Large truss vibration control controlled mode selection method based on optical performance index

Abstract

The invention provides a large truss vibration control controlled mode selection method based on optical performance indexes, which comprises the following steps of: 1, establishing a finite element model of a large truss structure, and performing mode analysis on the large truss structure to obtain mode information of vibration of the large truss structure; 2, a linear system of the large truss structure is built through a modal superposition method; 3, calculating the dynamic response of the large truss structure under the required working condition, and obtaining the size of each order of modality under the required working condition; step 4, according to the position of the optical measurement point, establishing a calculation expression of the optical performance index under the physical coordinate, and performing quadratic form fitting; and 5, calculating the modal value of each order of modal to each optical index under the required working condition, and carrying out sorting and screening according to the modal value. According to the invention, the problem of effective mode loss caused by a traditional mode truncation method is solved.

Description

Technical Field

[0001] The present invention belongs to the fields of aerospace and architecture, and particularly relates to a method for selecting controlled modes of large truss vibration control based on optical performance indexes. Background Art

[0002] With the increasing demand for aerospace missions and the continuous development of aerospace technology, spacecraft are developing towards complexity and large scale. Large aerospace structures such as ultra-large space telescopes, ultra-large space stations, and various large satellite platforms are increasingly widely used. The large space truss structure is a typical large aerospace structure. Its structure is simple, facilitating manufacturing and space assembly, so it is widely used in aerospace missions. It is a large discrete structure composed of structural units such as rods, beams, hinges, and their payloads according to specific aerospace mission requirements. In a complex and changing space environment, aircraft are often affected by external factors. At the same time, during the active working processes such as pose change and space operation of the aerospace structure, it is very easy to cause low-frequency vibration of the truss structure. In addition, due to the relatively low damping of the space truss itself and the vacuum environment it is in after deployment and locking, once the structure vibrates, the energy attenuation rate is very slow. If the vibration is not controlled, it may affect the working accuracy of the precision equipment connected to the end of the support truss, and subsequent targeted repair and adjustment may cost huge amounts of money. In a more serious situation, it may even lead to component failures of the aircraft or the failure of the entire aerospace mission. In order to ensure that the large flexible space structure can be successfully deployed and quickly stabilized to the equilibrium state after entering the orbit, effective dynamic modeling must be carried out in its design stage and a feasible control strategy must be established.

[0003] Due to the extremely large number of degrees of freedom of large space structures, the number of their vibration modes is large and dense, resulting in low computational efficiency. In order to improve the dynamic calculation efficiency, appropriate finite-order modes should be selected for control in order to achieve model reduction on the basis of hardly affecting the overall control effect. According to actual calculation experience, the contribution of the mode decreases with the increase of frequency, that is, only a few lower modes in the structural system are easily excited, while the high-order modes are not easily excited. Therefore, the traditional model reduction method is to directly truncate the modes of the structure, discard the high-order modes, and only superimpose the first few modes with low natural vibration frequencies to express the vibration state of the structure. However, for specific problems, the selection of the mode order also needs to be analyzed and judged using appropriate criteria in combination with the specific structure and dynamic load. If the contribution of each order mode to the system response cannot be well analyzed and the high-order modes are arbitrarily truncated, it may lead to mode loss, thus affecting the model. Summary of the Invention

[0004] To solve the problem of the loss of effective modes caused by the traditional modal truncation method, the present invention provides a method for selecting controlled modes of large truss vibration control based on optical performance indicators. Taking the truss structure of a large space telescope as the research object, an optical performance indicator is established as a modal value criterion according to its actual working requirements, and the controlled modes are selected based on this criterion.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for selecting controlled modes of large truss vibration control based on optical performance indicators, comprising the following steps:

[0007] Step 1: Establish a finite element model of the large truss structure, perform modal analysis on the large truss structure, and obtain the modal information of the vibration of the large truss structure;

[0008] Step 2: Build a linear system of the large truss structure by the modal superposition method;

[0009] Step 3: Calculate the dynamic response of the large truss structure under the required working conditions, and obtain the magnitudes of each order of modes under the required working conditions;

[0010] Step 4: According to the positions of the optical measurement points, establish a calculation expression of the optical performance indicator in the physical coordinates and perform quadratic form fitting;

[0011] Step 5: Calculate the modal value of each order of mode for each optical index under the required working conditions, and perform sorting and screening according to the magnitude of the modal value.

[0012] Further, in Step 1, the modal information of the vibration of the large truss structure includes a degree-of-freedom dictionary, a mass matrix, a stiffness matrix, a damping matrix, the modal coordinates of each order and their eigenvectors.

[0013] Further, the said Step 2 includes:

[0014] Perform modal analysis on the structure to obtain the first m non-rigid body modes, then the physical coordinates of the displacement are:

[0015] (1)

[0016] Wherein, is the structural displacement in the physical coordinate system, is the matrix composed of the eigenvectors of the first m modes, with the dimension of ; is the modal coordinate, with the dimension of ;

[0017] The dynamic equation of the structure in the physical coordinates is:

[0018] (2)

[0019] Among them, is the mass matrix, is the damping matrix, is the stiffness matrix, is the position matrix of the degrees of freedom where the external load is applied, is the external load;

[0020] Multiply both sides of the above equation on the left by to get:

[0021] (3)

[0022] Among them, the superscript T represents the transpose of the matrix;

[0023] Introduce , and Three intermediate matrices, then the original dynamic equation is converted to:

[0024] (4)

[0025] Among them, ;

[0026] Among them, is the m-order identity matrix;

[0027] Then equation (4) is written as:

[0028] (5)

[0029] Write the above equation as a state-space equation:

[0030] (6)

[0031] The above equation is the linear system of the large truss structure.

[0032] Furthermore, the third step includes:

[0033] Determine the numbers of the nodes applied in the demand working conditions in the finite element model and the degrees of freedom where the load is applied, and thus generate the position matrix of the degrees of freedom where the external load is applied in the second step, and its definition is as follows:

[0034] The position matrix depends on the positions of the node degrees of freedom among all the degrees of freedom in the finite element model. Let the position matrix of the degrees of freedom loaded on the truss be , and let the a, b, and c degrees of freedom of the loaded node A be the p, q, and r degrees of freedom of all the degrees of freedom in the finite element model, respectively. Then The elements in the p-th row and a-th column, q-th row and b-th column, and r-th row and c-th column of are 1, and the rest of the elements are 0;

[0035] Determine the type and magnitude of the load applied under the required working conditions, and generate the component magnitudes of the load at each time node in each loaded degree of freedom, that is, the external load matrix ;

[0036] Input the above parameters into the linear system of the large truss structure, solve the dynamic response of the truss at each time node, and use the modal coordinate magnitude at the end of the loading as the magnitude of each order of mode under the required working conditions.

[0037] Furthermore, step four includes:

[0038] Let the radius of the primary mirror be R, the radius of the secondary mirror be r, the original distance between the primary and secondary mirrors be L, and the three observation points on the primary and secondary mirrors be evenly distributed with an interval of 120°; taking the original center of the secondary mirror as the origin, the line connecting the original centers of the primary and secondary mirrors as the z-axis, and the direction from the center to the measurement point 1 of the secondary mirror as the x-axis, establish a three-dimensional coordinate system and calculate the normal vector of the primary mirror plane;

[0039] The approximate calculation formula for the deviation D of the distance between the mirrors from the nominal distance is:

[0040] ;

[0041] where is the vector connecting the center points of the primary and secondary mirrors, , and are the vibration displacements of the three measurement points of the secondary mirror in the z direction respectively, , and are the vibration displacements of the three measurement points of the primary mirror in the z direction respectively;

[0042] The number of non-zero eigenvalues of its quadratic form matrix is 1;

[0043] Furthermore, step four also includes:

[0044] The approximate calculation formula for the distance d from the geometric center of the secondary mirror to the normal vector of the primary mirror plane is:

[0045] ;

[0046] where the superscript T represents the transpose of the matrix, is the vector connecting the center points of the primary and secondary mirrors, is the normal vector of the primary mirror plane, is the vibration displacement matrix of six measurement points, , and are the characteristic matrices of the connection line between the center points of the primary and secondary mirrors in the x, y, and z directions respectively, is the characteristic matrix of the primary mirror plane;

[0047] The number of non-zero eigenvalues of its quadratic form matrix is 2.

[0048] Furthermore, the fourth step further includes:

[0049] The approximate calculation formula for the included angle α between the normal vectors of the primary and secondary mirror planes is:

[0050] (37)

[0051] where the superscript T represents the transpose of the matrix, is the normal vector of the primary mirror plane, is the normal vector of the secondary mirror plane, is the vibration matrix in the z direction of six measurement points, is the characteristic matrix of the primary mirror plane, is the characteristic matrix of the primary mirror plane;

[0052] The number of non-zero eigenvalues of its quadratic form matrix is 2.

[0053] Furthermore, the fifth step includes:

[0054] According to the approximate calculation formula of the optical performance index and the number of its non-zero eigenvalues, the performance index is transformed into the following form:

[0055] (38)

[0056] where the superscript T represents the transpose of the matrix, is the vibration displacement matrix of six measurement points, is the performance index of the eigenvector, with a total of one dimension, is the performance index of the eigenvector, with a total of two dimensions, which are respectively and , is the performance index of the eigenvector, with a total of two dimensions, which are respectively and .

[0057] Furthermore, the fifth step further includes:

[0058] The value coefficients of each order of mode on the performance index under no working conditions are as follows:

[0059] (39)

[0060] where, is the matrix composed of the eigenvectors of each order of mode, is the modal coordinate, is the influence coefficient of each order of mode on the optical performance index D, is the influence coefficient of each order mode on the optical performance index d, is the influence coefficient of each order mode on the optical performance index α, is the i-th order modal coordinate.

[0061] Furthermore, the fifth step further includes:

[0062] The value coefficients of each order mode on the performance index under the demand working condition are as follows:

[0063] (40)

[0064] Among them, is the matrix composed of the eigenvectors of each order mode, is the magnitude of the modal coordinate under the demand working condition, is the influence coefficient of each order mode on the optical performance index D under the demand working condition, is the influence coefficient of each order mode on the optical performance index d under the demand working condition, is the influence coefficient of each order mode on the optical performance index α under the demand working condition, is the magnitude of the i-th order modal coordinate under the demand working condition;

[0065] Quantitatively analyze the influence of each order mode on the optical performance index according to the above formula.

[0066] Beneficial effects:

[0067] 1. In the prior art, model reduction is carried out by the modal truncation method, which is easy to cause the loss of effective modes and reduce the control effect. The present invention carries out modal selection based on the optical performance index, directly targets the control objective of the optical load, and can intuitively reflect the contribution weight of each order mode to the control objective, which is beneficial to saving control resources and improving the control effect.

[0068] 2. Most of the prior art relies on empirical judgment, or needs to carry out repeated iterations of "modal selection - control simulation" to judge whether the selected modes can ensure the control effect. The present invention does not require a complex iteration process and does not necessarily require the operator's experience, reducing the time and labor costs, and the operation is simple and effective.

[0069] 3. The present invention has good extensibility and can theoretically be used for active vibration control tasks of large trusses with various sizes and structures, especially tasks with optical performance index requirements, which can improve the reliability of large flexible satellites and has practical application value, not limited to theory only. Description of the Drawings

[0070] Figure 1 is a schematic diagram of the finite element model of the truss structure.

[0071] Figure 2 It is the dynamic torque output curve of the working condition torque gyro machine.

[0072] Figure 3 It is the bar chart of the influence coefficient of each order mode on the performance index D 2

[0073] Figure 4 It is the bar chart of the influence coefficient of each order mode on the performance index D 2

[0074] Figure 5 It is the bar chart of the influence coefficient of each order mode on the performance index d 2

[0075] Figure 6 It is the bar chart of the influence coefficient of each order mode on the performance index d 2

[0076] Figure 7 It is the bar chart of the influence coefficient of each order mode on the performance index α 2

[0077] Figure 8 It is the bar chart of the influence coefficient of each order mode on the performance index α 2 Specific implementation manner

[0078] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0079] The present invention provides a method for selecting controlled modes of large truss vibration control based on optical performance indicators, which solves the problem of loss of effective modes caused by the traditional modal truncation method, and specifically includes the following steps:

[0080] Step 1: Establish a finite element model of the large truss structure, perform modal analysis on the large truss structure, and obtain the modal information of the vibration of the large truss structure;

[0081] Step 2: Build a linear system of the large truss structure by the modal superposition method;

[0082] Step 3: Calculate the dynamic response of the large truss structure under the required working conditions, and obtain the magnitudes of each order mode under the required working conditions;

[0083] Step 4: According to the positions of the optical measurement points, establish a calculation expression of the optical performance index in the physical coordinates and perform quadratic fitting;​​​​​​

[0084] Step 5: Calculate the modal values of each order of mode for each optical index under the required working conditions, and sort and screen according to the magnitude of the modal values.

[0085] Among them, in Step 1, the establishment of the finite element model of the large truss structure and the modal analysis of the large truss structure are realized by finite element software. The modal information of the vibration of the large truss structure includes the degree-of-freedom dictionary, mass matrix, stiffness matrix, damping matrix, and the modal coordinates of each order and their eigenvectors .

[0086] Among them, in Step 2, the specific method of building the linear system of the large truss structure by the modal superposition method is as follows:

[0087] Perform modal analysis on the structure to obtain the first m non-rigid body modes. Then the physical coordinates of the displacement are:

[0088] (1)

[0089] Among them, is the structural displacement in the physical coordinate system, is the matrix composed of the eigenvectors of the first m modes, and the dimension is ; is the modal coordinate, and the dimension is .

[0090] The dynamic equation of the structure in the physical coordinates is:

[0091] (2)

[0092] Among them, is the mass matrix, is the damping matrix, is the stiffness matrix, is the position matrix of the degrees of freedom where the external load is applied, is the external load.

[0093] Multiply both sides of the above formula on the left by to get:

[0094] (3)

[0095] Among them, the superscript T represents the transpose of the matrix.

[0096] Introduce , and three intermediate matrices, then the original dynamic equation can be converted to:

[0097] (4)

[0098] Among them, ;

[0099] Among them, is the m - order identity matrix. Then Equation (4) can be written as:

[0100] (5)

[0101] Write the above equation as the state - space equation:

[0102] (6)

[0103] The above equation is the linear system of the large - scale truss structure.

[0104] Among them, in step three, the specific method for calculating the dynamic response of the large - scale truss structure under the required working conditions to obtain the magnitudes of each order of modes under the required working conditions is as follows:

[0105] Determine the numbers of the nodes applied with the required working conditions in the finite - element model and the degrees of freedom for applying the loads, and thus obtain the position matrix of the external - load application degrees of freedom , which is defined as follows:

[0106] The position matrix depends on the positions of the node degrees of freedom among all the degrees of freedom in the finite - element model. Let the position matrix of the degrees of freedom loaded on the truss be . Suppose the a - th, b - th, and c - th degrees of freedom of the loaded node A are the p - th, q - th, and r - th degrees of freedom among all the degrees of freedom in the finite - element model, then The elements in the p - th row and a - th column, q - th row and b - th column, and r - th row and c - th column of are 1, and the rest of the elements are 0.

[0107] Determine the types and magnitudes of the loads applied with the required working conditions, and generate the component magnitudes of the loads at each time node under each loaded degree of freedom, that is, the external - load matrix .

[0108] Input the above - mentioned parameters into the linear system of the large - scale truss structure, solve the dynamic response of the truss at each time node, and take the modal - coordinate magnitudes at the end of the loading as the "magnitudes of each order of modes under the required working conditions".

[0109] Among them, in step four, the specific method for establishing the calculation expression of the optical performance index in the physical coordinates based on the positions of the optical measurement points and performing quadratic - form fitting is as follows:

[0110] Suppose the radius of the primary mirror is R, the radius of the secondary mirror is r, and the original distance between the primary and secondary mirrors is L. Taking the original center of the secondary mirror as the origin, the line connecting the original centers of the primary and secondary mirrors as the z - axis, and the direction from the center to the measurement point 1 of the secondary mirror as the x - axis, establish a three - dimensional coordinate system. The original position matrix of the primary mirror composed of three measurement points on the primary mirror As shown below:

[0111] (7)

[0112] Wherein, 、 and are the original position coordinates in three directions of the i-th measuring point of the primary mirror respectively.

[0113] Due to the displacement of the observation point caused by elastic vibration relative to the original coordinates is a small quantity, then there is an approximate calculation:

[0114] (8)

[0115] Wherein, is a third-order identity matrix.

[0116] Meanwhile, the initial positions of the measuring points satisfy the relationship:

[0117] (9)

[0118] Then after vibration occurs, the approximate calculation formula for the normal vector of the primary mirror plane is:

[0119] (10)

[0120] Wherein, 、 and are the vibration displacements in the z direction of the three measuring points of the secondary mirror respectively, 、 and are the vibration displacements in the z direction of the three measuring points of the primary mirror respectively. Thus, the expressions for the characteristic matrix of the primary mirror plane and the vibration matrix of the six measuring points in the z direction are respectively:

[0121] (11)

[0122] Similarly, the approximate calculation formula for the normal vector of the secondary mirror plane can be obtained as:

[0123] (12)

[0124] The three side vectors 、 and of the triangle formed by the measuring points of the primary mirror are respectively:

[0125] (13)

[0126] Among them, 、 and are the vibration displacements of the three measurement points of the primary mirror in the x direction respectively, 、 and are the vibration displacements of the three measurement points of the primary mirror in the y direction respectively.

[0127] Then there is: (14)

[0128] Among them, is the x - coordinate coefficient of the circumcenter of the triangle formed by the measurement points of the primary mirror.

[0129] (15)

[0130] Among them, is the y - coordinate coefficient of the circumcenter of the triangle formed by the measurement points of the primary mirror.

[0131] (16)

[0132] Among them, is the z - coordinate coefficient of the circumcenter of the triangle formed by the measurement points of the primary mirror.

[0133] The coordinates of the geometric center of the primary mirror satisfy:

[0134] (17)

[0135] Among them, 、 and are the coordinates of the geometric center of the primary mirror in the x, y, and z directions respectively.

[0136] Retaining the first - order small quantities, the approximate calculation formula is:

[0137] (18)

[0138] Among them, is the coefficient matrix of the geometric center of the primary mirror.

[0139] Similarly, the approximate calculation formula for the coordinates of the geometric center of the secondary mirror is:

[0140] (19)

[0141] Among them, the superscript C represents the values of each matrix in the secondary mirror.

[0142] Then the vector connecting the centers of the primary and secondary mirrors is:

[0143] (20)

[0144] Among them,

[0145] (21)

[0146] Substitute to solve the characteristic matrices of the line connecting the centers of the primary and secondary mirrors in the x, y, and z directions , and for their values.

[0147] The approximate calculation formula for the deviation D of the distance between the mirrors from the nominal distance is:[[]]

[0148] (22)

[0149] The number of non-zero eigenvalues of its quadratic form matrix is 1.

[0150] The approximate calculation formula for the distance d from the geometric center of the secondary mirror to the normal vector of the primary mirror plane is:[[]]

[0151] (23)

[0152] Among them, is the normal vector of the primary mirror plane.

[0153] (24)

[0154] Then is obtained by adding three parts:[[]]

[0155] (25)

[0156] (26)

[0157] (27)

[0158] Therefore, it can be obtained that:[[]]

[0159] (28)

[0160] For

[0161] (29)

[0162] Retaining the second-order small quantity gives:[[]]

[0163] (30)

[0164] The number of non-zero eigenvalues of its quadratic form matrix is 2.

[0165] The approximate calculation formula for the included angle α between the normal vectors of the primary and secondary mirror planes is:[[]]

[0166] (31)

[0167] Among them, is the normal vector of the primary mirror plane, is the normal vector of the secondary mirror plane; is the expression of the normal vector of the primary mirror plane, is the expression of the normal vector of the secondary mirror plane.

[0168] Keeping the first-order small quantity as:

[0169] (32)

[0170] Keeping the first-order small quantity as:

[0171] (33)

[0172] (34)

[0173] Keeping the second-order small quantity as:

[0174] (35)

[0175] It is also known that The first-order Taylor expansion at 0 is:

[0176] (36)

[0177] Among them, o(x) is the first-order small quantity of x.

[0178] Then the approximate calculation formula for the performance index is:

[0179] (37)

[0180] The number of non-zero eigenvalues of the quadratic form matrix is 2.

[0181] Among them, in step five, the calculation of the modal value of each order of mode for each optical index under the required working conditions and the sorting and screening according to the magnitude of the modal value are specifically:

[0182] According to the approximate calculation formula of the optical performance index and its number of non-zero eigenvalues, the performance index can be transformed into the following form:

[0183] (38)

[0184] Among them, is the performance index 's eigenvector (one-dimensional in total), is the performance index The eigenvectors (two-dimensional in total, namely and ), is the performance index The eigenvectors (two-dimensional in total, namely and ).

[0185] Then, the value coefficients of each order of mode on the performance index under no working condition are as follows:

[0186] (39)

[0187] Among them, is the influence coefficient of each order of mode on the optical performance index D, is the influence coefficient of each order of mode on the optical performance index d, is the influence coefficient of each order of mode on the optical performance index α, is the coordinate of the i-th order mode.

[0188] The value coefficients of each order of mode on the performance index under the required working condition are as follows:

[0189] (40)

[0190] Among them, is the matrix composed of the eigenvectors of each order of mode, is the magnitude of the mode coordinate under the required working condition, is the influence coefficient of each order of mode on the optical performance index D under the required working condition, is the influence coefficient of each order of mode on the optical performance index d under the required working condition, is the influence coefficient of each order of mode on the optical performance index α under the required working condition, is the magnitude of the i-th order mode coordinate under the required working condition.

[0191] According to the above formula, the influence of each order of mode on the optical performance index can be quantitatively analyzed.

[0192] Example:

[0193] The method for selecting controlled modes of large truss vibration control based on optical performance index in the embodiment of the present invention includes:

[0194] Step 1: Establish in the finite element software as Figure 1The finite element model of the truss structure shown; perform modal analysis to obtain bdf and h5 files. In the Bulk Data Section of this bdf, input PARAM, EXTOUT, DMIGPCH to output a pch file with the same name as the bdf. Use the h5read function and a self-written program to obtain information such as the structure's degree-of-freedom dictionary, mass matrix, stiffness matrix, damping matrix, modal coordinates of each order, and their eigenvectors.

[0195] Step 2: By the modal superposition method, select the first 50 modes to build the linear system of the large truss structure.

[0196] Step 3: In this embodiment, the moment application points of the truss maneuvering conditions are as Figure 1 shown. The moment gyroscopes are arranged on the satellite body, and their finite element node numbers are 628326. The working condition is a three-axis rotation condition for achieving earth orientation. The application time of the gyroscopic moment is 120 s, and the moment magnitudes in the X, Y, and Z directions vary with time as Figure 2 shown. Calculate the dynamic response of the large truss structure under this condition through the lsim function to obtain the magnitudes of each order of modes.

[0197] Step 4: Take 3 measurement points at the peripheries of the primary and secondary mirrors of the satellite (the 3 nodes selected for the primary mirror are 439204460822, 479246; the 3 nodes selected for the secondary mirror are 433738, 433785, 433832), as Figure 1 shown. According to the positions of the optical measurement points, establish the calculation expression of the optical performance index in the physical coordinates and perform quadratic fitting. The calculation results are shown in Table 1.

[0198] Table 1 Parameters of the calculation formula for optical performance index

[0199] Step 5: Calculate the modal values of the first 50 modes for each optical index under the working condition, sort and screen according to the magnitudes of the modal values. The calculation results are as follows:

[0200] The influence coefficients of each order of modes on the performance index D 2 are as Figure 3 shown. Select the 15 modes with the greatest influence on it among the first 50 modes, which are 28, 15, 27, 34, 25, 17, 24, 26, 7, 35, 22, 47, 12, 30, 29.

[0201] The influence coefficients of each order of modes on the performance index D 2 are as Figure 4As shown, among the first 50 modes, 15 modes with the greatest influence are selected, which are 1, 2, 4, 8, 16, 24, 18, 11, 17, 46, 20, 43, 19, 31, 28 respectively.

[0202] The influence coefficients of each mode on the performance index d 2 are as follows Figure 5 As shown, among the first 50 modes, 15 modes with the greatest influence are selected, which are 24, 11, 27, 10, 46, 2, 35, 26, 25, 9, 28, 1, 42, 18, 34 respectively.

[0203] The influence coefficients of each mode on the performance index d 2 under the working condition are as follows Figure 6 As shown, among the first 50 modes, 15 modes with the greatest influence are selected, which are 1, 2, 24, 11, 46, 4, 8, 27, 18, 35, 10, 28, 25, 34, 42 respectively.

[0204] The influence coefficients of each mode on the performance index α 2 are as follows Figure 7 As shown, among the first 50 modes, 15 modes with the greatest influence are selected, which are 35, 34, 46, 37, 10, 42, 32, 9, 7, 28, 36, 24, 38, 33, 44 respectively.

[0205] The influence coefficients of each mode on the performance index α 2 under the working condition are as follows Figure 8 As shown, among the first 50 modes, 15 modes with the greatest influence are selected, which are 2, 1, 35, 34, 46, 4, 24, 8, 28, 33, 16, 42, 11, 17, 10 respectively.

[0206] Through the approximate calculation formula of the optical performance index, quantitatively analyze the influence of each mode on the optical performance index, and establish a linear system of the vibration control system with the modal coordinates of a batch of modes with the greatest influence on the optical performance index.

Claims

1. A method for selecting controlled modes for large truss vibration control based on optical performance indicators, characterized in that: The steps include: Step 1: Establish a finite element model of a large truss structure, perform modal analysis on the large truss structure, and obtain modal information of the vibration of the large truss structure; Step 2: Build a linear system of large truss structures by modal superposition method; Step 3: Calculate the dynamic response of the large truss structure under the required working condition and obtain the size of each mode under the required working condition; Step 4: According to the position of the optical measurement point, establish the calculation expression of the optical performance index in physical coordinates and perform quadratic fitting; Step 5: Calculate the modal value of each order mode for each optical index under the required working conditions, and sort and select according to the modal value.

2. According to claim 1, a method for selecting controlled modes for large truss vibration control based on optical performance indicators is characterized in that: In step 1, the modal information of the vibration of the large truss structure includes the degree of freedom dictionary, mass matrix, stiffness matrix, damping matrix, coordinates of each order mode and its eigenvector.

3. The method for selecting controlled modes for large truss vibration control based on optical performance indicators according to claim 1, characterized in that: The second step comprises: Performing modal analysis on the structure, we can obtain the first m-order non-rigid modes, and the physical coordinates of the displacement are: （1） in, is the structural displacement in the physical coordinate system, is a matrix composed of the eigenvectors of the m-order mode, with a dimension of ; is the modal coordinate, and the dimension is ; The dynamic equation of the structure in physical coordinates is: （2） in, is the mass matrix, is the damping matrix, is the stiffness matrix, The position matrix of the degrees of freedom for the external loads, is the external load; Multiply both sides of the above formula by have to: （3） Where, the superscript T represents the transpose of the matrix; Introduction , and Three intermediate matrices, the original dynamic equation is converted to: （4） in, ; in, is the m-order identity matrix; Then formula (4) can be written as: （5） Write the above equation as a state space equation: （6） The above formula is the linear system of the large truss structure.

4. The method for selecting controlled modes for large truss vibration control based on optical performance index according to claim 3, characterized in that: The step three comprises: Determine the node number and load application degree of freedom of the required working condition in the finite element model, thereby generating the position matrix of the external load application degree of freedom in step 2, which is defined as follows: The position matrix depends on the position of the node degree of freedom in all degrees of freedom of the finite element model. Assume that the position matrix of the loaded degree of freedom on the truss is , assuming that the a, b, c degrees of freedom of the loaded node A are the p, q, r degrees of freedom of all the degrees of freedom of the finite element model, respectively, then The pth row and ath column, the qth row and bth column, and the rth row and cth column are 1, and the rest of the elements are 0; Determine the type and size of the load applied by the required working condition, and generate the component size of the load at each loaded degree of freedom at each time node, that is, the external load matrix ; The above parameters are input into the linear system of the large truss structure to solve the truss dynamic response at each time node and calculate the modal coordinate size at the end of the load. As the size of each mode under the demand conditions.

5. The method for selecting controlled modes for large truss vibration control based on optical performance indicators according to claim 1, characterized in that: The fourth step comprises: Assume that the radius of the primary mirror is R, the radius of the secondary mirror is r, the original distance between the primary and secondary mirrors is L, and the three observation points of the primary and secondary mirrors are evenly distributed with an interval of 120°; take the original center of the secondary mirror as the origin, the line connecting the original centers of the primary and secondary mirrors as the z-axis, and the direction of the center pointing to the secondary mirror measurement point 1 as the x-axis, establish a three-dimensional coordinate system, and calculate the normal vector of the primary mirror plane; The approximate calculation formula for the deviation D between the inter-mirror distance and the nominal distance is: ； in, is the line vector connecting the center points of the primary and secondary mirrors, , and are the vibration displacements of the three measuring points of the secondary mirror in the z direction, , and are the vibration displacements of the three measuring points of the primary mirror in the z direction; The number of non-zero eigenvalues ​​of its quadratic form matrix is ​​1.

6. The method for selecting controlled modes for large truss vibration control based on optical performance index according to claim 5, characterized in that: The step 4 also includes: The approximate calculation formula for the distance d from the geometric center of the secondary mirror to the normal vector of the primary mirror plane is: ； The superscript T represents the transpose of the matrix. is the line vector connecting the center points of the primary and secondary mirrors, is the normal vector to the primary mirror plane, is the vibration displacement matrix of the six measuring points, , and are the characteristic matrices of the line connecting the center points of the primary and secondary mirrors in the x, y, and z directions respectively, is the primary mirror plane characteristic matrix; The number of non-zero eigenvalues ​​of its quadratic form matrix is ​​2.

7. The method for selecting controlled modes for large truss vibration control based on optical performance index according to claim 6, characterized in that: The step 4 also includes: The approximate calculation formula for the angle α between the primary and secondary mirror planes is: （37） The superscript T represents the transpose of the matrix. is the normal vector to the primary mirror plane, is the secondary mirror plane normal vector, is the z-direction vibration matrix of the six measuring points, is the primary mirror plane characteristic matrix, is the primary mirror plane characteristic matrix; The number of non-zero eigenvalues ​​of its quadratic form matrix is ​​2.

8. The method for selecting controlled modes for large truss vibration control based on optical performance indicators according to claim 1 or 7, characterized in that: The step five comprises: According to the approximate calculation formula of the optical performance index and the number of non-zero eigenvalues, the performance index is converted into the following form: （38） The superscript T represents the transpose of the matrix. is the vibration displacement matrix of the six measuring points, For performance indicators The characteristic vector of is one-dimensional. For performance indicators The eigenvectors of are two-dimensional and are and , For performance indicators The eigenvectors of are two-dimensional and are and .

9. The method for selecting controlled modes for large truss vibration control based on optical performance index according to claim 8, characterized in that: The step five also includes: The value coefficients of each mode for performance indicators under no working conditions are as follows: （39） in, is the matrix composed of the eigenvectors of each mode, are the modal coordinates, is the influence coefficient of each mode on the optical performance index D, is the influence coefficient of each mode on the optical performance index d, is the influence coefficient of each mode on the optical performance index α, is the i-th order modal coordinate.

10. The method for selecting controlled modes for large truss vibration control based on optical performance indicators according to claim 9, characterized in that: The step five also includes: The value coefficients of each mode for performance indicators under demand conditions are as follows: （40） in, is the matrix composed of the eigenvectors of each mode, is the size of the modal coordinates under the required working conditions, is the influence coefficient of each mode on the optical performance index D under the required working conditions, is the influence coefficient of each mode on the optical performance index d under the required working conditions, is the influence coefficient of each mode on the optical performance index α under the required working conditions, is the size of the i-th order modal coordinate under the required working condition; According to the above formula, the influence of each mode on the optical performance index is quantitatively analyzed.

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