CN114780903A - Hemispherical resonator gyroscope X/Y channel drive gain asymmetry and electrode non-orthogonal error identification method - Google Patents

Hemispherical resonator gyroscope X/Y channel drive gain asymmetry and electrode non-orthogonal error identification method Download PDF

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CN114780903A
CN114780903A CN202210480919.XA CN202210480919A CN114780903A CN 114780903 A CN114780903 A CN 114780903A CN 202210480919 A CN202210480919 A CN 202210480919A CN 114780903 A CN114780903 A CN 114780903A
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解伟男
王奇
奚伯齐
孙一为
伊国兴
王常虹
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Abstract

A method for identifying the asymmetry of X/Y channel drive gain and non-orthogonal error of an electrode of a hemispherical resonator gyroscope belongs to the technical field of error parameter identification of hemispherical resonator gyroscopes. The invention solves the problems of standing wave azimuth drift and control loop error caused by inconsistent gains of two X/Y driving signals and non-orthogonality of driving electrodes. The method is based on the existence of a drive gain asymmetric coefficient k and an electrode non-orthogonal deflection angle
Figure DDA0003627818440000011
The time precession speed model identifies the error parameters by using an identification method, so that the driving gain asymmetric error coefficient and the electrode non-orthogonal deflection angle are calculated, the problems of standing wave azimuth drift and control loop errors are solved, and the performance of the hemispherical resonator gyroscope is improved. The method can be applied to the semi-spherical resonance gyroscopeAnd identifying the asymmetry of the driving gain of the spiral X/Y path and the non-orthogonal error of the electrode.

Description

Hemispherical resonator gyroscope X/Y path drive gain asymmetry and electrode non-orthogonal error identification method
Technical Field
The invention belongs to the technical field of hemispherical resonator gyroscope error parameter identification, and particularly relates to a hemispherical resonator gyroscope X/Y path drive gain asymmetry and electrode non-orthogonal error identification method.
Background
The hemispherical resonator gyroscope is a new generation high-precision gyroscope developed on the basis of the traditional mechanical rotor gyroscope and optical gyroscope, is a high-precision gyroscope with inertial navigation level performance in a Coriolis vibration gyroscope, is one of the mainstream high-precision inertial devices at present, and is widely applied to the fields of aviation, aerospace, navigation and the like. The hemispherical resonator gyroscope detects the position of the standing wave in real time through the X/Y signals, and then the external input angle and the angular speed can be measured. When the hemispherical resonator gyroscope works normally, an amplitude control loop is needed to stabilize the vibration amplitude of the harmonic oscillator, and an orthogonal control loop is needed to reduce the amplitude of orthogonal waves. The gyro parameters are influenced by factors such as parameter matching conditions, mechanical errors and environments of the X/Y driving circuits, so that gains of the X/Y driving signals are inconsistent, driving electrodes are not orthogonal, standing wave azimuth drift and control loop errors are caused, and the performance of the gyro is reduced. Therefore, it is very significant to provide a method for identifying the asymmetry of the driving gain of the X/Y path of the hemispherical resonator gyroscope and the non-orthogonal error of the electrode.
Disclosure of Invention
The invention aims to solve the problems of standing wave azimuth drift and control loop error caused by inconsistent gain of two X/Y driving signals and non-orthogonality of driving electrodes, and provides a method for identifying the asymmetry of the X/Y channel driving gain of a hemispherical resonator gyroscope and the non-orthogonality of the electrodes.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a hemispherical resonator gyroscope X/Y path drive gain asymmetry and electrode non-orthogonal error identification method specifically comprises the following steps:
step 1, solving out precession speed omega according to standing wave azimuth angle theta and vibration amplitude Ar(ii) a The specific process comprises the following steps:
Figure BDA0003627818420000011
wherein, Fx、FyElectrostatic forces applied to the x and y axis electrodes, respectively, when k isx≠kyAnd the y-axis electrode has an angle of deflection in the direction orthogonal to the x-axis
Figure BDA0003627818420000012
When F is turned onx、FyThe expression of (c) is:
Figure BDA0003627818420000013
wherein k isx、kyRespectively, the gain coefficients of the driving circuit in x and y axes, G is a harmonic oscillator kinematic model, omega0A given precessional rotation speed;
step 2, defining H ═ k0Gω0，k0The gain coefficients of the ideal x-axis and y-axis driving circuits;
and setting an initial value k (0) of a driving gain asymmetry coefficient k and a non-orthogonal deflection angle of an electrode
Figure BDA0003627818420000021
Initial value of (2)
Figure BDA0003627818420000022
And an initial value of H, H (0);
step 3, according to Pr＝AωrTo obtain
Figure BDA0003627818420000023
Then according to PrExpression of the computational function r (i):
r(i)＝Pd(i)-Pr(i)
wherein, Pr(i) Is PrCalculated value at time i, Pd(i) R (i) is an actual detection value obtained after processing the signal acquired at the moment i, and is a value function of the moment i;
step 4, calculating the Jacobian matrix J of the value function r (i)r(i) Then according to the Jacobian matrix Jr(i) Calculating increment of driving gain asymmetry coefficient k at the moment i and non-orthogonal deflection angle of electrode
Figure BDA0003627818420000024
And increments of H;
step 5, driving gain asymmetry coefficient k and electrode non-orthogonal deflection angle of each increment pair i +1 moment calculated in the step 4
Figure BDA0003627818420000025
And H, updating;
and 6, repeatedly executing the processes from the step 3 to the step 5 until no control system variable is input, and taking the driving gain asymmetric coefficient and the electrode non-orthogonal deflection angle obtained by the last iteration as final outputs, namely obtaining the identification results of the driving gain asymmetric coefficient and the electrode non-orthogonal deflection angle.
Further, the Jacobian matrix Jr(i) The expression of (a) is:
Figure BDA0003627818420000026
further, the function is according to a Jacobian matrix Jr(i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrode
Figure BDA0003627818420000027
The increment of (c) and the increment of (H) are specifically:
Figure BDA0003627818420000028
wherein, Δ k (i) is the increment of the driving gain asymmetry coefficient k at the time point i,
Figure BDA0003627818420000029
is non-orthogonal deflection angle of electrode
Figure BDA00036278184200000210
The increment at time i, Δ H (i), is the increment of H at time i, with superscript T representing the transpose of the matrix and superscript-1 representing the inverse of the matrix.
Further, the specific process of step 5 is as follows:
Figure BDA0003627818420000031
wherein k (i +1),
Figure BDA0003627818420000032
H (i +1) is the driving gain asymmetry coefficient k and the non-orthogonal deflection angle of the electrode
Figure BDA0003627818420000033
And the value of H at time i + 1.
Further, an initial value k (0) of the driving gain asymmetry coefficient k is 1.
Further, the electrodes are not orthogonally inclined
Figure BDA0003627818420000034
Initial value of
Figure BDA0003627818420000035
Further, the initial value H (0) of H is 0.
The invention has the beneficial effects that:
the method is based on the existence of a drive gain asymmetric coefficient k and an electrode non-orthogonal deflection angle
Figure BDA0003627818420000036
The time precession speed model identifies the error parameters by using an identification method, so that the driving gain asymmetric error coefficient and the electrode non-orthogonal deflection angle are calculated, the problems of standing wave azimuth drift and control loop errors are solved, and the performance of the hemispherical resonator gyroscope is improved.
Drawings
FIG. 1 is a graph of a driving gain asymmetry factor k identification;
FIG. 2 shows non-orthogonal deflection angles of electrodes
Figure BDA0003627818420000037
A graph is identified.
Detailed Description
The first embodiment is as follows: the method for identifying the X/Y channel drive gain asymmetry and the electrode non-orthogonal error of the hemispherical resonator gyroscope in the embodiment comprises the following specific processes:
step 1, calculating a precession velocity omega according to a standing wave azimuth angle theta and a vibration amplitude Ar(ii) a The specific process comprises the following steps:
Figure BDA0003627818420000038
wherein, Fx、FyElectrostatic forces applied to the x and y axis electrodes, respectively, when k isx≠kyAnd the y-axis electrode has a deflection angle with respect to the x-axis orthogonal direction
Figure BDA0003627818420000039
When F is presentx、FyThe expression of (c) is:
Figure BDA00036278184200000310
wherein k isx、kyRespectively, the gain coefficients of the driving circuit in x and y axes, G is a harmonic oscillator kinematic model, omega0A given precessional rotation speed;
step 2, defining H ═ k0Gω0，k0The gain coefficients of the ideal x-axis and y-axis driving circuits;
and giving an initial value k (0) of the driving gain asymmetry coefficient k and the non-orthogonal deflection angle of the electrode
Figure BDA0003627818420000041
Initial value of
Figure BDA0003627818420000042
And an initial value of H, H (0);
usually, the gain deviation value of the electrode is less than 10 percent, the non-orthogonal deflection angle of the electrode is less than 10 degrees, and H is invariable in the precession process;
wherein G is harmonic oscillator kinematic model, k0Is the gain coefficient of ideal x and y axis driving circuit, omega0A given precessional rotation speed;
step 3, according to Pr＝AωrTo obtain
Figure BDA0003627818420000043
Then according to PrThe expression of the computational value function r (i):
r(i)＝Pd(i)-Pr(i)
wherein, Pr(i) Is PrCalculated value at time i, Pd(i) R (i) is an actual detection value obtained after processing the signal acquired at the moment i, and is a value function of the moment i;
step 4, calculating the Jacobian matrix J of the value function r (i)r(i) Then according to the Jacobian matrix Jr(i) Calculating increment of driving gain asymmetry coefficient k at the moment i and non-orthogonal deflection angle of electrode
Figure BDA0003627818420000045
And increments of H;
step 5, driving gain asymmetry coefficient k and electrode non-orthogonal deflection angle of each increment pair i +1 moment calculated in the step 4
Figure BDA0003627818420000046
And H, updating;
and 6, repeatedly executing the processes from the step 3 to the step 5 until no control system variable is input, and taking the driving gain asymmetric coefficient and the electrode non-orthogonal deflection angle obtained by the last iteration as final outputs, namely obtaining the identification results of the driving gain asymmetric coefficient and the electrode non-orthogonal deflection angle.
In the embodiment, firstly, parameter excitation is carried out on the hemispherical harmonic oscillator, so that the vibration amplitude of the harmonic oscillator is stable; applying a constant electrostatic force along the direction vertical to the amplitude axis of the ideal standing wave to make the standing wave precess; then collecting parameters C related to harmonic oscillator standing wave vibrationx、Sx、Cy、SyAnd carrying out secondary combination to obtain a hemispherical resonant gyro control system variable E, Q, S, R signal.
Solving a standing wave azimuth angle theta and a vibration amplitude A according to the control system variables E, Q, S and R;
Figure BDA0003627818420000044
Figure BDA0003627818420000051
the second embodiment, the difference between the first embodiment and the second embodiment, are: the Jacobian matrix Jr(i) The expression of (c) is:
Figure BDA0003627818420000052
other steps and parameters are the same as those in the first embodiment.
The third embodiment and the first or second embodiment are different: said basis of Jacobian matrix Jr(i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrode
Figure BDA0003627818420000053
The increment of (c) and the increment of H are specifically:
Figure BDA0003627818420000054
wherein, Δ k (i) is the increment of the driving gain asymmetry coefficient k at the time point i,
Figure BDA0003627818420000055
is non-orthogonal deflection angle of electrode
Figure BDA0003627818420000056
The increment at time i, Δ H (i), is the increment of H at time i, with superscript T representing the transpose of the matrix and superscript-1 representing the inverse of the matrix.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth embodiment is different from the first to the third embodiments in that: the specific process of the step 5 is as follows:
Figure BDA0003627818420000057
wherein k (i +1),
Figure BDA0003627818420000058
H (i +1) is the driving gain asymmetry coefficient k and the non-orthogonal deflection angle of the electrode
Figure BDA0003627818420000059
And the value of H at time i + 1.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth embodiment is different from the first to the fourth embodiments in that: the initial value k (0) of the driving gain asymmetry coefficient k is 1.
Other steps and parameters are the same as in one of the first to fourth embodiments.
Sixth embodiment, the difference between this embodiment and one of the first to fifth embodiments, is: the electrode non-orthogonal deflection angle
Figure BDA00036278184200000510
Initial value of
Figure BDA00036278184200000511
Other steps and parameters are the same as in one of the first to fifth embodiments.
The seventh embodiment and the differences between the first to sixth embodiments are as follows: the initial value H (0) of H is 0.
Other steps and parameters are the same as those in one of the first to sixth embodiments.
Examples
The process of the invention implemented by taking a simulation experiment as an example is as follows:
step 1, performing parameter excitation on a hemispherical harmonic oscillator to stabilize the vibration amplitude of the harmonic oscillator;
step 2, setting the sampling frequency to be fs100Hz, sampling time t 100s, driving electrode gain ratio k 1.03, non-orthogonal electrode deflection angle
Figure BDA0003627818420000061
Applying a constant electrostatic force along the direction vertical to the amplitude axis of the ideal standing wave to make the standing wave precess;
step 3, collecting parameters C related to harmonic oscillator standing wave vibrationx、Sx、Cy、SyAnd performing secondary combination to obtain a hemispherical resonant gyroscope control system variable E, Q, S, R, and calculating a standing wave azimuth angle theta and a precession speed omegarAnd vibration amplitude A:
Figure BDA0003627818420000062
Figure BDA0003627818420000063
Figure BDA0003627818420000064
step 4, since the nonlinear least square identification method is a recursive algorithm, an initial estimation value must be given first
Figure BDA0003627818420000065
Figure BDA0003627818420000066
Normally, the gain deviation value of the electrode is less than 10%, the non-orthogonal deviation angle of the electrode is less than 10 degrees, and H is an invariant in the precession process. Therefore, the least square method is given to identify the initial value
Figure BDA0003627818420000067
H＝k0Gω0
Figure BDA0003627818420000068
Wherein G is harmonic oscillator kinematic model, k0Is the gain coefficient of ideal x and y axis driving circuit, omega0For a given precessional speed, kx、kyRespectively x-axis and y-axis drive circuit gain coefficients, k is a drive gain asymmetry coefficient,
Figure BDA0003627818420000069
is the non-orthogonal deflection angle of the electrode;
step 5, calculating a current time value function:
when the included angle between the amplitude axis of the standing wave and the x-axis electrode is theta, the parameter equation for driving the precession electrostatic force of the standing wave is as follows:
Figure BDA00036278184200000610
wherein, Fx、FyElectrostatic forces applied to the x and y axis electrodes, respectively.
When k is0＝kx≠kyAnd the y-axis electrode has an angle of deflection in the direction orthogonal to the x-axis
Figure BDA0003627818420000071
The parameter equation for driving the standing wave precession electrostatic force is as follows:
Figure BDA0003627818420000072
the precession speed perpendicular to the amplitude axis direction of the standing wave at this time is as follows:
Figure BDA0003627818420000073
simplifying to obtain:
Figure BDA0003627818420000074
the value function at this time: r (i) Pd(i)-Pr(i)
Wherein, P is A omegar，PdFor acquiring actual detection values after signal processing, PrCalculating a value according to a theoretical model;
step 6, calculating a Jacobian matrix of the value function at the current moment:
Figure BDA0003627818420000075
step 7, calculating the increment of the identification parameter at the current moment:
Figure BDA0003627818420000076
step 8, updating the identification parameters at the next moment:
Figure BDA0003627818420000077
step 9, judging whether a variable signal E, Q, S, R of the hemispherical resonator gyro control system is input, if so, jumping to step 5, and if not, jumping to step 10;
step 10, outputting the driving gain coefficient
Figure BDA0003627818420000078
In conclusion, the asymmetry of the X/Y channel driving gain of the half-sphere resonance gyroscope and the identification of the non-orthogonal error of the electrode are realized.
The simulation results are shown in FIG. 1 and FIG. 2, from which the final identification can be obtained
Figure BDA0003627818420000079
The method of the invention has high identification precision.
The above-described calculation examples of the present invention are merely to describe the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications can be made on the basis of the foregoing description, and it is not intended to exhaust all of the embodiments, and all obvious variations and modifications which fall within the scope of the invention are intended to be included within the scope of the invention.

Claims (7)

1. A hemispherical resonator gyroscope X/Y path drive gain asymmetry and electrode non-orthogonal error identification method is characterized by comprising the following steps:
step 1, calculating a precession velocity omega according to a standing wave azimuth angle theta and a vibration amplitude Ar(ii) a The specific process comprises the following steps:
Figure FDA0003627818410000011
wherein, Fx、FyElectrostatic forces applied to the x and y axis electrodes, respectively, when k isx≠kyAnd the y-axis electrode has a deflection angle with respect to the x-axis orthogonal direction
Figure FDA0003627818410000012
When F is turned onx、FyThe expression of (c) is:
Figure FDA0003627818410000013
wherein k isx、kyRespectively, the gain coefficients of the driving circuit in x and y axes, G is a harmonic oscillator kinematic model, omega0A given precessional rotation speed;
step 2, defining H ═ k0Gω0，k0The gain coefficients of the driving circuit are ideal x and y axes;
and setting an initial value k (0) of a driving gain asymmetry coefficient k and a non-orthogonal deflection angle of an electrode
Figure FDA0003627818410000014
Initial value of (2)
Figure FDA0003627818410000015
And an initial value of H, H (0);
step 3, according to Pr＝AωrTo obtain
Figure FDA0003627818410000016
Then according to PrThe expression of the computational value function r (i):
r(i)＝Pd(i)-Pr(i)
wherein, Pr(i) Is PrCalculated value at time i, Pd(i) R (i) is the value at time i, which is the actual detection value obtained after processing the signal acquired at time iA function;
step 4, calculating the Jacobian matrix J of the value function r (i)r(i) Then according to the Jacobian matrix Jr(i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrode
Figure FDA0003627818410000017
And increments of H;
step 5, according to the driving gain asymmetry coefficient k of each increment calculated in the step 4 to the i +1 moment and the non-orthogonal deflection angle of the electrode
Figure FDA0003627818410000018
And H, updating;
and 6, repeatedly executing the processes from the step 3 to the step 5 until no control system variable is input, and taking the driving gain asymmetric coefficient and the electrode non-orthogonal deflection angle obtained by the last iteration as final output, namely obtaining the identification results of the driving gain asymmetric coefficient and the electrode non-orthogonal deflection angle.
2. The method as claimed in claim 1, wherein the Jacobian matrix J is used for identifying X/Y channel drive gain asymmetry and electrode non-orthogonality error of the hemispherical resonator gyroscoper(i) The expression of (a) is:
Figure FDA0003627818410000021
3. the method as claimed in claim 2, wherein the method for identifying X/Y channel drive gain asymmetry and electrode non-orthogonality is based on Jacobian matrix Jr(i) Calculating increment of driving gain asymmetry coefficient k at the moment i and non-orthogonal deflection angle of electrode
Figure FDA0003627818410000022
And an increment of H, which is specifically：
Figure FDA0003627818410000023
Where Δ k (i) is the increment of the driving gain asymmetry factor k at time i,
Figure FDA0003627818410000024
is non-orthogonal deflection angle of electrode
Figure FDA0003627818410000025
The increment at time i, Δ H (i), is the increment of H at time i, the superscript T represents the transpose of the matrix, and the superscript-1 represents the inverse of the matrix.
4. The method as claimed in claim 3, wherein the specific process of step 5 is as follows:
Figure FDA0003627818410000026
wherein k (i +1),
Figure FDA0003627818410000027
H (i +1) is a driving gain asymmetry coefficient k and an electrode non-orthogonal deflection angle
Figure FDA0003627818410000028
And the value of H at time i + 1.
5. The method as claimed in claim 4, wherein the initial value k (0) of the asymmetry coefficient k is 1.
6. The method of claim 5The method for identifying the X/Y channel drive gain asymmetry and the electrode non-orthogonal error of the hemispherical resonator gyroscope is characterized in that the electrode non-orthogonal deflection angle
Figure FDA0003627818410000029
Initial value of
Figure FDA00036278184100000210
7. The method as claimed in claim 6, wherein the initial value of H is H (0) ═ 0.
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CN116625410A (en) * 2023-07-20 2023-08-22 中国船舶集团有限公司第七〇七研究所 Hemispherical resonator gyro excitation electrode gain calibration method
CN116625410B (en) * 2023-07-20 2023-09-19 中国船舶集团有限公司第七〇七研究所 Hemispherical resonator gyro excitation electrode gain calibration method

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