Method for predicting the whole satellite dynamics characteristics of a deployable structure during its deployment in orbit

Abstract

The application provides a method for predicting the whole satellite dynamics characteristics of a deployable structure during on-orbit deployment, which comprises the following steps: establishing a flexible dynamics equation of the whole satellite and a flexible multi-body dynamics equation set of the deployment process of the deployable structure; performing one-step numerical integration on the flexible multi-body dynamics equation set; replacing the hinges of the deployable structure which are deployed to the position or reach the preset jam with six-degree-of-freedom force element connections according to the integration results, locking the jammed hinges and the corresponding connection components, and establishing a multi-body dynamics structure dynamics model of the mixed semi-locking and semi-deployment; eliminating the rigid body mode through modal analysis to obtain a deployable structure dynamics model; and obtaining a semi-locking and semi-deployment dynamics model of the satellite during on-orbit deployment based on the deployable structure dynamics model and the flexible dynamics equation of the whole satellite; thus, the application can solve the whole satellite attitude stabilization control input and deployment failure disposal whole satellite model disposal problems caused by the locking during the on-orbit deployment of the satellite-borne deployable structure.

Description

Technical Field

[0001] The present invention relates to the field of satellite dynamics technology, and in particular to a method for predicting the dynamic characteristics of an entire satellite during the on-orbit deployment of a deployable structure. Background Art

[0002] High-orbit mobile communications satellites, very high-throughput communications satellites, mobile phone direct-link satellites, and high-resolution synthetic radar satellites for Earth observation all utilize high-precision, large-scale antennas as their primary payloads. These antennas often include dozens, even hundreds, of joints. Due to design or manufacturing errors, these antennas exhibit asynchronous deployment of their individual units during deployment, resulting in excessive stress on individual rods or hinge jamming, leading to anomalies in the antenna's on-orbit deployment. Furthermore, the asynchronous locking of antenna units can cause the entire satellite to exhibit a mixed structural and mechanical state while in orbit, resulting in significant variations in the satellite's on-orbit dynamic parameters and posing significant challenges to the stability of the satellite's attitude control system. To ensure the stability of satellite control systems equipped with antennas and to develop strategies for handling antenna deployment anomalies, it is urgent to address the problem of predicting the dynamic characteristics of the entire satellite during on-orbit deployment of deployable structures.

[0003] The prediction of the dynamic characteristics of the entire satellite during the in-orbit deployment of the deployable structure is a key technology that needs to be solved for the in-orbit deployment anomaly handling of high-value satellite antennas such as high-orbit mobile communication satellites, very high throughput communication satellites, mobile phone direct connection satellites, and high-resolution synthetic radar satellites for the Earth. It is of great value for formulating strategies for handling in-orbit deployment anomalies of antennas and designing control systems.

[0004] High-value satellites, such as high-orbit mobile communications satellites, very high-throughput communications satellites, mobile phone direct connection satellites, and high-resolution synthetic radar satellites, are complex, prone to in-orbit deployment asynchrony, and prone to failure. Statistics on in-orbit deployment anomalies for spacecraft with large mesh antennas show that antenna deployment failures account for 12.5% ​​of these spacecraft. Therefore, understanding the dynamic characteristics of the entire satellite during in-orbit deployment of deployable structures is crucial for developing strategies to address in-orbit antenna deployment anomalies and designing control systems.

[0005] Most existing research focuses on analyzing the dynamics of antenna deployment, with little attention paid to modeling the entire satellite's dynamics during on-orbit deployment of complex, time-varying antenna parameters. This is particularly true given the limited consideration of the impact of antenna deployment motion on the deployed, locked structure. This problem is particularly pronounced for ultra-large deployable antennas or antennas assembled in orbit. For example, existing methods employ natural coordinate and absolute node coordinate methods to develop dynamic models for large parabolic deployable antennas. However, these methods suffer from large computational scale and low efficiency, making them inadequate for the low-order model requirements required for attitude control and fault handling during on-orbit deployment. Another existing method proposes an antenna deployment dynamics analysis method that treats the cable net and flexible truss deployment process as a quasi-static process, analyzing the cable net tension during the final stages of antenna deployment. Furthermore, a Chinese patent (CN201510249518.3) discloses a large-scale antenna dynamics modeling method based on ANSYS and ADAMS. This method addresses the problem that existing modeling methods cannot accurately describe the rigid body motion of the antenna and cannot account for the rigid-elastic coupling during antenna motion. Chinese patents (CN201810828079.5) disclose a method for determining the flexible dynamics model of a satellite equipped with a large flexible antenna; Chinese patents (CN201610183019.3) disclose a dynamic modeling method for capturing the effects of antenna on-orbit vibration, primarily addressing the dynamic analysis of antenna structure vibration after on-orbit deployment. These methods either address only the dynamics model of antenna deployment or the dynamics model of the antenna after deployment and locking. Neither method addresses the problem of predicting the dynamic characteristics of the deployable structure's varying parameters due to asynchronous locking during antenna or space structure deployment. They also struggle to adapt to the satellite control system's need for low-order, fast simulation models during antenna deployment, and they are unable to address the computational issues of the dynamics model of the satellite's time-varying parameters during antenna deployment. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for predicting the dynamic characteristics of the entire satellite during the on-orbit deployment of a deployable structure, which is used to solve the problems of full-satellite attitude stability control input and deployment fault handling caused by the locking of large-scale space deployable structures on board during the on-orbit deployment.

[0007] To achieve the above-mentioned object, the present invention provides a method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure, comprising the following steps:

[0008] S1. Based on the pseudo-Lagrangian equation, the flexible dynamics equation of the entire star is established;

[0009] S2. establishing a set of flexible multi-body dynamics equations for the unfolding process of the unfoldable structure taking into account boundary constraints based on a recursive method according to the material mechanical properties, hinges, and geometric model of the unfoldable structure;

[0010] S3. If the flexible multi-body dynamics equations include constraint equations, converting the flexible multi-body dynamics equations into a system of ordinary differential equations described by generalized coordinates to eliminate the constraint equations;

[0011] S4. performing a one-step numerical integration on the flexible multi-body dynamics equations that do not include constraint equations or exclude the constraint equations;

[0012] S5. Determine, based on the numerical integration result, whether any hinge of the deployable structure has been deployed to its full extent or reached a preset stuck position. If so, replace the corresponding hinge with a six-degree-of-freedom force element connection; otherwise, return to step S4.

[0013] S6. Locking the stuck hinge and the corresponding connecting component according to the six-degree-of-freedom force metadata in the one-step numerical integration result, and establishing a multi-body dynamic structural dynamics model of the deployable structure with a semi-locked and semi-deployed hybrid;

[0014] S7. performing modal analysis on the multi-body dynamic structure dynamic model to eliminate rigid body modes, so as to obtain a deployable structural dynamic model described by modes during deployment;

[0015] S8. Using the modal vibration shape and frequency parameters of the deployable structure dynamic model as input, writing them into the whole satellite flexible dynamic equation to obtain a semi-locked and semi-deployed dynamic model of the satellite during on-orbit deployment;

[0016] S9. Determine whether the hinges of the deployable structure are all locked. If not, return to step S4 until the hinges of the deployable structure are all locked or in a stuck and fixed state.

[0017] Furthermore, the whole-satellite flexible dynamics equation derived based on the pseudo-Lagrangian equation is:

[0018]

[0019] Where M1 represents the satellite mass matrix; F tai F represents the coupling coefficient matrix of the i-th flexible attachment vibration to the spacecraft translation; sai A coupling coefficient matrix representing the vibration of the deployable structure to the rotation of the spacecraft; represents the second-order time derivative of the generalized coordinates of the vibration of the i-th flexible attachment; P s Represents the external force acting on the star; I s Represents the satellite's moment of inertia relative to its own center of mass coordinate system; ω s and They represent the satellite angular velocity and the first-order derivative of the satellite angular velocity with respect to time; T s represents the external moment matrix acting on the star; ηai 、 and represent the vibration generalized coordinates of the deployable structure, the first-order derivative of the vibration generalized coordinates of the deployable structure with respect to time, and the second-order derivative of the vibration generalized coordinates of the deployable structure with respect to time, respectively; ξ ai Represents the structural damping ratio; Ω ai represents the diagonal matrix of modal frequencies.

[0020] Furthermore, the flexible multi-body dynamics equations excluding the constraint equations are:

[0021]

[0022] Wherein, M2 represents the generalized mass matrix of the deployable structure; C represents the system damping matrix; K represents the generalized stiffness matrix; F represents the generalized external force matrix; q represents the system generalized coordinate array; and They represent the first-order and second-order derivatives of the generalized coordinate array of the entire star system with respect to time.

[0023] Furthermore, if the flexible multi-body dynamics equations include constraint equations, then the flexible multi-body dynamics equations are:

[0024]

[0025] The flexible multi-body dynamics equations are transformed to obtain the ordinary differential equations described by generalized coordinates:

[0026]

[0027]

[0028] Among them, Φ q represents the system constraint matrix; λ represents the Lagrange multiplier; γ represents the right-hand side term of the second-order derivative of the corresponding constraint equation with respect to time.

[0029] Furthermore, performing one-step numerical integration on the flexible multi-body dynamics equations without the constraint equations or excluding the constraint equations includes:

[0030] Based on the fourth-order Runge-Kutta method, the flexible multi-body dynamics equations without the constraint equations or without the constraint equations are integrated.

[0031] Furthermore, the multi-body dynamics structural dynamics model is:

[0032]

[0033] Among them, M sysrepresents the system mass matrix during the deployment of the deployable structure; q sys represents the generalized coordinates of the entire satellite during the on-orbit deployment of the deployable structure; and They represent the first-order and second-order derivatives of the system's generalized coordinates with respect to time; C sys and K sys Represent the system damping and stiffness matrices respectively; F sys represents the generalized external force matrix of the system.

[0034] Furthermore, performing modal analysis on the multi-body dynamic structure dynamic model to eliminate rigid body modes to obtain a deployable structural dynamic model described by modes during deployment includes:

[0035] Based on the mass matrix and stiffness matrix extracted from the multi-body dynamic structure dynamic model, modal analysis is performed to eliminate stiffness modes, thereby obtaining a deployable structure dynamic model that describes the modal state during deployment of the deployable structure.

[0036] The present invention aims to solve the prominent problems of large changes in the time-varying dynamic parameters of the whole satellite and low computational efficiency caused by the asynchronous locking during the on-orbit deployment of a large-scale deployable structure. The present invention provides a method for predicting the dynamic characteristics of the whole satellite during the on-orbit deployment of a deployable structure. The method establishes the flexible dynamic equations of the whole satellite based on the pseudo-Lagrangian equation; according to the material mechanical properties, hinges and geometric model of the deployable structure, a flexible multi-body dynamic equation group of the deployable structure deployment process considering boundary constraints is established based on the recursive method; if the flexible multi-body dynamic equation group contains constraint equations, the flexible multi-body dynamic equation group is converted into an ordinary differential equation group described by generalized coordinates to eliminate the constraint equations; a one-step numerical integration is performed on the flexible multi-body dynamic equation group that does not contain constraint equations or eliminates constraint equations; and according to the one-step numerical integration result, it is determined whether there is a deployable structure. If any hinge is deployed to its full position or reaches a preset stuck position, the corresponding hinge is replaced with a six-degree-of-freedom force element connection; otherwise, the numerical integration is returned; based on the six-degree-of-freedom force element data in the first step of the numerical integration result, the stuck hinge is locked with the corresponding connection component, and a multi-body dynamic structural dynamic model of the deployable structure with a semi-locked and semi-deployed hybrid is established; modal analysis is then performed on it to eliminate rigid body modes to obtain a deployable structural dynamic model with modal description during deployment; the modal vibration mode and frequency parameters of the deployable structural dynamic model are used as input to write the flexible dynamic equations of the entire satellite to obtain a semi-locked and semi-deployed dynamic model of the satellite during on-orbit deployment; it is determined whether all hinges of the deployable structure are locked. If not, the numerical integration is continued until all hinges of the deployable structure are locked or in a stuck and fixed state. In this way, the present invention can solve the problems of full-satellite attitude stability control input and deployment fault handling caused by the locking of large-scale space deployable structures during on-orbit deployment. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A flowchart of the steps of a method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of the deployable structure provided in one embodiment of the present invention;

[0038] Figure 2 A flexible dynamic structure model of the entire satellite for predicting the dynamic characteristics of the entire satellite during the on-orbit deployment of the deployable structure provided in one embodiment of the present invention;

[0039] Figures 3a-3c A diagram illustrating the deployment process of the deployable structure according to a method for predicting the dynamic characteristics of a satellite during on-orbit deployment of the deployable structure provided in one embodiment of the present invention;

[0040] Figure 4 Schematic diagram of a six-degree-of-freedom force element mechanics model applicable to the method for predicting the dynamic characteristics of the entire satellite during the on-orbit deployment of the deployable structure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, 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 intended to limit the present invention.

[0042] It should be noted that references to "one embodiment," "an embodiment," "an example embodiment," etc., in this specification indicate that the described embodiment may include specific features, structures, or characteristics, but not every embodiment must include these specific features, structures, or characteristics. Furthermore, such references do not necessarily refer to the same embodiment. Furthermore, when specific features, structures, or characteristics are described in conjunction with an embodiment, whether or not explicitly described, it is understood that incorporating such features, structures, or characteristics into other embodiments is within the knowledge of those skilled in the art.

[0043] In addition, certain words are used in the specification and subsequent claims to refer to specific components or parts. It should be understood by those with ordinary knowledge in the relevant field that manufacturers may use different nouns or terms to refer to the same component or part. This specification and subsequent claims do not use differences in names as a way to distinguish components or parts, but rather use differences in the functions of components or parts as the criteria for distinction. The words "including" and "comprising" mentioned throughout the specification and subsequent claims are open-ended terms and should be interpreted as "including but not limited to". In addition, the word "connect" here includes any direct and indirect electrical connection means. Indirect electrical connection means include connection through other devices.

[0044] Figure 1 A method for predicting the dynamic characteristics of a satellite during on-orbit deployment of a deployable structure provided by one embodiment of the present invention is shown, comprising the following steps:

[0045] S1: Based on the pseudo-Lagrangian equation, the flexible dynamics equation of the entire satellite is established; specifically, the deployable structure is regarded as a flexible body, and the flexible dynamics equation of the entire satellite during the deployment of the large-scale deployable structure on board can be derived according to the pseudo-Lagrangian equation. The deployable structure refers to a structure on a satellite or other spacecraft that is designed to be able to deploy under specific conditions in order to meet specific mission requirements and adapt to different stages of launch and on-orbit operation; such as Figure 2 The deployable structure of this embodiment specifically refers to a foldable and retractable solar wing panel.

[0046] Specifically, the whole-satellite flexible dynamics equation derived based on the pseudo-Lagrangian equation is:

[0047]

[0048] Where M1 represents the satellite mass matrix; F tai F represents the coupling coefficient matrix of the i-th flexible attachment vibration to the spacecraft translation; sai A coupling coefficient matrix representing the vibration of the deployable structure to the rotation of the spacecraft; represents the second-order time derivative of the generalized coordinates of the vibration of the i-th flexible attachment; P s Represents the external force acting on the star; I s Represents the satellite's moment of inertia relative to its own center of mass coordinate system; ω s and They represent the satellite angular velocity and the first-order derivative of the satellite angular velocity with respect to time; T s represents the external moment matrix acting on the star; η ai 、 and represent the vibration generalized coordinates of the deployable structure, the first-order derivative of the vibration generalized coordinates of the deployable structure with respect to time, and the second-order derivative of the vibration generalized coordinates of the deployable structure with respect to time, respectively; ξ ai Represents the structural damping ratio; Ω ai represents the diagonal matrix of modal frequencies.

[0049] The specific derivation process of deriving the above-mentioned flexible dynamic equation of the entire satellite based on the pseudo-Lagrangian equation can be found in the existing document "Spacecraft Dynamics Engineering" by Qu Guangji; this embodiment will not be repeated in detail.

[0050] F in the formula tai 、F sai ,ξ ai and Ω ai The input parameters of variables will be obtained through the following steps.

[0051] S2: Based on the material mechanical properties, hinges and geometric model of the deployable structure, a set of flexible multi-body dynamic equations for the deployment process of the deployable structure considering boundary constraints is established based on a recursive method. According to the system configuration, the initial value q0 of the generalized coordinates of the dynamic equations and the initial value of the first-order derivative of the generalized coordinates with respect to time can be obtained. Furthermore, after step S2, it is necessary to further determine whether the flexible multi-body dynamics equations obtained in step S2 contain constraint equations. If the deployable structure does not contain any constraints, the flexible multi-body dynamics equations during its on-orbit deployment are:

[0052]

[0053] Wherein, M2 represents the generalized mass matrix of the deployable structure; C represents the system damping matrix; K represents the generalized stiffness matrix; F represents the generalized external force matrix; q represents the system generalized coordinate array; and They represent the first-order and second-order derivatives of the generalized coordinate array of the entire star system with respect to time.

[0054] If the flexible multi-body dynamics equations include constraint equations, then the flexible multi-body dynamics equations for on-orbit deployment of the deployable structure are:

[0055]

[0056] Among them, Φ q represents the system constraint matrix; λ represents the Lagrange multiplier; γ represents the right-hand side term of the second-order derivative of the corresponding constraint equation with respect to time.

[0057] S3: If the flexible multibody dynamics equations include constraint equations, the flexible multibody dynamics equations are converted into a system of ordinary differential equations described using generalized coordinates to eliminate the constraint equations. Specifically, the flexible multibody dynamics equations are converted from a system of differential algebraic equations to a system of ordinary differential equations described using generalized coordinates.

[0058] Specifically, if the flexible multi-body dynamics equations obtained in step S2 include constraint equations, as shown in formula (5), it is necessary to further transform formula (5) to eliminate the constraint equations; that is, the flexible multi-body dynamics equations are transformed to obtain a set of ordinary differential equations described by generalized coordinates:

[0059]

[0060]

[0061] S4: performing one-step numerical integration on the flexible multi-body dynamics equations that do not contain constraint equations or exclude the constraint equations; that is, performing one-step numerical integration on the dynamics differential algebraic equations or ordinary differential equations of the deployable structure obtained in the above steps; optionally, step S4 includes: integrating the flexible multi-body dynamics equations that do not contain constraint equations or exclude the constraint equations based on the fourth-order Runge-Kutta method; in this embodiment, the fourth-order Runge-Kutta method is selected for integration, and the generalized coordinates q at the new moment can be obtained. t+Δt and the first-order time derivative of the generalized coordinates

[0062] S5: Based on the result of the one-step numerical integration, determine whether any of the hinges of the deployable structure has been deployed or reached a preset stuck position. If so, replace the corresponding hinge with a six-degree-of-freedom force element connection; otherwise, return to step S4. In specific implementation, combined with the integration results of the flexible multi-body dynamics equations of the deployable structure, determine whether any hinge of the deployable structure has been deployed or reached a preset stuck position. If at least one hinge has reached a locked or preset stuck position, the hinge is changed to a locked hinge, and the six-degree-of-freedom equivalent force element parameters are used to replace the hinge, thereby entering the next step; if the numerical integration result determines that no hinge has reached a locked or stuck position, return to step S4 to continue numerical integration, and after performing another step of numerical integration, enter step S5 to continue to determine whether the hinge of the deployable structure has been deployed or reached a preset stuck position. At the same time, after each numerical integration result determines that a hinge has been deployed or reached a preset stuck position, the process enters step S6 to execute subsequent steps.

[0063] See also Figure 4 The connection stiffness of the six-degree-of-freedom force element connection from point P to point Q in this embodiment is:

[0064]

[0065] Among them, K TX , K TY and K TZ They represent the three-axis tensile stiffness of the force element along the local coordinate system of point P, K RX , K RY and K RZ They represent the torsional stiffness of the force element along the three axes of the local coordinate system of point P.

[0066] S6: Based on the six-degree-of-freedom force data from the first step of numerical integration, the stuck hinge is locked with the corresponding connection component, and a multi-body dynamic structural dynamics model of the deployable structure with a semi-locked and semi-deployed hybrid is established. After replacing the stuck hinge with a six-degree-of-freedom connection, the six-degree-of-freedom force data can be used to form a structure with the stuck hinge and the corresponding connection part. The connection part here specifically refers to the connection part facing the star body. Figures 3a-3c The unfolding process of the unfoldable structure of this embodiment is shown, wherein, when the unfoldable structure is unfolded from Figure 3a The form is converted to Figure 3bWhen the form is formed, the hinge on the left is deployed in place or in a stuck position. Then, the hinge in this part is replaced with a six-degree-of-freedom link, and according to the six-degree-of-freedom force data, these hinges and the left connection structure are formed into a structure (i.e., locked into one). The other unlocked structures still serve as deployable mechanisms. At this time, the multi-body dynamics recursion method can be used to establish the multi-body dynamics equations in the mixed state of semi-locked and semi-deployed in the middle of the deployable structure. Specifically, the multi-body dynamics structure dynamics model is:

[0067]

[0068] Among them, M sys represents the system mass matrix during the deployment of the deployable structure; q sys represents the generalized coordinates of the entire satellite during the on-orbit deployment of the deployable structure; and They represent the first-order and second-order derivatives of the system's generalized coordinates with respect to time; C sys and K sys Represent the system damping and stiffness matrices respectively; F sys represents the generalized external force matrix of the system.

[0069] S7: Perform modal analysis on the multi-body dynamic structure dynamic model to eliminate rigid body modes to obtain a deployable structural dynamic model that describes the modal during deployment. In specific implementation, step S7 includes: based on the mass matrix M extracted from the multi-body dynamic structure dynamic model SYS and the stiffness matrix K sYS , modal analysis is performed to eliminate stiffness modes and obtain a dynamic model of the deployable structure described by the modes during the deployment of the deployable structure; that is, the modal vibration shape and frequency of the flexible body of the deployable structure are obtained.

[0070] S8: The modal vibration shape and frequency parameters of the deployable structure dynamic model are used as input and written into the satellite flexible dynamics equation to obtain the semi-locked and semi-deployed dynamic models of the satellite during on-orbit deployment. After obtaining the deployable structure dynamics equations describing the modalities during deployment in the above steps, this embodiment selects a modal sequence that has a significant impact on the satellite. The modal vibration shape and frequency parameters of the selected deployable structure modal sequence are then written into the satellite flexible dynamics model as input to obtain the semi-locked and semi-deployed dynamic models of the satellite during on-orbit deployment.

[0071] Specifically, the input is substituted into the above formulas (1) to (3) to calculate the corresponding F yai 、F sai ,ξ ai and Ω ai; In this way, the semi-locked and semi-deployed dynamic models of the satellite during on-orbit deployment are obtained, that is, the dynamic equations of the entire satellite during the deployment of the onboard deployable structure.

[0072] S9: Determine whether all hinges of the deployable structure are locked. If not, return to step S4 and continue numerical integration until all hinges of the deployable structure are locked or in a stuck state. Specifically, determine whether all hinges of the deployable structure are locked. If not, return to step S4 and continue numerical integration until all hinge parameters are locked or in a stuck state, thereby obtaining the structural dynamic parameters and the overall satellite dynamic parameters at each moment during the deployment process. If yes, the overall satellite dynamic analysis during the deployment of the deployable structure is complete; terminate the calculation, and obtain the dynamic equations at each moment during the deployment of the deployable structure.

[0073] In summary, the embodiments of the present invention aim at the prominent problems of large changes in the time-varying dynamic parameters of the whole satellite and low computational efficiency caused by the asynchronous locking during the on-orbit deployment of a large-scale deployable structure. The flexible dynamic equations of the whole satellite are established based on the pseudo-Lagrangian equation; according to the material mechanical properties, hinges and geometric models of the deployable structure, a flexible multi-body dynamic equation group of the deployable structure deployment process considering boundary constraints is established based on the recursive method; if the flexible multi-body dynamic equation group contains constraint equations, the flexible multi-body dynamic equation group is converted into a group of ordinary differential equations described by generalized coordinates to eliminate the constraint equations; a one-step numerical integration is performed on the flexible multi-body dynamic equation group that does not contain constraint equations or eliminates constraint equations; according to the result of the one-step numerical integration, it is determined whether any hinge of the deployable structure has been deployed in place or reached A stuck position is preset. If so, the corresponding hinge is replaced with a six-degree-of-freedom force element connection; otherwise, the numerical integration is returned; based on the six-degree-of-freedom force data in the first step of the numerical integration result, the stuck hinge is locked with the corresponding connecting component, and a multi-body dynamic structural dynamic model of the deployable structure with a semi-locked and semi-deployed hybrid is established; a modal analysis is then performed on it to eliminate the rigid body mode to obtain a deployable structural dynamic model with a modal description during deployment; the modal vibration shape and frequency parameters of the deployable structural dynamic model are used as input to write the whole satellite flexible dynamic equation to obtain a semi-locked and semi-deployed dynamic model of the satellite during on-orbit deployment; it is determined whether all hinges of the deployable structure are locked. If not, the numerical integration is continued until all hinges of the deployable structure are locked or in a stuck fixed state. In this way, the present invention realizes the prediction of the dynamic characteristics of the on-board variable topology space deployable structure while deploying and locking, provides a decision-making basis for the design of the control system during antenna deployment of such satellites with time-varying parameters and the determination of the whole satellite fault handling strategy during on-orbit abnormalities of the deployable structure, and effectively improves the reliability of high-value satellites with large space structures.

[0074] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure, characterized in that: Including steps: S1. Based on the pseudo-Lagrangian equation, the flexible dynamics equation of the entire star is established; S2. establishing a set of flexible multi-body dynamics equations for the unfolding process of the unfoldable structure taking into account boundary constraints based on a recursive method according to the material mechanical properties, hinges, and geometric model of the unfoldable structure; S3. If the flexible multi-body dynamics equations include constraint equations, converting the flexible multi-body dynamics equations into a system of ordinary differential equations described by generalized coordinates to eliminate the constraint equations; S4. performing a one-step numerical integration on the flexible multi-body dynamics equations that do not include constraint equations or exclude the constraint equations; S5. Determine, based on the numerical integration result, whether any hinge of the deployable structure has been deployed to its full extent or reached a preset stuck position. If so, replace the corresponding hinge with a six-degree-of-freedom force element connection; otherwise, return to step S4. S6. Locking the stuck hinge and the corresponding connecting component according to the six-degree-of-freedom force metadata in the one-step numerical integration result, and establishing a multi-body dynamic structural dynamics model of the deployable structure with a semi-locked and semi-deployed hybrid; S7. performing modal analysis on the multi-body dynamic structure dynamic model to eliminate rigid body modes, so as to obtain a deployable structural dynamic model described by modes during deployment; S8. Using the modal vibration shape and frequency parameters of the deployable structure dynamic model as input, writing them into the whole satellite flexible dynamic equation to obtain a semi-locked and semi-deployed dynamic model of the satellite during on-orbit deployment; S9. Determine whether the hinges of the deployable structure are all locked. If not, return to step S4 until the hinges of the deployable structure are all locked or in a stuck and fixed state.

2. The method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure according to claim 1, characterized in that: The whole-satellite flexible dynamics equation derived based on the pseudo-Lagrangian equation is: Where M1 represents the satellite mass matrix; F tai F represents the coupling coefficient matrix of the i-th flexible attachment vibration to the spacecraft translation; sai A coupling coefficient matrix representing the vibration of the deployable structure to the rotation of the spacecraft; represents the second-order time derivative of the generalized coordinates of the vibration of the i-th flexible attachment; P s Represents the external force acting on the star; I s Represents the satellite's moment of inertia relative to its own center of mass coordinate system; ω s and They represent the satellite angular velocity and the first-order derivative of the satellite angular velocity with respect to time; T s represents the external moment matrix acting on the star; η ai 、 and represent the vibration generalized coordinates of the deployable structure, the first-order derivative of the vibration generalized coordinates of the deployable structure with respect to time, and the second-order derivative of the vibration generalized coordinates of the deployable structure with respect to time, respectively; ξ ai Represents the structural damping ratio; Ω ai represents the diagonal matrix of modal frequencies.

3. The method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure according to claim 1, characterized in that: The flexible multi-body dynamics equations excluding the constraint equations are: Wherein, M2 represents the generalized mass matrix of the deployable structure; C represents the system damping matrix; K represents the generalized stiffness matrix; F represents the generalized external force matrix; q represents the system generalized coordinate array; and They represent the first-order and second-order derivatives of the generalized coordinate array of the entire star system with respect to time.

4. The method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure according to claim 3, characterized in that: If the flexible multibody dynamics equations include constraint equations, then the flexible multibody dynamics equations are: The flexible multi-body dynamics equations are transformed to obtain the ordinary differential equations described by generalized coordinates: Among them, Φ q represents the system constraint matrix; λ represents the Lagrange multiplier; γ represents the right-hand side term of the second-order derivative of the corresponding constraint equation with respect to time.

5. The method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure according to claim 1, characterized in that: The step of performing a numerical integration on the flexible multi-body dynamics equations that do not contain constraint equations or exclude the constraint equations comprises: Based on the fourth-order Runge-Kutta method, the flexible multi-body dynamics equations without the constraint equations or without the constraint equations are integrated.

6. The method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure according to claim 1, characterized in that: The multi-body dynamics structural dynamics model is: Among them, M sys represents the system mass matrix during the deployment of the deployable structure; q sys represents the generalized coordinates of the entire satellite during the on-orbit deployment of the deployable structure; and They represent the first-order and second-order derivatives of the system's generalized coordinates with respect to time; C sys and K sys Represent the system damping and stiffness matrices respectively; F sys represents the generalized external force matrix of the system.

7. The method for predicting the dynamic characteristics of a satellite during the on-orbit deployment of a deployable structure according to claim 1, characterized in that: The performing of modal analysis on the multi-body dynamic structure dynamic model to eliminate rigid body modes to obtain a deployable structural dynamic model described by modes during deployment includes: Based on the mass matrix and stiffness matrix extracted from the multi-body dynamic structure dynamic model, modal analysis is performed to eliminate stiffness modes, thereby obtaining a deployable structure dynamic model that describes the modal state during deployment of the deployable structure.

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