CN104932261A - Attitude-orbit integrated thrust distribution method for satellite - Google Patents

Abstract

The invention discloses an attitude-orbit integrated thrust distribution method for a satellite, and belongs to the technical field of satellite control. After the installation layout of a thruster is determined, a mathematical model of thrust distribution is built, and the initial solution of thrust distribution, namely the initial thrust distribution scheme, is obtained based on the conventional pseudo-inverse method; then, grouping is performed based on the initial solution, and the thrust distribution scheme based on a chain type distribution revised pseudo-inverse method is obtained; and finally, a thrust distribution optimization index is designed, overall algorithm optimization is realized with the combination of various indexes of the thruster, and thrust distribution is optimized. According to the method, the integrated control task of the satellite can be effectively accomplished within the load range configured by the thruster, fuels are effectively saved, the thrust distribution error brought by thrust configuration is reduced, and the control precision of the thrust is improved.

Description

The thrust distribution method of appearance rail one satellite

Technical field

The present invention relates to a kind of thrust distribution method of satellite, be specifically the thrust distribution method of a kind of appearance rail one satellite, belong to satellite control technology field.

Background technology

Appearance rail overall-in-one control schema is satellite in orbit in process, considers track and the attitude maneuver task of satellite simultaneously, realizes by shared set of execution mechanism configuration the gate control technology that track and attitude control simultaneously.Carry out the maneuverability that appearance rail overall-in-one control schema farthest can utilize topworks, save fractional hardware resource, improve the functional density of system, also can improve the utilization ratio of fuel simultaneously, reach fuel saving, the object in extend satellite serviceable life in-orbit.

Thruster, as a kind of conventional satellite executing mechanism, when the power that it acts on celestial body is not by celestial body barycenter, just can produce opplied moment, for appearance rail overall-in-one control schema provides possibility to celestial body simultaneously.For realizing taking thruster as the appearance rail overall-in-one control schema of topworks, after carrying out Configuration Design to the installation site of thruster on celestial body and installation direction, to realizing the maximization of overall-in-one control schema function while meeting various constraint condition.The configuration of thruster determines the size and Orientation of power that each thruster can produce in satellite body system and moment, i.e. a thrust vectoring.Because satellite generally produces required control desired amount by the combination of multiple thruster effect, therefore thruster be configured in the control ability determining thruster system to a great extent.

Propose various control distribution method in conjunction with practical problems at present, being mainly divided into unoptimizable apportion design and optimizing apportion design two class, being wherein widely used because having higher operation efficiency based on the pseudoinverse technique in the control allocation algorithm of constrained optimization.But traditional pseudoinverse technique cannot ensure to carry out good configuration when thruster is limited to thrust, affects the control of satellite.Therefore, people is had to propose on this basis based on the correction pseudoinverse technique of chain type distribution, the correction pseudoinverse technique etc. based on kernel.These pseudoinverse techniques etc. revised improve the limitation problem of traditional pseudoinverse technique, but all carry out overall optimization less than for the layout of thruster, every characteristic index in existing distribution method, cause its thrust to distribute error comparatively greatly, affect the control accuracy of thruster.

Summary of the invention

The technical matters of all solutions of the present invention is to overcome prior art defect, provides the thrust distribution method of the appearance rail one satellite that a kind of thrust distribution error is little, control accuracy is high.

In order to solve the problems of the technologies described above, the thrust distribution method of appearance rail one satellite provided by the invention, comprises the following steps:

1), n thruster is installed on satellite, makes C=[T; U], D=[A; B], set up thrust apportion model:

C＝DF

In formula, C is the steering order that control law provides, and T is the opplied moment T=AF that thrust produces at centroid of satellite place, and acting force is U=BF; A is the moment matrix of unit vector to satellite of all thrusters, A=[d ₁e ₁d ₂e ₂... d _ne _n], [d ₁d ₂... d _n] be the position vector matrix of n thruster centroid of satellite, [e ₁e ₂... e _n] be the specific thrust matrix that n thruster produces, D is thrust configuring matrix;

2), just step 1 is separated) described thrust apportion model, obtain F=D ^t(DD ^t) ^-1c, D ^t(DD ^t) ^-1for the pseudoinverse of D;

3), to step 2) the first solution that obtains divides into groups according to thrust is positive and negative:

$F_{\mathrm{pc}}=\left[\begin{array}{c}{F}_{\mathrm{pc}\_\mathrm{neg}}\\ F_{\mathrm{pc}\_\mathrm{pos}}\end{array}\right],$ F _{pc_neg}＜0,F _{pc_pos}＞0

Wherein, F _pcfor just separating the new matrix after positive and negative grouping, F _{pc_neg}for the submatrix of all negative solutions, F _{pc_pos}for the submatrix of all normal solutions;

By the grouping of efficiency matrix correspondence:

$D=\left[\begin{array}{c}{D}_{\mathrm{neg}}\\ D_{\mathrm{pos}}\end{array}\right]$

D _negfor F _{pc_neg}corresponding efficiency matrix submatrix, D _posfor corresponding F _{pc_pos}efficiency matrix submatrix;

By whole for the thrust of negative value group zero setting, obtain:

F _{pc_neg}＝u ₁＝[0 … 0]

To the desired amount sub-distribution again after distribution, obtain revised apportioning cost u ₂:

M _d＝D _posu ₂

M _dthe desired amount that the initial period desired amount C provided for control law obtains after distributing;

4), by step 3) middle D _posbe decomposed into the constant k of a row rank submatrix, simultaneously to u ₂decompose, again ask pseudoinverse, form following system of equations:

$M_d=D_{\mathrm{pos}}^1{u}_2^1$

.

.

.

$M_d=D_{\mathrm{pos}}^k{u}_2^k$

For each prescription journey, solve corresponding f _jvariable to be solved, F _j=[u ₁, u ₂], j=1 .., n, c _j,mfor known coefficient, represent the propelling dosage of jth platform thruster consumption, CDOP is the fuel consumption factor;

5), selecting step 4) in minimum one group of J perform.

Beneficial effect of the present invention is: the correction pseudoinverse technique of distributing based on pseudoinverse technique, chain type, by thruster performance index, thrust is optimized further, obtain the thrust secondary distribution method based on thruster configuration and control accuracy, this distribution method can effectively complete satellite overall-in-one control schema task in the loading range of thruster configuration, simultaneously fuel saving effectively, reduce the thrust distribution error that thrust configuration brings, improve the control accuracy of thruster.

Accompanying drawing explanation

Fig. 1 is the technical scheme figure of thrust distribution method of the present invention;

Fig. 2 is appearance rail one Satellite Engine configuration configuration schematic diagram;

Fig. 3 provides thrust comparison diagram for optimizing needed for the thruster of front and back;

Fig. 4 is for optimizing front and back CDOP comparison diagram.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

In the selection course of thruster, generally will consider that thrust is economized most, the departure that thrust configuration causes is minimum.Scale-up factor between the departure affected for reaction thruster relative geometrical relation and desired control amount, factor CDOP is as follows for definition fuel consumption:

CDOP＝tr[DD ^T]

Fuel consumption factor CDOP is less, and the departure that thrust configuration causes is less.When thruster layout one timing, along with the increase of the engine number of participating in the distribution, configuration fuel consumption factor CDOP, also in corresponding increase, distributes error in increase.Therefore, consider from the angle reducing to distribute error, the engine number of participating in the distribution must lack as far as possible.

Assigning process of the present invention is exactly according to thruster configuration, solves command assignment, and the index of the following design of order is minimum as optimum solution:

$\min J=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{c}_j{F}_j+c_m\mathrm{CDOP}$

s.t. 0≤F _j≤F _max

Wherein, F _jit is variable to be solved; c _j,mknown coefficient, represents the propelling dosage that jth platform thruster consumes; Constraint representation thruster in model can only produce unilateral thrust, and has the upper limit.

As shown in Figure 1, after first the present invention installs N number of thruster on satellite, set up the mathematical model that thrust is distributed, utilize allocation algorithm to obtain appearance rail one satellite distribution method and obtain optimum thrust allocative decision.Initial solution is obtained, i.e. the scheme of initial thrust distribution based on traditional pseudoinverse technique; Divide into groups in the basis of just separating, obtain the thrust allocative decision of the correction pseudoinverse technique of distributing based on chain type, solve the problem that thrust solution is limited, guarantee to separate F > 0; Finally, design thrust allocation optimized index, the index such as configuration, control accuracy, fuel consumption of combined propulsive force device carries out overall algorithm optimization, and be optimized back pressure allocative decision, gained solution F > 0 and unique.Its concrete steps are:

Step one, sets up satellite thrust and distributes mathematical model.

Thruster is after on satellite, mounting arrangement is determined, suppose to be provided with n thruster, the position vector matrix of their relative satellite barycenter is [d ₁d ₂... d _n], the specific thrust matrix that thruster produces is [e ₁e ₂... e _n], the thrust array of all thruster compositions is F=[F ₁f ₂... F _n] ^t.

The opplied moment that thrust produces at centroid of satellite place can be expressed as T=AF, and acting force can be expressed as U=BF.Wherein A is the moment matrix A=[d of unit vector to satellite of all thrusters ₁e ₁d ₂e ₂... d _ne _n], B is the moment battle array B=[e of unit vector to satellite of all thrusters ₁e ₂... e _n].Make C=[T; U], D=[A; B], then thrust distribution mathematical model can be described as:

C＝DF

D is thrust configuring matrix, is determined by thruster mounting arrangement, is also thrust efficiency matrix; C is for initially to expect controlled quentity controlled variable, and the moment phase comprised on m direction controls desired amount and power desired control amount.

After desired control amount C determines, the command assignment problem of thruster is generally described as and solves suitable F problem.For solution F

0≤F≤F _max

F _maxfor the maximum thrust that thruster can produce.

After providing desired control amount C by control law, adopt thrust allocation algorithm by control allocation on each thruster, thrust allocation algorithm determines rationality and the superiority of distribution.Therefore thrust allocation algorithm is the key point of research.

Step 2, applies traditional pseudoinverse technique and just separates step one satellite thrust distribution mathematical model, obtain the tentative programme that thrust is distributed.

Functional is considered in pseudoinverse technique:

$J\left(F\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{F_i}^2=F^{T}F$

The quadratic sum that the F tried to achieve should meet its all elements is minimum, and the thrust simultaneously produced must meet the control overflow of track and attitude, namely meets constraint condition:

C＝DF

Utilize method of Lagrange multipliers to solve, make multiplier be λ=[λ ₁λ ₂λ _n] ^t, defining scalar function H (F, λ), draw new functional:

$H(F,\mathrm{\λ})=\frac{1}{2}{F}^{T}F+{\mathrm{\λ}}^T(C-\mathrm{DF})$

According to the necessary condition of extreme value with ?

$\frac{\∂H(F,\mathrm{\λ})}{\∂F}=F^T-{\mathrm{\λ}}^{T}D=0$

$\frac{\∂H(F,\mathrm{\λ})}{\∂\mathrm{\λ}}=C-\mathrm{DF}=0$

That is:

$F^T={\mathrm{\λ}}^{T}D\⇔F=D^T\mathrm{\λ}$

C＝DF

Obtain:

C＝D(D ^Tλ)

Obtain through arrangement:

λ＝(DD ^T) ^-1C

D is multiplied by two ends simultaneously ^t:

D ^Tλ＝D ^T(DD ^T) ^-1C

And D ^tλ=F, so

F＝D ^T(DD ^T) ^-1C

D ^t(DD ^t) ^-1become the pseudoinverse of D.

Although the thrust utilizing traditional pseudoinverse technique to ask for can meet satellite control overflow, but still there is certain deficiency:

(1), F > 0 can not be ensured.Although solved F, the thrust device in reality might not provide such F.When thruster is mounted in pairs, when F < 0, positive thrust can be produced by thruster paired with it; When thruster non-paired is installed, then it is invalid to solve.

(2), F is unique solution.Although the F now tried to achieve can meet track and gesture stability requirement, it does not have alternative leeway, only considers and controls fuel optimum, and do not consider other problems, as thruster configuration and thruster use number.

Step 3, adopt chain type distribute correction pseudoinverse technique, step 2 traditional be pseudoinverse technique gained solution basis on, the first solution obtained is divided into groups according to thrust is positive and negative, obtains:

$F_{\mathrm{pc}}=\left[\begin{array}{c}{F}_{\mathrm{pc}\_\mathrm{neg}}\\ F_{\mathrm{pc}\_\mathrm{pos}}\end{array}\right],$ F _{pc_neg}＜0,F _{pc_pos}＞0

Wherein, F _pcfor the new matrix after the positive and negative grouping of first solution of pseudoinverse technique gained, comprise the submatrix F of all negative solutions _{pc_neg}with the submatrix F of all normal solutions _{pc_pos}.

Simultaneously by the grouping of efficiency matrix correspondence:

$D=\left[\begin{array}{c}{D}_{\mathrm{neg}}\\ D_{\mathrm{pos}}\end{array}\right]$

D _neg, D _poscorresponding F respectively _{pc_neg}, F _{pc_pos}efficiency matrix submatrix.

F _{pc_neg}the negative sense thrust that thruster cannot perform, by whole for the thrust of negative value group zero setting namely:

F _{pc_neg}＝u ₁＝[0 … 0]

Initial desired control amount C obtains desired amount M after over-allocation _d, again distribute, be in fact still initial desired amount and be all added on thruster, obtain revised apportioning cost u ₂:

M _d＝D _posu ₂

Finally obtain revised entirely positive thrust magnitude u ₂, be required revised apportioning cost.

The correction pseudoinverse technique correction distributed through chain type can ensure F > 0, wherein F=u ₂but still can not guarantee that F is unique solution, it still only considers and controls fuel optimum, and does not consider as thruster configuration and thruster use the problems such as number.

Step 4, based on the thrust secondary distribution optimized algorithm of thruster configuration and control accuracy, design thrust allocation optimized index, the index such as configuration, control accuracy, fuel consumption of combined propulsive force device carries out overall algorithm optimization, thrust is distributed and is optimized.

Consider the thrust allocation optimized index designed herein:

$\min J=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{c}_j{F}_j+c_m\mathrm{CDOP}$

For the M completing just sub-distribution _d=D _posu ₂, according to choosing, by D of row _posbe decomposed into the constant k of a row rank submatrix.Corresponding u ₂also complete decomposition, again ask pseudoinverse.Form:

$M_d=D_{\mathrm{pos}}^1{u}_2^1$

.

.

.

$M_d=D_{\mathrm{pos}}^k{u}_2^k$

Each solution of equation (i=1 .., k) represents a kind of thrust distribution method.For each prescription journey, solve corresponding wherein F _j=[u ₁, u ₂], j=1 .., n, c _j,mweighting coefficient is known coefficient, can stress to select according to self to thruster performance index.Choose one group of solution F that J is minimum _jas thrust allocative decision, this scheme meets the comprehensive constraint of thrust configuration, control accuracy, fuel consumption.

Simulating, verifying: as shown in Figure 2, satellite configures altogether 16 thrusters, n=16.Consider three axle track and gesture stability, on 6 directions, the moment phase controls desired amount and power desired control amount m=6 simultaneously.Suppose single thruster maximum thrust F _max=0.04N.Thruster is respectively r=0.02m, h=0.025m apart from the arm of force of barycenter; If equal β=44 ° of angle of each thruster of upper and lower surface and oxy plane, the diagonal line angle of thrust and square surface is θ=30 °, and thrust and coordinate axis angle are γ=30 °.The configuring matrix D of thruster can be drawn according to this configuration:

Obtain position vector matrix d:

$d=\left[\begin{array}{cccccccccccccccc}0.2& -0.2& -0.2& 0.2& 0.2& -0.2& -0.2& 0.2& 0.1& 0& -0.1& 0& 0.1& 0& -0.1& 0\\ 0.2& 0.2& -0.2& -0.2& 0.2& 0.2& -0.2& -0.2& 0& 0.1& 0& -0.1& 0& 0.1& 0& -0.1\\ 0.25& 0.25& 0.25& 0.25& -0.25& -0.25& -0.25& -0.25& 0.25& 0.25& 0.25& 0.25& -0.25& -0.25& 0.25& 0.25\end{array}\right]$

With unit force matrix B:

$\begin{array}{c}B=e\\ =\left[\begin{array}{cccccccccccccccc}0.6948& -0.6948& -0.6948& 0.6948& 0.1862& -0.1862& -0.1862& 0.1862& -0.6230& -0.3957& 0.623& 0.3957& -0.6230& 0.3957& 0.6230& -0.3957\\ 0.1862& 0.1862& -0.1862& -0.1862& 0.6948& 0.6948& -0.6948& -0.6948& 0.3957& -0.6230& -0.3957& 0.6230& -0.3957& -0.6230& 0.3957& 0.6230\\ -0.6947& -0.6947& -0.6947& -0.6947& 0.6947& 0.6947& 0.6947& 0.6947& -0.6947& -0.6947& -0.6947& 0.6947& 0.6947& 0.6947& 0.6947& 0.6947\end{array}\right]\end{array}$

Obtain specific torque matrix A:

$\begin{array}{c}A=d\&times;e\\ =\left[1,\begin{array}{cccccccccccccccc}-0.1855& -0.1855& 0.1855& 0.1855& 0.3126& 0.3126& -0.3126& -0.3126& -0.0899& 0.0863& -0.0899& -0.0863& -0.0899& -0.0863& -0.0899& -0.2252\\ 0.3126& -0.3126& -0.3126& 0.3126& -0.1855& 0.1855& 0.1855& -0.1855& -0.0863& 0.1557& 0.0863& 0.1557& 0.0863& -0.0899& 0.2252& -0.0899\\ -0.1017& 0.1017& -0.1017& 0.1017& 0.1017& -0.1017& 0.1017& -0.1017& 0.0360& 0.0360& -0.0360& 0.0360& -0.0360& -0.0360& -0.0360& -0.0360\end{array}\right]\end{array}$

Finally obtain configuring matrix D:

$\begin{array}{c}D=\left[\begin{array}{c}A\\ B\end{array}\right]\\ =\left[\begin{array}{cccccccccccccccc}-0.1855& -0.1855& 0.1855& 0.1855& 0.3126& 0.3126& -0.3126& -0.3126& -0.0899& 0.0863& 0.0899& -0.0863& 0.0899& -0.0863& -0.0899& -0.2252\\ 0.3126& -0.3126& -0.3126& 0.3126& -0.1855& 0.1855& 0.1855& -0.1855& -0.0863& -0.1557& 0.0863& 0.1557& 0.0863& -0.0899& 0.2252& -0.0899\\ -0.1017& 0.1017& -0.1017& 0.1017& 0.1017& -0.1017& 0.1017& -0.1017& 0.0360& 0.0360& -0.0360& 0.0360& -0.0360& -0.0360& -0.0360& -0.0360\\ 0.6948& -0.6948& -0.6948& 0.6948& 0.1862& -0.1862& -0.1862& 0.1862& -0.6230& -0.3957& 0.6230& 0.3957& -0.6230& 0.3957& 0.6230& -0.3957\\ 0.1862& 0.1862& -0.1862& -0.1862& 0.6948& 0.6948& -0.6948& -0.6948& 0.3957& -0.6230& -0.3957& 0.6230& -0.3957& -0.6230& 0.3957& 0.6230\\ -0.6947& -0.6947& -0.6947& -0.6947& 0.6947& 0.6947& 0.6947& 0.6947& -0.6947& -0.6947& -0.6947& -0.6947& 0.6947& 0.6947& 0.6947& 0.6947\end{array}\right]\end{array}$

Choose desired amount and steering order

C=[0.001NM 0.002NM 0.002NM 0.01N 0.01N 0.02N] ^t, by selecting the minimum one group of solution (J=44.4964) of J to be optimized back pressure allocative decision, this scheme is by thruster 4,5,6,7, the combination of 12,14,15 performs Satellite Attitude rail integrative control task, the corresponding thrust size of each thruster is respectively 0.0010,0.0141N, 0.0006N, 0.0077N, 0.0041N, 0.0014N, 0.0100N, all in thruster loading range, controls thrust summation ∑ F _j=0.0389N, CDOP desired value is 2.7713; And by thruster 4 before optimizing, 5,6,7,12,14,15,16 complete thrust distributes, now use thruster number than many after optimization, thrust summation ∑ F _j=0.0426N is rear than optimization large, and CDOP desired value is that 2.9563 ratios are optimized greatly rear.

Fig. 3 with Fig. 4 is under 6 groups of different desired control amounts, with the control thrust summation ∑ F optimizing back pressure allocative decision before optimizing _jdraw with CDOP index and contrast.

As shown in Figure 3, the thrust summation ∑ F of thruster generation _jbe directly proportional to fuel consumption.∑ F after optimization _jwith optimize before carry out contrast and can obtain: optimizes the thrust summation that required thrust device afterwards produces little.Adopt the thrust more economized just can obtain and obtain identical desired amount, the fuel consumption brought is less.

As shown in Figure 4, after as can be seen from the figure optimizing, CDOP value is less, and namely the error that causes of configuration needed for thruster is less.

The above is only the preferred embodiment of the present invention, it should be pointed out that for those skilled in the art, can also make some improvement under the premise without departing from the principles of the invention, and these improvement also should be considered as protection scope of the present invention.

Claims (1)

1. a thrust distribution method for appearance rail one satellite, is characterized in that comprising the following steps:

1), n thruster is installed on satellite, makes C=[T; U], D=[A; B], set up thrust apportion model:

C＝DF

In formula, C is the steering order that control law provides, and T is the opplied moment T=AF that thrust produces at centroid of satellite place, and acting force is U=BF; A is the moment matrix of unit vector to satellite of all thrusters, A=[d ₁e ₁d ₂e ₂... d _ne _n], [d ₁d ₂... d _n] be the position vector matrix of n thruster centroid of satellite, [e ₁e ₂... e _n] be the specific thrust matrix that n thruster produces, D is thrust configuring matrix;

2), just step 1 is separated) described thrust apportion model, obtain F=D ^t(DD ^t) ^-1c, D ^t(DD ^t) ^-1for the pseudoinverse of D;

3), to step 2) the first solution that obtains divides into groups according to thrust is positive and negative:

$F_{\mathrm{pc}}=\left[\begin{array}{c}{F}_{\mathrm{pc}\_\mathrm{neg}}\\ F_{\mathrm{pc}\_\mathrm{pos}}\end{array}\right],$ F _{pc_neg}＜0,F _{pc_pos}＞0

Wherein, F _pcfor just separating the new matrix after positive and negative grouping, F _{pc_neg}for the submatrix of all negative solutions, F _{pc_pos}for the submatrix of all normal solutions;

By the grouping of efficiency matrix correspondence:

$D=\left[\begin{array}{c}{D}_{\mathrm{neg}}\\ D_{\mathrm{pos}}\end{array}\right]$

D _negfor F _{pc_neg}corresponding efficiency matrix submatrix, D _posfor corresponding F _{pc_pos}efficiency matrix submatrix;

By whole for the thrust of negative value group zero setting, obtain:

F _{pc_neg}＝u ₁＝[0 … 0]

To the desired amount sub-distribution again after distribution, obtain revised apportioning cost u ₂:

M _d＝D _posu ₂

M _dthe desired amount that the initial period desired amount C provided for control law obtains after distributing;

4), by step 3) middle D _posbe decomposed into the constant k of a row rank submatrix, simultaneously to u ₂decompose, again ask pseudoinverse, form following system of equations:

$\begin{array}{c}{M}_d=D_{\mathrm{pos}}^1{u}_2^1\\ .\\ .\\ .\\ M_d=D_{\mathrm{pos}}^k{u}_2^k\end{array}$

For each prescription journey, solve corresponding f _jvariable to be solved, F _j=[u ₁, u ₂], j=1 .., n, c _j,mfor known coefficient, represent the propelling dosage of jth platform thruster consumption, CDOP is the fuel consumption factor;

5), selecting step 4) in minimum one group of J perform.