CN114156651B - Satellite-borne mesh-shaped reflector antenna beam forming method based on memory alloy actuator - Google Patents

Satellite-borne mesh-shaped reflector antenna beam forming method based on memory alloy actuator Download PDF

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CN114156651B
CN114156651B CN202111342246.3A CN202111342246A CN114156651B CN 114156651 B CN114156651 B CN 114156651B CN 202111342246 A CN202111342246 A CN 202111342246A CN 114156651 B CN114156651 B CN 114156651B
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cable
antenna
reflecting surface
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nodes
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CN114156651A (en
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宗亚雳
李帅鹏
史文璐
王晨曦
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Northwestern Polytechnical University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/50—Structural association of antennas with earthing switches, lead-in devices or lightning protectors
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/12—Supports; Mounting means
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q19/00—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic
    • H01Q19/10—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces
    • H01Q19/18—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces having two or more spaced reflecting surfaces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention relates to a satellite-borne mesh-shaped reflector antenna beam forming method based on a memory alloy actuator. The defects of the existing satellite-borne mesh antenna reflecting surface supporting structure form and the existing shaping technology are overcome, part of vertical cables needing to be pressed are replaced by the actuator, the flexible reflecting surface antenna can realize the shape of a convex-concave undulated shaped reflecting surface without greatly increasing the complexity of the structure, and the reflecting surface shape required by a shaped wave beam and the supporting structure mechanical state required by supporting the shape are obtained by solving through an optimized design method based on electromechanical integration design.

Description

Satellite-borne mesh-shaped reflector antenna beam forming method based on memory alloy actuator
Technical Field
The invention relates to the technical field of satellite antennas, in particular to a method for shaping satellite-borne mesh reflector antenna beams.
Background
The satellite-borne mesh-shaped reflector antenna has limited shaping capability because the reflector is formed by stretching a cable-rod structure and the shape of the convex-concave fluctuated reflector required by shaped beams cannot be generally realized.
In the aspect of beam forming design of a satellite-borne mesh reflecting surface antenna, the patent numbers provided by inventors such as Zhang Tree et al are as follows: 201210510289.2, with a patent name: in the text of the shaping method of the cable net reflector antenna profile based on sensitivity information, the reflector is shaped based on the sensitivity information, and the supporting capability of the cable net supporting structure is not taken into consideration. In the text of A Novel continuous Beam Synthesis Method for the control of Electromagnetic-Structural Design published in 2017 of Yang Decheig, the traditional pure cable rod structure is shaped, the constraint cable force must be a positive value, but the reflecting surface of the traditional pure cable rod structure cannot meet the requirement of a rugged shaped reflecting surface, so the shaping capability of the traditional pure cable rod structure is greatly limited.
In order to solve the problem of realizing the uneven shaped reflecting surface, the inventor of Zhang-Yi group provides the following patent numbers: 201610638630.0, with the patent name: the patent numbers provided by the inventor of the invention, such as the design method of a novel mesh antenna structure with shaped beams and the Yankee antenna structure, are as follows: 201510144508.3, patent names: a satellite-borne mesh antenna forming beam design method based on electromechanical integration adopts a three-layer cable rod structure to realize an uneven reflecting surface, improves the forming capability of a satellite-borne mesh reflecting surface antenna, but increases a layer of cable rod structure compared with the traditional antenna design scheme, thereby leading to the complication of the antenna structure and the great increase of the dead weight, leading to the failure of the spreading because the more complicated the cable rod structure of the antenna is, the more easily the cable rod structure of the antenna is hooked with other structures in the process of spreading on the track, and leading to the great increase of the dead weight of the antenna, thereby leading to the great rise of the satellite transmission cost.
Disclosure of Invention
The invention aims to avoid the defects of the prior art and provides a satellite-borne mesh reflecting surface antenna beam forming method based on a memory alloy actuator, which can realize the shape of an uneven formed reflecting surface required by a formed beam without increasing the self weight of the antenna.
In order to realize the purpose, the invention adopts the technical scheme that: a satellite-borne mesh-shaped reflector antenna beam forming method based on a memory alloy actuator comprises the following steps:
the method comprises the following steps of constructing a satellite-borne mesh-shaped reflector antenna supported by a cable-strut structure, wherein the cable-strut structure comprises an upper cable-strut surface (1), a lower cable-strut surface (2), a plurality of adjusting cables (3) for connecting the upper cable-strut surface and the lower cable-strut surface and a memory alloy actuator (4), and the method comprises the following steps: the nodes arranged on the upper cable net surface and the lower cable net surface of the reflecting surface antenna aperture surface are boundary supporting nodes (5); the nodes on the upper cable net surface and the lower cable net surface are cable net free nodes (6); the upper cable mesh surface divides the metal reflecting surface of the reflecting surface antenna into a plurality of plane surface patches;
then according to the topological relation of the cable-pole structure, defining a line segment between two connected nodes in the cable-pole structure as a line unit;
secondly, giving position coordinates of the boundary support nodes, giving a force density value of the line unit, and establishing a mathematical relationship model between the force density of the line unit and the cable net free node by adopting a force density method, so as to obtain a connection relationship matrix of all nodes forming the cable rod structure and cable net free node coordinates, and obtain the overall shape S of the reflecting surface supported by the cable rod structure;
step three, generating a beam coverage area of the satellite-borne mesh-shaped reflector antenna according to the coverage area required by the ground, sampling in the beam forming area according to a Nyquist criterion, and marking out sampling points;
step four, giving incident waves of the feed source, and calculating the directivity coefficient of a sampling point in a beam forming area corresponding to the integral shape of the current reflecting surface according to the integral shape S of the reflecting surface supported by the cable-strut structure obtained in the step two;
fifthly, establishing an optimized design model of the electromechanical integrated beam forming design by taking the force density value of the line unit as a design variable and taking the minimum value of the directivity coefficient at the maximized sampling point as a target function;
solving the optimized design model in the fifth step until the optimized design model meets the convergence conditions of the design variables and the objective function, and obtaining the overall shape S of the shaped cable-pole structure and the reflection surface supported by the cable-pole structure and the mechanical state of the cable-pole structure;
step seven, judging the positive and negative of all force density values in the shaped final cable-strut structure determined in the step six: if the line unit corresponding to the force density is a regulating cable structure and named as a cable unit, otherwise, the line unit corresponding to the force density is a rod structure formed by replacing a regulating cable with a memory alloy actuator and named as a rod unit, and the satellite-borne mesh reflector antenna cable-rod structure model is completed.
Further, the second step is specifically as follows:
giving the position coordinates of the supporting point of the boundary of the cable-strut structure as
Figure 877869DEST_PATH_IMAGE001
、
Figure 850504DEST_PATH_IMAGE002
And
Figure 417752DEST_PATH_IMAGE003
given the force density value of the thread unitq i （i=1,2,…,b），q i The value is a positive value or a negative value,bestablishing the force density of the wire units and the coordinates of the free nodes of the cable net on the cable rod structure for the total number of the wire units
Figure 575064DEST_PATH_IMAGE004
、
Figure 86817DEST_PATH_IMAGE005
And
Figure 722197DEST_PATH_IMAGE006
the mathematical relationship model comprises the following specific steps:
Figure 409531DEST_PATH_IMAGE007
wherein the content of the first and second substances,
Figure 347531DEST_PATH_IMAGE008
is linear unit force densityq i The diagonal matrix is formed by the two groups of the diagonal matrix,
Figure 221946DEST_PATH_IMAGE009
is a connection relation matrix of the free nodes of the cable network,
Figure 661017DEST_PATH_IMAGE010
for the connection relation matrix of the cable-strut structure boundary support nodes, superscript
Figure 61912DEST_PATH_IMAGE011
Which represents the transpose of the matrix,
Figure 295447DEST_PATH_IMAGE012
and
Figure 657158DEST_PATH_IMAGE013
connection relation matrix of all nodes capable of forming cable pole structure
Figure 775287DEST_PATH_IMAGE014
Is that is
Figure 906054DEST_PATH_IMAGE015
；
Is provided with
Figure 310490DEST_PATH_IMAGE016
And
Figure 159498DEST_PATH_IMAGE017
first, theiThe nodes at both ends of each cell are numbered and specified
Figure 330585DEST_PATH_IMAGE018
Matrix of rules
Figure 315859DEST_PATH_IMAGE019
The element in (A) is
Figure 891196DEST_PATH_IMAGE020
；
Through the steps, the free node coordinates of the cable-strut structure can be obtained
Figure 102866DEST_PATH_IMAGE021
、
Figure 687431DEST_PATH_IMAGE022
And
Figure 792790DEST_PATH_IMAGE023
obtaining the spatial positions of a series of plane surface patches of the reflecting surface of the antenna according to the coordinates of the free node and the boundary supporting node of the cable-strut structure, and finally obtaining the spatial positions of the reflecting surfaceThe overall shape S.
Further, the third step is specifically:
31 The map boundaries that the ground needs to cover are expressed in longitude and latitude;
32 Convert the longitude and latitude coordinate values to a Cartesian Earth coordinate system;
33 Convert coordinate values in a rectangular coordinate system of the earth into coordinates in a spherical coordinate system of the satellite-borne mesh reflector antenna
Figure 663663DEST_PATH_IMAGE024
；
34 Sampling within and at the boundaries of the coverage area to obtain coordinate values of the sampling points of
Figure 487263DEST_PATH_IMAGE025
，
Figure 344360DEST_PATH_IMAGE026
，NIs the total number of sampling points;
the density of sampling points depends on the aperture of the satellite-borne mesh reflector antennaDOn the antenna apertureDWhen the radiation field is far field, the longitude and latitude interval between the sampling points is as follows from Nyquist criterion
Figure 445172DEST_PATH_IMAGE027
In which
Figure 627891DEST_PATH_IMAGE028
Is the wavelength;
the coordinate value of the sampling point of the map to be covered under the spherical coordinate system of the satellite-borne mesh reflector antenna is obtained through the steps
Figure 673208DEST_PATH_IMAGE029
。
Further, the longitude and latitude intervals between the sampling points should be
Figure 333996DEST_PATH_IMAGE030
In which
Figure 798301DEST_PATH_IMAGE031
Is the wavelength.
Further, the fourth step specifically comprises:
41 The overall shape S of the reflecting surface supported by the cable-strut structure obtained in the step two is the shape of the reflecting surface spliced by the triangular patchS；
42 By antenna apertureDThe center of the surface is the origin O and the aperture of the antennaDEstablish rectangular coordinate system O on the facexyzWhich iszThe axis coincides with the axis of the paraboloid;
43 Given feed source incident wave magnetic field
Figure 886343DEST_PATH_IMAGE032
In whichr' is the position vector of any point on the reflecting surface;
44 Given cable net free node coordinates
Figure 418955DEST_PATH_IMAGE033
、
Figure 24380DEST_PATH_IMAGE034
And
Figure 958838DEST_PATH_IMAGE035
and coordinates of the supporting point position of the boundary of the cable-strut structure
Figure 217781DEST_PATH_IMAGE036
、
Figure 362324DEST_PATH_IMAGE037
And
Figure 630494DEST_PATH_IMAGE038
the formula for calculating the directivity coefficient at the sampling point in the beam forming region corresponding to the current reflecting surface shape by using a Physical optical transmission (PO) method is as follows:
Figure 419458DEST_PATH_IMAGE039
，
wherein the content of the first and second substances,rthe surface current at' is
Figure 255827DEST_PATH_IMAGE040
，jIs a plurality of, and
Figure 763032DEST_PATH_IMAGE041
，
Figure 303735DEST_PATH_IMAGE042
is the impedance of the wave in free space,kin order to be a free-space propagation constant,
Figure 337419DEST_PATH_IMAGE043
is taken as a unit of a dyadic vector,
Figure 938164DEST_PATH_IMAGE044
for far field observation point vectorrThe unit vector of (a) is,
Figure 932665DEST_PATH_IMAGE045
as vectors
Figure 418004DEST_PATH_IMAGE046
In the direction of the vector (c) of (a),
Figure 181561DEST_PATH_IMAGE047
is composed ofr' the unit normal vector of the reflecting surface,
Figure 218787DEST_PATH_IMAGE048
representing the antenna radiating surface being integrated,
Figure 435005DEST_PATH_IMAGE049
an integral surface element on the aperture surface of the antenna is represented;
coordinates of each sampling point
Figure 973302DEST_PATH_IMAGE050
，
Figure 591366DEST_PATH_IMAGE051
Substituting the formula into the formula to obtain the electric field strength value of each sampling point;
first, thepDirectivity coefficient at each sampling point
Figure 799493DEST_PATH_IMAGE052
Can be represented by field strength as:
Figure 378373DEST_PATH_IMAGE053
wherein the content of the first and second substances,
Figure 64569DEST_PATH_IMAGE054
is composed of
Figure 68297DEST_PATH_IMAGE055
The conjugate vector of (a);
the directivity coefficient value of the map to be covered at the sampling point under the spherical coordinate system of the satellite-borne mesh reflector antenna is obtained through the steps.
Further, the fifth step is specifically:
combining the relationship between the directivity coefficient of the sampling point obtained in the third step and the force density of the line unit, the beam forming of the satellite-borne mesh antenna can be expressed as a mathematical model of electromechanical integration optimization design as follows:
Figure 571960DEST_PATH_IMAGE056
wherein the content of the first and second substances,das a design variable, a vector consisting of the force densities of the line elements,
Figure 762770DEST_PATH_IMAGE057
and
Figure 252657DEST_PATH_IMAGE058
respectively the lower and upper limits of the design variable,Nthe number of sampling points in the service area,
Figure 579733DEST_PATH_IMAGE059
for the far field related objective function,
Figure 270609DEST_PATH_IMAGE060
the amount of directivity required for beam coverage within the service area,
Figure 948715DEST_PATH_IMAGE061
and
Figure 242293DEST_PATH_IMAGE062
are respectively the firstiThe stress of the individual wire units and their allowable stress, which is related to the force density, can be expressed as
Figure 814088DEST_PATH_IMAGE063
Wherein, the first and the second end of the pipe are connected with each other,
Figure 534920DEST_PATH_IMAGE064
is a cross-sectional area of the wire unit,
Figure 700322DEST_PATH_IMAGE065
the length of the ith line unit can be determined by nodes at two ends of the ith line unit
Figure 407378DEST_PATH_IMAGE066
And
Figure 240205DEST_PATH_IMAGE067
the calculation formula is as follows:
Figure 866358DEST_PATH_IMAGE068
；
thus obtaining the electromechanical integrated optimization design model of the beam forming design.
Further, the sixth step is specifically:
selecting an optimization design method, setting design variables and convergence conditions of the objective function, and solving the optimization design model in the step four:
the convergence condition is set as
Figure 643690DEST_PATH_IMAGE069
And
Figure 279071DEST_PATH_IMAGE070
whereinkFor optimizing the designkThe steps of the method are repeated for the second time,
Figure 435245DEST_PATH_IMAGE071
and
Figure 497879DEST_PATH_IMAGE072
taking convergence precision values of design variable and objective function respectively
Figure 513240DEST_PATH_IMAGE073
(ii) a When the convergence condition is satisfied, the iteration stops, the design variable at this time
Figure 952312DEST_PATH_IMAGE074
Namely the optimal solution, and the corresponding antenna surface is the optimal shaping surface.
Further, the specific analysis step of the seventh step is as follows:
in the mesh reflector antenna, takeiIndividual line unit of force densityq i Can be adjusted by cable force
Figure 228572DEST_PATH_IMAGE075
Is shown as
Figure 852320DEST_PATH_IMAGE076
Wherein the content of the first and second substances,
Figure 214032DEST_PATH_IMAGE077
is a firstiA length between two end points of each of the line units;
when the final cable-strut structural shape after shaping determined in the step six is: can be only in tension, not in compression, and
Figure 191215DEST_PATH_IMAGE078
the cable unit of (1), i.e. the cable unit, is, on the contrary, only compressible, not tensionable, and
Figure 462927DEST_PATH_IMAGE079
the wire unit of (2), using the rod unit.
The invention has the beneficial effects that: based on the existing memory alloy actuator which is used, the invention replaces part of vertical cables which need to be pressed with the actuator, and the actuator can enable the flexible reflecting surface antenna to realize the shape of a shaped reflecting surface which is convex-concave and fluctuant, and further, by the calculation method, the shape of the reflecting surface required by a shaped beam and the mechanical state of a supporting structure required for supporting the shape can be accurately obtained, the coordination of the beam shaping of the satellite-borne mesh reflecting surface antenna and the mechanical state of a cable-rod supporting structure is realized, and the realization of the shaped reflecting surface by the supporting structure is ensured.
Drawings
FIG. 1 is a schematic view of a cable support structure incorporating a temperature controlled shape memory alloy actuator;
FIG. 2 is a diagram illustrating cable-rod internal forces of a cable-rod support structure supporting a shaped reflective surface shape.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
In order to overcome the defects that the shape of a concave-convex shaped reflecting surface cannot be realized in the conventional satellite-borne mesh antenna reflecting surface supporting structure and the defects of the conventional shaping technology, the beam shaping design method of the satellite-borne mesh antenna reflecting surface provided by the invention has the advantages that the shape of the concave-convex reflecting surface can be realized by the satellite-borne mesh expanded antenna by applying the temperature-controlled shape memory alloy actuator, the beam shaping of the satellite-borne mesh expanded antenna is realized by adopting the method provided by the invention, the antenna design efficiency is improved, and the stable realization of the matching structure of the antenna and the cable-rod supporting structure is ensured.
In order to achieve the above object, the present invention provides the following embodiments:
example 1: as shown in fig. 1 to fig. 2, a method for forming a beam of a satellite-borne mesh reflector antenna based on a memory alloy actuator includes the following steps:
the method comprises the following steps of constructing a satellite-borne mesh-shaped reflector antenna supported by a cable-strut structure, wherein the cable-strut structure comprises an upper cable-strut surface (1), a lower cable-strut surface (2), a plurality of adjusting cables (3) for connecting the upper cable-strut surface and the lower cable-strut surface and a memory alloy actuator (4), and the method comprises the following steps: the nodes arranged on the upper cable net surface and the lower cable net surface of the reflecting surface antenna aperture surface are boundary supporting nodes (5); the nodes on the upper cable net surface and the lower cable net surface are cable net free nodes (6); the upper cable mesh surface divides the metal reflecting surface of the reflecting surface antenna into a plurality of plane surface patches;
then according to the topological relation of the cable-pole structure, defining a line segment between two connected nodes in the cable-pole structure as a line unit; the memory alloy actuator is disclosed in the patent numbers: 202110373436.5, patent name: a large space-borne mesh reflector antenna memory alloy actuator is provided.
Secondly, giving position coordinates of the boundary support nodes, giving a force density value of the line unit, establishing a mathematical relationship model between the force density of the line unit and the cable net free node by adopting a force density method, further obtaining a connection relationship matrix of all nodes forming the cable rod structure and cable net free node coordinates, and simultaneously obtaining the overall shape S of the reflecting surface supported by the cable rod structure;
the second step is specifically as follows:
giving the position coordinates of the supporting point of the boundary of the cable-strut structure as
Figure 867364DEST_PATH_IMAGE080
、
Figure 716371DEST_PATH_IMAGE081
And
Figure 362159DEST_PATH_IMAGE082
given the force density value of the thread unitq i （i=1,2,…,b），q i The value is a positive value or a negative value,bestablishing the force density of the wire units and the coordinates of the free nodes of the cable net on the cable rod structure for the total number of the wire units
Figure 878591DEST_PATH_IMAGE083
、
Figure 453929DEST_PATH_IMAGE084
And
Figure 665599DEST_PATH_IMAGE085
the mathematical relationship model comprises the following specific steps:
Figure 984585DEST_PATH_IMAGE086
wherein the content of the first and second substances,
Figure 355523DEST_PATH_IMAGE087
is linear unit force densityq i The diagonal matrix is formed by the two groups of the diagonal matrix,
Figure 226396DEST_PATH_IMAGE088
is a connection relation matrix of the free nodes of the cable network,
Figure 784416DEST_PATH_IMAGE089
for the connection relation matrix of the cable-strut structure boundary support nodes, superscript
Figure 172672DEST_PATH_IMAGE090
Which represents the transpose of the matrix,
Figure 7904DEST_PATH_IMAGE091
and
Figure 190624DEST_PATH_IMAGE092
connection relation matrix of all nodes capable of forming cable pole structure
Figure 501520DEST_PATH_IMAGE093
Is that is
Figure 286942DEST_PATH_IMAGE094
；
Is provided with
Figure 366893DEST_PATH_IMAGE016
And
Figure 720514DEST_PATH_IMAGE095
first, theiThe nodes at both ends of each cell are numbered and specified
Figure 128493DEST_PATH_IMAGE096
Matrix of time
Figure 858552DEST_PATH_IMAGE097
The element in (A) is
Figure 527430DEST_PATH_IMAGE098
；
Through the steps, the free node coordinates of the cable-strut structure can be obtained
Figure 176586DEST_PATH_IMAGE099
、
Figure 196495DEST_PATH_IMAGE100
And
Figure 199086DEST_PATH_IMAGE101
and obtaining the spatial positions of a series of plane surface patches of the antenna reflecting surface according to the coordinates of the free node and the boundary supporting node of the cable-strut structure, and finally obtaining the overall shape S of the reflecting surface.
Step three, generating a beam coverage area of the satellite-borne mesh-shaped reflector antenna according to the coverage area required by the ground, sampling in the beam forming area according to a Nyquist criterion, and marking out sampling points;
the third step is specifically as follows:
31 The map boundaries that the ground needs to cover are expressed in longitude and latitude;
32 Convert the longitude and latitude coordinate values to a Cartesian Earth coordinate system;
33 Convert coordinate values in a rectangular coordinate system of the earth into coordinates in a spherical coordinate system of the satellite-borne mesh reflector antenna
Figure 988050DEST_PATH_IMAGE102
；
34 Sampling within and at the boundaries of the coverage area to obtain coordinate values of the sampling points of
Figure 824419DEST_PATH_IMAGE103
，
Figure 66045DEST_PATH_IMAGE104
，NIs the total number of sampling points;
the density of sampling points depends on the aperture of the satellite-borne mesh reflector antennaDOn the antenna apertureDWhen the radiation field is far field, the longitude and latitude interval between the sampling points is as follows from Nyquist criterion
Figure 872327DEST_PATH_IMAGE105
Wherein
Figure 171590DEST_PATH_IMAGE106
Is the wavelength;
the coordinate value of the sampling point of the map to be covered under the spherical coordinate system of the satellite-borne mesh reflector antenna is obtained through the steps
Figure 772336DEST_PATH_IMAGE107
。
Step four, giving incident waves of the feed source, and calculating the directivity coefficient of a sampling point in a beam forming area corresponding to the integral shape of the current reflecting surface according to the integral shape S of the reflecting surface supported by the cable-strut structure obtained in the step two;
the fourth step is specifically as follows:
41 The overall shape S of the reflecting surface supported by the cable-strut structure obtained in the step two is the shape of the reflecting surface spliced by the triangular patchesS；
42 By antenna apertureDThe center of the plane is the origin O at the aperture of the antennaDEstablish rectangular coordinate system O on the facexyzWhich iszThe axis coincides with the axis of the paraboloid;
43 Given the incident wave magnetic field of the feed source
Figure 766836DEST_PATH_IMAGE108
Whereinr' is the position vector of any point on the reflecting surface;
44 Given cable net free node coordinates
Figure 986596DEST_PATH_IMAGE109
、
Figure 750153DEST_PATH_IMAGE034
And
Figure 787379DEST_PATH_IMAGE110
and coordinates of the supporting point position of the boundary of the cable-strut structure
Figure 393810DEST_PATH_IMAGE111
、
Figure 541894DEST_PATH_IMAGE112
And
Figure 159958DEST_PATH_IMAGE113
the formula for calculating the directivity coefficient at the sampling point in the beam forming region corresponding to the current reflecting surface shape by using a Physical optical transmission (PO) method is as follows:
Figure 509030DEST_PATH_IMAGE114
，
wherein the content of the first and second substances,rthe surface current at' is
Figure 212544DEST_PATH_IMAGE115
，jIs a plurality of, and
Figure 898741DEST_PATH_IMAGE116
，
Figure 636889DEST_PATH_IMAGE117
is the impedance of the wave in free space,kin order to be a free-space propagation constant,
Figure 874973DEST_PATH_IMAGE118
is taken as a unit of a dyadic vector,
Figure 65783DEST_PATH_IMAGE119
for far field observation point vectorrThe unit vector of (a) is,
Figure 555670DEST_PATH_IMAGE120
as vectors
Figure 289271DEST_PATH_IMAGE121
In the direction of the vector (c) of (a),
Figure 839201DEST_PATH_IMAGE122
is composed ofr' the unit normal vector of the reflecting surface,
Figure 517307DEST_PATH_IMAGE123
representing the antenna radiating surface being integrated,
Figure 935519DEST_PATH_IMAGE124
an integral surface element on the aperture surface of the antenna is represented;
coordinates of each sampling point
Figure 382680DEST_PATH_IMAGE125
，
Figure 103512DEST_PATH_IMAGE126
Substituting the formula into the above formula to obtain the electric field strength value at each sampling point;
first, thepDirectivity coefficient at each sampling point
Figure 268914DEST_PATH_IMAGE127
Can be represented by field strength as:
Figure 975970DEST_PATH_IMAGE128
wherein the content of the first and second substances,
Figure 543217DEST_PATH_IMAGE129
is composed of
Figure 434950DEST_PATH_IMAGE130
The conjugate vector of (a);
the directivity coefficient value of the map to be covered at the sampling point under the spherical coordinate system of the satellite-borne mesh reflector antenna is obtained through the steps.
Fifthly, establishing an optimized design model of the electromechanical integrated beam forming design by taking the force density value of the line unit as a design variable and taking the minimum value of the directivity coefficient at the maximized sampling point as a target function;
the fifth step is specifically as follows:
combining the relationship between the directivity coefficient of the sampling point obtained in the third step and the force density of the line unit, the beam forming of the satellite-borne mesh antenna can be expressed as a mathematical model of electromechanical integration optimization design as follows:
Figure 229860DEST_PATH_IMAGE131
wherein the content of the first and second substances,das a design variable, a vector consisting of the force densities of the line elements,
Figure 599662DEST_PATH_IMAGE132
and
Figure 21416DEST_PATH_IMAGE133
respectively the lower and upper limits of the design variable,Nthe number of sampling points in the service area,
Figure 224995DEST_PATH_IMAGE134
for the far field related objective function,
Figure 99410DEST_PATH_IMAGE135
the amount of directivity required for beam coverage within the service area,
Figure 538482DEST_PATH_IMAGE136
and
Figure 204955DEST_PATH_IMAGE137
are respectively the firstiThe stress of the individual wire units and their allowable stress, which is related to the force density, can be expressed as
Figure 438491DEST_PATH_IMAGE138
Wherein the content of the first and second substances,
Figure 800202DEST_PATH_IMAGE139
is a cross-sectional area of the wire unit,
Figure 652751DEST_PATH_IMAGE140
the length of the ith line unit can be divided into two end nodes
Figure 49097DEST_PATH_IMAGE141
And
Figure 453534DEST_PATH_IMAGE142
the calculation formula is as follows:
Figure 302541DEST_PATH_IMAGE143
；
thus obtaining the electromechanical integrated optimization design model of the beam forming design.
Solving the optimized design model in the fifth step until the optimized design model meets the convergence conditions of the design variables and the objective function, and obtaining the overall shape S of the shaped cable-pole structure and the reflection surface supported by the cable-pole structure and the mechanical state of the cable-pole structure;
the sixth step is specifically as follows:
selecting an optimization design method, setting design variables and convergence conditions of the objective function, and solving the optimization design model in the step four:
the convergence condition is set as
Figure 942470DEST_PATH_IMAGE144
And
Figure 193323DEST_PATH_IMAGE145
whereinkFor optimizing the designkThe steps are repeated for the next time,
Figure 768661DEST_PATH_IMAGE146
and
Figure 245910DEST_PATH_IMAGE147
taking convergence precision values of design variable and objective function respectively
Figure 564895DEST_PATH_IMAGE148
(ii) a When the convergence condition is satisfied, the iteration stops, the design variable at this time
Figure 670255DEST_PATH_IMAGE149
Namely the optimal solution, and the corresponding antenna surface is the optimal shaping surface.
Step seven, judging the positive and negative of all force density values in the shaped final cable-strut structure determined in the step six: if the line unit corresponding to the force density is a positive value, the line unit corresponding to the force density is an adjusting rope structure and is named as a rope unit, otherwise, the line unit corresponding to the force density is a rod structure formed by replacing an adjusting rope with a memory alloy actuator and is named as a rod unit, and the satellite-borne netted reflecting surface antenna rope-rod structure model is completed;
the concrete analysis steps of the seventh step are as follows:
in the mesh reflector antenna, takeiIndividual line unit of force densityq i Can be adjusted by cable force
Figure 806707DEST_PATH_IMAGE150
Is shown as
Figure 364727DEST_PATH_IMAGE151
Wherein the content of the first and second substances,
Figure 487404DEST_PATH_IMAGE152
is as followsiA length between two end points of each of the line units;
when the final cable-strut structural shape after shaping determined in the step six is: can be only in tension, not in compression, and
Figure 447270DEST_PATH_IMAGE153
the cable unit of (1), i.e. the cable unit, is, on the contrary, only compressible, not tensionable, and
Figure 239776DEST_PATH_IMAGE154
the wire unit of (2), using the rod unit.
Experimental example: the advantages of the present invention can be further illustrated by the following simulation experiments:
1. simulation parameters
The working frequency of the antenna is 3GHz, and the caliber D is 25
Figure 816251DEST_PATH_IMAGE155
Focal length 25
Figure 477040DEST_PATH_IMAGE155
Offset distance of 15.5
Figure 681625DEST_PATH_IMAGE156
The feed source is a Gaussian feed source, and the taper pin is-12 dB. This case takes a typical chinese map as the coverage target area.
2. Simulation result
Interval according to Nyquist criterion
Figure 35246DEST_PATH_IMAGE157
Sampling is carried out, the final sampling result is that 24 sampling points exist on the map boundary, the whole map has 97 sampling points, and the corresponding cable-rod unit internal force distribution is shown in figure 2.
3. Analysis of results
Conclusion 1: the directivity coefficient values in the shaped area are all above the required values, the design requirements are met, the shape of the isoline with the directivity coefficient of 27.82 is matched with the shaped area, and the interference to adjacent areas is reduced.
Conclusion 2: as can be seen from the results in fig. 2, there are 6 units with negative force densities, i.e. a temperature controlled shape memory alloy actuator that can withstand pressure needs to be used at these 6 units.
Conclusion 3: simulation data show that the optimized forming result meets the expected target, and the feasibility and the effectiveness of the theory and the method provided by the patent are verified.
Example 2: the same as in example 1, except that: the longitude and latitude interval between the sampling points is
Figure 567858DEST_PATH_IMAGE158
Wherein
Figure 642125DEST_PATH_IMAGE159
Is the wavelength. The sampling interval is taken to ensure the sampling precision without greatly increasing the number of sampling points.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (6)

1. A satellite-borne mesh reflector antenna beam forming method based on a memory alloy actuator is characterized by comprising the following steps:
the method comprises the following steps of constructing a satellite-borne mesh-shaped reflector antenna supported by a cable-strut structure, wherein the cable-strut structure comprises an upper cable-strut surface (1), a lower cable-strut surface (2), a plurality of adjusting cables (3) for connecting the upper cable-strut surface and the lower cable-strut surface and a memory alloy actuator (4), and the method comprises the following steps: the nodes arranged on the upper cable net surface and the lower cable net surface of the reflecting surface antenna aperture surface are boundary supporting nodes (5); the nodes on the upper cable net surface and the lower cable net surface are cable net free nodes (6); the upper cable mesh surface divides the metal reflecting surface of the reflecting surface antenna into a plurality of plane surface patches;
then according to the topological relation of the cable-pole structure, defining a line segment between two connected nodes in the cable-pole structure as a line unit;
secondly, giving position coordinates of the boundary support nodes, giving a force density value of the line unit, establishing a mathematical relationship model between the force density of the line unit and the cable net free node by adopting a force density method, further obtaining a connection relationship matrix of all nodes forming the cable rod structure and cable net free node coordinates, and simultaneously obtaining the overall shape S of the reflecting surface supported by the cable rod structure;
step three, generating a beam coverage area of the satellite-borne mesh-shaped reflector antenna according to the coverage area required by the ground, sampling in the beam forming area according to a Nyquist criterion, and marking out sampling points;
step four, giving incident waves of the feed source, and calculating the directivity coefficient of a sampling point in a beam forming area corresponding to the integral shape of the current reflecting surface according to the integral shape S of the reflecting surface supported by the cable-strut structure obtained in the step two;
fifthly, establishing an optimized design model of the electromechanical integrated beam forming design by taking the force density value of the line unit as a design variable and taking the minimum value of the directivity coefficient at the maximized sampling point as a target function;
solving the optimized design model in the fifth step until the optimized design model meets the convergence conditions of the design variables and the objective function, and obtaining the overall shape S of the shaped cable-pole structure and the reflection surface supported by the cable-pole structure and the mechanical state of the cable-pole structure;
step seven, judging the positive and negative of all force density values in the shaped final cable-strut structure determined in the step six: if the line unit corresponding to the force density is a positive value, the line unit corresponding to the force density is an adjusting rope structure and is named as a rope unit, otherwise, the line unit corresponding to the force density is a rod structure formed by replacing an adjusting rope with a memory alloy actuator and is named as a rod unit, and the satellite-borne netted reflecting surface antenna rope-rod structure model is completed;
the second step is specifically as follows:
giving the position coordinates of the supporting point of the boundary of the cable-strut structure as
Figure 129727DEST_PATH_IMAGE001
、
Figure 702659DEST_PATH_IMAGE002
And
Figure 13555DEST_PATH_IMAGE003
given the force density value of the thread unitq i （i=1,2,…,b），q i The value is a positive value or a negative value,bestablishing the force density of the wire units and the coordinates of the free nodes of the cable net on the cable rod structure for the total number of the wire units
Figure 815289DEST_PATH_IMAGE004
、
Figure 160819DEST_PATH_IMAGE005
And
Figure 373495DEST_PATH_IMAGE006
the mathematical relationship model comprises the following specific steps:
Figure 171687DEST_PATH_IMAGE007
wherein, the first and the second end of the pipe are connected with each other,
Figure 777112DEST_PATH_IMAGE008
is linear unit force densityq i The diagonal matrix is formed by the two groups of the diagonal matrix,
Figure 977149DEST_PATH_IMAGE010
is a connection relation matrix of the free nodes of the cable network,
Figure 626305DEST_PATH_IMAGE011
for the connection relation matrix of the cable-strut structure boundary support nodes, superscript
Figure 911793DEST_PATH_IMAGE012
Which represents the transpose of the matrix,
Figure 914384DEST_PATH_IMAGE010
and
Figure 844294DEST_PATH_IMAGE011
connection relation matrix of all nodes capable of forming cable pole structure
Figure 805296DEST_PATH_IMAGE013
That is to say that
Figure 696855DEST_PATH_IMAGE014
；
Is provided with
Figure 237557DEST_PATH_IMAGE015
And
Figure 146608DEST_PATH_IMAGE016
first, theiThe nodes at both ends of each cell are numbered and specified
Figure 888299DEST_PATH_IMAGE018
Matrix of rules
Figure 148379DEST_PATH_IMAGE013
The element in (A) is
Figure 617406DEST_PATH_IMAGE019
；
Through the steps, the free node coordinates of the cable-strut structure can be obtained
Figure 646542DEST_PATH_IMAGE004
、
Figure 683768DEST_PATH_IMAGE005
And
Figure 40931DEST_PATH_IMAGE006
obtaining the spatial positions of a series of plane surface patches of the antenna reflecting surface according to the coordinates of the free nodes and the boundary supporting nodes of the cable-strut structure, and finally obtaining the overall shape S of the reflecting surface;
the fourth step is specifically as follows:
41 The overall shape S of the reflecting surface supported by the cable-strut structure obtained in the step two is the shape of the reflecting surface spliced by the triangular patchS；
42 By antenna apertureDThe center of the surface is the origin O and the aperture of the antennaDEstablish rectangular coordinate system O on the facexyzWhich iszThe axis coincides with the axis of the paraboloid;
43 Given feed source incident wave magnetic field
Figure 189016DEST_PATH_IMAGE021
Whereinr' is the position vector of any point on the reflecting surface;
44 Given a cable net fromFrom node coordinates
Figure 197292DEST_PATH_IMAGE004
、
Figure 405419DEST_PATH_IMAGE005
And
Figure 374512DEST_PATH_IMAGE006
and coordinates of the supporting point position of the boundary of the cable-strut structure
Figure 936075DEST_PATH_IMAGE001
、
Figure 939803DEST_PATH_IMAGE002
And
Figure 709045DEST_PATH_IMAGE003
the formula for calculating the directivity coefficient at the sampling point in the beam forming region corresponding to the current reflecting surface shape by using a Physical optical transmission (PO) method is as follows:
Figure 899855DEST_PATH_IMAGE022
，
wherein the content of the first and second substances,rthe surface current at' is
Figure 655321DEST_PATH_IMAGE023
，jIs a plurality of, and
Figure 857763DEST_PATH_IMAGE024
，
Figure 673273DEST_PATH_IMAGE025
is the impedance of the wave in free space,kin order to be a free-space propagation constant,
Figure 351379DEST_PATH_IMAGE026
is taken as a unit of a dyadic vector,
Figure 35170DEST_PATH_IMAGE027
for far field observation point vectorrThe unit vector of (a) is,
Figure 482332DEST_PATH_IMAGE028
as a vector
Figure 937584DEST_PATH_IMAGE027
The vector of (a) is a vector of (b),
Figure 243931DEST_PATH_IMAGE030
is composed ofr' the unit normal vector of the reflecting surface,
Figure 75621DEST_PATH_IMAGE031
representing the antenna radiating surface being integrated,
Figure 33082DEST_PATH_IMAGE033
an integral surface element on the aperture surface of the antenna is represented;
coordinates of each sampling point
Figure 659235DEST_PATH_IMAGE034
，
Figure 311933DEST_PATH_IMAGE035
Substituting the formula into the formula to obtain the electric field strength value of each sampling point;
first, thepDirectivity coefficient at each sampling point
Figure 88259DEST_PATH_IMAGE036
Can be represented by field strength as:
Figure 244434DEST_PATH_IMAGE037
wherein the content of the first and second substances,
Figure 572647DEST_PATH_IMAGE038
is composed of
Figure 571696DEST_PATH_IMAGE039
The conjugate vector of (a);
the directivity coefficient value of the map to be covered at the sampling point under the spherical coordinate system of the satellite-borne mesh reflector antenna is obtained through the steps.
2. The method for forming a beam of a space-borne mesh reflector antenna based on a memory alloy actuator according to claim 1, wherein the third step is:
31 The map boundaries that the ground needs to cover are expressed in longitude and latitude;
32 Convert the longitude and latitude coordinate values to a Cartesian Earth coordinate system;
33 Convert coordinate values in a rectangular coordinate system of the earth into coordinates in a spherical coordinate system of the satellite-borne mesh reflector antenna
Figure 10768DEST_PATH_IMAGE040
；
34 Sampling within and at the boundaries of the coverage area to obtain coordinate values of the sampling points
Figure 552608DEST_PATH_IMAGE041
，
Figure 661509DEST_PATH_IMAGE042
，NIs the total number of sampling points;
the density of sampling points depends on the aperture of the satellite-borne mesh reflector antennaDOn the antenna apertureDWhen the radiation field is far field, the longitude and latitude interval between the sampling points is as follows from Nyquist criterion
Figure 288800DEST_PATH_IMAGE043
Wherein
Figure 265983DEST_PATH_IMAGE044
Is the wavelength;
the coordinate value of the sampling point of the map to be covered under the spherical coordinate system of the satellite-borne mesh reflector antenna is obtained through the steps
Figure 786963DEST_PATH_IMAGE045
。
3. The method as claimed in claim 2, wherein the latitudinal and longitudinal intervals between the sampling points are set as
Figure 191399DEST_PATH_IMAGE046
Wherein
Figure 181352DEST_PATH_IMAGE044
Is the wavelength.
4. The method for forming a satellite-borne mesh reflecting surface antenna beam based on a memory alloy actuator as claimed in claim 1, wherein the fifth step is specifically as follows:
combining the relationship between the directivity coefficient of the sampling point obtained in the third step and the force density of the line unit, the beam forming of the satellite-borne mesh antenna can be expressed as a mathematical model of electromechanical integration optimization design as follows:
Figure 696647DEST_PATH_IMAGE047
wherein the content of the first and second substances,das a design variable, a vector consisting of the force densities of the line elements,
Figure 213079DEST_PATH_IMAGE049
and
Figure 918910DEST_PATH_IMAGE051
respectively the lower and upper limits of the design variable,Nthe number of sampling points in the service area,
Figure 520793DEST_PATH_IMAGE052
for the far field related objective function,
Figure 839779DEST_PATH_IMAGE053
the amount of directivity required for beam coverage within the service area,
Figure 86083DEST_PATH_IMAGE054
and
Figure 832322DEST_PATH_IMAGE056
are respectively the firstiThe stress of the individual wire units and their allowable stress, which is related to the force density, can be expressed as
Figure 390343DEST_PATH_IMAGE057
Wherein the content of the first and second substances,
Figure 903233DEST_PATH_IMAGE059
is a cross-sectional area of the wire unit,
Figure 863098DEST_PATH_IMAGE061
the length of the ith line unit can be divided into two end nodes
Figure 921184DEST_PATH_IMAGE015
And
Figure 232080DEST_PATH_IMAGE016
the calculation formula is as follows:
Figure 158448DEST_PATH_IMAGE062
；
thus obtaining the electromechanical integrated optimization design model of the beam forming design.
5. The method for forming a beam of a space-borne mesh reflector antenna based on a memory alloy actuator according to claim 1, wherein the sixth step comprises:
selecting an optimization design method, setting design variables and convergence conditions of the objective function, and solving the optimization design model in the step four:
the convergence condition is set as
Figure 97454DEST_PATH_IMAGE063
And
Figure DEST_PATH_IMAGE064
whereinkFor optimizing the designkThe steps are repeated for the next time,
Figure DEST_PATH_IMAGE065
and
Figure DEST_PATH_IMAGE066
taking convergence precision values of design variable and objective function respectively
Figure DEST_PATH_IMAGE068
(ii) a When the convergence condition is satisfied, the iteration stops, the design variable at this time
Figure DEST_PATH_IMAGE069
Namely, the optimal solution, and the corresponding antenna surface is the optimal forming surface.
6. The method for forming a satellite-borne mesh reflecting surface antenna beam based on a memory alloy actuator as claimed in claim 1, wherein the concrete analysis steps of the seventh step are as follows:
in the mesh reflector antenna, takeiIndividual line unit of force densityq i Can adjust the cable force
Figure DEST_PATH_IMAGE071
Is shown as
Figure DEST_PATH_IMAGE072
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE073
is as followsiA length between two end points of each of the line units;
when the final cable-strut structural shape after shaping determined in the step six is: can be only in tension, not in compression, and
Figure DEST_PATH_IMAGE074
the cable unit of (1), i.e. the cable unit, is, on the contrary, only compressible, not tensionable, and
Figure DEST_PATH_IMAGE075
the wire unit of (2), using the rod unit.
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