CN109813340A - Hemispherical reso nance gyroscope signal detection system and the detection method for considering detecting electrode Form and position error - Google Patents
Hemispherical reso nance gyroscope signal detection system and the detection method for considering detecting electrode Form and position error Download PDFInfo
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Abstract
Hemispherical reso nance gyroscope signal detection system and the detection method for considering detecting electrode Form and position error, are related to technical field of inertial.The present invention is in order to improve the output accuracy of HRG.The detection system includes 8 detection capacitors being uniformly distributed on interior pedestal, and each detection capacitor is formed by the detecting electrode that is placed on interior pedestal outer surface and with the part-spherical harmonic oscillator spherical surface of the detecting electrode face；The detection system further includes two for capacitance signal to be converted to voltage signal buffer amplifier, two bandpass filters, derived reference signal, two multipliers, two low-pass filters.The detection error of hemispherical reso nance gyroscope is calculated according to the Form and position error of detecting electrode and signal detection system；Signal analysis is carried out to detection error according to signal demodulation principle；Signal errors amount is detected according to calculated hemispherical reso nance gyroscope, the measurement output of hemispherical reso nance gyroscope is compensated.With the application of the invention, the output accuracy of hemispherical reso nance gyroscope can be improved.
Description
Technical field
The present invention relates to technical field of inertial more particularly to the signal detections and output error meter of hemispherical reso nance gyroscope
Calculate compensation method.
Background technique
HRG (Hemispherical Resonant Gyro, hemispherical reso nance gyroscope) is a kind of high reliability, high-precision
Inertial navigation grade solid oscillation gyro, with small in size, low in energy consumption, light-weight, starting is fast, capability of resistance to radiation is strong, anti shock and vibration
Well, the advantages that service life is long is one of 21 century ideal inertia component, is widely used in submarine and hides, deep space exploration, defends
In the inertial navigation systems in fields such as star communication, location navigation.
In HRG, detecting electrode is mainly used for the detection of hemispherical resonator vibration information.In the process of harmonic oscillator vibration
In, the capacitance of detecting electrode can also generate corresponding variation, and the variation of capacitor is read by circuit, can calculate vibration
Amplitude and vibration shape angle.Detecting electrode is a highly important ring in HRG, there is important influence to the precision of HRG.In the reality of gyro
In border manufacture and assembling process, the Form and position error of detecting electrode is inevitable, they can be such that vibration detecting system output produces
Raw error, causes gyro performance parameter to be drifted about.The Form and position error of detecting electrode is specified to the Influencing Mechanism of gyro performance, is
It formulates corresponding error compensating scheme and improves the basis of batch gyro stability, have a very important significance.
Document number provides a kind of micro- hemispherical reso nance gyroscope using DSP and FPGA for the prior art of CN105716597B
Control and signal detection system and method, being directed to is micro- hemispherical reso nance gyroscope (micron-sized).In the prior art for centimetre
The hemispherical reso nance gyroscope signal detection and error analysis of grade do not provide specific research in detail.
Summary of the invention
The technical problem to be solved by the present invention is
The purpose of the present invention is to provide a kind of hemispherical reso nance gyroscope signal detection system and consider that detecting electrode morpheme is missed
The detection method of difference is mentioned with being compensated according to the detection system model of foundation, detection capacitance error model to the output of HRG
The output accuracy of high HRG.
The technical solution adopted by the present invention to solve the above technical problem is:
A kind of hemispherical reso nance gyroscope signal detection system, the detection system include 8 be uniformly distributed on interior pedestal
Detect capacitor, each detection capacitor by the detecting electrode that is placed on interior pedestal outer surface and with the part half of the detecting electrode face
Spherical harmonic oscillator spherical surface composition；8 detection capacitor D1~D8It indicates；
The detection system further includes two for capacitance signal to be converted to the buffer amplifier of voltage signal, the two
Amplification factor is respectively Kcc, Kss；Two bandpass filters, derived reference signal, two multipliers, two low-pass filters, definition
D1As the detection capacitor of 0 ° of electrode axis of interior pedestal, 0 ° of electrode axis capacitance signal C is exporteds, by D2Detection as 45 ° of electrode axis
Capacitor exports 45 ° of electrode axis capacitance signal Cc；
D1Capacitance signal CsThrough amplifying KssVoltage signal V is obtained after timess, a bandpass filter is inputed to, voltage letter is obtained
Number Vs1Corresponding low-pass filter, which is transmitted to, through a multiplier obtains Sva。D2Capacitance signal CcThrough amplifying KccVoltage letter is obtained after times
Number Vc, a bandpass filter is inputed to, voltage signal V is obtainedc1Corresponding low-pass filter is transmitted to through a multiplier to obtain
Sam.Pass through intermediate variable Sva、SamCalculate the vibration shape angle of hemispherical harmonic oscillatorAnd amplitude Aa, two multipliers connect jointly
One derived reference signal.
A kind of hemispherical reso nance gyroscope signal detecting method based on the considerations of above system detecting electrode Form and position error, it is described
The realization process of method are as follows:
Step 1: amplitude and the vibration shape angle of given hemispherical reso nance gyroscope harmonic oscillator second order resonant state, and according to having determined that
Harmonic oscillator second order resonant state kinetics equation calculate harmonic oscillator deformation u2、v2、w2；u2It hangs down to be parallel to detecting electrode
Histogram to displacement, v2For displacement, the w for being parallel to detecting electrode horizontal direction2For the displacement of vertical detection electrode direction；
Step 2: will test capacitor D respectively1、D2Spatial domain carry out grid dividing, and be added and the morpheme analyzed needed to miss
Difference；
Step 3: calculating the capacitance gap on each mesh point of detecting electrode according to calculated harmonic oscillator deformation；
Step 4: integrating out capacitance C using discrete capacitance gapcAnd Cs；
Step 5: calculating output quantity S according to signal demodulation principleva、Sam；
Step 6: to Sva、SamIt is demarcated, exports vibration shape angleAnd amplitude Aa, and the output valve and step 2 are considered
The output valve respective value of detecting electrode Form and position error is compared, and obtains the output of detection system ideal and examines with Form and position error bring
The relationship for surveying output error is compensated according to error of the relationship to output result.
Further, the detailed process of step 1 are as follows:
Harmonic oscillator has under second order resonant state:
In formula:For vibration shape angle；U2、V2、W2For the Ruili benefit function of second_mode vibration, U2=V2=sin θ tan2θ/2,
W2=-(2+cos θ) tan2θ/2；ω2For resonance frequency；T is the time；P (t), q (t) are and time correlation coefficient；θ is harmonic oscillator
Spherical surface sector latitude scope,For harmonic oscillator spherical surface sector longitude range,
In addition, p (t), q (t) meet following formula when harmonic oscillator enters second order steady vibration
M, n in formula 4 are p (t), the coefficient of q (t) respectively；
It is substituted into formula 3 and is obtained
In formula:
In formula:Referred to as vibration shape angle；AaReferred to as amplitude.
Further, the detailed process of step 2 are as follows:
Each detection capacitor includes two electrode plates, i.e. detection in the electrode plate and gyro of harmonic oscillator inner surface on pedestal
Electrode, detecting electrode are assumed to spherical surface sector structure, wherein θdt, θdbFor the latitude scope of spherical surface sector,For spherical surface
Fan-shaped longitude range；(latitude scope of each electrode is 75 degree to 85 degree under no error condition, and longitude width is 20
Degree, is globally uniformly distributed；)
1) detecting electrode pole plate is defined as along the centroid error of warp direction
In formula: edpFor centroid error；It is pole plate along the ideal position of form center of warp direction；
2) detecting electrode pole plate is defined as along warp direction width error
In formula: edwIt is pole plate along warp direction width error；It is pole plate along the ideal width of warp direction；
3) detecting electrode plate is along weft direction latitude scope upper limit error edt；
4) detecting electrode plate is along weft direction latitude scope lower limit error edb。
Further, the detailed process of step 3 are as follows:
Go out capacitance gap d by the deformation calculation of harmonic oscillator, specifically:
Assuming that being moved to N ' point, then N ' corresponding displacement vector ON ', N point after substance point N deformation on face in harmonic oscillator
The relationship of corresponding displacement vector ON and deformation vector NN ' is
ON '=ON+NN ' (formula 11)
Wherein, the O point in straight line ON ' is the centre of sphere of harmonic oscillator spherical surface.
In harmonic oscillator coordinate system xryrzrUnder component form be
In formula: u2、v2、w2Indicate deformation when harmonic oscillator enters second order resonant state；R indicates harmonic oscillator spherical radius；
Any point M in detecting electrode areal extent, straight line OM is taken to intersect at point N ' with face in deformed harmonic oscillator, this
Locate OM=Rin, it is assumed that ON '=Rd, then capacitance gap expression formula are as follows:
D=Rd-Rin- h (formula 13)
Straight line OM intersects with face in harmonic oscillator and meets following equation:
In formula:For detection capacitor in pedestal pole plate latitude and longitude, andFor
Known quantity；θ,For straight line OM and the substance point that face is intersected in harmonic oscillator after deformation when undeformed where latitude and longitude,
And and RdIt is all unknown quantity to be asked, RinFor interior pedestal spherical radius；H is the half of harmonic oscillator shell thickness.
Further, the detailed process of step 4 are as follows:
Unit flat capacitor device expression formula is
In formula: ε0For dielectric constant；ε is capacitivity；RinFor interior pedestal spherical radius；D is interior pedestal spherical surface infinitesimal along method
Capacitance gap between direction and harmonic oscillator surface；DS is the unit area of interior pedestal spherical surface, and
Thus detection capacitor is
So far, the numerical value of capacitor output of the detection capacitor under harmonic oscillator Vibration Condition can be found out using formula 10, formula 14
Solve CcAnd Cs。
Further, output quantity S is calculated according to signal demodulation principle in step 5va、Sam, detailed process are as follows:
By D1As the detection capacitor of 0 ° of electrode axis, 0 ° of electrode axis capacitance signal C is exporteds；By D2As 45 ° of electrode axis
Capacitor is detected, 45 ° of electrode axis capacitance signal C are exportedc；
Assuming that the detection capacitance detecting of 0 ° and 45 ° electrode axis to capacitance signal meet following form:
In formula: C0For constant value capacitive component；C1For the first harmonic component amplitude of detection capacitor output；For harmonic oscillator vibration
Type angle；ω2Vibrate angular frequency；φ ' is the initial phase of vibration；CcnAnd CsnFor the high fdrequency component of detection capacitor output；
Capacitance signal is converted into voltage signal using buffer amplifier, meets following formula
Vc=KccCc(formula 17)
Vs=KssCs(formula 18)
In formula: Kcc, KssFor amplification factor；
The purpose that vibration shape angle resolves is to pass through VcAnd VsSignal find outFor this purpose, being removed first by bandpass filter straight
Flow component and high fdrequency component, signal at this time become
Take reference signal
Vrc=Ar sin(ω2T+ φ) (formula 21)
In formula: ArFor the amplitude of reference signal；φ is the initial phase angle of reference signal；
By reference signal VrcRespectively with Vc1, Vs1It is mutually multiplied and filter out high fdrequency component and obtain:
In formula: δ φ=φ '-φ is the phase difference of reference signal and vibration signal；
In force feedback type HRG, since the work of vibration shape angle is near zero-bit, S in formula in small angle rangevaExpression formula can
By be reduced to it is following in the form of
At this time directly by SvaOutput as vibration shape angleMeasured value；
At this point, the amplitude stability of force feedback type HRG harmonic oscillator, near uniform amplitude, this up-to-date style is approximately
Therefore SamIt can be used as the detection signal of harmonic oscillator amplitude.
The error analysis method of the hemispherical reso nance gyroscope detecting electrode of the present invention addressed, mainly Form and position error institute band
The vibration shape angle detection error and amplitude detection error come.After error has been determined, so that it may the output of HRG is compensated, thus
Improve the output accuracy of HRG.Hemispherical reso nance gyroscope is calculated according to the Form and position error of detecting electrode and signal detection system
Detection error；Signal analysis is carried out to detection error according to signal demodulation principle；It is detected according to calculated hemispherical reso nance gyroscope
Signal errors amount compensates the measurement output of hemispherical reso nance gyroscope.
Amplitude and vibration shape angle by hemispherical reso nance gyroscope harmonic oscillator second order resonant state, and according to fixed harmonic oscillator
The kinetics equation of second order resonant state calculates the deformation of harmonic oscillator；The spatial domain that will test capacitor carries out grid dividing, and adds
Enter the Form and position error for needing to analyze；According to calculated harmonic oscillator deformation, the plate electricity on each mesh point of detecting electrode is calculated
Hold plate gap；Capacitance is integrated out using discrete capacitance gap；Output quantity is calculated according to signal demodulation principle, and to defeated
Vibration shape angle and amplitude out is demarcated.With the application of the invention, can be with the Form and position error of quantitative analysis detecting electrode to output accuracy
Influence, according to detection output error the output of hemispherical reso nance gyroscope is compensated, improve hemispherical reso nance gyroscope output essence
Degree.
The beneficial effects of the present invention are:
The present invention solves the problems, such as detecting electrode signal quantization and capacitance detecting signal according to detecting electrode Form and position error
The problems such as output.It is crossed in kind in error analysis, needs to model vibration detecting system, construct capacitive detection scheme, and right
The capacitance signal of detection carries out analysis of components, can just obtain the specific influence that HRG detecting electrode Form and position error exports gyro.
Detailed description of the invention
Attached drawing is used to provide further understanding of the present invention, and constitutes part of specification, with reality of the invention
The mode of applying is used together to explain the present invention, is not construed as limiting the invention.In the accompanying drawings:
Fig. 1 is detector electrode structure figure, and Fig. 2 is detection scheme configuration structure, and Fig. 3 is vibration detecting system schematic diagram,
Fig. 4 is to obtain C based on capacitive detection scheme shown in Fig. 2 with emulation modecAnd CsThe flow diagram of signal (calculate by detection capacitor emulation
Method block diagram), Fig. 5 is hemispherical reso nance gyroscope signal detecting method flow diagram (the detection capacitor for considering detecting electrode Form and position error
Form and position error simulation algorithm).
Specific embodiment
As shown in Fig. 1 to 5, present embodiment is to the hemispherical reso nance gyroscope signal detection system and considers detecting electrode
Form and position error is illustrated as follows:
According to an aspect of the present invention, the quantitative description of hemispherical reso nance gyroscope detecting electrode Form and position error is first provided.
One detection capacitor includes two electrode plates, i.e. detection in the electrode plate and gyro of harmonic oscillator inner surface on pedestal
Electrode.Detecting electrode is assumed to spherical surface sector structure, as shown in Figure 1.Wherein θdt, θdbFor the latitude scope of spherical surface sector,For the longitude range of spherical surface sector.
(1) detecting electrode pole plate is defined as along the centroid error of warp direction
In formula: edpFor centroid error；It is pole plate along the ideal position of form center of warp direction.
(2) detecting electrode pole plate is defined as along warp direction width error
In formula: edwIt is pole plate along warp direction width error；It is pole plate along the ideal width of warp direction.
(3) detecting electrode plate is along weft direction latitude scope upper limit error edt。
(4) detecting electrode plate is along weft direction latitude scope lower limit error edb。
According to another aspect of the present invention, the deformation calculation side of the hemispherical reso nance gyroscope resonant state harmonic oscillator is provided
Method, comprising:
N=2 is taken under harmonic oscillator second order resonant state, i.e.,
In formula:For vibration shape angle of precession；U2、V2、W2For the Rayleigh function of second_mode, U2=V2=sin θ tan2θ/2, W2
=-(2+cos θ) tan2θ/2；ωnFor resonance angular frequency；T is the time；P (t), q (t) are and time correlation coefficient.
In addition, p (t), q (t) meet following formula when harmonic oscillator enters second order steady vibration
It is substituted into formula 3 and is obtained
In formula:
In formula:Referred to as vibration shape angle；AaReferred to as amplitude.
According to the third aspect of the present invention, the detection capacitance calculating side including Form and position error and harmonic oscillator deformation is provided
Method, specifically:
Unit flat capacitor device expression formula is
In formula: ε0For dielectric constant；ε is capacitivity；RinFor interior pedestal spherical radius；D is interior pedestal spherical surface infinitesimal along method
Capacitance gap between direction and harmonic oscillator surface；DS is the unit area of interior pedestal spherical surface, and
Thus detection capacitor is
Further, by the deformation of harmonic oscillator, capacitance gap d is calculated, specifically:
Assuming that be moved to N ' point after substance point N deformation on face in harmonic oscillator, then N ' corresponding displacement vector ON ' and N point
The relationship of corresponding displacement vector ON and deformation vector NN ' is
ON '=ON+NN ' (formula 11)
In harmonic oscillator coordinate system xryrzrUnder component form be
Middle face deformation u, v, w for studying in this method only include deformation u when harmonic oscillator enters second order resonant state2、v2、
w2。
As shown in Figure 1, any point M in detecting electrode areal extent is taken, straight line OM and face phase in deformed harmonic oscillator
Point N ' is met at, herein OM=Rin, it is assumed that ON '=Rd, then capacitance gap expression formula are as follows:
D=Rd-Rin- h (formula 13)
Straight line OM intersects with face in harmonic oscillator and meets following equation:
In formula:For detection capacitor in pedestal pole plate latitude and longitude, andFor
Known quantity；θ,For straight line OM and the substance point that face is intersected in harmonic oscillator after deformation when undeformed where latitude and longitude,
And and RdIt is all unknown quantity to be asked.
So far, the numerical value of capacitor output of the detection capacitor under harmonic oscillator Vibration Condition can be found out using formula 10, formula 14
Solution.
Finally provide the calculation method of vibration shape angle and amplitude, comprising:
Detection system is made of 8 detections capacitor equally distributed on interior pedestal, is divided into 45 °, D as shown in Figure 21~
D8Longitude and latitude range it is as shown in table 1.This 8 detection capacitors are subjected to reasonable combination, can be detected out the vibration shape of harmonic oscillator
State.
Table 1 detects capacitance electrode range
Due to the symmetry of harmonic oscillator second order resonant state, being separated by 90 ° of detection capacitor has reversed nature, is separated by 180 °
Detection capacitor there is same phase behaviour, therefore can be by D1As the detection capacitor of 0 ° of electrode axis, 0 ° of electrode axis capacitor letter is exported
Number Cs.By D2As the detection capacitor of 45 ° of electrode axis, 45 ° of electrode axis capacitance signal C are exportedc.As shown in Fig. 2, this is a kind of letter
Single easy detection system structural form.
Further, the resolving at the vibration shape angle and amplitude, specifically:
Assuming that the detection capacitance signal of 0 ° and 45 ° electrode axis meets following form:
In formula: C0For constant value capacitive component；C1For the first harmonic component amplitude of detection capacitor output.For harmonic oscillator vibration
Type angle；ω2Vibrate angular frequency；φ ' is the initial phase of vibration；CcnAnd CsnFor the high fdrequency component of detection capacitor output.
In Project Realization, capacitance signal is usually converted into voltage signal using buffer amplifier, meets following formula
Vc=KccCc(formula 17)
Vs=KssCs(formula 18)
In formula: Kcc, KssFor amplification factor.
The purpose that vibration shape angle resolves is to pass through VcAnd VsSignal find outFor this purpose, being removed first by bandpass filter straight
Flow component and high fdrequency component, signal at this time become
Take reference signal
Vrc=Ar sin(ω2T+ φ) (formula 21)
In formula: ArFor the amplitude of reference signal；φ is the initial phase angle of reference signal.
By reference signal VrcRespectively with Vc1, Vs1It is mutually multiplied and filter out high fdrequency component and obtain:
In formula: δ φ=φ '-φ is the phase difference of reference signal and vibration signal.
In force feedback type HRG, since the work of vibration shape angle is near zero-bit, S in formula in small angle rangevaExpression formula can
By be reduced to it is following in the form of
It at this time can be directly by SvaOutput conductMeasured value.
As can be seen from the above equation, the amplification factor K of loopss(including C/V converter, filter etc.), the amplitude of harmonic oscillator
And reference signal determines the resolution ratio to vibration shape angular measurement relative to the phase difference of resonance signal together.Actual design process
In can with reference to above formula carry out circuit parameter distribution.
At this point, the amplitude stability of force feedback type HRG harmonic oscillator, near uniform amplitude, this up-to-date style is approximately
Therefore SamIt can be used as the detection signal of harmonic oscillator amplitude.The testing principle of force feedback type HRG vibration shape angle and amplitude is such as
Shown in Fig. 3.
According to another aspect of the present invention, a kind of capacitor output signal calculation process is additionally provided, comprising:
It is analyzed with capacitive detection scheme shown in Fig. 2, C can be obtained by way of emulationcAnd CsSignal.Emulation system
Establishment process of uniting is as shown in Figure 4.
The detailed process of error analysis method is as shown in Figure 5.
It is as follows to present invention verifying:
The range that above-mentioned 4 error sources are arranged is to execute algorithm shown in Fig. 5 between -0.1 °~0.1 °, available respectively
Pole plate is missed along warp direction width error, pole plate along the weft direction latitude scope upper limit along the centroid error of warp direction, pole plate
The detection error at difference, pole plate vibration shape angle and amplitude caused by the Form and position errors such as weft direction latitude scope lower limit error.
From above scheme as can be seen that can specifically be counted process provides process a set of reliable and with feasibility
Calculate hemispherical reso nance gyroscope detecting electrode Form and position error to output caused by influence, and by post-processing to this error into
Row targetedly compensates, and is finally reached the purpose for improving hemispherical reso nance gyroscope precision.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Anyone skilled in the art in the technical scope disclosed by the present invention, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (7)
1. a kind of hemispherical reso nance gyroscope signal detection system, which is characterized in that the detection system includes being uniformly distributed in interior base
8 detection capacitors on seat, each detection capacitor by the detecting electrode that is placed on interior pedestal outer surface and with the detecting electrode just
Pair part-spherical harmonic oscillator spherical surface composition；8 detection capacitor D1~D8It indicates；
The detection system further includes two for capacitance signal to be converted to the buffer amplifier of voltage signal, the amplification of the two
Multiple is respectively Kcc, Kss；Two bandpass filters, derived reference signal, two multipliers, two low-pass filters define D1Make
For the detection capacitor of 0 ° of electrode axis of interior pedestal, 0 ° of electrode axis capacitance signal C is exporteds, by D2As the detection capacitor of 45 ° of electrode axis,
Export 45 ° of electrode axis capacitance signal Cc；
D1Capacitance signal CsThrough amplifying KssVoltage signal V is obtained after timess, a bandpass filter is inputed to, voltage signal V is obtaineds1
Corresponding low-pass filter, which is transmitted to, through a multiplier obtains Sva。D2Capacitance signal CcThrough amplifying KccVoltage signal is obtained after times
Vc, a bandpass filter is inputed to, voltage signal V is obtainedc1Corresponding low-pass filter, which is transmitted to, through a multiplier obtains Sam。
Pass through intermediate variable Sva、SamCalculate the vibration shape angle of hemispherical harmonic oscillatorAnd amplitude Aa, two multipliers connect one jointly
Derived reference signal.
2. it is a kind of using described in claim 1 the considerations of system detecting electrode Form and position error hemispherical reso nance gyroscope signal detection side
Method, which is characterized in that the realization process of the method are as follows:
Step 1: amplitude and the vibration shape angle of given hemispherical reso nance gyroscope harmonic oscillator second order resonant state, and according to fixed humorous
The kinetics equation of oscillator second order resonant state calculates the deformation u of harmonic oscillator2、v2、w2；u2To be parallel to detecting electrode Vertical Square
To displacement, v2For displacement, the w for being parallel to detecting electrode horizontal direction2For the displacement of vertical detection electrode direction；
Step 2: will test capacitor D respectively1、D2Spatial domain carry out grid dividing, and be added and need the Form and position error analyzed；
Step 3: calculating the capacitance gap on each mesh point of detecting electrode according to calculated harmonic oscillator deformation；
Step 4: integrating out capacitance C using discrete capacitance gapcAnd Cs；
Step 5: calculating output quantity S according to signal demodulation principleva、Sam；
Step 6: to Sva、SamIt is demarcated, exports vibration shape angleAnd amplitude Aa, and the output valve and step 2 are considered into detection electricity
The output valve respective value of pole Form and position error is compared, and obtains the output of detection system ideal and exports with the detection of Form and position error bring
The relationship of error is compensated according to error of the relationship to output result.
3. the hemispherical reso nance gyroscope signal detecting method according to claim 2 for considering detecting electrode Form and position error, special
Sign is, the detailed process of step 1 are as follows:
Harmonic oscillator has under second order resonant state:
In formula:For vibration shape angle；U2、V2、W2For the Ruili benefit function of second_mode vibration, U2=V2=sin θ tan2θ/2, W2=-
(2+cosθ)tan2θ/2；ω2For resonance frequency；T is the time；P (t), q (t) are and time correlation coefficient；θ is harmonic oscillator spherical surface
Fan-shaped latitude scope,For harmonic oscillator spherical surface sector longitude range,
In addition, p (t), q (t) meet following formula when harmonic oscillator enters second order steady vibration
M, n in formula 4 are p (t), the coefficient of q (t) respectively；
It is substituted into formula 3 and is obtained
In formula:
In formula:Referred to as vibration shape angle；AaReferred to as amplitude.
4. the hemispherical reso nance gyroscope signal detecting method according to claim 3 for considering detecting electrode Form and position error, special
Sign is, the detailed process of step 2 are as follows:
Each detection capacitor includes two electrode plates, i.e., the detection electricity in the electrode plate and gyro of harmonic oscillator inner surface on pedestal
Pole, detecting electrode are assumed to spherical surface sector structure, wherein θdt, θdbFor the latitude scope of spherical surface sector,For spherical surface fan
The longitude range of shape；
1) detecting electrode pole plate is defined as along the centroid error of warp direction
In formula: edpFor centroid error；It is pole plate along the ideal position of form center of warp direction；
2) detecting electrode pole plate is defined as along warp direction width error
In formula: edwIt is pole plate along warp direction width error；It is pole plate along the ideal width of warp direction；
3) detecting electrode plate is along weft direction latitude scope upper limit error edt；
4) detecting electrode plate is along weft direction latitude scope lower limit error edb。
5. the hemispherical reso nance gyroscope signal detecting method according to claim 4 for considering electrode Form and position error, feature exist
In, which is characterized in that the detailed process of step 3 are as follows:
Go out capacitance gap d by the deformation calculation of harmonic oscillator, specifically:
Assuming that being moved to N ' point after substance point N deformation on face in harmonic oscillator, then N ' corresponding displacement vector ON ', N point are corresponding
Displacement vector ON and deformation vector NN ' relationship be ON '=ON+NN ' (formula 11)
Wherein, the O point in straight line ON ' is the centre of sphere of harmonic oscillator spherical surface.
In harmonic oscillator coordinate system xryrzrUnder component form be
In formula: u2、v2、w2Indicate deformation when harmonic oscillator enters second order resonant state；R indicates harmonic oscillator spherical radius；
Any point M in detecting electrode areal extent, straight line OM is taken to intersect at point N ' with face in deformed harmonic oscillator, herein OM
=Rin, it is assumed that ON '=Rd, then capacitance gap expression formula are as follows:
D=Rd-Rin- h (formula 13)
Straight line OM intersects with face in harmonic oscillator and meets following equation:
In formula:For detection capacitor in pedestal pole plate latitude and longitude, andIt is known
Amount；θ,For straight line OM and the substance point that face is intersected in harmonic oscillator after deformation when undeformed where latitude and longitude, and and Rd
It is all unknown quantity to be asked, RinFor interior pedestal spherical radius；H is the half of harmonic oscillator shell thickness.
6. the hemispherical reso nance gyroscope signal detecting method according to claim 5 for considering electrode Form and position error, feature exist
In the detailed process of step 4 are as follows:
Unit flat capacitor device expression formula is
In formula: ε0For dielectric constant；ε is capacitivity；RinFor interior pedestal spherical radius；D is interior pedestal spherical surface infinitesimal along normal direction side
Capacitance gap between harmonic oscillator surface；DS is the unit area of interior pedestal spherical surface, and
Thus detection capacitor is
So far, the numerical solution C of capacitor output of the detection capacitor under harmonic oscillator Vibration Condition can be found out using formula 10, formula 14cWith
Cs。
7. the hemispherical reso nance gyroscope signal detecting method according to claim 6 for considering electrode Form and position error, feature exist
In calculating output quantity S according to signal demodulation principle in step 5va、Sam, detailed process are as follows:
By D1As the detection capacitor of 0 ° of electrode axis, 0 ° of electrode axis capacitance signal C is exporteds；By D2Detection as 45 ° of electrode axis
Capacitor exports 45 ° of electrode axis capacitance signal Cc；
Assuming that the detection capacitance detecting of 0 ° and 45 ° electrode axis to capacitance signal meet following form:
In formula: C0For constant value capacitive component；C1For the first harmonic component amplitude of detection capacitor output；For harmonic oscillator vibration shape angle；
ω2Vibrate angular frequency；φ ' is the initial phase of vibration；CcnAnd CsnFor the high fdrequency component of detection capacitor output；
Capacitance signal is converted into voltage signal using buffer amplifier, meets following formula
Vc=KccCc(formula 17)
Vs=KssCs(formula 18)
In formula: Kcc, KssFor amplification factor；
The purpose that vibration shape angle resolves is to pass through VcAnd VsSignal find outFor this purpose, removing direct current point by bandpass filter first
Amount and high fdrequency component, signal at this time become
Take reference signal
Vrc=Arsin(ω2T+ φ) (formula 21)
In formula: ArFor the amplitude of reference signal；φ is the initial phase angle of reference signal；
By reference signal VrcRespectively with Vc1, Vs1It is mutually multiplied and filter out high fdrequency component and obtain:
In formula: δ φ=φ '-φ is the phase difference of reference signal and vibration signal；
In force feedback type HRG, since the work of vibration shape angle is near zero-bit, S in formula in small angle rangevaExpression formula can letter
Turn to following form
At this time directly by SvaOutput as vibration shape angleMeasured value；
At this point, the amplitude stability of force feedback type HRG harmonic oscillator, near uniform amplitude, this up-to-date style is approximately
Therefore SamIt can be used as the detection signal of harmonic oscillator amplitude.
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