A method for posture control of a multi-body flexible platform

Abstract

The application discloses a kind of attitude control methods for multi-body flexible satellite platform, comprising: based on micro-element method, the dynamics modeling of multi-body flexible satellite platform is carried out, and the dynamics model is obtained;Multi-body flexible satellite platform includes: central rigid body B and several controlled flexible accessories A i ;Based on the dynamics model, the vibration mode of each controlled flexible accessory A i Is decomposed using modal identity, and the division of control space is completed;On the basis of control space division, system controller design is carried out, and attitude control is carried out based on the designed system controller.The method described in the application carries out control structure division and design to the multi-body flexible satellite platform containing controlled flexible accessory, effectively improves the driving control performance and vibration suppression effect of controlled flexible accessory.

Description

Technical Field

[0001] This invention belongs to the field of satellite attitude control technology, and in particular relates to an attitude control method for multi-body flexible platforms. Background Technology

[0002] Typical examples of satellite platforms with flexible attachments include optical or communication satellites with sun-oriented solar panels, and satellites with large Earth-scanning reflector antennas. These satellites require one-dimensional or multi-dimensional actuation control of the flexible attachments and suppression of flexible vibrations. These control requirements pose significant challenges to traditional attitude control structures and methods, particularly given the high degree of coupling between satellite attitude, attachment pointing, and attachment vibration suppression. The low gain, weak damping, and passive stability characteristics of traditional control technologies cannot meet the real-time and high-precision control requirements of such complex satellite composite control. Therefore, there is an urgent need to seek new control structures and methods to design high-performance composite control systems. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide an attitude control method for multi-body flexible satellite platforms. The method divides and designs the control structure for multi-body flexible satellite platforms containing controlled flexible accessories, effectively improving the driving control performance of the controlled flexible accessories and the vibration suppression effect.

[0004] To address the aforementioned technical problems, this invention discloses an attitude control method for multi-body flexible satellite platforms, comprising:

[0005] Based on the infinitesimal element method, a dynamic model of a multi-body flexible satellite platform is obtained; the multi-body flexible satellite platform includes: a central rigid body B and several controlled flexible attachments A. i ;

[0006] Based on the dynamic model and using modal identities, each controlled flexible attachment A is analyzed. i The vibration modes are decomposed to complete the division of the control space;

[0007] Based on the control space partitioning, the system controller is designed, and attitude control is performed based on the designed system controller.

[0008] In the aforementioned attitude control method for multi-body flexible satellite platforms, the dynamic model includes: controlled flexible accessory A. i The vibration equations, the relative motion equations of the system's center of mass, the rotational dynamics equations of the system, and the controlled flexible attachment A i The rotational dynamics equation.

[0009] In the aforementioned attitude control method for multi-body flexible satellite platforms, the controlled flexible accessory A... iThe vibration equation is expressed as follows:

[0010]

[0011] Where D represents the damping matrix, Λ 2 Let η represent the stiffness matrix and η represent the controlled flexible attachment A. i modal coordinates, Indicates controlled flexible accessory A i The coupling coefficient matrix between the vibration and satellite translation, R i Indicates each controlled flexible accessory A i Fixed coordinate system before deformation The fixed coordinate system F relative to the central rigid body B B The transformation matrix is ​​given by v0, where v0 represents the satellite's non-gravitational velocity, ω represents the satellite's inertial angular velocity around the system's center of mass O, and c represents the system's center of mass O relative to the center of mass O of the central rigid body B. B vector, Indicates controlled flexible accessory A i The coupling coefficient matrix between vibration and satellite rotation, Indicates controlled flexible accessory A i The coupling coefficient matrix of vibration and rotation, ω i Indicates each controlled flexible accessory A i Fixed coordinate system before deformation The fixed coordinate system F relative to the central rigid body B B The relative rotational speed.

[0012] In the attitude control method for the above-mentioned multi-body flexible satellite platform, the relative motion equation of the system's center of mass is expressed as follows:

[0013]

[0014] in, Indicates each controlled flexible accessory A i Center of mass before deformation Relative hinge point O i vector, Indicates controlled flexible accessory A i quality, m S Indicates the total mass of the system. m B The mass m of the central rigid body B is... B F bj This represents the external forces other than gravity acting on the central rigid body B. Indicates controlled flexible accessory A i External forces other than gravity.

[0015] In the attitude control method for the aforementioned multi-body flexible satellite platform, the system rotational dynamics equation is expressed as follows:

[0016]

[0017] Among them, I S J represents the moment of inertia of the satellite relative to the system's center of mass O. i Indicates controlled flexible accessory A i Relative hinge point O i The moment of inertia, H w T represents the angular momentum of the angular momentum exchange mechanism of the central rigid body B. d The torque r represents the environmental forces acting on the satellite. bj This represents the position vector of the point of application of the external force acting on the central rigid body B relative to the coordinate system of the system's center of mass. Indicates controlled flexible accessory A i The torque formed by the external force relative to the center of mass of the system.

[0018] In the aforementioned attitude control method for multi-body flexible satellite platforms, the controlled flexible accessory A... i The rotational dynamics equation is expressed as follows:

[0019]

[0020] in, Indicates controlled flexible accessory A i Relative hinge point O before deformation i The inertia matrix, c i Indicates controlled flexible accessory A i The position of the centroid relative to the body coordinate system of the attachment, o i Indicates hinge point O i The coordinates relative to the system's centroid O This indicates that the central rigid body B applies force to the controlled flexible attachment A. i The hinge torque, Indicates controlled flexible accessory A i The torque generated by external forces other than gravity.

[0021] In the aforementioned attitude control method for multi-body flexible satellite platforms, based on a dynamic model and using modal identities, the attitude control of each controlled flexible accessory A is... i The vibration modes are decomposed, including:

[0022] Determine the controlled flexible accessory A i Modal identity:

[0023]

[0024] Where E3 represents a 3x3 identity matrix;

[0025] remember: The positive definite square root is Let the spatial projection matrix be T, and let S be the orthogonal complement of the spatial projection matrix T. Then we have:

[0026]

[0027] satisfy:

[0028]

[0029] as well as:

[0030]

[0031] Where U represents the orthogonal decomposition matrix of Φ, Φ represents the mode shape matrix of the controlled flexible attachment, and E represents n q *n q The identity matrix, n q Indicates controlled flexible accessory A i The number of finite elements in the partition, M i Indicates controlled flexible accessory A i n q A diagonal array composed of element mass matrices;

[0032] 3×n q The modal coordinates η are projected onto three-dimensional space and 3×(n) respectively. q -1) An orthogonal complementary space, denoted as:

[0033] ζ = Tη, ζ = Sη

[0034] Where ζ represents the rotational modal coordinates and ζ represents the orthogonal complementary modal coordinates;

[0035] Decompose η into:

[0036] η = T T ζ+S T ζ

[0037] Multiply the controlled flexible attachment A by T and S respectively. i From the vibration equation, we get:

[0038]

[0039] Based on controlled flexible attachment A i The modal identities are rearranged to obtain the separated controlled flexible attachment A. i Modal equations:

[0040]

[0041] Where D represents the damping matrix of the controlled flexible attachment's flexible modes.

[0042] In the aforementioned attitude control method for multi-body flexible satellite platforms, the system controller design includes: controlled flexible accessory A. i The design of the PD control law and the PID control law of the central rigid body B.

[0043] In the aforementioned attitude control method for multi-body flexible satellite platforms, the controlled flexible accessory A... i PD control law It is expressed as follows:

[0044]

[0045] Where, k d Let k represent the differential control coefficient matrix of the PD control law. p δω represents the proportional control coefficient matrix of the PD control law. i Indicates controlled flexible accessory A i Angular velocity control error, Q iv Indicates controlled flexible accessory A i The vector part of the error quaternion.

[0046] In the attitude control method for the aforementioned multi-body flexible satellite platform, the PID control law T of the central rigid body B... PID It is expressed as follows:

[0047] T PID =-I S (2K P Q v +K D δω+2K I ∫Q v dt)

[0048] Among them, K P K represents the proportional coefficient matrix of the PID controller. D K represents the differential coefficient matrix of the PID controller. I Q represents the integral coefficient matrix of the PID controller. v Let δω represent the vector part of the error quaternion of the central rigid body B, t represent the angular velocity control error, and t represent the system time.

[0049] The present invention has the following advantages:

[0050] (1) This invention discloses an attitude control method for a multi-body flexible satellite platform. The method divides and designs the control structure for a multi-body flexible satellite platform containing controlled flexible accessories, which effectively improves the driving control performance of the controlled flexible accessories and the vibration suppression effect.

[0051] (2) This invention discloses an attitude control method for multi-body flexible satellite platforms, which can realize integrated active control of controlled flexible attachment driving and flexible vibration suppression, and the control effect is better than simply using attachment smooth driving and relying on the flexible vibration itself for passive stabilization.

[0052] (3) This invention discloses an attitude control method for multi-body flexible satellite platforms, which can achieve rapid stabilization by increasing the flexible compensation amount of specific non-zero space. Compared with the traditional active vibration suppression method, this invention has better targeting and more ideal flexible vibration control effect. Attached Figure Description

[0053] Figure 1 This is a flowchart of an attitude control method for a multi-body flexible satellite platform according to an embodiment of the present invention;

[0054] Figure 2 This is a schematic diagram of dynamic modeling in an embodiment of the present invention;

[0055] Figure 3 This is a control principle diagram of a conventional control method in an embodiment of the present invention;

[0056] Figure 4 This is a control principle diagram of an attitude control method for a multi-body flexible satellite platform according to an embodiment of the present invention;

[0057] Figure 5 This is a schematic diagram illustrating the convergence of the solar panel angular velocity under different algorithms in an embodiment of the present invention;

[0058] Figure 6 This is a schematic diagram illustrating the convergence of the first-order torsional mode coordinates of a solar panel under different algorithms in an embodiment of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0060] Reference Figure 1 In this embodiment, the attitude control method for a multi-body flexible satellite platform includes:

[0061] Step 1: Based on the infinitesimal element method, perform dynamic modeling on the multibody flexible satellite platform to obtain the dynamic model.

[0062] In this embodiment, the multi-body flexible satellite platform includes: a central rigid body B and several controlled flexible attachments A. i Based on the infinitesimal element method, a model containing a central rigid body B and several controlled flexible attachments A is applied. iThe dynamic model obtained by dynamic modeling a multi-body flexible satellite platform includes: controlled flexible accessory A. i The vibration equations, the relative motion equations of the system's center of mass, the rotational dynamics equations of the system, and the controlled flexible attachment A i The rotational dynamics equations. For example... Figure 2 As shown:

[0063] Controlled Flexible Accessory A i The vibration equation is expressed as follows:

[0064]

[0065] Where D represents the damping matrix, Λ 2 Let η represent the stiffness matrix and η represent the controlled flexible attachment A. i modal coordinates, Indicates controlled flexible accessory A i The coupling coefficient matrix between the vibration and satellite translation, R i Indicates each controlled flexible accessory A i Fixed coordinate system before deformation The fixed coordinate system F relative to the central rigid body B B The transformation matrix is ​​given by v0, where v0 represents the satellite's non-gravitational velocity, ω represents the satellite's inertial angular velocity around the system's center of mass O, and c represents the system's center of mass O relative to the center of mass O of the central rigid body B. B vector, Indicates controlled flexible accessory A i The coupling coefficient matrix between vibration and satellite rotation, Indicates controlled flexible accessory A i The coupling coefficient matrix of vibration and rotation, ω i Indicates each controlled flexible accessory A i Fixed coordinate system before deformation The fixed coordinate system F relative to the central rigid body B B The relative rotational speed.

[0066] The equations of motion of the system's center of mass relative to each other are expressed as follows:

[0067]

[0068] in, Indicates each controlled flexible accessory A i Center of mass before deformation Relative hinge point O i vector, Indicates controlled flexible accessory A i quality, m S Indicates the total mass of the system. m B The mass m of the central rigid body B is... BF bj This represents the external forces other than gravity acting on the central rigid body B. Indicates controlled flexible accessory A i External forces other than gravity.

[0069] The system's rotational dynamics equations are expressed as follows:

[0070]

[0071] Among them, I S J represents the moment of inertia of the multi-body flexible satellite platform relative to the system's center of mass O. i Indicates controlled flexible accessory A i Relative hinge point O i The moment of inertia, H w T represents the angular momentum of the angular momentum exchange mechanism of the central rigid body B. d The torque r represents the environmental forces acting on the satellite. bj This represents the position vector of the point of application of the external force (excluding gravity) acting on the central rigid body B relative to the coordinate system of the system's center of mass. Indicates controlled flexible accessory A i The torque formed by the external force (excluding gravity) relative to the center of mass of the system.

[0072] Controlled Flexible Accessory A i The rotational dynamics equation is expressed as follows:

[0073]

[0074] in, Indicates controlled flexible accessory A i Relative hinge point O before deformation i The inertia matrix, c i Indicates controlled flexible accessory A i The position of the centroid relative to the body coordinate system of the attachment, o i Indicates hinge point O i The coordinates relative to the system's centroid O This indicates that the central rigid body B applies force to the controlled flexible attachment A. i The hinge torque, Indicates controlled flexible accessory A i The torque generated by external forces other than gravity.

[0075] Step 2: Based on the dynamic model, using the modal identities, perform analysis on each controlled flexible attachment A. i The vibration modes are decomposed to complete the division of the control space.

[0076] In this embodiment, for each controlled flexible accessory A iThe vibration modes are decomposed as follows: the vibration modes of controlled flexible attachment rotation and those coupled with rotation are classified as generalized rotation, and the vibration modes not coupled with rotation are classified as orthogonal complementary modes of the former.

[0077] Controlled Flexible Accessory A i The following modal identity exists:

[0078]

[0079] Here, E3 represents a 3x3 identity matrix.

[0080] remember: The positive definite square root is Let the spatial projection matrix be T, and let S be the orthogonal complement of the spatial projection matrix T. Then we have:

[0081]

[0082] satisfy:

[0083]

[0084] as well as:

[0085]

[0086] Where U represents the orthogonal decomposition matrix of Φ, Φ represents the mode shape matrix of the controlled flexible attachment, and E represents n q *n q The identity matrix, n q Indicates controlled flexible accessory A i The number of finite elements in the partition, M i Indicates controlled flexible accessory A i n q A diagonal array composed of element mass matrices;

[0087] 3×n q The modal coordinates η are projected onto three-dimensional space and 3×(n) respectively. q -1) An orthogonal complementary space, denoted as:

[0088] ζ = Tη, ζ = Sη

[0089] Where ζ represents the rotational modal coordinates and ζ represents the orthogonal complementary modal coordinates;

[0090] Decompose η into:

[0091] η = T T ζ+S T ζ

[0092] Multiply the controlled flexible attachment A by T and S respectively. i From the vibration equation, we get:

[0093]

[0094] Based on controlled flexible attachment A i The modal identities are rearranged to obtain the separated controlled flexible attachment A. i Modal equations:

[0095]

[0096] Where D represents the damping matrix of the controlled flexible attachment's flexible modes.

[0097] It can be seen that: (1) Only ζ is related to the controlled flexible attachment A i The rotation is coupled, while ζ is coupled with the controlled flexible attachment A. i (1) The rotations are uncoupled; (2) There is a certain coupling between the motions of ζ and ζ (for example, the differential equation of ζ contains TΛ). 2 S T The ζ term, the differential equation of ζ contains SΛ 2 T T The ζ term, but since T and S are orthogonal, the eigenvalues ​​of the coupling matrix are generally very small; conversely, TΛ 2 T T ,SΛ 2 S T The characteristic parameters are much larger. Therefore, the two modal spaces mentioned above are essentially decoupled. The orthogonal complementary mode is decoupled from the rotational equations, and only has weak coupling with the rotational mode. After the above processing, redundant degrees of freedom of motion can be removed, laying the foundation for designing an efficient controller.

[0098] Step 3: Based on the control space partitioning, design the system controller and perform attitude control based on the designed system controller.

[0099] In this embodiment, the system controller design mainly includes: controlled flexible accessory A i The design of the PD control law and the PID control law of the central rigid body B.

[0100] (31) Controlled flexible accessory A i PD control law design

[0101] For a typical three-degree-of-freedom rotation, the controlled flexible attachment A is known. i Rotation control requires tracking or maintaining the target attitude quaternion and the target angular velocity, respectively, Q. i,c and ω i,c Without loss of generality, consider the case where the target attitude changes uniformly or remains fixed, i.e., ω i,c It is a constant vector, and the controlled flexible attachment A i The actual attitude quaternion Qi and ω i Satisfying the attitude motion equations, the purpose of rotation control is to make: Q i →Q i,c ω i →ω i,c It meets certain dynamic requirements; at the same time, the vibration decay is zero, that is, η→0.

[0102] Based on the aforementioned control space division, the controlled flexible accessory A i It contains two governing equations, namely:

[0103] Controlled Flexible Accessory A i The rotational control equations are as follows:

[0104] Convert ζ to an angle-based variable, let Then the controlled flexible accessory A i The rotational control equation is expressed as:

[0105]

[0106] In the formula:

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] Where, θ ζ T represents the angular displacement corresponding to ζ. E1 T represents the torque term related to the angular velocity of the celestial body and its appendages. E2 T represents the torque term related to angular acceleration and acceleration. E3 C represents the torque term related to modal vibration. D Let G represent the transformed damping matrix. D H represents the transformed stiffness matrix. i Indicates controlled flexible accessory A i angular momentum, Indicates and The relevant second-order torque is small.

[0113] Controlled Flexible Accessory A i Orthogonal complementary modal equations:

[0114]

[0115] For controlled flexible accessory A i The rotational comprehensive control equation is simplified as follows: common term T E1 Measurable and calculable, in The feedforward term is canceled out in the design, and it is ignored as it does not affect the result; the translational effects and the change of the center of mass are ignored, and it is assumed that the system's angular velocity control is stable, then T E2 Ignore; Simplified Controlled Flexible Accessory A i The comprehensive control equation for rotation is:

[0116]

[0117] Controlled flexible accessory A i The control error is:

[0118]

[0119] Where, δQ i Indicates controlled flexible accessory A i The error quaternion, the vector part is denoted as Q. iv The scalar part is denoted as q. i0 Before use, δQ i Normalization process makes q i0 Non-negative; δω i Indicates controlled flexible accessory A i Angular velocity control error.

[0120] like Figure 3 As shown, in traditional designs, the generalized rotational state is considered. As a feedback quantity, the designed PD control law as follows:

[0121]

[0122]

[0123] Where, k d Let k represent the differential control coefficient matrix of the PD control law. p ω represents the proportional control coefficient matrix of the PD control law. ic This represents the bandwidth of the PD controller, typically taken as 0.1 to 0.2; ξ ic This indicates the damping ratio of the PD controller, which is typically around 0.7.

[0124] In the above PD control law Under the influence of the system, the Lyapunov function V1 is:

[0125]

[0126] The convergence rate of V1 is:

[0127]

[0128] Clearly, the system energy is approximately exponentially expressed as exp(-ξ). ic ω ic t) converges.

[0129] like Figure 4 As shown, the present invention uses the narrow rotational state {δω} i 2Q iv As a feedback quantity, the designed PD control law as follows:

[0130]

[0131] In the above PD control law Under the influence of the system, the Lyapunov function V2 is:

[0132]

[0133] The convergence rate of V2 is:

[0134]

[0135] The comparison shows that the convergence rates of V1 and V2 depend on θ. ζ The convergence rate, according to the modal identity:

[0136]

[0137] Where, ω in Indicates controlled flexible accessory A i First-order modal characteristic frequency (with ω) ic (basically equivalent or smaller), ξ i Indicates controlled flexible accessory A i The first-order modal damping ratio, and The above formula shows that, Under control, the system's energy convergence rate depends on the damping of the first-order flexible mode of the controlled flexible attachment, therefore:

[0138]

[0139] As can be seen from the above comparison, the PD controller with generalized rotational mode design has better dynamic performance, and its convergence speed is significantly better than that of the controller with narrow rotational mode design.

[0140] (32) Design of PID control law for central rigid body B

[0141] The central rigid body B needs to maintain its orientation relative to the ground or the inertial frame. The target attitude quaternion and target angular velocity of the central rigid body B are Q, respectively.c and ω c If the satellite's real-time attitude and angular velocity are Q(t) and ω(t) respectively, then the control objective is: Q(t) → Q c , ω(t)→ω c .

[0142] Let the control error of the central rigid body B be:

[0143]

[0144] Where δQ represents the error quaternion of the central rigid body B, and the vector part is denoted as Q. v The scalar part is denoted as q0; before use, δQ is normalized to make q0 non-negative; δω represents the angular velocity control error; Q represents the real-time attitude quaternion.

[0145] The PID control law T of rigid body B in the design center PID as follows:

[0146] T PID =-I S (2K P Q v +K D δω+2K I ∫Q v dt)

[0147] Among them, Q v Let K be the vector part of the error quaternion of the central rigid body B, where δω represents the angular velocity control error and t represents the system time; P K represents the proportional coefficient matrix of the PID controller. D K represents the differential coefficient matrix of the PID controller. I This represents the integral coefficient matrix of the PID controller.

[0148] K P K D K I It is a positive definite PID gain matrix. A diagonal matrix can be used to achieve three-axis decoupling. Its size is determined by dynamic performance requirements, stability, and stability margin. For example, consider the following:

[0149]

[0150] Where, ω c ξ represents the bandwidth of the PID controller closed-loop feedback system, typically taken as 0.01Hz to 0.1Hz; c γ represents the damping ratio of the PID controller, which is generally taken as around 0.7; γ represents the integral coefficient, which is generally taken as γ < 0.2 to ensure stability margin.

[0151] In summary, this invention discloses an attitude control method for multi-body flexible satellite platforms. It performs dynamic modeling of the multi-body flexible satellite platform and, based on modal identities, proposes a control structure that is essentially decoupled between attitude system control and appendage pointing / vibration suppression. The method partitions the control space of the coupled dynamics of "satellite attitude-appendage pointing-appendage vibration." Then, based on the control space partitioning results, controllers are designed for the two types of control spaces respectively, ultimately realizing the controller design for "satellite attitude-appendage pointing-appendage vibration," achieving more efficient appendage pointing control, appendage flexibility suppression, and other multiple control effects.

[0152] Based on the above embodiments, a specific example will be used for illustration below.

[0153] Assume a multi-body flexible satellite platform is equipped with a single-wing flexible solar panel along the pitch axis (Y-axis) and needs to drive the solar panel with an orbital angular velocity (0.06° / s) to achieve solar orientation.

[0154] The modal frequencies of the solar panel are {0.20, 0.70, 1.21, 2.02, 3.11} Hz, and the mode shapes are first-order external bending, first-order internal bending, second-order external bending, first-order torsion, and third-order external bending, respectively. Obviously, the first-order torsion mode is consistent with the driving direction of the flexible solar panel and constitutes a generalized rotation with the rotation of the solar panel.

[0155] Satellite body rotational inertia J b for:

[0156] J b = [1028.8716 -10.9150 -23.6426;]

[0157] -10.9150 1026.2444 -17.8563;

[0158] -23.6426 -17.8563 1117.2465]kgm 2

[0159] Position of the solar panel's center of mass relative to the hinge point in the solar panel's coordinate system for:

[0160]

[0161] Solar panel quality It weighs 85.74 kg;

[0162] Then, the moment of inertia of the solar panel relative to its hinge point for:

[0163] 9.3024 28.7784 2.2498;

[0165] 0.0576 2.2498 1076.3055]kgm 2

[0166] The coordinates of the solar panel hinge point relative to the system's center of mass O. i for:

[0167] o i =[-0.02764 0.78871 -0.00844]'m

[0168] The moment of inertia J of the solar panel relative to the hinge point i for:

[0169]

[0170] Then, the moment of inertia of the satellite relative to the system's center of mass is I. S for:

[0171] I S =J b +J i

[0172] The coupling coefficient matrix between solar panel vibration and satellite translation for:

[0173]

[0174] The coupling coefficient matrix of vibration and rotation of solar panels for:

[0175]

[0176] Construct matrix T and its orthogonal complement S to complete the partitioning of the control space, and then obtain...

[0177] The overall attitude control objective is three-axis stabilization, with the solar panels rotating at an orbital angular velocity of 0.06° / s. Using the control method described in this invention, the simulation results are as follows: Figure 5 and Figure 6 As shown, where Figure 5 This indicates that under the control method described in this invention, the solar panel angular velocity has a faster convergence speed. Figure 6 This indicates that under the control of the control method described in this invention, the first-order torsional mode related to the rotation of the solar panel converges rapidly, demonstrating better control performance compared to traditional methods.

[0178] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0179] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. An attitude control method for a multi-body flexible satellite platform, characterized in that, include: Based on the infinitesimal element method, a dynamic model of a multi-body flexible satellite platform is obtained; the multi-body flexible satellite platform includes: a central rigid body. and several controlled flexible accessories ; Based on the dynamic model, modal identities are used to analyze each controlled flexible accessory. The vibration modes are decomposed to complete the division of the control space; among them, the dynamic model includes: controlled flexible attachments. The vibration equations, the relative motion equations of the system's center of mass, the rotational dynamics equations of the system, and the controlled flexible attachments The rotational dynamics equations; Based on the control space partitioning, the system controller is designed, and attitude control is performed based on the designed system controller; Controlled flexible attachments The vibration equation is expressed as follows: in, Represents the damping matrix. Represents the stiffness matrix. Indicates controlled flexible attachment modal coordinates, Indicates controlled flexible attachment The coupling coefficient matrix between the vibration and the satellite translation. Indicates each controlled flexible accessory Fixed coordinate system before deformation Relative central rigid body Fixed coordinate system The transformation matrix, Indicates the satellite's non-gravitational velocity. Indicates the satellite's orbit around the system's center of mass. The inertial angular velocity of rotation, Represents the system's centroid Relative central rigid body center of mass vector, Indicates controlled flexible attachment The coupling coefficient matrix between vibration and satellite rotation, Indicates controlled flexible attachment The coupling coefficient matrix of vibration and rotation, Indicates each controlled flexible accessory Fixed coordinate system before deformation Relative central rigid body Fixed coordinate system The relative rotational speed; The equations of motion of the system's center of mass relative to each other are expressed as follows: in, Indicates each controlled flexible accessory Center of mass before deformation Relative hinge point vector, Indicates controlled flexible attachment quality Indicates the total mass of the system. , Represents the central rigid body quality , Represents the central rigid body External forces other than gravity Indicates controlled flexible attachment External forces other than gravity; The rotational dynamics equations of the system are expressed as follows: in, Indicates the satellite's position relative to the system's center of mass. Moment of inertia, Indicates controlled flexible attachment Relative hinge point Moment of inertia, Represents the central rigid body Angular momentum of an angular momentum exchange mechanism This indicates the environmental torque acting on the satellite. Indicates the action on the central rigid body The position vector of the point of application of the external force relative to the coordinate system of the system's center of mass. Indicates controlled flexible attachment The torque formed by the external force relative to the system's center of mass; Controlled flexible attachments The rotational dynamics equation is expressed as follows: in, Indicates controlled flexible attachment Relative hinge point before deformation The inertia matrix, Indicates controlled flexible attachment The position of the centroid relative to the coordinate system of the attached body. Represents the hinge point relative system centroid coordinates Represents the central rigid body Apply to controlled flexible attachments The hinge torque, Indicates controlled flexible attachment The torque generated by external forces other than gravity; Based on the dynamic model, modal identities are used to analyze each controlled flexible accessory. The vibration modes are decomposed, including: Determine the controlled flexible attachment Modal identity: in, Represents a 3x3 identity matrix; remember: The positive definite square root is The spatial projection matrix is Spatial projection matrix The orthogonal complement matrix is Then we have: satisfy: as well as: ， in, express The orthogonal decomposition matrix, This represents the mode shape matrix of the controlled flexible attachment. express The identity matrix, Indicates controlled flexible attachment The number of finite elements in the division. Indicates controlled flexible attachment of A diagonal array composed of element mass matrices; Will 3D modal coordinates Projected into three-dimensional space respectively and Orthogonal space complement, denoted as: ， in, Represents rotational modal coordinates. Represents the coordinates of the orthogonal complementary modes; Will Decomposed into: Use respectively , Left-hand controlled flexible attachment From the vibration equation, we get: Based on controlled flexible attachments The modal identities are rearranged to obtain the separated controlled flexible attachments. Modal equations: in, The damping array represents the flexible modes of the controlled flexible attachment.

2. The attitude control method for a multi-body flexible satellite platform according to claim 1, characterized in that, System controller design, including: controlled flexible accessories PD control law design and central rigid body PID control law design.

3. The attitude control method for a multi-body flexible satellite platform according to claim 2, characterized in that, Controlled flexible attachments PD control law It is expressed as follows: in, Let represent the differential control coefficient matrix of the PD control law. This represents the proportional control coefficient matrix of the PD control law. Indicates controlled flexible attachment Angular velocity control error, Indicates controlled flexible attachment The vector part of the error quaternion.

4. The attitude control method for a multi-body flexible satellite platform according to claim 3, characterized in that, Central rigid body PID control law It is expressed as follows: in, This represents the proportional coefficient matrix of the PID controller. This represents the differential coefficient matrix of the PID controller. This represents the integral coefficient matrix of the PID controller. Represents the central rigid body The vector part of the error quaternion is denoted as , Indicates angular velocity control error. Indicates the system time.

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