CN103984785A - Satellite orbit control engine installation optimization method based on genetic algorithm - Google Patents

Abstract

The invention provides a satellite orbit control engine installation optimization method based on a genetic algorithm. The method comprises the following steps that (1) an objective function of the engine installation optimization is determined according to the requirement of a control system on the satellite layout; (2) according to the engine geometrical parameters and the installation requirements, a constraint function of the engine installation optimization is determined; (3) an AMTLB genetic algorithm toolkit is used for carrying out engine installation parameter optimization. The satellite orbit control engine installation optimization method has the advantages that the interference moment in the orbital transfer period is further reduced, so the satellite fuel is saved, and the satellite on-orbit life is prolonged.

Description

A kind of satellite rail control engine based on genetic algorithm is installed optimization method

Technical field

The present invention relates to a kind of installation optimization method of satellite rail control engine, particularly a kind of satellite rail control engine based on genetic algorithm is installed optimization method.

Background technology

The rail control engine of satellite is that it completes the major equipment that becomes rail strategy.Engine is arranged on the engine support being connected with satellite center loaded cylinder.Because thrust vectoring deviation and centroid of satellite and mechanical coordinate are that center is laterally having the impact of the factors such as deviation, cause engine to there is thrust deviation characteristic, during engine ignition, can produce the disturbance torque to satellite.In the satellite assembly stage, satellite, totally according to the heat mark data of reseach of engine unit, needs to propose the installation requirement to engine.The target of pursuing when engine is installed is mainly to make the disturbance torque during Satellite Orbit Maneuver the smaller the better.And whole star barycenter during the size of disturbance torque and engine thermal mark parameter and Satellite Orbit Maneuver is relevant.

Set the engine installation of satellite and only consider engine thermal mark parameter, according to heat mark parameter, propose the angle to motor power main shaft and three axis of orientations of satellite machinery coordinate system.Not yet consider the impact of centroid of satellite on disturbance torque, so just may have engine jamming moment is not that minimum, installation parameter are not optimum problems, even may occur comparing the larger problem of disturbance torque before adjusting after engine angular setting.

So, be necessary to study a kind of optimization method of definite engine installation parameter.Even because worry that engine thermal mark may exist reverse possibility, reduce to some extent and engine is adjusted to parameter, by the invention provides method, designer also can know the least interference moment that engine used can produce.Because the space constraint that the adjustment of engine installation parameter is subject to engine is relevant, and space constraint is non-linear constrain, cannot find optimum adjustment parameter by simple calculating, so the present invention solves this single goal nonlinear optimal problem by genetic algorithm.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of satellite rail control engine based on genetic algorithm that optimization method is installed, the present invention has reduced the disturbance torque during change rail, saves satellite fuel, and raising satellite is the life-span in-orbit.

The present invention, when definite engine installation parameter, considers the factor of engine thermal mark parameter and centroid of satellite two aspects, to reach minimum this optimization aim of disturbance torque.Even if do not consider centroid of satellite, be about to centroid of satellite and be set in that desirable (0,0, H) (H is that satellite is the center of mass values of Z-direction at mechanical coordinate) located, and also can provide than existing engine installation parameter and determine the engine installation parameter that method is more excellent.

Technical solution of the present invention is: the constraint condition being subject to while installing due to engine is more, and be non-linear constrain, so the present invention is incorporated into the optimization of genetic algorithm in the determining of installation parameter of engine, research is meeting under the prerequisite of constraint condition, how to obtain engine installation parameter, so that the problem of objective function optimum.

Specific implementation step is as follows:

(1) requirement to satellite layout according to satellite control system, determines the objective function that engine installation is optimized;

Engine is installed the objective function of optimizing: $T_{\mathrm{sc}}=\min \sqrt{T_x^2+T_y^2+T_z^2}$

Engine is installed in the objective function of optimizing:

$\left[\begin{array}{c}{T}_x\\ T_y\\ T_z\end{array}\right]=\left[\begin{array}{c}(-f_y*(p_z-x_c)+f_z*(p_y-y_c))/1000\\ (-f_z*(p_x-x_c)+f_x*(p_z-z_c))/1000\\ (-f_x*(p_y-x_c)+f_y*(p_x-x_c))/1000\end{array}\right]$

[f _x f _y f _z]=F[sin(α)sin(γ) -sin(α)cos(γ) cos(α)]R

[p _x p _y p _z]=[δsin(β) -δcos(β) h]R+[λ ₁ λ ₂ λ ₃]

$R=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\α}}_1\right)& \sin \left({\mathrm{\α}}_1\right)\\ 0& -\sin \left({\mathrm{\α}}_1\right)& \cos \left({\mathrm{\α}}_1\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\α}}_2\right)& 0& -\sin \left({\mathrm{\α}}_2\right)\\ 0& 1& 0\\ \sin \left({\mathrm{\α}}_2\right)& 0& \cos \left({\mathrm{\α}}_2\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\α}}_3\right)& \sin \left({\mathrm{\α}}_3\right)& 0\\ -\sin \left({\mathrm{\α}}_3\right)& \cos \left({\mathrm{\α}}_3\right)& 0\\ 0& 0& 1\end{array}\right]$

" min " represents minimum value;

[T _xt _yt _z]-around the disturbance torque of satellite machinery coordinate system OscXsc axle, OscYsc axle, 3 coordinate axis of OscZsc axle, unit is Nm;

[f _xf _yf _z]-motor power vector is in the thrust component of satellite machinery coordinate system OscXsc axle, OscYsc axle, three directions of OscZsc axle, and unit is N;

[p _xp _yp _zthe motor power application point coordinate figure of]-under satellite machinery coordinate system, unit is mm;

[x _cy _cz _cthe barycenter of the relative mechanical coordinate of]-satellite system, unit is mm;

The theoretical thrust of F-thruster, unit is N;

The rotation matrix of the relative satellite machinery of R-engine coordinate system;

α ₁, α ₂, α ₃-being respectively engine to install while adjusting, engine is around the anglec of rotation of satellite machinery coordinate system OscXsc axle, OscYsc axle and OscZsc axle, and unit is degree;

λ ₁, λ ₂, λ ₃-being respectively engine to install while adjusting, engine is along the translational movement of satellite machinery coordinate system OscXsc axle, OscYsc axle and OscZsc axle, and unit is mm;

α-thrust vectoring angle of deviation, take X-axis as benchmark, unit degree;

The traversing position angle of β-thrust vectoring, take Y-axis as benchmark, by engine top view direction counterclockwise for just, unit degree;

γ-thrust vectoring deflected position angle, take Y-axis as benchmark, by engine top view direction counterclockwise for just, unit degree;

The traversing amount of δ-thrust vectoring, apart from the distance of engine coordinate origin, the mm of unit.

(2), according to engine geometry parameter and installation requirement, determine the constraint function that engine installation is optimized; Engine is installed the constraint function of optimizing:

$\min ({(C_{\mathrm{ix}\_\mathrm{up}}^{\′}-H_{\mathrm{ix}})}^2+{(C_{\mathrm{iy}\_\mathrm{up}}^{\′}-H_{\mathrm{iy}})}^2)\≥{\left(\frac{d}{2}\right)}^2,i=\mathrm{1,2,3}$

$\min ({(C_{\mathrm{ix}\_\mathrm{down}}^{\′}-H_{\mathrm{ix}})}^2+{(C_{\mathrm{iy}\_\mathrm{down}}^{\′}-H_{\mathrm{iy}})}^2)\≥{\left(\frac{d}{2}\right)}^2,i=\mathrm{1,2,3}$

max(P _iz)≤MAX _z i=1,2,...,6

min(P _iz)≤MIN _z i=1,2,...,6

Engine is installed in the constraint function of optimizing:

H _ix=r ₁cos(θ _i) i=1,2,3

H _iy=r ₁sin(θ _i) i=1,2,3

$\left[\begin{array}{ccc}{C}_{\mathrm{ix}\_\mathrm{up}}^{\′}& C_{\mathrm{iy}\_\mathrm{up}}^{\′}& C_{\mathrm{iz}\_\mathrm{up}}^{\′}\end{array}\right]=\left[\begin{array}{ccc}{H}_{\mathrm{ix}}+\frac{D}{2}\cos \left(\mathrm{\κ}\right)& H_{\mathrm{iy}}+\frac{D}{2}\sin \left(\mathrm{\κ}\right)& h\end{array}\right]R+\left[\begin{array}{ccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\λ}}_3\end{array}\right],i=\mathrm{1,2,3}$

$\left[\begin{array}{ccc}{C}_{\mathrm{ix}\_\mathrm{down}}^{\′}& C_{\mathrm{iy}\_\mathrm{down}}^{\′}& C_{\mathrm{iz}\_\mathrm{down}}^{\′}\end{array}\right]=\left[\begin{array}{ccc}{H}_{\mathrm{ix}}+\frac{D}{2}\cos \left(\mathrm{\κ}\right)& H_{\mathrm{iy}}+\frac{D}{2}\sin \left(\mathrm{\κ}\right)& h-l\end{array}\right]R+\left[\begin{array}{ccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\λ}}_3\end{array}\right],i=\mathrm{1,2,3}$

[P _ix P _iy P _iz]=[r ₂cos(ψ _i) r ₂sin(ψ _i) h]R+[λ ₁ λ ₂ λ ₃]i=1,2,...,6

ψ _i∈[θ _j,(θ _j+θ ₁₀)]i=1,2,...,6;j=4,5,...,9

" max " represents maximal value;

The nominal diameter of the screw being connected between d-engine mounting flange and engine support, unit is mm;

θ _i3 mounting hole centers that (i=1,2,3)-engine mounting flange is connected with engine support and the subtended angle of engine coordinate origin line and engine coordinate system+Z axis, unit is degree;

θ _j(j=4,5 ..., 9) and 6 lug right sides on-engine mounting flange and the subtended angle of engine coordinate origin line and engine coordinate system+Z axis, unit is degree;

H _ix(i=1,2,3), H _iywhen (i=1,2,3)-be respectively engine does not rotate with translation, X, the Y coordinate figure of the center of 3 connecting holes under satellite machinery coordinate system between engine mounting flange and engine support, unit is mm;

R ₁place, connecting hole center radius of a circle between-engine mounting flange and engine support, unit is mm;

3 mounting hole diameters on D-engine mounting flange, unit is mm;

C' _{ix_up}, C' _{iy_up}, C' _{iz_up}-be respectively after engine rotation and translation, X, Y, the Z coordinate figure of any point on the circumference of 3 mounting holes of engine mounting flange upper surface under satellite machinery coordinate system, unit is mm, i=1,2,3;

C' _{ix_down}, C' _{iy_down}, C' _{iz_down}-be respectively after engine rotation and translation, X, Y, the Z coordinate figure of any point on the circumference of 3 mounting holes of engine mounting flange lower surface under satellite machinery coordinate system, unit is mm, i=1,2,3;

When h-engine does not rotate with translation, the Z coordinate figure of the upper surface of engine mounting flange under satellite machinery coordinate system, unit is mm;

The thickness of l-engine mounting flange, unit is mm;

κ∈[0°,360°]；

P _ix, P _iy, P _iz-be respectively engine to install after adjustment (rotation and translation), X, Y, the Z coordinate figure of the outer rim of 6 lugs under satellite machinery coordinate system on engine mounting flange, unit is mm, i=1,2 ..., 6; MAX _zthe Z-direction coordinate figure of-engine mounting bracket ring flange lower surface under satellite machinery coordinate system, unit is mm;

MIN _zthe Z-direction coordinate figure of the upper surface of the flat shim of-engine and engine support junction under satellite machinery coordinate system, unit is mm;

ψ _ithe angle of the relative satellite machinery in the both sides of 6 lugs coordinate system OscXsc on-engine mounting flange, unit is degree, i=1,2 ..., 6;

θ ₁₀the left side of each lug and the subtended angle between right side on-engine mounting flange, unit is degree;

R ₂-engine mounting flange lug outer rim place radius of a circle, unit is mm.

(3) use MATLAB GAs Toolbox to carry out the optimization of engine installation parameter.

The present invention's beneficial effect is compared with prior art:

(1) the present invention is directed in the requirement of engine Installation and adjustment and do not consider longitudinal adjustment, and do not consider the situation of centroid of satellite, propose a kind of engine that considers whole factors optimization method is installed.The disturbance torque minimum that the method be take during Satellite Orbit Maneuver is optimization aim, and the geometrical constraint when engine of take is installed is constraint condition, uses genetic algorithm to choose this single goal multiple constraint nonlinear optimal problem to engine installation parameter and solves.

(2) by setting the emulation of engine parameter, prove that the method can further reduce to become the disturbance torque during rail than current engine installation parameter confirmation method, thereby save satellite fuel, raising satellite is the life-span in-orbit.

Accompanying drawing explanation

Fig. 1 is engine body coordinate system and satellite machinery coordinate system schematic diagram;

Fig. 2 is the scheme of installation of engine on engine support;

Fig. 3 is securing member scheme of installation between engine and engine support;

Fig. 4 is engine mounting flange vertical view;

Fig. 5 is the space schematic diagram of engine thermal mark parameter under engine coordinate system;

Fig. 6 is disturbance torque Optimal Curve figure;

Fig. 7 is realization flow figure of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail.

As shown in Figure 1, be engine body coordinate system and satellite machinery coordinate system schematic diagram.In Fig. 1,1 is engine, and 2 is engine support.

Satellite machinery coordinate system is defined as follows:

Coordinate origin Osc-be positioned at satellite lower end frame and carrier rocket machinery parting plane, the center of circle of the theory forming with pin in satellite interface circle overlaps;

OscXsc axle-consistent with satellite east plate theory normal direction, positive dirction is consistent with eastern plate outer normal direction;

OscYsc axle-consistent with satellite north plate theory normal direction, positive dirction is consistent with southern plate outer normal direction;

The parting plane that is connected of OscZsc axle-perpendicular to satellite with carrier rocket, its positive dirction is pointed to floor from initial point;

OscXscYscZsc coordinate system meets right-hand rule.

Engine self also has a coordinate system, it is H place that its initial point is positioned at its initial point of distance on the Zsc axle of satellite machinery coordinate system, the X-axis forward of engine coordinate system is identical with the Zsc axle forward of satellite machinery coordinate system, the Y-axis forward of engine coordinate system is identical with the Ysc axle negative sense of satellite machinery coordinate system, and the Z axis of engine coordinate system and X-axis, Y-axis meet right-hand rule.

As shown in Figure 2, be the scheme of installation of engine on engine support.In Fig. 2,1 is engine, and 2 is engine support, and 3 is engine mounting flange, and 4 is the top surface edge of engine mounting flange, and 5 is the lower surface edge of engine mounting flange, the 6th, and engine support ring flange, the 7th, engine mounting screw.

As shown in Figure 3, be securing member scheme of installation between engine and engine support.In Fig. 3,1 is engine (partial sectional view), and 2 is engine support (partial sectional view), and 7 for installing the screw of use between engine mounting flange and engine support, and 8 is spring washer and flat shim, and 9 is heat insulating washer and flat shim.

As shown in Figure 4,10 is the lug on engine mounting flange, totally 6.H ₁, H ₂, H ₃3 connecting holes that hole is engine and engine support of mark; θ _i(i=1,2,3) are respectively the subtended angles of 3 connecting hole centers and OscXsc axle; θ _i(i=4,5 ..., 9) and be respectively the right side of 6 lugs on engine mounting flange and the subtended angle of OscXsc axle; θ ₁₀the left side of each lug on engine mounting flange and the subtended angle between right side; r ₁it is place, connecting hole center radius of a circle between engine and engine support; r ₂it is engine mounting flange lug outer rim place radius of a circle.

Fig. 5 is the space schematic diagram of engine thermal mark parameter under engine coordinate system, and wherein X, Y, Z represent the coordinate axis of engine coordinate system, and other meaning of parameters is as follows:

α-thrust vectoring angle of deviation (take X-axis as benchmark), unit degree;

The traversing position angle of β-thrust vectoring (take Y-axis as benchmark, by engine top view direction counterclockwise for just), unit degree;

γ-thrust vectoring deflected position angle (take Y-axis as benchmark, by engine top view direction counterclockwise for just), unit degree;

The traversing amount of δ-thrust vectoring (apart from the distance of true origin), the mm of unit.

P is motor power application point, represent thrust vectoring.

Fig. 6 is disturbance torque Optimal Curve figure, wherein (a) is the schematic diagram that desired value optimizing process changes, (b) be objective function while reaching optimum, the value of variable, engine is installed 3 rotation parameters (unit is degree) of adjusting and 3 translation parameterss (unit be millimeter).

As shown in Figure 7, specific implementation step of the present invention is as follows:

(1) first, the requirement according to control system to satellite layout, determines the objective function that engine installation is optimized

Introduce satellite machinery coordinate system, engine coordinate system and the disturbance torque calculating formula relevant with engine jamming Calculating Torque during Rotary below.The calculating of disturbance torque is relative subhost tool coordinate system all.

Satellite machinery coordinate system is defined as follows:

Coordinate origin Osc-be positioned at satellite lower end frame and carrier rocket machinery parting plane, the center of circle of the theory forming with pin in satellite interface circle overlaps;

OscXsc axle-consistent with satellite east plate theory normal direction, positive dirction is consistent with eastern plate outer normal direction;

OscYsc axle-consistent with satellite north plate theory normal direction, positive dirction is consistent with southern plate outer normal direction;

The parting plane that is connected of OscZsc axle-perpendicular to satellite with carrier rocket, its positive dirction is pointed to floor from initial point;

OscXscYscZsc coordinate system meets right-hand rule.

Engine self also has a coordinate system, it is H place that its initial point is positioned at its initial point of distance on the Zsc axle of satellite machinery coordinate system, the X-axis forward of engine coordinate system is identical with the Zsc axle forward of satellite machinery coordinate system, the Y-axis forward of engine coordinate system is identical with the Ysc axle negative sense of satellite machinery coordinate system, and the Z axis of engine coordinate system and X-axis, Y-axis meet right-hand rule.

Satellite machinery coordinate system and engine coordinate system are shown in Fig. 1.

Engine is arranged on engine support, adopts the screw that 3 nominal diameters are d to connect between engine mounting flange and engine support, and engine support is fixed with 3 the relative satellite machinery of screw coordinate systems.3 mounting hole diameters on engine mounting flange are D, D>d, so engine is when mounted, 6 parameters below can changing by the mode of increase adjustment pad (see figure 3) on 3 mounting screws of engine support and engine: the rotation angle around 3 coordinate axis of satellite machinery coordinate system (is set α ₁, α ₂, α ₃be respectively engine and install while adjusting, engine is around the anglec of rotation of satellite machinery coordinate system OscXsc axle, OscYsc axle and OscZsc axle, and unit is degree) and (set λ along three translations of axes of satellite machinery coordinate system ₁, λ ₂, λ ₃be respectively engine and install while adjusting, engine is along the translational movement of satellite machinery coordinate system OscXsc axle, OscYsc axle and OscZsc axle, and unit is mm).By adjusting this 6 parameters, reach the object of adjusting motor power vectors directed.

The disturbance torque of engine calculates as the formula (1):

$\left[\begin{array}{c}{T}_x\\ T_y\\ T_z\end{array}\right]=\left[\begin{array}{c}(-f_y*(p_z-x_c)+f_z*(p_y-y_c))/1000\\ (-f_z*(p_x-x_c)+f_x*(p_z-z_c))/1000\\ (-f_x*(p_y-x_c)+f_y*(p_x-x_c))/1000\end{array}\right]---\left(1\right)$

In formula (1), each meaning of parameters is as follows:

[T _xt _yt _z] for being the disturbance torque of OscXsc axle, OscYsc axle, 3 coordinate axis of OscZsc axle around mechanical coordinate, unit is Nm;

[f _xf _yf _z] be motor power vector in the thrust component of satellite machinery coordinate system OscXsc axle, OscYsc axle, three directions of OscZsc axle, unit is N, formula (2) is shown in its calculating;

[p _xp _yp _z] be the motor power application point coordinate figure under satellite machinery coordinate system, unit is mm, formula (3) is shown in its calculating;

[x _cy _cz _c] be the barycenter of the relative mechanical coordinate of satellite system, unit is mm.

[f _x f _y f _z]=F[sin(α)sin(γ) -sin(α)cos(γ) cos(α)]R （2）

[p _x p _y p _z]=[δsin(β) -δcos(β) h]R+[λ ₁ λ ₂ λ ₃] （3）

In formula (2), the theoretical thrust that F is thruster, unit is N; R is the rotation matrix of the relative satellite machinery of engine coordinate system:

$R=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\α}}_1\right)& \sin \left({\mathrm{\α}}_1\right)\\ 0& -\sin \left({\mathrm{\α}}_1\right)& \cos \left({\mathrm{\α}}_1\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\α}}_2\right)& 0& -\sin \left({\mathrm{\α}}_2\right)\\ 0& 1& 0\\ \sin \left({\mathrm{\α}}_2\right)& 0& \cos \left({\mathrm{\α}}_2\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\α}}_3\right)& \sin \left({\mathrm{\α}}_3\right)& 0\\ -\sin \left({\mathrm{\α}}_3\right)& \cos \left({\mathrm{\α}}_3\right)& 0\\ 0& 0& 1\end{array}\right]---\left(4\right)$

In formula (2) and formula (3), other parameter-definition is as follows:

α-thrust vectoring angle of deviation (take X-axis as benchmark), unit degree;

The traversing position angle of β-thrust vectoring (take Y-axis as benchmark, by engine top view direction counterclockwise for just), unit degree;

γ-thrust vectoring deflected position angle (take Y-axis as benchmark, by engine top view direction counterclockwise for just), unit degree;

The traversing amount of δ-thrust vectoring (apart from the distance of true origin), the mm of unit.

The definition of above-mentioned each parameter referring to Fig. 3 (in Fig. 3, P is motor power application point, represent thrust vectoring).

Satellite is controlled subsystem: satellite is during becoming rail, because thrust vectoring deviation and centroid of satellite and mechanical coordinate are that center is laterally having the impact of the factors such as deviation, the disturbance torque of the OscXsc axle around satellite machinery coordinate system of generation, OscYsc axle, OscZsc axle is not more than respectively M ₁, M ₂, M ₃.In addition, along with the consumption of propellant, when satellite generally becomes rail the last time, barycenter is the most severe, and disturbance torque is also maximum.So the centroid of satellite that the present invention is usingd while becoming rail is for the last time as the input of barycenter, the integrated interference moment while becoming rail for the last time (around the square root of the disturbance torque quadratic sum of 3 coordinate axis of satellite machinery coordinate system) of usining is minimum as optimization aim.Be that optimization aim is:

$T_{\mathrm{sc}}=\min \sqrt{T_x^2+T_y^2+T_z^2}---\left(5\right)$

Association type (1)～formula (5) objective function that is optimized.

(2), according to engine geometry parameter and installation requirement, determine the constraint function that engine installation is optimized

The scheme of installation of engine is shown in Fig. 2 and Fig. 3, and with reference to figure 3 and Fig. 4, the constraint that engine is installed is mainly space geometry constraint:

A) engine mounting hole must not surpass the constraint of mounting screw after rotation, translation;

B) top surface edge of engine mounting flange must not be higher than engine support ring flange lower surface;

C) lower surface of engine mounting hole must not be lower than the upper surface of flat shim.

To retrain and a) be converted into expression formula:

$\min ({(C_{\mathrm{ix}\_\mathrm{up}}^{\′}-H_{\mathrm{ix}})}^2+{(C_{\mathrm{iy}\_\mathrm{up}}^{\′}-H_{\mathrm{iy}})}^2)\≥{\left(\frac{d}{2}\right)}^2,i=\mathrm{1,2,3}$

$\min \left({{(C_{\mathrm{ix}\_\mathrm{down}}-H_{\mathrm{ix}})}^2+(C_{\mathrm{iy}\_\mathrm{down}}^{\′}-H_{\mathrm{iy}})}^2\right)\≥{\left(\frac{d}{2}\right)}^2,i=\mathrm{1,2,3}$

H _ix=r ₁cos(θ _i) i=1,2,3 （6）

H _iy=r ₁sin(θ _i) i=1,2,3

$\left[\begin{array}{ccc}{C}_{\mathrm{ix}\_\mathrm{up}}^{\′}& C_{\mathrm{iy}\_\mathrm{up}}^{\′}& C_{\mathrm{iz}\_\mathrm{up}}^{\′}\end{array}\right]=\left[\begin{array}{ccc}{H}_{\mathrm{ix}}+\frac{D}{2}\cos \left(\mathrm{\κ}\right)& H_{\mathrm{iy}}+\frac{D}{2}\sin \left(\mathrm{\κ}\right)& h\end{array}\right]R+\left[\begin{array}{ccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\λ}}_3\end{array}\right],i=\mathrm{1,2,3}$

$\left[\begin{array}{ccc}{C}_{\mathrm{ix}\_\mathrm{down}}^{\′}& C_{\mathrm{iy}\_\mathrm{down}}^{\′}& C_{\mathrm{iz}\_\mathrm{down}}^{\′}\end{array}\right]=\left[\begin{array}{ccc}{H}_{\mathrm{ix}}+\frac{D}{2}\cos \left(\mathrm{\κ}\right)& H_{\mathrm{iy}}+\frac{D}{2}\sin \left(\mathrm{\κ}\right)& h-l\end{array}\right]R+\left[\begin{array}{ccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\λ}}_3\end{array}\right],i=\mathrm{1,2,3}$

In formula (6), d be engine mounting flange with engine support between the nominal diameter of the screw that is connected, unit is mm; H _ix(i=1,2,3), H _iy(i=1,2,3) are respectively engines while not rotating with translation, X, the Y coordinate figure of the center of 3 connecting holes under satellite machinery coordinate system between engine mounting flange and engine support, and unit is mm; r ₁be place, connecting hole center radius of a circle between engine mounting flange and engine support, unit is mm; θ _i(i=1,2,3) are 3 mounting hole centers being connected with engine support of engine mounting flange and the subtended angle of engine coordinate origin line and engine coordinate system+Z axis; D is 3 mounting hole diameters on engine mounting flange, and unit is mm; C' _{ix_up}(i=1,2,3), C' _{iy_up}(i=1,2,3), C' _{iz_up}after (i=1,2,3) are respectively engine rotation and translation, X, Y, the Z coordinate figure of any point on the circumference of 3 mounting holes of engine mounting flange upper surface under satellite machinery coordinate system, unit is mm; C' _{ix_down}(i=1,2,3), C' _{iy_down}(i=1,2,3), C' _{iz_down}after (i=1,2,3) are respectively engine rotation and translation, X, Y, the Z coordinate figure of any point on the circumference of 3 mounting holes of engine mounting flange lower surface under satellite machinery coordinate system, unit is mm; H is engine while not rotating with translation, the Z-direction coordinate figure of the upper surface of engine mounting flange under satellite machinery coordinate system, and unit is mm; L is the thickness of engine mounting flange, and unit is mm; κ ∈ [0 °, 360 °].

To retrain b) and c) be converted into expression formula:

max(P _iz)≤MAX _z i=1,2,...,6

min(P _iz)≤MIN _z i=1,2,...,6

[P _ix P _iy P _iz]=[r ₂cos(ψ _i) r ₂sin(ψ _i) h]R+[λ ₁ λ ₂ λ ₃] i=1,2,...,6 （7）

ψ _i∈[θ _j,(θ _j+θ ₁₀)] i=1,2,...,6;j=4,5,...,9

In formula (7), P _ix, Pi _y, P _iz(i=1,2 ..., 6) be respectively that engine is installed after adjustment (rotation and translation), X, Y, the Z coordinate figure of the outer rim of 6 lugs under satellite machinery coordinate system on engine mounting flange, unit is mm;

MAX _zfor the Z-direction coordinate figure of engine mounting bracket ring flange lower surface under satellite machinery coordinate system, unit is mm;

MIN _zfor the upper surface of the flat shim of engine and the engine support junction Z-direction coordinate figure under satellite machinery coordinate system, unit is mm;

ψ _i(i=1,2 ..., 6) and be the angle of the both sides relative satellite machinery coordinate system OscXsc of 6 lugs on engine mounting flange, unit is degree;

θ _j(j=4,5 ..., 9) and be 6 lug right sides on engine mounting flange and the subtended angle of engine coordinate origin line and engine coordinate system+Z axis, unit is degree;

θ ₁₀for the left side of each lug on engine mounting flange and the subtended angle between right side, unit is degree;

R ₂for engine mounting flange lug outer rim place radius of a circle, unit is mm.

(3) use MATLAB GAs Toolbox to carry out the optimization of engine installation parameter

The installation optimization problem of engine belongs to single goal nonlinear optimal problem.Utilize the ga function in MATLAB GAs Toolbox (GAOT) that such restricted problem is optimized and is solved.

Be implemented as follows:

(31), in MATLAB, set engine rotation angle α ₁, α ₂, α ₃with translational movement λ ₁, λ ₂, λ ₃for (6) six variablees of x (1)～x;

(32) engine is installed to the objective function of optimizing and be converted to code, save as myfit function;

(33) engine is installed after the constraint function of optimizing is programmed and saved as myconst function;

(34) use ga function to be optimized:

options=gaoptimset('populationsize',20,'SelectionFcn',selectionuniform,'Muta tionFcn',mutationuniform,'CrossoverFcn',crossoverintermediat e,'generations',30);

[x,Tsc,flag,output,population,scores]=ga((x)myfit(x),20,[],[],[],[],[],[],(x)my constr(x),options)

X is 1 * 20 array, and wherein x (1)～x (6) is α ₁, α ₂, α ₃and λ ₁, λ ₂, λ ₃, Tsc is engine the objective function T optimizing is installed _sc.

The thrust vectoring angle of deviation of setting certain engine is 0.25 °, and the traversing position angle of thrust vectoring is 282 °, and thrust vectoring deflected position angle is 96 °, and the traversing amount of thrust vectoring is 0.70mm, and centroid of satellite is [5mm ,-5mm, 1550mm].If engine is not adjusted, the root-mean-square value of the disturbance torque quadratic sum around three coordinate axis of satellite machinery coordinate system obtaining is 2.73Nm.If only consider heat mark parameter, the root-mean-square value of the disturbance torque quadratic sum around three coordinate axis of satellite machinery coordinate system after adjusting is 3.74Nm, also large when not adjusting, this is mainly because do not consider centroid of satellite, so can produce the more more inclined to one side problem of tune.Utilizing gaoptimset function setup population scale is 20, genetic algebra is 30, according to the termination for default condition of ga function, use ga function operation program, the optimizing process that Fig. 6 (a) is objective function, horizontal ordinate is optimization algebraically, the optimum results that ordinate is target function value, and the least interference moment obtaining is 5.87 * 10 ^-4nm.Disturbance torque engine rotation angle and translational movement hour is shown in Fig. 6 (b), and in Fig. 6 (b), variable 1～6 is objective function α hour ₁, α ₂, α ₃and λ ₁, λ ₂, λ ₃value.

Non-elaborated part of the present invention belongs to techniques well known.

Claims (1)

1. the satellite rail control engine based on genetic algorithm is installed an optimization method, and its feature is as follows at performing step:

(1) requirement to satellite layout according to satellite control system, determines the objective function that engine installation is optimized;

Engine is installed the objective function of optimizing: $T_{\mathrm{sc}}=\min \sqrt{T_x^2+T_y^2+T_z^2}$

Engine is installed in the objective function of optimizing:

$\left[\begin{array}{c}{T}_x\\ T_y\\ T_z\end{array}\right]=\left[\begin{array}{c}(-f_y*(p_z-x_c)+f_z*(p_y-y_c))/1000\\ (-f_z*(p_x-x_c)+f_x*(p_z-z_c))/1000\\ (-f_x*(p_y-x_c)+f_y*(p_x-x_c))/1000\end{array}\right]$

[f _x f _y f _z]=F[sin(α)sin(γ) -sin(α)cos(γ) cos(α)]R

[p _x p _y p _z]=[δsin(β) -δcos(β) h]R+[λ ₁ λ ₂ λ ₃]

$R=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left({\mathrm{\α}}_1\right)& \sin \left({\mathrm{\α}}_1\right)\\ 0& -\sin \left({\mathrm{\α}}_1\right)& \cos \left({\mathrm{\α}}_1\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\α}}_2\right)& 0& -\sin \left({\mathrm{\α}}_2\right)\\ 0& 1& 0\\ \sin \left({\mathrm{\α}}_2\right)& 0& \cos \left({\mathrm{\α}}_2\right)\end{array}\right]\left[\begin{array}{ccc}\cos \left({\mathrm{\α}}_3\right)& \sin \left({\mathrm{\α}}_3\right)& 0\\ -\sin \left({\mathrm{\α}}_3\right)& \cos \left({\mathrm{\α}}_3\right)& 0\\ 0& 0& 1\end{array}\right]$

" min " represents minimum value;

[T _xt _yt _z]-around the disturbance torque of satellite machinery coordinate system OscXsc axle, OscYsc axle, 3 coordinate axis of OscZsc axle;

[f _xf _yf _z]-motor power vector is in the thrust component of satellite machinery coordinate system OscXsc axle, OscYsc axle, three directions of OscZsc axle;

[p _xp _yp _zthe motor power application point coordinate figure of]-under satellite machinery coordinate system;

[x _cy _cz _cthe barycenter of the relative mechanical coordinate of]-satellite system;

The theoretical thrust of F-thruster;

The rotation matrix of the relative satellite machinery of R-engine coordinate system;

α ₁, α ₂, α ₃-being respectively engine to install while adjusting, engine is around the anglec of rotation of satellite machinery coordinate system OscXsc axle, OscYsc axle and OscZsc axle;

λ ₁, λ ₂, λ ₃-being respectively engine to install while adjusting, engine is along the translational movement of satellite machinery coordinate system OscXsc axle, OscYsc axle and OscZsc axle;

α-thrust vectoring angle of deviation, take X-axis as benchmark;

The traversing position angle of β-thrust vectoring, take Y-axis as benchmark, by engine top view direction counterclockwise for just;

γ-thrust vectoring deflected position angle, take Y-axis as benchmark, by engine top view direction counterclockwise for just;

The traversing amount of δ-thrust vectoring, apart from the distance of engine coordinate origin;

(2), according to engine geometry parameter and installation requirement, determine the constraint function that engine installation is optimized; Engine is installed the constraint function of optimizing:

$\min ({(C_{\mathrm{ix}\_\mathrm{up}}^{\′}-H_{\mathrm{ix}})}^2+{(C_{\mathrm{iy}\_\mathrm{up}}^{\′}-H_{\mathrm{iy}})}^2)\≥{\left(\frac{d}{2}\right)}^2,i=\mathrm{1,2,3}$

$\min \left({{(C_{\mathrm{ix}\_\mathrm{down}}^{\′}-H_{\mathrm{ix}})}^2+(C_{\mathrm{iy}\_\mathrm{down}}^{\′}-H_{\mathrm{iy}})}^2\right)\≥{\left(\frac{d}{2}\right)}^2,i=\mathrm{1,2,3}$

max(P _iz)≤MAX _z i=1,2,...,6

min(P _iz)≤MIN _z i=1,2,...,6

Engine is installed in the constraint function of optimizing:

H _ix=r ₁cos(θ _i) i=1,2,3

H _iy=r ₁sin(θ _i) i=1,2,3

$\left[\begin{array}{ccc}{C}_{\mathrm{ix}\_\mathrm{up}}^{\′}& C_{\mathrm{iy}\_\mathrm{up}}^{\′}& C_{\mathrm{iz}\_\mathrm{up}}^{\′}\end{array}\right]=\left[\begin{array}{ccc}{H}_{\mathrm{ix}}+\frac{D}{2}\cos \left(\mathrm{\κ}\right)& H_{\mathrm{iy}}+\frac{D}{2}\sin \left(\mathrm{\κ}\right)& h\end{array}\right]R+\left[\begin{array}{ccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\λ}}_3\end{array}\right],i=\mathrm{1,2,3}$

$\left[\begin{array}{ccc}{C}_{\mathrm{ix}\_\mathrm{down}}^{\′}& C_{\mathrm{iy}\_\mathrm{down}}^{\′}& C_{\mathrm{iz}\_\mathrm{down}}^{\′}\end{array}\right]=\left[\begin{array}{ccc}{H}_{\mathrm{ix}}+\frac{D}{2}\cos \left(\mathrm{\κ}\right)& H_{\mathrm{iy}}+\frac{D}{2}\sin \left(\mathrm{\κ}\right)& h-l\end{array}\right]R+\left[\begin{array}{ccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\λ}}_3\end{array}\right],i=\mathrm{1,2,3}$

[P _ix P _iy P _iz]=[r ₂cos(ψ _i) r ₂sin(ψ _i) h]R+[λ ₁ λ ₂ λ ₃]i=1,2,...,6；

ψ _i∈[θ _j,(θ _j+θ ₁₀)]i=1,2,...,6;j=4,5,...,9；

" max " represents maximal value;

The nominal diameter of the screw being connected between d-engine mounting flange and engine support;

θ _i3 mounting hole centers that-engine mounting flange is connected with engine support and the subtended angle of engine coordinate origin line and engine coordinate system+Z axis, i=1,2,3;

θ _j6 lug right sides on-engine mounting flange and the subtended angle of engine coordinate origin line and engine coordinate system+Z axis, j=4,5 ..., 9;

H _ix, H _iy-be respectively engine while not rotating with translation, X, the Y coordinate figure of the center of 3 connecting holes under satellite machinery coordinate system between engine mounting flange and engine support, i=1,2,3;

R ₁place, connecting hole center radius of a circle between-engine mounting flange and engine support;

3 mounting hole diameters on D-engine mounting flange;

C' _{ix_up}, C' _{iy_up}, C' _{iz_up}-be respectively after engine rotation and translation X, Y, the Z coordinate figure of any point on the circumference of 3 mounting holes of engine mounting flange upper surface under satellite machinery coordinate system, i=1,2,3;

C' _{ix_down}, C' _{iy_down}, C' _{iz_down}-be respectively after engine rotation and translation X, Y, the Z coordinate figure of any point on the circumference of 3 mounting holes of engine mounting flange lower surface under satellite machinery coordinate system, i=1,2,3;

When h-engine does not rotate with translation, the Z-direction coordinate figure of the upper surface of engine mounting flange under satellite machinery coordinate system;

The thickness of l-engine mounting flange;

κ∈[0°,360°]；

P _ix, P _iy, P _iz-be respectively engine to install after adjustment (rotation and translation), X, Y, the Z coordinate figure of the outer rim of 6 lugs under satellite machinery coordinate system on engine mounting flange, i=1,2 ..., 6;

MAX _zthe Z-direction coordinate figure of-engine mounting bracket ring flange lower surface under satellite machinery coordinate system;

MIN _zthe Z-direction coordinate figure of the upper surface of the flat shim of-engine and engine support junction under satellite machinery coordinate system;

ψ _ithe angle of the relative satellite machinery in the both sides of 6 lugs coordinate system OscXsc on-engine mounting flange, i=1,2 ..., 6;

θ ₁₀the left side of each lug and the subtended angle between right side on-engine mounting flange;

R ₂-engine mounting flange lug outer rim place radius of a circle;

(3) use MATLAB GAs Toolbox to carry out the optimization of engine installation parameter.