CN114780903B - 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 PDFInfo
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Abstract
A method for identifying the asymmetry of X/Y channel drive gain and non-orthogonal error of electrode of hemispherical resonator gyroscope belongs to the technical field of identification of error parameters 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 angleThe 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 identifying the asymmetry of the X/Y channel drive gain of the half-sphere resonance gyroscope and the non-orthogonal error of the electrode.
Description
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 environment of the X/Y driving circuits, so that gains of the X/Y driving signals are inconsistent and driving electrodes are not orthogonal, problems such as 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 method for identifying the asymmetry of X/Y channel drive gain and non-orthogonal error of an electrode of a hemispherical resonator gyroscope specifically comprises the following steps:
wherein, F x 、F y Electrostatic forces applied to the x and y axis electrodes, respectively, when k is x ≠k y And the y-axis electrode has an angle of deflection in the direction orthogonal to the x-axisWhen F is present x 、F y The expression of (a) is:
wherein k is x 、k y Respectively x-axis and y-axis drive circuit gain coefficients, G is harmonic oscillator kinematic model, omega 0 A given precessional rotation speed;
and giving an initial value k (0) of the driving gain asymmetry coefficient k and the non-orthogonal deflection angle of the electrodeInitial value ofAnd an initial value of H, H (0);
step 3, according to P r =Aω r To obtain
Then according to P r Expression of the calc function r (i):
r(i)=P d (i)-P r (i)
wherein, P r (i) Is P r Calculated value at time i, P d (i) R (i) is a value function of the moment i, and is an actual detection value obtained after processing a signal collected at the moment i;
step 4, calculating the Jacobian matrix J of the value function r (i) r (i) Then according to the Jacobian matrix J r (i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrodeAnd 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 4And 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 J r (i) The expression of (a) is:
further, the function is according to a Jacobian matrix J r (i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrodeThe increment of (c) and the increment of H are specifically:
wherein, the delta k (i) is the increment of the driving gain asymmetry coefficient k at the moment i,for non-orthogonal deflection angles of electrodesThe 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.
Further, the specific process of step 5 is as follows:
wherein k (i + 1),H (i + 1) is the driving gain asymmetry coefficient k and the non-orthogonal deflection angle of the electrodeAnd the value of H at time i + 1.
Further, an initial value k (0) =1 of the driving gain asymmetry coefficient k.
Further, an initial value H (0) =0 of H.
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 angleAnd the time precession speed model identifies the error parameters by using an identification method, so that the asymmetric error coefficient of the driving gain and the non-orthogonal deflection angle of the electrode are calculated, the problems of standing wave azimuth drift and control loop error are solved, and the performance of the hemispherical resonant gyroscope is improved.
Drawings
FIG. 1 is a graph of a driving gain asymmetry coefficient k identification;
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:
wherein, F x 、F y Electrostatic forces applied to the x and y axis electrodes, respectively, when k is x ≠k y And the y-axis electrode has a deflection angle with respect to the x-axis orthogonal directionWhen F is present x 、F y The expression of (a) is:
wherein k is x 、k y Respectively, the gain coefficients of the driving circuit in x and y axes, G is a harmonic oscillator kinematic model, omega 0 A given precessional rotation speed;
and giving an initial value k (0) of the driving gain asymmetry coefficient k and the non-orthogonal deflection angle of the electrodeInitial value ofAnd 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, k 0 Is the gain coefficient, omega, of an ideal x-axis and y-axis drive circuit 0 A given precessional rotation speed;
step (ii) of3. According to P r =Aω r To obtain
Then according to P r Expression of the calc function r (i):
r(i)=P d (i)-P r (i)
wherein, P r (i) Is P r Calculated value at time i, P d (i) R (i) is a value function of the i moment, and is an actual detection value obtained after the signal acquired at the i moment is processed;
step 4, calculating the Jacobian matrix J of the value function r (i) r (i) Then according to the Jacobian matrix J r (i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrodeAnd 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 electrodeAnd 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, the hemispherical harmonic oscillator is subjected to parameter excitation, 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 vibration x 、S x 、C y 、S y And performing secondary combination to obtain a hemispherical resonator 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;
the second embodiment, which is different from the first embodiment, is: the Jacobian matrix J r (i) The expression of (a) is:
other steps and parameters are the same as those in the first embodiment.
The third embodiment, which is different from the first or second embodiment, is: the Jacobian matrix J r (i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrodeThe increment of (c) and the increment of H are specifically:
wherein, the delta k (i) is the increment of the driving gain asymmetry coefficient k at the moment i,for non-orthogonal deflection angles of electrodesThe 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.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth embodiment and the differences between this embodiment and the first to the third embodiments are: the specific process of the step 5 is as follows:
wherein k (i + 1),H (i + 1) is the driving gain asymmetry coefficient k and the non-orthogonal deflection angle of the electrodeAnd 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: an initial value k (0) =1 of the driving gain asymmetry coefficient k.
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 angleInitial value of (2)
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment and the differences between the first to sixth embodiments are as follows: an initial value H (0) =0 of the H.
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 3, collecting parameters C related to harmonic oscillator standing wave vibration x 、S x 、C y 、S y And performing secondary combination to obtain a hemispherical resonator gyro control system variable E, Q, S, R, and calculating a standing wave azimuth angle theta and a precession speed omega r And vibration amplitude A:
step 4, since the nonlinear least square identification method is a recursive algorithm, an initial estimation value must be given first 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
H=k 0 Gω 0
Wherein G is harmonic oscillator kinematic model, k 0 Is the gain coefficient, omega, of an ideal x-axis and y-axis drive circuit 0 For a given precessional speed, k x 、k y Respectively x-axis and y-axis drive circuit gain coefficients, k is a drive gain asymmetry coefficient,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 static electricity force of the standing wave precession is as follows:
wherein, F x 、F y Electrostatic forces applied to the x and y axis electrodes, respectively.
When k is 0 =k x ≠k y And the y-axis electrode has an angle of deflection in the direction orthogonal to the x-axisThe parameter equation of the static electricity force for driving the standing wave precession is as follows:
the precession speed perpendicular to the amplitude axis direction of the standing wave is as follows:
simplifying to obtain:
the value function at this time: r (i) = P d (i)-P r (i)
Wherein, P = A ω r ,P d For acquiring actual detection values after signal processing, P r Calculating a value according to a theoretical model;
step 6, calculating a Jacobian matrix of the function at the current moment:
step 7, calculating the increment of the identification parameter at the current moment:
step 8, updating the identification parameters at the next moment:
step 9, judging whether a hemispherical resonator gyro control system variable signal E, Q, S, R is input, if so, jumping to step 5, and if not, jumping to step 10;
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 obtainedThe 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 of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.
Claims (5)
1. A method for identifying the asymmetry of X/Y channel drive gain and non-orthogonal error of an electrode of a hemispherical resonator gyroscope is characterized by comprising the following steps:
step 1, solving out precession speed omega according to standing wave azimuth angle theta and vibration amplitude A r (ii) a The specific process comprises the following steps:
wherein, F x 、F y Electrostatic forces applied to the x and y axis electrodes, respectively, when k is x ≠k y And the non-orthogonal off-angle of the electrode isWhen F is present x 、F y The expression of (a) is:
wherein k is x 、k y Respectively x-axis and y-axis drive circuit gain coefficients, G is harmonic oscillator kinematic model, omega 0 A given precessional rotation speed;
step (ii) of2. Definition H = k 0 Gω 0 ,k 0 The 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 electrodeInitial value ofAnd an initial value of H, H (0);
step 3, according to P r =Aω r To obtain
Then according to P r Expression of the calc function r (i):
r(i)=P d (i)-P r (i)
wherein, P r (i) Is P r Calculated value at time i, P d (i) R (i) is a value function of the moment i, and is an actual detection value obtained after processing a signal collected at the moment i;
step 4, calculating the Jacobian matrix J of the value function r (i) r (i) Then according to the Jacobian matrix J r (i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrodeAnd increments of H;
the Jacobian matrix J r (i) The expression of (a) is:
the Jacobian matrix J r (i) Calculating increment of driving gain asymmetry coefficient k at moment i and non-orthogonal deflection angle of electrodeThe increment of (c) and the increment of H are specifically:
wherein Δ k (i) is the increment of the driving gain asymmetry coefficient k at the moment i,for non-orthogonal deflection angles of electrodesDelta H (i) is the increment of H at the moment i, an upper superscript T represents the transposition of the matrix, and an upper superscript-1 represents the inverse of the matrix;
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 electrodeAnd 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.
2. The 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 as claimed in claim 1, wherein the specific process of the step 5 is as follows:
3. The method for identifying the X/Y channel driving gain asymmetry and the electrode non-orthogonality error of the hemispherical resonator gyroscope of claim 2, wherein an initial value k (0) =1 of the driving gain asymmetry coefficient k.
5. The method as claimed in claim 4, wherein the initial value of H is H (0) =0.
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