CN101750200A - Method for determining flutter response of high-resolution minisatellites - Google Patents

Abstract

The invention provides a method for determining flutter response of high-resolution minisatellites. Through a determination method of adopting a single frame to control disturbing torque produced by the dynamic imbalance of moment gyroscope rotors, the invention solves the problem of determining the flutter interference of the high-resolution minisatellites of the type. The method realizes the decoupling and degree reduction of a satellite-flutter vibration mechanical equation among degrees of freedom through appropriate state variable settings and replacement, transforms the vibration mechanical equation into a first order differential equation, and utilizes a numerical solution to determine attitude response produced by satellites under the action of flutter interference sources, so the method is concise and normative. For the attitude response of the satellites caused by the action of flutter interference, the method combines satellite attitude control laws to eliminate controllable parts in flutter attitude response, and finally determines the flutter response of the satellites under the action of the flutter interference sources. The determination method can also adjust and control the disturbing torque of moment gyroscopes by regulating the installation modes and machining accuracy of the gyroscopes so as to achieve the aim of improving image quality.

Description

A kind of method for determining flutter response of high-resolution minisatellites

Technical field

The present invention relates to a kind of method for determining flutter response of high-resolution minisatellites, particularly adopt the flutter response of the high resolving power moonlet of control-moment gyro topworks to determine method, belong to the satellite dynamics technical field, can be used for attitude of satellite interference, flutter analysis.

Background technology

During the satellite imagery, the flexibility of movable part motion, satellite structure etc. can make satellite main body and CCD camera produce disturbance, and the part that wherein amplitude is less, frequency is higher, control system can't observing and controlling is flutter.The high resolving power moonlet is compared with large satellite, and inertial mass is light, is more vulnerable to disturbing effect.

2003 in stepping on cloud, Wang Yueyu etc. in " remote sensing satellite flutter response analysis technical research " and " practical approach of remote sensing satellite flutter response analysis " literary composition, inquire into regard to trembling vibration mechanical analysis technology, provided remote sensing satellite kinetic model and disturbing source disturbing moment model thereof, provided the numerical analysis result of satellite celestial body flutter response under the stepping of sun battle array, magnetic tape station and momenttum wheel kinematic synthesis disturb when considering sun battle array and camera flexibility based on Lagrangian method.

People such as NASA Ge Dade flight center Kuo-Chia Liu in 2008 and Peiman Maghami have introduced sun power surveillance program SDO at interference modeling and the flutter analysis done at the main interference source reaction wheel of rail in " Reaction Wheel Disturbance Modeling; Jitter Analysis; and Validation Tests forSolar Dynamics Observatory " literary composition, describe the ground validation test of the checking correction of interference model and retroaction flutter analysis in detail and require the measure of reaction wheel rotating speed speed limit etc. for the flutter of satisfying observation instrument.More than research all is primarily aimed at reaction wheel interference etc. and carries out the satellite flutter analysis, can not satisfy the needs that the flutter of high resolving power moonlet is determined.

The present invention is directed to present technological gap, propose a kind of disturbance torque that utilizes the unbalance dynamic of single frame control-moment gyro to produce first and determined the flutter response of satellite, the disturbance torque that utilizes the present invention to determine, can carry out attitude disturbance analysis, flutter analysis to quick moonlet, thereby pass judgment on the satellite imagery quality, the resolution of test satellite can also finally make the resolution of satellite reach designing requirement by the disturbance torque of adjusting control-moment gyro.

The quick maneuverability of high resolving power moonlet obtains paying attention to and development day by day, this type of high resolving power moonlet mainly adopts control-moment gyro as topworks, has not yet to see interference modeling and flutter analysis for the main interference source control-moment gyro of this type of high resolving power moonlet.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of method for determining flutter response of high-resolution minisatellites is provided, fill up the prior art blank, the inventive method provides foundation for the impact analysis and the final satellite imagery quality of improving of satellite imagery quality.

Technical solution of the present invention is: a kind of method for determining flutter response of high-resolution minisatellites, realize by following steps:

The first step is set up the trembling vibration mechanical equation of high resolving power moonlet according to formula (1),

Wherein, I _bBe star rotation inertia; ω _bBe star rotation angular velocity; F _SkBe the coupling coefficient of the flexibility of k sun wing annex to the satellite rotation, τ _k=[τ _K1τ _K2τ _K6] ^T, be k the preceding 6 rank modal coordinate arrays of sun wing annex, μ is the ratio of damping of sun wing annex, Ω _k=diag (ω _K1ω _K2ω _K6), be k the preceding 6 rank model frequency arrays of sun wing annex, ω _Kj(j=1,2 ..., 6) and be k sun wing j rank model frequency, K is the sum of sun wing annex, T _dBe the disturbance torque of satellite control system topworks single frame control-moment gyro group motion imbalance to the satellite body generation;

In second step, determine the disturbance torque T that satellite single frame control-moment gyro group motion imbalance produces satellite body _d

The 3rd step is according to definite disturbance torque T of second step _d, utilize the trembling vibration mechanical equation of setting up in the first step, determine the attitude response of high resolving power moonlet under the effect of flutter disturbance torque,

(3.1) the trembling vibration mechanical equation of formula (1) is rewritten as the form of formula (9),

$M\stackrel{\·\·}{x}+C\stackrel{\·}{x}+\mathrm{Kx}=Q---\left(9\right)$

Wherein,

The generalized coordinate variable

, wherein

θ, ψ are roll angle, the angle of pitch and the crab angle of satellite centrosome;

(3.2) second order ordinary differential equation of formula (9) is converted into the single order state equation form of formula (10):

Wherein,

N is the trembling vibration mechanical equation group number of degrees of freedom, of satellite system, I _{N * n}It is the unit matrix of n * n;

(3.3) utilize the derivation algorithm solution formula (10) of One first-order ordinary differential equation initial-value problem to obtain rolling, pitching and yaw-position response, i.e. roll angle, the angle of pitch and the crab angle of satellite under the effect of flutter disturbance torque;

In the 4th step, utilize attitude of satellite control rule to determine that the controlled attitude in the satellite flexible dynamics equation of first step foundation responds;

The 5th step with the attitude response of satellite under the effect of flutter disturbance torque of determining in the 3rd step, deducted the 4th and goes on foot the controlled attitude response of determining, obtained the flutter response that satellite causes under the effect of flutter disturbance torque.

Disturbance torque T in described second step _dDetermine according to following steps,

(2.1) utilize the rotor quality characteristic test method, obtain the amount J of the principal axis of inertia relative rotation axi line inclined degree of tolerance gyrorotor _Xz, J _Yz

(2.2) obtain the dynamic unbalance value and the starting phase angle of gyrorotor according to formula group (2),

Wherein, I ₀Be the dynamic unbalance value of gyrorotor, φ is the starting phase angle that gyrorotor changes degree of unbalancedness;

(2.3) satellite control system topworks measure portion record each gyrorotor relatively the corner of self framework be angle of rotor γ _iThe corner of relative gyro pedestal with framework is framework corner ζ _i, and the angular velocity that rotates around turning axle of rotor

I=1,2 ... N, N are the sums of gyro;

(2.4) utilize step (2.2) to obtain I ₀The angular velocity that obtains with φ and step (2.3)

, obtain gyrorotor at rotor coordinate system ox according to formula (3) _my _mz _mMiddle disturbance torque,

T wherein _DmFor gyrorotor at rotor coordinate system ox _my _mz _mThe disturbance torque of following generation,

Be rotor coordinate system ox _my _mz _mx _mTo, y _mTo unit vector;

(2.5) the angle of rotor γ that utilizes step (2.3) to obtain _iWith framework corner ζ _i, obtaining frame coordinates according to formula (4), (5) is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix A _RsiWith rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix A _Mri,

A _RsiThe frame coordinates that is i gyro is the transition matrix of relative gyro base coordinate system, A _MriIt is the transition matrix of the relative frame coordinates of the rotor coordinate system system of i gyro;

(2.6) obtain the gyro base coordinate system ox of the positive taper gyro group formed by N gyro by formula (6) _sy _sz _sTo celestial body coordinate system o _bx _by _bz _bTransition matrix, the gimbal axis of each gyro in the gyro group and satellite celestial body coordinate system o _bx _by _bz _bZ _bAxle coplane, and and z _bThe angle of axle is β, and gimbal axis is at satellite celestial body coordinate plane x _by _bProjection and x _bAxle clamp angle α _i,

Wherein, M _SbiBe the transition matrix of the gyro base coordinate system of i gyro to the celestial body coordinate system;

(2.7) utilize the transition matrix A that obtains in the step (2.5) _Rsi, A _MriAnd the transition matrix M that obtains of step (2.6) _Sbi, formula (3) through three coordinate conversion, is transformed into satellite celestial body coordinate system from the rotor coordinate system, obtain the disturbance torque T of every i gyrorotor in satellite celestial body coordinate system _Di,

$T_{\mathrm{di}}={M_{\mathrm{sbi}}}^T\·A_{\mathrm{rsi}}^T\·A_{\mathrm{mri}}^T\·T_{\mathrm{dm}}---\left(7\right);$

(2.8) obtain the disturbance torque T of gyro group in satellite celestial body coordinate system according to formula (8) _d,

$T_d=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{di}}$

Design concept of the present invention:

For the high resolving power moonlet, consider the flexibility of the sun wing, adopt the flexible spacecraft dynamic modeling method, set up satellite trembling vibration mechanical equation, set up the disturbance torque model that main interference source single frame frame control moment gyro dynamic unbalance produces then, carry out attitude of satellite response analysis, determine the flutter response of satellite at last in conjunction with attitude control result.Comprise the following steps:

1, sets up satellite trembling vibration mechanical equation.According to the flexible spacecraft dynamic modeling method, in conjunction with the stiffness characteristics of moonlet parts, mainly consider the flexibility of the sun wing, set up moonlet flexible spacecraft trembling vibration mechanical equation;

2, set up the disturbance torque mathematical model that main interference source single frame control-moment gyro produces.Unbalance dynamic by the dead axle rotatable parts is set out to the disturbance torque that its rotating shaft produces, two-freedom in conjunction with single frame control-moment gyro rotor rotates, be rotor with respect to the rotation of framework and framework with respect to the rotation of gyro pedestal, obtain the disturbance torque mathematical model that the unbalance dynamic of single frame control-moment gyro rotor produces satellite by continuous coordinate transform.

(1) sets up the coordinate system of using in the analysis

Definition rotor coordinate system ox _my _mz _m, be the rotor body coordinate system, be connected with rotor;

Definition frame coordinate system ox _ry _rz _r, coordinate axis along gimbal axis, axis of torque and rotor angular momentum axle, is connected with framework respectively, initial time ox _ry _rz _rAnd ox _my _mz _mOverlap;

Definition gyro base coordinate system ox _sy _sz _s, when frame corners was zero, it and frame coordinates were ox _ry _rz _rOverlap.Arrange according to the configuration of gyro group and the direction of each gyro gimbal axle, can determine the installation matrix M of each gyro pedestal.Each coordinate system as shown in Figure 5.

(2) conversion between each coordinate system

The corner of the relative framework of control-moment gyro rotor is designated as γ, and the corner of the relative gyro pedestal of framework is designated as ζ.The gyro base coordinate system can be obtained by twice rotation to the conversion of rotor coordinate system, promptly earlier around x _rAxle turns over ζ, again around z _mAxle turns over γ.

Frame coordinates is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix be

Rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix be

For the single frame control-moment gyro group of taper configuration, a certain axon of the gimbal axis of every gyro and celestial body (for example z axle) coplane, with this axle clamp angle β, gimbal axis is at celestial body coordinate plane x _by _bProjection and x _bAxle clamp angle α, the angular momentum of frame corners zero-bit is parallel to x _by _bThe plane can determine that each gyro base coordinate system gets transition matrix to the celestial body coordinate system, and promptly the installation matrix of gyro pedestal is

(3) determine disturbance torque that the rotor unbalance dynamic produces according to d'Alembert principle under the rotor coordinate system, the moment of inertia that during rotation of dead axle rotatable parts rotation axis is produced is:

Particularly when constant speed is rotated

$U_d=\stackrel{\→}{k}\×(J_{\mathrm{xz}}\stackrel{\→}{i}+J_{\mathrm{yz}}\stackrel{\→}{j})$

Wherein

Be the angular velocity that rotatable parts rotate around dead axle, U _dBe unbalance dynamic, do not overlap by rotor principal axis of inertia and rotation and cause J _Xz, J _YzBe the amount of the principal axis of inertia relative rotation axi line inclined degree of tolerance rotor, obtain by the rotor quality characteristic test.

For the single frame control-moment gyro, its rotor is done uniform rotation around the axis of angular momentum, so the disturbance torque T of rotor unbalance dynamic generation _DmAt rotor coordinate system o _mx _my _mz _mIn be

Order

I ₀Be unbalance dynamic size tolerance, then following formula can be expressed as

(4) determine the disturbance torque that the rotor unbalance dynamic produces under the celestial body coordinate system

Disturbance torque expression formula according to the rotor unbalance dynamic produces under the rotor coordinate system is transformed into it under celestial body coordinate system by continuous coordinate transform, finally determines the disturbance torque that the rotor unbalance dynamic produces under the celestial body coordinate system.

At celestial body o _bx _by _bz _bIn the coordinate system, T _dFor

$T_d={M_{\mathrm{sb}}}^T\·A_{\mathrm{rs}}^T\·A_{\mathrm{mr}}^T\·T_{\mathrm{dm}}$

With each transition matrix substitution above, must the rotor unbalance dynamic be to the disturbance torque that satellite body produces

3, determine the attitude response of flexible spacecraft under the effect of flutter disturbance torque.The trembling vibration mechanical equation is the second order ordinary differential equation group, equation number of degrees of freedom, height, and coupling is serious between each degree of freedom.For ease of analysis, at first define system generalized coordinate x=[x ₁x ₂X _n] ^T(n is system's broad sense number of degrees of freedom) is rewritten into the trembling vibration mechanical equation

$M\stackrel{\·\·}{x}+C\stackrel{\·}{x}+\mathrm{Kx}=Q$

Wherein M is the generalized mass matrix of Space Vehicle System, and C is the broad sense damping matrix of system, and K is the broad sense stiffness matrix of system, and Q is the suffered broad sense external force of system.

If state variable $y=\left[\begin{array}{c}x\\ \stackrel{\·}{x}\end{array}\right]$ , replace by state variable, the trembling vibration mechanical equation of system is converted into One first-order ordinary differential equation

$\stackrel{\·}{y}=\mathrm{Ay}+P$

Wherein

Thereby the derivation algorithm that can utilize the One first-order ordinary differential equation initial-value problem obtains the attitude response of satellite under the effect of flutter disturbance torque;

4, determine the flutter response of spacecraft.For the attitude response of satellite under the effect of flutter disturbance torque, wherein a part is controlled attitude, according to the 1 moonlet flexible dynamics equation of setting up, according to the definite attitude that can control of attitude of satellite control rule.With the attitude response of 3 satellites of determining under the effect of flutter disturbance torque, deduct the controlled attitude part of satellite attitude control system, finally obtain the flutter response that satellite causes under the effect of flutter disturbance torque.The flutter response of satellite can be used for the image quality analysis and evaluation, also provides technical foundation for the satellite imagery quality improvement.

The present invention compared with prior art beneficial effect is:

(1) the present invention adopts definite method of the disturbance torque of single frame control-moment gyro rotor unbalance dynamic generation, and problem identificatioin is disturbed in the flutter that has solved this type of high resolving power moonlet;

(2) the present invention is by suitable state variable setting and replacement, realize decoupling zero and depression of order between satellite trembling vibration mechanical equation degree of freedom, be translated into differential equation of first order, utilize numerical solution, determine the attitude response that satellite produces under the effect of flutter interference source, the simple and clear standard of method;

(3) the present invention responds for the attitude that satellite causes under the flutter interference effect, in conjunction with the controllable part in the response of attitude of satellite control rule elimination flutter attitude, determines that finally the flutter of satellite under the effect of flutter interference source responds;

(4) machining precision of mounting means that definite method of the present invention can also be by regulating gyro and gyro is adjusted the disturbance torque of control-moment gyro, finally reaches the purpose that improves picture quality.

Description of drawings

Fig. 1 is a single frame control-moment gyro coordinate system synoptic diagram of the present invention;

The positive five face cone shape control-moment gyro configuration synoptic diagram of Fig. 2 for adopting in the embodiment of the present invention;

Fig. 3 is for utilizing certain quick high resolving power moonlet body rolling flutter angle behind the present invention;

Fig. 4 is for utilizing certain quick high resolving power moonlet body pitching flutter angle behind the present invention;

Fig. 5 is for utilizing certain quick high resolving power moonlet body driftage flutter angle behind the present invention.

Embodiment

For the high resolving power moonlet, the main flexibility of considering the sun wing, adopt the flexible spacecraft dynamic modeling method, set up satellite trembling vibration mechanical equation, on the one hand by setting up the disturbance torque model that main flutter interference source single frame control-moment gyro produces, carry out attitude of satellite response analysis, obtain the controlled attitude response of satellite on the other hand according to the satellite attitude control system control law, from the attitude response of satellite under the effect of flutter interference source, eliminate the flutter response that the attitude that can control is partly determined satellite at last, for the satellite imagery quality evaluation provides foundation.

According to instantiation definite method of the present invention is described below.

With 3 sun wings of a fixed installation, employing single frame control-moment gyro is that the moonlet of control executing mechanism is an example, and the concrete steps that its flutter response is determined are:

One, sets up satellite trembling vibration mechanical equation

According to the flexible spacecraft dynamic modeling method, as rigid body, the sun wing is considered the flexibility of the sun wing as annex, gets preceding 6 rank mode, sets up the trembling vibration mechanical equation of satellite system with the satellite centrosome:

In the formula, I _bBe star rotation inertia; ω _bBe star rotation angular velocity; F _SkBe the coupling coefficient of annex k flexibility to the satellite rotation; τ _k=[τ _K1τ _K2τ _K6] ^T, be 6 rank modal coordinate arrays before the annex k; μ is the ratio of damping of sun wing annex; Ω _k=diag (ω _K1ω _K2ω _K6), be 6 rank model frequency arrays before the annex k.

Two, set up the disturbance torque model that main flutter interference source single frame frame control moment gyro dynamic unbalance produces

Unbalance dynamic by the dead axle rotatable parts is set out to the disturbance torque that its rotating shaft produces, two-freedom in conjunction with single frame control-moment gyro rotor rotates, be rotor shaft with respect to framework rotate and framework with respect to the rotation of gyro pedestal, obtain the disturbance torque mathematical model of single frame control-moment gyro rotor unbalance dynamic by continuous coordinate transform to the satellite generation.

1, the gimbal axis of each gyro in the gyro group and satellite celestial body coordinate system o _bx _by _bz _bZ _bAxle coplane, and and z _bThe angle of axle is β, and gimbal axis is at satellite celestial body coordinate plane x _by _bProjection and x _bAxle clamp angle α _i, i=1,2 ... 5, each gyro base coordinate system ox then _sy _sz _sTo celestial body coordinate system o _bx _by _bz _bTransition matrix M _SbiFor

As shown in Figure 2, five face cone shape single frame gyro groups, the gimbal axis of each gyro in the gyro group is at satellite celestial body coordinate plane x _by _bProjection and x _bThe axle clamp angle is respectively α ₁=90 °, α ₂=π-18 °, α ₃=-(π-54 °), α ₄=-54 °, α ₅=18 °, can get the installation matrix of five gyro pedestals in the substitution formula (6).

2, utilize the rotor quality characteristic test method, obtain the amount J of the principal axis of inertia relative rotation axi line inclined degree of each gyrorotor of tolerance _Xz, J _Yz

3, obtain the dynamic unbalance value and the starting phase angle of gyrorotor according to formula group (2),

Wherein, I ₀Be the dynamic unbalance value of gyrorotor, φ is the starting phase angle of gyrorotor dynamic unbalance.

4, satellite control system topworks measure portion record each gyrorotor relatively the corner of self framework be angle of rotor γ _iThe corner of relative gyro pedestal with framework is framework corner ζ _i, and the angular velocity that rotates around turning axle of rotor

5, obtain each gyrorotor at rotor coordinate system ox according to formula (3) _my _mz _mMiddle disturbance torque,

T wherein _DmFor gyrorotor at rotor coordinate system ox _my _mz _mMiddle disturbance torque,

Be rotor coordinate system ox _my _mz _mx _mTo, y _mTo unit vector.

6, obtaining frame coordinates according to formula (4), (5) is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix A _RsiWith rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix A _Mri

A _RsiThe frame coordinates that is i gyro is the transition matrix of relative gyro base coordinate system, A _MriIt is the transition matrix of the relative frame coordinates of the rotor coordinate system system of i gyro;

7, utilize the transition matrix M of formula (6) _SbiAnd the transition matrix A of formula (4), (5) _Rsi, A _Mri, formula (3) through three coordinate conversion, is transformed into satellite celestial body coordinate system from the rotor coordinate system, obtain the disturbance torque T of i gyrorotor in satellite celestial body coordinate system _Di,

$T_{\mathrm{di}}={M_{\mathrm{sbi}}}^T\·A_{\mathrm{rsi}}^T\·A_{\mathrm{mri}}^T\·T_{\mathrm{dm}}---\left(7\right).$

8, obtain the disturbance torque T of gyro group in satellite celestial body coordinate system according to formula (8) _d,

$T_d=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{di}}$

For the single frame moment gyro group of five face cone shape configurations, ignore the starting phase angle φ of rotor dynamic unbalance _i, can get its rotor unbalance dynamic and be total disturbance torque that celestial body produces

In the formula, ζ _i(i=1,2 ..., 5) and be respectively the corner of five frameworks; γ is the corner of rotor, and five control-moment gyro angle of rotor are identical, is provided by satellite control system topworks measure portion.

Three, determine the attitude response of flexible spacecraft under the effect of flutter disturbance torque

Trembling vibration mechanical equation group formula (1) number of degrees of freedom, of above-mentioned satellite system is n=21, and the generalized coordinate variable is set

Wherein

θ, ψ are centrosome roll angle, the angle of pitch and crab angle, and the system dynamics equation is rewritten as

$M\stackrel{\·\·}{x}+C\stackrel{\·}{x}+\mathrm{Kx}=Q$

Wherein

If state variable $y=\left[\begin{array}{c}x\\ \stackrel{\·}{x}\end{array}\right]$ , second order ordinary differential equation is converted into state equation (first-order equation) form:

$\stackrel{\·}{y}=\mathrm{Ay}+P,$ $A=\left[\begin{array}{cc}{0}_{n\×n}& I_{n\×n}\\ -M^{-1}K& -M^{-1}C\end{array}\right],$ $P=\left[\begin{array}{c}{0}_{n\×1}\\ M^{-1}Q\end{array}\right]$

Utilize the derivation algorithm of One first-order ordinary differential equation initial-value problem to obtain the attitude response of satellite under the effect of flutter disturbance torque.

Four, determine the flutter attitude response of spacecraft

For the attitude response of determining in the step 3, wherein a part is the attitude that can control, moonlet flexible dynamics equation according to step 1 foundation, (this is a general knowledge known in this field according to attitude of satellite control rule, concrete analysis is referring to " attitude of satellite dynamics and control ", and Tu Shancheng edits in the Yuhang Publishing House, 1999 the 1st edition, P239～P296) determines controlled attitude response.The attitude response of satellite under the effect of flutter disturbance torque with step 3 is determined deducts the controlled attitude response of satellite attitude control system, finally obtains the flutter response that satellite causes under the effect of flutter disturbance torque.

Definite method according to above-mentioned satellite flutter response, determined the flutter attitude angle of this satellite body under the control-moment gyro unbalance dynamic is disturbed, Fig. 2-Fig. 4 is respectively rolling, pitching, the driftage flutter angle of this satellite body, satellite body is respectively along the maximum flutter angular displacement of rolling, pitching, three directions of driftage as seen from the figure: 0.0057 rad, 0.0071 rad and 0.0252 rad, thus carry out flutter and provide the input foundation for follow-up the impact evaluation of image quality.

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

Claims (2)

1. method for determining flutter response of high-resolution minisatellites is characterized in that realizing by following steps:

The first step is set up the trembling vibration mechanical equation of high resolving power moonlet according to formula (1),

$\left\{\begin{array}{c}{I}_b{\stackrel{\·}{\mathrm{\ω}}}_b+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{F}_{\mathrm{sk}}{\stackrel{\·\·}{\mathrm{\τ}}}_k=T_d\\ F_{\mathrm{sk}}^T{\stackrel{\·}{\mathrm{\ω}}}_b+{\stackrel{\·\·}{\mathrm{\τ}}}_k+2\mathrm{\μ}{\mathrm{\Ω}}_k{\stackrel{\·}{\mathrm{\τ}}}_k+{{\mathrm{\Ω}}_k}^2{\mathrm{\τ}}_k=0(k=\mathrm{1,2},\·\·\·,K)\end{array}\right.---\left(1\right)$

Wherein, I _bBe star rotation inertia; ω _bBe star rotation angular velocity; F _SkBe the coupling coefficient of the flexibility of k sun wing annex to the satellite rotation, τ _k=[τ _K1τ _K2τ _K6] ^T, be k the preceding 6 rank modal coordinate arrays of sun wing annex, μ is the ratio of damping of sun wing annex, Ω _k=diag (ω _K1ω _K2ω _K6), be k the preceding 6 rank model frequency arrays of sun wing annex, ω _Kj(j=1,2 ..., 6) and be k sun wing j rank model frequency, K is the sum of sun wing annex, T _dBe the disturbance torque of satellite control system topworks single frame control-moment gyro group motion imbalance to the satellite body generation;

In second step, determine the disturbance torque T that satellite single frame control-moment gyro group motion imbalance produces satellite body _d

The 3rd step is according to definite disturbance torque T of second step _d, utilize the trembling vibration mechanical equation of setting up in the first step, determine the attitude response of high resolving power moonlet under the effect of flutter disturbance torque,

(3.1) the trembling vibration mechanical equation of formula (1) is rewritten as the form of formula (9),

$M\stackrel{\·\·}{x}+C\stackrel{\·}{x}+\mathrm{Kx}=Q---\left(9\right)$

Wherein,

The generalized coordinate variable

Wherein

θ, ψ are roll angle, the angle of pitch and the crab angle of satellite centrosome;

(3.2) second order ordinary differential equation of formula (9) is converted into the single order state equation form of formula (10):

$\stackrel{\·}{y}=\mathrm{Ay}+P---\left(10\right)$

Wherein, $y=\left[\begin{array}{c}x\\ \stackrel{\·}{x}\end{array}\right],$ $A=\left[\begin{array}{cc}{0}_{n\×n}& I_{n\×n}\\ {-M}^{-1}K& {-M}^{-1}C\end{array}\right],$ $P=\left[\begin{array}{c}{0}_{n\×1}\\ M^{-1}Q\end{array}\right];$ N is the trembling vibration mechanical equation group number of degrees of freedom, of satellite system, I _{N * n}It is the unit matrix of n * n;

(3.3) utilize the derivation algorithm solution formula (10) of One first-order ordinary differential equation initial-value problem to obtain rolling, pitching and yaw-position response, i.e. roll angle, the angle of pitch and the crab angle of satellite under the effect of flutter disturbance torque;

In the 4th step, utilize attitude of satellite control rule to determine that the controlled attitude in the satellite flexible dynamics equation of first step foundation responds;

The 5th step with the attitude response of satellite under the effect of flutter disturbance torque of determining in the 3rd step, deducted the 4th and goes on foot the controlled attitude response of determining, obtained the flutter response that satellite causes under the effect of flutter disturbance torque.

2. a kind of method for determining flutter response of high-resolution minisatellites according to claim 1 is characterized in that: disturbance torque T in described second step _dDetermine according to following steps,

(2.1) utilize the rotor quality characteristic test method, obtain the amount J of the principal axis of inertia relative rotation axi line inclined degree of tolerance gyrorotor _Xz, J _Yz

(2.2) obtain the dynamic unbalance value and the starting phase angle of gyrorotor according to formula group (2),

$\left\{\begin{array}{c}{I}_0=\sqrt{{J_{\mathrm{xz}}}^2+{J_{\mathrm{yz}}}^2}\\ \cos \mathrm{\φ}=-J_{\mathrm{yz}}/I_0\\ \sin \mathrm{\φ}=J_{\mathrm{xz}}/I_0\end{array}\right.---\left(2\right)$

Wherein, I ₀Be the dynamic unbalance value of gyrorotor, φ is the starting phase angle that gyrorotor changes degree of unbalancedness;

(2.3) satellite control system topworks measure portion record each gyrorotor relatively the corner of self framework be angle of rotor γ _iThe corner of relative gyro pedestal with framework is framework corner ζ _i, and the angular velocity that rotates around turning axle of rotor

I=1,2 ... N, N are the sums of gyro;

(2.4) utilize step (2.2) to obtain I ₀The angular velocity that obtains with φ and step (2.3)

Obtain gyrorotor at rotor coordinate system ox according to formula (3) _my _mz _mMiddle disturbance torque,

T wherein _DmFor gyrorotor at rotor coordinate system ox _my _mz _mThe disturbance torque of following generation,

Be rotor coordinate system ox _my _mz _mx _mTo, y _mTo unit vector;

(2.5) the angle of rotor γ that utilizes step (2.3) to obtain _iWith framework corner ζ _i, obtaining frame coordinates according to formula (4), (5) is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix A _RsiWith rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix A _Mri,

$A_{\mathrm{rsi}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\ζ}}_i& \sin {\mathrm{\ζ}}_i\\ 0& -{\sin \mathrm{\ζ}}_i& \cos {\mathrm{\ζ}}_i\end{array}\right]---\left(4\right)$

$A_{\mathrm{mri}}=\left[\begin{array}{ccc}\cos {\mathrm{\γ}}_i& \sin {\mathrm{\γ}}_i& 0\\ -{\sin \mathrm{\γ}}_i& \cos {\mathrm{\γ}}_i& 0\\ 0& 0& 1\end{array}\right]---\left(5\right)$

A _RsiThe frame coordinates that is i gyro is the transition matrix of relative gyro base coordinate system, A _MriIt is the transition matrix of the relative frame coordinates of the rotor coordinate system system of i gyro;

(2.6) obtain the gyro base coordinate system ox of the positive taper gyro group formed by N gyro by formula (6) _sy _sz _sTo celestial body coordinate system o _bx _by _bz _bTransition matrix, the gimbal axis of each gyro in the gyro group and satellite celestial body coordinate system o _bx _by _bz _bZ _bAxle coplane, and and z _bThe angle of axle is β, and gimbal axis is at satellite celestial body coordinate plane x _by _bProjection and x _bAxle clamp angle α _i,

$M_{\mathrm{sbi}}=\left[\begin{array}{ccc}\sin \mathrm{\β}\cos {\mathrm{\α}}_i& \sin \mathrm{\β}\sin {\mathrm{\α}}_i& \cos \mathrm{\β}\\ -\cos \mathrm{\β}\cos {\mathrm{\α}}_i& -\cos \mathrm{\β}\sin {\mathrm{\α}}_i& \sin \mathrm{\β}\\ \sin {\mathrm{\α}}_i& -{\cos \mathrm{\α}}_i& 0\end{array}\right]---\left(6\right)$

Wherein, M _SbiBe the transition matrix of the gyro base coordinate system of i gyro to the celestial body coordinate system;

(2.7) utilize the transition matrix A that obtains in the step (2.5) _Rsi, A _MriAnd the transition matrix M that obtains of step (2.6) _Sbi, formula (3) through three coordinate conversion, is transformed into satellite celestial body coordinate system from the rotor coordinate system, obtain the disturbance torque T of every i gyrorotor in satellite celestial body coordinate system _Di,

$T_{\mathrm{di}}={M_{\mathrm{sbi}}}^T\·A_{\mathrm{rsi}}^T\·A_{\mathrm{mri}}^T\·T_{\mathrm{dm}}---\left(7\right);$

(2.8) obtain the disturbance torque T of gyro group in satellite celestial body coordinate system according to formula (8) _d, $T_d=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{di}}$

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