Telescope main reflection surface shape real-time evaluation and on-demand adjustment integration method

Abstract

The invention discloses a telescope main reflection surface shape real-time evaluation and on-demand adjustment integration method. An adjustment reference attitude and a reference temperature field are used as error zero points, and the whole process is calculated based on relative quantity. A gravity deformation database, a three-dimensional Chebyshev (or Legendre) temperature basis function unit response deformation database and a temperature control actuator unit temperature change influence matrix database are established offline. Regular least square fitting is performed on temperature sensor data on line to obtain a temperature coefficient, linear combination is performed to obtain relative displacement caused by temperature, the relative displacement and relative displacement caused by gravity are superposed to form relative node coordinates, and a reference surface is fitted to output a surface shape relative RMS. And solving quadratic programming based on first-order linearization under temperature upper and lower limits and smoothness constraint to obtain an actuator temperature increment instruction, and issuing the actuator temperature increment instruction, thereby realizing closed-loop compensation without online thermal-structural coupling and absolute morphology measurement.

Description

Technical Field

[0001] This invention relates to the fields of precision control of the main reflector surface shape of a telescope, structural deformation assessment and deformation compensation technology, and specifically to an integrated method for real-time assessment of the main reflector deformation and on-demand adjustment and optimization of the actuator, using the assembled and adjusted state as the zero point of error and calculating relative quantities throughout the entire process. Background Technology

[0002] Due to factors such as changes in gravity, temperature field, wind load, and solar radiation, the primary mirror of a telescope will deform, thus affecting its observation performance. Although holographic measurement, photogrammetry, and laser tracking can be used in engineering to obtain and correct the shape of the primary reflector, these methods are usually time-consuming and interfere with the observation operation, making it difficult to achieve continuous real-time evaluation.

[0003] Finite element analysis (FEM) can accurately predict structural deformation caused by gravity and temperature loads, but high-fidelity models have a large number of nodes and complex thermal boundaries. Directly performing thermo-structural coupling analysis and searching for the optimal adjustment command within the multi-actuator space during the online phase results in high computational complexity and struggles to meet the demands of rapid engineering decision-making. For systems using temperature-controlled supports (e.g., steel rod supports / columns / support rods combined with thermoelectric cooling or heating modules) as thermal actuators, the actuators adjust the surface shape by changing the effective support length through thermal expansion and contraction. Thermal inertia leads to response lag, and frequent adjustments during observation may affect observation stability. Therefore, it is more suitable to generate and execute adjustment commands on demand during non-observation windows or predetermined maintenance windows.

[0004] Furthermore, finite element models often struggle to directly characterize static geometric errors introduced by manufacturing and assembly. Relying on absolute topography for evaluation and compensation significantly increases calibration and measurement costs and reduces engineering maintainability. However, by using the assembled reference state as the zero point of error and solving only for relative changes, static geometric errors can be absorbed as constants, thereby reducing reliance on absolute topography measurements and complex calibrations. Summary of the Invention

[0005] The purpose of this invention is to provide an integrated method for real-time evaluation and on-demand adjustment of the main reflector. This method uses the reference attitude and reference temperature field after assembly and adjustment as a benchmark, treating this benchmark as a zero-error state. Subsequent nodal coordinates, displacements, residuals, and surface shape error indices under arbitrary attitudes and temperature fields are all expressed and solved relative to this benchmark. Through offline finite element pre-calculation and database generation, the following are calculated: (i) gravity-induced deformation response, (ii) unit response deformation of the three-dimensional Chebyshev (or Legendre) temperature basis function, and (iii) actuator unit adjustment influence matrix. In the online stage, relative deformation is rapidly synthesized based on zenith angle and temperature sensor data, and surface shape fitting is performed to obtain the relative RMS surface shape error and normal residual. Under engineering constraints such as actuator adjustment limits and smoothness, on-demand adjustment commands are solved and executed through quadratic programming based on first-order linearization, thereby achieving rapid compensation for surface shape errors caused by factors such as gravity and temperature, without requiring online thermo-structural coupled finite element solution and absolute morphology measurement.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An integrated method for real-time evaluation and on-demand adjustment of the main reflector surface shape of a telescope is proposed. This method uses the reference attitude and temperature field after assembly and adjustment as a benchmark, treating this benchmark as a zero-error state. Subsequent nodal coordinates, displacements, residuals, and surface shape error indices under arbitrary attitudes and temperature fields are all expressed and solved relative to this benchmark. Offline finite element analysis is used to pre-calculate and database the gravity-induced deformation response, the unit response deformation of the three-dimensional Chebyshev or Legendre temperature basis functions, and the actuator unit adjustment influence matrix. In the online stage, relative deformation is rapidly synthesized based on zenith angle and temperature data, and surface shape fitting is performed to obtain the relative RMS surface shape error and normal residual. Under actuator engineering constraints, on-demand shape adjustment commands are solved and executed using a first-order linearized quadratic programming approach, thereby achieving rapid compensation for surface shape errors without requiring online thermo-structural coupled finite element analysis and absolute topography measurement.

[0008] Furthermore, the method includes the following steps:

[0009] S1, referencing zenith angle α rig The shape of the lower primary reflector after assembly and adjustment is defined as the reference shape. M evaluation nodes are extracted from the surface nodes of the primary reflector structure model, and their reference coordinate matrix L is recorded. The temperature field T during assembly and adjustment is selected. rig (Under a uniform isothermal field) is used as a relative temperature reference, and the state corresponding to the reference shape and the reference temperature field is regarded as a reference state with zero error, so that the displacement, coordinate, residual and surface error calculated in the subsequent calculation are all expressed as relative quantities;

[0010] S2. Establish an offline gravity deformation database and interpolate online to obtain the gravity displacement matrix D(α) at ​​any zenith angle α, and relative to α rig Calculate the relative displacement of nodes caused by gravity ;

[0011] S3. Establish an offline temperature-based response deformation database: in [-1,1] 3 In a normalized coordinate system, the temperature field is represented as a three-dimensional Chebyshev (or Legendre) basis function expansion. Under offline conditions, structural analysis or calibration of the unit temperature distribution corresponding to each basis function is performed to obtain the evaluation node displacement matrix D. I (I is the lexicographical index of the basis functions) and store it in the database; online, the coefficient vector C(t) is obtained from the temperature sensor data (composed of each coefficient). (arranged by stacking columns), and linearly combined to obtain the relative displacement of nodes caused by temperature. ;

[0012] S4. Offline establishment of temperature control actuator influence matrix database: Apply unit temperature change to N temperature control actuators numbered j=1 to N respectively and obtain the displacement vectors of the evaluation node in the x, y, and z directions to construct the displacement influence matrix A of the j-th temperature control actuator. j And store it in the database;

[0013] S5. Relate L, ΔD(α), and ΔD temp The real-time evaluation node coordinate matrix L1(α,t) is obtained by superimposing (t) the coordinates of the nodes. temp (t), performing surface fitting on L1(α,t) yields the unit normal vector n of the i-th node on the fitted surface. i It also outputs the relative RMS surface shape error.

[0014] S6. Read A from the database for each temperature control actuator j. j And calculate b for each evaluation node i ij =n i ·a ij Construct a normal influence matrix (Jacobi matrix) B, where a ij For A j The displacement vector corresponding to the evaluation node i;

[0015] S7, Limit constraints k for actuator temperature regulation min ≤k≤k maxThe following method establishes and solves a quadratic programming problem based on first-order linearization, using the actuator temperature adjustment vector k as the decision variable. This minimizes the normal residual vector after adjustment and introduces a regularization term to limit the instruction increment and amplitude, resulting in the optimal adjustment instruction k*. k* is then converted into the temperature setpoint of each temperature control actuator and issued for execution.

[0016] Furthermore, in step S1, the zenith angle α will be referenced. rig The reference shape is considered to be in a zero-error state, so that the static geometric errors of manufacturing and assembly are absorbed in the form of constants, and the evaluation and optimization are carried out on the relative error changes.

[0017] Furthermore, the gravity displacement matrix mentioned in step S2 includes at least two boundary zenith angles, α=0° and α=90°, with displacement matrices D(0) and D(90) respectively, and D(α) is calculated online according to D(α)=D(0)·cosα + D(90)·sinα.

[0018] Furthermore, in step S3:

[0019] In step S3, the order P of the three-dimensional Chebyshev (or Legendre) basis functions is any non-negative integer, and the number of basis functions H = (P + 1). 3 ;

[0020] The temperature at which assembly and adjustment are completed is used as the reference temperature field T. rig ;

[0021] In step S3 or step S5, the coefficient vector C(t) is solved by least squares method with Tikhonov regularization. Singular value decomposition (SVD) is used during the solution process to improve numerical stability.

[0022] The number of temperature sensors P s The number should be at least 10, preferably 50 to 500;

[0023] Before solving for the coefficient vector C(t), outlier detection is performed on the temperature sensor data, and outliers are removed or downweighted.

[0024] Furthermore, in step S7:

[0025] The adjusted node coordinate matrix is ​​composed of Received, among which The temperature change of the j-th actuator constitutes the adjustment instruction k*;

[0026] The surface shape fitting is performed on the adjusted node coordinate matrix to obtain the adjusted surface node normal residual vector r;

[0027] Step S7 employs a first-order linearized iteration: using the current adjustment vector k hatLet u be the linearization point and u be the increment for a single iteration. Construct a first-order approximation r(k) for the adjusted surface node normal residual vector r. hat +u)≈r(k hat )+B·u, and under constraint k min ≤k hat +u≤k max Next, solve the quadratic programming problem with respect to u, and iteratively update k. hat Until the convergence condition is met; the convergence condition includes: the average absolute value of the instruction increment is lower than a preset threshold and the relative improvement rate of the objective function is lower than a preset threshold, or the number of iterations reaches the maximum value;

[0028] In step S7, the objective function of the quadratic programming based on first-order linearization simultaneously minimizes the root mean square of the normal residual, the adjustment amount, and the adjustment amount increment of the current adjustment amount relative to the previous adjustment.

[0029] Furthermore, the on-demand shaping adopts a phased strategy: the first phase solves for the baseline command only for gravity-induced deformation at multiple discrete zenith angles and interpolates the discrete results to obtain the attitude-command baseline; the second phase uses the baseline as the initial value or constraint center under the current thermal environment to solve for the total command after superimposed temperature compensation.

[0030] Furthermore, the adjustment data for gravity deformation is saved to the database.

[0031] Furthermore, the reference zenith angle α rig The optimal selection is made by minimizing the maximum relative RMS surface shape error within a predetermined zenith angle range.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] (1) The entire process takes the assembly reference state as the zero point of error and uses relative quantity to solve. The static geometric error of manufacturing and assembly is absorbed and canceled in the form of constant, reducing the dependence on absolute shape measurement and complex calibration.

[0034] (2) By pre-calculating offline and database-based gravity deformation, temperature-based response deformation and actuator influence matrix, continuous real-time surface shape evaluation and on-demand shape adjustment command generation can be achieved without thermal-structural coupling finite element solution in the online stage.

[0035] (3) The temperature field is stably fitted by three-dimensional Chebyshev (or Legendre) basis functions, and noise and high-order overfitting are suppressed by regularized least squares to improve the accuracy and numerical stability of temperature-induced deformation synthesis.

[0036] (4) An optimization model is constructed based on the reference surface normal residual, and the adjustment command is solved under the actuator temperature upper and lower limits and smoothness constraints, so that the command can be implemented, continuous and meets the engineering safety boundary.

[0037] (5) With optional first-order linearization and phased strategies, it can solve quickly with a large number of actuators, and can still maintain availability by using the gravity baseline in the event of temperature sensor malfunction. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method of the present invention;

[0039] Figure 2 This is a schematic diagram of the main reflector, support structure, and temperature control actuator.

[0040] Figure 3 This is a schematic diagram showing the position of the temperature control actuator at the bottom of the main reflector.

[0041] The markings in the diagram are: 1-Segmentation primary mirror; 2-Secondary mirror support; 3-Secondary mirror; 4-Actuator; 5-Back frame; 6-Mounting platform. Detailed Implementation

[0042] The present invention will now be described in further detail with reference to the accompanying drawings.

[0043] The integrated method for real-time evaluation and on-demand adjustment of the telescope's primary reflector proposed in this invention is as follows: Figure 1 As shown, the structure of the relevant device is as follows: Figure 2 As shown, it mainly includes a primary mirror 1, a secondary mirror support 2, a secondary mirror 3, an actuator 4, a back frame 5, and a mounting platform 6. The temperature control actuator is located at the bottom of the primary reflector as shown. Figure 3 As shown.

[0044] The method includes the following steps:

[0045] S1. Determine the reference state and relative quantity benchmark: Set the reference zenith angle α rig Below, the shape of the main reflector after assembly is defined as the reference shape; M evaluation nodes are extracted from the surface nodes of the main reflector structural model (preferably the finite element model), and their reference coordinate matrix L is recorded; the temperature field T during assembly is selected. rig (Under a uniform isothermal field) is used as a temperature relative reference; and the state corresponding to the reference shape and the reference temperature field is regarded as the reference state with zero error, so that the displacement, coordinate, residual and surface shape error calculated in the subsequent calculation are all expressed as relative quantities.

[0046] S2. Offline establishment of a gravity deformation database and online relativization: Under offline conditions, the gravity displacement matrix of the evaluation node is calculated at multiple discrete zenith angles, or at least at boundary zenith angles α=0° and α=90°, and stored in the database; in the online stage, the gravity displacement matrix at any zenith angle α is obtained by interpolation from the database based on the principle of linear elasticity. and with α rigThe relative displacement matrix of the reflecting surface nodes caused by gravity is obtained by subtracting from the reference. .

[0047] S3. Establish an offline temperature-based response deformation database and relativize it online: in [-1,1] 3 In a normalized coordinate system, the temperature field is represented as a three-dimensional Chebyshev (or Legendre) basis function expansion. The number of basis functions is H. Let be the temperature field corresponding to the i-th three-dimensional Chebyshev (or Legendre) basis functions (arranged in lexicographical order). The coefficients to be determined are: Under offline conditions, a unit temperature distribution load corresponding to each basis function is applied to the structure. Structural analysis or calibration is performed to evaluate and obtain the nodal displacement matrix D. I And store it in the database.

[0048] S4. Offline Establishment of Temperature Control Actuator Influence Matrix Database: Identify N temperature control actuators numbered j=1 to N; while keeping the reference states of other actuators unchanged, apply a unit temperature change to each actuator and perform structural analysis or calibration to obtain the displacement vectors of the evaluation nodes in the x, y, and z directions, thus constructing the displacement influence matrix A of the j-th actuator. j And store it in the database, where A j This method describes the effect of a unit temperature increment on the nodal displacement of the actuator. It is also applicable to non-temperature-sensitive actuators, such as displacement actuators, by converting the temperature-induced change in actuator length into displacement.

[0049] S5. Online temperature field fitting and temperature deformation synthesis: Online acquisition of P s The measurements from each temperature sensor form a measurement vector S(t), which maps the three-dimensional coordinates of the temperature sensors to [-1, 1]. 3 Normalized space; coefficients obtained by fitting temperature sensor data. The relative displacement of the reflector nodes caused by temperature is obtained by the subsequent linear combination. The coefficient vector C(t) consists of the coefficients of each coefficient. The coefficient vector C(t) is formed by stacking columns. The least squares method with Tikhonov regularization is used to solve for the coefficient vector C(t), and singular value decomposition (SVD) is used during the solution process to improve numerical stability.

[0050] S6. Real-time surface shape evaluation (relative quantity): This involves comparing the reference coordinate matrix L with the relative gravity displacement matrix ΔD(α) and the relative temperature displacement matrix ΔD. temp The relative coordinate matrix of the real-time evaluation node is obtained by superimposing (t) the matrix L1(α,t)=L+ΔD(α)+ΔD temp(t); Perform surface fitting on L1(α,t), preferably parabolic fitting, and simultaneously solve for the optimal curvature parameters, rigid body translation and rigid body rotation parameters; use its root mean square value as the relative RMS surface error output, and simultaneously output the unit normal vector n of the i-th node. i .

[0051] S7. Construct the influence matrix of the normal actuators: For each actuator j, read A from the database. j Adjusted node relative coordinate matrix ,in Let be the adjustment amount for the j-th actuator (defined as the temperature increment of each actuator relative to its reference temperature setpoint). Perform surface fitting on the adjusted node coordinate matrix to obtain the adjusted surface node normal residual vector r. Calculate b for each evaluation node i. ij =n i ·a ij To construct the normal influence matrix B, where a ij For A j The displacement vector corresponding to the evaluation node i;

[0052] S8. Solve for and issue the on-demand adjustment command under engineering constraints: using the actuator temperature adjustment vector k (from... The decision variables are (stacked in columns); under the box constraint k min ≤k≤k max Under optional linear equality constraints, a quadratic programming problem based on first-order linearization is established and solved to minimize the second norm of the normal residual vector after the shape adjustment. A regularization term is introduced to limit the instruction increment and instruction amplitude to obtain the optimal shape adjustment instruction k*. k* is then converted into the temperature setpoint of each temperature control actuator and issued for execution.

[0053] Preferably, step S8 employs a first-order linearization iteration based on the residual vector: using the current adjustment vector k hat Let u be the linearization point and u be the increment for a single iteration. Construct a first-order approximation r(k) for the adjusted surface node normal residual vector r. hat +u)≈r(k hat )+B·u, where B is the Jacobian matrix (the matrix elements are the projections of the nodal displacements of the reflecting surface caused by the unit adjustment of each actuator onto the normal direction of the fitting surface); under constraint k min ≤k hat +u≤k max Next, solve the quadratic programming problem with respect to u and update k. hat ←k hat +u, iterate until the convergence condition is met.

[0054] More preferably, the calculation of on-demand deformation adjustment adopts a phased strategy: the first phase solves for the baseline command only for gravity-induced deformation at multiple discrete zenith angles and interpolates to obtain the attitude-command baseline; the second phase uses the baseline as the initial value or constraint center under the current thermal environment to solve for the total command after superimposed temperature compensation, so as to improve robustness and engineering maintainability.

[0055] I. Explanation of Terms and Symbols

[0056] 1) Reference zenith angle α rig The zenith angle during mirror assembly (considered as error-free after assembly) is considered as the zero-error reference state in this invention, corresponding to the state of the reference temperature field.

[0057] 2) Reference coordinate matrix L: The coordinate matrix of the evaluated nodes under the reference state with zero error, which is used as the basis for the superposition of relative coordinates.

[0058] 3) Gravity-induced relative displacement matrix of the reflecting surface nodes ΔD(α): Gravity displacement matrix at any zenith angle α relatively The difference component.

[0059] 4) Relative displacement ΔD of the reflector surface nodes caused by temperature temp (t): The coefficient vector C(t) obtained by fitting the temperature field and the displacement matrix D of the temperature basis response of the I-th three-dimensional Chebyshev (or Legendre) basis function. I The displacement obtained by linear combination.

[0060] 5) Node relative coordinate matrices L1(α,t) and L2(α,t): The reference coordinate matrix L is combined with the relative gravity displacement matrix ΔD(α) and the relative temperature displacement matrix ΔD. temp The relative coordinate matrix of the real-time evaluation node is obtained by superimposing (t) the matrix L1(α,t)=L+ΔD(α)+ΔD temp L2(α,t) is the adjusted node relative coordinate matrix.

[0061] 6) Actuator Incremental Model: A j Let be the evaluation node displacement influence matrix caused by the unit temperature increment of the j-th temperature controller actuator; k is the temperature increment command (vector) relative to the reference setpoint; B is the Jacobian matrix, and the matrix elements are the projections of the reflection surface node displacement values ​​caused by the unit adjustment of each actuator onto the normal direction of the fitting surface.

[0062] 7) Adjust the surface node normal residual vector r relative to the surface shape RMS: using A jAfter adjusting the relative node coordinate matrix and fitting the adjusted surface nodes to the reference surface, the residuals of the nodes along the unit normal direction of the reference surface constitute the normal residual vector r. The root mean square of the normal residuals of the surface nodes is the relative RMS of the adjusted surface shape.

[0063] II. Offline Database Construction

[0064] (1) Gravity Deformation Database: In the offline stage, linear elastic gravity analysis is performed at multiple discrete zenith angles to obtain D(α) and store them in the database; preferably, only the displacement matrices D(0) and D(90) under the two boundary attitudes of α=0° and α=90° are calculated, and the online calculation is performed according to D(α)=D(0)·cosα + D(90)·sinα, and the results are presented in the database. Subtracting them yields ΔD(α).

[0065] (2) Temperature-based response deformation database: Select a three-dimensional Chebyshev (or Legendre) order P and construct H=(P+1). 3 One basis function; maps the structure node coordinates to [-1, 1] 3 Range; adjusted under a reference temperature (uniform temperature field, temperature T) rig Using as a baseline, thermal loads are applied to the unit temperature distribution corresponding to each basis function, and structural analysis is performed to obtain the displacement matrix D. I Concurrent database.

[0066] (3) Actuator Influence Matrix Database: Apply a unit temperature change (e.g., 1°C) to each temperature control actuator and obtain the evaluation node displacement to form A. j Concurrent database.

[0067] III. Online Real-Time Assessment

[0068] (1) Temperature field fitting: Normalize the coordinates of the temperature sensor to [-1,1] 3 In the space, the coefficient vector C(t) is solved using the least squares method with Tikhonov regularization. Singular value decomposition (SVD) is used during the solution process to improve numerical stability.

[0069] (2) Relative node coordinate synthesis and surface fitting: based on ΔD(α) and ΔD temp (t) Obtain L1(α,t)=L+ΔD(α)+ΔD temp (t), perform parabolic fitting and simultaneously solve for curvature parameters, rigid body translation and rotation angles to minimize the root mean square of the normal residual; output the relative RMS surface error and the unit normal vector n of node i. i .

[0070] (3) Optional outlier handling: Perform outlier removal / weight reduction on temperature sensor data or fitting residuals to improve robustness.

[0071] IV. On-demand adjustment, optimization, and implementation

[0072] (1) Quadratic programming solution: under box constraint k min ≤k≤k max Next, solve the objective function. We obtain k*; where The normal residual vector of the reflection surface node relative to the fitted parabola after adjustment by the adjustment amount corresponding to k, where w1, w2, and w3 are positive weights, and k prev This represents the command vector for adjacent attitudes or adjacent time steps. Preferably, the solution process employs a first-order linearized iteration based on the residual vector: using the current adjustment vector k... hat Let u be the linearization point and u be the increment for a single iteration. Construct a first-order approximation r(k) of the residual. hat +u)≈r(k hat )+B·u, where B is the Jacobian matrix (the matrix elements are the projections of the nodal displacements of the reflecting surface caused by the unit adjustment of each actuator onto the normal direction of the fitting surface); under constraint k min ≤k hat +u≤k max Next, solve the quadratic programming problem with respect to u and update k. hat ←k hat +u, iterate until the convergence condition is met.

[0073] (2) Save the adjustment data for gravity deformation to the database: Gravity deformation is invariant. Saving the adjustment data for gravity deformation can maintain availability even in cases of abnormal temperature sensors.

[0074] (3) Execution: Convert k* into temperature setpoints for each actuator and send them to the temperature controller for execution; output the predicted relative RMS surface shape error after adjustment and the command.

[0075] V. Optional Reference Zenith Angle Optimization

[0076] To reduce the maximum relative surface shape error across the entire working angle range, the zenith angle α during mirror assembly and adjustment... rig It can be used as an optimizable parameter. Optionally, based on an offline gravity deformation database, the α value that minimizes the relative RMS maximum under the boundary conditions can be solved within a predetermined zenith angle range. rig and the obtained α rig This serves as a benchmark for subsequent real-time evaluation and adjustment.

[0077] In summary, this invention provides an integrated method for real-time evaluation and on-demand adjustment of the telescope's primary reflector. Using the installation reference attitude and reference temperature field as the zero-error points, the entire process is based on relative quantity calculations. Offline, a gravity deformation database, a three-dimensional Chebyshev (or Legendre) temperature basis function unit response deformation database, and a database of the influence matrix of unit temperature change on the temperature control actuator are established. Online, temperature sensor data is fitted with regular least squares to obtain the temperature coefficient, and a linear combination is used to obtain the relative displacement caused by temperature. This displacement is then superimposed with the relative displacement caused by gravity to form relative node coordinates. The relative RMS and normal residuals are output from the fitted reference surface. Under temperature upper and lower limits and smoothness constraints, a quadratic programming problem based on first-order linearization is solved to obtain and issue the actuator temperature increment command, achieving closed-loop compensation without online thermo-structural coupling and absolute topography measurement.

[0078] The above embodiments are merely typical implementations of the present invention and are not intended to limit the present invention. Any equivalent substitutions or improvements made within the scope of the claims of the present invention are within the protection scope of the present invention.

Claims

1. A method for real-time evaluation and on-demand adjustment of the principal reflector surface shape of a telescope, characterized in that, The reference attitude and reference temperature field after assembly and adjustment are used as the benchmark, and the benchmark is regarded as the error is zero. The node coordinates, displacements, residuals and surface shape error indices under any attitude and any temperature field are all expressed and solved in terms of quantities relative to the benchmark. The gravity-induced deformation response, the unit response deformation of the three-dimensional Chebyshev or Legendre temperature basis functions, and the actuator unit adjustment influence matrix are pre-calculated and database-based using offline finite element methods. In the online stage, relative deformation is rapidly synthesized based on zenith angle and temperature data, and surface shape fitting is performed to obtain the relative RMS surface shape error and normal residual. Under actuator engineering constraints, the surface shape error is rapidly compensated by solving the required shape adjustment command based on first-order linearized quadratic programming, without the need for online thermo-structural coupled finite element solution and absolute topography measurement.

2. The method according to claim 1, characterized in that, Includes the following steps: S1, referencing zenith angle α rig The assembled shape of the lower primary reflector is defined as the reference shape, and M evaluation nodes are extracted from the surface nodes of the primary reflector structural model, their reference coordinate matrix L is recorded, and the reference temperature field T is selected. rig As a relative temperature reference, and considering the state of the reference shape corresponding to the reference temperature field as the reference state with zero error, the displacement, coordinate, residual and surface error calculated in the subsequent calculation are all expressed as relative quantities; S2. Establish an offline gravity deformation database and interpolate online to obtain the gravity displacement matrix D(α) at ​​any zenith angle α, and relative to α rig Calculate the relative displacement of the nodes ΔD(α) caused by gravity; S3. Offline establishment of temperature basis response deformation database: In a normalized coordinate system, the temperature field is represented as a three-dimensional Chebyshev or Legendre basis function expansion. Under offline conditions, structural analysis or calibration is performed on the unit temperature distribution corresponding to each basis function to obtain the evaluation node displacement matrix D. I And store it in the database, where I is the index of the basis function arranged in hierarchical lexicographical order; The coefficient vector C(t) is obtained online from temperature sensor data, and the relative displacement ΔD of the nodes caused by temperature is obtained by linear combination. temp (t); S4. Offline establishment of temperature control actuator influence matrix database: Apply unit temperature change to N temperature control actuators numbered j=1 to N respectively and obtain the displacement vectors of the evaluation node in the x, y, and z directions to construct the displacement influence matrix A of the j-th temperature control actuator. j And store it in the database; S5. Relate L, ΔD(α), and ΔD temp The coordinates of the real-time evaluation nodes are obtained by superimposing (t) the coordinates of the nodes. Then, surface fitting is performed on L1(α,t) to obtain the unit normal vector n of the i-th node on the fitted surface. i It also outputs the relative RMS surface shape error. S6. Read A from the database for each temperature control actuator j. j And construct the normal influence matrix B based on the normal displacement of each evaluation node relative to the fitting surface caused by the unit temperature change of each temperature controller actuator; S7. Under the constraints of the upper and lower limits of actuator temperature regulation, establish and solve a quadratic programming problem based on first-order linearization with the actuator temperature regulation vector as the decision variable, minimize the normal residual vector after adjustment, and introduce a regularization term to limit the instruction increment and instruction amplitude to obtain the optimal adjustment instruction k*. Convert k* into the temperature setpoint of each temperature control actuator and issue it for execution.

3. The method according to claim 2, characterized in that, In step S1, the reference zenith angle α will be used. rig The reference shape is considered to be in a zero-error state, so that the static geometric errors of manufacturing and assembly are absorbed in the form of constants, and the evaluation and optimization are carried out on the relative error changes.

4. The method according to claim 2, characterized in that, The gravity displacement matrix mentioned in step S2 includes at least two boundary zenith angles, α=0° and α=90°, with displacement matrices D(0) and D(90) respectively, and D(α) is calculated online according to D(α)=D(0)·cosα +D(90)·sinα.

5. The method according to claim 2, characterized in that, In step S3: The order P of the three-dimensional Chebyshev or Legendre basis functions is any non-negative integer, and the number of basis functions H = (P + 1). 3 ; The temperature at which assembly and adjustment are completed is used as the reference temperature field T. rig ; In step S3, the coefficient vector C(t) is solved by least squares with Tikhonov regularization. Singular value decomposition (SVD) is used during the solution process to improve numerical stability. Before solving for the coefficient vector C(t), outlier detection is performed on the temperature sensor data, and outliers are removed or downweighted.

6. The method according to claim 2, characterized in that, In step S7: The adjusted node coordinate matrix is ​​composed of Received, among which The temperature change of the j-th actuator constitutes the adjustment instruction k*; The surface shape fitting is performed on the adjusted node coordinate matrix to obtain the adjusted surface node normal residual vector r; First-order linearized iteration is used: with the current adjustment vector k hat Let u be the linearization point and u be the increment for a single iteration. Construct a first-order approximation r(k) for the adjusted surface node normal residual vector r. hat +u)≈r(k hat )+B·u, and under constraint k min ≤k hat +u≤k max Next, solve the quadratic programming problem with respect to u, and iteratively update k. hat Until the convergence condition is met; the convergence condition includes: the average absolute value of the instruction increment is lower than a preset threshold and the relative improvement rate of the objective function is lower than a preset threshold, or the number of iterations reaches the maximum value; The objective function of the quadratic programming based on first-order linearization simultaneously minimizes the root mean square of the normal residual, the adjustment amount, and the increment of the current adjustment amount relative to the previous adjustment.

7. The method according to claim 1, characterized in that, On-demand shaping adopts a phased strategy: the first phase solves for the baseline command for gravity-induced deformation only at multiple discrete zenith angles and interpolates the discrete results to obtain the attitude-command baseline; In the second stage, using the baseline as the initial value or constraint center under the current thermal environment, the total command after superimposed temperature compensation is solved.

8. The method according to claim 7, characterized in that, The adjustment data for gravity-induced deformation is saved to the database.

9. The method according to claim 2, characterized in that, The reference zenith angle is optimized by minimizing the maximum relative RMS surface error within a predetermined zenith angle range.

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