CN106299722B - Fast determination method towards paraboloidal large-scale figuration surface antenna active panel adjustment amount - Google Patents
Fast determination method towards paraboloidal large-scale figuration surface antenna active panel adjustment amount Download PDFInfo
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
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- 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
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- H—ELECTRICITY
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Abstract
The invention discloses a kind of fast determination methods towards paraboloidal large-scale figuration surface antenna active panel adjustment amount, including determine antenna model and actuator support node；Determine figuration face fit equation and the paraboloidal normal equation of target；Extract the nodal information of all active panels of Shaped reflector；Extract the nodal information of e block panel；Calculate the best-fit paraboloid of the active panel；Determine the actuator support node of e block panel；It determines figuration surface antenna panel and the paraboloidal corresponding node of target, calculates the root-mean-square error of all nodes in overall reflective face after actuator adjustment amount and adjustment；Judge whether antenna gain meets the requirements, exports actuator optimal adjustable value.The present invention can be calculated directly and accurately towards paraboloidal large-scale figuration surface antenna active surface actuator optimal adjustable value, significantly improve antenna electric performance, ensure the accurate transformation function of antenna type below two kinds of different working modes, there is important academic significance and engineering application value.
Description
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to a method for quickly determining adjustment quantity of an active panel of a large-scale shaped surface antenna facing a paraboloid, which is used for actively adjusting the position of a reflecting surface panel of the large-scale shaped surface antenna and realizing the accurate conversion function of the surface type of the antenna panel in two working modes, and has important academic significance and engineering application value.
Background
The large reflector antenna is mainly used in communication radar, astronomical observation, strategic remote early warning and other heavy projects, and in recent years, with the complexity of the working environment and the diversification of working modes of the reflector antenna, different functions put forward different profile requirements on the large antenna, so that the development of the large reflector antenna is promoted, and the shaped surface antenna is produced. The shaped reflector antenna is used for shaping the reflector of the antenna, improving the effective radiation of a certain area by optimizing the shape of the reflector, reducing the radiation interference outside the area, and meeting the design requirements of high gain, high isolation, low side lobe and the like of a radiation coverage area. The large reflector antenna has the characteristics of high gain and narrow beam, and antenna designers gradually start to adopt a shaping surface design in the construction of the large reflector antenna or the constructed large reflector antenna at home and abroad at present, so that the antenna meets more use functions.
The shaping and active surface adjustment of the reflecting surface of the large antenna become research hotspots gradually in recent years, and related research focuses mainly on reconstruction and optimal design of the shaping reflecting surface and an optimal compensation method for realizing electrical performance by adjusting the panel of the active surface and the feed source or the auxiliary reflecting surface. In the existing achievements, in the 'shape-preserving and electromechanical comprehensive optimization design of large antenna reflecting surface' of the cold country and the 'shaping double-reflecting surface antenna structure deformation real-time compensation method based on secondary surface' of the Lihui, the main reflecting surface of the deformed shaping antenna is subjected to segment fitting, and the secondary surface obtained according to the matching relation between the main reflecting surface and the secondary surface on the basis is inaccurate, the optimal antenna electrical property cannot be obtained, and the calculation rate is slow; yan Feng et al 'an accurate calculation method for adjusting the main surface precision and the main and auxiliary surfaces of a shaped card antenna' considers the adjustment of the main and auxiliary surfaces of the antenna based on the best fitting paraboloid of a shaped surface panel, but the method cannot really achieve the accurate adjustment of the antenna panel, and the electrical property of the adjusted antenna cannot guarantee the best.
Therefore, it is necessary to combine with an electromechanical coupling theory, a method for directly calculating the optimal adjustment quantity of the actuator of the large-scale shaped surface antenna active panel facing the paraboloid is provided by determining the best fitting paraboloid with the minimum root mean square error of fitting with the shaped surface, so that the integral antenna reflecting surface formed by the shaped surface panel after active adjustment is closer to the target paraboloid, the electrical property of the antenna is improved, the method is used for guiding the accurate conversion of the surface type of the large-scale shaped surface antenna in two working modes in actual engineering, and the process is the method for quickly determining the adjustment quantity of the large-scale shaped surface antenna active panel facing the paraboloid.
Disclosure of Invention
Aiming at the determination of a method for adjusting a shaping surface to a paraboloid, the invention provides a method for quickly determining the adjustment quantity of an active panel of a large shaping surface antenna facing the paraboloid.
In order to achieve the above object, the method for rapidly calculating the adjustment amount of the active panel of the large paraboloid-oriented antenna comprises the following steps:
(1) establishing an antenna structure finite element model under an ideal condition in mechanical analysis software according to the structure scheme of the large reflector antenna and the position of the actuator, and determining an actuator supporting node;
(2) because the antenna reflecting surface is a shaping surface, a Zernike polynomial is adopted to determine a fitting equation of the shaping surface;
(3) extracting node information of all active panels of the shaping reflecting surface by using an antenna structure finite element model and an actuator support node;
(4) for the e-th panel on the antenna panel, extracting node information of the active panel;
(5) calculating the best fitting paraboloid of the active panel by using a least square method based on the node information on the active panel and the focal length of the target paraboloid;
(6) determining an actuator support node for the e-th panel;
(7) determining the expansion and contraction direction of the point actuator (the normal direction of the point where the actuator is located) and a linear equation of the point where the actuator is located according to the position of the support node of the actuator, and calculating the adjustment amount of the panel actuator through the intersection point distance between a straight line and the best-fit paraboloid as well as the intersection point distance between the straight line and the target paraboloid;
(8) judging whether the panel is the last panel, if so, calculating the root mean square error of the adjusted integral reflecting surface, and turning to the step (9); if not, turning to the step (4) to start the calculation of the adjustment quantity of the next panel;
(9) calculating the root mean square error between the shaping surface and the target paraboloid according to all the node information of the adjusted shaping surface;
(10) calculating the adjusted antenna gain of the shaping reflector based on the antenna electromechanical coupling model;
(11) judging whether the antenna gain meets the index requirement, if not, changing the position of the actuator, updating the antenna structure model, and turning to the step (3); if the requirements are met, the adjustment quantity of the actuator is output, and therefore the optimal adjustment quantity of the shaped antenna active panel facing the paraboloid is obtained.
In the step (1), the structural finite element model of the reflector antenna comprises panel node information, back frame node information and actuator support node information, and the panel node information, the back frame node information and the actuator support node information are determined to be used for antenna calculation.
The step (2) of determining a fitting equation of the shaped surface comprises the following processes:
(2a) setting the parameters of the caliber surface as t and psi, then setting any point P on the shaping surfaces(xs,ys,zs) Can be expressed as:
xs＝xs(t,ψ),ys＝ys(t,ψ),zs＝zs(t,ψ)
therefore, the method comprises the following steps:
wherein: t is more than or equal to 0 and less than or equal to 1, psi is more than or equal to 0 and less than or equal to 2 pi, a and b are respectively half-axial lengths along the x and y directions on the projection caliber A, (x)0,y0) The coordinate of the center of a circle of the projection caliber A;
(2b) for the equation with the antenna reflection surface as a shaping surface, the equation is expressed by using Zernike polynomials as follows:
wherein (x)s,ys,zs) The points represented represent points on the shaping surface, z1(x, y, j, i) is a function expressed by a Zernike polynomial, j and i are orders expressed by the Zernike polynomial, f is working frequency, lambda is wavelength, and the distance from the H feed source to the center of the elliptic caliber surface;
wherein,is a radial polynomial, Cij、DijThe fitting coefficient of the shaping surface can be obtained by the following formula:
wherein,ρ is the polar length in polar coordinates.
The step (5) of calculating the best fitting paraboloid of the active panel comprises the following processes:
(5a) extracting theoretical coordinates P (x) of N sampling nodes on an ideal design surface based on an antenna structure finite element modeli,yi,zi) Extracting N sampling points P on the antenna reflecting surface according to the node information of the antenna reflecting surface1(x0,y0,z0) Let P be0(x0',y0',z0') is one of N sampling nodes on the best-fit paraboloid of the antenna, and the coordinate error of the best-fit paraboloid is r (P) by utilizing the antenna shaping surface1)-r(P0) According to the least square principle, an equation set A. β ═ H is constructed,
β＝(Δx Δy Δz φx φy)Τ，
wherein A is coefficient, β is parameters of the best fitting paraboloid of the antenna, N is the number of sampling points, f1Is the focal length of the best fitting paraboloid, namely the focal length of the target paraboloid, and is respectively the displacement of the target paraboloid node in the coordinate system relative to the best fitting paraboloid node of the antenna shaping surface, phix、φyThe rotation angles of the focal axes of the best fitting paraboloids of the antenna shaping surface around the coordinate axes x and y respectively, T is a matrix transposition symbol, and z isi' best-fit z-axis coordinates of points on the paraboloid for the antenna;
(5b) solving the equation set to obtain parameters β of the best fitting paraboloid of the antenna, and changing β to (delta x delta y delta z phi)x φy)ΤSubstituting the parameters into an equation and determining the best fitting parabolic equation of the antenna shaping surface as follows:
where h is the distance in the z direction between the target parabola and the best-fit parabola.
The step (7) of calculating the adjustment amount of the e-th panel actuator comprises the following processes:
(7a) the actuator has the equation of a paraboloid as follows:
wherein f is2The focal length of the paraboloid where the actuator is located; x is the number of0,y0Is a sampling point P1(x0,y0,z0) X of0,y0Coordinates;
normal to the nodal point on the paraboloid on which the panel is supported by the actuatorDirection cosine, obtaining the direction cosine (u) of the normal line of the shaped surface moving from the initial position to the adjusted positioni,vi,wi)：
Through actuator support node Oi(xi,yi,zi) Normal equation of (c):
(7b) solving the normal equation to obtain an intersection O ' (x ') of a normal direction straight line passing through the antenna actuator support node and an initial best-fit paraboloid of the shaping surface '0,y'0,z'0) And the intersection O "(x ″) of the shifted best-fit parabolas0,y″0,z″0) The distance (distance between AA ') that the shaped surface panel moves under the action of the actuator is exactly equivalent to the distance between OO ', namely the distance between the OO ' and the shaped surface panel
(7c) Determining the adjustment coefficient delta, i.e. the intersection O "(x ″) of the target parabola and the straight line on which the actuator moves0,y″0,z″0) Is located at an intersection O ' (x ') along the antenna forming surface and the normal direction of the actuator '0,y'0,z'0) And actuator support point Oi(xi,yi,zi) When the line is formed outside, delta is 1, and the intersection point O' (x) of the target paraboloid and the normal direction of the actuator0”,y0”,z0") is located between OO' segments, then δ is taken to be-1;
(7d) upper node A ' (x ') of shaping surface 'a,y'a,z'a) Normal deviation of the corresponding points with respect to the antenna target reflection plane O ":
(7e) according to the determined adjustment coefficient delta and the normal deviation of the corresponding point of the node A 'on the shaping surface relative to the target paraboloid O' of the antenna:
the step (9) of calculating the root mean square error between the shape-imparting surface and the target paraboloid comprises the following processes:
(9a) solving the normal equation obtained in the step (7a) to obtain the intersection point coordinates of the actuator motion direction straight line and the best fitting paraboloid and the node A ' (x ') on the shaping surface after the antenna panel moves 'a,y'a,z'a) Corresponding point O "(x ″) of the corresponding antenna target paraboloid0,y″0,z″0) And calculating the normal deviation of the node A 'on the shaping surface relative to the corresponding point of the target paraboloid O' of the antenna by using the following formula:
(9b) according to the normal deviation of each node, calculating the normal root mean square error of the shaped surface of the whole antenna as follows:
in the step (11), the panel is axially adjusted to a new position along the actuator to form a paraboloid again, the antenna back frame structure is not changed at the moment, the position parameters of the antenna panel are changed, and the finite element model of the antenna structure is updated.
The invention has the following characteristics:
(1) the invention is based on the active structure of the large-scale antenna panel, and can quickly, directly and accurately calculate the optimal adjustment quantity of each actuator of the active surface of the large-scale shaped surface antenna facing the paraboloid, so that the integral reflection surface of the antenna formed by the shaped surface panel after active adjustment is closer to the target paraboloid, and the electrical property of the antenna can be obviously improved; the method can be applied to an active reflecting surface control system, is simple in calculation method, and can ensure that the antenna has good electrical property after the reflecting surface is adjusted.
(2) The method provided by the invention is used for adjusting the active panel of the large-scale shaped surface antenna, so that the precise conversion function of the surface type of the large-scale shaped surface antenna under two different working modes is realized, the focal length of the best fitting paraboloid of the shaped surface of the antenna panel is the same as that of the target paraboloid, and the spatial position of the antenna reflection panel is directly changed, so that the electrical property of the antenna is ensured, and the method has important academic significance and engineering application value.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 shows an ANSYS structure model of the shaped surface antenna;
FIG. 3 is a schematic view of an active panel and actuator arrangement;
FIG. 4 is a schematic diagram of the adjustment of the antenna's integral reflector and active panel;
fig. 5 is a graph comparing the electrical performance of the antenna with the ideal shaping surface after adjustment.
Detailed Description
The invention is further explained below with reference to the drawings and examples.
As shown in fig. 1, a method for rapidly determining an adjustment amount of an active panel of a large paraboloid-oriented antenna includes the following steps:
step 1, determining a parabolic antenna structure scheme and an actuator position, establishing an antenna structure finite element model, and determining an actuator support node
Determining an antenna structure scheme and an actuator initial position according to the structural parameters, the working frequency and the material attributes of the large parabolic antenna, establishing an antenna structure finite element model under an ideal condition in mechanical analysis software, and determining an actuator support node; the structural model of the reflector antenna comprises panel node information, back frame node information and actuator supporting node information which are determined to be used for antenna calculation.
Step 2, determining a fitting equation of the shaped surface by adopting a Zernike polynomial
2.1 setting the parameters of the caliber surface as t and psi, then setting any point P on the shaping surfaces(xs,ys,zs) Can be expressed as:
xs＝xs(t,ψ),ys＝ys(t,ψ),zs＝zs(t,ψ)
therefore, the method comprises the following steps:
wherein: t is more than or equal to 0 and less than or equal to 1, psi is more than or equal to 0 and less than or equal to 2 pi, a and b are respectively half-axial lengths along the x and y directions on the projection caliber A, (x)0,y0) Is the center coordinate of the projection caliber A.
2.2 for the equation with the antenna reflection surface as a shaping surface, using Zernike polynomials, the following is expressed:
wherein (x)s,ys,zs) The points represented represent points on the shaping surface, z1(x, y, j, i) is a function expressed by a Zernike polynomial, j and i are orders expressed by the Zernike polynomial, f is working frequency, lambda is wavelength, and the distance from the H feed source to the center of the elliptic caliber surface;
wherein:is a radial polynomial, Cij、DijFor the fitting coefficient of the shaping surface, the following formula can be used for solving:
wherein,ρ is the polar length in polar coordinates.
Step 3, extracting node information of all active panels of the shaped reflecting surface
And extracting node information of all active panels of the antenna-shaped reflecting surface by using the established antenna structure model and the support nodes of the actuator.
Step 4, extracting the node information of the e-th active panel of the shaped reflecting surface
Because coupling linkage is not considered among all panels of the antenna, the node information of the e-th panel on the reflecting surface can be directly extracted.
Step 5, based on the node information on the active panel and the focal length f of the target paraboloid1Calculating the best fitting paraboloid of the active panel by using the least square method
5.1 extracting theoretical coordinates P (x) of N sampling nodes on the ideal design surface based on the finite element model of the antenna structurei,yi,zi) Extracting N sampling points P on the antenna reflecting surface according to the node information of the antenna reflecting surface1(x0,y0,z0) Let P be0(x0',y0',z0') is one of N sampling nodes on the best-fit paraboloid of the antenna, and the coordinate error of the best-fit paraboloid is r (P) by utilizing the antenna shaping surface1)-r(P0) According to the least square principle, an equation set A. β ═ H is constructed,
β＝(Δx Δy Δz φx φy)Τ，
wherein A is coefficient, β is parameters of the best fitting paraboloid of the antenna, N is the number of sampling points, f1To best fit the focal length of the paraboloid, the focal length of the paraboloid is taken as the focal length of the target paraboloid, and Δ x, Δ y, Δ z, φxAnd phiyWherein Δ x, Δ y, Δ z are displacements of the target parabolic node in the coordinate system relative to the best-fit parabolic node of the antenna shaping surface, φx、φyRespectively shaped to the antennaThe rotation angles of the focal axis of the best fitting paraboloid around the coordinate axes x and y are positive anticlockwise and are minute quantities. T is the transposed sign of the matrix, zi' best-fit z-axis coordinates of points on the paraboloid for the antenna;
5.2 solve the above equation set to obtain β parameters of the best-fit paraboloid of the antenna, and change β to (Δ x Δ y Δ z φ)xφy)ΤSubstituting the parameters into an equation and determining the best fitting parabolic equation of the antenna shaping surface as follows:
where h is the distance in the z direction between the target parabola and the best-fit parabola.
Step 6, determining an actuator support node of the e-th block panel
Corresponding to the e-th panel for determining the reflecting surface of the antenna, determining an actuator supporting node of the panel;
step 7, determining the expansion direction of the actuator (the normal direction of the point where the actuator is located) according to the actuator support node, determining a linear equation, a best-fit paraboloid and a target paraboloid equation of the actuator, and calculating the adjustment quantity of the panel actuator according to the intersection point distance between the linear and the two parabolas
7.1 the actuator is represented by the equation for the paraboloid:
wherein f is2The focal length of the paraboloid where the actuator is located; x is the number of0,y0Is a sampling point P1(x0,y0,z0) X of0,y0Coordinates;
by an actuator supporting panelThe cosine of the normal direction of the node on the paraboloid is obtained to obtain the cosine of the normal direction (u) of the movement of the shape-giving surface from the initial position to the adjusting positioni,vi,wi)：
Through actuator support node Oi(xi,yi,zi) Normal equation of (c):
7.2 solving the normal equation to obtain the intersection O ' (x ') of the normal direction straight line passing through the antenna actuator support node and the initial best fitting paraboloid when the shape-imparting surface is not moved '0,y'0,z'0) And the intersection O "(x ″) of the shifted best-fit parabolas0,y″0,z″0) The distance (distance between AA ') that the shaped surface panel moves under the action of the actuator is exactly equivalent to the distance between OO ', namely the distance between the OO ' and the shaped surface panel
7.3 determining the adjustment factor delta, i.e. the point of intersection O' (x) of the target parabola with the normal direction of the actuator0”,y0”,z0") is located at an intersection O ' (x ') along the antenna forming surface and the normal direction of the actuator '0,y'0,z'0) And actuator support point Oi(xi,yi,zi) When the line segment is formed, delta is 1; when the intersection point O' of the target paraboloid and the normal direction of the actuator0”,y0”,z0") is located between OO' segments, then δ is taken to be-1;
7.4upper node A ' (x ') of shaping surface 'a,y'a,z'a) Normal deviation of the corresponding points with respect to the antenna target reflection plane O ":
7.5, according to the determined adjustment coefficient delta and the normal deviation of the corresponding point of the node A 'on the shaping surface relative to the antenna target reflecting surface O':
step 8, judging whether the panel is the last panel, if so, calculating the root mean square error of the adjusted integral reflecting surface, and turning to step 9; if not, go to step 4 and start the calculation of the adjustment amount of the next panel
And each panel of the antenna reflecting surface is adjusted, so that the root mean square error of the adjusted whole reflecting surface is ensured to be minimum.
9, calculating the root mean square error between the shaping reflecting surface and the target paraboloid according to all the node information of the adjusted integral shaping reflecting surface
9.1 solving the normal equation to obtain the z coordinate of the intersection point of the normal direction straight line passing through the node on the shaping surface of the antenna and the best fitting paraboloid, and obtaining the antenna node A ' (x ') on the shaping surface after the antenna panel moves 'a,y'a,z'a) Corresponding point O "(x ″) of the target parabolic surface of the corresponding antenna0,y″0,z″0) And calculating the normal deviation of the node A 'on the shaping surface relative to the corresponding point of the target paraboloid O' of the antenna by using the following formula:
9.2 according to the normal deviation of each node, calculating the normal root mean square error of the whole antenna shaping surface as follows:
step 10, calculating the adjusted antenna gain of the shaped reflector based on the antenna electromechanical coupling model
The adjustment of the antenna panel is performed with respect to the adjustment amount calculated in step 9. Now with the adjusted antenna reflector, the gain of the new antenna reflector is calculated using ANSYS software.
Step 11, judging whether the antenna gain meets the index requirement
Judging whether the antenna gain meets the index requirement, if not, changing the panel to adjust to a new position along the normal direction of the actuator, recombining the shaping surface, changing the position parameter of the antenna panel when the antenna back frame structure is unchanged, updating the finite element model of the antenna structure, and going to step 3; if the requirements are met, the adjustment quantity of the actuator is output, and therefore the optimal adjustment quantity of the shaped antenna active panel facing the paraboloid is obtained.
The present invention can be further illustrated by the following simulation
1. Establishing a finite element model of a large-scale shape-imparting surface structure in ANSYS
In this embodiment, an ANSYS structure finite element model of an 8-meter antenna is taken as a case for analysis, beam188 is adopted as a beam unit in the model, shell63 is adopted as a shell unit, and the built ANSYS structure model is shown in fig. 2, wherein the antenna focal length is 3 meters, the working frequency band is 5GHz, an antenna back frame is a steel structure, and the elastic modulus of the material is 2.1 × 107MPa, density 7.85X 10- 3kg/cm2(ii) a The panel is made of aluminum alloy and has a density of 2.73 × 10-3kg/cm3The thickness is 4 mm.
2. Because the antenna reflecting surface is the shaping surface, the Zernike polynomial is adopted to determine the fitting equation of the shaping surface
In this embodiment, the aperture surface of the antenna reflection surface is a circle, the projection aperture is 8 m, the offset distance H-a is 1 m, and the wavelength λ is 0.06 m. Taking n as 3 and m as 2, generating the data in table 1 and table 2 by using Zernike polynomial, and further determining the antenna shaping surface fitting equation as follows:
wherein (x)s,ys,zs) Representing the coordinates of points on the shaped surface.
TABLE 1Expression formula
TABLE 2 characteristic coefficients of shaped surfaces
3. Extracting node information of all active panels of reflecting surface
And extracting the node coordinates of all active panels on the shaping surface based on an antenna ANSYS structural model. 4. Extracting node information of the active panel
And for the e-th panel on the shaped antenna panel, extracting the node information of the active panel.
5. Based on node information on the active panel and the focal length f of the target paraboloid1By usingLeast square method for calculating the best-fit paraboloid of the active panel
And calculating parameters of the target surface equation with the minimum fitting root mean square error relative to the forming surface by using the panel node coordinate information extracted in the previous step, wherein five parameters are delta x, delta y, delta z and phixAnd phiyEqual to 0.0000005822mm, 0.0000009075mm, 1.149317699mm, 0.0054557916rad, -0.0034934086rad, respectively. The target curved surface can be determined by utilizing five parameters, and the equation of the target curved surface is as follows:
6. determining actuator support node for e-th block panel
For the e-th panel, the position of each support point of the actuator is determined, and the normal vector of the actuator is determined.
7. Calculating an adjustment amount of a panel actuator
And calculating the corresponding actuator adjustment quantity according to the positive direction or the negative direction of the position of the corresponding node along the position of the actuator supporting node. In this embodiment, the antenna structure model has 36 active panels and 144 actuators, which are schematically distributed as shown in fig. 3, and after the actuator adjustment amount of the e-th panel is calculated, the next panel on the same ring is calculated, and after the calculation of the same ring, the next ring is calculated, and so on, the actuator adjustment amounts of all the panels are calculated.
8. Judging whether all the panels are adjusted
Judging whether the panel is the last panel, if so, calculating the root mean square error of the adjusted integral reflecting surface, and turning to the step 9; if not, turning to the step 4, and starting the adjustment quantity calculation of the next panel;
9. calculating the root mean square error between the shaped reflecting surface and the target paraboloid
(1) Solving a normal equation to obtain a z coordinate of an intersection point of a straight line passing through a normal direction of a node on the antenna shaping surface and the best fitting paraboloid and an antenna node A ' (x ') on the shaping surface after the antenna panel moves 'a,y'a,z'a) Corresponding point O "(x ″) of corresponding antenna target reflection surface0,y″0,z″0) The coordinates, as shown in fig. 4, are a schematic diagram of adjusting the whole reflection surface and the active panel of the antenna, and the normal deviation of the node a' on the shaping surface relative to the corresponding point of the target paraboloid O ″ of the antenna is calculated by using the following formula:
(2) according to the normal deviation of each node, calculating the normal root mean square error of the shaping surface of the whole antenna as follows:
bringing into the above formula can obtain: the normal root mean square error is 0.392 mm.
10, calculating the antenna gain after the antenna adjustment of the shaped reflector
For the antenna gain after the shaping reflector antenna is adjusted, the electromechanical coupling model formula is used to calculate and compare the electrical performance directional diagrams of the target paraboloid and the fitted paraboloid antenna after the panel is adjusted, as shown in fig. 5. As can be seen from the figure, the coincidence degree of the two curves is high, which indicates that the whole reflecting surface of the adjusted antenna is very close to the target paraboloid. According to the electrical property value of the antenna, compared with an ideal parabolic antenna, the gain loss of the antenna after the shaped active panel is adjusted is 0.407dB, and the antenna engineering index requirement is met.
The following conclusions can be drawn from the above simulation: the method can quickly determine the optimal adjustment quantity of the large-scale shaped surface antenna actuator facing the paraboloid, and realize the accurate conversion of two working surface types of the large-scale reflecting surface antenna in the service process, thereby ensuring that the electrical performance of the large-scale shaped surface antenna can meet the index requirement under two working modes of the paraboloid and the shaped surface.
Claims (6)
1. The method for quickly determining the adjustment quantity of the active panel of the large shaping surface antenna facing to the paraboloid is characterized by comprising the following steps of:
(1) establishing an antenna structure finite element model under an ideal condition in mechanical analysis software according to the structure scheme of the large reflector antenna and the position of the actuator, and determining an actuator supporting node;
(2) because the antenna reflecting surface is a shaping surface, a Zernike polynomial is adopted to determine a fitting equation of the shaping surface;
the step (2) is carried out according to the following processes:
(2a) setting the parameters of the caliber surface as t and psi, then setting any point P on the shaping surfaces(xs,ys,zs) Can be expressed as:
xs＝xs(t,ψ),ys＝ys(t,ψ),zs＝zs(t,ψ)
therefore, the method comprises the following steps:
wherein t is more than or equal to 0 and less than or equal to 1, psi is more than or equal to 0 and less than or equal to 2 pi, a and b are respectively half-axial lengths along the x and y directions on the projection caliber A, (x)0,y0) Is a sampling point P1(x0,y0,z0) The center coordinates of the projection caliber A;
(2b) for the equation with the antenna reflecting surface as a shaping surface, the Zernike polynomial is expressed as follows:
wherein (x)s,ys,zs) Coordinates representing points on the shaping surface, z1(x, y, j, i) is a function expressed by a Zernike polynomial, j and i are orders expressed by the Zernike polynomial, f is working frequency, lambda is wavelength, and the distance from the H feed source to the center of the elliptic caliber surface;
thus, there are obtained:
wherein,is a radial polynomial, Cij、DijFitting coefficients of the shaping surfaces; the following formula is used to obtain:
wherein,rho is the polar length under polar coordinates;
(3) extracting node information of all active panels of the shaping reflecting surface by using an antenna structure finite element model and an actuator support node;
(4) for the e-th panel on the antenna panel, extracting node information of the active panel;
(5) based on node information on the active panel and the focal length f of the target paraboloid1Calculating the best fitting paraboloid of the active panel by using a least square method;
(6) determining an actuator support node for the e-th panel;
(7) determining the normal direction of the point where the actuator is located and a linear equation of the actuator according to the position of the support node of the actuator, and calculating the adjustment quantity of the panel actuator according to the intersection point distance of the linear, the best-fit paraboloid and the target paraboloid;
(8) judging whether the panel is the last panel, if so, calculating the root mean square error of the adjusted integral reflecting surface, and turning to the step (9); if not, turning to the step (4) to start the calculation of the adjustment quantity of the next panel;
(9) calculating the root mean square error between the shaping surface and the target paraboloid according to all the node information of the adjusted shaping surface;
(10) calculating the adjusted antenna gain of the shaping reflector based on the antenna electromechanical coupling model;
(11) judging whether the antenna gain meets the index requirement, if not, changing the position of the actuator, updating the antenna structure model, and turning to the step (3); if the requirements are met, the adjustment quantity of the actuator is output, and therefore the optimal adjustment quantity of the shaped antenna active panel facing the paraboloid is obtained.
2. The method for rapidly determining the adjustment amount of the active panel of the large paraboloid-oriented surface antenna according to claim 1, wherein in the step (1), the structural finite element model of the surface antenna comprises panel node information, back frame node information and actuator support node information.
3. The method for rapidly determining the adjustment amount of the active panel of the large paraboloid-oriented antenna according to claim 1, wherein the step (5) is performed according to the following process:
(5a) extracting theoretical coordinates P (x) of N sampling nodes on an ideal design surface based on an antenna structure finite element modeli,yi,zi) Extracting N sampling points P on the antenna reflecting surface according to the node information of the antenna reflecting surface1(x0,y0,z0) Let P be0(x0',y0',z0') is one of N sampling nodes on the best-fit paraboloid of the antenna, and the coordinate error of the best-fit paraboloid is r (P) by utilizing the antenna shaping surface1)-r(P0) According to the least square principle, an equation set gamma β is constructed as H,
β＝(Δx Δy Δz φx φy)Τ，
wherein gamma is coefficient, β is parameter of best fitting paraboloid of antenna, N is number of sampling points, f1Is the focal length of the best fitting paraboloid, namely the focal length of the target paraboloid, and is respectively the best fitting of the target paraboloid node in the coordinate system relative to the antenna shaping surfaceDisplacement of parabolic nodes, phix、φyThe rotation angles of the focal axes of the best fitting paraboloids of the antenna shaping surface around the coordinate axes x and y respectively, T is a matrix transposition symbol, and z isi' best-fit z-axis coordinates of points on the paraboloid for the antenna;
(5b) solving the equation set to obtain parameters β of the best fitting paraboloid of the antenna, and changing β to (delta x delta y delta z phi)xφy)ΤSubstituting the parameters into an equation and determining the best fitting parabolic equation of the antenna shaping surface as follows:
where h is the distance in the z direction between the target parabola and the best-fit parabola.
4. The method for rapidly determining the adjustment amount of the active panel of the large paraboloid-oriented antenna according to claim 1, wherein the step (7) is performed according to the following process:
(7a) the actuator has the equation of a paraboloid as follows:
wherein f is2The focal length of the paraboloid where the actuator is located; x is the number of0,y0Is a sampling point P1(x0,y0,z0) X of0,y0Coordinates;
the cosine of the normal direction of the node on the paraboloid where the actuator supports the panel is obtained by the cosine of the normal direction (u) of the movement of the shape-giving surface from the initial position to the adjusted positioni,vi,wi)：
Through actuator support node Oi(xi,yi,zi) Normal equation of (c):
(7b) solving the normal equation to obtain an intersection O ' (x ') of a normal direction straight line passing through the antenna actuator support node and the initial best fit paraboloid when the shaping surface is not moved '0,y'0,z'0) And the intersection O '(x') of the shifted best-fit paraboloids0,y″0,z″0) The distance that the shaped surface panel moves under the action of the actuator is just equivalent to the distance between OO ', namely the distance between OO' and the shaped surface panel
(7c) Determining the adjustment coefficient delta, i.e. when the intersection O ″ (x) of the target parabola with the normal direction of the actuator0″,y0″,z0") is located at an intersection O ' (x ') along the antenna forming surface and the actuator normal direction '0,y'0,z'0) And actuator support point Oi(xi,yi,zi) When the line segment is formed, delta is 1; when the target paraboloid is in the intersection O' (x) with the normal direction of the actuator0″,y0″,z0") is located between OO' line segments, then δ is taken to be-1;
(7d) upper node A ' (x ') of shaping surface 'a,y'a,z'a) Normal deviation of the corresponding point with respect to the antenna target reflection plane O ″:
(7e) according to the determined adjustment coefficient delta and the normal deviation of the corresponding point of the node A 'on the shaping surface relative to the antenna target reflecting surface O':
5. the method for rapidly determining the adjustment amount of the active panel of the large paraboloid-oriented antenna according to claim 4, wherein the step (9) is performed according to the following process:
(9a) solving the normal equation obtained in the step (7a) to obtain a z coordinate of an intersection point of a normal direction straight line passing through a node on the antenna shaping surface and the best fitting paraboloid, and an antenna node A ' (x ') on the shaping surface after the antenna panel moves 'a,y'a,z'a) Corresponding point O '(x') of the target paraboloid of the corresponding antenna0,y″0,z″0) And calculating the normal deviation of the node A 'on the shaping surface relative to the corresponding point of the target paraboloid O' of the antenna by using the following formula:
(9b) according to the normal deviation of each node, calculating the normal root mean square error of the shaped surface of the whole antenna as follows:
6. the method for rapidly determining the adjustment amount of the active panel of the large parabolic-oriented shaped panel antenna according to claim 1, wherein in the step (11), the panel is adjusted to a new position along the normal direction of the actuator to re-form the shaped panel, and at the moment, the antenna back frame structure is not changed, the position parameters of the antenna panel are changed, and the finite element model of the antenna structure is updated.
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