Angle control voltage coefficient calibration method for hemispherical resonator gyroscope

Abstract

The invention provides a hemispherical resonator gyroscope angle control voltage coefficient calibration method, which comprises the following steps: driving a gyroscope standing wave azimuth angle to rotate by using a fixed angle control voltage, and obtaining a gyroscope output angular rate; modeling the angular rate error of the gyroscope in the driving process by using a least square method, and compensating the angular rate of the gyroscope; and according to the compensated angular rate of the gyroscope, estimating the change parameter of the angular rate along with the voltage by adopting a Kalman filtering algorithm, and completing the calibration of the angle control voltage coefficient. Fixed angle control voltage is used for driving the standing wave azimuth angle of the gyroscope to rotate, modeling is carried out according to the change of the angular rate along with the standing wave azimuth angle, and the change part of the angular rate is compensated, so that the output angular rate and the control voltage are in a linear relation; and then designing a Kalman filter, and estimating the change parameter of the angular rate along with the voltage by utilizing controllable voltage input and the calculated angular rate of the gyroscope. The output accuracy and stability of the hemispherical resonator gyroscope are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of hemispherical resonant gyroscopes, and in particular relates to a method for calibrating a voltage coefficient of an angle control of a hemispherical resonant gyroscope. Background Art

[0002] The components of the hemispherical resonator gyroscope mainly include a hemispherical resonator and a flat electrode. A capacitor is formed between the lip edge of the hemispherical resonator and the flat electrode. The working mode adopts a detection and drive time-sharing multiplexing mode. In the working state, a stable four-antinode vibration standing wave is formed on the lip edge of the hemispherical resonator. In the detection cycle of the gyroscope, the vibration is detected by detecting the current change caused by the capacitance change. In the driving cycle of the gyroscope, the electrostatic force is generated by changing the voltage across the capacitor to control the vibration of the gyroscope.

[0003] The calibration of the angle control voltage coefficient of the hemispherical resonant gyroscope is the premise for realizing the gyro rotation modulation. In order to realize the coefficient calibration, it is necessary to obtain the gyro control voltage and the angular velocity of the gyro driven by the voltage. The main factor affecting the calibration result is the angular velocity error of the gyroscope. The error mainly comes from the asymmetric gain of the detection, the asymmetric damping and the asymmetric gain of the drive. If these three errors are not eliminated, it will eventually affect the accuracy of the coefficient calibration. The angular velocity after error compensation can be used to calibrate the coefficient. Summary of the invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art.

[0005] The invention provides a method for calibrating a hemispherical resonant gyroscope angle control voltage coefficient, the method comprising: using a fixed angle control voltage to drive the gyroscope standing wave azimuth rotation to obtain the gyroscope output angular velocity; using the least square method to model the gyroscope angular velocity error in the driving process and compensate the gyroscope angular velocity; according to the compensated gyroscope angular velocity, using a Kalman filter algorithm to estimate the variation parameters of the angular velocity with voltage to complete the calibration of the angle control voltage coefficient.

[0006] The technical solution of the present invention is applied to provide a method for calibrating the voltage coefficient of the angle control of a hemispherical resonant gyroscope. The method uses a fixed angle control voltage to drive the azimuth angle of the gyro standing wave, models the change of the angular velocity with the azimuth angle of the standing wave, compensates for the change of the angular velocity, and makes the output angular velocity and the control voltage have a linear relationship; then a Kalman filter is designed, and the parameters of the change of the angular velocity with the voltage are estimated by using the controllable voltage input and the gyro angular velocity obtained by the solution. The present invention improves the accuracy and stability of the output of the hemispherical resonant gyroscope. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The accompanying drawings included are used to provide a further understanding of the embodiments of the present invention, which form a part of the specification, for illustrating the embodiments of the present invention, and for explaining the principles of the present invention together with the written description. Obviously, the drawings in the following description are only some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0008] Figure 1 The flowchart of the calibration method for the angle control voltage coefficient of a hemispherical resonator gyroscope provided according to a specific embodiment of the present invention is shown. Specific Embodiments

[0009] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. The following description of at least one exemplary embodiment is actually only illustrative and in no way limits the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0010] It should be noted that the terms used here are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used here, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or their combinations.

[0011] Unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions, and values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that for the convenience of description, the sizes of the various parts shown in the drawings are not drawn in actual proportional relationships. Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and devices should be regarded as part of the specification. In all the examples shown and discussed here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values.

[0012] As Figure 1 shown, a calibration method for the angle control voltage coefficient of a hemispherical resonator gyroscope is provided according to a specific embodiment of the present invention, and the method includes:

[0013] Use a fixed - angle control voltage to drive the rotation of the azimuth angle of the gyro's standing wave, and obtain the output angular rate of the gyro;

[0014] Use the least - squares method to model the angular rate error of the gyro during the driving process, and compensate the angular rate of the gyro;

[0015] According to the compensated angular rate of the gyro, use the Kalman filter algorithm to estimate the variation parameters of the angular rate with respect to the voltage, and complete the calibration of the angle - control voltage coefficient.

[0016] Applying this configuration method, a calibration method for the angle - control voltage coefficient of a hemispherical resonator gyro is provided. This method uses a fixed - angle control voltage to drive the rotation of the azimuth angle of the gyro's standing wave, models the variation of the angular rate with respect to the standing - wave azimuth angle, compensates the varying part of the angular rate, and makes the output angular rate and the control voltage show a linear relationship; then designs a Kalman filter, and uses the controllable voltage input and the calculated gyro angular rate to estimate the variation parameters of the angular rate with respect to the voltage. The present invention improves the accuracy and stability of the output of the hemispherical resonator gyro.

[0017] First of all, in the present invention, a fixed - angle control voltage is used to drive the rotation of the azimuth angle of the gyro's standing wave; the least - squares method is used to model the angular rate error of the gyro during the driving process, and the angular rate of the gyro is compensated.

[0018] During the detection and driving process, due to errors in the capacitance and the processing and installation of the hemispherical resonator, the output angular rate also has an error that varies with the standing - wave azimuth. During the process of driving the standing wave to rotate, due to the existence of errors, the relationship between the angle - control voltage and the angular rate is not completely linear, which affects the calibration of the control coefficient.

[0019] The angular rate error of the gyro varies with the standing - wave angle. Using the Fourier series, the noise is approximately fitted as a trigonometric function of the standing - wave angle. Conduct a driving - rotation test of the gyro on a static base. Through the values of the control - voltage input, the calculated angular rate, and the standing - wave angle, use the least - squares method to establish an error model, complete the compensation of the angular rate error, and make the output angular rate and the angle - control voltage show a linear relationship.

[0020] Furthermore, in the present invention, according to the compensated angular rate of the gyro, use the Kalman filter algorithm to estimate the variation parameters of the angular rate with respect to the voltage, and complete the calibration of the angle - control voltage coefficient.

[0021] After the aforementioned compensation of the angular rate error of the gyro, the error of the angular rate will no longer affect the calibration of the coefficient. Continue to use the Kalman filter to calibrate the angle - control voltage coefficient. By changing the amount of the control voltage, make the angular rate reach different values, and use the Kalman filter algorithm to calculate the estimated values of the angular rate and the control coefficient.

[0022] With the gyro angular rate and the angle control voltage coefficient as the state vector: X = [ωb] T , according to the relationship formula between the angular rate and the control voltage, the state equation is constructed as:

[0023]

[0024] where ω k is the gyro angular rate compensated at time k, b k-1 and b k are the angle control voltage coefficients at times k - 1 and k respectively, V s|k-1 is the angle control voltage at time k - 1, w ω and w b are the noises of the angular rate and the angle control parameter respectively.

[0025] The measurement equation is constructed as:

[0026] Z k = ω k + v k

[0027] where the observed value Z k is the calculation result of the angular rate, and v k is the measurement noise.

[0028] The state equation and the measurement equation are rewritten in the augmented form with respect to the state vector X:

[0029]

[0030] where w k = [w ω w b T is the process noise.

[0031] The coefficient matrix is:

[0032]

[0033] where V s|k is the angle control voltage at time k.

[0034] The Kalman filter equation is constructed:

[0035]

[0036] where F k and H k are the coefficient matrices of the state equation and the measurement equation respectively, Q k-1 and R k are the covariance matrices of the process noise and the measurement noise respectively; X k and X k-1 ​They are the filtering results of the state variable X at times k-1 and k, respectively, P k and P k-1 They are the filtering results of the covariance matrix P of the state variable X at times k-1 and k, respectively, X k|k-1 and P k|k-1 They are the one-step predicted values of the state variable and its covariance matrix, K k is the filtering gain, Z k is the observed value, and I is the identity matrix.

[0037] The method for calibrating the angle control voltage coefficient of the hemispherical resonator gyroscope according to the present invention analyzes the sources of the gyro angular rate noise and proposes a compensation method; after compensating the errors, the algorithm of Kalman filtering is used to estimate the control coefficient of the angle control voltage on the angular rate, obtaining an accurate control relationship, providing a basis for the subsequent rotation modulation process of the gyroscope and improving the calculation accuracy of the angular rate.

[0038] To further understand the present invention, the method for calibrating the angle control voltage coefficient of the hemispherical resonator gyroscope according to the present invention will be described in detail below in conjunction with specific embodiments.

[0039] This embodiment provides a method for calibrating the angle control voltage coefficient of a hemispherical resonator gyroscope, and the method specifically includes the following steps.

[0040] First, fix the gyroscope on a static base. When the vibration state of the gyroscope is stable, input the set angle control voltage value to make the standing wave azimuth angle change at a fixed rate. Simplify the angular rate error model into a Fourier series form:

[0041]

[0042] where, Δω is the gyro angular rate error; θ is the standing wave azimuth angle; a i and b i are both error model parameters, and the error model parameters a i and b i can be calculated by using the least squares method according to the input of the control voltage, the calculated angular rate and the value of the standing wave angle; a 0 is a constant value and does not need to be compensated; other parameters select appropriate orders according to the accuracy of the gyroscope after compensation, discard the high-order terms, and improve the calculation efficiency; i = 2, 3,... +∞.

[0043] Then, fix the gyroscope on a static base, input the set angle control voltage value to drive the standing wave to rotate. After compensating the error of the angular rate changing with the standing wave, the relationship between the angular rate of the gyroscope and the angle control voltage can be simplified as:

[0044] ω = V s b + Δω

[0045] where ω is the compensated gyro angular rate; V s is the angle control voltage input; b is the angle control voltage coefficient; Δω is the gyro angular rate error, which can be regarded as Gaussian white noise after compensating the error model and meets the conditions for using the Kalman filter. The process of calibrating the control coefficient using the Kalman filter algorithm is as follows:

[0046] Taking the gyro angular rate and the angle control voltage coefficient as the state vector: X = [ω b] T , according to the relationship formula between the angular rate and the control voltage, the state equation is constructed as:

[0047]

[0048] The measurement equation is constructed as:

[0049] Z k = ω k + v k .

[0050] Rewrite the state equation and the measurement equation into an augmented form with respect to the state vector X:

[0051]

[0052] The coefficient matrix is:

[0053]

[0054] The measurement noise intensity is determined according to the angular rate error compensation result. Using the above filter and the Kalman filter algorithm, the calibrated value of the angle control voltage coefficient can be obtained, improving the accuracy of the angular rate calculation.

[0055] In summary, the present invention provides a method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro. By analyzing the source of the gyro angular rate error, a method for calibrating the angle control voltage coefficient is designed, thereby realizing the rotation modulation of the gyro and improving the accuracy and stability of the gyro.

[0056] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for calibrating the angle control voltage coefficient of a hemispherical resonant gyroscope, characterized in that: The hemispherical resonant gyroscope angle control voltage coefficient calibration method comprises: The fixed angle control voltage is used to drive the gyro standing wave azimuth to rotate, and the gyro output angular rate is obtained; The least square method is used to model the gyro angular rate error during the driving process and compensate the gyro angular rate; According to the compensated gyro angular rate, the Kalman filter algorithm is used to estimate the variation parameters of the angular rate with voltage, and the calibration of the angle control voltage coefficient is completed.

2. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 1, characterized in that: according to Construct an angular rate error model, where Δω is the gyro angular rate error; θ is the standing wave azimuth; a i and b i All are error model parameters, a0 is a constant value; i=2,3,…+∞.

3. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 2, characterized in that: Error model parameter a i and b i The least square method is used to solve the problem based on the control voltage input, the calculated angular velocity and the standing wave angle.

4. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 2, characterized in that: The compensated gyro angular rate is expressed as: ω = V s b+Δω, where ω is the gyro angular rate after compensation; V s is the angle control voltage input; b is the angle control voltage coefficient; Δω is the gyro angular rate error.

5. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 4, characterized in that: In the Kalman filter algorithm, the gyro angular rate and angle control voltage coefficient are used as the state vector X: X = [ωb] T .

6. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 5, characterized in that: The state equation is constructed as Among them, ω k is the gyro angular rate after compensation at time k, b k-1 and b k are the angle control voltage coefficients at time k-1 and time k, V s|k-1 is the angle control voltage at time k-1, w ω With w b are the noise of the angular rate and angle control parameters respectively.

7. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 6, characterized in that: The measurement equation is constructed as: Z k =ω k +v k , where the observed value Z k is the result of the angular velocity solution, v k To measure noise.

8. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 7, characterized in that: Construct the Kalman filter equation: Among them, F k With H k are the coefficient matrices of the state equation and the measurement equation, Q k-1 With R k are the covariance of process noise and measurement noise, respectively, X k With X k-1 are the filtering results of the state variable X at time k-1 and time k, respectively, k With P k-1 are the filtering results of the covariance matrix P of the state variable X at time k-1 and time k, respectively. k|k-1 With P k|k-1 are the one-step prediction values ​​of the state variables and their covariance matrices, K k is the filter gain, Z k is the observed value, and I is the unit matrix.

9. The method for calibrating the angle control voltage coefficient of a hemispherical resonant gyro according to claim 8, characterized in that: The coefficient matrix of the state equation The coefficient matrix H of the measurement equation k =[1 0], where V s|k is the angle control voltage at time k.

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