A method and system for identifying and suppressing the non - linear error of a hemispherical resonant gyro

Abstract

The present invention relates to the technical field of intelligent instruments and meters, and particularly to a method and system for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope. The method includes: operating the hemispherical resonant gyroscope in a full-angle mode; setting an initial nonlinear compensation matrix, an initial amplitude gap ratio, and a traversal rule for the amplitude gap ratio; collecting an amplitude differential signal during the operation of the hemispherical resonant gyroscope, identifying the amplitude of the eighth harmonic in the amplitude differential signal by using an RLS algorithm filter, and finding the amplitude gap ratio corresponding to the lowest harmonic amplitude; adjusting the initial nonlinear compensation matrix based on the amplitude gap ratio to obtain a nonlinear compensation matrix, and compensating the demodulated signal based on the nonlinear compensation matrix to complete the identification and compensation of the nonlinear error of the hemispherical resonant gyroscope. The present invention can accurately identify and calibrate the electrode nonlinear error existing in the hemispherical resonant gyroscope.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent instruments and meters, and particularly to a method and system for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope. Background Art

[0002] In the detection and control process of a hemispherical resonant gyroscope, a small variable-capacitance capacitor formed by the detection electrode of the gyroscope and the metal film layer of the hemispherical resonator will introduce a detection nonlinear error into the system, which is specifically manifested as an eighth-harmonic error related to the precession angle in the amplitude signal and the angular rate signal, and this will directly affect important indicators such as the detection accuracy of the precession angular rate of the gyroscope and the zero-bias stability.

[0003] However, in existing research, there is a lack of accurate identification and calibration for the detection nonlinear error in the hemispherical resonant gyroscope. In addition, the existing detection nonlinear compensation technology is limited by the structure of the detection front-end amplifier circuit and is not applicable in other amplifier circuit environments. Therefore, the present invention proposes a method and system for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope. Summary of the Invention

[0004] The purpose of the present invention is to overcome the problem that it is difficult to accurately identify and suppress the nonlinear error in the hemispherical resonant gyroscope system during the actual operation process, and to provide a method and system for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope by using the recursive least squares algorithm.

[0005] To achieve the above purpose, the present invention provides the following solutions:

[0006] A method for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope, comprising:

[0007] Operating the hemispherical resonant gyroscope in the full-angle mode;

[0008] Setting an initial nonlinear compensation matrix, an initial amplitude gap ratio, and a traversal rule for the amplitude gap ratio;

[0009] Collecting an amplitude differential signal during the operation of the hemispherical resonant gyroscope, identifying the eighth-harmonic amplitude in the amplitude differential signal by using an RLS algorithm filter, and finding the amplitude gap ratio corresponding to the lowest harmonic amplitude;

[0010] Adjusting the initial nonlinear compensation matrix based on the amplitude gap ratio to obtain a nonlinear compensation matrix, and compensating the demodulated signal based on the nonlinear compensation matrix to complete the identification and compensation of the nonlinear error of the hemispherical resonant gyroscope.

[0011] Optionally, the amplitude differential signal is:

[0012]

[0013] In the formula, is the differential signal of the amplitude component, a is the amplitude component, θ is the precession angle, τ is the damping decay time constant, A1 and A2 are the damping anisotropy related error coefficients respectively, and A3 and A4 are the electrode nonlinearity related error coefficients respectively.

[0014] Optionally, identifying the octave harmonic amplitude in the amplitude differential signal by using the RLS algorithm filter includes:

[0015] S1. Select a state matrix based on the amplitude differential signal, and initialize the covariance matrix, the state transition matrix, and the forgetting factor;

[0016] S2. Multiply the state signal in the state matrix by the corresponding state transition matrix to obtain an output signal;

[0017] S3. By comparing the output signal with the actual measured signal, obtain an error signal, and update the state matrix based on the error signal. Repeat S2 - S3 until the RLS algorithm converges to obtain the final state matrix;

[0018] S4. Calculate the octave harmonic amplitude in the amplitude differential signal based on the final state matrix.

[0019] Optionally, the octave harmonic amplitude is:

[0020]

[0021] In the formula, A n_8θ = is the octave harmonic amplitude, A3(k) and A4(k) are the discretized electrode nonlinear error coefficients respectively, and k is the number of discretization points.

[0022] Optionally, the nonlinear compensation matrix adjusted based on the amplitude gap ratio is:

[0023]

[0024] In the formula, r e is the amplitude gap ratio corresponding to the lowest harmonic amplitude, and θ is the precession angle.

[0025] Optionally, the demodulated signal compensated based on the nonlinear compensation matrix is:

[0026]

[0027] In the formula, cx’, cy’, sx’, and sy’ are the demodulated signals compensated based on the nonlinear compensation matrix, and cx, cy, sx, and sy are the demodulated signals.

[0028] To further achieve the above object, the present invention also provides a system for identifying and suppressing the non - linear error of a hemispherical resonant gyroscope, comprising:

[0029] An operation setting module, configured to set the operation mode of the hemispherical resonant gyroscope, wherein the operation mode is the full - angle mode;

[0030] An initial parameter setting module, configured to set an initial non - linear compensation matrix, an initial amplitude gap ratio, and a traversal rule for the amplitude gap ratio;

[0031] An operation data acquisition module, configured to acquire an amplitude differential signal during the operation of the hemispherical resonant gyroscope;

[0032] An error identification module, configured to identify the amplitude of the eighth - order harmonic in the amplitude differential signal by using an RLS algorithm filter and find the amplitude gap ratio corresponding to the lowest harmonic amplitude;

[0033] An error compensation module, configured to adjust the initial non - linear compensation matrix based on the amplitude gap ratio, obtain a non - linear compensation matrix, and compensate the demodulated signal based on the non - linear compensation matrix.

[0034] The beneficial effects of the present invention are as follows:

[0035] The method and system proposed by the present invention can accurately identify and calibrate the electrode non - linear error existing in the hemispherical resonant gyroscope. In addition, the existing non - linear compensation detection technologies are limited by the structure of the pre - amplifier circuit of the detection channel and do not have strong applicability in different control circuit environments. However, the functions of the present invention are easy to implement, without the need to adjust the circuit and hardware modules, and the overall identification and compensation are completed by the program. In addition, the present invention accurately completes the identification of the amplitude gap ratio, and the compensation matrix based on the amplitude gap ratio has strong applicability and does not depend on the control system environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings without creative efforts based on these drawings.

[0037] Figure 1 It is a flowchart of a method for identifying and suppressing the non - linear error of a hemispherical resonant gyroscope according to an embodiment of the present invention;

[0038] Figure 2 It is the amplitude component differential of an embodiment of the present invention The relationship curve corresponding to the change when θ = 0 - 2π;

[0039] Figure 3 Schematic diagram of the nonlinear behavior at the detection electrode of the hemispherical resonant gyro according to an embodiment of the present invention. Detailed implementation manners

[0040] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0041] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0042] This embodiment provides a method for identifying and suppressing the nonlinear error of a hemispherical resonant gyro, including:

[0043] Operating the hemispherical resonant gyro in a full-angle mode;

[0044] Setting an initial nonlinear compensation matrix, an initial amplitude gap ratio, and a traversal rule for the amplitude gap ratio;

[0045] Collecting amplitude differential signals during the operation of the hemispherical resonant gyro, identifying the amplitude of the eighth harmonic in the amplitude differential signals using an RLS algorithm filter, and finding the amplitude gap ratio corresponding to the lowest harmonic amplitude;

[0046] Adjusting the initial nonlinear compensation matrix based on the amplitude gap ratio to obtain a nonlinear compensation matrix, and compensating the demodulated signal based on the nonlinear compensation matrix to complete the identification and compensation of the nonlinear error of the hemispherical resonant gyro.

[0047] Specifically, this embodiment can accurately identify and calibrate the electrode nonlinear error in the hemispherical resonant gyro. In addition, the existing detection nonlinear compensation technology is limited by the structure of the pre-amplification circuit of the detection channel and does not have strong applicability in different control circuit environments. However, the function of this embodiment is easy to implement, without adjusting the circuit and hardware modules, and the overall identification and compensation are completed by the program.

[0048] Different pre-amplification circuits and drive voltages make it difficult to accurately estimate the amplitude gap ratio r of the hemispherical resonant gyro. Even if the initial plate spacing d0 is determined, it is very difficult to estimate the small vibration displacement x of the resonator. Therefore, a method is needed to effectively and accurately estimate and identify the amplitude gap ratio r to complete the calculation of the electrode nonlinear error compensation matrix. The following will be combined with Figures 1 - 3 A method for identifying and suppressing the nonlinear error of a hemispherical resonant gyro proposed in this embodiment will be described in detail, specifically including:

[0049] Step 1: Fix the hemispherical resonant gyro on a single-axis rate turntable and operate the hemispherical resonant gyroscope in the full-angle mode.

[0050] Step 2: Set the initial nonlinear compensation matrix and set the compensation strategy, that is, multiply the initial nonlinear error compensation matrix by the signals cx, cy, sx, and sy obtained by real-time demodulation, and set the initial amplitude gap ratio a / d0 = r to 0. At this time, the demodulation signal is actually not compensated.

[0051] Step 3: Use the RLS algorithm filter to identify the amplitude of the eighth harmonic error term in the collected amplitude differential signal At the same time, in the compensation program, adjust the amplitude gap ratio r to accumulate once every 0.001 within the range of 0 to 0.1. Based on the convergence time of the RLS algorithm, adjust the traversal interval. Further sacrificing the algorithm traversal speed can improve the identification accuracy of the amplitude gap ratio. For example, reduce the traversal interval to 0.0005 to improve the identification accuracy of the final amplitude gap ratio.

[0052] Step 4: Compare the amplitudes of the eighth harmonics identified by the RLS algorithm during the entire traversal process of the amplitude gap ratio. The lowest value is the actual amplitude gap ratio r of the corresponding hemispherical resonant gyro system e ; Finally, based on the actual amplitude gap ratio r of the system e Adjust the nonlinear error compensation matrix in Step 2 to achieve compensation for the electrode nonlinear error.

[0053] Furthermore, the definition and representation of the amplitude differential signal in Step 3 are as follows:

[0054] Based on the amplitude component differential of the traditional elliptic parameter equation of the hemispherical resonant gyro, consider the electrode nonlinear error. Based on existing related research, it is known that this nonlinear error is mainly composed of the non-rotation coupling term A n1 sin8(θ + θ n1 ) and the rotation coupling term [A n2 sin8(θ + θ n2 )]γΩ. Then, the elliptic parameter equation of the amplitude component affected by the electrode nonlinearity is:

[0055]

[0056] where θ is the precession angle, a is the amplitude component, q is the quadrature component, γ is the precession factor, Ω is the external rotation speed of the gyroscope, and θ τ are the damping anisotropy and damping misalignment angle respectively, and Δω and θ ωThey are the stiffness anisotropy and the stiffness misalignment angle, respectively, A n1 and A n2 is the amplitude of the eighth harmonic caused by the electrode nonlinear error, θ n1 and θ n2 is the electrode nonlinear phase shift. Orthogonal control makes the orthogonal component much smaller than the amplitude component. As shown in Equation (1), the fourth harmonic in the amplitude differential signal comes from the effects of damping non-uniformity and stiffness non-uniformity, while the eighth harmonic component comes from the electrode nonlinear error. In addition, this error is also affected by the coupling of the external rotational speed. Simplifying and transforming Equation (1), we can get:

[0057]

[0058] Simplifying Equation (2), let:

[0059]

[0060] Then the differential equation of the amplitude component affected by the damping mismatch error and the nonlinear error can be written as:

[0061]

[0062] From Equation (4), the relationship curve of the amplitude component differential when θ = 0 to 2π is as shown in Figure 2 shown.

[0063] Furthermore, the specific process of identifying the amplitude of the eighth harmonic error term in the collected amplitude differential signal using the RLS algorithm filter in step 3 includes:

[0064] S1. Select the state matrix based on the amplitude differential signal, and initialize the covariance matrix, the state transition matrix, and the forgetting factor;

[0065] S2. Multiply the state signal in the state matrix by the corresponding state transition matrix to obtain the output signal;

[0066] S3. Compare the output signal with the actual measured signal to obtain the error signal, and update the state matrix based on the error signal. Repeat S2 - S3 until the RLS algorithm converges to obtain the final state matrix;

[0067] S4. Calculate the amplitude of the eighth harmonic in the amplitude differential signal based on the final state matrix.

[0068] Specifically, in this embodiment, an RLS algorithm filter is constructed for identifying the nonlinear error, that is, the identification of the amplitude of the eighth harmonic. The steps are as follows:

[0069] (1) Select the state matrix

[0070] (2) Initialize the covariance matrix P(k) and the forgetting factor λ;

[0071] (3) Initialize the state transition matrix H(k) = [1(k) cos4θ(k) sin4θ(k) sin8θ(k) cos8θ(k)] T ;

[0072] (4) Multiply the state signal in the state matrix by the corresponding state transition matrix to obtain the output signal Y(k);

[0073] (5) Subtract the theoretical measurement value from the actual measurement value to obtain the error signal e(k) for updating the state matrix;

[0074] (6) The overall identification algorithm flow is given by formula (5):

[0075]

[0076] Where K(k) is the gain vector for updating the state vector.

[0077] After the algorithm converges, further calculation using the weight coefficients gives the identification result of the non - linear error, i.e., the amplitude of the eighth - harmonic error term: After completing the correction and compensation of the non - linear error, the amplitude component and the eighth - harmonic error in the angular rate signal can be made to approach zero.

[0078] Furthermore, in step 4, based on the actual amplitude gap ratio r of the system e Adjusting the non - linear error compensation matrix in step 2 includes:

[0079] The detection electrode of the hemispherical resonant gyro and the metal film layer of the resonator form a variable - spacing capacitor, and the detection - end pre - amplifier circuit is composed of a charge amplifier. As Figure 3 shown. The differential voltage equation here is:

[0080] V Sx = V Sx+ - V Sx- ≈ K s x + K sn x 3 (6)

[0081] Where K s is the detection loop coefficient, K sn is the non - linear coefficient of the detection loop, V Sx is the detection voltage, V Sx+ is the detection voltage at the x + electrode of the hemispherical resonant gyro, and V Sx- is the detection voltage at the x - electrode of the hemispherical resonant gyro.

[0082] In full-angle mode, the demodulation signal affected by the electrode nonlinear effect is as follows:

[0083]

[0084] where N1 is the demodulation signal gain coefficient, N2 is the nonlinear error gain coefficient in the demodulation signal, and δ is the system phase difference.

[0085] The nonlinear compensation matrix adjusted based on the amplitude gap ratio is as follows:

[0086]

[0087] In the formula, r e is the amplitude gap ratio corresponding to the lowest harmonic amplitude, and θ is the precession angle.

[0088] The demodulation signal compensated based on the nonlinear compensation matrix is as follows:

[0089]

[0090] In the formula, cx’, cy’, sx’, and sy’ are the demodulation signals compensated based on the nonlinear compensation matrix, and cx, cy, sx, and sy are the demodulation signals.

[0091] To further optimize the technical solution, this embodiment also provides a system for identifying and suppressing the nonlinear error of a hemispherical resonator gyroscope, which is used to implement a method for identifying and suppressing the nonlinear error of a hemispherical resonator gyroscope, including:

[0092] An operation setting module, which is used to set the operation mode of the hemispherical resonator gyroscope, where the operation mode is full-angle mode;

[0093] An initial parameter setting module, which is used to set the initial nonlinear compensation matrix, the initial amplitude gap ratio, and the traversal rule of the amplitude gap ratio;

[0094] An operation data acquisition module, which is used to acquire the amplitude differential signal during the operation of the hemispherical resonator gyroscope;

[0095] An error identification module, which is used to identify the octave harmonic amplitude in the amplitude differential signal by using an RLS algorithm filter and find the amplitude gap ratio corresponding to the lowest harmonic amplitude;

[0096] An error compensation module, which is used to adjust the initial nonlinear compensation matrix based on the amplitude gap ratio, obtain the nonlinear compensation matrix, and compensate the demodulation signal based on the nonlinear compensation matrix.

[0097] The embodiments described above are only descriptions of the preferred embodiments of the present invention and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for identifying and suppressing nonlinear errors of a hemispherical resonant gyroscope, characterized in that: include: Run the hemispherical resonant gyro in full-angle mode; Setting the initial nonlinear compensation matrix, the initial amplitude-gap ratio and the traversal rule of the amplitude-gap ratio; During the operation of the hemispherical resonant gyroscope, an amplitude differential signal is collected, an eighth harmonic amplitude in the amplitude differential signal is identified using an RLS algorithm filter, and an amplitude gap ratio corresponding to the lowest harmonic amplitude is found; The initial nonlinear compensation matrix is ​​adjusted based on the amplitude gap ratio to obtain a nonlinear compensation matrix, and a demodulated signal is compensated based on the nonlinear compensation matrix to complete the identification and compensation of the nonlinear error of the hemispherical resonant gyroscope; The demodulated signal is compensated based on the nonlinear compensation matrix as follows: Where cx', cy', sx', sy' are the demodulated signals after compensation based on the nonlinear compensation matrix, cx, cy, sx, sy are the demodulated signals, and r e is the amplitude gap ratio corresponding to the lowest harmonic amplitude, and θ is the precession angle.

2. The method for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope according to claim 1, characterized in that: The amplitude differential signal is: In the formula, is the differential signal of the amplitude component, a is the amplitude component, θ is the precession angle, τ is the damping decay time constant, A1 and A2 are the damping anisotropy related error coefficients, A3 and A4 are the electrode nonlinearity related error coefficients.

3. The method for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope according to claim 1, characterized in that: Using the RLS algorithm filter to identify the eighth harmonic amplitude in the amplitude differential signal includes: S1. Selecting a state matrix based on the amplitude differential signal, initializing a covariance matrix, a state transfer matrix and a forgetting factor; S2, multiplying the state signal in the state matrix by the corresponding state transfer matrix to obtain an output signal; S3, obtaining an error signal by comparing the output signal with the actual measurement signal, and updating the state matrix based on the error signal, repeating S2-S3 until the RLS algorithm converges, and obtaining a final state matrix; S4. Calculate the eighth harmonic amplitude in the amplitude differential signal based on the final state matrix.

4. The method for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope according to claim 1, characterized in that: The eighth harmonic amplitude is: In the formula, A n_8θ is the eighth harmonic amplitude, A3(k) and A4(k) are the discretized electrode nonlinear error coefficients, and k is the number of discrete points.

5. The method for identifying and suppressing the nonlinear error of a hemispherical resonant gyroscope according to claim 1, characterized in that: The nonlinear compensation matrix after adjustment based on the amplitude gap ratio is: In the formula, r e is the amplitude gap ratio corresponding to the lowest harmonic amplitude, and θ is the precession angle.

6. A system for identifying and suppressing nonlinear errors of a hemispherical resonator gyroscope, used for implementing the method for identifying and suppressing nonlinear errors of a hemispherical resonator gyroscope as claimed in any one of claims 1 to 5, characterized in that: include: An operation setting module, used to set the operation mode of the hemispherical resonant gyroscope, wherein the operation mode is a full-angle mode; An initial parameter setting module, used to set an initial nonlinear compensation matrix, an initial amplitude-gap ratio, and an ergodic rule for the amplitude-gap ratio; An operation data acquisition module is used to collect amplitude differential signals during the operation of the hemispherical resonant gyroscope; An error identification module is used to identify the eighth harmonic amplitude in the amplitude differential signal by using an RLS algorithm filter, and find the amplitude gap ratio corresponding to the lowest harmonic amplitude; an error compensation module, configured to adjust the initial nonlinear compensation matrix based on the amplitude gap ratio, obtain a nonlinear compensation matrix, and compensate the demodulated signal based on the nonlinear compensation matrix; The demodulated signal is compensated based on the nonlinear compensation matrix as follows: Where cx', cy', sx', sy' are the demodulated signals after compensation based on the nonlinear compensation matrix, cx, cy, sx, sy are the demodulated signals, and r e is the amplitude gap ratio corresponding to the lowest harmonic amplitude, and θ is the precession angle.

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