A Composite Attitude Control Method for Spacecraft with Nonlinear Sloshing and Large Flexible Appendages

Abstract

A method for composite attitude control of a spacecraft with nonlinear sloshing and large flexible appendages disclosed by the present invention belongs to the technical field of spacecraft control. The implementation method of the present invention is as follows: various non-conservative disturbance torques acting on the spacecraft during on-orbit operation are characterized by Te; the attitude motion of the spacecraft body at any angle is described by Euler quaternions; the elastic vibration of 1 to m flexible appendages is described by the assumed mode discretization method; the motion description of the equivalent spherical pendulum model of liquid sloshing is improved by using the split variable technique; a large-range motion dynamics model of a liquid-filled spacecraft with large flexible appendages is established; the spacecraft attitude dynamics model is linearized; an output feedback attitude control law for a liquid-filled flexible spacecraft designed according to the Lyaponuv stability theorem; an input shaping-output feedback composite attitude controller for a liquid-filled flexible spacecraft designed based on the output feedback attitude control law of the liquid-filled flexible spacecraft and the Euler quaternion input command, thereby realizing active vibration suppression and improving the accuracy of spacecraft composite attitude control.

Description

Technical Field

[0001] The present invention relates to a method for composite attitude control of a spacecraft with nonlinear sloshing and large flexible appendages, belonging to the technical field of spacecraft control. Background Technique

[0002] The dynamic and control problems of spacecrafts with large flexible appendages and liquid-filled tanks have always been the hotspots and difficulties in the field of aerospace research. With the continuous improvement of space mission requirements, higher requirements are put forward for the overall configuration optimization design and control ability of spacecrafts. Aerospace engineering practices at home and abroad are paying more and more attention to the dynamic and control problems of spacecrafts caused by liquid sloshing in the tanks.

[0003] In current aerospace engineering practices, in order to weaken the interference of liquid sloshing in the propellant tank on the dynamics and control system of the spacecraft, anti-sloshing designs are adopted for the propellant tank to passively suppress the liquid sloshing in the tank. For example, new types of tanks such as bladder-type, diaphragm-type and metal bellows-type are selected to store propellants, and the compatibility between these tanks and the propellants is poor; another example is to install anti-sloshing devices such as mechanical baffles and split partitions inside the tank. The passive anti-sloshing design of the tank usually increases the ineffective working medium and sacrifices the propellant filling amount to a certain extent. In addition, for large tanks, the suppression effect of passive anti-sloshing measures on liquid sloshing is inferior to that of small tanks. On the other hand, aerospace engineering practices in China still stay at using two traditional linear models, namely spring-mass-damper or single pendulum, to deal with the liquid sloshing problem in the spacecraft tank, lacking systematic research, verification and application of the equivalent mechanical models such as large-amplitude liquid sloshing. Under the applicable conditions of the liquid sloshing linear model, the control of liquid-filled flexible spacecrafts mostly adopts relatively conservative continuous small-range and slow maneuvering methods, which are beneficial to avoiding prominent problems caused by violent sloshing of the liquid in the tank, but cannot fundamentally solve the spacecraft control problems brought by liquid sloshing.

[0004] Therefore, in order to meet the urgent needs of the rapid development of aerospace engineering, it is urgent to carry out research on the rigid-liquid-flexible-control coupling dynamics and control methods of spacecrafts with both liquid nonlinear sloshing and large flexible appendage vibration. Summary of the Invention

[0005] The main object of the present invention is to provide a method for composite attitude control of a spacecraft with nonlinear sloshing and large flexible appendages, which can realize large-range attitude smooth maneuvering in orbit and active suppression control of flexible appendage vibration for a liquid-filled spacecraft with large flexible appendages, and improve the accuracy of composite attitude control of the spacecraft.

[0006] The object of the present invention is achieved by the following technical solutions:

[0007] A method for composite attitude control of a spacecraft with nonlinear sloshing and large flexible appendages disclosed by the present invention includes the following steps:

[0008] Step 1: Establish the dynamic model of a liquid-filled spacecraft with large flexible appendages for large-scale motion by applying Lagrange's equations in mixed coordinates. During the modeling of the liquid-filled spacecraft with large flexible appendages, let T e represent various non-conservative disturbance torques acting on the spacecraft, and the gravity gradient torque T g be the only non-conservative disturbance torque; use Euler quaternions to describe the arbitrary angular attitude motion of the spacecraft body; use the assumed mode discretization method to describe the elastic vibrations of 1 to m flexible appendages, achieving an efficient and concise representation of the elastic vibrations of the flexible appendages; use the split variable technique to improve the motion description of the equivalent spherical pendulum model of liquid sloshing, achieving a clear representation of the overall rigid body motion and non-linear sloshing of the liquid propellant relative to the 1 to n storage tanks, where the non-linear sloshing includes finite-amplitude lateral sloshing and rotational sloshing.

[0009] Step 1.1: Define the motions of various parts of the spacecraft system, including the position and velocity of the centroid of the spacecraft's main rigid platform relative to the inertial reference frame, the angular velocity of the main rigid platform relative to the inertial reference frame, the angular velocity of the attitude control three-axis reaction wheels relative to the inertial reference frame, the position and velocity of any mass element on the flexible appendage relative to the inertial reference frame, and the position and velocity of the lumped mass of the equivalent spherical pendulum model of liquid sloshing relative to the inertial reference frame.

[0010] Step 1.2: Derive the total kinetic energy and total potential energy of the spacecraft system.

[0011] The total kinetic energy of the spacecraft system is expressed as the following matrix calculation formula

[0012]

[0013] The total potential energy of the spacecraft system includes the strain energy V sp stored during the vibration of the flexible appendages and the gravitational potential energy V p of the equivalent spherical pendulum during liquid sloshing, which are two parts.

[0014] Step 1.3: The Lagrangian function of the spacecraft system's motion is the difference between the total kinetic energy and the total potential energy of the system. The Lagrangian function L representing the total energy of the spacecraft system is

[0015] L = T - (V sp + V p ) (2)

[0016] The Lagrange's equation in terms of the spacecraft's angular velocity is

[0017]

[0018] The Lagrange's equations describing the vibration of the sailboard and the motion of the spherical pendulum in generalized coordinates are respectively

[0019]

[0020]

[0021] Substituting (1) into (2) gives the specific expression of the Lagrangian function of the spacecraft system. Then, substituting (2) into the Lagrangian equations describing the motion of each part of the spacecraft system in (3), (4), and (5) respectively, the attitude dynamics model of the spacecraft with a single partially liquid-filled spherical tank and two symmetrically installed flexible solar panels is derived as shown in Equation (6).

[0022]

[0023] In the formula: I mb represents the inertia matrix of the spacecraft body with respect to the spacecraft's own coordinate system. The spacecraft body includes three parts: the spacecraft main rigid body, two solar panels, and an equivalent spherical pendulum; ω is the coordinate matrix of the spacecraft angular velocity vector expressed in the spacecraft's own coordinate system, is the time derivative of ω; P is the coupling coefficient matrix between the vibration of the first solar panel and the spacecraft attitude motion; q is the generalized coordinate matrix composed of the first three vibration mode coordinates of the vibration of the first solar panel; Q is the coupling coefficient matrix between the spherical pendulum motion and the spacecraft attitude motion; ρ is the generalized coordinate matrix composed of the Euler angles describing the motion of the equivalent spherical pendulum model relative to the tank; I w is the inertia matrix of the three-axis reaction wheel with respect to the spacecraft's own coordinate system; Ω is the coordinate matrix of the relative angular velocity vector of the three-axis reaction wheel expressed in the own coordinate system; represents the skew-symmetric dual matrix of ω; T g is the gravity gradient torque acting on the spacecraft; M sp is the modal mass matrix of the vibration of one solar panel; K sp is the modal stiffness matrix of the vibration of one solar panel; M p is the generalized mass matrix of the spherical pendulum motion; C p is the equivalent damping coefficient matrix of the spherical pendulum motion; K p is the generalized stiffness matrix of the equivalent spherical pendulum motion; is the rigid body coordinate of the equivalent liquid rigid body motion of the spherical pendulum model; T w is the coordinate matrix of the control reaction torque output by the attitude control three-axis reaction wheel expressed in the spacecraft's own coordinate system.

[0024] Step 2: Linearize the spacecraft attitude dynamics model obtained in Step 1 to obtain an apparently uncoupled attitude dynamics model; introduce error variables into the Lyaponuv function in the appropriate state space of the liquid-filled flexible spacecraft system to perform state estimation on relevant state variables; apply the Lyaponuv stability theory to design an output feedback attitude control law for the liquid-filled flexible spacecraft to ensure the asymptotic stability of the spacecraft attitude motion and the vibration of the solar panels.

[0025] Step 2.1: For the fully coupled form of the liquid-filled flexible spacecraft attitude dynamics model (6) established in Step 1; then, since the vibration of the flexible solar panel and the liquid sloshing are both small-amplitude motions, neglect the small quantities above the second order and directly linearize the spacecraft attitude dynamics model, and use the following variable substitution

[0026]

[0027] to obtain an apparently uncoupled form of the attitude dynamics model that is convenient for subsequent design of the output feedback attitude control law

[0028]

[0029] Step 2.2: Since the actual spacecraft is an under-observed system, introduce error variables as shown in formula (4) into the Lyaponuv function in the spacecraft system state space to perform state estimation on the state variables related to the vibration of the solar panel and the liquid sloshing

[0030]

[0031] Step 2.3: Select the following Lyaponuv function in the state space of the liquid-filled flexible spacecraft system

[0032]

[0033] where: B1 and B3 are undetermined symmetric positive definite matrices; B2 and B4 are undetermined symmetric positive semi-definite matrices.

[0034] And according to the Lyaponuv stability theorem, design a dynamic estimator for the vibration of the solar panel, a dynamic estimator for the liquid sloshing, and a control torque when the time derivative of the Lyaponuv function satisfies global semi-negativity, and design an output feedback attitude control law for the liquid-filled flexible spacecraft according to the dynamic estimator for the vibration of the solar panel, the dynamic estimator for the liquid sloshing, and the control torque, to obtain the output feedback attitude control law for the liquid-filled flexible spacecraft as shown in formula (6):

[0035]

[0036] where: E n is the n-order identity matrix; 0 m×nis an m×n dimensional zero matrix; k p and k d are control gain coefficients; The specific expressions of F1 and F2 are

[0037]

[0038]

[0039] In Equation (6), the first fraction is the dynamic estimation of the sailboard vibration; the second fraction is the dynamic estimation of the liquid sloshing; the third fraction is the control reaction torque output by the attitude control reaction wheel, and the third fraction is calculated using the output signals measured by the spacecraft attitude and angular velocity sensors as feedback information.

[0040] Step 3: According to the main vibration mode of the sailboard, design the corresponding ZVD shaper pulse sequence, and convolve the ZVD shaper pulse sequence with the target attitude quaternion in sequence to obtain the integerized Euler quaternion input command.

[0041]

[0042] Convolve it with the target attitude quaternion to obtain the integerized Euler quaternion input command.

[0043] Step 4: Combine the liquid-filled flexible spacecraft output feedback attitude control law obtained in Step 2 and the Euler quaternion input command obtained in Step 3 to design a liquid-filled flexible spacecraft input shaping-output feedback composite attitude controller. Through the liquid-filled flexible spacecraft input shaping-output feedback composite attitude controller, ensure the asymptotic stability of the spacecraft attitude motion and the sailboard vibration, and further realize the large-range attitude smooth maneuvering of the liquid-filled spacecraft with large flexible appendages in orbit and the active suppression control of the flexible appendage vibration.

[0044] Beneficial effects:

[0045] 1. A spacecraft attitude composite control method with nonlinear sloshing and large flexible appendages disclosed by the present invention, through T eCharacterize the various non-conservative interference torques acting on the spacecraft during on-orbit operation; use Euler quaternions to describe the arbitrary angular attitude motion of the spacecraft body; use the assumed mode discretization method to describe the elastic vibrations of 1 to m flexible appendages, achieving an efficient and concise representation of the elastic vibrations of the flexible appendages; use the split variable technique to improve the motion description of the liquid sloshing equivalent spherical pendulum model, realizing a clear representation of the overall rigid body motion and non-linear sloshing of the liquid propellant relative to the 1 to nth storage tanks; on this basis, establish a large-scale motion dynamics model of a liquid-filled spacecraft with large flexible appendages; linearize the spacecraft attitude dynamics model to obtain an apparently uncoupled attitude dynamics model; design an output feedback attitude control law for the liquid-filled flexible spacecraft based on the attitude dynamics model, actively suppressing the oscillatory disturbances brought by the solar panel vibrations and liquid sloshing to the spacecraft attitude motion, and realizing the large-scale attitude stable maneuver of the liquid-filled spacecraft with large flexible appendages in orbit.

[0046] 2. For a spacecraft attitude composite control method with non-linear sloshing and large flexible appendages disclosed in the present invention, during the process of designing the output feedback attitude control law for the liquid-filled flexible spacecraft based on the attitude dynamics model, according to the Lyapunov stability theorem, design a solar panel vibration dynamics estimator, a liquid sloshing dynamics estimator and a control torque when the time derivative of the Lyapunov function satisfies global semi-negativity, and design an output feedback attitude control law for the liquid-filled flexible spacecraft based on the solar panel vibration dynamics estimator, the liquid sloshing dynamics estimator and the control torque, further ensuring the asymptotic stability of the spacecraft attitude motion and the solar panel vibrations, and significantly weakening the residual vibrations.

[0047] 2. For a spacecraft attitude composite control method with non-linear sloshing and large flexible appendages disclosed in the present invention, design a corresponding ZVD shaper pulse sequence based on the main vibration mode, perform a convolution operation on the ZVD shaper pulse sequence with the target attitude quaternion in sequence to obtain an integerized Euler quaternion input command, and combine the Euler quaternion input command with the output feedback attitude control law of the liquid-filled flexible spacecraft to obtain an input shaping-output feedback composite attitude controller for the liquid-filled flexible spacecraft. Solve the control-structure coupling problem through the input shaping-output feedback composite attitude controller, effectively suppressing the solar panel vibrations and significantly weakening the residual vibrations. Description of the Drawings

[0048] Figure 1 is a schematic diagram of a liquid-filled flexible spacecraft on which the spacecraft attitude composite controller with non-linear sloshing and large flexible appendages of the present invention depends;

[0049] Figure 2 is a flowchart of the spacecraft attitude composite controller with non-linear sloshing and large flexible appendages of the present invention;

[0050] Figure 3is the input shaping-output feedback composite controller obtained by the present invention (sub Figure 3 c) and the traditional proportional derivative (PD) controller (sub Figure 3 a), the output feedback controller (sub Figure 3 b) Comparison results of the time history response of the spacecraft attitude angular velocity under the action;

[0051] Figure 4 are the comparison results of the time history response of the vibration deformation of the solar panel under the action of the input shaping-output feedback composite controller and the output feedback controller obtained by the present invention. Detailed implementation manners

[0052] The following combines the drawings and embodiments to make a detailed description of the attitude composite controller of the spacecraft with nonlinear sloshing and large flexible appendages of the present invention.

[0053] Embodiment 1

[0054] In this embodiment, for a spacecraft with a single partially filled spherical tank and two symmetrically installed flexible solar panels ( Figure 1 is a schematic diagram of its physical model), a corresponding input shaping-output feedback composite attitude controller is designed.

[0055] As Figure 2 shown, a spacecraft attitude composite control method with nonlinear sloshing and large flexible appendages disclosed in this embodiment specifically includes the following implementation steps:

[0056] Step 1: Establish the attitude dynamics model of the spacecraft with a single partially filled spherical tank and two symmetrically installed flexible solar panels by applying the Lagrange equation in the sense of hybrid coordinates. In this modeling process, the Euler quaternion is used to describe the attitude motion of any angle of the spacecraft main body; it is assumed that the vibration deformation of the two symmetric solar panels is in an antisymmetric form, and the assumed mode discretization method is used to describe the elastic vibration of the flexible solar panels; the split variable technique is used to improve the motion description of the liquid sloshing equivalent spherical pendulum model, so that it can clearly describe the overall rigid body motion and nonlinear sloshing of the liquid propellant relative to the spherical tank (including finite amplitude lateral sloshing and rotational sloshing). Step 1 is implemented in the following sub-steps:

[0057] Sub-step 1.1: Define the motions of each part of the spacecraft system, including the rotational angular velocity of the spacecraft main rigid body platform relative to the spacecraft centroid orbit reference frame (when ignoring the spacecraft orbit motion, it is determined that the orbit reference frame is an inertial reference frame), the rotational angular velocity of the attitude control three-axis reaction wheels relative to the orbit reference frame, the position and velocity of any mass microelement on the flexible appendage relative to the orbit reference frame, and the position and velocity of the concentrated mass of the liquid sloshing equivalent spherical pendulum model relative to the orbit reference frame.

[0058] Sub-step 1.2: Deduce the total kinetic energy and total potential energy of the spacecraft system.

[0059] In Step 1.3, the Lagrangian function of the spacecraft system's motion is the difference between the total kinetic energy and the potential energy of the system. Substitute them into the Lagrangian equations describing the motion of each part of the spacecraft system respectively, and then the attitude dynamics model of the spacecraft with a single partially liquid-filled spherical tank and two symmetrically installed flexible solar panels can be derived. Its specific expression is as follows:

[0060]

[0061] In the formula: I mb represents the inertia matrix of the spacecraft body (including three parts: the main rigid body of the spacecraft, two solar panels, and an equivalent spherical pendulum, etc.) with respect to the spacecraft's own coordinate system; ω is the coordinate matrix of the spacecraft's angular velocity vector expressed in the spacecraft's own coordinate system, is the time derivative of ω; P is the coupling coefficient matrix between the vibration of the first solar panel and the attitude motion of the spacecraft; q is the generalized coordinate matrix composed of the first three vibration mode coordinates of the vibration of the first solar panel; Q is the coupling coefficient matrix between the spherical pendulum motion and the attitude motion of the spacecraft; ρ is the generalized coordinate matrix composed of the Euler angles describing the motion of the equivalent spherical pendulum model relative to the tank; I w is the inertia matrix of the three-axis reaction wheel with respect to the spacecraft's own coordinate system; Ω is the coordinate matrix of the relative angular velocity vector of the three-axis reaction wheel expressed in the own coordinate system; represents the skew-symmetric dual matrix of ω; T g is the gravity gradient torque acting on the spacecraft; M sp is the modal mass matrix of the vibration of one solar panel; K sp is the modal stiffness matrix of the vibration of one solar panel; M p is the generalized mass matrix of the spherical pendulum motion; C p is the equivalent damping coefficient matrix of the spherical pendulum motion; K p is the generalized stiffness matrix of the equivalent spherical pendulum motion; is the rigid body coordinate of the equivalent liquid rigid body motion of the spherical pendulum model; T w is the coordinate matrix of the control reaction torque output by the attitude control three-axis reaction wheel expressed in the spacecraft's own coordinate system.

[0062] Step 2: Apply Lyapunov stability theory to design the output feedback attitude control law of the spacecraft in the embodiment. Step 2 is implemented in the following sub-steps:

[0063] In Sub-step 2.1, for the fully coupled form of the liquid-filled flexible spacecraft attitude dynamics model (Equation 1) established in Step 1; then, it can be assumed that the vibration of the flexible solar panel and the liquid sloshing are both small-amplitude motions, and the second-order and higher-order (including second-order) small quantities are ignored to directly linearize the spacecraft attitude dynamics model, and the following variable substitution is adopted:

[0064]

[0065] An apparent decoupled form of the attitude dynamics model that facilitates subsequent design of output feedback attitude control laws can be obtained:

[0066]

[0067] In step 2.2, considering that actual spacecraft are usually under-observed systems, the present invention performs state estimation on state variables related to solar panel vibration and liquid sloshing, and error variables are introduced as follows:

[0068]

[0069] In step 2.3, the following Lyaponuv function in the state space of the liquid-filled flexible spacecraft system is selected:

[0070]

[0071] Where: B1 and B3 are undetermined symmetric positive definite matrices; B2 and B4 are undetermined symmetric positive semi-definite matrices.

[0072] And according to the Lyaponuv stability theorem, a solar panel vibration dynamics estimator, a liquid sloshing dynamics estimator, and a control torque are designed to satisfy the condition that the time derivative of the Lyaponuv function has global semi-negativity. This is the output feedback attitude control law designed in step 2, and the specific expressions are as follows:

[0073]

[0074] Where: E n is the n-order identity matrix; 0 m×n is the m×n-dimensional zero matrix; k p and k d are control gain coefficients; the specific expressions of F1 and F2 are

[0075]

[0076]

[0077] It can be seen from equation (6) that the first fraction is the dynamics estimation of the solar panel vibration; the second fraction is the dynamics estimation of the liquid sloshing; the third fraction is the control reaction torque output by the attitude control reaction wheel, which is calculated using the output signals measured by the spacecraft attitude and angular velocity sensors as feedback information. Therefore, this type of controller is called an output feedback attitude controller.

[0078] Step 3: Consider the first two vibration modes of the windsurfing board and design the following ZVD pulse sequence:

[0079]

[0080] Perform a convolution operation on it with the target attitude quaternion to obtain the integerized Euler quaternion input command.

[0081] Step 4: Combine the output feedback attitude control law of the liquid-filled flexible spacecraft designed in Step 3 (Equation 6) and the Euler quaternion input command obtained in Step 4, and then the input shaping-output feedback composite attitude controller of the liquid-filled flexible spacecraft to be designed in the present invention can be obtained.

[0082] According to the established spacecraft attitude dynamics model with a single partially liquid-filled spherical tank and two symmetrically installed flexible solar windsurfing boards (Equation 1), compile the corresponding MATLAB simulation calculation program, conduct a three-axis stable attitude maneuver simulation example for the spacecraft in the embodiment, and obtain the dynamic response results of the spacecraft in the embodiment under the actions of the traditional proportional derivative (PD) controller, the output feedback controller, and the input shaping-output feedback composite controller designed in the present invention.

[0083] Figure 3 The comparison results of the time history responses of the spacecraft attitude angular velocity under the actions of the traditional proportional derivative (PD) controller (sub Figure 3 a), the output feedback controller (sub Figure 3 b), and the input shaping-output feedback composite controller obtained in the present invention (sub Figure 3 c) are given. It can be seen that there are very obvious local oscillations in the roll angular velocity of the spacecraft under the action of the traditional proportional derivative (PD) controller (sub Figure 3 a), which are caused by the dynamic coupling effects of liquid sloshing and windsurfing board vibration on the spacecraft attitude motion; sub Figure 3 b and sub Figure 3 c show that both the output feedback controller and the input shaping-output feedback composite controller obtained in the present invention can well suppress the oscillation disturbances brought by windsurfing board vibration and liquid sloshing to the spacecraft attitude motion. Figure 4 The comparison results of the time history responses of the windsurfing board vibration deformation under the actions of the output feedback controller and the input shaping-output feedback composite controller obtained in the present invention are shown. It can be seen that the output feedback controller will excite obvious vibration responses of the windsurfing board and cause prominent control-structure coupling problems. However, the input shaping-output feedback composite controller obtained in the present invention can effectively suppress the windsurfing board vibration and greatly weaken the residual vibration, and well solve the control-structure coupling problem.

[0084] The above are the preferred embodiments of the present invention, and the present invention should not be limited to the content disclosed in this embodiment and the drawings. Any equivalent or modification completed without departing from the spirit disclosed by the present invention falls within the protection scope of the present invention.

Claims

1. A method for attitude composite control of a spacecraft with nonlinear sloshing and large flexible appendages, characterized in that: including the following steps, Step 1. Establish a dynamic model for the large - scale motion of a liquid - filled spacecraft with large flexible appendages using Lagrange's equations in hybrid coordinates; during the modeling of the liquid - filled spacecraft with large flexible appendages, use T e to represent various non - conservative disturbance torques acting on the spacecraft, and the gravity gradient torque T g as the only non - conservative disturbance torque; use Euler quaternions to describe the arbitrary - angle attitude motion of the spacecraft body; use the assumed - mode discretization method to describe the elastic vibrations of 1 - m flexible appendages, achieving an efficient and concise representation of the elastic vibrations of the flexible appendages; use the split - variable technique to improve the motion description of the equivalent spherical pendulum model of liquid sloshing, achieving a clear representation of the overall rigid - body motion and nonlinear sloshing of the liquid propellant relative to the 1 - nth storage tanks, where the nonlinear sloshing includes finite - amplitude lateral sloshing and rotational sloshing; Step 2: Linearize the spacecraft attitude dynamics model obtained in Step 1 to obtain an apparent uncoupled attitude dynamics model; introduce error variables into the Lyaponuv function in the appropriate state space of the liquid-filled flexible spacecraft system to perform state estimation on relevant state variables; apply the Lyaponuv stability theory to design the output feedback attitude control law of the liquid-filled flexible spacecraft to ensure the asymptotic stability of the spacecraft attitude motion and the vibration of the solar panels; Step 3: According to the main vibration mode of the solar panel, design the corresponding ZVD shaper pulse sequence, and convolve the ZVD shaper pulse sequence with the target attitude quaternion in turn to obtain the integerized Euler quaternion input command; Step 4: Combine the output feedback attitude control law of the liquid-filled flexible spacecraft obtained in Step 2 and the Euler quaternion input command obtained in Step 3 to design the input shaping-output feedback composite attitude controller of the liquid-filled flexible spacecraft; ensure the asymptotic stability of the spacecraft attitude motion and the vibration of the solar panels through the input shaping-output feedback composite attitude controller of the liquid-filled flexible spacecraft, and realize the large-range attitude smooth maneuvering of the liquid-filled spacecraft with large flexible appendages in orbit and the active suppression control of the vibration of the flexible appendages.

2. A method for composite attitude control of a spacecraft with nonlinear sloshing and large flexible appendages as claimed in claim 1, characterized in that: The implementation method of Step 1 is as follows, Step 1.1: Define the motions of each part of the spacecraft system, including the position and velocity of the center of mass of the main rigid body platform of the spacecraft relative to the inertial reference frame, the angular velocity of the main rigid body platform relative to the inertial reference frame, the angular velocity of the attitude control three-axis reaction wheels relative to the inertial reference frame, the position and velocity of any mass element on the flexible appendage relative to the inertial reference frame, and the position and velocity of the lumped mass of the liquid sloshing equivalent spherical pendulum model relative to the inertial reference frame; Step 1.2: Deduce the total kinetic energy and total potential energy of the spacecraft system; The total kinetic energy of the spacecraft system is expressed as the following matrix calculation formula The total potential energy of the spacecraft system includes the strain energy V stored during the vibration of flexible appendages sp and the gravitational potential energy V of the equivalent spherical pendulum during liquid sloshing p These are two parts; Step 1.3: The Lagrangian function L of the spacecraft system motion is the difference between the total kinetic energy and the potential energy of the system, expressed as L = T - (V sp + V p ) (2) The Lagrangian equation under the spacecraft angular velocity is The Lagrangian equations describing the vibration of the solar panel and the motion of the spherical pendulum under the generalized coordinates are respectively Substitute (1) into (2) to obtain the specific expression of the Lagrangian function of the spacecraft system, and then substitute (2) into the Lagrangian equations describing the motions of each part of the spacecraft system in (3), (4), and (5) respectively, and then deduce the attitude dynamics model of the spacecraft with a single liquid-filled spherical tank and two symmetrically installed flexible solar panels as shown in formula (6) Where: I mb represents the inertia matrix of the spacecraft body with respect to the spacecraft body frame, and the spacecraft body includes three parts: the spacecraft main rigid body, two solar panels, and an equivalent spherical pendulum; ω is the coordinate matrix of the spacecraft angular velocity vector expressed in the spacecraft body frame, is the time derivative of ω; P is the coupling coefficient matrix between the vibration of the first solar panel and the spacecraft attitude motion; q is the generalized coordinate matrix composed of the first three vibration mode coordinates of the vibration of the first solar panel; Q is the coupling coefficient matrix between the spherical pendulum motion and the spacecraft attitude motion; ρ is the generalized coordinate matrix composed of the Euler angles describing the motion of the equivalent spherical pendulum model relative to the tank; I w is the inertia matrix of the three-axis reaction wheel with respect to the spacecraft body frame; Ω is the coordinate matrix of the relative angular velocity vector of the three-axis reaction wheel expressed in the body frame; represents the skew-symmetric dual matrix of ω; T g is the gravity gradient torque acting on the spacecraft; M sp is the modal mass matrix of the vibration of one solar panel; K sp is the modal stiffness matrix of the vibration of one solar panel; M p is the generalized mass matrix of the spherical pendulum motion; C p is the equivalent damping coefficient matrix of the spherical pendulum motion; K p is the generalized stiffness matrix of the equivalent spherical pendulum motion; is the rigid body coordinate of the equivalent liquid rigid body motion of the spherical pendulum model; T w is the coordinate matrix of the control reaction torque output by the attitude control three-axis reaction wheel expressed in the spacecraft body frame.

3. A method for composite attitude control of a spacecraft with nonlinear sloshing and large flexible appendages as described in claim 2, characterized in that: The implementation method of Step 2 is as follows, Step 2.1: For the fully coupled liquid-filled flexible spacecraft attitude dynamics model (6) established in Step 1; then, since the vibration of the flexible solar panel and the liquid sloshing are both small-amplitude motions, neglect the small quantities above the second order and directly linearize the spacecraft attitude dynamics model, and use the following variable substitution Obtain an apparent uncoupled form of the attitude dynamics model that is convenient for subsequent design of the output feedback attitude control law Step 2.2: Since the actual spacecraft is an under-observed system, by introducing the error variables shown in Equation (4) into the Lyapunov function in the spacecraft system state space, state estimation is performed on the state variables related to the panel vibration and liquid sloshing. Step 2.3: Select the following Lyapunov function in the state space of the liquid-filled flexible spacecraft system where: B1 and B3 are symmetric positive definite matrices to be determined; B2 and B4 are symmetric positive semi-definite matrices to be determined; And according to the Lyapunov stability theorem, a panel vibration dynamics estimator, a liquid sloshing dynamics estimator, and a control torque are designed when the time derivative of the Lyapunov function satisfies global semi-negativity. And based on the panel vibration dynamics estimator, the liquid sloshing dynamics estimator, and the output feedback attitude control law designed by the control torque, the output feedback attitude control law of the liquid-filled flexible spacecraft is obtained as shown in Equation (6): where: E n is the n-order identity matrix; 0 m×n is an m×n dimensional zero matrix; k p and k d are control gain coefficients; The specific expressions of F1 and F2 are In Equation (6), the first fraction is the dynamics estimation of the panel vibration; the second fraction is the dynamics estimation of the liquid sloshing; the third fraction is the control reaction torque output by the attitude control reaction wheel, and the third fraction is calculated using the output signals measured by the spacecraft attitude and angular velocity sensors as feedback information.

4. A spacecraft attitude composite control method with nonlinear sloshing and large flexible appendages as described in claim 3, characterized in that: The implementation method of Step 3 is as follows According to the main vibration mode of the panel, design the corresponding ZVD shaper pulse sequence, and convolve the ZVD shaper pulse sequence with the target attitude quaternion in turn according to Equation (7) to obtain the integerized Euler quaternion input command; Perform a convolution operation on it with the target attitude quaternion to obtain the integerized Euler quaternion input command.

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