CN102023051B - Method for measuring high frequency micro vibration of triaxial angular displacement of satellite payload - Google Patents

Abstract

The invention relates to a method for measuring high frequency micro vibration of triaxial angular displacement of satellite payload. The method comprises the steps of measuring linear acceleration and utilizing the amplification effect generated by twice integration of a high frequency signal, thus realizing high accuracy measurement at low cost. Analysis shows that an acceleration meter with the accuracy of 10-4g can be adopted for 50Hz angular displacement with the amplitude of 10-6 degrees under the condition of a 1m reference line, thus greatly reducing the accuracy of an instrument and reducing the measurement cost. The invention provides a method for measuring the vibration quantity under two conditions of full time and time window.

Description

A kind of method of measuring the little vibration of useful load three shaft angle displacement high frequencies on the star

Technical field

The present invention relates to the measuring method of the little vibration of three shaft angle displacement high frequencies on the star; Be applicable to the useful load three shaft angle displacement high frequency (frequencies that exceed the satellite control system bandwidth on the star; Usually greater than tens hertz), the measuring method of little vibration (rad level below), belong to spacecraft high precision high stability degree attitude control technology field.

Background technology

Large complicated satellite such as the complicated satellite that is representative with the earth observation of 0.1m very high resolution and 1: 10000 stereo mapping, is multi-functional, high-performance large-scale system.These complicated satellites often present typical large-scale many bodies flexible space structure; Mainly show: the multi-functional and proportion high performance requirements useful load constantly increases; And common modules such as division center, antenna, solar array will lightness, therefore must be with it as flexible multi-body structure satellite.On the other hand, these complicated satellites an urgent demand are again realized very high-precision attitude control, to satisfy the requirement of earth observation of satellite very high resolution and mapping.

Moving components such as spaceborne momenttum wheel, control-moment gyro, retroaction air jet system can make the spacecraft platform produce shake again to some extent; Cause that the accurate optical sensitive device and the performance index of observation load significantly reduce, significantly reduce even lose observed object etc. like image quality.Therefore, need measure and assess the little vibration information of useful load high frequency.

Yet because the existence of movable part on the star, for example the momenttum wheel of high rotation and control-moment gyro, windsurfing driving mechanism etc. very likely cause the high dither at celestial body and useful load place, thereby have a strong impact on the serviceability of useful load.Therefore, high dither measuring method on the research star, and then the control of high dither on the realization star have significance for earth observation of satellite very high resolution and mapping.

U.S.'s solar dynamics observation satellite (SDO) is through setting up execution unit model, celestial body finite element model and shake propagation model; Utilize mathematical simulation, the vibratory output level of having calculated celestial body is that the vibratory output at two useful load places was 0.047 " with 0.053 ".U.S. geo-stationary orbit weather satellite GOES-N has tested the shake angular velocity of momenttum wheel under different rotating speeds at rail; Three shake angular velocity adopts inertia device (AVS, 800Hz) measurement of high bandwidth; The jitter-sensitive device is directly installed on the useful load pedestal; Through data processing, obtain shaking the amplitude and the frequency distribution of angular velocity.The senior land observation satellite ALOS of Japan directly measures and shakes angle on the star; Employing is based on magnetofluidodynamic high bandwidth (2Hz-500Hz) jitter-sensitive device (ADS); Be installed on the optical sensor pedestal; Realized measuring of 10-6deg magnitude shake angle at rail.See that from present foreign technology progress these methods mainly adopt direct measurement shake angular displacement signal, but for the little vibration of angular displacement on the star (below the rad level), be characterized in that amplitude is little, frequency is high, and it is big therefore directly to measure difficulty, and cost is high.

At present, the attitude measurement sensor of domestic satellite in orbit (star is quick, gyro etc.) also can't measure attitude vibratory output information because the restriction of sensitivity and bandwidth.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiency of prior art, a kind of measuring method that realizes the little vibration of useful load three shaft angle displacement high frequencies such as optical camera on the star is provided.

Technical solution of the present invention is: a kind of method of measuring the little vibration of useful load three shaft angle displacement high frequencies on the star, realize through following steps:

The first step is installed the three axis accelerometer assembly

The three axis accelerometer assembly is installed on the mounting bracket platform of useful load; One cover three axis accelerometer assembly promptly respectively is installed on former and later two surfaces of useful load; Every cover three axis accelerometer assembly comprises three accelerometers that are used for measuring three shaft vibration amounts of useful load; The sensitive axes pairwise orthogonal of three accelerometers is in a bit; Two accelerometer sensitive axles measuring the same direction vibration of useful load are parallel to each other, and promptly the sensitive axes of accelerometer is parallel in twos in the two cover three axis accelerometer assemblies, the line of accelerometer sensitive axle intersection point and the central axes of useful load;

Second step, gather the linear acceleration signal on former and later two planes of useful load that measure of accelerometer in the first step, utilize formula (1) to obtain the angular acceleration a (t) of useful load,

$a\left(t\right)=\frac{a_1-a_2}{L}---\left(1\right)$

Wherein, a ₁, a ₂Be the linear acceleration signal that accelerometer measures that two sensitive axes are parallel to each other obtains, L is for measuring base length, i.e. distance between the accelerometer that is parallel to each other of two sensitive axes, and t is a Measuring Time;

The 3rd step; The angular acceleration a (t) that is obtained useful load second step is converted into frequency domain power spectral density function A (f); The angular velocity power density

of utilizing formula (2) to obtain useful load utilizes formula (3) to obtain useful load angular displacement power spectrum density θ (f)

$\stackrel{\·}{\mathrm{\θ}}\left(f\right)=\frac{A\left(f\right)}{2\mathrm{\πf}}---\left(2\right)$

$\mathrm{\θ}\left(f\right)=\frac{A\left(f\right)}{{\left(2\mathrm{\πf}\right)}^2}---\left(3\right)$

F is the frequency of linear acceleration signal;

In the 4th step, utilize formula (4) to obtain the angular vibration amount Φ in Measuring Time on direction of principal axis of useful load _Rms,

Φ ² _rms＝∑θ ²(f)·Δf (4)；

The 5th step, calculate the angular vibration amount on direction of principal axis of useful load in certain time window T,

A5.1, utilize formula (5) to obtain the subcritical frequency f ₀The angular vibration amount Δ θ of scope ₀,

$\mathrm{\&Delta;}{\mathrm{\&theta;}}_0=\underset{i}{\mathrm{\&Sigma;}}\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HSA00000291315500021.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{0,i}---\left(5\right)$

Wherein

Be the subcritical frequency f of utilizing formula (2) to obtain ₀The angular velocity amplitude of each chattering frequency, i ∈ [1,2 ... I], I is the subcritical frequency f ₀The sum of angular velocity amplitude of chattering frequency, threshold frequency f ₀=1/ (π T);

A5.2, utilize formula (6) to obtain being higher than threshold frequency f ₀The angular vibration amount Δ θ of scope ₁,

$\mathrm{\&Delta;}{\mathrm{\&theta;}}_1=\sqrt{{\&Integral;}_{{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HSA00000291315500021.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}^{+\&infin;}{\mathrm{\&theta;}}_1^2\left(f\right)\mathrm{df}}---\left(6\right)$

θ wherein ₁Be higher than threshold frequency f for what utilize that formula (3) obtains ₀The angle amplitude of each chattering frequency;

A5.3, utilize formula (7) to obtain the angular vibration amount Δ θ of the useful load in time window T,

Δθ＝Δθ ₀+Δθ ₁ (7)；

The 6th step repeated～the five step of second step, obtained the angular vibration amount of all the other two axles of useful load.

Key points in design of the present invention:

1, measurement scheme

As shown in Figure 1, right cylinder is a useful load on the star, supposes that it is a rigidity, in its front and rear surfaces one cover three axis accelerometer assembly, former and later two surperficial linear acceleration signal a1 and a2 of synchro measure is installed respectively;

Through difference, and, can obtain angular acceleration according to measuring base length L;

$a\left(t\right)=\frac{a1-a2}{L}$

The angular acceleration signal carries out spectrum analysis, according to spectral characteristic design BPF., reduces the influence of measuring noise and environmental disturbances;

Calculate the dither amount.

2, measurement precision analysis

Consider that frequency is the angular acceleration signal a of f, the magnitude relation of itself and angular displacement

a＝(2πf) ²·θ

For the angular acceleration signal of 50Hz, reach 10 ^-6The precision of deg, then the measuring accuracy of linear acceleration is superior to 10 ^-3M/s ²Get final product (＜10 ^-4G), as shown in Figure 3.

The present invention compared with prior art beneficial effect is:

(1) the present invention is through the slotted line acceleration, the enlarge-effect that produces after having utilized high-frequency signal through twice integration, thus to realize high-acruracy survey than low-cost, analysis shows, is 10 for the 50Hz amplitude ^-6The angular displacement of degree is measured at 1m under the situation of baseline, adopts 10 ^-4The accelerometer of g precision gets final product, and the precision that greatly reduced instrument has reduced the measurement cost;

(2) the invention provides in whole period, time window the measuring method of vibratory output under two prerequisites.

Description of drawings

Fig. 1 measures installation diagram for the present invention;

Fig. 2 measures installation diagram for star loaded camera of the present invention;

Fig. 3 is for satisfying 10 ^-6The angular displacement vibration frequency of degree resolution and the graph of a relation of acceleration amplitude;

Fig. 4 is a process flow diagram of the present invention.

Embodiment

The high resolving power detailed survey is reconnaissance satellite over the ground, two very important index is arranged: image definition and resolution.The design objective of these two indexs and control system is in close relations.For guaranteeing that picture quality generally will claim to attitude stability.But it is multiple that the formulation of attitude stability has, and dimension has angle that angular velocity is also arranged, and notion is indeterminate, and saying is disunity also.For this reason, it is following that the present invention defines the attitude vibratory output: be in the time of getting a piece image and a pixel, and the attitude misalignment that satellite body produces at three direction of principal axis, promptly in some time window T interval, the attitude variation of generation.

Practical implementation of the present invention divides three steps:

One of which, accelerometer type selecting and configuration; Its two, amplify with AD through electric charge and to change acquired signal; Its three, data analysis is handled.

Below be example with the star loaded camera, specify the present invention, flow process of the present invention is as shown in Figure 4.

1) accelerometer type selecting

According to aforementioned analysis, in order to satisfy the high-frequency jitter signal Testing requirement, the accelerometer of selecting to measure shake will guarantee enough bandwidth and signal to noise ratio (S/N ratio).Typical in piezoelectric accelerometer, its resolution 1 * 10 ^-5G; Bandwidth 0.3Hz～10KHz can meet the demands.

2) configuration mode

Can select to be installed on the mounting bracket platform of camera on the star, two accelerometer sensitive axles measuring same direction shake are parallel to each other, and should be vertical with the camera optical axis.Shown in 2 figure; The accelerometer of two sensitive axes quadratures respectively is installed in the front and rear surfaces of camera; The accelerometer 1 that wherein is installed in surface behind the camera and accelerometer 2 quadratures, be installed in the accelerometer 3 and accelerometer 4 quadratures of camera front surface; And accelerometer 1 is parallel with accelerometer 3 sensitive axes, and accelerometer 2 is parallel with accelerometer 4 sensitive axes.Because for camera; Therefore the vibratory output of its optical axis direction, can only can only install two accelerometers parallel with optical axis in its front and rear surfaces to not influence of camera; And the computing method of each shaft vibration amount are consistent; Therefore, measuring three does not have essential distinction with the methods of measuring diaxon, below is that example is explained with one (accelerometer 1 and accelerometer 3) only.

3) data processing method

(1) differential data pre-service

Accelerometer 1 measures time-domain signal a ₁, accelerometer 3 measures time-domain signal a ₂, utilize formula (1) to obtain the angular acceleration a (t) of useful load,

$a\left(t\right)=\frac{a_1-a_2}{L}---\left(1\right)$

L is for measuring base length, i.e. distance between the accelerometer that is parallel to each other of two sensitive axes, and t is a Measuring Time.

Two accelerometer measures time-domain signals are subtracted each other; Reason is that same section is the external environment noise in two accelerometer time domain measurements; Different piece is useful signal and a self-noise separately; So; Two accelerometer time domains are subtracted each other can deduct the external environment noise, but self-noise separately then is synthesized, and mean square deviation expands original to doubly.And after the useful signal difference, be angular acceleration signal divided by measuring baseline L again.

(2) data spectrum analysis

Angular acceleration a (t) carries out power spectrumanalysis, is transformed into frequency domain power spectral density function A (f), and then corresponding angular velocity power spectrum density is:

$\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\left(f\right)=\frac{A\left(f\right)}{2\mathrm{\&pi;f}},(\mathrm{deg}/s/\mathrm{<figure-callout\; id="1"\; label="H\; z"\; filenames="HSA00000291315500021.png"\; state="\{\{state\}\}">H</figure-callout>}{z}^{}{}^{1/2})---\left(2\right)$

The angular displacement power spectrum density is:

$\mathrm{\&theta;}\left(f\right)=\frac{A\left(f\right)}{{\left(2\mathrm{\&pi;f}\right)}^2},(\mathrm{deg}/\mathrm{<figure-callout\; id="1"\; label="H\; z"\; filenames="HSA00000291315500021.png"\; state="\{\{state\}\}">H</figure-callout>}{z}^{}{}^{1/2})---\left(3\right)$

F is the frequency of linear acceleration signal.

Calculate the root-mean-square value of angular displacement

${\mathrm{\&Phi;}}_{\mathrm{rms}}=\sqrt{\&Integral;{\mathrm{\&theta;}}^2\left(f\right)\mathrm{df}},\left(\mathrm{deg}\right)$

Following formula can reflect that (root-mean-square value is Φ for the level of angle of throw displacement _Rms, 1 σ).Above-mentioned integration then adopts the discrete integration form in practical application, promptly

Φ ² _rms＝∑θ ²(f)·Δf (4)

This method advantage is that spectral leakage is few, and noise resisting ability is strong.So far, utilize formula (4) to obtain the angular vibration amount Φ in Measuring Time on direction of principal axis of useful load _Rms

For example, following to the spectrum analysis result of the linear acceleration of certain test, its chattering frequency is mainly 67Hz, and amplitude is 4.30 * 10 ^-3G; Measure baseline L=1m in the test, obtain corresponding angular velocity and the jitter amplitude of angular displacement is respectively 5.85 * 10 according to formula (2)～(4) ^-3Deg/s and 13.9 * 10 ^-6Deg.

(3) the angular vibration amount under the time window is calculated

If will be directed against certain time window T (for example 2ms), then corresponding threshold frequency f ₀=1/ (π T), the vibratory output computing method are following so:

One of which is with threshold frequency f ₀Be the boundary, according to above-mentioned spectrum analysis result, respectively to being lower than f ₀Be higher than f ₀Frequency range, the amplitude of picking up main frequency.

Its two, the subcritical frequency f ₀Scope, its angular vibration amount is calculated by following formula

$\mathrm{\&Delta;}{\mathrm{\&theta;}}_0=\underset{i}{\mathrm{\&Sigma;}}\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HSA00000291315500021.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{0,i}---\left(5\right)$

Wherein

Be the subcritical frequency f ₀The angular velocity amplitude of each chattering frequency, obtain by formula (2), i ∈ [1,2 ... I], I is the subcritical frequency f ₀The sum of angular velocity amplitude of chattering frequency.

Its three, be higher than threshold frequency f ₀Scope, its angular vibration amount is calculated by following formula

$\mathrm{\&Delta;}{\mathrm{\&theta;}}_1=\sqrt{{\&Integral;}_{{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HSA00000291315500021.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}^{+\&infin;}{\mathrm{\&theta;}}_1^2\left(f\right)\mathrm{df}},\left(\mathrm{deg}\right)---\left(6\right)$

θ wherein ₁For being higher than threshold frequency f ₀The angle amplitude of each chattering frequency, obtain by formula (3).

Angular vibration amount Δ θ in time window T is above-mentioned two parts sum, promptly

Δθ＝Δθ ₀+Δθ ₁ (7)

Utilize formula (7) finally to obtain the angular vibration amount Δ θ of the star loaded camera in time window T.

For example, time window T=2ms, corresponding adjacent frequency f ₀=159Hz, the angular oscillation amount in certain test in the time window T is 5.85 * 10 ^-6Deg.

The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (1)

1. method of measuring the little vibration of useful load three shaft angle displacement high frequencies on the star is characterized in that realizing through following steps:

The first step is installed the three axis accelerometer assembly

The three axis accelerometer assembly is installed on the mounting bracket platform of useful load, and a cover three axis accelerometer assembly promptly respectively is installed on former and later two surfaces of useful load; Every cover three axis accelerometer assembly comprises three accelerometers that are used for measuring three shaft vibration amounts of useful load, and the sensitive axes pairwise orthogonal of three accelerometers is in a bit, and wherein two accelerometers are vertical with the central shaft of useful load; Two accelerometer sensitive axles measuring the same direction vibration of useful load are parallel to each other, and promptly the sensitive axes of accelerometer is parallel in twos in the two cover three axis accelerometer assemblies, the line of accelerometer sensitive axle intersection point and the central axes of useful load;

Second step, gather the linear acceleration signal on former and later two planes of useful load that measure of accelerometer in the first step, utilize formula (1) to obtain the angular acceleration a (t) of useful load,

$a\left(t\right)=\frac{a_1-a_2}{L}---\left(1\right)$

Wherein, a ₁, a ₂Be the linear acceleration signal that accelerometer measures that two sensitive axes are parallel to each other obtains,

L is for measuring base length, i.e. distance between the accelerometer that is parallel to each other of two sensitive axes,

T is a Measuring Time;

The 3rd step; Obtained the angular acceleration a of useful load second step; (t) be converted into frequency domain power spectral density function A; (f); Utilize formula; (2) the angular velocity power density

that obtains useful load is utilized formula; (3) obtain useful load angular displacement power spectrum density θ; (f)

$\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\left(f\right)=\frac{A\left(f\right)}{2\mathrm{\&pi;f}}---\left(2\right)$

$\mathrm{\&theta;}\left(f\right)=\frac{A\left(f\right)}{{\left(2\mathrm{\&pi;f}\right)}^2}---\left(3\right)$

F is the frequency of linear acceleration signal;

In the 4th step, utilize formula (4) to obtain the angular vibration amount Φ in Measuring Time on direction of principal axis of useful load _Rms,

Φ ² _rms＝∑θ ²(f)·Δf (4)；

The 5th step, calculate the angular vibration amount on direction of principal axis of useful load in certain time window T,

A5.1, utilize formula (5) to obtain the subcritical frequency f ₀The angular vibration amount Δ θ of scope ₀,

${\mathrm{\&Delta;\&theta;}}_0=\underset{i}{\mathrm{\&Sigma;}}\frac{T}{2}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{0,i}---\left(5\right)$

Wherein

Be the subcritical frequency f of utilizing formula (2) to obtain ₀The angular velocity amplitude of each chattering frequency, i ∈ [1,2 ... I], I is the subcritical frequency f ₀The sum of angular velocity amplitude of chattering frequency, threshold frequency f ₀=1/ (π T);

A5.2, utilize formula (6) to obtain being higher than the angular vibration amount Δ θ of threshold frequency f0 scope ₁,

${\mathrm{\&Delta;\&theta;}}_1=\sqrt{{\&Integral;}_{f_0}^{+\&infin;}{{\mathrm{\&theta;}}_1}^2\left(f\right)\mathrm{df}}---\left(6\right)$

θ wherein ₁Be higher than threshold frequency f for what utilize that formula (3) obtains ₀The angle amplitude of each chattering frequency;

A5.3, utilize formula (7) to obtain the angular vibration amount Δ θ of the useful load in time window T,

Δθ＝Δθ ₀+Δθ ₁ (7)；

The 6th step repeated～the five step of second step, obtained the angular vibration amount of all the other two axles of useful load.

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