A star tracking analysis method for active cable-net reflector of FAST telescope

Abstract

The present invention relates to the field of radio telescope structure analysis, and discloses a method for tracking and analyzing the star of the active cable net reflector of the FAST telescope, comprising: step 1: establishing a dynamic relaxation method numerical model of the FAST cable net reflector structure; step 2: setting the accuracy limit of the telescope reflector, model parameters, and convergence conditions; step 3: identifying the main cable nodes within the irradiation range; step 4: calculating the radial distance from the main cable point to the working parabola; step 5: applying forced displacement to the lower end point of the lower cable; step 6: performing iterative calculation to obtain an equilibrium state model; step 7: repeating steps 3 to 6 until all main cable nodes to the working parabola meet the accuracy limit requirements of the telescope reflector; step 8: repeating the previous steps for tracking and analysis. The present invention innovatively adopts the dynamic relaxation method to perform star tracking and analysis, avoiding the problems of singular stiffness matrix and non-convergence of iteration when performing complex structure analysis using the traditional finite element method.

Description

Technical Field

[0001] The invention relates to the field of radio telescope structure analysis, and in particular to a method for tracking and analyzing stars on an active cable net reflection surface of a FAST telescope. Background Art

[0002] With an aperture of 500 meters, FAST is the world's largest single-aperture radio telescope to date. Its sensitivity and resolution are far higher than any previous radio telescope. Figure 1 , Figure 2 , Figure 3 , Figure 4 and attached Figure 5 As shown in FIG. 1 , the reflective surface structure is composed of a main cable net, a lower cable, a peripheral support structure, a back frame structure, and a reflective panel. The main cable net is fixed on the support structure on all sides. A lower cable is set below the main cable node, and an actuator is set at the lower end of the lower cable. Figure 6 As shown in the figure, the reflection surface is shaped and displaced by adjusting the length of the actuator. The back frame structure is connected to the main cable node through the corner point, and the reflection panel is laid on the back frame structure, as shown in the figure. Figure 7 As shown, during the operation of FAST, the cable net reflective surface within the illumination range needs to be adjusted to the specified working parabola following the observed celestial body, so that the parallel electromagnetic waves emitted by the celestial body are reflected by the reflective surface and focused on one point.

[0003] The displacement process of the cable net reflector can be divided into two processes: alignment and tracking. The alignment process is to adjust the length of the actuator within the irradiation range so that the main cable nodes within the irradiation range are adjusted from the reference spherical surface to the specified parabola position, and the main cable nodes outside the irradiation range are not actively adjusted to achieve the observation of the specified celestial body. The tracking process is to adjust the main cable nodes within the irradiation range to the specified parabola position in real time following the movement of the celestial body, and restore the main cable nodes outside the irradiation range to the reference state. The tracking process moves very slowly, and the moving speed of the working parabola on the reflector is about 21.8mm / s. Therefore, the tracking process can be regarded as a series of continuous alignment processes.

[0004] There are many main cables and lower cables in the FAST cable net reflector system. The reflector needs to be adjusted in real time according to the observation requirements. It is a complex cable net structure with large deformation. At present, the nonlinear finite element method is mainly used to find the form of the reflector, and then adjust the telescope to the corresponding position to achieve real-time displacement control and precise tracking observation of the FAST cable net reflector. The use of traditional nonlinear finite element methods may cause problems such as singular stiffness matrix and non-convergence of iterations in the process of reflector shape finding, which affects the accuracy of the reflector. Therefore, in order to ensure that FAST has reliable reflector accuracy when observing celestial bodies in various orientations, it is urgent to establish an efficient and reasonable active reflector star tracking analysis method. Summary of the invention

[0005] The present invention aims to provide a method for tracking and analyzing stars on the active cable-net reflector of the FAST telescope, so as to solve the problem that FAST currently has a complex cable-net structure with large deformations and it is difficult to ensure the accuracy of the reflector when tracking using the traditional finite element analysis method.

[0006] To achieve the above object, the present invention adopts the following technical solution: a FAST telescope active cable net reflection surface star tracking analysis method, comprising the following steps:

[0007] Step 1: Establish a dynamic relaxation numerical model of the FAST cable net reflector structure;

[0008] Step 2: Set the preset threshold of the distance from the main cable node to the working parabola, the iteration step h of the dynamic relaxation method numerical model, and the virtual damping , and iterative convergence conditions;

[0009] Step 3: Identify and obtain the main cable node within the illumination range of the active reflection surface of the telescope;

[0010] Step 4: Calculate the radial distance from the main cable point to the working parabola;

[0011] Step 5: A forced displacement from the reference spherical surface to the working parabola is applied to the lower end points of all the lower cables within the irradiation range in the radial direction, and the displacement magnitude is the distance from the main cable node at the upper end of the lower cable to the working parabola;

[0012] Step 6: Iteratively calculate the cable net reflective surface structure until the convergence condition is met to obtain an equilibrium state model; the iterative convergence condition includes that the maximum residual force of the particle is less than a preset residual force value;

[0013] Step 7: Repeat steps 3 to 6 on the basis of the equilibrium model until the distances from all main cable nodes to the working parabola in the equilibrium model within the irradiation range are less than the preset threshold of the distances from the main cable nodes to the working parabola, and calculate the length that the actuator needs to be adjusted to complete the star alignment analysis of the active reflector;

[0014] Step 8: Repeat steps 3 to 7 to track and analyze the active reflecting surface of the telescope.

[0015] Preferably, the step 1 specifically includes:

[0016] Step 11: Obtain the cable net reflector structure layout information, cable net prestressing, main cable material properties, lower cable material properties, back frame quality and panel quality;

[0017] Step 12: Discretize the cable net reflector structure into a number of massive particles and massless cable units. The mass of the cable net, back frame and reflector panel are all concentrated on the particles; the mass of particle i It is expressed as:

[0018] ,in, , , denote the masses of the cable net, back frame, and reflection panel assigned to particle i respectively;

[0019] Step 13: Distribute the structure's self-weight to each particle, and the particle external force P i It is expressed as:

[0020] , where g is the acceleration due to gravity;

[0021] Step 14: Apply the prestressing effect to the cable element, and the element strain It is expressed as:

[0022] , where , represent the initial stress and elastic modulus of element j respectively;

[0023] Step 15: Set the lower end node of the down-cable and the nodes around the main cable net as fixed points.

[0024] Preferably, the cable net reflective surface structure arrangement information includes topological relationships and boundary conditions.

[0025] Preferably, the material properties include elastic modulus, density and cross-sectional area.

[0026] Preferably, the step 3 specifically includes:

[0027] Step 31: Calculate the illumination direction vector according to the azimuth of the observed celestial body:

[0028] , where p and q represent the angles between the irradiation direction and the x and z axes, respectively;

[0029] Step 32: Calculate the distance from the main cable node i to the direction vector , identify the main cable nodes within the irradiation range:

[0030]

[0031] In the formula, , , Respectively represent the spatial position coordinates of node i, When the distance is less than or equal to the preset value, node i is within the working parabola.

[0032] Preferably, the iterative convergence condition includes that the particle residual force is less than a preset residual force value, and step 4 specifically includes:

[0033] Step 41: Calculate the FAST telescope working parabola equation:

[0034] , where , , They respectively represent the spatial position of the working parabola in the corresponding local coordinate system;

[0035] Step 42: Calculate the radial distance from all main cable nodes to the working parabola within the irradiation range :

[0036] , where , , respectively represent the distance from the main cable node i to the center of the sphere on the reference sphere and the distance from the main cable node i to the center of the sphere on the working parabola.

[0037] Preferably, the step 6 specifically includes:

[0038] Step 61: Calculate the particle displacement by the difference principle, according to The particle position at time , particle external force , particle internal force calculate The particle position at the moment is expressed as:

[0039] , where , ;

[0040] Step 62: Calculate particle internal forces based on unit length changes:

[0041]

[0042] In the formula, is the number of cable units connected to particle i, For the unit The inner strength of the moment, , is the elastic modulus and cross-sectional area of ​​the jth element, , For unit j in , the length of the moment;

[0043] Step 63: Superimpose the particle's external force and internal force to obtain the particle's residual force:

[0044] ;

[0045] Step 64: Determine whether the residual force of the particle meets the convergence condition. If the residual force of the particle meets the convergence condition, obtain the equilibrium static model; otherwise, update the node coordinates, stress and external force, and return to step 1.

[0046] It should be noted that the particle in this application is the name for the numerical model of the dynamic relaxation method (such as calculating displacement, internal force, residual force), while the node is the name for the physical model of the cable net structure (calculating radial distance, actuator length). Particles and nodes are actually different ways of representing the same object (cable net node).

[0047] Advantages of this solution:

[0048] 1. This invention proposes for the first time the principle of active displacement of the main cable nodes during the alignment and tracking process of the active reflector surface of the FAST telescope;

[0049] 2. The present invention introduces the numerical simulation process of satellite tracking in detail, and simulates the change of actuator length when the cable net is displaced by applying forced displacement to the lower end node of the lower cable within the irradiation range, so as to obtain a more accurate length of the actuator that needs to be adjusted;

[0050] 3. The present invention innovatively adopts the dynamic relaxation method to perform star tracking analysis, making static problems dynamic. By iteratively adjusting the particle displacement step by step, it can directly and effectively deal with large deformation problems of large-scale cable net structures without repeatedly adjusting the stiffness matrix, greatly simplifying the complexity of nonlinear analysis and avoiding the problems of stiffness matrix singularity and iterative non-convergence in traditional finite element analysis when performing complex structural analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is the overall cable net structure diagram of the background technology of the present invention.

[0052] Figure 2 It is a top view schematic diagram of the overall cable net structure of the background technology of the present invention.

[0053] Figure 3 This is the distribution diagram of the lower cables of the overall cable net which is the background technology of the present invention.

[0054] Figure 4 This is the main cable net division diagram of the overall cable net of the background technology of the present invention.

[0055] Figure 5 The back frame structure and reflective panel diagram are the background technology of the present invention.

[0056] Figure 6 This is a diagram of actuator-controlled forming displacement in the background technology of the present invention.

[0057] Figure 7The following is a diagram of the reference sphere and working parabola of the background technology of the present invention.

[0058] Figure 8 Schematic diagram of a flow chart of an embodiment of the present invention.

[0059] Fig. 9 Schematic diagram of the irradiation area (0°, 15°) of an embodiment of the present invention.

[0060] Fig.10 This is a distribution diagram of the satellite displacement when the azimuth angle is (0°, 15°) according to an embodiment of the present invention.

[0061] Fig.11 This is a diagram of the cable force distribution on the star when the azimuth angle is (0°, 15°) according to an embodiment of the present invention.

[0062] Fig.12 Schematic diagram of the irradiation area (-15°, -15°) of an embodiment of the present invention.

[0063] Fig.13 Schematic diagram of the irradiation area (0°, 0°) according to an embodiment of the present invention.

[0064] Fig.14 Schematic diagram of the irradiation area (15°, 15°) according to an embodiment of the present invention.

[0065] Fig.15 This is a displacement distribution diagram tracked by an embodiment of the present invention when the azimuth angle is (-15°, -15°).

[0066] Fig.16 This is a cable force distribution diagram tracked when the azimuth angle is (-15°, -15°) according to an embodiment of the present invention.

[0067] Fig.17 This is a displacement distribution diagram tracked by an embodiment of the present invention when the azimuth angle is (0°, 0°).

[0068] Fig.18 This is a cable force distribution diagram tracked when the azimuth angle is (0°, 0°) according to an embodiment of the present invention.

[0069] Fig.19 This is a displacement distribution diagram tracked by an embodiment of the present invention when the azimuth angle is (15°, 15°).

[0070] Fig. 20 This is a cable force distribution diagram tracked when the azimuth angle is (15°, 15°) according to an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The following is further described in detail through specific implementation methods:

[0072] A star tracking analysis method for the active cable net reflector of the FAST telescope is shown in the attached figure. Figure 8 As shown, the following steps are included:

[0073] Step 11: Obtain the cable net reflector structure layout information, cable net prestressing, main cable material properties, lower cable material properties, back frame quality and panel quality.

[0074] The layout information of the cable net reflective surface structure includes topological relationships and boundary conditions. The topological conditions of the cable net structure mainly include the geometric layout of the grid, the connection method of the nodes, and the direction of the cable segments. Geometric layout of the grid: The cable net structure is usually composed of multiple cable segments connected by nodes, forming a certain grid structure. These grids are mostly regular geometric shapes, such as squares, triangles or hexagons, to ensure the uniformity and stability of the structure; Node connection method: The nodes in the cable net structure are the places where multiple cable segments meet, and their connection method is crucial to the overall performance of the structure; The direction of the cable segment: The cable segment is the basic element of the cable net structure, and its direction will affect the mechanical properties of the cable net. The cable segments usually have the same direction to ensure that each part is evenly stressed and avoid stress concentration leading to local damage.

[0075] Boundary conditions involve supporting structures, prestressing, and load conditions. Supporting structures: The boundaries of the cable net are usually fixed by connecting to surrounding structures. These supporting structures need to be strong enough to provide stable constraints to prevent the cable net from excessive displacement or instability under external forces; Prestressing: In order to improve the stiffness and stability of the cable net, prestressing is usually applied to the cable net during construction. The size and distribution of the prestress will directly affect the initial shape of the cable net and its performance under load; Load conditions: The cable net will be subject to a variety of loads during use, including deadweight, wind load, snow load, etc.

[0076] Material properties include elastic modulus, density and cross-sectional area. Elastic modulus, commonly known as Young's modulus, is a physical quantity that describes the material's ability to resist deformation when subjected to external forces. It is the ratio of the tensile or compressive stress of the material within the elastic range to the corresponding strain; density refers to the mass of the material per unit volume, usually in kilograms per cubic meter (kg / m³). The density of the material reflects the compactness of its mass distribution; cross-sectional area refers to the size of the cross section perpendicular to the material's axis. In solid materials, the cross-sectional area is usually measured in square millimeters (mm²) or square centimeters (cm²).

[0077] Step 12: Discretize the cable net reflector structure into a number of massive particles and massless cable units. The mass of the cable net, back frame and reflector panel are all concentrated on the particles. The mass of particle i It is expressed as:

[0078] (1), where , , denote the masses of the cable net, back frame, and reflection panel assigned to particle i respectively;

[0079] Step 13: Distribute the structure's self-weight to each particle, and the particle external force P i It is expressed as:

[0080] (2), where g is the acceleration due to gravity;

[0081] Step 14: Apply the prestressing effect to the cable element, and the element strain It is expressed as:

[0082] (3), where , represent the initial stress and elastic modulus of element j respectively;

[0083] Step 15: Set the lower end node of the down-cable and the nodes around the main cable net as fixed points.

[0084] Step 2: Set the preset threshold of the distance from the main cable node to the working parabola, the iteration step h of the dynamic relaxation method numerical model, and the virtual damping , and iterative convergence conditions.

[0085] In this scheme, the distance from the main cable node to the working parabola within the irradiation range is less than 0.1mm.

[0086] The iterative convergence condition includes that the maximum residual force of the particle is less than the preset residual force value. In this embodiment, when the convergence condition is met, that is, the maximum residual force <10 -4 N.

[0087] Step 31: Calculate the illumination direction vector according to the azimuth of the observed celestial body:

[0088] (4), where p and q represent the angles between the irradiation direction and the x and z axes, respectively;

[0089] Step 32: Calculate the distance from the main cable node i to the direction vector , identify the main cable nodes within the irradiation range:

[0090] (5)

[0091] In the formula, , , Respectively represent the spatial position coordinates of node i, When the distance is less than or equal to the preset distance value, the preset distance value is 150m, which is half of the working parabola aperture, and node i is inside the working parabola. Identify and obtain the main cable node within the illumination range of the active reflector of the telescope.

[0092] Step 4: Calculate the radial distance from the main cable point to the working parabola.

[0093] Preferably, the iterative convergence condition includes that the particle residual force is less than a preset residual force value, and step 4 specifically includes:

[0094] Step 41: Calculate the FAST telescope working parabola equation:

[0095] (6), where , , They respectively represent the spatial position of the working parabola in the corresponding local coordinate system;

[0096] Step 42: Calculate the radial distance from all main cable nodes to the working parabola within the irradiation range :

[0097] (7), where , , respectively represent the distance from the main cable node i to the center of the sphere on the reference sphere and the distance from the main cable node i to the center of the sphere on the working parabola.

[0098] Step 5: A forced displacement from the reference sphere to the working parabola is applied radially to the lower end points of all the lower cables within the irradiation range. The displacement is the distance from the main cable node at the upper end of the lower cable to the working parabola.

[0099] Step 6: Perform iterative calculations on the cable net reflective surface structure until the convergence conditions are met and the equilibrium model is obtained.

[0100] Preferably, step 6 specifically includes:

[0101] Step 61: Calculate the particle displacement by the difference principle, according to The particle position at time , particle external force , particle internal force calculate The particle position at the moment is expressed as:

[0102] (8), where , ;

[0103] Step 62: Calculate particle internal forces based on unit length changes:

[0104] (9)

[0105] In the formula, is the number of cable units connected to particle i, For the unit The inner strength of the moment, , is the elastic modulus and cross-sectional area of ​​the jth element, , For unit j in , the length of the moment;

[0106] Step 63: Superimpose the particle's external force and internal force to obtain the particle's residual force:

[0107] (10);

[0108] Step 64: Determine whether the residual force of the particle meets the convergence condition. If the residual force of the particle meets the convergence condition, obtain the equilibrium static model; otherwise, update the node coordinates, stress and external force, and return to step 1.

[0109] Step 7: Repeat steps 3 to 6 based on the equilibrium model until the distance from all main cable nodes to the working parabola in the equilibrium model within the irradiation range is less than the preset threshold of the distance from the main cable node to the working parabola, and calculate the length that the actuator needs to be adjusted to complete the star analysis of the active reflector.

[0110]

[0111] In the formula, represents the length of the actuator connected to node i that needs to be adjusted, represents the radial distance from the main cable node to the working parabola calculated in the t-th repetition of steps 3 to 6 (see step 42 for details), and times represents the total number of repetitions.

[0112] Step 8: Repeat steps 3 to 7 to track and analyze the active reflecting surface of the telescope.

[0113] The following is an example of star alignment: Fig. 9 As shown, taking a typical irradiation area (0°, 15°) as an example, the black big circle in the figure represents the 500m diameter reflection surface, the red small circle represents the 300m diameter working surface in the irradiation direction during operation, and (0°, 15°) means that the angles between the irradiation direction and the x and z axes are 0 degrees and 15 degrees respectively. The main cable has a diameter of 25mm, the lower cable has a diameter of 10mm, and the elastic modulus is 205GPa. A prestress of 400MPa is applied to all cable segments, and the star analysis is performed according to steps (1) to (7). The distribution of model displacement (unit m) and cable force (unit MPa) is shown as follows Fig.10 , Fig.11 shown.

[0114] The following is an example of a trace: Fig.12 , Fig.13 , Fig.14 As shown in Figure 2, take the observed celestial body moving from azimuth (-15°, -15°) to azimuth (0°, 0°) to azimuth (15°, 15°) as an example, and perform tracking analysis according to steps (1) to (8). The deformation (unit: m) and cable force (unit: MPa) of the model at the initial azimuth (-15°, -15°), the intermediate azimuth (0°, 0°), and the equilibrium azimuth (15°, 15°) are shown in Figure 2. Fig.15 , Fig.16 , Fig.17 , Fig.18 , Fig.19 , Fig. 20 shown.

[0115] The present invention innovatively adopts the dynamic relaxation method to perform star alignment and tracking analysis, avoiding the problems of stiffness matrix singularity and iterative non-convergence in traditional finite element analysis of complex structures; the numerical simulation process of star alignment and tracking is introduced in detail, and the change in actuator length when the cable net is displaced is simulated by applying forced displacement to the lower end node of the down-pull cable within the irradiation range; the principle of active displacement of the main cable nodes during the star alignment and tracking process of the active reflecting surface of the FAST telescope is proposed.

[0116] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical schemes and / or characteristics in the scheme is not described in detail here. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the technical scheme of the present invention. In the present invention, unless otherwise clearly specified and limited, the terms "install", "connect", "connect", "fix" and the like should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected, or indirectly connected through an intermediate medium, or it can be the internal connection of two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. The scope of protection claimed in this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for tracking and analyzing stars on the active cable net reflection surface of the FAST telescope, characterized in that: The following steps are involved: Step 1: Establish a dynamic relaxation numerical model of the FAST cable net reflector structure; Step 2: Set the preset threshold of the distance from the main cable node to the working parabola, the iteration step h of the dynamic relaxation method numerical model, the virtual damping α, and the iteration convergence condition; Step 3: Identify and obtain the main cable node within the illumination range of the active reflection surface of the telescope; Step 4: Calculate the radial distance from the main cable point to the working parabola; Step 5: A forced displacement from the reference spherical surface to the working parabola is applied to the lower end points of all the lower cables within the irradiation range in the radial direction, and the displacement magnitude is the distance from the main cable node at the upper end of the lower cable to the working parabola; Step 6: Iteratively calculate the cable net reflective surface structure until the convergence condition is met to obtain an equilibrium state model; the iterative convergence condition is that the maximum residual force of the particle is less than a preset residual force value; Step 7: Repeat steps 3 to 6 on the basis of the equilibrium model until the distances from all main cable nodes to the working parabola in the equilibrium model within the irradiation range are less than the preset threshold of the distances from the main cable nodes to the working parabola, and calculate the length that the actuator needs to be adjusted to complete the satellite analysis of the active reflector; Step 8: Repeat steps 3 to 7 to track and analyze the active reflector of the telescope; The step 6 specifically includes: Step 61: Calculate the particle displacement by the difference principle, according to t n The particle position X at the moment i,n , particle external force P i,n , particle internal force F i,n Calculate t n+1 The particle position at the moment is expressed as: In the formula, α2＝1-0.5αh； Step 62: Calculate particle internal forces based on unit length changes: Where num is the number of cable units connected to particle i, F ej,n For the unit at t n The inner force of the moment, E j , A j is the elastic modulus and cross-sectional area of ​​unit j, l j,n , l j,n+1 For unit j at t n ,t n+1 The length of the moment, ε j is the unit strain, x i is the spatial position x coordinate of node i; Step 63: Superimpose the particle's external force and internal force to obtain the particle's residual force: f i,n+1 =P i,n+1 +F i,n+1 ; Step 64: Determine whether the residual force of the particle meets the convergence condition. If the residual force of the particle meets the convergence condition, obtain the equilibrium static model; otherwise, update the node coordinates, stress and external force, and return to step 1.

2. The method for tracking and analyzing stars on the active cable net reflection surface of the FAST telescope according to claim 1, characterized in that: The step 1 specifically includes: Step 11: Obtain the cable net reflector structure layout information, cable net prestressing, main cable material properties, lower cable material properties, back frame quality and panel quality; Step 12: Discretize the cable net reflector structure into a number of massive particles and massless cable units. The mass of the cable net, back frame and reflector panel are all concentrated on the particles; the mass of particle i is M i It is expressed as: Μ i =M i,1 +Μ i,2 +Μ i,3 , where M i，1 、M i，2 、M i，3 denote the masses of the cable net, back frame, and reflection panel assigned to particle i respectively; Step 13: Distribute the structure's self-weight to each particle, and the particle external force P i It is expressed as: P i =M i ×g, where g is the acceleration due to gravity; Step 14: Apply the prestressing effect to the cable element, and the element strain ε j It is expressed as: ε j =σ j / E j , where σ j 、E j represent the initial stress and elastic modulus of element j respectively; Step 15: Set the lower end node of the down-cable and the nodes around the main cable net as fixed points.

3. A method for tracking and analyzing stars on an active cable net reflection surface of a FAST telescope according to claim 2, characterized in that: The cable net reflective surface structure arrangement information includes topological relationships and boundary conditions.

4. The method for tracking and analyzing stars on the active cable net reflection surface of the FAST telescope according to claim 2, characterized in that: The material properties include elastic modulus, density and cross-sectional area.

5. The method for tracking and analyzing stars on the active cable net reflection surface of the FAST telescope according to claim 2, characterized in that: The step 3 specifically includes: Step 31: Calculate the illumination direction vector according to the azimuth of the observed celestial body: In the formula, p and q represent the angles between the irradiation direction and the x and z axes, respectively; Step 32: Calculate the distance D from the main cable node i to the direction vector and identify the main cable nodes within the irradiation range: In the formula, x i ,y i 、z i Represent the spatial position coordinates of node i, D i When the distance is less than or equal to the preset value, node i is within the working parabola.

6. A method for tracking and analyzing stars on an active cable net reflector surface of a FAST telescope according to claim 5, characterized in that: The step 4 specifically includes: Step 41: Calculate the FAST telescope working parabola equation: In the formula, x i ′、y i ′、z i ′ respectively represent the spatial position of the working parabola in the corresponding local coordinate system; Step 42: Calculate the radial distance d from all main cable nodes to the working parabola within the irradiation range i : In the formula, They respectively represent the distance from the main cable node i to the center of the sphere on the reference sphere and the distance from the main cable node i to the center of the sphere on the working parabola.

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