Method for predicting whole-satellite dynamic characteristics of deployable structure during on-orbit deployment

Abstract

The invention provides a whole-satellite dynamic characteristic prediction method for an expandable structure during in-orbit expansion. The whole-satellite dynamic characteristic prediction method comprises the following steps: establishing a whole-satellite flexible dynamic equation and a flexible multi-body dynamic equation set in an expansion process of the expandable structure; carrying out one-step numerical integration on the flexible multi-body dynamics equation set; according to the integral result, the hinge which is unfolded in place or reaches preset clamping stagnation in the expandable structure is replaced by six-degree-of-freedom force element connection, the clamped hinge and the corresponding connecting part are locked, and a semi-locking and semi-unfolding mixed multi-body dynamic structure dynamic model is established; through modal analysis, rigid body modals are eliminated, and a deployable structure dynamic model is obtained; on the basis of the deployable structure dynamic model and the whole satellite flexible dynamic equation, obtaining a semi-locking dynamic model and a semi-unfolding dynamic model during the on-orbit unfolding period of the satellite; therefore, the problems of whole-satellite attitude stable control input and unfolding fault handling and whole-satellite model handling caused by the fact that the satellite-borne deployable structure is unfolded and locked at the same time during the on-orbit unfolding period can be solved.

Description

Technical Field

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

[0002] High-orbit mobile communication satellites, very high throughput communication satellites, mobile phone direct connection satellites, and high-resolution synthetic radar satellites for the Earth all use high-precision, large-size antennas as their main payloads. These antennas often include dozens or even hundreds of joint hinges. Due to design reasons or manufacturing errors, these antennas exhibit asynchrony in the deployment of each unit during deployment, causing excessive force on individual rods or hinge jamming, resulting in abnormal deployment of the antenna in orbit. At the same time, the asynchronous locking of the antenna units will cause the entire satellite to present a mixed state of structure and mechanism in orbit, and the dynamic parameters of the entire satellite in orbit will vary greatly, and the stability of the satellite attitude control system will face severe challenges. In order to ensure the stability of the control system of satellites with antennas or provide a disposal strategy for abnormal deployment of antennas in orbit, it is urgent to solve the problem of predicting the dynamic characteristics of the entire satellite during the deployment of the deployable structure in orbit.

[0003] The prediction of the whole satellite dynamic characteristics 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 antenna in-orbit deployment anomaly handling strategies and control system design.

[0004] High-value satellites 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 have complex structures, unsynchronized deployment in orbit, and are prone to failures; according to the statistics of abnormal deployment of spacecraft with large mesh antennas in orbit, the proportion of spacecraft with antenna deployment failures in this type of spacecraft is 12.5%. Therefore, understanding the dynamic characteristics of the entire satellite during the deployment of the deployable structure in orbit is of great value for formulating strategies for handling abnormal deployment of antennas in orbit and designing control systems.

[0005] Most of the existing research work focuses on how to solve the dynamic analysis of the antenna deployment process, and rarely pays attention to the modeling of the whole satellite dynamic model during the on-orbit deployment of such complex time-varying parameter antennas. The main reason is that the impact of the antenna deployment movement on the deployed locked part structure is rarely considered. This problem is particularly prominent in the case of ultra-large deployable antennas or antennas assembled on orbit. For example, the existing technology uses the natural coordinate method and the absolute node coordinate method to establish a large parabolic cylindrical deployable antenna deployment dynamic model, but it has the problems of large calculation scale and low efficiency, and it is difficult to adapt to the low-order model requirements for attitude control and fault handling during the on-orbit deployment of satellites; the existing technology also proposes an antenna deployment dynamic analysis method that regards the cable net and flexible truss deployment process as a quasi-static process, and analyzes the cable net tension force in the later stage of the antenna deployment process; in addition, the Chinese patent (CN201510249518.3) discloses a large antenna dynamic modeling method based on ANSYS and ADAMS, which mainly solves the problem that the existing modeling method cannot accurately describe the rigid body motion of the antenna, but cannot consider the rigid-elastic coupling during the antenna motion process. Chinese patent (CN201810828079.5) discloses a method for determining the flexible dynamics model of a whole satellite equipped with a large flexible antenna; Chinese patent (CN201610183019.3) discloses a dynamic modeling method for obtaining the impact of antenna on-orbit vibration, which mainly solves the vibration dynamics analysis method of the antenna structure after the antenna is deployed on-orbit. These methods either only solve the antenna deployment dynamics model or solve the dynamics model after the antenna is deployed and locked. They cannot solve the problem of predicting the dynamic characteristics of the deployable structure with variable parameters caused by asynchronous locking during the deployment of the antenna or space structure. It is difficult to adapt to the satellite control system's demand for low-order and fast simulation models during the deployment of the antenna, and cannot solve the problem of calculating the dynamic model of the time-varying parameters of the whole satellite during the deployment of the antenna. Summary of the invention

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

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

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

[0009] S2. According to the material mechanical properties, hinges and geometric model of the deployable structure, a set of flexible multi-body dynamic equations of the deployment process of the deployable structure considering boundary constraints is established based on a recursive method;

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

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

[0012] S5. According to the result of the numerical integration step, determine whether any hinge of the deployable structure has been deployed to the desired position or has 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. According to the six-degree-of-freedom force metadata in the one-step 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 semi-locking and semi-deployment mixed is established;

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

[0015] S8, taking the modal vibration shape and frequency parameters of the deployable structure dynamics model as input, writing them into the whole satellite flexible dynamics equation, and obtaining the semi-locked and semi-deployed dynamics model of the satellite during on-orbit deployment;

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

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

[0018]

[0019] Where M1 represents the satellite mass matrix; F tai represents the coupling coefficient matrix of the i-th flexible attachment vibration to the spacecraft translation; F 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 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 respectively; T s represents the external moment array acting on the star; ηai , and denote 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 respectively 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, 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, 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:

[0030] Based on the fourth-order Runge-Kutta method, the flexible multi-body dynamics equations without constraint equations or excluding 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 Respectively represent the system damping and stiffness matrices; F sys Represents the generalized external force matrix of the system.

[0034] Further, the performing modal analysis on the multi-body dynamic structure dynamics model to eliminate rigid body modes to obtain a deployable structural dynamics 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 modes during deployment of the deployable structure.

[0036] The present invention aims at the prominent problems of large changes in time-varying dynamic parameters of the whole satellite and low calculation efficiency caused by asynchronous locking during the on-orbit deployment of a large-scale deployable structure, and 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 a 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. Any hinge is deployed in place or reaches a preset stuck position. If so, the corresponding hinge is replaced with a six-degree-of-freedom force element connection; otherwise, the numerical integration is returned; according to the six-degree-of-freedom force element data in the one-step numerical integration result, the stuck hinge is locked with the corresponding connection component, and a multi-body dynamic structure dynamic model of a semi-locked and semi-deployed hybrid of the deployable structure is established; then a modal analysis is performed on it to eliminate the rigid body mode to obtain a deployable structure dynamic model of the modal description during the deployment period; the modal vibration shape and frequency parameters of the deployable structure dynamic model are used as inputs and written into the flexible dynamics equation of the whole satellite to obtain a semi-locked and semi-deployed dynamic model of the satellite during the on-orbit deployment; it is determined whether the hinges of the deployable structure are all locked, if not, the numerical integration is returned to continue until the hinges of the deployable structure are all locked or in a stuck fixed state. By this, the present invention can solve the problem of the whole satellite attitude stability control input and deployment fault handling whole satellite model handling caused by the deployment and locking of the large-scale space deployable structure on board during the 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 whole satellite during the on-orbit deployment of the deployable structure provided in one embodiment of the present invention;

[0038] Figure 2 A whole-satellite flexible dynamics structure model for a whole-satellite dynamics characteristics prediction method during the on-orbit deployment of the deployable structure provided in one embodiment of the present invention;

[0039] Figure 3a to Figure 3c A diagram showing the unfolding process of the unfoldable structure of the method for predicting the dynamic characteristics of the entire satellite during the on-orbit unfolding of the unfoldable structure provided by one embodiment of the present invention;

[0040] Figure 4 It is a schematic diagram of a six-degree-of-freedom force element mechanics model applicable to a method for predicting the dynamic characteristics of a whole 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 solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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", "embodiment", "example embodiment", etc. in this specification refer to the embodiment described, which may include specific features, structures or characteristics, but not every embodiment must include these specific features, structures or characteristics. In addition, such expressions do not refer to the same embodiment. Furthermore, when describing specific features, structures or characteristics in conjunction with an embodiment, whether or not there is an explicit description, it has been shown that it is within the knowledge of those skilled in the art to combine such features, structures or characteristics into other embodiments.

[0043] In addition, certain words are used in the specification and subsequent claims to refer to specific components or parts. Those with ordinary knowledge in the relevant field should understand that manufacturers can 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 use differences in the functions of components or parts as the criteria for distinction. "Including" and "including" 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 "connected" 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 the on-orbit deployment of a deployable structure provided by an 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 whole satellite is established; specifically, the deployable structure is regarded as a flexible body, and the flexible dynamics equation of the whole 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 designed on a satellite or other spacecraft that can be deployed under specific conditions in order to meet specific mission requirements and adapt to different stages of launch and on-orbit operation; Figure 2 The deployable structure of this embodiment specifically refers to a foldable and retractable solar wing panel.

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

[0047]

[0048] Where M1 represents the satellite mass matrix; F tai represents the coupling coefficient matrix of the i-th flexible attachment vibration to the spacecraft translation; F 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 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 respectively; T s represents the external moment array acting on the star; η ai , and denote 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 whole satellite flexible dynamics equation based on the pseudo-Lagrangian equation can be found in the existing document "Spacecraft Dynamics Engineering", written by Qu Guangji; this embodiment will not be repeated here.

[0050] F in the formula tai 、F sai , 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 the recursive method. According to the system configuration, the initial value q0 of the generalized coordinates of the dynamic equation 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 respectively 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, 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 multi-body dynamics equations include constraint equations, the flexible multi-body dynamics equations are converted into ordinary differential equations described by generalized coordinates to eliminate the constraint equations. That is, the differential algebraic equations of the flexible multi-body dynamics equations are converted into ordinary differential equations described by 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 multibody 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 multibody 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 time can be obtained. t+Δt and the first-order derivative of the generalized coordinates with respect to time

[0062] S5: According to the result of one-step numerical integration, determine whether any hinge of the deployable structure is deployed in place or reaches the 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 integral result of the flexible multi-body dynamics equation group of the deployed structure, determine whether any hinge of the deployable structure is deployed in place or reaches the preset stuck position. If at least one hinge reaches the 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, so as to enter the next step; if it is determined from the numerical integration result that no hinge reaches the 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 is deployed in place or reaches the preset stuck position. At the same time, after each numerical integration result determines that a hinge is deployed in place or reaches the preset stuck position, it enters step S6 to perform 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 tensile stiffness of the force element along the three axes of the local coordinate system of point P, K RX , K RY and K RZ They respectively represent the torsional stiffness of the force element along the three axes of the local coordinate system of point P.

[0066] S6: According to the six-degree-of-freedom force data in the one-step numerical integration result, the stuck hinge is locked with the corresponding connection part, and a multi-body dynamic structural dynamics model of a semi-locked and semi-deployed hybrid of the deployable structure is established. After the stuck hinge is replaced 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, where the connection part specifically refers to the connection part facing the star body; Figure 3a to Figure 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 shape is formed, the hinge on the left is unfolded in place or in a stuck position, and then the hinge of 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 form a structure (that is, locked as a whole), and other unlocked structures are still used 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-expanded 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 Respectively represent the system damping and stiffness matrices; 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, so as to obtain a deployable structural dynamic model described by modes 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 the stiffness mode and obtain the dynamic model of the deployable structure described by the mode 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, written into the whole satellite flexible dynamics equation, and the semi-locked and semi-deployed dynamics model of the satellite during the on-orbit deployment is obtained. After the deployable structure dynamics equation describing the modality during the deployment is obtained in the above steps, the present embodiment selects a modal sequence that has a great impact on the satellite; then the modal vibration shape and frequency parameters of the modal sequence of the deployable structure are selected as input, written into the whole satellite flexible dynamics model, and the semi-locked and semi-deployed dynamics model of the satellite during the on-orbit deployment is obtained.

[0071] Specifically, the input is substituted into the above formulas (1) to (3) to calculate the corresponding F yai 、F sai , ai and Ω ai; In this way, the semi-locked and semi-deployed dynamic models of the satellite during in-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 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 fixed state. That is, determine whether the hinges of all deployable structures are locked. If not, return to step S4 to continue numerical integration until all hinge parameters are locked or in a stuck fixed state, and obtain the structural dynamic parameters and the whole satellite dynamic parameters at each moment of the deployment process of the deployable structure. If yes, it means that the whole satellite dynamic analysis during the deployment of the deployable structure is completed; 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 such as large changes in time-varying dynamic parameters of the whole satellite and low computational efficiency caused by 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 equations. According to the material mechanical properties, hinges and geometric models of the deployable structure, a group of flexible multi-body dynamic equations for the deployment process of the deployable structure considering boundary constraints is established based on a recursive method. If the group of flexible multi-body dynamic equations contains constraint equations, the group of flexible multi-body dynamic equations 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 group of flexible multi-body dynamic equations 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 is deployed in place or reaches The stuck position is preset, if it is, the corresponding hinge is replaced with a six-degree-of-freedom force element connection; otherwise, the numerical integration is returned; according to the six-degree-of-freedom force element data in the one-step numerical integration result, the stuck hinge is locked with the corresponding connection part, and a multi-body dynamic structure dynamic model of a semi-locked and semi-deployed hybrid of the deployable structure is established; then a modal analysis is performed on it, and the rigid body mode is eliminated to obtain a deployable structure dynamic model with modal description during deployment; the modal vibration shape and frequency parameters of the deployable structure dynamic model are used as input, and the whole satellite flexible dynamic equation is written to obtain a semi-locked and semi-deployed dynamic model of the satellite during on-orbit deployment; it is determined whether the hinges of the deployable structure are all locked, if not, the numerical integration is continued until the hinges of the deployable structure are all locked or in a stuck fixed state. By this, the present invention realizes the prediction of the dynamic characteristics of the satellite-borne variable topology space deployable structure while being deployed and locked, and provides a decision-making basis for the design of the control system during the deployment of the antenna of such satellites with time-varying parameters and the determination of the whole satellite fault handling strategy during the on-orbit abnormality of the deployable structure, effectively improving 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: Includes steps: S1. Based on the pseudo-Lagrangian equation, the flexible dynamics equation of the whole star is established; S2. According to the material mechanical properties, hinges and geometric model of the deployable structure, a set of flexible multi-body dynamic equations of the deployment process of the deployable structure considering boundary constraints is established based on a recursive method; S3. If the flexible multi-body dynamics equations include constraint equations, converting the flexible multi-body dynamics equations into ordinary differential equations described by generalized coordinates to eliminate the constraint equations; S4, performing one-step numerical integration on the flexible multi-body dynamics equations that do not contain constraint equations or exclude the constraint equations; S5. According to the result of the numerical integration step, determine whether any hinge of the deployable structure has been deployed to the desired position or has 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. According to the six-degree-of-freedom force metadata in the one-step 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 semi-locking and semi-deployment mixed is established; S7, performing modal analysis on the multi-body dynamic structure dynamics model to eliminate rigid body modes, so as to obtain a deployable structural dynamics model described by the modes during deployment; S8, taking the modal vibration shape and frequency parameters of the deployable structure dynamics model as input, writing them into the whole satellite flexible dynamics equation, and obtaining the semi-locked and semi-deployed dynamics model of the satellite during on-orbit deployment; S9, determining whether the hinges of the deployable structure are all locked, if not, returning 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 the entire satellite during the on-orbit deployment of the deployable structure according to claim 1, characterized in that: The whole-star flexible dynamics equation derived based on the pseudo-Lagrangian equation is: Where M1 represents the satellite mass matrix; F tai represents the coupling coefficient matrix of the i-th flexible attachment vibration to the spacecraft translation; F 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 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 respectively; T s represents the external moment array acting on the star; η ai , and denote 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 the entire satellite during the on-orbit deployment of the 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 respectively 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 the entire satellite during the on-orbit deployment of the 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 one-step 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 constraint equations or excluding 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 Respectively represent the system damping and stiffness matrices; 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 modes during deployment of the deployable structure.

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