Offset reflector antenna actuator initial layout design method based on space mapping

Abstract

The invention discloses an initial layout design method for an offset reflector antenna actuator based on space mapping. The method comprises the following steps: (1) establishing a geometric model of an offset reflector antenna; (2) determining a mapping relation between a 2D circular projection coordinate system and a 3D offset reflection surface coordinate system of the antenna; (3) designing multi-layer concentric circle distribution of the actuator on the 2D circular projection coordinate system, and obtaining projection points; step (4), calculating parameters of elliptical distribution of the projection points through a coordinate mapping algorithm; (5) converting the projection points designed in the step (3) into 3D space coordinates one by one by using the coordinate mapping relation in the step (2) and the parameters of the elliptical distribution obtained in the step (4), obtaining the elliptical distribution, and outputting the initial layout of the actuator; (6) optimizing and adjusting the initial layout; and (7) verifying the rationality and effectiveness of the layout. The method can effectively solve the problem of geometric non-fitting of a traditional method.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology, specifically relating to an initial layout design method for a bias reflector antenna actuator based on spatial mapping. Background Technology

[0002] As a key component of modern communication systems, the surface accuracy of reflector antennas directly affects their electrical performance. With the ever-increasing demands on antenna performance in fields such as satellite communication and radio astronomy, traditional passive surface control methods are no longer sufficient to meet the requirements of high precision and rapid response. Active reflector technology, by arranging actuators on the reflector surface to achieve real-time surface adjustment, has become an effective way to solve this technical challenge.

[0003] Offset reflector antennas possess unique geometric characteristics: their projection onto the focal plane is a standard circle, while the spatial reflector surface is elliptical. This geometric feature presents new challenges and opportunities for actuator layout design. On the one hand, the offset structure avoids feed obstruction, improving antenna efficiency; on the other hand, the asymmetrical geometry requires the actuator layout to adapt to this spatial deformation characteristic. How to effectively apply the core logic of the initial elliptical layout to offset reflector antennas to achieve optimized actuator configuration is a pressing technical problem that needs to be solved.

[0004] Existing actuator layout optimization methods, such as the patent with publication number CN114156656B, employ a broad-based optimization strategy that pre-selects a large number of candidate points on the reflective surface and then uses mechanical simulation combined with optimization algorithms for screening. While this type of method can determine the actuator position to some extent, it lacks a direct and precise mathematical correlation between its design starting point (candidate point set) and the unique geometric features of the offset reflective surface. The entire optimization process is computationally complex, relies on black-box iteration, and has poor interpretability and predictability of the results. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, the present invention aims to provide an initial layout design method for offset reflector antenna actuators based on spatial mapping. This method, through in-depth analysis of the geometric characteristics of the offset reflector antenna, proposes a reverse design approach based on "circular projection → spatial mapping," extending the elliptical layout theory of standard parabolic antennas to offset structures. It effectively solves the problem of geometric misfit in traditional methods, and its effectiveness and practicality are proven through engineering verification.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for initial layout design of a bias reflector antenna actuator based on spatial mapping includes the following steps; Step (1): Establish the geometric model of the bias reflector antenna; Step (2): Based on the geometric model, determine the mapping relationship between the antenna's 2D circular projection coordinate system and the 3D offset reflector coordinate system; Step (3): Design the multi-layered concentric circle distribution of the actuator on the 2D circular projection coordinate system and obtain the projection points; Step (4): Calculate the parameters of the elliptical distribution of the projected points using a coordinate mapping algorithm; Step (5): Using the coordinate mapping relationship in step (2) and the parameters of the elliptical distribution obtained in step (4), each projection point designed in step (3) is converted into 3D spatial coordinates one by one to obtain the elliptical distribution and output the initial layout of the actuator. Step (6): Optimize and adjust the initial layout; Step (7): Verify the rationality and effectiveness of the layout.

[0007] The specific steps (1) are as follows: Using the coordinate system O-XYZ where the offset reflecting surface is located as the reference, the equation of the basic parabolic surface is defined, and the method of intercepting the offset reflecting surface is determined. The offset reflecting surface is the intercepted portion where a stretched cylinder based on a circle in the focal plane intersects with the standard parabolic surface—the axis of the cylinder is parallel to the Z-axis. After interception, the spatial reflecting surface is elliptical, and its projection onto the focal plane (perpendicular to the Z-axis) is a standard circle. The focal length is then determined. F Offset angle (The angle between the Z-axis and the axis of the reflecting surface determines the degree of stretching in the X-direction), radius of the projected circle. (The radius of the circular projection on the focal plane determines the aperture size of the reflecting surface.)

[0008] Step (2) specifically involves: To establish accurate coordinate mapping relationships, it is necessary to explicitly define each coordinate system; the circular projected coordinate system O-XY serves as the baseline 2D for actuator distribution design, and adopts polar coordinates. (p) k ,i n ） It means that among them r k Let be the radius of the circular projection of the k-th layer. i n The polar angle of the nth actuator ( 0≤θ n <360° The offset reflector coordinate system O-XYZ is used to describe the actual 3D installation position of the actuator, where the offset angle is... α Defined as the angle between the Z-axis and the axis of the reflecting surface, the equation of the ideal offset parabolic surface is: in f Focal length dThis is the bias value; The mathematical expression for the coordinate mapping relationship is: in , f The focal length of the offset reflecting surface. r k Let be the radius of the circular projection of the k-th layer. i n The polar angle of the nth actuator (0≤θ) n <360°） X, Y, and Z are the 3D spatial coordinates of the actuator in the offset reflective surface coordinate system O-XYZ, which are the mapped target coordinates used to characterize the actual installation position of the actuator. x and y are the coordinates of the actuator on the circular projection surface.

[0009] The specific steps (3) are as follows: An initial actuator layout is generated on the circular projection surface of the offset reflector. The initial layout consists of multiple concentric circles, with the number of actuators in each layer increasing outwards. The spacing between each layer is consistent to ensure that the initial distribution of actuators is uniform and covers all effective deformation areas.

[0010] Step (4) specifically involves: Through coordinate mapping, each actuator on the circular projection is transformed into an elliptical distribution on the offset plane, with the major axis of the ellipse... a k short axis b k With offset angle α Projection parameters r k The relationship is as follows: in α The offset angle, r k Let be the projection radius of the k-th layer; Long axis a k Extending along the offset direction (X-axis), due to the offset angle α The presence of this element creates a stretching effect; the minor axis b k Perpendicular to the offset direction (Y-axis), consistent with the projected radius, with no stretching effect; the eccentricity of the ellipse e=sina Only with the offset angle α related; In-layer actuator angle f n With projection polar angle i n The relationship is: That is, the polar angle of the actuator on the ellipse is consistent with the polar angle of the projection; However, due to the stretching effect of coordinate mapping, the angle between adjacent actuators in actual space will change. Let the angle between the nth and (n+1)th actuators in space be... f' n ,but: in The angle difference on the projection, This represents the total number of actuators in the k-th layer of the biased reflector.

[0011] Step (5) specifically involves: Substitute the projection points generated in step (3) into the mapping formula in step (2) to calculate the spatial coordinates. The actuators of the same layer k form a spatial ellipse after mapping. The elliptical layout is a spatial layout transformed from the circular layout through coordinate mapping. The core objective is to inherit the density strategy of the circular layout and adapt the elliptical geometry of the offset reflective surface.

[0012] The specific steps (6) are as follows: The spatial layout obtained from the initial mapping directly inherits the circular uniformity of the projection surface. However, due to the offset stretching effect, it may lead to uneven actuator distribution density on the spatial reflection surface, thus affecting the uniformity and efficiency of surface correction, requiring further optimization; adjusting the polar coordinates of the projection surface. Especially the starting angle of each layer The distribution of points within the layer is determined to minimize the objective function, which is the variance of the Euclidean distances between all adjacent actuators in three-dimensional space. in , Its adjacent points; Meanwhile, considering that the edge of the reflective panel may undergo greater deformation due to support or environmental factors, the actuator density of the outermost ellipse (near the endpoint of the major axis) can be appropriately increased. The curvature change of the central region (near the vertex projection) is relatively gentle, so the number of inner actuators can be appropriately reduced or the spacing between inner layers can be increased, saving the number of actuators without significantly affecting the correction capability.

[0013] The specific steps (7) are as follows: Check whether the spatial coordinates (X, Y) of all actuators projected onto the focal plane (O-XY plane) completely fall into and uniformly cover the circular area with a diameter equal to the radius of the specified projection circle, and whether there are any actuators exceeding the effective aperture; recalculate the coordinates (X, Y, Z) of all optimized actuators to verify whether they strictly satisfy the offset parabolic equation and ensure that the theoretical position of the actuator mounting base is located on the ideal reflecting surface.

[0014] The beneficial effects of this invention are: 1. This invention effectively solves the geometric misfit problem of traditional methods when designing the layout of offset reflector antenna actuators. It achieves this by using a directional adaptation mechanism of "circular projection → spatial mapping," combined with the offset angle... The stretching effect and parabolic constraint ensure that the actuator layout fits the unique geometric features of the offset reflector surface, which is "projected circle-spatial ellipse". At the same time, it fits the "regional electrical performance weight difference". In the multivariable, nonlinear (parabolic mapping) design space, it achieves a balance between surface accuracy and actuator efficiency, avoiding insufficient accuracy in the core area or redundancy in the edge area.

[0015] 2. Traditional actuator layout methods are mostly designed for standard parabolic surfaces and rely on empirical design or complex 3D optimization, resulting in high computational costs and poor adaptability. This invention, however, employs a reverse design logic, first completing a simplified distribution design on a 2D projection surface, and then rapidly transforming it into a 3D spatial layout through linear mapping. Furthermore, mathematical verification through conformity preservation, elliptic parameters, and reflective surface constraints ensures quantifiable layout reliability. Simultaneously, this invention utilizes offset angles... Parametric design, when When the angle is 0°, it can degenerate into a circular layout of a standard parabola. This is not limited to biased reflector antennas, but can also be extended to the actuator layout design of standard parabola antennas, and has strong versatility and engineering promotion value. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating an initial layout design method for a bias reflector antenna actuator based on spatial mapping, provided in an embodiment of the present invention.

[0017] Figure 2 The layout diagram of the offset reflector antenna circular projection → spatial mapping actuator provided in the embodiment of the present invention.

[0018] Figure 3 This is a diagram showing the initial layout of the bias reflector antenna actuator provided in an embodiment of the present invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings.

[0020] Please see Figure 1 , Figure 1 A flowchart of an initial layout design method for a bias reflector antenna actuator based on spatial mapping, provided for implementation of the present invention, includes: (1) Establish the geometric model of the biased reflector antenna.

[0021] To establish a precise and unified geometric benchmark for the entire layout design, the basic parabolic equation should be defined based on the O-XYZ coordinate system where the offset reflecting surface is located, and the interception method of the offset reflecting surface should be determined. The offset reflecting surface is the section where a stretched cylinder, based on a circle within the focal plane, intersects with a standard parabolic surface. The cylinder's axis is parallel to the Z-axis, resulting in an elliptical spatial reflecting surface. Projected onto the focal plane (perpendicular to the Z-axis), it forms a standard circle, thus defining the focal length. F Offset angle (The angle between the Z-axis and the axis of the reflecting surface determines the degree of stretching in the X-direction), radius of the projected circle. (The radius of the circular projection on the focal plane determines the aperture size of the reflecting surface.) This step transforms the complex three-dimensional geometry problem of the offset reflector into a problem solved by a few key parameters ( F, a, R The rigorously defined mathematical model provides a unique and accurate geometric input for all subsequent coordinate system definitions, mapping relationship derivations, and layout calculations.

[0022] (2) Determine the antenna coordinate system and mapping relationship.

[0023] In order to establish accurate coordinate mapping relationships and build a precise mathematical bridge from the simplified design plane (two-dimensional projection) to the complex target surface (three-dimensional space), it is necessary to clearly define each coordinate system; The circular projected coordinate system O-XY serves as the reference (2D) for actuator distribution design, using polar coordinates ( r k ,i n ) represents, where ρ k Let be the radius of the circular projection of the k-th layer. i n The polar angle of the nth actuator ( 0≤θ n <360° The offset reflector coordinate system O-XYZ is used to describe the actual installation position (3D) of the actuator, where the offset angle is... α Defined as the angle between the Z-axis and the axis of the reflecting surface, the equation of the ideal offset parabolic surface is: in f Focal length d This is the bias value.

[0024] The mathematical expression for the coordinate mapping relationship is: in , f The focal length of the offset reflecting surface. r kLet be the radius of the circular projection of the k-th layer. i n The polar angle of the nth actuator ( 0≤θ n <360° X, Y, and Z are the 3D spatial coordinates of the actuator in the offset reflective surface coordinate system O-XYZ, which are the mapped target coordinates used to characterize the actual installation position of the actuator. x and y are the coordinates of the actuator on the circular projection surface. This step establishes a precise and calculable one-to-one correspondence between projection points and spatial points. It allows for the initial uniform and regular distribution design on an intuitive two-dimensional circular plane, and then the three-dimensional spatial layout can be obtained automatically and accurately using this mapping, greatly reducing the design complexity.

[0025] (3) Design the actuators in multiple concentric circles on the circular projection surface to ensure uniformity between and within layers.

[0026] In order to generate a comprehensive and uniformly distributed initial actuator layout on an easily manageable two-dimensional projection plane as a high-quality seed layout for subsequent spatial mapping, the initial actuator layout needs to be generated on the circular projection surface of the offset reflector. The initial layout is a multi-layer concentric circle distribution, with the number of actuators in each layer increasing outwards, and the spacing between each layer being consistent to ensure that the initial actuator distribution is uniform and covers all effective deformation areas. This step yields an initial actuator distribution scheme that is fully covered and uniformly distributed on a two-dimensional plane.

[0027] (4) Calculate the parameters of the elliptical distribution using a coordinate mapping algorithm.

[0028] To achieve precise parametric design of spatial distribution, it is necessary to directly correlate the two-dimensional projection parameters with the three-dimensional ellipse parameters, thereby quantifying the elliptical features after the two-dimensional circular distribution is mapped to three-dimensional space. Through coordinate mapping, each actuator on the circular projection is transformed into an elliptical distribution on the offset plane. The major axis of the ellipse... a k short axis b k With offset angle α Projection parameters r k The relationship is as follows: in α The offset angle, r k Let be the projection radius of the k-th layer; Long axis a k Extending along the offset direction (X-axis), due to the offset angle αThe presence of this element creates a stretching effect; the minor axis b k Perpendicular to the offset direction (Y-axis), consistent with the projected radius, with no stretching effect; the eccentricity of the ellipse e=sina Only with the offset angle α related; In-layer actuator angle f n With projection polar angle i n The relationship is: That is, the polar angle of the actuator on the ellipse is consistent with the polar angle of the projection; However, due to the stretching effect of coordinate mapping, the angle between adjacent actuators in actual space will change. Let the angle between the nth and (n+1)th actuators in space be... f' n ,but: in The angle difference on the projection, This represents the total number of actuators in the k-th layer of the biased reflector.

[0029] This step involves deriving the major axis of the ellipse. a k 、 short axis b k 、 Eccentricity e With offset angle α Projection radius r k The mathematical relationship clarifies the impact of the offset stretching effect on spatial layout.

[0030] (5) The projection points are converted into spatial points, resulting in an elliptical distribution.

[0031] In order to convert the initial layout on the two-dimensional plane into spatial points that fit the offset reflective surface, it is necessary to substitute each projection point into the mapping formula to calculate the spatial coordinates. The actuators of the same layer k form a spatial ellipse after mapping. The elliptical layout is a spatial layout transformed from the circular layout through coordinate mapping. This step generates an initial spatial layout for the actuator that conforms to the geometry of the offset reflector, inheriting the density strategy of the circular layout and adapting to the elliptical geometry of the offset reflector.

[0032] (6) Optimize and adjust the initial layout.

[0033] To avoid uneven actuator distribution density on the spatial reflection surface due to the offset stretching effect, which could affect the uniformity and efficiency of surface correction, further optimization of the initial layout is required. Adjusting the polar coordinates of the projection plane Especially the starting angle of each layer The distribution of points within the layer is determined to minimize the objective function, which is the variance of the Euclidean distances between all adjacent actuators in three-dimensional space. in , Its adjacent points; Meanwhile, considering that the edge of the reflective panel may undergo greater deformation due to support or environmental factors, the actuator density of the outermost ellipse (near the endpoint of the major axis) can be appropriately increased. The curvature change of the central region (near the vertex projection) is relatively gentle, so the number of inner actuators can be appropriately reduced or the spacing between inner layers can be increased, saving the number of actuators without significantly affecting the correction capability.

[0034] (7) Verify the rationality and effectiveness of the layout.

[0035] To ensure that all actuator positions in the initial layout are reasonable and can effectively adjust the deformation of the reflective surface, it is necessary to check whether the spatial coordinates (X, Y) of all actuators projected onto the focal plane (O-XY plane) completely fall into and uniformly cover the circular area with a diameter equal to the radius of the specified projection circle, and whether there are any actuators exceeding the effective aperture. Recalculate the coordinates (X, Y, Z) of all optimized actuators and verify whether they strictly satisfy the offset parabolic equation to ensure that the theoretical position of the actuator mounting base is located on the ideal reflective surface.

[0036] In this invention, the core geometric parameters (focal length) of the offset reflecting surface are first defined. Offset angle Define the basic parabolic equation and interception method to provide a unified geometric reference for subsequent coordinate system definition, mapping relationship establishment and layout design; then, based on the geometric model established in step (1), clearly define the 2D circular projection coordinate system (actuator distribution design reference) and the 3D offset reflective surface coordinate system (actuator actual installation position description), derive the precise coordinate mapping formula between the two, construct the mathematical bridge of "projection surface design → spatial surface landing", and then, based on the circular projection coordinate system defined in step (2), design a uniform multi-layer concentric circle initial distribution (consistent inter-layer spacing, and the number of actuators in the layer increases outwards) to ensure coverage of all effective deformation areas and provide uniform and reasonable projection end input for subsequent mapping transformation; based on the mapping relationship in step (2) and the projection distribution parameters in step (3) r k 、then ), Derivation of the key parameters of the spatial ellipse (major axis) a k short axis b k eccentricity e Angle of actuator within the layer f n ), convert the circular distribution parameters of the projection end into spatial elliptical parameters that are adapted to the offset reflective surface, and provide a calculation basis for the next step of spatial point conversion; using the coordinate mapping formula of step (2) and the elliptical parameters derived in step (4), convert each projection point designed in step (3) into 3D spatial coordinates one by one, so that the actuators in the same layer form a spatial ellipse, complete the core conversion of "circular projection → spatial ellipse", and output the initial layout of the actuator; then, for the elliptical initial layout obtained in step (5), combined with the difference in electrical performance weights of different regions of the reflective surface, on the basis of inheriting the initial distribution uniformity, optimize the matching degree between the layout and the electrical performance requirements by increasing or decreasing the number of actuators and adjusting the distribution density, and avoid redundancy or insufficient accuracy; based on the layout optimized in step (6), ensure that the initial layout is reasonable and can cover all effective deformations, and finally verify the rationality of the layout generated in the above steps according to the requirements of step (7).

[0037] The beneficial effects of this invention are reflected in the following detailed operational steps: First, input the core geometric and electrical performance parameters of the offset reflector antenna; determine the layout design objectives and design variables; establish the initial layout design model of the actuator based on the logic of "circular projection → spatial mapping"; then, combine the coordinate mapping algorithm with the layout model; in the design process, initialize the multi-layer concentric circle distribution parameters of the projection surface, and then convert the projection points into spatial points through the coordinate mapping formula, calculate and classify the geometric compatibility (boundary constraints and interference constraints) of the mapping points; determine whether the layout rationality conditions are met, and if the conditions are met, output the spatial coordinates of the actuator ( X kn ,Y kn ,Z kn ) and elliptical distribution parameters (major axis) a k short axis b k If the rationality conditions are not met, the projection surface distribution parameters are re-initialized and the compatibility is calculated until the requirements are met.

[0038] The advantages of this invention are further illustrated by the following simulation experiments: 1. Simulation conditions for reflector antennas: The reflector antenna is a standard parabolic antenna, and its parameters are shown in Table 1: Table 1 Parameters of the Offset Reflector Antenna 2. Simulation results: This invention employs an initial layout design method for a bias reflector antenna actuator. Please refer to [link to relevant documentation]. Figure 3 , Figure 3 This is the final result diagram of the initial layout design of the actuator in the optimized method of this invention. The actuators are arranged on the antenna reflector surface. First, a uniform distribution of the actuators is designed on the circular projection surface, as shown below. Figure 2 As shown, (a) is the circular distribution of actuators in the projection, and (b) is the elliptical layout mapped onto the offset reflecting surface. These points are then transformed onto the offset reflecting surface through coordinate mapping to form an elliptical distribution. Figure 3 This method is used to design the initial actuator layout for a bias reflector antenna. Based on the reverse design approach of "circular projection → spatial mapping," an elliptical, layered actuator layout is generated to ensure that the actuator layout conforms to the geometric characteristics of the bias reflector and covers the main deformation areas of the bias reflector. Figure 3 It can be seen that this design method is highly compatible with the performance requirements and actuator characteristics of the bias reflector antenna, providing an engineering-feasible solution for the active deformation control of the bias reflector antenna.

[0039] The parts not described in detail in this embodiment are common and well-known methods in the industry, and will not be described in detail here. The above examples are merely illustrative of the present invention and do not constitute a limitation on the scope of protection of the present invention. All designs that are the same as or similar to the present invention are within the scope of protection of the present invention.

Claims

1. A method for initial layout design of an offset reflector antenna actuator based on spatial mapping, characterized in that, Includes the following steps; Step (1): Establish the geometric model of the bias reflector antenna; Step (2): Based on the geometric model, determine the mapping relationship between the antenna's 2D circular projection coordinate system and the 3D offset reflector coordinate system; Step (3): Design the multi-layered concentric circle distribution of the actuator on the 2D circular projection coordinate system and obtain the projection points; Step (4): Calculate the parameters of the elliptical distribution of the projected points using a coordinate mapping algorithm; Step (5): Using the coordinate mapping relationship in step (2) and the parameters of the elliptical distribution obtained in step (4), each projection point designed in step (3) is converted into 3D spatial coordinates one by one to obtain the elliptical distribution and output the initial layout of the actuator. Step (6): Optimize and adjust the initial layout; Step (7): Verify the rationality and effectiveness of the layout.

2. The initial layout design method for a bias reflector antenna actuator based on spatial mapping according to claim 1, characterized in that, The specific steps (1) are as follows: Using the coordinate system O-XYZ where the offset reflecting surface is located as the reference, the equation of the basic parabolic surface is defined, and the method of intercepting the offset reflecting surface is determined. The offset reflecting surface is the intercepted portion where a stretched cylinder with a circle in the focal plane as the reference intersects with the standard parabolic surface—the axis of the cylinder is parallel to the Z-axis. After interception, the spatial reflecting surface is elliptical, and its projection onto the focal plane is a standard circle. The focal length is then determined. F Offset angle Radius of the projected circle .

3. The initial layout design method for a bias reflector antenna actuator based on spatial mapping according to claim 2, characterized in that, Step (2) specifically involves: The 2D circular projection coordinate system O-XY serves as the reference for actuator distribution design, employing polar coordinates on the projection surface. (ρ) k ,θ n ） It means that, among them ρ k Let be the radius of the circular projection of the k-th layer. θ n The polar angle of the nth actuator ( 0≤θ n <360° The 3D offset reflector coordinate system O-XYZ is used to describe the actual installation position of the actuator, where the offset angle is... α Defined as the angle between the Z-axis and the axis of the reflecting surface, the equation of the ideal offset parabolic surface is: in f Focal length d This is the bias value; The mathematical expression for the coordinate mapping relationship is: in , f The focal length of the offset reflecting surface. ρ k Let be the radius of the circular projection of the k-th layer. θ n The polar angle of the nth actuator (0≤θ) n <360°） X, Y, and Z are the 3D spatial coordinates of the actuator in the offset reflective surface coordinate system O-XYZ, which are the mapped target coordinates used to characterize the actual installation position of the actuator. x and y are the coordinates of the actuator on the circular projection surface.

4. The initial layout design method for an offset reflector antenna actuator based on spatial mapping according to claim 3, characterized in that, The specific steps (3) are as follows: An initial actuator layout is generated on the circular projection surface of the offset reflector. The initial layout consists of multiple concentric circles, with the number of actuators in each layer increasing outwards. The spacing between each layer is consistent to ensure that the initial distribution of actuators is uniform and covers all effective deformation areas.

5. The initial layout design method for an offset reflector antenna actuator based on spatial mapping according to claim 4, characterized in that, Step (4) specifically involves: Through coordinate mapping, each actuator on the circular projection is transformed into an elliptical distribution on the offset plane, with the major axis of the ellipse... a k short axis b k With offset angle α Projection parameters ρ k The relationship is as follows: in α The offset angle, ρ k Let be the projection radius of the k-th layer; Long axis a k Extending along the offset direction, due to the offset angle α The presence of this produces a stretching effect; short axis b k Perpendicular to the offset direction, consistent with the projected radius, with no stretching effect; the eccentricity of the ellipse e=sinα Only with the offset angle α related; In-layer actuator angle φ n With projection polar angle θ n The relationship is: That is, the polar angle of the actuator on the ellipse is consistent with the polar angle of the projection.

6. The initial layout design method for an offset reflector antenna actuator based on spatial mapping according to claim 5, characterized in that, ... The angle between the nth and (n+1)th actuators in space is φ' n ,but: in The angle difference on the projection, This represents the total number of actuators in the k-th layer of the biased reflector.

7. The initial layout design method for a bias reflector antenna actuator based on spatial mapping according to claim 6, characterized in that, Step (5) specifically involves: Substitute the projection points generated in step (3) into the mapping formula in step (2) to calculate the spatial coordinates. The actuators of the same layer k form a spatial ellipse after mapping. The elliptical layout is a spatial layout transformed from the circular layout through coordinate mapping.

8. The initial layout design method for an offset reflector antenna actuator based on spatial mapping according to claim 7, characterized in that, The specific steps (6) are as follows: Adjusting the polar coordinates of the projection plane Especially the starting angle of each layer The distribution of points within the layer is determined to minimize the objective function, which is the variance of the Euclidean distances between all adjacent actuators in three-dimensional space. in , Its adjacent points; Meanwhile, considering that the edges of the reflective panel may deform more due to support or environmental factors, the actuator density of the outermost ellipse is increased, the curvature change in the central area is relatively gentle, the number of inner actuators is reduced or the spacing between inner layers is increased, and the number of actuators is saved without significantly affecting the correction capability.

9. The initial layout design method for a bias reflector antenna actuator based on spatial mapping according to claim 8, characterized in that, The specific steps (7) are as follows: Check whether the spatial coordinates (X, Y) of all actuators projected onto the focal plane completely fall into and uniformly cover the circular area with a diameter equal to the radius of the specified projection circle, and whether there are any actuators exceeding the effective aperture; recalculate the coordinates (X, Y, Z) of all optimized actuators to verify whether they strictly satisfy the offset parabolic equation and ensure that the theoretical position of the actuator mounting base is located on the ideal reflecting surface.

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