CN114543843B - Method for calibrating and correcting channel error of resonant gyroscope - Google Patents
Method for calibrating and correcting channel error of resonant gyroscope Download PDFInfo
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Abstract
The invention relates to a resonant gyroscope channel error calibration methodThe correction method comprises the following steps: 1. establishing a channel error identification model, and placing the model in a control system of a resonant gyroscope; 2. determining the number n of error parameters to be identified, and calling an identification model; 3. initializing a standing wave azimuth angle theta, and placing the standing wave azimuth angle theta at a random initial position theta 0 The method comprises the steps of carrying out a first treatment on the surface of the 4. Moving θ to be positioned at θ i ＝θ 0 +ipi/2 n; 5. calculate each θ i Additional drift angle at
6. Identifying and calculating n error parameters; 7. substituting the error parameters into an error model, and correcting the current loop coefficient; 8. determining calculation residual error e of each parameter k Whether or not the set termination condition e is satisfied k <e set Counting the number k of parameters subjected to correction; 9. updating the number n of parameters to be identified and a channel error identification model; 10. if the parameter n to be identified is not zero, updating the random initial standing wave azimuth angle theta 0 ＝θ 0 +r, return to step 2. Otherwise, the iteration is stopped. The method improves zero offset and resolution performance of the gyroscope and improves scale factor nonlinearity.
Description
Technical Field
The invention belongs to the technical field of inertial instrument control, and particularly relates to a method for calibrating and correcting channel errors of a resonant gyroscope.
Background
Compared with the traditional force feedback mode, the full angle mode resonant gyroscope has the outstanding advantages of wide range, high dynamic performance, stable calibration factor and the like. The stable control and the angle reading of the standing wave are realized by driving and detecting the vibration mode of the harmonic oscillator through the fixed electrode. As an angle sensor, the standing wave azimuth angle is directly sensitive to external angle change, so that the angle sensor can be positioned at any position of the annular harmonic oscillator. In practical application, due to the consistency of processing and manufacturing and devices, additional measurement errors are overlapped and coupled with a harmonic oscillator dynamics model, and the performance index of the gyroscope is seriously affected.
Besides frequency splitting and damping non-uniformity caused by defects of a harmonic oscillator body, errors caused by inconsistent electrodes and circuits can be uniformly equivalent to inconsistent errors of gains, positions and phase shifts of the electrodes. The electrodes are classified into driving channel errors and detecting channel errors according to their application to driving or detection. The presence of these errors introduces, on the one hand, an additional zero offset drift in the gyro output; on the other hand, the measurement accuracy of the standing wave angle is disturbed, and the error is superimposed on the mapping coefficient of the standing wave angle and the external angle, namely the Blaine coefficient, so that the periodic characteristic along with the standing wave position is shown.
To achieve good gyroscopic performance, channel errors need to be corrected. In the traditional mode, a single index such as zero offset, scale factors and the like is compensated and corrected in an experimental data fitting mode. However, because the channel error parameters are more and are coupled with the harmonic oscillator errors, nonlinearity is generated, and a good correction effect is difficult to achieve in a later stage fitting compensation mode.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for calibrating and correcting the channel error of a resonant gyroscope, which can improve zero offset and resolution performance of the gyroscope, reduce the error of a scale factor and improve the nonlinearity of the scale factor.
The above object of the present invention is achieved by the following technical solutions:
a method for calibrating and correcting channel errors of a resonant gyroscope is characterized by comprising the following steps of: the method comprises the following steps:
step 3, initializing a standing wave azimuth angle theta and placing the standing wave azimuth angle theta at a random initial position theta 0 ；
Step 4, moving the standing wave azimuth angle theta to be positioned at the theta i ＝θ 0 +iπ/2n，i＝1,…,n；
Step 5, calculating the angle extra drift amount at each standing wave azimuth angle thetai in the process of moving the standing wave azimuth angle thetai n times in the step 4;
step 6, according to the additional drift angle
The channel error identification model is used for identifying and calculating n error parameters;
step 7, substituting the calculated error parameters into the corresponding positions of the error model to correct the current loop coefficient;
step 8, judging the calculation residual error e of each parameter k Whether or not the set termination condition e is satisfied k <e set Counting the number k of parameters subjected to correction;
step 9, updating the number n of parameters to be identified and a channel error identification model;
step 10, if the parameter n to be identified is not zero, updating the random initial standing wave azimuth angle θ 0 ＝θ 0 +r, returning to step 2; otherwise, the iteration is stopped.
Further: the channel errors involved in step 1 include a detection channel error a and a drive channel error B;
detecting channel error A includes electrode gain offset Δk d Electrode position deviation delta theta d Electrode phase shift deviation delta phi d For the detection channel error A, the standing wave angle is calculated
Real angle with standing wave->
There is an error related to the standing wave azimuth angle θ as shown in equation (1).
Wherein-a is the antinode amplitude;
b is the node amplitude;
——
calculating a standing wave angle;
——Δk d to detect electrode gain deviation;
——Δθ d to detect electrode position deviations;
——Δφ d to detect the electrode phase shift deviation;
the driving channel error B includes the electrode gain deviation Deltak e Deviation of electrode position
And->
Electrode phase shift deviation delta phi e The method comprises the steps of carrying out a first treatment on the surface of the For the drive channel error B, it is mainly manifested as cross-coupling of the control signals, thereby causing additional drift Δε at each standing wave azimuth angle θ e An error equation of the driving error B to the standing wave azimuth angle theta is established as shown in a formula (2):
in-Deltak e Driving the electrode gain bias for X;
——
x, Y drive electrode position deviations;
——Δφ e phase shift deviation for Y driving electrode;
——Δε e introducing additional drift for drive error;
SF is the electrode force application scale factor;
——
inducing a standing wave azimuth drift angle for the driving error;
——C a is a stable control signal;
——C q is a quadrature control signal;
the real angle of the standing wave is detected by the existence of the channel error A
Unknown, the standing wave angle θ in the driving error equation (2) is rewritten as an angle calculation value +.>
Obtaining a channel error identification model as shown in (3)
Further: in step 4, the rotation of the standing wave can be provided by the external carrier rotation speed omega, or by applying the active precession signal C p Providing.
Further: in step 5, an additional drift angle is calculated when the rotation is provided using the external carrier
The formula is as follows:
middle- (2)
Is an additional drift angle;
——
is the azimuth angle theta of the standing wave i Calculating the azimuth angle theta of the standing wave at the position;
-alpha is the Blaine coefficient truth value;
omega is the rotation speed of the external carrier;
t is the rotation time.
Further: the method for obtaining the real value of the Blaine coefficient comprises the following steps:
since the detection channel error matrix A has various anisotropic characteristics, the Coriolis force term in the harmonic oscillator dynamics equation generates additional errors, an equivalent Blaine coefficient is introduced, and the relation between the equivalent Blaine coefficient alpha' (theta) and the vibration azimuth angle theta is shown in a formula (5):
α′＝α+Δαcos[2(θ-θ α )] (5)
wherein-alpha' is an equivalent Blaine coefficient;
- θ is the standing wave azimuth;
——θ α an error angle is added to the Blaine coefficients.
According to the formula (5), the Blaine coefficient true value is obtained through calibration in a full-angle mode in a mode of the average and measurement information of the whole period, and the formula (6) is shown as follows:
further: in step 5, when active precession is employed, an additional drift angle is calculated
The formula is as follows:
wherein-SF is the force application scale;
——C p is an applied active precession signal.
The invention has the advantages and positive effects that:
1. according to the calibration correction method, the channel error is calculated and corrected on line in a mode of iteratively identifying the channel error parameter by independently moving the standing wave azimuth angle.
2. According to the calibration correction method, the additional error of angle calculation caused by the detection channel is corrected, and the accuracy of angle measurement is improved.
3. The calibration correction method corrects the additional error of the angle mapping coefficient to lead the angle mapping coefficient to tend to the Blaine coefficient, improves the dynamic characteristic and the angle detection nonlinearity, and improves the nonlinearity and the stability of the scale factor.
4. The calibration correction method reduces the extra drift rate caused by the driving channel, improves the angular resolution of the gyroscope and improves the zero offset stability of the gyroscope.
Drawings
FIG. 1 is a schematic plan view of a resonator;
FIG. 2 is a flow chart of a method for calibrating and correcting channel errors of a resonant gyroscope.
Detailed Description
The structure of the present invention will be further described by way of examples with reference to the accompanying drawings. It should be noted that the present embodiments are illustrative and not restrictive.
Fig. 1 is a schematic plan view of a harmonic oscillator, wherein the harmonic oscillator 1 is a core sensitive unit of a gyroscope, and materials of the harmonic oscillator can be quartz, silicon base, metal and the like according to different application requirements and precision grades. The electrodes 2 are used for driving and detecting the vibration of the harmonic oscillator, and comprise contact type and non-contact type, such as piezoelectric ceramics, capacitors and the like.
Fig. 2 is a flowchart of a method for calibrating and correcting channel errors of a resonant gyroscope according to the present invention.
The specific calibration correction steps and principles are as follows:
and step 1, establishing a channel error identification model, and placing the established model in a control system of the resonant gyroscope. The method comprises the following steps:
as for the channel error, it includes detecting the channel error a and driving the channel error B. Wherein the detection channel error A comprises electrode gain biasDifference Deltak d Electrode position deviation delta theta d Electrode phase shift deviation delta phi d . Electrode gain error Δk d The proportionality coefficient of vibration information reflected by the characterization orthogonal two-axis signals is inconsistent, so that the angle calculation
Non-linearities are created at different locations standing wave azimuth angles θ. Electrode position deviation delta theta d Characterization of the two-axis detection Signal V x 、V y The spatial position orthogonality is not strictly maintained, so the detected signal cannot truly reflect the two modes of vibration. Electrode phase shift deviation delta phi d Two-axis vibration information V representing the same time x 、V y Failing to be acquired synchronously, aliasing occurs in the time domain. Thereby the detection channel error a will commonly interfere with the angle +.>
Is biased, i.e. the calculated standing wave angle +.>
Real angle with standing wave->
There is an error related to the standing wave azimuth angle θ as shown in equation (1).
Wherein-a is the antinode amplitude;
b is the node amplitude;
——
calculating a standing wave angle;
——Δk d to detect electrode gain deviation;
——Δθ d to detect electrode position deviationDifference;
——Δφ d to detect electrode phase shift deviations.
The driving channel error B indicates that the driving V is applied with force X 、V Y In the event of errors in the electrodes and the lines, the actual effect of the applied force deviates from the expected, i.e. control signal (amplitude-stabilized control signal C a Quadrature control signal C q Active precession signal C p ) Coupling occurs on both modalities. Such defects may be equivalently drive electrode bias, respectively electrode gain bias Δk e Deviation of electrode position
And->
Electrode phase shift deviation delta phi e . For the drive channel error B, it is mainly manifested as cross-coupling of the control signals, thereby causing additional drift Δε at each standing wave azimuth angle θ e An error equation of the driving error B to the standing wave azimuth angle θ is established as shown in equation (2).
in-Deltak e Driving the electrode gain bias for X;
——
x, Y drive electrode position deviations;
——Δφ e phase shift deviation for Y driving electrode;
——Δε e introducing additional drift for drive error;
SF is the electrode force application scale factor;
——
inducing a standing wave azimuth drift angle for the driving error;
——C a is a stable control signal;
——C q is a quadrature control signal.
From equation (2), the additional drift term Δε e Is related to the azimuth angle theta of the standing wave and is derived from the harmonic control signal (amplitude-stabilized control signal C a Quadrature control signal C q Active precession signal C p ) Is coupled to the coupling of (a). In actual operation, due to the existence of the detection channel error A, the real angle of the standing wave
Since it is unknown, the standing wave angle θ in the error equation (2) needs to be rewritten as an angle calculation value (observation value)/(observation value)>
Obtaining a channel error identification model as shown in formula (3):
equation (3) is a seven-element one-time overrunning equation, and has an analytical solution, so that the error parameter can be solved and calculated according to the coupling state.
and (5) preparing before checking, and determining error parameters to be identified according to the working state and the precision grade requirement of the gyroscope. Due to the different physical sources of the error parameters, the stability of each parameter varies. For scenes with low requirements on environment state stability and precision, only partial parameters such as gain k and the like need to be identified; when the device is placed for a long time, the state change is large or the device is used with high precision, the whole parameters (the detection electrode gain deviation Deltak can be identified d Detecting electrode position deviation delta theta d Detecting electrode phase shift deviation delta phi d Gain deviation Deltak of driving electrode e Positional deviation of driving electrode
And->
Phase shift deviation delta phi of driving electrode e ). And if the number of parameters to be identified is large, the model complexity is high, the calculation cost is high, and the convergence speed is low. According to the number n of parameters to be identified, n independent observation data are required to be established for subsequent identification calculation.
Step 3, initializing a standing wave azimuth angle theta and placing the standing wave azimuth angle theta at a random initial position theta 0 . Specific:
excitation of vibration, rotation of vibration mode and detection of signal are carried out by electrode 2, and according to conventional full angle control, vector synthesis formula is adopted, and angle force application decomposition is carried out according to X axis and Y axis to generate drive electrode voltage V X 、V Y And realizing stable control of the gyro state of each standing wave azimuth angle theta. Initially, the standing wave azimuth angle theta is positioned at a random azimuth angle theta 0 。
Step 4, moving the standing wave azimuth angle theta to be positioned at the theta i ＝θ 0 +i pi/2n, i=1, …, n. Specific:
the rotation of the standing wave can be provided by the external carrier rotation speed omega, or by applying an active precession signal C p Providing. When active precession is applied, a precession signal C is calculated according to the application scale SF p And a rotation time t, to achieve a shift in the azimuth angle θ of the standing wave (i.e., θ t ＝θ 0 +C p SF.t). It should be noted that the applied voltage signal C is characterized by the applied force scale SF p And the generated standing wave rotation rate
Is different from the angle detection mapping coefficient, the brane coefficient alpha. In addition, the applied force scale SF is also affected by errors, so care should be taken to correct it during calibration to ensure additional drift Δε e Accuracy of the acquisition. The following description takes the external carrier rotation as an example, and if active precession is employed, there is the equation Ω=c p SF/alpha (for active precession and external carrier rotationConversion formula of operation
Step 5, calculating azimuth angles theta of the standing waves in the process of moving the azimuth angles theta of the standing waves in the step 4 for n times i Additional amount of angular drift at
Specific:
when the standing wave azimuth angle theta is moved to different positions theta i At this time, an additional drift angle is calculated
When external carrier is used to provide transfer Time of movementThe formula is as follows:
middle- (2)
Is an additional drift angle;
——
is the azimuth angle theta of the standing wave i Calculating the azimuth angle theta of the standing wave at the position;
-alpha is the Blaine coefficient truth value;
omega is the rotation speed of the external carrier;
t is the rotation time.
The Blaine coefficient true value alpha can be obtained through factory experiment calibration, and has very good stability because the Blaine coefficient true value alpha is only related to the geometric parameters of the harmonic oscillator, so the Blaine coefficient true value alpha can be used as a constant in the using process. The detection channel error matrix A has various anisotropic characteristics, so that the Coriolis force term in the harmonic oscillator dynamics equation generates additional errors, and the equivalent Braun coefficient alpha' (theta) caused by the additional errors becomes dependent on the vibration azimuth angle theta, and the formula is as follows:
α′＝α+Δαcos[2(θ-θ α )] (5)
wherein-alpha' is an equivalent Blaine coefficient;
- θ is the standing wave azimuth;
——θ α an error angle is added to the Blaine coefficients.
According to the formula (5), the Blaine coefficient true value can be obtained through calibration in a full-angle mode in a mode of the average and measurement information of the whole period, and the formula (6) is shown as follows:
when active precession is employedThe formula is as follows:
wherein-SF is the force application scale;
——C p for applying active precession signals
Step 6, according to the additional drift angle
And the channel error identification model is used for identifying and calculating n error parameters. The coupling degree is used as an evaluation index for identification by acquiring n independent equations which are equal to the number of parameters to be corrected, and the identification calculation of each error parameter can be carried out by a system identification method. The identification method can adopt traditional least square method, recursive least square method and the like, and can also adopt advanced algorithms such as genetic algorithm, particle swarm algorithm and the like.
And 7, substituting the calculated error parameters into the corresponding positions of the channel error identification model established in the step 1, and correcting the current loop coefficient. Specifically, the identified parameters are corrected according to the analytic equations (1) and (2) to the loop. The convergence rate varies due to the different expression of the parameters.
Step 8, judging the calculation residual error e of each parameter k Whether or not the set termination condition e is satisfied k <e set And counting the number k of parameters subjected to correction. Specific: in order to reduce the calculation cost, accelerate the convergence process and the stability, set independent termination conditions for each parameter, and after one iteration is completed, identify the residual error e according to each parameter k (i.e. the difference between the current calculated value and the last calculated value) is less than a set threshold e set And counting the number k of parameters meeting the termination condition.
And 9, updating the number n of parameters to be identified and the identification model. Specific: when a certain parameter meets the termination condition e k <e set And (3) setting the corresponding parameter in the error equation in the step (1) as a calculated fixed value, and eliminating identification correction. The remainder not meeting the termination condition e k <e set And (3) continuing the identification calculation in the next iteration. At this time, the parameter number to be identified becomes n=n-k, and all parameter identification is completed until n=0, iteration is stopped, and correction is completed.
Step 10, if the parameter n to be identified is not zero, updating the random initial standing wave azimuth angle θ 0 ＝θ 0 And +r, returning to the step 2, and repeating the identification process until all parameters are corrected. Wherein, to generate random standing wave azimuth angle theta 0 ＝θ 0 +r as the initial azimuth θ of the current recognition 0 The reason for (2) is: in order to keep the random characteristic of each iteration data, the recognition result is prevented from falling into a local optimal solution.
Although the embodiments of the present invention and the accompanying drawings have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments and the disclosure of the drawings.
Claims (5)
1. A method for calibrating and correcting channel errors of a resonant gyroscope is characterized by comprising the following steps of: the method comprises the following steps:
step 1, establishing a channel error identification model, and placing the established model in a control system of a resonant gyroscope;
step 2, determining the number n of error parameters to be identified according to task requirements, and calling a channel error identification model;
step 3, initializing a standing wave azimuth angle theta and placing the standing wave azimuth angle theta at a random initial position theta 0 ；
Step 4, moving the standing wave azimuth angle theta to be positioned at the theta i ＝θ 0 +iπ/2n，i＝1,…,n；
Step 5, calculating additional drift angles at each standing wave azimuth angle thetai in the process of moving the standing wave azimuth angle thetai n times in step 4
；
Step 6, according to the additional drift angle
The channel error identification model is used for identifying and calculating n error parameters;
step 7, substituting the calculated error parameters into the corresponding positions of the error model to correct the current loop coefficient;
step 8, judging the calculation residual error e of each parameter k Whether or not the set termination condition e is satisfied k <e set Counting the number k of parameters subjected to correction;
step 9, updating the number n of parameters to be identified and a channel error identification model;
step 10, if the parameter n to be identified is not zero, updating the random initial standing wave azimuth angle θ 0 ＝θ 0 +r, returning to step 2; otherwise, stopping iteration;
the channel errors involved in step 1 include a detection channel error a and a drive channel error B;
detecting channel error A includes electrode gain offset Δk d Electrode position deviation delta theta d Electrode phase shift deviation delta phi d For the detection channel error A, the standing wave angle is calculated
Real angle with standing wave->
There is an error related to the standing wave azimuth angle θ as shown in equation (1):
wherein-a is the antinode amplitude;
b is the node amplitude;
——
calculating a standing wave angle;
——Δk d to detect electrode gain deviation;
——Δθ d to detect electrode position deviations;
——Δφ d to detect the electrode phase shift deviation;
the driving channel error B includes the electrode gain deviation Deltak e Deviation of electrode position
And->
Electrode phase shift deviation delta phi e The method comprises the steps of carrying out a first treatment on the surface of the For the drive channel error B, it is mainly manifested as cross-coupling of the control signals, thereby causing additional drift Δε at each standing wave azimuth angle θ e An error equation of the driving error B to the standing wave azimuth angle theta is established as shown in a formula (2):
in-Deltak e Driving the electrode gain bias for X;
——
x, Y drive electrode position deviations;
——Δφ e phase shift deviation for Y driving electrode;
——Δε e introducing additional drift for drive error;
SF is the electrode force application scale factor;
——
is an additional drift angle;
——C a is a stable control signal;
——C q is a quadrature control signal;
the real angle of the standing wave is detected by the existence of the channel error A
Unknown, the standing wave angle θ in the driving error equation (2) is rewritten as an angle calculation value +.>
Obtaining a channel error identification model as shown in formula (3):
2. the method for calibrating and correcting the channel error of the resonant gyroscope according to claim 1, wherein the method comprises the following steps: in step 4, the rotation of the standing wave can be provided by the external carrier rotation speed omega, or by applying the active precession signal C p Providing.
3. The method for calibrating and correcting the channel error of the resonant gyroscope according to claim 2, wherein the method comprises the following steps: in step 5, an additional drift angle is calculated when the rotation is provided using the external carrier
The formula is as follows:
middle- (2)
Is an additional drift angle;
——
is the azimuth angle theta of the standing wave i Calculating the azimuth angle theta of the standing wave at the position;
-alpha is the Blaine coefficient truth value;
omega is the rotation speed of the external carrier;
t is the rotation time.
4. The method for calibrating and correcting the channel error of the resonant gyroscope according to claim 3, wherein the method comprises the following steps: the method for obtaining the real value of the Blaine coefficient comprises the following steps:
since the detection channel error matrix A has various anisotropic characteristics, the Coriolis force term in the harmonic oscillator dynamics equation generates additional errors, an equivalent Blaine coefficient is introduced, and the relation between the equivalent Blaine coefficient alpha' (theta) and the vibration azimuth angle theta is shown in a formula (5):
α′＝α+Δαcos[2(θ-θ α )] (5)
wherein-alpha' is an equivalent Blaine coefficient;
- θ is the standing wave azimuth;
——θ α adding an error angle to the Blaine coefficient;
according to the formula (5), the Blaine coefficient true value is obtained through calibration in a full-angle mode in a mode of the average and measurement information of the whole period, and the formula (6) is shown as follows:
5. the resonating gyroscope of claim 4The calibrating and correcting method for the channel error of the screw instrument is characterized by comprising the following steps of: in step 5, when active precession is employed, an additional drift angle is calculated
The formula is as follows:
wherein-SF is the force application scale;
——C p is an applied active precession signal.
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| CN110865580A (en) * | 2019-11-27 | 2020-03-06 | 中国船舶重工集团公司第七0七研究所 | Hemispherical resonant gyroscope fully-differential control system and control method based on time division multiplexing |
| CN112506040A (en) * | 2020-11-16 | 2021-03-16 | 哈尔滨工程大学 | Single-channel control system and method for full-angle hemispherical resonator gyroscope |
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