CN102636817B - A kind of mass compensation method for designing of pure Universal gravitation AF panel - Google Patents

Abstract

A kind of mass compensation method for designing of pure Universal gravitation AF panel, comprise the following steps: 1. obtain spacecraft mass distributed data, determine the action scope that universal gravitation disturbs, calculate the universal gravitation interference in action scope, and the requirement of clear and definite universal gravitation AF panel; 2. choose reference point, the universal gravitation AF panel target of reference point is set; 3. determine mass compensation design result; 4. mass compensation design result is added in spacecraft mass distributed data, recalculate the universal gravitation interference in action scope; 5. check Compensation Design result whether to meet the universal gravitation AF panel requirement of action scope; 6. according to the check conclusion of step 5, if meet the demands, then obtain available Compensation Design result; If do not meet the demands, then reset the universal gravitation AF panel target of reference point, repeat step 3-step 5.By method of the present invention, obtain realizing the mass compensation scheme to the pure Universal gravitation AF panel in specific region.

Description

A kind of mass compensation method for designing of pure Universal gravitation AF panel

Technical field

The present invention relates to astrodynamics technical field, particularly relate to a kind of mass compensation method for designing of pure Universal gravitation AF panel.

Background technology

Some take Fundamental Physics Experiments as the space tasks of task object, as detected gravitational waves and checking LISA and the ASTROD task of general relativity, verification quality is needed to fly (article " integrated model (The LISA integrated model) of LISA " and periodical " atomic nuclear physics B " (Nuclear Physics B) the 166th volume 153-158 page article " ASTROD (Laser synchrotron source) and ASTROD I " in 2007 see periodical " classical and quantum gravity " (Classicaland Quantum Gravity) the 20th volume in 2003) along pure Attractive Orbit.Equally, utilize verification quality along the pure Attractive Orbit flight of near-earth, and obtain the pure Attractive Orbit of verification quality, can be used in accurately measuring earth gravity field (" adopting the pure Attractive Orbit of accurate formation flight technical limit spacing (Acquirement ofpure gravity orbit using precision formation flying technology) " see periodical " international aerospace joint conference periodical " (ActaAstronautica) special issue article in 2012).For the scientific goal of these tasks, it is a main perturbed force that outer spacecraft acts on the qualitative universal gravitation of internal verification, affects the performance level (article " the remaining acceleration error of current LISA is estimated (Current errorestimates for LISA spurious accelerations) " see " classical and quantum gravity " (Classical and Quantum Gravity) the 21st volume the 5th phase S653-S660 page in 2004) of pure Attractive Orbit.Therefore, suppressing the universal gravitation interference of pure Attractive Orbit, is the important content improving pure Attractive Orbit performance.

In prior art, LISA model team establishes the numerical computation method of universal gravitation interference, the node quality adopting spacecraft finite element model to provide and position, and each unit is approximately particle and calculates its gravitation to verification quality, moment and gradient effect, then entire amount (article " LISA is from gravitation analytical model (Self-gravitymodeling for LISA) " see " classical and quantum gravity " (Classical and QuantumGravity) the 22nd volume the 10th phase S395-S402 page in 2005) is obtained to all unit summations.Because universal gravitation interference has exceeded allowed band, LISA model team devises an annular compensation block for its priori task LISA pathfinder, achieves the effective suppression (article " the universal gravitation interference compensation (Gravitational compensation for the LISA pathfinder) of LISA pathfinder " see " classical and quantum gravity " (Classical and Quantum Gravity) the 22nd volume the 10th phase S501-S507 page in 2005) to universal gravitation and gradient thereof.

But in LISA task, the side-play amount of verification quality its nominal position relative is in a μm magnitude, therefore universal gravitation interference compensation can be considered as offsetting outer spacecraft at certain any universal gravitation, and widely in pure gravitation aerial mission, verification quality has the position deviation of cm magnitude relative to its nominal position, therefore, LISA verification quality universal gravitation interference compensation can not meet the effect suppressed the universal gravitation of specific region.

Summary of the invention

The object of the invention is to the mass compensation method for designing proposing a kind of novel pure Universal gravitation AF panel, solve the problem.

To achieve these goals, the technical scheme of the mass compensation method for designing employing of the present invention's pure Universal gravitation AF panel is as follows:

Step S101, obtains spacecraft mass distributed data, determines the action scope that universal gravitation disturbs, and calculates the universal gravitation interference in described action scope, and the universal gravitation AF panel requirement in clearly described action scope;

Step S102, chooses reference point, arranges the universal gravitation AF panel target of described reference point;

Step S103, determines mass compensation design result;

Step S104, adds to described mass compensation design result in described spacecraft mass distributed data, recalculates the universal gravitation interference in described action scope;

Step S105, checks described Compensation Design result whether to meet the universal gravitation AF panel requirement of described action scope;

Step S106, according to the check conclusion of step S105, if meet the universal gravitation AF panel requirement of described action scope, then obtains an available Compensation Design result, according to size and the installation site of described available Compensation Design result determination compensation block; If do not meet the universal gravitation AF panel requirement of described action scope, then reset the universal gravitation AF panel target of described reference point, repeat step S103-step S105.

Described mass compensation design result is determined according to the universal gravitation AF panel target of described reference point and to compensation block processing and the engineering of installation accuracy and process constraint.

Described reference point is positioned at described action scope.

The universal gravitation AF panel target of described reference point is determined by following formula:

|F _j,t|<|F _j,r|,j＝x,y,z

|F _j,t|+||T _t|| ₂·d<|F _j,r|,j＝x,y,z

F _tfor the universal gravitation of described reference point, T _tfor the suppression target of described reference point gradient, d is the Envelope radius of described action scope.

The universal gravitation interference of described reference point and described reference point gradient suppress to be calculated by following formula:

Wherein, r _othe cavity radius comprising verification quality, F _{x, 0}, F _{y, 0}, F _{z, 0}the universal gravitation of spacecraft at verification quality nominal position place before compensating, V _{xx, 0}, v _{xy, 0}v _{xz, 0}v _{yz, 0}the universal gravitation gradient component of spacecraft at verification quality nominal position place before compensating, F _x,c, F _y,c, F _z,c, V _{xx, c}, V _{yy, c}, V _{zz, c}, v _{xz, c}v _{yz, c}the universal gravitation after compensating and its gradient component respectively.

The quality of described compensation block and installation site are according to being retrained the compensation block quality set up by the quality of described reference point universal gravitation AF panel target and compensation block and installation site and installation site Constraint Anchored Optimization is determined.

The quality of described compensation block is

$m_i=\frac{4}{3}\mathrm{\&pi;}{r}_i^3{\mathrm{\&rho;}}_c,i=\mathrm{1,2},...n$

Wherein, if the number of compensation block is n, r _ifor described n is to the radius of compensation block, i=1,2 ... n, ρ _cfor the density of compensation block.

Size and the installation site Constraint Anchored Optimization of described compensation block are determined by following formula:

Target: $\min \underset{i}{\mathrm{\&Sigma;}}{m}_i,i=\mathrm{1,2},...,n$

r _i≥0,0≤θ _i≤π,

Constraint: | F _j,c|≤| F _j,t|, j=x, y, z

N is increased gradually from 1, until n=n ₀time occur can using compensation design result; If spendable design compensation result can not be obtained, then adjust F _twith || T _t|| ₂, again the size of described compensation block and installation site Constraint Anchored Optimization are solved.

Beneficial effect of the present invention can be summarized as follows: in pure Attractive Orbit space system, can adopt less compensation quality, realizes the suppression to the universal gravitation interference in verification quality coverage pattern.

Accompanying drawing explanation

Fig. 1 is method for designing process flow diagram of the present invention;

Fig. 2 be the present invention with verification quality nominal position for initial point, the right angle orbital coordinate system o (x, y, z) of foundation and spherical coordinate system

Embodiment

In order to make technical matters solved by the invention, technical scheme and beneficial effect clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

Method for designing process flow diagram of the present invention as shown in Figure 1, the mass compensation method for designing of pure Universal gravitation AF panel of the present invention, be an Iterative Design method, step is as follows:

Step S101, obtains spacecraft mass distributed data, determines the action scope that universal gravitation disturbs, and calculates the universal gravitation interference in action scope, and the universal gravitation AF panel requirement in clear and definite action scope;

Step S102, chooses reference point, according to the position of reference point in action scope, arranges the universal gravitation AF panel target of reference point;

Step S103, the reference point universal gravitation AF panel target set by step S102, and the size of compensation block and installation site constraint, set up compensation block quality and installation site Constraint Anchored Optimization, and solve mass compensation design result;

Step S104, according to the solving result of step S103, according to compensation block processing and the engineering of installation accuracy and process constraint, determines a Compensation Design result;

Step S105, by the Compensation Design result of step S104 gained, adds in spacecraft mass distributed data, and recalculate the universal gravitation interference in action scope, whether inspection meets the requirement of universal gravitation AF panel;

Step S106, according to the check conclusion of step S105, if meet the demands, then obtains an available Compensation Design result; If do not meet the universal gravitation AF panel requirement of described action scope, then reset the universal gravitation AF panel target of described reference point, repeat step S103-step S105.

The advantage of the mass compensation method for designing of pure Universal gravitation AF panel of the present invention is: in pure Attractive Orbit space system, can adopt less compensation quality, realizes the suppression to the universal gravitation interference in verification quality coverage pattern.

The present invention as shown in Figure 2 with verification quality nominal position for initial point, the right angle orbital coordinate system o (x, y, z) of foundation and spherical coordinate system can calculate as follows:

According to Newton's law of gravitation, the universal gravitation between two particles is

$F={\mathrm{GM}}_1{M}_2\frac{\stackrel{\&RightArrow;}{r}}{{\left|\stackrel{\&RightArrow;}{r}\right|}^3}---\left(1\right)$

Wherein, G is universal gravitational constant, M ₁, M ₂be the quality of two particles, it is the radius vector between two particles.

In coordinate system o (x, y, z), if the coordinate of two particles is respectively (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), then M ₁to M ₂universal gravitation be

$F=\left[\begin{array}{c}{F}_x\\ F_y\\ F_z\end{array}\right]=\frac{{\mathrm{GM}}_1{M}_2}{{[{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2]}^{3/2}}\left[\begin{array}{c}{x}_1-x_2\\ y_1-y_2\\ z_1-z_2\end{array}\right]---\left(2\right)$

Wherein, F _x, F _y, F _zbe respectively the universal gravitation component along three change in coordinate axis direction.It should be noted that, when calculating the universal gravitation of spacecraft to verification quality, generally representing universal gravitation with the verification quality acceleration that it causes.

Universal gravitation is potent, and namely it exists corresponding bit function V (x, y, z), and the partial derivative of bit function to each coordinate axis equals the component of gravitation along corresponding coordinate axle.Gravitation bit function meets Laplace's equation, so the mark of universal gravitation gradient tensor is zero, universal gravitation gradient tensor meets symmetry simultaneously, therefore has 5 isolated components.Universal gravitation gradient tensor is

$\begin{array}{c}T=\left(\begin{array}{ccc}{V}_{\mathrm{xx}}& V_{\mathrm{xy}}& V_{\mathrm{xz}}\\ V_{\mathrm{yx}}& V_{\mathrm{yy}}& V_{\mathrm{yz}}\\ V_{\mathrm{zx}}& V_{\mathrm{zy}}& V_{\mathrm{zz}}\end{array}\right)=\left(\begin{array}{ccc}\frac{\&PartialD;F_x}{\&PartialD;x}& \frac{\&PartialD;F_x}{\&PartialD;y}& \frac{\&PartialD;F_x}{\&PartialD;z}\\ V_{\mathrm{yx}}& \frac{\&PartialD;F_y}{\&PartialD;y}& \frac{\&PartialD;F_y}{\&PartialD;z}\\ V_{\mathrm{zx}}& V_{\mathrm{zy}}& \frac{\&PartialD;F_z}{\&PartialD;z}\end{array}\right)\\ =\frac{{\mathrm{GM}}_1{M}_2}{{\left|\stackrel{\&RightArrow;}{r}\right|}^5}\left[\begin{array}{ccc}2{(x_1-x_2)}^2-{(y_1-y_2)}^2-{(z_1-z_2)}^2& -3(x_1-x_2)(y_1-y_2)& -3(x_1-x_2)(z_1-z_2)\\ F_{\mathrm{yx}}& -{(x_1-x_2)}^2+2{(y_1-y_2)}^2-{(z_1-z_2)}^2& -3(y_1-y_2)(z_1-z_2)\\ F_{\mathrm{zx}}& F_{\mathrm{zy}}& -{(x_1-x_2)}^2-{(y_1-y_2)}^2+2{(z_1-z_2)}^2\end{array}\right]\end{array}---\left(3\right)$

Choose verification quality nominal position as a reference point.If in clear and definite action scope, universal gravitation AF panel requires as F _r, the suppression target of the universal gravitation and gradient thereof that arrange nominal position place is respectively F _tand T _t, the Envelope radius of action scope is d, then following condition is necessary

|F _j,t|<|F _j,r|,j＝x,y,z (4)

|F _j,t|+||T _t|| ₂·d<|F _j,r|,j＝x,y,z (5)

Wherein || * || ₂two norm operators of tensor matrix.Reduce gradually | F _t| with || T _t|| ₂, available Compensation Design result can be obtained.

If adopt n compensation block to suppress the universal gravitation interference in action scope.The unified spheroid for uniform density of compensation block, so that directly can be considered as particle in universal gravitation calculates.The density of compensation block is ρ _c, unification is arranged on the outer wall of the cavity comprising verification quality.

If the radius of n compensation block is r _i, i=1,2 ..., n, the installation position under coordinate system shown in Fig. 2 is the quality of compensation block is

$m_i=\frac{4}{3}\mathrm{\&pi;}{r}_i^3{\mathrm{\&rho;}}_c,i=\mathrm{1,2},...n---\left(6\right)$

Universal gravitation for verification quality nominal position place disturbs and gradient suppression is

Wherein, r _othe cavity radius comprising verification quality, F _{x, 0}, F _{y, 0}, F _{z, 0}the universal gravitation of spacecraft at verification quality nominal position place before compensating, V _{xx, 0}, v _{xy, 0}v _{xz, 0}v _{yz, 0}the universal gravitation gradient component of spacecraft at verification quality nominal position place before compensating, F _x,c, F _y,c, F _z,c, V _{xx, c}, V _{yy, c}, V _{zz, c}, v _{xz, c}v _{yz, c}the universal gravitation after compensating and its gradient component respectively.

Under a certain number n, to solving of compensation block quality and installation site, be one with for the constrained optimization problem of independent variable

Target: $\min \underset{i}{\mathrm{\&Sigma;}}{m}_i,i=\mathrm{1,2},...,n---\left(9\right)$

r _i≥0,0≤θ _i≤π,

Constraint: | F _j,c|≤| F _j,t|, j=x, y, z (10)

Adopt genetic algorithm to solve the problems referred to above, n is increased gradually from 1, until n=n ₀time there is feasible solution.

Consider processing and the installation accuracy constraint of compensation block, the solution of compensation block quality and position is remained into appropriate accuracy, just obtains a Compensation Design result.Design result is added in spacecraft mass distributed data, recalculate the universal gravitation interference in action scope, inspection inhibition.If inhibition meets the universal gravitation AF panel requirement in action scope, then this design result is available; Otherwise, adjustment F _twith || T _t|| ₂, again the Constraint Anchored Optimization that formula (9) and (10) form is solved, is compensated design result and again checks the universal gravitation interference suppressioning effect in action scope.Repeat this process, available design result can be obtained.

The present invention is described in detail in preferred embodiment above by concrete; but those skilled in the art should be understood that; the present invention is not limited to the above embodiment; within the spirit and principles in the present invention all; any amendment of doing, equivalent replacement etc., all should be included within protection scope of the present invention.

Claims (8)

1. a mass compensation method for designing for pure Universal gravitation AF panel, is characterized in that: comprising:

Step S101, obtains spacecraft mass distributed data, determines the action scope that universal gravitation disturbs, and calculates the universal gravitation interference in described action scope, and the universal gravitation AF panel requirement in clearly described action scope;

Step S102, chooses reference point, arranges the universal gravitation AF panel target of described reference point;

Step S103, determines mass compensation design result;

Step S104, adds to described mass compensation design result in described spacecraft mass distributed data, recalculates the universal gravitation interference in described action scope;

Step S105, checks described Compensation Design result whether to meet the universal gravitation AF panel requirement of described action scope;

Step S106, according to the check conclusion of step S105, if meet the universal gravitation AF panel requirement of described action scope, then obtains an available Compensation Design result, according to size and the installation site of described available Compensation Design result determination compensation block; If do not meet the universal gravitation AF panel requirement of described action scope, then reset the universal gravitation AF panel target of described reference point, repeat step S103-step S105.

2. the mass compensation method for designing of pure Universal gravitation AF panel according to claim 1, is characterized in that: described mass compensation design result is determined according to the universal gravitation AF panel target of described reference point and to compensation block processing and the engineering of installation accuracy and process constraint.

3. the mass compensation method for designing of pure Universal gravitation AF panel according to claim 1, is characterized in that: described reference point is positioned at described action scope.

4. the mass compensation method for designing of pure Universal gravitation AF panel according to claim 1 and 2, is characterized in that: the universal gravitation AF panel target of described reference point is determined by following formula:

|F _j,t|<|F _j,r|,j＝x,y,z

|F _j,t|+‖T _t‖ ₂·d<|F _j,r|,j＝x,y,z

F _rfor the universal gravitation AF panel requirement in action scope, F _tfor the gravitational suppression target of described reference point, T _tfor the suppression target of described reference point gradient, d is the Envelope radius of described action scope; Described x, y, z represent the horizontal ordinate of reference point in right angle orbital coordinate system o (x, y, z) respectively, ordinate, ordinate.

5. the mass compensation method for designing of pure Universal gravitation AF panel according to claim 1, is characterized in that: the universal gravitation interference of described reference point and described reference point gradient suppress to be calculated by following formula:

Wherein, m _irepresent the quality of i-th compensation block, r _iwhat represent is the radius of i-th compensation block, θ _iwith the respectively elevation angle in cavity spherical coordinate system of i-th compensation block and position angle, r _othe cavity radius comprising verification quality, F _{x, 0}, F _{y, 0}, F _{z, 0}the universal gravitation of spacecraft at verification quality nominal position place before compensating, V _{xx, 0}, V _{yy, 0}, V _{zz, 0}, V _{xy, 0}, V _{xz, 0}, V _{yz, 0}the universal gravitation gradient component of spacecraft at verification quality nominal position place before compensating, F _x,c, F _y,c, F _z,c, V _{xx, c}, V _{yy, c}, V _{zz, c}, V _{xy, c}, V _{xz, c}, V _{yz, c}the universal gravitation after compensating and its gradient component respectively; Described x, y, z represent the horizontal ordinate of reference point in right angle orbital coordinate system o (x, y, z) respectively, ordinate, ordinate.

6. the mass compensation method for designing of pure Universal gravitation AF panel according to claim 1, is characterized in that: the quality of described compensation block and installation site are according to being retrained the compensation block quality set up by the quality of described reference point universal gravitation AF panel target and compensation block and installation site and installation site Constraint Anchored Optimization is determined.

7. the mass compensation method for designing of pure Universal gravitation AF panel according to claim 6, is characterized in that: the quality of described compensation block is

$m_i=\frac{4}{3}\mathrm{\&pi;}{r}_i^3{\mathrm{\&rho;}}_c,i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;n$

Wherein, if the number of compensation block is n, r _ibe the radius of i-th compensation block, i=1,2 ... n, ρ _cfor the density of compensation block.

8. the mass compensation method for designing of the pure Universal gravitation AF panel according to claim 5 or 7, is characterized in that: size and the installation site Constraint Anchored Optimization of described compensation block are determined by following formula:

Target: $\min \underset{i}{\mathrm{\&Sigma;}}{m}_i,i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n$

r _i≥0,0≤θ _i≤π,

|F _j,c|≤|F _j,t|,j＝x,y,z

Constraint: max (| V _{xx, c}|, | V _{yy, c}|, | V _{zz, c}|, | V _{xy, c}|| V _{xz, c}|| V _{yz, c}|)≤‖ T _t‖ ₂

N is increased gradually from 1, until n=n ₀time occur can using compensation design result; If spendable design compensation result can not be obtained, then adjust F _twith ‖ T _t‖ ₂, again the size of described compensation block and installation site Constraint Anchored Optimization are solved;

Wherein, m _irepresent the quality of i-th compensation block, r _irepresent the radius of i-th compensation block, θ _iwith the respectively elevation angle in cavity spherical coordinate system of i-th compensation block and position angle, F _x,c, F _y,c, F _z,c, V _{xx, c}, V _{yy, c}, V _{zz, c}, V _{xy, c}, V _{xz, c}, V _{yz, c}the universal gravitation after compensating and its gradient component respectively, | F _j,t| expression be gravitational suppression target, F _tfor the gravitational suppression target of described reference point, T _tfor the suppression target of described reference point gradient; Described x, y, z represent the horizontal ordinate of reference point in right angle orbital coordinate system o (x, y, z) respectively, ordinate, ordinate.