Harmonic oscillator characteristic parameter identification method of hemispherical resonator gyroscope

Abstract

The invention discloses a harmonic oscillator characteristic parameter identification method of a hemispherical resonator gyroscope, and belongs to the technical field of inertial devices. The objective of the invention is to solve the problem of long time consumption of a traditional harmonic oscillator characteristic parameter identification method. The method specifically comprises the following steps: step 1, according to a basic control equation of the hemispherical resonator gyroscope, respectively obtaining an amplitude control force when amplitude control is applied and an orthogonal control force when orthogonal control is applied; step 2, exciting the standing wave azimuth angle to perform virtual precession in the forward direction and the reverse direction respectively, and in the forward and reverse virtual precession processes, continuously collecting the demodulation amount, the amplitude control force and the orthogonal control force output by the hemispherical resonator gyroscope through an upper computer; identifying coefficients of the amplitude control force and the orthogonal control force according to the acquired demodulation quantity, the amplitude control force and the orthogonal control force; and step 3, calculating harmonic oscillator characteristic parameters of the hemispherical resonator gyroscope according to an identification result in the step 2. The method can be applied to harmonic oscillator characteristic parameter identification.

Description

Technical Field

[0001] The present invention belongs to the technical field of inertial devices, and particularly relates to a method for identifying the characteristic parameters of a resonator of a hemispherical resonant gyroscope. Background Art

[0002] A hemispherical resonant gyroscope is a vibration gyroscope that uses the Coriolis effect to detect changes in external angles or angular rates. Due to its high precision and high reliability, it is widely used in fields such as aerospace and navigation, and has become one of the mainstream inertial devices.

[0003] The core component of a hemispherical resonant gyroscope is the hemispherical resonator inside the gyroscope. The quality factor (Q), quality factor non-uniformity (ΔQ), and frequency splitting (Δω) of the resonator are the key characteristic parameters for measuring the vibration performance of the resonator. Among them: the quality factor (Q) represents the ability of the resonator to store its own vibration energy. The higher the Q value, the stronger the ability of the gyroscope to maintain vibration, and the smaller the compensation of external energy required; the quality factor non-uniformity (ΔQ) represents the degree of asymmetry of the resonator material and processing. The smaller ΔQ is, the smaller the dead zone threshold of the gyroscope and the higher the angular velocity resolution; the frequency splitting (Δω) represents the difference in the eigen-vibration angular frequencies of the resonator in two degrees of freedom. The Δω of a perfectly symmetric resonator should be zero. The smaller Δω is, the higher the sensitivity of the gyroscope.

[0004] Therefore, it is necessary to identify the quality factor (Q), quality factor non-uniformity (ΔQ), and frequency splitting (Δω) of the resonator during the production and processing of hemispherical resonant gyroscopes. However, it takes a long time to identify the characteristic parameters of the resonator using traditional methods. Therefore, it is necessary to propose a method for quickly and accurately identifying the characteristic parameters of the resonator in order to screen out gyroscopes with excellent performance and provide a guiding direction for the improvement of processing technology. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem of the long time-consuming traditional method for identifying the characteristic parameters of a resonator, and to propose a method for identifying the characteristic parameters of a resonator of a hemispherical resonant gyroscope.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a method for identifying the characteristic parameters of a resonator of a hemispherical resonant gyroscope, the method specifically includes the following steps:

[0007] Step 1: According to the basic control equation of the hemispherical resonant gyroscope, obtain the amplitude control force when applying amplitude control and the orthogonal control force when applying orthogonal control respectively;

[0008] Step 2: After driving the hemispherical resonator gyroscope to start oscillating, the azimuth angles of the exciting standing waves precess virtually in the forward and reverse directions respectively. During the forward and reverse virtual precession processes, the demodulation quantity, amplitude control force, and quadrature control force output by the hemispherical resonator gyroscope are continuously collected by the host computer, and the coefficients of the amplitude control force and quadrature control force are identified based on the collected demodulation quantity, amplitude control force, and quadrature control force;

[0009] Step 3: Calculate the characteristic parameters of the resonator of the hemispherical resonator gyroscope according to the identification results in Step 2.

[0010] Further, the basic control equation of the hemispherical resonator gyroscope is:

[0011]

[0012] Where: represents the first derivative of E, and E represents the vibration energy, represents the first derivative of Q, and Q represents the vibration quadrature quantity, and τ is the energy decay time constant, τ 1 and τ 2 are respectively the energy decay time constants of the resonators on the two damped normal axes, is the non-equal damping error coefficient, θ τ is the angle between the damped normal axis x and the 0-degree motor axis, represents the first derivative of θ, θ represents the azimuth angle of the standing wave, ω is the resonance frequency, ω 1 and ω 2 are respectively the natural vibration angular frequencies of the resonators on the two stiffness normal axes, Δω is the non-equal elasticity error coefficient, θ ω is the angle between the stiffness normal axis x and the 0-degree motor axis, K D is the drive gain, f as is the amplitude control force, f qc is the quadrature control force, k represents the scale factor of the gyroscope, Ω represents the external rotation angular velocity, f qs represents the applied virtual precession force.

[0013] Further, the specific process of Step 1 is:

[0014] When amplitude and quadrature controls are applied, there is Q≈0, then according to the basic control equation of the hemispherical resonator gyroscope, we have:

[0015]

[0016] Further, after driving the hemispherical resonator gyroscope to start oscillating, the azimuth angles of the exciting standing waves precess virtually in the forward and reverse directions respectively, specifically:

[0017] After the hemispherical resonant gyro starts to oscillate, by applying a constant virtual precession force to excite the standing wave azimuth angle to precess in the positive virtual direction, and by applying a constant virtual precession force to excite the standing wave azimuth angle to precess in the reverse virtual direction;

[0018] And the virtual precession force and the virtual precession force satisfy:

[0019] Furthermore, the specific process of identifying the coefficient of the amplitude control force is as follows:

[0020] Step 1: Calculate the vibration state quantity according to the collected demodulation quantity, and then calculate the standing wave azimuth angle θ at each moment using the vibration state quantity k ;

[0021] And initialize P 0 =

[000] , initialize Ψ 0 =

[000] T , and set the forgetting factor λ = 0.99;

[0022] Step 2: Initialize the moment k = 1;

[0023] Step 3: Calculate the intermediate variable H k according to the standing wave azimuth angle θ at the k moment k :

[0024] H k = [sin4θ k cos4θ k 1] T (9)

[0025] where the superscript T represents transpose;

[0026] Step 4: Calculate K k according to H k :

[0027]

[0028] Step 5: Calculate Ψ k and P k according to K k :

[0029]

[0030] where f k,as represents the amplitude control force at the k moment;

[0031] Step 6: Judge Ψ kWhether it converges;

[0032] If Ψ k converges, then take the Ψ obtained in the last iteration k as the final identification result of the amplitude control force coefficient:

[0033]

[0034] If Ψ k does not converge, then let k = k + 1 and return to step 3.

[0035] Furthermore, the specific process of judging whether Ψ k converges is as follows:

[0036] Judge whether Ψ k satisfies |Ψ k - Ψ k-1 | < ε, where ε is a set threshold, and |Ψ k - Ψ k-1 | represents the distance between Ψ k and Ψ k-1 ;

[0037] If |Ψ k - Ψ k-1 | < ε is satisfied, then Ψ k converges;

[0038] If |Ψ k - Ψ k-1 | < ε is not satisfied, then Ψ k does not converge.

[0039] Furthermore, the specific process of identifying the coefficient of the orthogonal control force is as follows:

[0040] Step 1: Initialize P 0 = [0 0 0], initialize Ψ' 0 = [0 0 0] T , and set the forgetting factor λ = 0.99;

[0041] Step 2: Initialize the time k = 1;

[0042] Step 3: Calculate the intermediate variable H k according to the standing wave azimuth angle θ at time k k :

[0043] H k = [sin4θ k cos4θ k 1] T (14)

[0044] where the superscript T represents transpose;

[0045] Step 4. Calculate K according to H k k :

[0046]

[0047] Step 5. Calculate Ψ′ and P according to K k k k :

[0048]

[0049] where f k,qc represents the orthogonal control force at time k;

[0050] Step 6. Determine whether Ψ′ converges k

[0051] If Ψ′ converges, take the Ψ′ obtained in the last iteration as the final identification result of the orthogonal control force coefficient: k k

[0052]

[0053] If Ψ′ does not converge, let k = k + 1, and return to Step 3 k

[0054] Furthermore, the specific process of determining whether Ψ′ converges is as follows k

[0055] Determine whether Ψ′ satisfies |Ψ′ k - Ψ′ k | < ε′, where ε′ is a set threshold, and |Ψ′ k-1 - Ψ′ k | represents the distance between Ψ′ k-1 and Ψ′ k ; k-1

[0056] If |Ψ′ k - Ψ′ k-1 | < ε′, then Ψ′ k converges;

[0057] If |Ψ′ k - Ψ′ k-1 | ≥ ε′, then Ψ′ k does not converge

[0058] Furthermore, the specific process of Step 3 is as follows

[0059] ​​​​​​​​​Calculate the vibration state quantity data based on the demodulation quantity collected during the forward virtual precession process, and then calculate the standing wave azimuth angle θ according to the vibration state quantity data + and the standing wave azimuth angular velocity Calculate the vibration state quantity data based on the demodulation quantity collected during the reverse virtual precession process, and then calculate the standing wave azimuth angle θ according to the vibration state quantity data - and the standing wave azimuth angular velocity Substitute θ + and into Equation (19), and substitute θ - and into Equation (20):

[0060]

[0061] Take the average of θ + within the range of to obtain

[0062]

[0063] where θ +0 is an arbitrary initial angular position during the forward virtual precession process, is the average value within the range of ;

[0064] Take the average of θ - within the range of to obtain

[0065]

[0066] where θ -0 is an arbitrary initial angular position during the reverse virtual precession process, is the average value within the range of ;

[0067] Subtract Equation (22) from Equation (21) to obtain

[0068]

[0069] From Equations (13), (18) and (23), we get:

[0070]

[0071] Then according to Equations (24) and (25), we get:

[0072]

[0073] The beneficial effects of the present invention are:

[0074] The method of the present invention is implemented based on forward and reverse virtual precession. During virtual precession, specific parameters in the basic control force equation of the gyroscope are identified. By using the magnitudes of the parameters in the identified control force equation and combining the relationships between the forward and reverse virtual precession forces and the output angular velocity of the gyroscope, various characteristic parameter values of the hemispherical resonant gyroscope can be quickly and accurately identified, solving the problem that the traditional method requires a long time for characteristic parameter identification, and being more conducive to screening out gyroscopes with excellent performance and guiding the improvement of the processing technology. Description of the Drawings

[0075] Figure 1 It is a flowchart of a method for identifying the characteristic parameters of the resonator of a hemispherical resonant gyroscope according to the present invention. Detailed Embodiments

[0076] Detailed Embodiment 1: Combined with Figure 1 This embodiment is described. A method for identifying the characteristic parameters of the resonator of a hemispherical resonant gyroscope according to this embodiment specifically includes the following steps:

[0077] Step 1: According to the basic control equation of the hemispherical resonant gyroscope, the amplitude control force when applying amplitude control and the orthogonal control force when applying orthogonal control are respectively obtained;

[0078] Step 2: After driving the hemispherical resonant gyroscope to start oscillating, the excitation standing wave azimuth angle precesses forward and backward virtually respectively. During the forward and backward virtual precession processes, the demodulation quantity, amplitude control force, and orthogonal control force output by the hemispherical resonant gyroscope are continuously collected by the host computer, and the coefficients of the amplitude control force and the orthogonal control force are identified according to the collected demodulation quantity, amplitude control force, and orthogonal control force;

[0079] Step 3: Calculate the characteristic parameters of the resonator of the hemispherical resonant gyroscope according to the identification results in Step 2.

[0080] Detailed Embodiment 2: The difference between this embodiment and Detailed Embodiment 1 is that: the basic control equation of the hemispherical resonant gyroscope is:

[0081]

[0082] Where: represents the first derivative of E, and E represents the vibration energy, represents the first derivative of Q, and Q represents the vibration orthogonal quantity, τ is the energy decay time constant, τ 1 and τ 2 are respectively the energy decay time constants of the resonators on two damped normal axes (where, τ 1 is the energy decay time constant of the resonator on the damped normal axis x, τ 2is the energy decay time constant of the harmonic oscillator on the damped principal axis y-axis), is the non-equal damping error coefficient, θ τ is the angle between the damped principal axis x-axis and the 0-degree motor axis, represents the first derivative of θ, θ represents the standing wave azimuth angle, ω is the resonance frequency, ω 1 and ω 2 are respectively the natural vibration angular frequencies of the harmonic oscillators on the two stiffness principal axes (where, ω 1 is the natural vibration angular frequency on the stiffness principal axis y-axis, ω 2 is the natural vibration angular frequency on the stiffness principal axis x-axis), Δω is the non-equal elasticity error coefficient, θ ω is the angle between the stiffness principal axis x-axis and the 0-degree motor axis, K D is the drive gain, f as is the amplitude control force, f qc is the orthogonal control force, k represents the scale factor of the gyroscope, Ω represents the external rotation angular velocity, f qs represents the applied virtual precession force.

[0083] Other steps and parameters are the same as those in the first specific implementation manner.

[0084] Specific implementation manner three: The difference between this implementation manner and the first or second specific implementation manner is that: The specific process of the first step is:

[0085] When amplitude and orthogonal controls are applied, there is Q≈0, then according to the basic control equation of the hemispherical resonator gyroscope, we get:

[0086]

[0087] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0088] Specific implementation manner four: The difference between this implementation manner and one of the first to third specific implementation manners is that: After the driven hemispherical resonator gyroscope starts to oscillate, the excitation standing wave azimuth angle precesses virtually in the forward and reverse directions respectively, specifically:

[0089] After the hemispherical resonator gyroscope starts to oscillate, by applying a constant virtual precession force to excite the standing wave azimuth angle to precess virtually in the forward direction, and by applying a constant virtual precession force to excite the standing wave azimuth angle to precess virtually in the reverse direction;

[0090] And the virtual precession force and the virtual precession force satisfy:

[0091] Other steps and parameters are the same as those in any one of the first to third specific embodiments.

[0092] The starting method of the hemispherical resonator gyroscope is as follows: Place the hemispherical resonator gyroscope and its control circuit board on a flat workbench, power on the control circuit board, and execute the starting program for the hemispherical resonator gyroscope to make it work in the rate integration mode. At the same time, collect the demodulated output C of the hemispherical resonator gyroscope through the host computer x , S x , C y , S y , and use the following formula to solve its vibration state quantity:

[0093]

[0094] Among them, E represents the vibration energy, Q represents the vibration orthogonality, R and S represent the vibration azimuth angle, and L represents the phase-locked phase difference.

[0095] Wait for each vibration state quantity to stabilize, indicating that the gyroscope has completed starting. The standing wave azimuth angle can be solved by the following formula:

[0096]

[0097] Specific embodiment five: The difference between this embodiment and any one of the first to fourth specific embodiments is that: the identification of the coefficient of the amplitude control force according to the collected data is specifically as follows:

[0098] Step 1: Calculate the vibration state quantities (S and R) according to the collected demodulated quantities, and then use the vibration state quantities to calculate the standing wave azimuth angle θ at each moment k ;

[0099] And initialize P 0 =

[000] , initialize Ψ 0 =

[000] T , and set the forgetting factor λ = 0.99;

[0100] Step 2: Initialize the time k = 1;

[0101] Step 3: Calculate the intermediate variable H k according to the standing wave azimuth angle θ at the kth moment k :

[0102] H k = [sin4θ k cos4θ k 1] T (9)

[0103] Among them, the superscript T represents the transpose;

[0104] Step 4: According to Hk Calculate K k :

[0105]

[0106] Step 5: According to K k Calculate Ψ k and P k :

[0107]

[0108] where f k,as represents the amplitude control force at time k;

[0109] Step 6: Determine whether Ψ k converges;

[0110] If Ψ k converges, then take the Ψ obtained in the last iteration k as the final identification result of the amplitude control force coefficient:

[0111]

[0112] If Ψ k does not converge, then set k = k + 1 and return to Step 3.

[0113] Other steps and parameters are the same as those in any one of the first to fourth specific embodiments.

[0114] In this embodiment, the data used for identifying the coefficients in the amplitude control force calculation formula (4) can be the data collected by the host computer during the forward virtual precession process or the data collected by the host computer during the reverse virtual precession process. The coefficient identification methods that can be used in the present invention include, but are not limited to, the above methods. For example, other identification algorithms such as Kalman filtering can be used to implement.

[0115] Specific Embodiment Six: The difference between this embodiment and any one of the first to fifth specific embodiments is that: the determination of whether Ψ k converges is specifically:

[0116] Determine whether Ψ k satisfies |Ψ k - Ψ k-1 | < ε, where ε is a set threshold, and |Ψ k - Ψ k-1 | represents the distance between Ψ k and Ψ k-1 ;

[0117] If |Ψ k - Ψ k-1 | < ε, then Ψ k converges;

[0118] If |Ψ k - Ψ k-1 | < ε is not satisfied, then Ψ k does not converge.

[0119] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0120] Specific Embodiment Seven: The difference between this embodiment and any one of the first to sixth specific embodiments is that: the coefficient of the orthogonal control force is identified according to the collected data, specifically:

[0121] Step 1: Initialize P 0 = [0 0 0], initialize Ψ′ 0 = [0 0 0] T , and set the forgetting factor λ = 0.99;

[0122] Step 2: Initialize the time k = 1;

[0123] Step 3: Calculate the intermediate variable H k according to the standing wave azimuth angle θ k at time k:

[0124] H k = [sin4θ k cos4θ k 1] T (14)

[0125] where the superscript T represents transpose;

[0126] Step 4: Calculate K k according to H k :

[0127]

[0128] Step 5: Calculate Ψ′ k and P k according to K k :

[0129]

[0130] where f k,qc represents the orthogonal control force at time k;

[0131] Step 6: Determine whether Ψ′ k converges;

[0132] If Ψ′ k converges, then take the Ψ′ k obtained in the last iteration as the final identification result of the orthogonal control force coefficient:

[0133]

[0134] If Ψ′ k does not converge, let k = k + 1, and return to step 3.

[0135] Other steps and parameters are the same as those in any one of the first to sixth specific embodiments.

[0136] Specific embodiment eight: The difference between this embodiment and any one of the first to seventh specific embodiments is that: the judgment of whether Ψ′ k converges is specifically as follows:

[0137] Judge whether Ψ′ k satisfies |Ψ′ k - Ψ′ k-1 | < ε′, where ε′ is a set threshold, and |Ψ′ k - Ψ′ k-1 | represents the distance between Ψ′ k and Ψ′ k-1 ;

[0138] If |Ψ′ k - Ψ′ k-1 | < ε′ is satisfied, then Ψ′ k converges;

[0139] If |Ψ′ k - Ψ′ k-1 | < ε′ is not satisfied, then Ψ′ k does not converge.

[0140] Other steps and parameters are the same as those in any one of the first to seventh specific embodiments.

[0141] Specific embodiment nine: The difference between this embodiment and any one of the first to eighth specific embodiments is that the specific process of step 3 is as follows:

[0142] Calculate the vibration state quantity data according to the demodulation quantity collected during the forward virtual precession process, and then calculate the standing wave azimuth angle θ + and the standing wave azimuth angular velocity Calculate the vibration state quantity data according to the demodulation quantity collected during the reverse virtual precession process, and then calculate the standing wave azimuth angle θ - and the standing wave azimuth angular velocity Substitute θ + and into equation (19), and substitute θ - and into equation (20):

[0143]

[0144] Take the left and right sides of Equation (19) with respect to θ + In range, take the average to obtain

[0145]

[0146] where θ +0 is any initial angular position during the forward virtual precession process, is In range of the average value;

[0147] Take the left and right sides of Equation (20) with respect to θ - In range, take the average to obtain

[0148]

[0149] where θ -0 is any initial angular position during the reverse virtual precession process, is In range of the average value;

[0150] Subtract Equation (22) from Equation (21) to obtain

[0151]

[0152] From Equation (13), Equation (18) and Equation (23), we have:

[0153]

[0154] Then according to Equation (24) and Equation (25), we have:

[0155]

[0156] where the resonance frequency ω can be obtained from the gyro phase-locked loop.

[0157] Other steps and parameters are the same as those in any one of the specific embodiments one to eight.

[0158] The above examples of the present invention are only to illustrate in detail the calculation model and calculation process of the present invention, rather than to limit the embodiments of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the embodiments here. Any obvious changes or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for identifying characteristic parameters of a resonator of a hemispherical resonant gyroscope, characterized in that: The method specifically comprises the following steps: Step 1: According to the basic control equation of the hemispherical resonant gyroscope, the amplitude control force when the amplitude control is applied and the orthogonal control force when the orthogonal control is applied are obtained respectively; Step 2: After the hemispherical resonant gyroscope is driven to vibrate, the standing wave azimuth is excited to precess in the forward and reverse directions respectively. During the forward and reverse directions, the demodulation amount, amplitude control force and orthogonal control force output by the hemispherical resonant gyroscope are continuously collected by the host computer, and the coefficients of the amplitude control force and the orthogonal control force are identified according to the collected demodulation amount, amplitude control force and orthogonal control force. Step 3: Calculate the characteristic parameters of the resonator of the hemispherical resonant gyroscope according to the identification result in step 2.

2. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 1, characterized in that: The basic control equation of the hemispherical resonant gyroscope is: in: represents the first-order derivative of E, which represents the vibration energy, represents the first-order derivative of Q, Q represents the vibration orthogonal quantity, τ is the energy decay time constant, τ1 and τ2 are the energy decay time constants of the two damped normal axis resonators, is the unequal damping error coefficient, θ τ is the angle between the damping axis x and the motor shaft at 0 degrees, represents the first-order derivative of θ, θ represents the standing wave azimuth, ω is the resonant frequency, ω1 and ω2 are the natural vibration angular frequencies of the resonators on the two stiffness normal axes, Δω is the non-isoelastic error coefficient, θ ω K is the angle between the x-axis of the rigidity and the motor shaft at 0 degrees. D is the driving gain, f as is the amplitude control force, f qc is the orthogonal control force, k is the scale factor of the gyroscope, Ω is the external rotation angular velocity, and f qs represents the virtual precession force applied.

3. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 2, characterized in that: The specific process of step one is: When amplitude and quadrature control are applied, we have Q≈0, then according to the basic control equation of the hemispherical resonant gyroscope:

4. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 3, characterized in that: After the driven hemispherical resonant gyroscope is vibrated, the exciting standing wave azimuth angles are virtually precessed in the positive and reverse directions respectively, specifically: After the hemispherical resonant gyroscope is started, a constant virtual precession force is applied. To stimulate the virtual precession of the standing wave azimuth along the positive direction, by applying a constant virtual precession force To stimulate the standing wave to precess virtually in the opposite direction along the azimuth angle; Virtual driving force With virtual momentum satisfy:

5. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 4, characterized in that: The specific process of identifying the coefficient of the amplitude control force is as follows: Step 1: Calculate the vibration state quantity based on the collected demodulation quantity, and then use the vibration state quantity to calculate the standing wave azimuth θ at each moment k ; And initialize P0 = [000], initialize Ψ0 = [000] T , set the forgetting factor λ = 0.99; Step 2, initialization time k=1; Step 3: According to the standing wave azimuth angle θ at time k k Calculate the intermediate variable H k : H k =[sin4θ k cos4θ k 1] T (9) Among them, the superscript T represents transpose; Step 4: According to H k Calculate K k : Step 5: According to K k Calculate Ψ k and P k : Among them, f k,as represents the amplitude control force at time k; Step 6: Determine k Whether it converges; If k Convergence, then the Ψ obtained in the last iteration is k As the final identification result of the amplitude control force coefficient: If k If it does not converge, set k=k+1 and return to step 3.

6. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 5, characterized in that: The judgment Ψ k Whether it converges, specifically: Judgment k Is it satisfied? k -Ψ k-1 |<ε, where ε is the set threshold, |Ψ k -Ψ k-1 | indicates Ψ k With k-1 The distance between If |Ψ k -Ψ k-1 |<ε, then Ψ k convergence; If not satisfied |Ψ k -Ψ k-1 |<ε, then Ψ k Not convergent.

7. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 4, characterized in that: The specific process of identifying the coefficients of the orthogonal control force is as follows: Step 1: Initialize P0 = [0 0 0], initialize Ψ′0 = [0 0 0] T , set the forgetting factor λ = 0.99; Step 2, initialization time k=1; Step 3: According to the standing wave azimuth angle θ at time k k Calculate the intermediate variable H k : H k =[sin4θ k cos4θ k 1] T (14) Among them, the superscript T represents transpose; Step 4: According to H k Calculate K k : Step 5: According to K k Calculate Ψ′ k and P k : Among them, f k,qc represents the orthogonal control force at time k; Step 6: Determine Ψ′ k Whether it converges; If Ψ′ k Convergence, then the Ψ′ obtained in the last iteration k As the final identification result of the orthogonal control force coefficient: If Ψ′ k If it does not converge, set k=k+1 and return to step 3.

8. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 7, characterized in that: The judgment Ψ′ k Whether it converges, specifically: Judgment Ψ′ k Whether |Ψ′ is satisfied k -Ψ′ k-1 |<ε′, where ε′ is the set threshold, |Ψ′ k -Ψ′ k-1 | indicates Ψ′ k and Ψ′ k-1 The distance between If |Ψ′ is satisfied k -Ψ′ k-1 |<ε′, then Ψ′ k convergence; If |Ψ′ is not satisfied k -Ψ′ k-1 |<ε′, then Ψ′ k Not convergent.

9. The method for identifying characteristic parameters of a resonator of a hemispherical resonator gyroscope according to claim 6 or 8, characterized in that: The specific process of step three is: The vibration state quantity data is calculated based on the demodulated quantity collected during the forward virtual precession process, and then the standing wave azimuth angle θ is calculated based on the vibration state quantity data. + and the azimuthal velocity of the standing wave The vibration state quantity data is calculated based on the demodulated quantity collected during the reverse virtual precession process, and then the standing wave azimuth angle θ is calculated based on the vibration state quantity data - and the azimuthal velocity of the standing wave θ + and Substituting into equation (19), we can get θ - and Substitute into formula (20): For θ + exist Find the average within the range, and we get Among them, θ +0 is any initial angular position during the forward virtual precession process, yes exist The average value within the range; For θ - exist Find the average within the range, and we get Among them, θ -0 is any initial angular position during the reverse virtual precession process, yes exist The average value within the range; Subtracting equation (22) from equation (21), we get From equation (13), equation (18) and equation (23), we can get: According to formula (24) and formula (25), we can get:

Images