A method for controlling thermal vibration of a thin film antenna based on electrostatic force

Abstract

The application discloses a kind of thin film antenna thermal vibration control methods based on electrostatic force, belong to the technical field of vibration analysis and control of spaceborne antenna structure.Method includes: establishing thin film antenna in-orbit thermal analysis model, extracts the transient temperature information of in and out shadow area;Establish nonlinear dynamics model, carry out thermal vibration analysis as load with transient temperature, obtain vibration information without control;Based on electrostatic force actuation mode, construct active control model;Optimization solution to control model, obtain the best control electrostatic force and apply to thin film antenna.The application realizes the thin film antenna thermal vibration analysis under the typical thermal environment of in and out shadow area in orbit, and utilizes non-contact electrostatic force to carry out active control, without attaching intelligent actuator, avoid the influence on the stiffness and dynamics characteristics of thin film antenna itself, with fast response, no mechanical friction and other advantages, can effectively suppress thermal vibration, improve the in-orbit stability of thin film antenna.

Description

Technical Field

[0001] This invention belongs to the field of vibration analysis and control technology of spaceborne antenna structures, and particularly relates to a method for controlling the thermal vibration of thin-film antennas based on electrostatic force. Background Technology

[0002] my country's manned spaceflight, Earth observation, and communication fields have created an urgent need for large, deployable spaceborne antennas to meet mission requirements such as high throughput, multi-band operation, and high gain. Among various types of deployable spaceborne antennas, spaceborne thin-film antennas possess unique advantages such as light weight, high packing ratio, and easy folding and deployment, making them highly valuable for engineering applications and strategic research. Spaceborne thin-film antennas mainly consist of a cable-membrane flexible structure and a deployable support truss. After deployment in orbit, their array shape and dynamic characteristics are highly susceptible to the influence of the in-orbit thermal environment, causing deterioration of the antenna profile. In severe cases, this can lead to significant vibrations on the membrane surface, resulting in antenna failure. Therefore, considering the vibration analysis and control of spaceborne thin-film antennas under actual in-orbit thermal conditions is of significant research importance.

[0003] Vibration analysis and control of thin-film antennas has been extensively studied by scholars both domestically and internationally. In the field of thin-film antenna vibration analysis, some scholars, based on the von Karman large deformation assumption and considering the geometric nonlinearity of thin-film structures, have established a rigid-flexible coupled dynamic model for thin-film solar sails. Other scholars, addressing the dynamic response of large flexible spacecraft in the thermal environment of space caused by temperature gradients, have proposed a thermo-flexible fully parameterized plate element based on absolute nodal coordinate formulas to uniformly describe the displacement and temperature fields. A nonlinear vibration analysis model for thin-film structures under on-orbit thermal conditions has been established, considering the influence of temperature on the stress, deformation, and vibration in a vacuum, clarifying the significant influence of temperature stress on the vibration frequency and amplitude of the thin-film structure. Regarding thin-film antenna vibration control, addressing the problems of low efficiency in controlling large-amplitude nonlinear vibrations of thin-film structures and poor adaptability of traditional control methods, a deep reinforcement learning-based active vibration control method for thin-film structures has been proposed. A vibration control method for parabolic thin-film reflectors based on photoactivated shape memory polymers (LaSMP) has also been proposed. However, attaching smart actuators to thin film structures can significantly affect the stiffness and dynamic characteristics of the thin film structures themselves. Therefore, it is necessary to comprehensively consider the material properties, patch size, arrangement density and installation method of the smart actuators, and minimize their impact on the original mechanical properties of the thin film structures while ensuring vibration control accuracy and response speed.

[0004] In summary, existing technologies have the following technical problems regarding the vibration analysis and control of thin-film structures: (1) Existing vibration analysis of thin film structures has not yet conducted thermal vibration analysis of thin film antennas in the actual thermal environment when the satellite antenna enters and exits the shadow area; (2) Existing active control methods for thin film structures with attached intelligent actuators have a significant impact on the stiffness and dynamic characteristics of large thin film antennas.

[0005] Therefore, how to conduct thermal vibration analysis on the actual on-orbit thermal environment of spaceborne antennas, and how to achieve active control of thin-film antenna vibration using non-contact external electrostatic force, are technical problems that urgently need to be solved by those skilled in the art. Summary of the Invention

[0006] To solve the above problems, the technical solution of the present invention is: a method for controlling the thermally induced vibration of a thin-film antenna based on electrostatic force, comprising the following steps: S1. Establish an on-orbit thermal analysis model for the thin-film antenna and extract transient temperature information of the thin-film antenna when entering and exiting the shadow region; S2. Establish a nonlinear dynamic model of the thin-film antenna, apply the transient temperature information extracted in S1 as a transient temperature load to the nonlinear dynamic model of the thin-film antenna, perform thermal vibration analysis, and obtain the on-orbit thermal vibration information of the thin-film antenna without external control. S3. Construct an active control model for the thermal vibration of a thin-film antenna based on electrostatic force actuation; S4. Optimize and solve the active control model of the thermal-induced vibration of the thin-film antenna to obtain the optimal control electrostatic force, and actively control the thermal-induced vibration of the thin-film antenna according to the optimal control electrostatic force.

[0007] Furthermore, S1 includes: S11. Establish the geometric model of the thin-film antenna: generate a length of... Width is The thin film surface is generated with a length of Width is The supporting truss structure is constructed, and boundary cables are generated on the thin film surface, resulting in a geometric model of the thin film antenna composed of the thin film surface, the supporting truss structure, and the boundary cables; among which, The length of the thin film surface (m); The width of the film surface (m); The length (m) of the supporting truss structure; Width (m) of the supporting truss structure; S12. Perform thermal analysis mesh generation on the thin-film antenna geometric model established in S11: Use triangular thermal analysis thin-film elements to mesh the thin-film surface, use thermal analysis beam elements to mesh the supporting truss structure, and use thermal analysis cable elements to mesh the boundary cables to obtain the thin-film antenna thermal analysis mesh model. S13. Given the thermal analysis material parameters of the thin-film antenna: Given the thermal conductivity, specific heat capacity, emissivity, and absorptivity of the thin-film surface, supporting truss structure, and boundary cables, establish a finite element model for the thermal analysis of the thin-film antenna based on the mesh model obtained in S12: ; In the formula, The heat capacity matrix assembled in the global coordinate system; The node temperature column vector; Time (s); The heat conduction matrix is ​​assembled in the global coordinate system; The thermal radiation matrix assembled in the global coordinate system; This is the column vector of nodal heat flux loads assembled in the global coordinate system;

[0008] S14. Given the on-orbit thermal analysis solution parameters for the thin-film antenna: Given the time interval for the thin-film antenna to enter and exit the shadow region. The finite element model for thermal analysis of the thin-film antenna established in S13 was solved to obtain the time interval. The node temperature values ​​that vary with time; among which, The starting time (s) for the thin-film antenna to enter the shadow region; The end time (s) when the thin-film antenna leaves the shadow region; S15. Save the time-varying node temperature values ​​obtained from S14 to a file to obtain the transient temperature information file of the thin-film antenna entering and exiting the shadow area, providing transient temperature load data for the thermal vibration analysis in S2.

[0009] Furthermore, S2 includes: S21. Perform finite element mesh generation on the geometric model of the thin film antenna: use triangular thin film elements to mesh the thin film surface, use two-node beam elements to mesh the supporting truss structure, and use two-node cable elements to mesh the tension cable to obtain the finite element mesh model of the thin film antenna structure. S22. Given the material parameters of the thin-film antenna structure: Given the elastic modulus, mass density, Poisson's ratio and thermal expansion coefficient of the thin-film surface, supporting truss structure and tension cable, provide material parameters for the establishment of the nonlinear dynamic model of the thin-film antenna; S23. Given the constraints of the thin-film antenna: The two nodes of the supporting truss structure boundary are subjected to full displacement constraints. Based on the finite element mesh model of the thin-film antenna structure obtained in S21 and the structural material parameters given in S22, a nonlinear dynamic analysis model of the thin-film antenna is established: ; In the formula, The overall mass matrix of the thin-film antenna; The nodal acceleration vector; The overall damping matrix of the thin-film antenna; The node velocity vector; This is the stiffness matrix of the cable structure related to the initial tension value of the cable; The initial tension value of the cable (N). Related to the temperature load of the thin-film antenna; This is the film structure stiffness matrix related to the initial tension value of the film; The initial tension value (N) of the film. Related to the temperature load of the thin-film antenna; Here is the stiffness matrix of the truss structure; The nodal displacement vector; The external load vector (N); S24. Apply the transient temperature information extracted in S1 as an external load to the nonlinear dynamic analysis model of the thin-film antenna established in S23, perform transient dynamic solution, and obtain the dynamic response of each node of the thin-film antenna under transient temperature load. S25. Extract the relationship between the nodal displacement and time of the thin-film antenna to obtain the on-orbit thermally induced vibration information of the thin-film antenna without external control, and provide a comparison benchmark for the vibration mode comparison before and after applying electrostatic force control in S4.

[0010] Furthermore, S3 includes: S31. Establishing a nonlinear dynamic model of a thin-film antenna under electrostatic force based on the nonlinear finite element method: ; In the formula, The displacement vector of the thin film structure nodes; Let V be the voltage vector of the electrostatic field; the point above the vector represents the derivative of the vector with respect to time. The mass matrix of the thin-film antenna structure; The damping matrix of the thin-film antenna structure; This is the stiffness matrix of the thin-film antenna structure; Here is the stiffness matrix of the cable structure; and This is the coupling stiffness matrix generated by the coupling effect between the electrostatic field and the thin film structure field. This is the additional coupling stiffness matrix caused by electrostatic force; Here is the stiffness matrix caused by the electrostatic field; This is the stiffness matrix of the additional electric field caused by electrostatic force; N represents the external force load vector of the thin film structure. C is the vector of external charge load caused by the electric field. S32. The nonlinear dynamic model of the thin-film antenna under electrostatic force established in S31 is reduced in order to obtain the reduced-order model in the modal coordinate system: ; ; In the formula, Modal displacement; Mode voltage (V); Time (s); Here is the modal mass matrix; Here is the modal damping matrix; Here is the modal stiffness matrix; The electrostatic field-structure field coupling matrix in modal coordinates; The external load (N) is in the modal coordinate system. Modal capacitance (F); This is the transpose of the electrostatic-structural field coupling matrix in modal coordinates; Mode charge (C); S33. Based on the reduced-order model obtained in S32, establish the state-space equations of the nonlinear coupled model: ; In the formula, ; in, It is a state vector; The input vector; The state matrix; The input matrix; It is the identity matrix; The equivalent resistance (Ω) in modal coordinates; Furthermore, S4 includes: S41. Using the membrane vibration displacement and velocity as state variables, and taking the vibration suppression effect and control energy consumption as comprehensive optimization objectives, establish an optimization control problem: ; In the formula, To comprehensively optimize the objective function; It is a state vector; This is the transpose of the state vector; This is the state weight matrix; To control the input vector; To control the transpose of the input vector; To control the weight matrix; Time (s); S42. Solve the optimization control problem established in S41 to obtain the optimal feedback gain matrix: ; In the formula, The optimal feedback gain matrix; To control the weight matrix; The input matrix; This is the transpose of the input matrix; The matrix represents the symmetric positive definite solution of the Riccati algebraic equation; then, the optimal control electrostatic force is obtained based on the optimal feedback gain matrix. ; In the formula, This is the control input vector corresponding to the optimal control of the electrostatic force; It is a state vector; S43. Substitute the optimal control electrostatic force obtained in S42 into the state-space equation of the nonlinear coupling model established in S33, and solve for the thermal vibration response of the thin-film antenna under the control of the optimal control electrostatic force. S44. Compare the vibration modes of the thin-film antenna before and after applying electrostatic force control to verify the vibration suppression effect of active control of thermally induced vibration of the thin-film antenna based on electrostatic force.

[0011] The beneficial effects of this invention are as follows: The electrostatic force-based thin-film antenna thermal vibration control method provided by this invention establishes an on-orbit thermal analysis model of the thin-film antenna and extracts transient temperature information of the antenna entering and exiting the shadow area. The transient temperature information is then applied as a load to the nonlinear dynamic model of the thin-film antenna for thermal vibration analysis, which can realize thermal vibration analysis of thin-film antennas under typical thermal environments such as entering and exiting the shadow area on-orbit. This invention utilizes electrostatic force, a non-contact actuation method, for active vibration control of thin-film antennas. It eliminates the need to attach intelligent actuators to the thin-film structure, thus avoiding significant impacts on the antenna's stiffness and dynamic characteristics. Furthermore, it offers advantages such as fast response speed and the absence of mechanical friction and hysteresis. Attached Figure Description

[0012] Figure 1 This is a flowchart of the electrostatic force-based thin-film antenna thermal vibration control method of the present invention; Figure 2 This is a flowchart of the present invention for establishing an on-orbit thermal analysis model of a thin-film antenna to extract transient temperature information of the antenna entering and exiting the shadow region; Figure 3 This is a flowchart of the present invention for establishing a nonlinear dynamic model of a thin-film antenna and applying a transient temperature load to perform thermal vibration analysis; Figure 4 This is a flowchart of the active control model for the thermal vibration of a thin-film antenna based on electrostatic force, as presented in this invention. Figure 5This invention provides a flowchart for optimizing and solving the thermal vibration control model of a thin-film antenna to obtain the optimal control electrostatic force. Figure 6 This is a geometric model diagram of a thin-film antenna provided in an embodiment of the present invention; Figure 7 This is a thermal analysis grid diagram of a thin-film antenna provided in an embodiment of the present invention; Figure 8 This is a temperature change diagram of the thin-film antenna entering and exiting the shadow area provided in an embodiment of the present invention; Figure 9 This is a thermally induced vibration curve of the thin-film antenna before active control, provided in an embodiment of the present invention. Figure 10 This is a graph showing the thermally induced vibration of a thin-film antenna under electrostatic control, provided in an embodiment of the present invention. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] The electrostatic force-based thin-film antenna thermal vibration control method provided by this invention, such as... Figure 1 As shown, it includes the following steps: S1. Establish an on-orbit thermal analysis model for the thin-film antenna and extract transient temperature information of the antenna entering and exiting the shadow region; S2. Establish a nonlinear dynamic model of the thin-film antenna and perform thermal vibration analysis by applying transient temperature loads. S3. Construct an active control model for the thermal vibration of a thin-film antenna based on electrostatic force; S4. Optimize the control model of thermal vibration of thin film antenna to obtain the optimal control electrostatic force.

[0015] in, Figure 1 This is a flowchart of an embodiment of the present invention for a method for controlling the thermal vibration of a thin-film antenna based on electrostatic force.

[0016] like Figure 2 As shown, step S1 above specifically involves the following steps: S11. Establish the geometric model of the thin-film antenna: generate a length of... Width is The thin film surface is generated with a length of Width is The supporting truss structure generates membrane surface boundary cables; among which, The length of the thin film surface (m); The width of the film surface (m); The length (m) of the supporting truss structure; Width (m) of the supporting truss structure; S12. Perform thermal analysis mesh generation on the geometric model of the thin film antenna: use triangular thermal analysis thin film elements to mesh the thin film surface, use thermal analysis beam elements to mesh the supporting truss, and use thermal analysis cable elements to mesh the boundary cables. S13. Given the material parameters for thermal analysis of the thin-film antenna: given the thermal conductivity, specific heat capacity, emissivity, and absorptivity of the thin-film surface, supporting truss, and boundary cables, the finite element model for thermal analysis of the thin-film antenna is established as follows: ; In the formula, The heat capacity matrix assembled in the global coordinate system; The node temperature column vector; Time (s); The heat conduction matrix is ​​assembled in the global coordinate system; The thermal radiation matrix assembled in the global coordinate system; This is the column vector of nodal heat flux loads assembled in the global coordinate system; S14. Given the on-orbit thermal analysis solution parameters for the thin-film antenna: given the time interval for entering and exiting the shadow region. The on-orbit thermal analysis model of the thin-film antenna was solved; among them, The starting time (s) for the thin-film antenna to enter the shadow region; The end time (s) when the thin-film antenna leaves the shadow region; S15. Save the temperature values ​​that change with time to a file to obtain the transient temperature information of the thin-film antenna entering and exiting the shadow area.

[0017] like Figure 3 As shown, step S2 above specifically involves the following steps: S21. Finite element mesh generation of the thin-film antenna geometric model: Mesh generation of the thin-film surface, supporting truss and tension cable is performed using triangular thin-film elements, two-node beam elements and two-node cable elements respectively; S22. Given the material parameters of the thin-film antenna structure: given the elastic modulus, mass density, Poisson's ratio and coefficient of thermal expansion of the thin-film surface, supporting truss and tension cable; S23. Given the constraints of the thin-film antenna: By applying full displacement constraints to the two nodes of the supporting truss boundary, the nonlinear dynamic analysis model of the thin-film antenna is established as follows: ; In the formula, The overall mass matrix of the thin-film antenna; The nodal acceleration vector; The overall damping matrix of the thin-film antenna; The node velocity vector; This is the stiffness matrix of the cable structure related to the initial tension value of the cable; The initial tension value of the cable (N); This is the film structure stiffness matrix related to the initial tension value of the film; The initial tension value (N) of the film; , Related to the temperature load of the thin-film antenna; Here is the stiffness matrix of the truss structure; The nodal displacement vector; The external load vector (N); S24. Apply transient temperature information as an external load to the nonlinear dynamic model of the thin-film antenna to solve for transient dynamics. S25. Extract the relationship between the nodal displacement of the thin-film antenna and time to obtain the on-orbit thermally induced vibration information of the thin-film antenna without external control.

[0018] like Figure 4 As shown, step S3 above specifically involves the following steps: S31. Establishing a nonlinear dynamic model of a thin-film antenna under electrostatic force based on the nonlinear finite element method: ; In the formula, The displacement vector of the thin film structure nodes; Let V be the electrostatic field voltage vector; the point above the vector represents the time derivative of the vector. , and These represent the mass matrix, damping matrix, and stiffness matrix of the thin-film antenna structure, respectively. Here is the stiffness matrix of the cable structure; and This is the coupling stiffness matrix generated by the coupling effect between the electrostatic field and the thin film structure field. This is the additional coupling stiffness matrix caused by electrostatic force; Here is the stiffness matrix caused by the electrostatic field; This is the stiffness matrix of the additional electric field caused by electrostatic force; N is the external force load vector of the thin film structure. C is the vector of external charge load caused by the electric field. S32. Reduce the order of the nonlinear dynamic model of the thin-film antenna to obtain the reduced-order model in the modal coordinate system: ; ; In the formula, Modal displacement; Mode voltage (V); Time (s); , , These are the modal mass matrix, modal damping matrix, and modal stiffness matrix, respectively. The electrostatic field-structure field coupling matrix in modal coordinates; The external load (N) is in the modal coordinate system. Modal capacitance (F); This is the transpose of the electrostatic-structural field coupling matrix in modal coordinates; Mode charge (C); S33. Establish the state-space equations of the nonlinear coupled model: ; In the formula, ; in, It is a state vector; The input vector; The state matrix; The input matrix; It is the identity matrix; The equivalent resistance (Ω) is given in the modal coordinate system.

[0019] like Figure 5 As shown, step S4 above specifically involves the following steps: S41. Taking the membrane vibration displacement and velocity as state variables, and the vibration suppression effect and control energy consumption as comprehensive optimization objectives, the optimization control problem is as follows: ; In the formula, To comprehensively optimize the objective function; It is a state vector; This is the transpose of the state vector; This is the state weight matrix; To control the input vector; To control the transpose of the input vector; To control the weight matrix; Time (s); S42. Solve the thermal-induced vibration optimization control model of the thin-film antenna to obtain the optimal feedback gain matrix: ; In the formula, The optimal feedback gain matrix; To control the weight matrix; The input matrix; This is the transpose of the input matrix; The matrix of the symmetric positive definite solution to the Riccati algebraic equation is given; thus, the optimal control electrostatic force is obtained: ; In the formula, This is the control input vector corresponding to the optimal control of the electrostatic force; It is a state vector; S43. Substitute the optimal control electrostatic force into the state-space equation of the nonlinear coupling model. Solve for the thermally induced vibration response of the thin-film antenna under optimal electrostatic control; S44. Compare the vibration modes of the thin-film antenna before and after applying electrostatic force control.

[0020] Example 1: This example describes in detail the application effect of the present invention in conjunction with simulation experiments.

[0021] Simulation conditions: The length of the thin film surface is set to... Width is The length of the supporting truss structure is set as Width is The geometric model and mesh generation model of the spaceborne thin-film antenna, established using the geometric information of the thin-film antenna, are respectively shown in [reference 1]. Figure 6 and Figure 7 The orbital type of the spaceborne thin-film antenna is defined as geosynchronous orbit. The changes in maximum and minimum temperatures when the thin-film antenna enters and exits the shadow region are shown in [reference needed]. Figure 8 It can be seen that the temperature changes are quite drastic when entering and exiting the shadow region, which easily leads to thermal vibration effects. The thermal vibration response curves of the spaceborne thin-film antenna before and after active control are shown in [reference 1]. Figure 9 and Figure 10 It can be seen that the on-orbit thermal-induced vibration response of the spaceborne thin-film antenna after active control can decay more quickly, achieving the effect of thermal-induced vibration control. The electrostatic-based thin-film antenna vibration control method can effectively improve the on-orbit stability of the thin-film antenna. This simulation experiment was only conducted for a thin-film antenna of a specific size. This invention is still applicable to other types of thin-film antennas, cable-net antennas, etc.

[0022] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for controlling the thermally induced vibration of a thin-film antenna based on electrostatic force, characterized in that, Includes the following steps: S1. Establish an on-orbit thermal analysis model for the thin-film antenna and extract transient temperature information of the thin-film antenna when entering and exiting the shadow region; S2. Establish a nonlinear dynamic model of the thin-film antenna, apply the transient temperature information extracted in S1 as a transient temperature load to the nonlinear dynamic model of the thin-film antenna, perform thermal vibration analysis, and obtain the on-orbit thermal vibration information of the thin-film antenna without external control. S3. Construct an active control model for the thermal vibration of a thin-film antenna based on electrostatic force actuation; S4. Optimize and solve the active control model of the thermal vibration of the thin film antenna to obtain the optimal control electrostatic force, and actively control the thermal vibration of the thin film antenna according to the optimal control electrostatic force. S41. Using the membrane vibration displacement and velocity as state variables, and taking the vibration suppression effect and control energy consumption as comprehensive optimization objectives, establish an optimization control problem: ； In the formula, To comprehensively optimize the objective function; It is a state vector; This is the transpose of the state vector; This is the state weight matrix; To control the input vector; To control the transpose of the input vector; To control the weight matrix; For time; S42. Solve the optimization control problem established in S41 to obtain the optimal feedback gain matrix: ； In the formula, The optimal feedback gain matrix; To control the weight matrix; The input matrix; This is the transpose of the input matrix; The matrix represents the symmetric positive definite solution of the Riccati algebraic equation; then, the optimal control electrostatic force is obtained based on the optimal feedback gain matrix. ； In the formula, This is the control input vector corresponding to the optimal control of the electrostatic force; This is the state vector.

2. The method for controlling the thermally induced vibration of a thin-film antenna based on electrostatic force according to claim 1, characterized in that, S1 includes: S11. Establish the geometric model of the thin-film antenna: generate a length of... Width is The thin film surface is generated with a length of Width is The supporting truss structure is constructed, and boundary cables are generated on the thin film surface, resulting in a geometric model of the thin film antenna composed of the thin film surface, the supporting truss structure, and the boundary cables; among which, The length of the thin film surface; The width of the film surface; The length of the supporting truss structure; To support the width of the truss structure; S12. Perform thermal analysis mesh generation on the thin-film antenna geometric model established in S11: Use triangular thermal analysis thin-film elements to mesh the thin-film surface, use thermal analysis beam elements to mesh the supporting truss structure, and use thermal analysis cable elements to mesh the boundary cables to obtain the thin-film antenna thermal analysis mesh model. S13. Given the thermal analysis material parameters of the thin-film antenna: Given the thermal conductivity, specific heat capacity, emissivity, and absorptivity of the thin-film surface, supporting truss structure, and boundary cables, establish a finite element model for the thermal analysis of the thin-film antenna based on the mesh model obtained in S12: ； In the formula, The heat capacity matrix is ​​assembled in the global coordinate system; The node temperature column vector; For time; The heat conduction matrix is ​​assembled in the global coordinate system; The thermal radiation matrix assembled in the global coordinate system; This is the column vector of nodal heat flux loads assembled in the global coordinate system; S14. Given the on-orbit thermal analysis solution parameters for the thin-film antenna: Given the time interval for the thin-film antenna to enter and exit the shadow region. The finite element model for thermal analysis of the thin-film antenna established in S13 was solved to obtain the time interval. The node temperature values ​​that vary with time; among which, This is the starting moment when the thin-film antenna enters the shadow region; This is the moment when the thin-film antenna leaves the shadow region. S15. Save the time-varying node temperature values ​​obtained from S14 to a file to obtain the transient temperature information file of the thin-film antenna entering and exiting the shadow area, providing transient temperature load data for the thermal vibration analysis in S2.

3. The method for controlling the thermally induced vibration of a thin-film antenna based on electrostatic force according to claim 1, characterized in that, S2 includes: S21. Perform finite element mesh generation on the geometric model of the thin film antenna: Use triangular thin film elements to mesh the thin film surface, use two-node beam elements to mesh the supporting truss structure, and use two-node cable elements to mesh the tension cable to obtain the finite element mesh model of the thin film antenna structure. S22. Given the material parameters of the thin-film antenna structure: Given the elastic modulus, mass density, Poisson's ratio and thermal expansion coefficient of the thin-film surface, supporting truss structure and tension cable, provide material parameters for the establishment of the nonlinear dynamic model of the thin-film antenna; S23. Given the constraints of the thin-film antenna: The two nodes of the supporting truss structure boundary are subjected to full displacement constraints. Based on the finite element mesh model of the thin-film antenna structure obtained in S21 and the structural material parameters given in S22, a nonlinear dynamic analysis model of the thin-film antenna is established: ； In the formula, The overall mass matrix of the thin-film antenna; The nodal acceleration vector; The overall damping matrix of the thin-film antenna; The node velocity vector; This is the stiffness matrix of the cable structure related to the initial tension value of the cable; The initial tension value of the cable. Related to the temperature load of the thin-film antenna; This is the film structure stiffness matrix related to the initial tension value of the film; This represents the initial tension value of the film. Related to the temperature load of the thin-film antenna; Here is the stiffness matrix of the truss structure; The nodal displacement vector; This is the external load vector; S24. Apply the transient temperature information extracted in S1 as an external load to the nonlinear dynamic analysis model of the thin-film antenna established in S23, perform transient dynamic solution, and obtain the dynamic response of each node of the thin-film antenna under transient temperature load. S25. Extract the relationship between the nodal displacement and time of the thin-film antenna to obtain the on-orbit thermally induced vibration information of the thin-film antenna without external control, and provide a comparison benchmark for the vibration mode comparison before and after applying electrostatic force control in S4.

4. The method for controlling the thermally induced vibration of a thin-film antenna based on electrostatic force according to claim 1, characterized in that, S3 includes: S31. Establishing a nonlinear dynamic model of a thin-film antenna under electrostatic force based on the nonlinear finite element method: ； In the formula, The displacement vector of the thin film structure nodes; Let be the electrostatic field voltage vector; the point above the vector represents the time derivative of the vector. The mass matrix of the thin-film antenna structure; The damping matrix of the thin-film antenna structure; This is the stiffness matrix of the thin-film antenna structure; Here is the stiffness matrix of the cable structure; and This is the coupling stiffness matrix generated by the coupling effect between the electrostatic field and the thin film structure field. This is the additional coupling stiffness matrix caused by electrostatic force; Here is the stiffness matrix caused by the electrostatic field; This is the stiffness matrix of the additional electric field caused by electrostatic force; This represents the external force load vector of the thin film structure. The vector of external charge loads induced by the electric field; S32. The nonlinear dynamic model of the thin-film antenna under electrostatic force established in S31 is reduced in order to obtain the reduced-order model in the modal coordinate system: ； ； In the formula, Modal displacement; Modal voltage; For time; Here is the modal mass matrix; Here is the modal damping matrix; Here is the modal stiffness matrix; The electrostatic field-structure field coupling matrix in modal coordinates; External load in modal coordinate system; Modal capacitance; This is the transpose of the electrostatic-structural field coupling matrix in modal coordinates; Modal charge; S33. Based on the reduced-order model obtained in S32, establish the state-space equations of the nonlinear coupled model: ； In the formula, ； in, It is a state vector; The input vector; The state matrix; The input matrix; It is the identity matrix; This is the equivalent resistance in the modal coordinate system.

5. The method for controlling the thermally induced vibration of a thin-film antenna based on electrostatic force according to claim 4, characterized in that, S4 further includes: S43. Substitute the optimal control electrostatic force obtained in S42 into the state-space equation of the nonlinear coupling model established in S33, and solve for the thermal vibration response of the thin-film antenna under the control of the optimal control electrostatic force. S44. Compare the vibration modes of the thin-film antenna before and after applying electrostatic force control to verify the vibration suppression effect of active control of thermally induced vibration of the thin-film antenna based on electrostatic force.

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