of the standing wave relative to the excitation electrode, θ is the position of the detection electrode relative to the excitation electrode, and t is the time;

[0046] Then, due to the influence of frequency splitting on the vibration characteristics, the vibration distribution of the standing wave at the end of the electrostatic excitation process is expressed as follows:

[0047] w(θ,t)=A0cos2(θ-θ ω )cos2(θ0-θ ω )cosω x t+A0sin2(θ-θ ω )sin2(θ0-θ ω )sinω y t

[0048] Among them, θ ω is the azimuth angle of the oscillator's rigid axis;

[0049] During the electrostatic adjustment process, the detection electrode and the excitation electrode are separated by 180°, so the vibration form of the standing wave can be simplified:

[0050] w(θ,t)=A0(cos2θ ω ) 2 cosω x t+A0(sin2θ ω ) 2 sinω y t

[0051] Step 3.2: Analyze the standing wave vibration form obtained in step 3.1 to obtain the range of the azimuth angle of the rigid axis of the resonant structure:

[0052] Modal analysis of the vibration form of the above standing wave shows that when the excitation frequency is ω x When the vibration amplitude detected is A x =A0(cos2θ ω ) 2 , similarly when the excitation frequency is ω y When the vibration amplitude detected is A y =A0(sin2θ ω ) 2 , so the approximate range of the azimuth angle of the rigid axis of the resonant structure can be obtained by the amplitude ratio of the two modes, as follows:

[0053]

[0054] According to the above, the rigid axis azimuth angle θ ω The value range is between 0 and π / 4;

[0055] The rigid axis azimuth angle calculated in this step has a limited value range, but it can still guide the selection of the gyro direct term adjustment electrode, so as to facilitate the subsequent rapid and accurate identification of the gyro's rigid axis azimuth angle and electrode adjustment coefficient.

[0056] Step 33: Determine the electrodes for gyro direct term adjustment based on the interval of the resonant rigid axis azimuth angle obtained in step 32:

[0057] When θ ω ∈[0,22.5°), the electrode with the same direction as the detection electrode is selected as the electrode for gyro direct adjustment;

[0058] When θ ω ∈(22.5°,45°], the electrode in the direction orthogonal to the detection electrode is selected as the electrode for gyro direct adjustment;

[0059] If θ ω If the angle is 22.5°, there is no need to use any direct term electrode for adjustment;

[0060] Step 34: Apply a DC voltage to the gyro direct-term adjustment electrode determined in step 33, and perform a modal test on the gyro to obtain the relationship between the direct-term adjustment voltage and frequency splitting.

[0061] Step 4: Use the nonlinear optimization method to fit the relationship between the direct term trimming voltage and frequency splitting obtained in step 3, and identify the gyro's rigid axis azimuth, electrostatic trimming coefficient, and the optimal direct term trimming voltage:

[0062] Step 4.1. Obtain the equation of motion of the oscillator:

[0063]

[0064]

[0065]

[0066] ωΔω=(ω x 2 -ω y 2 ) / 2

[0067] ω 2 =(ω x 2 +ω y 2 ) / 2

[0068] Where k is the precession factor, θ ω is the rigid axis angle of the resonant structure, F y and F x is the electrostatic force caused by the flat electrode in the two modes, F xi and F yi is the electrostatic force projection of the i-th flat electrode on the two modes, K is the electrostatic force coefficient, m0 is the equivalent mass of the resonator, d is the average capacitance gap, U is the voltage difference between the end face of the resonator and the flat electrode, and the intermediate variable γ = K / 2d 3 m0, x, y are the vibration displacements of the two modes of the oscillator, is the vibration velocity of the two modes of the oscillator, is the acceleration of the two-mode vibration of the resonator, τ is the time constant of the resonator, Ω is the input angular rate, and i∈[1,16] is the label of the plate electrode;

[0069] Step 42: Divide the 16 flat electrodes of the micro-hemispherical resonant gyroscope into four groups, complete the diagonal adjustment (direct term adjustment) and off-diagonal adjustment (coupling term adjustment) of the dynamic model stiffness matrix, and obtain the identification parameters of the electrostatic adjustment;

[0070] Step 421: Divide the 16 flat electrodes of the micro-hemispherical resonant gyroscope into four groups, and obtain the electrostatic forces exerted by the four groups of electrodes on the resonator, specifically:

[0071] U x Group: cos4θ(i)=1,θ(i)=90n°,n∈Z, the electrostatic force exerted on the oscillator is:

[0072]

[0073] Where n is a positive integer, It's U x The electrostatic force exerted by the group on the resonator;

[0074] U y Group: cos4θ(i)=-1,θ(i)=π / 4+πn / 2,n∈Z, the electrostatic force exerted on the oscillator is:

[0075]

[0076] in, It's U y The electrostatic force exerted by the group on the resonator;

[0077] U c Group: sin4θ(i)=1,θ(i)=π / 8+πn / 2,n∈Z, the electrostatic force exerted on the oscillator is:

[0078]

[0079] in, It's U c The electrostatic force exerted by the group on the resonator;

[0080] U s Group: sin4θ(i)=-1,θ(i)=π / 8+πn / 2,n∈Z, the electrostatic force exerted on the oscillator is:

[0081]

[0082] Among them, Ux, Uy, Uc, and Us represent the voltages applied to the Ux, Uy, Uc, and Us electrode groups, respectively. It's U s The electrostatic force exerted by the group on the resonator;

[0083] Step 422: Substitute the electrostatic forces exerted on the resonator by the four groups of electrodes obtained in step 421 into the motion equation of the resonator obtained in step 41 to obtain the stiffness matrix of the resonator under each electrostatic adjustment:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Among them, k 11 、k 12 、k21 、k 22 is an element in the matrix, j∈[1,4] is the number of accumulations;

[0090] Step 423: Obtain the frequency decomposition rewriting form of the resonator, i.e., the identification equation of the gyro modal parameters and the electrostatic adjustment coefficient, based on the stiffness matrix of the resonator under each electrostatic adjustment obtained in step 422:

[0091]

[0092] Wherein, υ = 2γ / ω is the electrostatic adjustment coefficient;

[0093] Step 424: Rewrite the identification equations of the gyro modal parameters and electrostatic adjustment coefficients obtained in step 423 into the following form:

[0094]

[0095] From the above formula, we can see that U c Group and U s The group of electrodes is used to adjust the modal coupling term so that there is no frequency coupling between the two modes. x Group and U y The electrode group is responsible for the direct adjustment of the mode, so that the vibration frequencies of the two modes tend to be consistent, thus achieving mode matching. Therefore, different adjustment electrodes will be used for different rigid axis azimuths. In order to facilitate subsequent control and compensation, the direct adjustment electrode U x and U y Each group uses one electrode to complete the electrostatic adjustment, U c and U s Two electrodes are used per group to complete the electrostatic trimming.

[0096] Step 425: Based on the rewritten gyro modal parameters and electrostatic adjustment coefficients obtained in step 424, the gyro rigid axis azimuth angle θ is calculated using a nonlinear optimization method. ω , electrostatic adjustment coefficient υ and direct optimal adjustment voltage U diropt Perform identification and obtain parameter identification results:

[0097] S1: Discretize the direct term of the identification equation obtained in step 424 to obtain the following formula:

[0098]

[0099] Where l is the serial number of the experimental point, N(l) is the set of zero-mean interference and noise signals;

[0100] S2: Use the principle of minimum sum of squared errors to establish the objective function J based on the Δω(l) obtained in S1 z, as follows:

[0101]

[0102] Among them, N z is the total number of experimental points, Δω z (l) is the actual frequency decomposition of the gyro measured by modal analysis, and l is the number of the experimental point;

[0103] S3: Use the simplex method to obtain J z The minimum value of the rigid axis azimuth θ of the gyroscope is obtained ω And the electrostatic adjustment coefficient υ;

[0104] S4: Use the identified rigid axis azimuth and electrostatic adjustment coefficient to obtain the optimal adjustment voltage of the direct term:

[0105]

[0106] Step 5: Use the gyro performance parameters to obtain the coupling term adjustment electrode and its optimal adjustment voltage:

[0107] Step 51: Determine the gyro coupling term and adjust the electrode according to the interval of the resonant rigid axis azimuth angle obtained in step 425:

[0108] When sin4θ ω When >0, the electrodes of group Uc are selected as the electrodes for gyro direct adjustment;

[0109] When sin4θ ω When <0, the electrodes of the Us group are selected as the electrodes for direct adjustment of the gyro;

[0110] When sin4θ ω When =0, no coupling electrode set is required for adjustment.

[0111] Step 52: Use gyro performance parameters to obtain the optimal adjustment voltage for the coupling term:

[0112] Step 6: Direct term adjustment electrode obtained in step 3, gyro performance parameters obtained in step 4 and direct term adjustment optimal adjustment voltage U diropt , Step 5 obtains the optimal adjustment voltage U for the coupling term adjustment cropt Realize high-precision electrostatic adjustment of the micro-hemispherical resonant gyroscope.

[0113] Example:

[0114] Step 1: fix the micro-hemispherical resonant gyroscope on the test circuit, and connect the electrode signal interface to the test circuit;

[0115] Step 2: xTwo electrodes in the micro-hemisphere are used as detection electrodes and one electrode is used as the excitation electrode of the gyroscope. The modal test of the micro-hemisphere resonant structure is carried out to observe the amplitude-frequency characteristic curve of the micro-hemisphere resonant structure.

[0116] Step 3: The frequency decomposition Δf and the quality factor Q of the micro-hemispherical resonant structure are tested using the amplitude-frequency characteristic curve. The test results show that the initial frequency decomposition Δf of the resonant structure is 11.067 Hz and the quality factor is 100,000.

[0117] Step 4, selecting the corresponding adjustment electrode through the amplitude-frequency characteristic curve to perform direct adjustment of frequency splitting;

[0118] The specific process of adjusting the gyro frequency cracking direct item is as follows:

[0119] S1: Determine the selection of direct term electrodes. In this process, the vibration amplitude detected at the low natural frequency obtained by modal analysis is A y =0.0020V, the natural frequency detected at the high natural frequency is A x =0.0053V, passed The calculated rigid axis azimuth is about 15.96°, so the direct term electrode U is selected in the same direction as the detection electrode. x Perform direct term adjustments for frequency splitting.

[0120] S2: Determine the direct adjustment electrode U x Afterwards, a DC voltage was applied to the electrodes to perform a modal test on the gyroscope. Five groups of experiments were repeated for each trimming voltage to obtain the average value of the frequency cracking. The corresponding relationship between the direct trimming voltage and the frequency cracking was recorded, as shown in Table 1.

[0121] Table 1 Relationship between direct adjustment voltage and frequency cracking

[0122]

[0123]

[0124] Step 5: Fit the direct term adjustment data points using a nonlinear optimization method to identify the gyro's rigid axis azimuth, electrostatic adjustment coefficient, and optimal direct term adjustment voltage.

[0125] The specific identification steps are as follows:

[0126] S1: Using electrode U in direct term adjustment x To achieve this, the identification equation is discretized for the direct voltage term to obtain:

[0127]

[0128] Where n is the serial number of the experimental point, and N(n) is the set of zero-mean interference and noise signals.

[0129] S2: Assume that the actual frequency decomposition of the gyro is measured to be Δω through modal analysis z (n), according to the principle of minimum sum of square errors, the target J can be established z function:

[0130]

[0131] Then the simplex method (NMS) was used to obtain J z The minimum value of the gyro's rigid axis azimuth θ is identified ω =-12.0125° and electrostatic adjustment coefficient υ = 0.0023, the fitting results of direct adjustment voltage and frequency decomposition are as follows Figure 2 shown.

[0132] S3: Use the identified rigid axis azimuth and electrostatic adjustment coefficient to obtain the optimal adjustment voltage of the direct term:

[0133]

[0134] Step 6: Using the gyroscope performance parameters to obtain the coupling term adjustment electrode and its optimal voltage, to achieve high-precision electrostatic adjustment of the micro-hemispherical resonant gyroscope.

[0135] The rigid axis azimuth angle θ is obtained from the above identification results ω =-12.0125°, from step 5 we know that we need to select the adjustment electrode U s To achieve the adjustment of the frequency splitting coupling term, the optimal adjustment voltage of the coupling term is:

[0136]

[0137] The optimal values of the direct and coupled trimming voltages were applied to the trimming electrodes of the gyroscope, and the frequency splitting of the gyroscope was tested. The test results showed that the frequency splitting was reduced from 11.067 Hz to 0.06 Hz after electrostatic trimming. This demonstrates that the method of the present invention can identify and electrostatically trim gyroscope performance parameters. The present invention significantly improves the efficiency of electrostatic trimming and the accuracy of rigid axis azimuth angle identification. During the test, a laser vibrometer is not required; only the measurement and control module is required to test the gyroscope. External testing equipment such as a laser vibrometer is completely independent of the present invention. Therefore, the present invention has strong adaptability and wide application.

Claims

1. A method for identifying performance parameters of a micro-hemispherical resonant gyroscope and electrostatic adjustment, characterized in that The specific process of the method is: Step 1: Fix the micro-hemispherical resonant gyroscope on the test circuit, connect the electrode signal interface to the test circuit, perform a modal test on the micro-hemispherical resonant structure, and obtain an amplitude-frequency characteristic curve of the micro-hemispherical resonant structure; Step 2: Use the amplitude-frequency characteristic curve to test and obtain the circular frequency mismatch of the micro-hemispherical resonant structure Δω=ω x -ω y and quality factor Q; Among them, ω x 、ω y They are f x 、f y The corresponding circular frequency; f x 、f y are the excitation frequencies corresponding to the two peaks on the amplitude-frequency characteristic curve; Step 3: Use the ω obtained in step 2 x 、ω y , select the direct term trimming electrode and obtain the relationship between the direct term trimming voltage and frequency splitting; Step 4: Using a nonlinear optimization method, fit the relationship between the direct term adjustment voltage and the frequency splitting obtained in step 3 to identify the gyro performance parameters; The gyro performance parameters include: the gyro's rigid axis azimuth angle θ ω , electrostatic adjustment coefficient υ and direct optimal adjustment voltage U diropt ; Step 5: Use the gyro performance parameters to obtain the coupling term adjustment electrode and its optimal adjustment voltage U cropt ; Step 6: Use the direct term obtained in step 3 to adjust the electrode and the direct term obtained in step 4 to adjust the optimal voltage U diropt And the coupling term obtained in step 5 to adjust the electrode and its optimal adjustment voltage U cropt Realize electrostatic adjustment of micro-hemispherical resonant gyroscope.

2. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 1, characterized in that: The step 2 of using the amplitude-frequency characteristic curve to test and obtain the quality factor Q of the micro-hemispherical resonant structure includes the following steps: Step 2.1 Obtain the maximum velocity amplitude of the particle in steady-state vibration (v m ) max : First, obtain the amplitude ν of the particle velocity in the steady-state vibration m : f=ω / (2π) f0=ω0 / (2π) Where f0 is the natural frequency of vibration, f is the excitation frequency, ω0 and ω are the circular frequencies corresponding to f0 and f, and the unit of f0 and f is Hz. δ is the damping coefficient of the system, and p is the amplitude of the excitation force. Then, let ω=ω0, f=f0, and obtain the maximum velocity amplitude of the particle in steady-state vibration (v m ) max : Step 22: According to the (v obtained in step 21 m ) max Get the quality factor Q: Among them, f1 and f2 are the amplitude-frequency characteristic curves of v m Pick The horizontal axis at the time, BW = f2-f1 is the passband width of the spectrum.

3. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 2, characterized in that: In the step 2, the amplitude-frequency characteristic curve is used to test and obtain the circular frequency mismatch value of the micro-hemispherical resonant structure Δω=ω x -ω y , as follows: Give = oh x -oh y =2πΔf Δf=f x -f y The frequency decomposition of the resonant structure is the difference between the two natural frequencies on the amplitude-frequency characteristic curve, that is, Δf = f x -f y , Δω is the circular frequency mismatch, f x 、f y are the excitation frequencies corresponding to the two peaks on the amplitude-frequency characteristic curve, ω x =2πf x ω y =2πf y f x 、f y The corresponding circular frequency.

4. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 3, characterized in that: The step three uses step two to obtain ω x 、ω y , selecting a direct-term trimming electrode and obtaining a relationship between the direct-term trimming voltage and the frequency splitting, including the following steps: Step 3.

1. Obtain the vibration form equation of the standing wave during the electrostatic adjustment process, specifically: First, obtain the vibration distribution of the radial displacement standing wave of the resonant structure under electrostatic excitation when there is no frequency splitting in the resonant structure: w(θ,t)=A0cos2(θ-θ0)cosω0t Where A0 is the initial amplitude, ω0 is the vibration frequency, θ0 is the position of the standing wave relative to the excitation electrode, θ is the position of the detection electrode relative to the excitation electrode, and t is the time; Then, the vibration distribution of the radial displacement standing wave of the resonant structure under electrostatic excitation is rewritten as the vibration distribution form of the standing wave at the end of the electrostatic excitation process: w(θ,t)=A0cos2(θ-θ ω )cos2(θ0-θ ω )cosω x t+A0sin2(θ-θ ω )sin2(θ0-θ ω )sinω y t Finally, simplify w(θ,t) and rewrite w(θ,t) as follows: w(θ,t)=A0(cos2θ ω ) 2 I'm sorry. x t+A0(sin2θ ω ) 2 sin y t Among them, θ ω is the rigid axis azimuth; Step 32: Use the vibration form equation obtained in step 31 to obtain the interval [0,π / 4] of the azimuth angle of the rigid axis of the resonant structure; Step 33: determining the gyro direct term adjustment electrode according to the interval of the resonant rigid axis azimuth angle obtained in step 32; Step 34: Apply a DC voltage to the gyro direct-term adjustment electrode determined in step 33, and perform a modal test on the gyro to obtain the relationship between the direct-term adjustment voltage and frequency splitting.

5. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 4, characterized in that: In step 32, the vibration form equation obtained in step 31 is used to obtain the interval [0, π / 4] of the azimuth angle of the rigid axis of the resonant structure, specifically: First, get A x and θ ω The relational expression of A y and θ ω The relational expression is: A x =A0(cos2θ ω ) 2 (1) A y =A0(sin2θ ω ) 2 (2) Then, according to formula (1) and formula (2), the following formula is obtained: Among them, A x The excitation frequency is ω x The vibration amplitude at y The excitation frequency is ω y The vibration amplitude at ; Finally, due to A x and A y is a positive number, thus determining tan2θ ω The value range is [0,+∞], so the interval of the azimuth angle of the rigid axis of the resonant structure is [0,π / 4].

6. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 5, characterized in that: The step 33 in which the gyro direct term adjustment electrode is determined according to the interval of the resonant rigid axis azimuth angle obtained in step 32 is specifically as follows: When θ ω ∈[0,22.5°), the electrode with the same direction as the detection electrode is selected as the electrode for gyro direct adjustment; When θ ω ∈(22.5°,45°], the electrode in the direction orthogonal to the detection electrode is selected as the electrode for gyro direct adjustment; If θ ω If the angle is 22.5°, no direct term electrode is used for adjustment.

7. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 6, characterized in that: The fourth step uses a nonlinear optimization method to fit the relationship between the direct term trimming voltage obtained in the third step and the frequency splitting, and identifies the gyroscope's rigid axis azimuth, electrostatic trimming coefficient, and the optimal direct term trimming voltage, including the following steps: Step 4.

1. Obtain the equation of motion of the oscillator, as follows: ωδω=(ω x 2 -oh y 2 ) / 2 oh 2 =(ω x 2 +oh y 2 ) / 2 γ=K / 2d 3 m0 Where k is the precession factor, F y and F x is the electrostatic force caused by the flat electrode in the two modes, F xi and F yi is the electrostatic force projection of the i-th plate electrode on the two modes, K is the electrostatic force coefficient, m0 is the equivalent mass of the resonator, d is the average capacitance gap, U is the voltage difference between the end face of the resonator and the plate electrode, γ is the intermediate variable, x, y are the vibration displacements of the two modes of the resonator, is the vibration velocity of the two modes of the oscillator, is the acceleration of the two-mode vibration of the resonator, τ is the time constant of the resonator, Ω is the input angular rate, and i∈[1,16] is the label of the plate electrode; Step 42: Divide the flat electrodes of the micro-hemispherical resonant gyroscope into four groups, and use the grouped electrodes to adjust the azimuth angle θ of the gyroscope's rigid axis. ω , electrostatic adjustment coefficient υ and direct optimal adjustment voltage U diropt To identify.

8. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 7, characterized in that: In the step 42, the plate electrodes of the micro-hemispherical resonant gyroscope are divided into four groups, and the grouped electrodes are used to adjust the azimuth angle θ of the gyroscope rigid axis. ω , electrostatic adjustment coefficient υ and direct optimal adjustment voltage U diropt Identification includes the following steps: Step 421: Divide the 16 flat electrodes of the micro-hemispherical resonant gyroscope into four groups, and obtain the electrostatic forces exerted by the four groups of electrodes on the resonator, specifically: U x Group: cos4θ(i)=1,θ(i)=90n°,n∈Z, the electrostatic force exerted on the oscillator is: Where n is a positive integer, It's U x The electrostatic force exerted by the group on the resonator; U y Group: cos4θ(i)=-1,θ(i)=π / 4+πn / 2,n∈Z, the electrostatic force exerted on the oscillator is: in, It's U y The electrostatic force exerted by the group on the resonator; U c Group: sin4θ(i)=1,θ(i)=π / 8+πn / 2,n∈Z, the electrostatic force exerted on the oscillator is: in, It's U c The electrostatic force exerted by the group on the resonator; U s Group: sin4θ(i)=-1,θ(i)=π / 8+πn / 2,n∈Z, the electrostatic force exerted on the oscillator is: Among them, Ux, Uy, Uc, and Us represent the voltages applied to the Ux, Uy, Uc, and Us electrode groups, respectively. It's U s The electrostatic force exerted by the group on the resonator; Step 422: Substitute the electrostatic forces exerted by the four groups of electrodes on the resonator obtained in step 421 into the motion equation of the resonator obtained in step 41 to obtain the stiffness matrix K of the resonator under each electrostatic adjustment. k : Among them, k 11 、k 12 、k 21 、k 22 is an element in the matrix, j∈[1,4] is the number of accumulations; Step 423: Obtain the frequency decomposition rewriting form of the resonator, i.e., the identification equation of the gyro modal parameters and the electrostatic adjustment coefficient, based on the stiffness matrix of the resonator under each electrostatic adjustment obtained in step 422: Wherein, υ = 2γ / ω is the electrostatic adjustment coefficient; Step 424: Rewrite the identification equations of the gyro modal parameters and electrostatic adjustment coefficients obtained in step 423 into the following form: Step 425: Based on the rewritten gyro modal parameters and electrostatic adjustment coefficients obtained in step 424, the gyro rigid axis azimuth angle θ is calculated using a nonlinear optimization method. ω , electrostatic adjustment coefficient υ and direct optimal adjustment voltage U diropt Perform identification and obtain parameter identification results.

9. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 8, characterized in that: The identification equation of the rewritten gyro modal parameters and electrostatic adjustment coefficients obtained in step 424 in step 425 uses a nonlinear optimization method to calculate the azimuth angle θ of the gyro rigid axis. ω , electrostatic adjustment coefficient υ and direct optimal adjustment voltage U diropt Performing identification to obtain parameter identification results includes the following steps: S1. Discretize the direct term of the identification equation obtained in step 424 to obtain the following formula: Where l is the serial number of the experimental point, N(l) is the set of zero-mean interference and noise signals; S2, using the principle of minimum sum of squared errors to establish the objective function J based on the Δω(l) obtained in S1 z , as follows: Among them, N z is the total number of experimental points, Δω z (l) The actual frequency decomposition of the gyro is measured by modal analysis; S3. Use the simplex method to obtain J z The minimum value of the rigid axis azimuth θ of the gyroscope is obtained ω And the electrostatic adjustment coefficient υ; S4. Use the identified rigid axis azimuth and electrostatic adjustment coefficient to obtain the optimal adjustment voltage of the direct term:

10. The method for identifying performance parameters and electrostatic adjustment of a micro-hemispherical resonator gyroscope according to claim 9, characterized in that: In step 5, the coupling term is used to adjust the electrode and its optimal adjustment voltage U by using the gyro performance parameters. cropt , including the following steps: Step 51: Determine the gyro coupling term and adjust the electrode according to the interval of the resonant rigid axis azimuth angle obtained in step 425: When sin4θ ω When >0, the electrodes of group Uc are selected as the electrodes for gyro direct adjustment; When sin4θ ω When <0, the electrodes of the Us group are selected as the electrodes for direct adjustment of the gyro; When sin4θ ω =0, no need to use any set of coupling term electrodes for adjustment; Step 52: Use gyro performance parameters to obtain the optimal adjustment voltage for the coupling term:

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