CN103984785B - A kind of satellite precise tracking based on genetic algorithm installs optimization method - Google Patents

Abstract

A kind of satellite precise tracking based on genetic algorithm installs optimization method, comprises the following steps that：（1）According to the requirement that control system is laid out to satellite, determine that engine installs the object function of optimization；（2）According to engine geometry parameter and installation requirement, determine that engine installs the constraint function of optimization；（3）Engine installation parameter optimization is carried out using MATLAB GAs Toolboxes.It is of the invention further to reduce the disturbance torque become during rail, so as to save satellite fuel, improve satellite life-span in-orbit.

Description

A kind of satellite precise tracking based on genetic algorithm installs optimization method

Technical field

The present invention relates to a kind of installation optimization method of satellite precise tracking, particularly a kind of defending based on genetic algorithm Star precise tracking installs optimization method.

Background technology

The precise tracking of satellite is that it completes to become the capital equipment of rail strategy.Engine is arranged on and satellite hub load On the connected engine support of cylinder.Because thrust vectoring deviation and centroid of satellite are laterally having deviation etc. with mechanical coordinate system center The influence of factor, causes engine to have the disturbance torque that can be produced during thrust deviation characteristic, engine ignition to satellite. Satellite assembly stage, the overall heat mark data according to reseach of engine unit of satellite need to propose the installation requirement to engine.Hair Disturbance torque during the target that motivation is pursued when installing mainly is so that Satellite Orbit Maneuver is the smaller the better.And the size of disturbance torque It is related to the whole star barycenter during engine thermal mark parameter and Satellite Orbit Maneuver.

The engine for setting satellite installs only consideration engine thermal mark parameter, is proposed to motor power according to heat mark parameter Main shaft and satellite machinery three angles of axis of orientation of coordinate system.Not yet consider influence of the centroid of satellite to disturbance torque, thus There may be that engine jamming torque is not minimum, installation parameter is not optimal problem, in some instances it may even be possible to engine angle occur Than the bigger problem of disturbance torque before adjustment after adjustment.

Thus, it is necessary to study a kind of optimization method for determining engine installation parameter.Even if because worrying engine thermal Mark there may be reverse possibility, and engine adjusting parameter has been reduced, and by the method provided by the present invention, designer also can Know the least interference torque that engine used can be generated.It is subject to due to the adjustment of engine installation parameter and engine Space constraint is relevant, and space constraint is nonlinear restriction, it is impossible to find optimal adjusting parameter, institute by simple calculating So that the present invention solves this single goal nonlinear optimal problem by genetic algorithm.

The content of the invention

Technology solve problem of the invention is：Overcome the deficiencies in the prior art, there is provided a kind of satellite based on genetic algorithm Precise tracking installs optimization method, present invention decreases the disturbance torque become during rail, saves satellite fuel, improves satellite and exists The rail life-span.

The present invention is it is determined that during engine installation parameter, consider of both engine thermal mark parameter and centroid of satellite Factor, to reach minimum this optimization aim of disturbance torque.Even if not considering centroid of satellite, will centroid of satellite be set in ideal 's（0,0, H）（H is center of mass values of the satellite in mechanical coordinate system Z-direction）Place, can also provide more true than existing engine installation parameter Determine the more excellent engine installation parameter of method.

Technical solution of the invention is：The constraints being subject to when being installed due to engine is more, and for non-linear Constraint, so be incorporated into the determination of the installation parameter of engine for the optimization of genetic algorithm by the present invention, research is meeting constraint On the premise of condition, engine installation parameter how is obtained, with the problem for causing object function optimal.

Implement step as follows：

（1）According to the requirement that satellite control system is laid out to satellite, determine that engine installs the object function of optimization；

Engine installs the object function for optimizing：

Engine is installed in the object function of optimization：

[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+[λ₁ λ₂ λ₃]

" min " represents minimum value；

[T_x T_y T_z]-around satellite machinery coordinate system OscXsc axles, OscYsc axles, 3 interference of reference axis of OscZsc axles Torque, unit is Nm；

[f_x f_y f_z]-motor power vector is in satellite machinery coordinate system OscXsc axles, OscYsc axles, OscZsc axles three The thrust component in individual direction, unit is N；

[p_x p_y p_zThe motor power application point coordinate value of]-under satellite machinery coordinate system, unit is mm；

[x_C y_C z_CThe barycenter of]-satellite relative mechanical coordinate system, unit is mm；

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

The spin matrix of R-engine relative satellite mechanical coordinate system；

α₁、α₂、α₃- be respectively engine mounting and adjusting when, engine is around satellite machinery coordinate system OscXsc axles, OscYsc The anglec of rotation of axle and OscZsc axles, unit is degree；

λ₁、λ₂、λ₃- be respectively engine mounting and adjusting when, engine is along satellite machinery coordinate system OscXsc axles, OscYsc The translational movement of axle and OscZsc axles, unit is mm；

α-thrust vectoring angle of deviation, on the basis of X-axis, unit degree；

The traversing position angle of β-thrust vectoring, is counterclockwise just unit degree by engine top view direction on the basis of Y-axis；

γ-thrust vectoring deflected position angle, is counterclockwise just unit degree by engine top view direction on the basis of Y-axis；

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

（2）According to engine geometry parameter and installation requirement, determine that engine installs the constraint function of optimization；Engine is pacified Filling the constraint function for optimizing is：

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 optimization：

H_ix=r₁cos(θ_i) i=1,2,3

H_iy=r₁sin(θ_i) i=1,2,3

[P_ix P_iy P_iz]=[r₂cos(ψ_i) r₂sin(ψ_i) h]R+[λ₁ λ₂ λ₃]i=1,2,...,6

ψ_i∈[θ_j,(θ_j+θ₁₀)]i=1,2,...,6;j=4,5,...,9

" max " represents maximum；

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

θ_i（i=1,2,3）3 mounting hole centers that-motor mounting flange is connected with engine support are sat with engine The subtended angle of mark system origin line and engine coordinate system+Z axis, unit is degree；

θ_j（j=4,5,…,9）On-motor mounting flange 6 lugs right side with engine coordinate system origin line and The subtended angle of engine coordinate system+Z axis, unit is degree；

H_ix（i=1,2,3）、H_iy（i=1,2,3）- when being respectively the non-rotation and translation of engine, motor mounting flange with X, Y-coordinate value of 3 centers of connecting hole under satellite machinery coordinate system between engine support, unit is mm；

r₁The radius of circle where connecting hole center between-motor mounting flange and engine support, unit is mm；

3 installation bore dias on D-motor mounting flange, unit is mm；

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

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

During the non-rotation and translation of h-engine, the Z of the upper surface of motor mounting flange under satellite machinery coordinate system sits Scale value, unit is mm；

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

κ∈[0°,360°]；

P_ix、P_iy、P_iz- it is respectively engine mounting and adjusting（Rotation and translation）Afterwards, 6 lugs on motor mounting flange Outer rim satellite machinery coordinate system under X, Y, Z coordinate value, unit is mm, i=1,2 ..., 6；MAX_z- engine installs branch Z-direction coordinate value of the frame ring flange lower surface under satellite machinery coordinate system, unit is mm；

MIN_zZ-direction of the upper surface of the flat shim of-engine and engine support junction under satellite machinery coordinate system Coordinate value, unit is mm；

ψ_i6 angles of the both sides relative satellite mechanical coordinate system OscXsc of lug, unit on-motor mounting flange It is degree, i=1,2 ..., 6；

θ₁₀Subtended angle on-motor mounting flange between the left side and right side of each lug, unit is degree；

r₂The radius of circle where-motor mounting flange lug outer rim, unit is mm.

（3）Engine installation parameter optimization is carried out using MATLAB GAs Toolboxes.

Present invention beneficial effect compared with prior art is：

（1）The present invention does not consider longitudinally adjusted in being directed to engine installation and adjustment requirement, and does not consider centroid of satellite Situation, proposes that a kind of engine for considering whole factors installs optimization method.The method is with the interference during Satellite Orbit Maneuver The minimum optimization aim of torque, geometrical constraint when being installed with engine is pacified using genetic algorithm as constraints to engine Dress parameter is chosen this single goal multiple constraint nonlinear optimal problem and is solved.

（2）By the emulation to setting engine parameter, it was demonstrated that the method is than current engine installation parameter confirmation side Method can further reduce the disturbance torque become during rail, so as to save satellite fuel, improve satellite life-span in-orbit.

Brief description of the drawings

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

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

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

Fig. 4 is motor mounting flange top view；

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

Fig. 6 is disturbance torque Optimal Curve figure；

Fig. 7 realizes flow chart for of the invention.

Specific embodiment

Below in conjunction with the accompanying drawings and embodiment the present invention is described in detail.

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

Satellite machinery coordinate system is defined as follows：

Coordinate origin Osc-be located in satellite lower end frame and the mechanically decoupled face of carrier rocket, with pin in satellite interface The center of circle of the theoretical circle for being constituted overlaps；

OscXsc axles-consistent with satellite east plate theory normal direction, positive direction is consistent with eastern plate exterior normal direction；

OscYsc axles-consistent with satellite north plate theory normal direction, positive direction is consistent with southern plate exterior normal direction；

OscZsc axles-and perpendicular to satellite and the connection parting surface of carrier rocket, its positive direction is pointed to floor from origin；

OscXscYscZsc coordinate systems meet right-hand rule.

Engine itself also has a coordinate system, and its origin is located on the Zsc axles of satellite machinery coordinate system apart from its origin At H, the X-axis of engine coordinate system is positive identical with the Zsc axle forward directions of satellite machinery coordinate system, the Y-axis of engine coordinate system Positive identical with the Ysc axle negative senses of satellite machinery coordinate system, Z axis and X-axis, the Y-axis of engine coordinate system meet right-hand rule.

As shown in Fig. 2 the scheme of installation for being engine on engine support.In Fig. 2,1 is engine, and 2 is to start Machine support, 3 is motor mounting flange, and 4 is the top surface edge of motor mounting flange, and 5 under motor mounting flange Marginal surface, 6 is engine support ring flange, and 7 is engine mounting screw.

As shown in figure 3, being fastener scheme of installation between engine and engine support.In Fig. 3,1 is engine（Office Portion's sectional view）, 2 is engine support（Partial sectional view）, 7 is installation between motor mounting flange and engine support Screw, 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 motor mounting flange, totally 6.H₁、H₂、H₃3 holes of mark are to start The connecting hole of machine and engine support；θ_i（I=1,2,3）It is respectively the subtended angle at 3 connecting hole centers and OscXsc axles；θ_i（I=4, 5 ..., 9）It is respectively the subtended angle of 6 right sides of lug and OscXsc axles on motor mounting flange；θ₁₀It is motor mounting flange Subtended angle between the left side and right side of upper each lug；r₁It is circle where connecting hole center between engine and engine support Radius；r₂It is the radius of circle where motor mounting flange lug outer rim.

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

α-thrust vectoring angle of deviation（On the basis of X-axis）, unit degree；

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

γ-thrust vectoring deflected position angle（On the basis of Y-axis, by engine top view direction counterclockwise for just）, unit Degree；

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

P is motor power application point,Represent thrust vectoring.

Fig. 6 is disturbance torque Optimal Curve figure, wherein (a) is the schematic diagram of desired value optimization process change, (b) is target When function is optimal, the value of variable, i.e. the 3 of engine mounting and adjusting rotation parameter（Unit is degree）With 3 translation parameters （Unit is millimeter）.

As shown in fig. 7, the present invention to implement step as follows：

（1）First, the requirement being laid out to satellite according to control system, determines that engine installs the object function of optimization

The satellite machinery coordinate system related to engine jamming Calculating Torque during Rotary, engine coordinate system and perturbed force is described below Square calculating formula.The calculating of disturbance torque is with respect to subhost tool coordinate system.

Satellite machinery coordinate system is defined as follows：

Coordinate origin Osc-be located in satellite lower end frame and the mechanically decoupled face of carrier rocket, with pin in satellite interface The center of circle of the theoretical circle for being constituted overlaps；

OscXsc axles-consistent with satellite east plate theory normal direction, positive direction is consistent with eastern plate exterior normal direction；

OscYsc axles-consistent with satellite north plate theory normal direction, positive direction is consistent with southern plate exterior normal direction；

OscZsc axles-and perpendicular to satellite and the connection parting surface of carrier rocket, its positive direction is pointed to floor from origin；

OscXscYscZsc coordinate systems meet right-hand rule.

Engine itself also has a coordinate system, and its origin is located on the Zsc axles of satellite machinery coordinate system apart from its origin At H, the X-axis of engine coordinate system is positive identical with the Zsc axle forward directions of satellite machinery coordinate system, the Y-axis of engine coordinate system Positive identical with the Ysc axle negative senses of satellite machinery coordinate system, Z axis and X-axis, the Y-axis of engine coordinate system meet right-hand rule.

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

Engine is arranged on engine support, straight using 3 nominals between motor mounting flange and engine support Footpath is the mode connects for screw of d, and engine support and 3 screw relative satellite mechanical coordinate systems are fixed.Motor mounting flange On 3 mounting holes a diameter of D, D>D, so engine is when mounted, can be by 3 of engine support and engine Increase adjust pad on mounting screw（See Fig. 3）Mode change following 6 parameters：Around satellite machinery 3 coordinates of coordinate system The anglec of rotation of axle（Setting α₁、α₂、α₃Respectively engine mounting and adjusting when, engine around satellite machinery coordinate system OscXsc axles, The anglec of rotation of OscYsc axles and OscZsc axles, unit is degree）With along satellite machinery coordinate system three translations of axes（Setting λ₁、λ₂、λ₃Respectively engine mounting and adjusting when, engine is along satellite machinery coordinate system OscXsc axles, OscYsc axles and OscZsc The translational movement of axle, unit is mm）.By adjusting this 6 parameters, the purpose that adjustment motor power vector is pointed to is reached.

The disturbance torque of engine is calculated such as formula（1）It is shown：

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

[T_x T_y T_z] be around mechanical coordinate system OscXsc axles, OscYsc axles, 3 disturbance torques of reference axis of OscZsc axles, Unit is Nm；

[f_x f_y f_z] for motor power vector in satellite machinery coordinate system OscXsc axles, OscYsc axles, OscZsc axles three The thrust component in individual direction, unit is N, and formula is shown in its calculating（2）；

[p_x p_y p_z] it is the motor power application point coordinate value under satellite machinery coordinate system, unit is mm, its calculating See formula（3）；

[x_C y_C z_C] it is the barycenter of satellite relative mechanical coordinate 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+[λ₁ λ₂ λ₃] （3）

Formula（2）In, F is the theoretical thrust of thruster, and unit is N；R is the rotation of engine relative satellite mechanical coordinate system Matrix：

Formula（2）And formula（3）In, other parameters are defined as follows：

α-thrust vectoring angle of deviation（On the basis of X-axis）, unit degree；

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

γ-thrust vectoring deflected position angle（On the basis of Y-axis, by engine top view direction counterclockwise for just）, unit Degree；

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

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

Satellite control subsystem be to the requirement that satellite is laid out：Satellite due to thrust vectoring deviation and is defended during rail is become Star barycenter is with mechanical coordinate system center in the influence for laterally having the factors such as deviation, the OscXsc around satellite machinery coordinate system of generation Axle, OscYsc axles, the disturbance torque of OscZsc axles are not more than M respectively₁、M₂、M₃.In addition, with the consumption of propellant, satellite one As last time become rail when barycenter it is the most severe, disturbance torque is also maximum.So, the defending when present invention becomes rail with last time Star barycenter becomes integrated interference torque during rail with last time as the input of barycenter（Around satellite machinery 3 reference axis of coordinate system Disturbance torque quadratic sum square root）Minimum is used as optimization aim.I.e. optimization aim is：

Association type（1）~formula（5）Obtain optimization object function.

（2）According to engine geometry parameter and installation requirement, determine that engine installs the constraint function of optimization

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

A) engine mounting holes must not exceed the constraint of mounting screw after rotation, translation；

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

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

To constrain and a) be converted into expression formula：

H_ix=r₁cos(θ_i) i=1,2,3 （6）

H_iy=r₁sin(θ_i) i=1,2,3

Formula（6）In, d is the nominal diameter of the screw of connection between motor mounting flange and engine support, and unit is mm；H_ix（i=1,2,3）、H_iy（i=1,2,3）When being respectively the non-rotation and translation of engine, motor mounting flange and engine X, Y-coordinate value of 3 centers of connecting hole under satellite machinery coordinate system between support, unit is mm；r₁It is that engine is installed The radius of circle where connecting hole center between flange and engine support, unit is mm；θ_i（i=1,2,3）It is engine Method for Installation 3 mounting hole centers be connected with engine support of orchid and engine coordinate system origin line and engine coordinate system+Z axis are opened Angle；D is 3 installation bore dias on motor mounting flange, and unit is mm；C'_{ix_up}（i=1,2,3）、C'_{iy_up}（i=1,2, 3）、C'_{iz_up}（i=1,2,3）Be respectively engine rotation and translation after, 3 circles of mounting hole of motor mounting flange upper surface X, Y, the Z coordinate value of any point on week 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}（i=1,2,3）Be respectively engine rotation and translation after, motor mounting flange lower surface 3 circumference of mounting hole on any point satellite machinery coordinate system under X, Y, Z coordinate value, unit is mm；H is to start During the non-rotation and translation of machine, the Z-direction coordinate value of the upper surface of motor mounting flange under satellite machinery coordinate system, unit is mm；L is the thickness of motor mounting flange, and unit is mm；κ∈[0°,360°].

To constrain 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]=[r₂cos(ψ_i) r₂sin(ψ_i) h]R+[λ₁ λ₂ λ₃] i=1,2,...,6 （7）

ψ_i∈[θ_j,(θ_j+θ₁₀)] i=1,2,...,6;j=4,5,...,9

Formula（7）In, P_ix、Pi_y、P_iz（i=1,2,...,6）It is respectively engine mounting and adjusting（Rotation and translation）Afterwards, start X, Y, Z coordinate value of 6 outer rims of lug under satellite machinery coordinate system on machine mounting flange, unit is mm；

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

MIN_zIt is the Z-direction of the upper surface under satellite machinery coordinate system of engine and the flat shim of engine support junction Coordinate value, unit is mm；

ψ_i（i=1,2,…,6）It is 6 both sides relative satellite mechanical coordinate system OscXsc of lug on motor mounting flange Angle, unit for degree；

θ_j（j=4,5,…,9）For on motor mounting flange 6 lugs right side with engine coordinate system origin line and The subtended angle of engine coordinate system+Z axis, unit is degree；

θ₁₀It is the subtended angle on motor mounting flange between the left side and right side of each lug, unit is degree；

r₂The radius of circle where motor mounting flange lug outer rim, unit is mm.

（3）Engine installation parameter optimization is carried out using MATLAB GAs Toolboxes

The installation optimization problem of engine belongs to single goal nonlinear optimal problem.Using MATLAB GAs Toolboxes （GAOT）In the such restricted problem of ga function pairs optimize solution.

It is implemented as follows：

（31）In MATLAB, engine rotation angle α is set₁、α₂、α₃With translational movement λ₁、λ₂、λ₃For x (1)~x (6) six Variable；

（32）The object function that engine installs optimization is converted into code, myfit functions are saved as；

（33）Myconst functions are saved as after the constraint function programming that engine is installed optimization；

（34）Optimized using ga functions：

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 α₁、α₂、α₃And λ₁、λ₂、λ₃, it is excellent that Tsc is engine installation The object function T of change_sc。

The thrust vectoring angle of deviation for setting certain engine is 0.25 °, and the traversing position angle of thrust vectoring is 282 °, thrust arrow Amount 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 Do not adjust, the root-mean-square value of the disturbance torque quadratic sum around satellite machinery three reference axis of coordinate system for obtaining is 2.73Nm.If Only consider heat mark parameter, the root mean square of the disturbance torque quadratic sum around satellite machinery three reference axis of coordinate system after being adjusted It is 3.74Nm to be worth, and also big during than not adjusting, this is primarily due to not consider centroid of satellite, so can produce that adjusts more inclined and more inclined to ask Topic.It is 20 using gaoptimset function setups population scale, genetic algebra is 30, according to the termination for default condition of ga functions, Using ga function operation programs, Fig. 6 (a) is the optimization process of object function, and abscissa is optimization algebraically, and ordinate is target letter The optimum results of numerical value, the least interference torque for obtaining is 5.87 × 10^-4Nm.Engine rotation angle when disturbance torque is minimum and Translational movement is shown in Fig. 6 (b), and in Fig. 6 (b), variable 1~6 is α during object function minimum₁、α₂、α₃And λ₁、λ₂、λ₃Value.

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

Claims (1)

1. a kind of satellite precise tracking based on genetic algorithm installs optimization method, and its feature is to realize step as follows：

(1) requirement being laid out to satellite according to satellite control system, determines that engine installs the object function of optimization；

Engine installs the object function for optimizing：Engine installs the object function of optimization In：

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

[f_x f_y f_z]=F [sin (α) sin (γ)-sin (α) cos (γ) cos (α)] R

[p_x p_y p_z]=[δ sin (β)-δ cos (β) h] R+ [λ₁ λ₂ λ₃]

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

" min " represents minimum value；

[T_x T_y T_z]-around satellite machinery coordinate system OscXsc axles, OscYsc axles, 3 disturbance torques of reference axis of OscZsc axles；

[f_x f_y f_z]-motor power vector is in satellite machinery coordinate system OscXsc axles, OscYsc axles, three sides of OscZsc axles To thrust component；

[p_x p_y p_zThe motor power application point coordinate value of]-under satellite machinery coordinate system；

[x_C y_C z_CThe barycenter of]-satellite relative mechanical coordinate system；

The theoretical thrust of F-thruster；

The spin matrix of R-engine relative satellite mechanical coordinate system；

α₁、α₂、α₃- be respectively engine mounting and adjusting when, engine around satellite machinery coordinate system OscXsc axles, OscYsc axles and The anglec of rotation of OscZsc axles；

λ₁、λ₂、λ₃- be respectively engine mounting and adjusting when, engine along satellite machinery coordinate system OscXsc axles, OscYsc axles and The translational movement of OscZsc axles；

α-thrust vectoring angle of deviation, on the basis of engine coordinate system X-axis；

The traversing position angle of β-thrust vectoring, on the basis of engine coordinate system Y-axis, by engine top view direction counterclockwise for just；

γ-thrust vectoring deflected position angle, on the basis of engine coordinate system Y-axis, be counterclockwise by engine top view direction Just；

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

(2) according to engine geometry parameter and installation requirement, determine that engine installs the constraint function of optimization；Engine is installed excellent The constraint function of change is：

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

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

max(P_iz)≤MAX_zI=1,2 ..., 6

min(P_iz)≤MIN_zI=1,2 ..., 6

Engine is installed in the constraint function of optimization：

H_ix=r₁cos(θ_i) i=1,2,3

H_iy=r₁sin(θ_i) i=1,2,3

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

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

[P_ix P_iy P_iz]=[r₂cos(ψ_i) r₂sin(ψ_i) h]R+[λ₁ λ₂ λ₃] i=1,2 ..., 6；

ψ_i∈[θ_j,(θ_j+θ₁₀)] i=1,2 ..., 6；J=4,5 ..., 9；

" max " represents maximum；

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

θ_i3 mounting hole centers that-motor mounting flange is connected with engine support and engine coordinate system origin line and The subtended angle of engine coordinate system+Z axis, i=1,2,3；

θ_j6 lugs right side and engine coordinate system origin line and engine coordinate system+Z axis on-motor mounting flange Subtended angle, j=4,5 ..., 9；

H_ix、H_iy- when being respectively the non-rotation and translation of engine, 3 connecting holes between motor mounting flange and engine support Center satellite machinery coordinate system under X, Y-coordinate value, i=1,2,3；

r₁The radius of circle where connecting hole center between-motor mounting flange and engine support；

3 installation bore dias on D-motor mounting flange；

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

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

During the non-rotation and translation of h-engine, the Z-direction coordinate of the upper surface of motor mounting flange under satellite machinery coordinate system Value；

The thickness of l-motor mounting flange；

κ∈[0°,360°]；

P_ix、P_iy、P_iz- be respectively engine mounting and adjusting (rotation and translation) after, 6 lugs is outer on motor mounting flange X, Y, Z coordinate value of the edge under satellite machinery coordinate system, i=1,2 ..., 6；

MAX_zThe Z-direction coordinate value of-engine mounting bracket ring flange lower surface under satellite machinery coordinate system；

MIN_zZ-direction coordinate of the upper surface of the flat shim of-engine and engine support junction under satellite machinery coordinate system Value；

ψ_i6 angles of the both sides relative satellite mechanical coordinate system OscXsc of lug on-motor mounting flange, i=1,2 ..., 6；

θ₁₀Subtended angle on-motor mounting flange between the left side and right side of each lug；

r₂The radius of circle where-motor mounting flange lug outer rim；

(3) engine installation parameter optimization is carried out using MATLAB GAs Toolboxes.