Spacecraft on-orbit attitude control and structural dynamics coupling simulation method and system

Abstract

The application provides a spacecraft on-orbit attitude control and structure dynamics coupling simulation method and system, establishes a simplified three-dimensional model of the spacecraft; defines analysis steps, torques and concentrated forces, studies attitude control and flexible structure vibration suppression equations and compiles the equations into UAMP subprograms, simulates attitude control torques and flexible structure vibration suppression dynamics; and finally evaluates whether the attitude angle accuracy and the flexible structure vibration suppression effect of the spacecraft reach the expectation. The application considers the influence of the motion and deformation of each flexible component of the spacecraft on the attitude of the central rigid body, the mass center displacement, reveals the structure dynamics characteristics of the large flexible spacecraft under the on-orbit attitude control condition, and provides a new technical approach for the evaluation of the structure mechanics performance, reliability and pointing accuracy of the spacecraft.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of dynamics simulation, in particular, to a method and system for coupling simulation of on-orbit attitude control and structural dynamics of a large flexible spacecraft by using Abaqus software. BACKGROUND

[0002] When a spacecraft is in orbit, in order to complete a specific task, change orbit or avoid danger, attitude stabilization or attitude maneuvering control is needed. Early spacecrafts were small in size and high in structural rigidity, and for the simulation of on-orbit attitude control of the spacecraft, the spacecraft was only regarded as a simple rigid body or rigid system, and the structural dynamic response of the spacecraft itself was ignored. For the spacecraft configuration of "large mass center rigid body + small mass flexible appendage", which is the most common one at present, the coupling coefficient method is generally used to extract the constraint modal of the flexible appendage, calculate the inertia force of each order modal shape, and finally convert it into the reaction force or torque acting on the large mass center rigid body, so as to carry out the simulation of on-orbit attitude control of the spacecraft.

[0003] However, with the development of modern spacecraft design concept and application demand, "large flexible spacecraft with high integration of payload and platform" (hereinafter referred to as large flexible spacecraft) has become one of the important development directions at present. For example, high-orbit imaging satellites with super-large aperture optical payloads, which have large width, super-high resolution and long-time continuous observation capability, are important tools for serving meteorological research, scientific search and rescue activities. This type of satellite configuration has a large amount of lightweight and low-damping truss structure to reduce weight, and has large size but not significant center rigid body characteristics, large structural flexibility but low fundamental frequency, and dispersed mass characteristics but dense modal. Since the coupling coefficient method does not pay attention to the influence of the motion and deformation of the flexible appendage on the attitude and center of mass displacement of the center rigid body, and the large flexible spacecraft is difficult to clearly distinguish the center rigid body and the flexible appendage in structural design, the coupling coefficient method cannot realize the coupling simulation analysis of on-orbit attitude control and structural dynamics of the large flexible spacecraft, and further meet the evaluation requirements of the mechanical properties and reliability of the flexible structure of the spacecraft under large amplitude attitude maneuvering, pointing accuracy, etc.

[0004] Abaqus is a powerful engineering simulation finite element software, which not only has a dynamic analysis module for solving simple linear or complex nonlinear problems of various structures, but also provides a wide range of flexible subprogram interfaces, allowing users to define complex material constitutive, elements or various physical fields such as acoustics, optics, electricity, heat and magnetism to meet specific coupling analysis requirements. At present, there is still a lack of attention to the coupling simulation analysis of on-orbit attitude control and structural dynamics of large flexible spacecraft. Since in actual engineering problems, the spacecraft attitude is indirectly changed by applying force or torque rather than directly given the attitude motion parameters of the spacecraft, the coupling analysis of on-orbit attitude motion and structural dynamic characteristics of the spacecraft is more close to the actual engineering requirements. SUMMARY

[0005] In view of the defects in the prior art, the purpose of the present application is to provide a spacecraft on-orbit attitude control and structural dynamics coupling simulation method and system.

[0006] According to the spacecraft on-orbit attitude control and structural dynamics coupling simulation method provided by the present application, the method comprises the following steps:

[0007] Step S1: a three-dimensional simplified geometric model of the spacecraft is established in a finite element analysis software, the model is meshed and material parameters of each component are assigned;

[0008] Step S2: implicit dynamics is taken as an analysis step, geometric nonlinearity is turned on, the total simulation time, the initial increment step, the minimum increment step and the maximum increment step are defined;

[0009] Step S3: three-axis moments and concentrated forces are set at the central star body and the truss of the three-dimensional simplified geometric model to simulate attitude control moments and flexible structure vibration suppression forces, and coefficients and amplitudes of the three-axis moments and the concentrated forces are set;

[0010] Step S4: an attitude control equation and a flexible structure vibration suppression equation of the spacecraft are established, and are compiled into a subprogram script of the finite element analysis software;

[0011] Step S5: an implicit dynamics analysis task is established, the subprogram script is selected and submitted for calculation, an attitude angle curve and three index curves for measuring the flexible structure vibration suppression effect are drawn, and whether the stable attitude angle accuracy and the flexible structure vibration suppression effect of the spacecraft reach the expectation is analyzed.

[0012] Further, the three-dimensional simplified geometric model comprises a primary mirror, a secondary mirror, a primary mirror segment truss, a secondary mirror segment truss and a central star body.

[0013] When modeling, specific structures are ignored, and equivalent is performed in the manner of uniform mass or mass point; the primary mirror, the secondary mirror, the central star body and the triangular plates in the truss cells are modeled by shell elements, and the truss structure is modeled by beam elements; when meshing the model, the number of meshes is controlled, and the calculation accuracy and the calculation amount of the model are taken into account.

[0014] Further, the finite element analysis software adopts Abaqus software.

[0015] The step S3 comprises: in the Load module of the Abaqus software, coefficients and amplitudes of the flexible structure vibration suppression forces and the attitude control moments are set, the amplitude type is selected as user, and it is indicated that the UAMP subprogram interface is allowed to be called.

[0016] The size of the attitude control moment and the flexible structure vibration suppression force is a moment or a coefficient of the moment multiplied by the amplitude.

[0017] Further, the step S4 comprises: compiling the attitude control equation of the spacecraft and the flexible structure vibration suppression equation into a UAMP subroutine interface script based on the Fortran language, selecting the call in the CAE interface of the Abaqus software when submitting the calculation; and the output quantity of the UAMP subroutine script is the amplitude of the attitude control torque and the flexible structure vibration suppression action force.

[0018] Further, in the step S5:

[0019] The pointing angle of the central star body in the axial direction is taken as the attitude angle of the spacecraft, the pointing angle is characterized by means of a follow-up coordinate system established by some unit nodes on the central star body, and the target pointing and the current real-time pointing attitude angle are represented by a group of quaternions;

[0020] The deviation D of the geometric center distance of the primary mirror and the secondary mirror from the nominal distance of the spacecraft in the axial direction, the distance d of the geometric center of the secondary mirror to the normal vector of the primary mirror plane, and the included angle α of the normal vectors of the primary mirror and the secondary mirror plane are taken as three indexes for measuring the vibration suppression effect of the spacecraft structure, and when the three indexes are all less than the expected value, it is considered that the flexible structure vibration of the spacecraft is effectively suppressed.

[0021] According to the spacecraft on-orbit attitude control and structure dynamics coupling simulation system provided by the application, the spacecraft on-orbit attitude control and structure dynamics coupling simulation system comprises:

[0022] Module M1: a three-dimensional simplified geometric model of the spacecraft is established in the finite element analysis software, the model is meshed, and material parameters of each component are assigned;

[0023] Module M2: implicit dynamics is taken as the analysis step, the geometric nonlinearity is enabled, the total simulation time, the initial increment step, the minimum increment step, and the maximum increment step are defined;

[0024] Module M3: three-axis torques and concentrated forces are set at the central star body and the truss of the three-dimensional simplified geometric model to simulate the attitude control torque and the flexible structure vibration suppression action force, and the coefficients and amplitudes of the three-axis torques and the concentrated forces are set;

[0025] Module M4: an attitude control equation and a flexible structure vibration suppression equation of the spacecraft are established and compiled into a subroutine script of the finite element analysis software;

[0026] Module M5: an implicit dynamics analysis task is established, the subroutine script is selected and calculation is submitted, an attitude angle curve and three index curves for measuring the flexible structure vibration suppression effect are drawn, and whether the stable attitude angle precision and the flexible structure vibration suppression effect of the spacecraft reach the expectation is analyzed.

[0027] Further, the three-dimensional simplified geometric model comprises: a primary mirror, a secondary mirror, a primary mirror segment truss, a secondary mirror segment truss, and a central star body.

[0028] The specific structure is ignored during modeling, and the equivalent is carried out in the manner of uniformly distributed mass or mass point; the primary mirror, the secondary mirror, the central star body and the triangular plate in the truss cell are modeled by shell elements, and the truss structure is modeled by beam elements; when the model is meshed, the number of meshes is controlled, and the calculation precision and the calculation amount of the model are considered.

[0029] Further, the finite element analysis software adopts Abaqus software.

[0030] The module M3 comprises: in the Load module of the Abaqus software, the coefficients and the amplitude of the attitude control moment and the flexible structure vibration suppression dynamic force are set, the amplitude type is selected as user, and it is indicated that the UAMP subroutine interface is allowed to be called.

[0031] The size of the attitude control moment and the flexible structure vibration suppression dynamic force is the moment or the coefficient of the moment multiplied by the amplitude.

[0032] Further, the module M4 comprises: based on the Fortran language, the attitude control equation and the flexible structure vibration suppression equation of the spacecraft are compiled into the UAMP subroutine interface script, and the calling is selected in the CAE interface of the Abaqus software when the calculation is submitted; the output quantity of the UAMP subroutine script is the amplitude of the attitude control moment and the flexible structure vibration suppression dynamic force.

[0033] Further, in the module M5:

[0034] The pointing angle of the central star body in the axial direction is taken as the attitude angle of the spacecraft, the pointing angle is characterized by means of a follow-up coordinate system established by some element nodes on the central star body, the target pointing and the current real-time pointing are both represented by a group of quaternions;

[0035] The deviation D of the distance between the geometric centers of the primary mirror and the secondary mirror and the nominal distance of the axial direction of the spacecraft, the distance d of the geometric center of the secondary mirror to the normal vector of the primary mirror plane and the included angle alpha of the normal vectors of the primary mirror plane and the secondary mirror plane are taken as three indexes for measuring the vibration suppression effect of the spacecraft structure, and when the three indexes are all less than the expected value, it is considered that the flexible structure vibration of the spacecraft is effectively suppressed.

[0036] Compared with the prior art, the present application has the beneficial effects as follows:

[0037] The application considers the influence of the motion and deformation of each flexible component on the central rigid body attitude and the center of mass displacement during the on-orbit attitude control of the large flexible spacecraft, can reveal the structural dynamics characteristics of the large flexible spacecraft under the on-orbit attitude control condition, realize the coupling simulation of the structural dynamics of the large flexible spacecraft under the on-orbit attitude control, and provide a new technical approach for the structural mechanical performance, reliability and pointing accuracy evaluation of the large flexible spacecraft, further reduce the technical risk in the spacecraft development, and shorten the design cycle of the spacecraft. BRIEF DESCRIPTION OF DRAWINGS

[0038] Other features, objects and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments thereof, read in conjunction with the accompanying drawings:

[0039] Figure 1 The flow chart of the simulation method proposed in the application.

[0040] Figure 2 A three-dimensional geometric model of a large flexible spacecraft with fused load and platform height in an embodiment of the application is established by using Abaqus software.

[0041] Figure 3 A distribution diagram of six observation points for structural vibration suppression of the large flexible spacecraft in an embodiment of the application.

[0042] Figure 4 An attitude angle curve diagram of the large flexible spacecraft during large amplitude maneuvering in an embodiment of the application.

[0043] Figure 5 A deviation D curve of the distance between the geometric centers of the primary mirror and the secondary mirror of the large flexible spacecraft and the axial nominal distance L in an embodiment of the application.

[0044] Figure 6 A distance d curve of the secondary mirror geometric center to the normal vector of the primary mirror plane in an embodiment of the application.

[0045] Figure 7 An angle alpha curve of the included angle between the normal vectors of the primary mirror and the secondary mirror plane in an embodiment of the application. DETAILED DESCRIPTION

[0046] The application will be described in detail below with specific embodiments. The following embodiments will help those skilled in the art to further understand the application, but do not limit the application in any form. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the application. These all belong to the protection scope of the application.

[0047] As Figure 1As shown, the application provides a large flexible spacecraft in-orbit attitude control and structure dynamics coupling simulation method using Abaqus software, comprising:

[0048] Step one: taking a large flexible spacecraft with certain load and platform height fusion as the research object, analyzing the configuration composition of the large flexible spacecraft, obtaining the structural material parameters of the large flexible spacecraft, and the layout, performance parameters of the flywheel or torque gyro and truss actuator.

[0049] Step two: using Abaqus software to establish a three-dimensional geometric model of the large flexible spacecraft, ignoring the specific structure of each load type single machine of the spacecraft, equivalent to uniformly distributed mass and mass point, taking the platform structure of the large flexible spacecraft as the main part, using shell element and beam element to establish a simplified model, and performing model meshing and assigning material parameters to each component.

[0050] Step three: selecting "implicit dynamics" as the analysis step, opening the geometric nonlinearity, defining the total simulation time, initial increment step, minimum increment step and maximum increment step.

[0051] Step four: according to the layout and performance parameters of the flywheel or torque gyro and truss actuator in step one, setting three-axis torque and concentrated force at the central star body and truss of the model, simulating attitude control torque and flexible structure vibration suppression action, and setting the coefficients and amplitudes of the above forces and torques, and selecting user for amplitude type to allow calling UAMP subroutine interface.

[0052] Step five: establishing attitude control equations and flexible structure vibration suppression equations of the large flexible spacecraft, and compiling UAMP subroutine scripts based on Fortran language.

[0053] Step six: establish an implicit dynamics analysis task, select the UAMP subroutine script and submit the calculation, draw the attitude angle curve and the three index curves for measuring the flexible structure vibration suppression effect, and analyze whether the stable attitude angle accuracy and flexible structure vibration suppression effect of the large flexible spacecraft meet the expectations according to the simulation results.

[0054] For step one, the flywheel or torque gyro outputs the attitude control torque of the spacecraft, and the truss actuator outputs the actuation force for suppressing the vibration of the flexible structure, realizing the vibration suppression of the spacecraft; the attitude control torque and the structure vibration suppression actuation force required for large amplitude maneuver simulation of the large flexible spacecraft are calculated by the attitude control equation and the structure vibration suppression equation, and the input of the two algorithms is the structural deformation and rigid body displacement of the large flexible spacecraft during maneuvering, and the output is the attitude control torque and the actuation force.

[0055] The simplified large flexible space platform is composed of a primary mirror, a secondary mirror, a primary mirror segment truss, a secondary mirror segment truss and a central star body, a flywheel or a torque gyro is arranged at the central star body, and the truss actuator is arranged on the primary mirror segment truss in an optimal layout. The primary mirror and the secondary mirror are made of wood, and the central star body and the truss are made of aluminum alloy.

[0056] The material properties of wood are shown in the following table:

[0057]

[0058] The material properties of aluminum alloy are shown in the following table:

[0059]

[0060] For step two, the three-dimensional geometric model of the large flexible space platform of the embodiment of the application is composed of a primary mirror, a secondary mirror, a primary mirror segment truss, a secondary mirror segment truss and a central star body after simplification, and the specific structure is ignored during modeling, and the equivalent is performed in the form of uniformly distributed mass or mass point; the primary mirror, the secondary mirror, the central star body and the triangular plate in the truss cell are modeled by shell elements, and the truss structure is modeled by beam elements; when the model is meshed, the number of meshes needs to be appropriately controlled, and the calculation accuracy and the calculation amount of the model are taken into account.

[0061] A large number of measurement and control load units and power supplies will be arranged at the central star body, and the specific structure of these loads will be ignored during modeling in the Abaqus software, and the equivalent is performed in the form of uniformly distributed mass, and the optical imaging system with extremely complex structure will be arranged at the secondary mirror, and the optical imaging system is also simplified as a mass point with equal mass. The primary mirror, the secondary mirror, the central star body and the triangular plate in the truss cell are modeled by shell elements, and the truss structure is modeled by beam elements. When the model is meshed by the Mesh of the Abaqus software, the number of meshes needs to be appropriately controlled, and the calculation accuracy and the calculation amount of the model are taken into account. Figure 2 The model in the embodiment includes 42175 S4R shell elements and 3367 B31 beam elements after meshing, a total of 46837 nodes and 281022 degrees of freedom.

[0062] For step three, the following is specifically described. For large amplitude maneuver and structure vibration suppression simulation of the flexible spacecraft, the total simulation time is tens of seconds to hundreds of seconds. For such long time dynamic simulation, an implicit algorithm should be used, and considering that there is a large rotation angle and a large displacement in the simulation, the geometric nonlinear option in the Abaqus software analysis step should be turned on to ensure the authenticity of the results. The implicit analysis has convergence difficulty problems, and the initial increment step, the minimum increment step and the maximum increment step in the analysis step should be reasonably set to improve the calculation convergence of the simulation. The maximum increment step is generally set to one fifth to one tenth of the sampling period or the control period of the control system. The control period of the control system in the embodiment of the application is 0.1s, and therefore the maximum increment step is set to 0.2s. The initial increment step has a great influence on the simulation convergence, and after debugging, the initial increment step is set to 1x10 -13 s, which has good convergence. The minimum increment step is set to 1x10 -15 s, and the total simulation time is set to 650s. The analysis step setting of the embodiment of the application is as follows:

[0063]

[0064] For step four, in the Load module of the Abaqus software, the coefficients and amplitudes of the structure vibration suppression force and the attitude control moment are set. The amplitude type is selected as user, which means that the UAMP subroutine interface is allowed to be called. The size of the attitude control moment and the flexible structure vibration suppression actuator force is a moment or a moment coefficient multiplied by the amplitude.

[0065] In the embodiment of the application, the moment vector of the attitude control moment at the central star body points to the positive direction of the Y axis, and the upper limit of the moment is set to 1000N·m. According to the layout scheme of the truss actuator, 15 flexible structure vibration suppression actuators are set, and the upper limit of a single actuator is 500N. In the load module of the Abaqus software, the coefficients and amplitudes of the above forces and moments are set. The amplitude type is selected as user, which means that the UAMP subroutine interface is allowed to be called.

[0066] For step five, the attitude control equation and the structure vibration suppression equation of the large flexible spacecraft are compiled into the UAMP subroutine interface script based on the Fortran language, and the calling is selected in the CAE interface of the Abaqus software when submitting the calculation. The output of the UAMP subroutine script is the amplitude of the attitude control moment and the flexible structure vibration suppression actuator force.

[0067] In this embodiment of the invention, the attitude control torque and structural vibration suppression force required for the large-amplitude maneuver simulation of a highly flexible spacecraft are calculated by the attitude control equation and the structural vibration suppression equation, respectively. The inputs of the two algorithms are the structural deformation and rigid body displacement during the maneuver of the highly flexible spacecraft, and the outputs are the attitude control torque and the force.

[0068] (1) The attitude control equation for a highly flexible spacecraft is a PID algorithm with additional saturation state constraints, and its expression is as follows:

[0069]

[0070] Among them, τ=(τ1,τ2,τ3),||τ|| ∞ =max{|τ1|,|τ2|,|τ3|}; J is the rotational inertia matrix of the controlled object; k, T, and c are the control parameters corresponding to the proportional, integral, and derivative elements of the PID algorithm, respectively. In this embodiment, parameters k = 9.54, T = 10, and c = 0.55; e = (e1, e2, e3) is the error vector between the current attitude and the target attitude of the controlled object; ω = (ω1, ω2, ω3) is the angular velocity vector; u = (u1, u2, u3) is the attitude control torque vector; U is the maximum allowable output attitude control torque; sat(*) is the saturation state function, defined as follows:

[0071]

[0072] (2) Vibration suppression of the highly flexible spacecraft structure in this embodiment of the invention requires real-time observation of the distance changes of six observation points on the primary and secondary mirrors. The distribution of the observation points is as follows: Figure 3 As shown. The structural vibration suppression equation contains a total of 15 observations, where each observation is the relative distance d between any two observation points, defined as follows:

[0073] d=(d 12 d 13 d 14 d 15 d 16 d 23 d 24 d 25 d 26 d 34 d 35 d 36 d 45 d 46 d 56 )

[0074]

[0075] in, Xi0represents the initial coordinate of the i-th observation point.

[0076] The observation quantity needs to be filtered, and a fourth-order Bessel low-pass filter is used in the embodiment of the present application, with a cutoff frequency of 0.5 Hz. According to the modal characteristics of the large flexible spacecraft in the embodiment of the present application, the filter is written in the form of a linear system as follows:

[0077]

[0078] wherein y is the input signal of the low-pass filter; is the output signal of the low-pass filter.

[0079] The output structural vibration suppression action force is the axial thrust and pull force along the truss (the thrust is defined as a positive value, and the pull force is defined as a negative value), and the action force vector F c is calculated according to the following formula:

[0080]

[0081] wherein, is the measured quantity of the relative deformation after passing through the low-pass filter; is the time differential of the measured quantity of the relative deformation after passing through the low-pass filter; G y and G v are the flexible structure vibration control rate matrices in the embodiment of the present application, which are related to the modal characteristics of the large flexible spacecraft in the embodiment.

[0082] (3) Based on the Fortran language, the attitude control equation and the structural vibration suppression equation of the large flexible spacecraft are compiled into the UAMP subroutine interface script, and the call is selected in the CAE interface of the Abaqus software when submitting the calculation. The UAMP subroutine allows the user to extract the deformation, displacement and coordinate information of the specified nodes or elements of the model in real time during the calculation, and finally obtains the amplitude (AMPVALUENEW) of the force or torque through the script program calculation. The Abaqus software help document has provided a UAMP subroutine interface script template, and the user only needs to edit the program output amplitude parameter AMPVALUENEW in the reserved compilation section.

[0083] For step six, the pointing angle of the central star axial direction is used as the attitude angle of the large flexible spacecraft, the pointing angle is characterized by means of a servo coordinate system established by some unit nodes on the central star, and the target pointing and the current real-time pointing attitude angle are represented by a group of quaternions. The deviation D of the geometric center distance of the primary and secondary mirrors from the axial nominal distance of the large flexible spacecraft, the distance d of the geometric center of the secondary mirror to the normal vector of the primary mirror plane, and the included angle a of the normal vectors of the primary and secondary mirror planes are used as three indexes for measuring the vibration suppression effect of the large flexible spacecraft structure, and when the above three indexes are less than the expected value, it is considered that the vibration of the spacecraft flexible structure is effectively suppressed.

[0084] (1) The representation method of the attitude angle of the large flexible spacecraft is as follows:

[0085] In the embodiment of the application, the pointing angle of the central star axial direction is used as the attitude angle of the large flexible spacecraft, and the pointing angle needs to define a group of servo coordinate systems bound to the central star for characterization. However, in Abaqus software, a local coordinate system that moves with the central star cannot be established, so a servo coordinate system can only be established by means of some unit nodes on the central star. In the embodiment of the application, a servo coordinate system is established on one end face of one of the central star cabins, the axial direction of the large flexible spacecraft is used as the Z axis of the servo coordinate system, and the X and Y axes are directed in the same direction as the global coordinate system of the model.

[0086] The target pointing and the current real-time pointing attitude angle of the large flexible spacecraft model are represented by a group of quaternions, and the specific method is as follows:

[0087] Let a rotation matrix R be:

[0088]

[0089] Wherein, n x =(R 11 ,R 21 ,R 31 ) T , n Y =(R 12 ,R 22 ,R 32 ) T And n Z =(R 13 ,R 23 ,R 33 ) T are the unit column vectors of the X, Y and Z axes of the servo coordinate system, respectively.

[0090] The quaternion Q c of the current real-time pointing attitude angle is represented as:

[0091] Q c =(a,b,c,w)

[0092]

[0093] In the embodiment of the application, the quaternion of the target pointing attitude angle is set as:

[0094]

[0095] which indicates that the large flexible spacecraft will rotate 5° in the XZ plane.

[0096] (2) In the embodiment of the application, there are three indexes for measuring the vibration suppression effect of the large flexible spacecraft structure, which are the deviation D of the distance between the geometric centers of the primary and secondary mirrors and the nominal distance L of the large flexible spacecraft, the distance d of the geometric center of the secondary mirror to the normal vector of the primary mirror plane, and the angle α between the normal vectors of the primary and secondary mirror planes. When the above three indexes are all less than the expected value, it can be considered that the flexible structure vibration of the spacecraft is effectively suppressed. The calculation methods of the three indexes are as follows:

[0097] As shown in FIG. 1, the coordinates of the three observation points on the primary and secondary mirrors are respectively Figure 3 and and where i = 1, 2, 3. The three observation points on the primary or secondary mirror can determine a plane equation:

[0098] Ax+By+Cz+D=0

[0099] Let D = 1, then the coordinates of the three observation points on the primary mirror satisfy the equation:

[0100]

[0101] Define and as the normal vectors of the primary mirror plane and the secondary mirror plane respectively, then:

[0102]

[0103] where O and O' are the centers of the circumscribed circles of the triangles formed by the three observation points on the primary and secondary mirrors respectively. Therefore, the deviation D of the distance between the geometric centers of the primary and secondary mirrors and the nominal distance L of the large flexible spacecraft can be expressed as:

[0104]

[0105] The distance d of the geometric center of the secondary mirror to the normal vector of the primary mirror plane can be expressed as:

[0106]

[0107] The angle α between the normal vectors of the primary and secondary mirror planes can be expressed as:

[0108]

[0109] (3) Simulation Result Analysis

[0110] The total analysis time for the simulation results in this embodiment of the invention is 650s, divided into two stages. In the first stage (0s–250s), attitude control is activated, causing the highly flexible spacecraft to turn towards the target (rotating 5° in the XZ plane). After the spacecraft reaches the target attitude angle, in the second stage (250s–650s), actuator control is activated, while maintaining attitude control in the active state throughout this process. Based on the simulation results, the attitude angle curve, the deviation curve D between the distance between the geometric centers of the primary and secondary mirrors and the nominal axial distance L of the highly flexible spacecraft, the distance d from the geometric center of the secondary mirror to the normal vector of the primary mirror plane, and the angle α between the normal vectors of the primary and secondary mirror planes are plotted, as follows: Figures 4 to 7 As shown.

[0111] Simulation results show that the attitude control torque did not exceed the preset upper limit of 1000 N·m during the entire simulation, indicating that the saturation constraint condition in the PID algorithm is effective. After approximately 250 seconds, the attitude angle of the highly flexible spacecraft (e.g., ...) Figure 4 The angle (as shown) is 4.990595°, with a deviation of 3.3858 arcseconds, indicating high attitude control accuracy in the simulation. After approximately 400 seconds, the attitude control torque approaches 0 N·m, indicating that the attitude control torque converges after the large flexible spacecraft's attitude is effectively controlled. However, the attitude angle curve still exhibits some overshoot, requiring further adjustment of the k, T, and c parameters of the PID controller. The vibration suppression force for the flexible structure is applied after approximately 250 seconds. Throughout the simulation, the force does not exceed the 500N upper limit, indicating the effectiveness of the saturation constraint in the PID algorithm. After approximately 350 seconds, the force stabilizes within the ±100N range. Figures 5 to 7 The curves represent the deviation D between the geometric center distance of the primary and secondary mirrors and the nominal axial distance L of the large flexible spacecraft, the distance d from the geometric center of the secondary mirror to the normal vector of the primary mirror plane, and the angle α between the normal vectors of the primary and secondary mirror planes, respectively. The curves show that all three indicators approach zero after 350 seconds (i.e., 100 seconds after the flexible structure vibration suppression is activated), close to the initial state of the model. This indicates that the structural vibration of the large flexible spacecraft in this embodiment of the invention is effectively suppressed.

[0112] In summary, this invention proposes a coupled simulation method for on-orbit attitude control and structural dynamics of highly flexible spacecraft using Abaqus software. This method simulates the structural dynamics of highly flexible spacecraft under on-orbit attitude control, achieving attitude pointing control and structural vibration suppression of highly flexible spacecraft under large-amplitude attitude maneuvers. It provides a new technical approach for evaluating the structural mechanical performance, reliability, and pointing accuracy of highly flexible spacecraft.

[0113] The application further provides a spacecraft in-orbit attitude control and structural dynamics coupling simulation system, which can be realized by executing the flow steps of the spacecraft in-orbit attitude control and structural dynamics coupling simulation method, that is, the spacecraft in-orbit attitude control and structural dynamics coupling simulation method can be understood as a preferred embodiment of the spacecraft in-orbit attitude control and structural dynamics coupling simulation system by those skilled in the art.

[0114] A spacecraft in-orbit attitude control and structural dynamics coupling simulation system comprises:

[0115] Module M1: a three-dimensional simplified geometric model of the spacecraft is established in finite element analysis software, model meshing is performed, and material parameters of each component are assigned.

[0116] Module M2: implicit dynamics is taken as an analysis step, geometric nonlinearity is enabled, and total simulation time, initial increment step, minimum increment step and maximum increment step are defined.

[0117] Module M3: three-axis moments and concentrated forces are set at the central star body and the truss of the three-dimensional simplified geometric model to simulate attitude control moments and flexible structure vibration suppression dynamics, and coefficients and amplitudes of the three-axis moments and the concentrated forces are set.

[0118] Module M4: attitude control equations and flexible structure vibration suppression equations of the spacecraft are established, and are compiled into a subprogram script of the finite element analysis software.

[0119] Module M5: an implicit dynamics analysis task is established, the subprogram script is selected and submitted for calculation, attitude angle curves and three index curves for measuring flexible structure vibration suppression effects are drawn, and whether the stable attitude angle accuracy and the flexible structure vibration suppression effect of the spacecraft meet the expectations is analyzed.

[0120] Those skilled in the art know that, in addition to implementing the system and each device, module and unit thereof provided by the application in the form of pure computer readable program code, the system and each device, module and unit thereof provided by the application can also be implemented in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps to achieve the same functions. Therefore, the system and each device, module and unit thereof provided by the application can be considered as a hardware component, and the devices, modules and units included therein for achieving various functions can also be considered as structures in the hardware component; the devices, modules and units for achieving various functions can also be considered as both software modules for implementing the method and structures in the hardware component.

[0121] The specific embodiments of the present application are described above. It needs to be understood that the present application is not limited to the specific embodiments described above, and various changes or modifications can be made by those skilled in the art within the scope of the claims, which does not affect the essential content of the present application. The embodiments of the present application and the features in the embodiments can be combined with each other at will without conflict.

Claims

1. A method for coupling simulation of spacecraft on-orbit attitude control and structural dynamics, characterized in that, Comprise: Step S1: in finite element analysis software, the three-dimensional simplified geometric model of spacecraft is established, the model is meshed and the material parameters of each component are given; Step S2: implicit dynamics is used as analysis step, geometric nonlinearity is opened, total simulation time, initial increment step, minimum increment step and maximum increment step are defined; Step S3: three-axis torque and concentrated force are set at the central star body and truss of the three-dimensional simplified geometric model to simulate attitude control torque and flexible structure vibration suppression power, and the coefficients and amplitudes of three-axis torque and concentrated force are set; Step S4: the attitude control equation and the flexible structure vibration suppression equation of the spacecraft are established, and are compiled into a subprogram script of the finite element analysis software; Step S5: implicit dynamics analysis task is established, the subprogram script is selected and submitted for calculation, attitude angle curve and three index curves for measuring flexible structure vibration suppression effect are drawn, and whether the stable attitude angle accuracy and the flexible structure vibration suppression effect of the spacecraft reach the expectation is analyzed; The step S4 comprises: based on Fortran language, the attitude control equation and the flexible structure vibration suppression equation of the spacecraft are compiled into UAMP subprogram interface script; The attitude control equation is a PID algorithm with additional saturated state constraint condition; In the structural vibration suppression equation, the distance changes of six observation points on the primary mirror and the secondary mirror need to be observed in real time, and the observation quantity is the relative distance between any two observation points d ; The output structural vibration suppression action force is a pushing and pulling force along the truss axis, and the action force vector F c The calculation formula is: wherein, is a measure of relative deformation after passing through a low-pass filter; is a time derivative of the measure of relative deformation after passing through a low-pass filter; G y and G v is a flexible structure vibration control rate matrix, which is related to modal characteristics of a large flexible spacecraft; In the step S5: The pointing angle of the central star body is used as the attitude angle of the spacecraft, the pointing angle is characterized by means of a follow-up coordinate system established by some unit nodes on the central star body, and the target pointing and the current real-time pointing attitude angle are represented by a group of quaternions; a distance between a primary mirror geometric center and a secondary mirror geometric center D a distance from a secondary mirror geometric center to a primary mirror plane normal vector d an angle between a primary mirror plane normal vector and a secondary mirror plane normal vector When the three indexes are all less than expected values, it is considered that the spacecraft flexible structure vibration is effectively suppressed.

2. The method of claim 1, wherein, The three-dimensional simplified geometric model comprises: primary mirror, secondary mirror, primary mirror segment truss, secondary mirror segment truss and central star body; A large number of TT&C load single machines and power supplies are arranged at the central star body, the specific structures of these loads are ignored when modeling in Abaqus software, and are equivalently modeled in the form of uniform mass or mass point; the primary mirror, the secondary mirror, the central star body and the triangular plates in the truss cells are modeled by shell elements, and the truss structure is modeled by beam elements; when the model is meshed, the number of meshes is controlled, and the calculation accuracy and the calculation amount of the model are considered.

3. The method of claim 1, wherein, The finite element analysis software adopts Abaqus software; the step S3 comprises: in the Load module of Abaqus software, the coefficients and amplitudes of the flexible structure vibration suppression power and the attitude control torque are set, the amplitude type is selected as user, and it is indicated that the UAMP subprogram interface is allowed to be called; The size of the attitude control torque and the flexible structure vibration suppression power is torque or the coefficient of torque multiplied by amplitude.

4. The method of claim 3, wherein, When submitting calculation in the CAE interface of Abaqus software, the calling is selected; the output quantity of the UAMP subprogram script is the amplitude of the attitude control torque and the flexible structure vibration suppression power.

5. A spacecraft on-orbit attitude control and structural dynamics coupled simulation system, characterized in that, Comprise: Module M1: in finite element analysis software, the three-dimensional simplified geometric model of spacecraft is established, the model is meshed and the material parameters of each component are given; Module M2: implicit dynamics is used as analysis step, geometric nonlinearity is opened, total simulation time, initial increment step, minimum increment step and maximum increment step are defined; Module M3: setting three-axis moment and concentrated force at central star and truss of three-dimensional simplified geometric model, simulating attitude control moment and flexible structure vibration suppression action force, and setting coefficient and amplitude of three-axis moment and concentrated force; Module M4: establishing attitude control equation and flexible structure vibration suppression equation of spacecraft, and compiling into subprogram script of finite element analysis software; Module M5: establishing implicit dynamic analysis task, selecting the subprogram script and submitting calculation, drawing attitude angle curve and three index curves of measuring flexible structure vibration suppression effect, and analyzing whether stability attitude angle precision and flexible structure vibration suppression effect of spacecraft reach expectation; The module M4 comprises: compiling attitude control equation and flexible structure vibration suppression equation of spacecraft into UAMP subprogram interface script based on Fortran language; The attitude control equation is a PID algorithm with additional saturated state constraint condition; In the structural vibration suppression equation, the distance changes of six observation points on the primary mirror and the secondary mirror need to be observed in real time, and the observation quantity is the relative distance between any two observation points d ; The output structural vibration suppression action force is a pushing and pulling force along the truss axis, and the action force vector F c The calculation formula is: wherein, is a measure of relative deformation after passing through a low-pass filter; is a time derivative of the measure of relative deformation after passing through a low-pass filter; G y and G v is a flexible structure vibration control rate matrix, which is related to modal characteristics of a large flexible spacecraft; In the module M5: The pointing angle of central star axis is taken as the attitude angle of spacecraft, and the pointing angle is characterized by means of follow-up coordinate system established by some unit nodes on the central star, and the target pointing and current real-time pointing attitude angle are represented by a group of quaternions; a distance between a primary mirror geometric center and a secondary mirror geometric center D a distance from a secondary mirror geometric center to a primary mirror plane normal vector d an angle between a primary mirror plane normal vector and a secondary mirror plane normal vector When the three indexes are all less than expected values, it is considered that the spacecraft flexible structure vibration is effectively suppressed.

6. The system of claim 5, wherein the system is configured to: The three-dimensional simplified geometric model comprises: primary mirror, secondary mirror, primary mirror segment truss, secondary mirror segment truss and central star; A large number of TT&C load units and power supplies are arranged at the central star, and these loads are ignored in modeling in the Abaqus software, and are equivalent in the form of uniform mass or mass point; the triangular plates in the primary mirror, the secondary mirror, the central star and the truss cells are modeled by shell elements, and the truss structure is modeled by beam elements; when the model is meshed, the number of meshes is controlled, and the calculation precision and the calculation amount of the model are considered.

7. The system of claim 5, wherein the system is configured to: The finite element analysis software adopts the Abaqus software; The module M3 comprises: setting coefficient and amplitude of flexible structure vibration suppression action force and attitude control moment in the Load module of the Abaqus software, and selecting user as the amplitude type, which represents that the UAMP subprogram interface is allowed to be called; The size of the attitude control moment and the flexible structure vibration suppression action force is a moment or a coefficient of the moment multiplied by the amplitude.

8. The system of claim 7, wherein the system is configured to: The UAMP subprogram interface is selected and called when the calculation is submitted in the CAE interface of the Abaqus software; and the output quantity of the UAMP subprogram script is the amplitude of the attitude control moment and the flexible structure vibration suppression action force.

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