Collaborative Attitude Control and Distributed Vibration Damping Method for Ultra-Large-Scale Flexible Spacecraft

Abstract

The present invention discloses a collaborative attitude control and distributed vibration suppression method for ultra-large-scale flexible spacecraft. The method includes the following steps: Step 1, construct a rigid-flexible coupling dynamics model of an ultra-large-scale spacecraft with multiple flexible structures; Step 2, decompose the coupling dynamics model based on singular perturbation theory to obtain slow-varying attitude and fast-varying vibration subsystems respectively; Step 3, use an adaptive switching and input-saturated terminal sliding mode controller to complete high-precision and high-stability attitude control; Step 4, use distributed piezoelectric actuators based on consensus theory and feedback collaborative controllers to complete high-precision and fast vibration suppression. The beneficial effects of the present invention are as follows: precise dimensionality reduction of the ultra-large-scale flexible spacecraft model is achieved; attitude and vibration active controllers are designed relatively independently; the accuracy and stability of attitude control and vibration suppression of the ultra-large-scale flexible spacecraft are improved simultaneously in a shorter time.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and particularly relates to a collaborative attitude control and distributed vibration suppression method for ultra-large-scale flexible spacecrafts. Background Art

[0002] Remote sensing satellites, as the products of space technology and carriers of scientific exploration, have undertaken major space missions such as earth observation, deep space exploration, and navigation and positioning. Among them, the rapid progress of space technology has promoted the leapfrog development of spaceborne antennas. In order to improve the information transmission capacity and achieve high-resolution remote sensing, the requirement for large-scale antenna structures has been put forward. Each major space power has increased its investment in large spaceborne antennas, and large antenna structures have become a research hotspot in the aerospace field. However, large flexible structures are prone to generate nonlinear low-frequency vibrations containing multiple modes, which are complex in form and difficult to attenuate. There is also a coupled dynamic behavior between satellite attitude maneuvers and structural vibrations during the on-orbit operation stage. As the remote sensing mission progresses, multiple space disturbances such as solar radiation torque and gravity gradient torque will exacerbate the coupling effect, having a great impact on the attitude pointing accuracy and stability of spaceborne antennas. In addition, the vibration states of antenna arrays and battery arrays are difficult to directly obtain, and there are uncertainties in structural characteristics and model parameters, which pose great challenges to the collaborative control of satellite attitude and vibration. Therefore, it is necessary to design an active control method for the attitude motion and structural vibration of ultra-large-scale spacecrafts with strong robustness to disturbances, and at the same time achieve high-precision and high-stability attitude control and high-precision and fast vibration suppression. Summary of the Invention

[0003] In order to solve the problems existing in the prior art, the present invention proposes a collaborative attitude control and distributed vibration suppression method for ultra-large-scale flexible spacecrafts to achieve high-precision and high-stability attitude control and high-precision and fast vibration suppression. Based on the singular perturbation theory, the rigid-flexible coupling dynamic model of ultra-large-scale flexible spacecrafts is accurately decomposed. A terminal sliding mode controller with adaptive switching and input saturation is designed respectively to achieve high-precision and high-stability attitude control, and a distributed piezoelectric actuator based on the consensus theory and feedback collaborative controller is designed to achieve high-precision and fast vibration suppression.

[0004] A collaborative attitude control and distributed vibration suppression method for ultra-large-scale flexible spacecrafts provided by the present invention is characterized by including the following steps:

[0005] Step 1: Establish a rigid-flexible coupling dynamic model of an ultra-large-scale spacecraft with multiple flexible structures under space disturbances based on Hamilton's principle;

[0006] Step 2: Decompose the coupling dynamic model by using the singular perturbation method to obtain the slow-varying attitude subsystem and the fast-varying vibration subsystem on different time scales for subsequent active controller design;

[0007] Step 3: In the slow-varying attitude subsystem, an attitude control is performed on the ultra-large-scale flexible spacecraft by using a terminal sliding mode controller with adaptive switching and input saturation;

[0008] Step 4: In the fast-varying vibration subsystem, based on the leader-follower consensus theory, a vibration suppression method based on distributed piezoelectric actuators is designed. An undirected topology communication structure is adopted among the actuators, and combined with a negative feedback cooperative controller for structural vibration suppression, high-precision vibration suppression of the ultra-large-scale flexible structure is quickly achieved.

[0009] Further, the said Step 1 includes:

[0010] Based on Hamilton's principle, a rigid-flexible coupling dynamic model of the ultra-large-scale flexible spacecraft is obtained:

[0011] ;

[0012] ;

[0013] ;

[0014] In the formula: , , are the total kinetic energy, strain energy, and external work of the spacecraft respectively; is the variational operator, t1 and t2 are the starting and ending times respectively; the superscript T represents the transpose of the matrix;

[0015] J represents the moment of inertia matrix of the spacecraft; represents the modal vector of the spacecraft; represents the modal damping ratio of the spacecraft; represents the modal frequency matrix of the spacecraft; represents the attitude control torque applied to the spacecraft; represents the space disturbance composed of the solar radiation torque and the gravity gradient torque; represents the modal input force; represents the flexible structure number;

[0016] is the coupling coefficient matrix between the spacecraft rigid body and the flexible structure:

[0017] ;

[0018] In the formula: is the vector from the connection point p of the kth flexible structure to the centroid O; represents the vector from the jth node of the flexible structure to the kth p; is the mass of the jth node; is the orthogonal function of the k-th flexible structure;

[0019] represents the three-axis angular velocity of the spacecraft in the body coordinate system, and

[0020] ;

[0021] represents the transformation matrix from the orbital coordinate system to the body coordinate system:

[0022] ;

[0023] defines the three-axis attitude angles of the spacecraft, represented by as:

[0024] , ;

[0025] obtains the final expression of the rigid-flexible coupling dynamics model of the ultra-large-scale flexible spacecraft:

[0026] ,

[0027] ;

[0028] In the formula: is the first derivative of the attitude angle; is the second derivative of the attitude angle; is the resultant external moment.

[0029] Furthermore, the specific content of step 2 is as follows:

[0030] S21, defines the generalized coordinates including the attitude angles and vibration modes as:

[0031] ;

[0032] rewrites the rigid-flexible coupling dynamics model as:

[0033] ;

[0034] ;

[0035] In the formula: , , are the positive definite mass, damping and stiffness matrices respectively; , , represent the modular matrices corresponding to the matrices , , respectively; Denote the attitude matrix composed of roll angle , pitch angle and yaw angle ; Denote the vector composed of the first four vibration modes in the generalized coordinates ;

[0036] Write the formula with positive definite mass, damping, and stiffness matrix modules in the form of state - space equations:

[0037] ;

[0038] ;

[0039] Define , and based on singular perturbation theory, introduce the following variables:

[0040] , ;

[0041] In the formula: Denote finding the minimum eigenvalue of , Denote the obtained minimum eigenvalue, , where ; The vibration mode is expressed by the variable as:

[0042] ;

[0043] In the formula: Denote the singular perturbation coefficient;

[0044] S22 Decompose the state - space equation into models under two time scales:

[0045] ;

[0046] S23 For the slow - varying attitude subsystem, set to obtain the degenerate form of the equation in step S22, and introduce the subscript slow to represent the three - axis attitude , control torque physical quantities in the slow - varying attitude subsystem; The three - axis attitude is expressed as:

[0047] ;

[0048] ;

[0049] S24 According to singular perturbation theory, stretch the time scale of the fast subsystem to , where denotes time, , introduce fast to represent the variables in the fast-varying vibrator subsystem , and the control torque , and the form of the fast-varying vibrator subsystem is obtained as follows:

[0050] ;

[0051] In the formula: represents the first derivative of the variable ; represents the first derivative of with respect to ; represents the second derivative of with respect to ;

[0052] Furthermore, the specific content of step three is as follows:

[0053] S31 Set the form of the sliding mode surface as:

[0054] ;

[0055] In the formula: and represent positive definite diagonal matrices to be designed; is the expression of the attitude angle in the slow-varying subsystem; represents a piecewise function, as shown below:

[0056] ;

[0057] In the formula: represents the row number of the matrix; , , respectively represent the specific elements of the matrices , and ; represents the boundary layer thickness of the sliding mode surface; and represent the terminal sliding mode parameters; the two control parameters , as well as the specific elements of the sliding mode surface are respectively expressed as:

[0058] , ,

[0059] ;

[0060] In the formula: and respectively represent the matrices and the specific elements; , , denote the identity matrix of the corresponding dimension;

[0061] Substitute into the sliding mode surface to obtain the first derivative of the sliding mode surface :

[0062] ;

[0063] Design a fixed-time reaching law with adaptive switching and write the sliding mode surface in the following form:

[0064] ;

[0065] where: and denote the diagonal matrices to be designed; and denote the power exponents; Express the sig function and the adaptation law as:

[0066] , ;

[0067] , ;

[0068] where: , denote the positive gains to be designed; is the specific element of matrix ; is 's maximum value, and sat represents the saturation function:

[0069] ;

[0070] The attitude control law considering input saturation is designed as:

[0071] .

[0072] Furthermore, the specific content of Step 4 is as follows:

[0073] S41. Express the dynamic equation of the fast-varying vibration subsystem and its required control input as:

[0074] ;

[0075] where: ,

[0076] ;

[0077] The state of the first flexible structure is expressed in the fast-varying vibration subsystem as:

[0078] ;

[0079] where: , , respectively represent the matrix modules corresponding to the first flexible structure;

[0080] Multiple distributed piezoelectric actuators form a cooperative multi-agent system, and the communication topology is expressed as:

[0081] ;

[0082] where, represents the node set of the distributed piezoelectric actuators; represents the boundary set; The adjacent matrix of is expressed as:

[0083] ;

[0084] If , , then there is a communication connection between the i c and j c th actuators in the topological structure, and self-communication of a single actuator is not considered, that is ; Given that the communication graph is undirected, then holds;

[0085] Introduce the Laplacian matrix , which is expressed as:

[0086] , ;

[0087] Design the distributed cooperative control law with consensus and feedback as follows:

[0088] ;

[0089] where: represents the control force generated by the i c th piezoelectric actuator on the first flexible structure; represents the modal shape matrix; and are the displacements of the flexible structure under the action of the i c and j c th piezoelectric actuators respectively; represents the vibration displacement The first derivative; , , denotes a control parameter; denotes the inverse matrix of.

[0090] Advantages of the present invention:

[0091] The present invention takes into account the actual engineering applications, introduces the singular perturbation theory into the rigid-flexible coupling dynamics modeling and cooperative active control of ultra-large scale flexible spacecraft. The singular perturbation method realizes the high-precision decoupling of the attitude and vibration of the ultra-large scale flexible spacecraft, and relatively independently designs the attitude and vibration active controllers. A terminal sliding mode controller with adaptive switching and input saturation is designed, which improves the attitude control accuracy and stability of the ultra-large scale flexible spacecraft through finite-time attitude convergence. The distributed piezoelectric actuators are combined with the consensus theory and feedback cooperative control, and effectively suppress the long-term low-frequency vibration of the ultra-large scale structure by virtue of the high-precision and fast convergence characteristics. Description of the drawings

[0092] Figure 1 is the system block diagram of a method for cooperative attitude control and distributed vibration suppression of an ultra-large scale flexible spacecraft according to the present invention;

[0093] Figure 2 is the system dynamics model diagram of a method for cooperative attitude control and distributed vibration suppression of an ultra-large scale flexible spacecraft according to the present invention;

[0094] Figure 3 In, (a) to (c) are the three-axis attitude angle curves of a method for cooperative attitude control and distributed vibration suppression of an ultra-large scale flexible spacecraft according to the present invention;

[0095] Figure 4 In (a) to (c) are the three-axis angular velocity curves of a method for cooperative attitude control and distributed vibration suppression of an ultra-large scale flexible spacecraft according to the present invention;

[0096] Figure 5 In (a) to (c) are the three-axis control torque curves of a method for cooperative attitude control and distributed vibration suppression of an ultra-large scale flexible spacecraft according to the present invention;

[0097] Figure 6 In (a) to (d) are the vibration displacement curves of the ultra-large scale antenna of a method for cooperative attitude control and distributed vibration suppression of an ultra-large scale flexible spacecraft according to the present invention;

[0098] Figure 7 In (a) to (d) are the vibration displacement curves of the solar panels of a method for cooperative attitude control and distributed vibration suppression of an ultra-large scale flexible spacecraft according to the present invention. Detailed implementation mode

[0099] As Figure 1 shown, a collaborative attitude control and distributed vibration suppression method for ultra-large-scale flexible spacecrafts, the specific steps include:

[0100] Step 1: Considering multiple space disturbances, construct a rigid-flexible coupling dynamic model of an ultra-large-scale spacecraft with multiple flexible structures.

[0101] Step 2: Based on singular perturbation theory, use the singular perturbation parameter to complete the decomposition of the coupling dynamic model on the time scale, and obtain the slow-varying attitude and fast-varying vibration subsystems respectively for subsequent active controller design.

[0102] Step 3: Design a finite-time terminal sliding mode controller with strong robustness, introduce an adaptive switching law and consider the input saturation characteristic, and achieve high-precision and high-stability attitude control in a short time;

[0103] Step 4: Based on the leader-follower consensus theory, design a vibration suppression method based on distributed piezoelectric actuators, adopt an undirected topology communication structure between actuators, and combine a negative feedback collaborative controller to quickly achieve high-precision vibration suppression of ultra-large-scale flexible structures.

[0104] In step 1, establish a rigid-flexible coupling dynamic model of an ultra-large-scale flexible spacecraft with multiple flexible structures:

[0105] ;

[0106] ;

[0107] ;

[0108] In the formula: , , respectively represent the total kinetic energy, strain energy and external work of the spacecraft; is the variational operator, t1 and t2 respectively represent the starting and ending times; the superscript T represents the transpose of the matrix.

[0109] J represents the moment of inertia matrix of the spacecraft; represents the modal vector of the spacecraft; represents the modal damping ratio of the spacecraft; represents the modal frequency matrix of the spacecraft; represents the attitude control torque applied to the spacecraft; represents the space disturbance applied to the spacecraft, mainly composed of solar radiation torque and gravity gradient torque; represents the modal input force; Represents the flexible structure number; Is the first derivative of the attitude angle; Is the second derivative of the attitude angle.

[0110] Denotes the coupling coefficient matrix between the spacecraft rigid body and the flexible structure, and is calculated as follows:

[0111] ;

[0112] In the formula: Represents the vector from the p point of the k-th flexible structure connection to the centroid O; Represents the vector from the j-th node of the flexible structure to the k-th p; Is the mass of the j-th node; Is the orthogonal shape function of the k-th flexible structure.

[0113] Denotes the three-axis angular velocity of the spacecraft in the body coordinate system, and its skew-symmetric matrix is:

[0114] ;

[0115] Represents the transformation matrix from the orbital coordinate system to the body coordinate system:

[0116]

[0117] Defines the three-axis attitude angles (roll, pitch, yaw) by the matrix Denotes, then there is

[0118] , ;

[0119] The final form of the rigid-flexible coupling dynamics equation of the ultra-large scale flexible spacecraft is obtained as:

[0120] ;

[0121] .

[0122] In step two, the coupling dynamics model is decomposed on the time scale to obtain the slow-varying attitude subsystem and the fast-varying vibration subsystem respectively:

[0123] The generalized coordinates including the three-axis attitude angles and the vibration modes of all flexible structures can be defined as:

[0124] ;

[0125] Rewrite the above rigid-flexible coupling dynamics equation as:

[0126]

[0127] ;

[0128] In the formula: , , respectively represent the mass, damping, and stiffness matrices of the spacecraft, all of which are positive definite matrices; , , respectively represent the modal matrices corresponding to the matrices , , ; represents the attitude matrix composed of the roll angle , pitch angle , and yaw angle ; represents the vector containing the first four vibration modes.

[0129] Write the above formula with mass, damping, and stiffness matrix modules in state - space form:

[0130] ;

[0131] ;

[0132] Define , and based on singular perturbation theory, introduce the variable :

[0133] ,

[0134] In the formula: represents finding the minimum eigenvalue of , represents the obtained minimum eigenvalue, , where . The vibration modes can be expressed by the singular perturbation parameter as:

[0135] .

[0136] Therefore, the above state - space equation can be decomposed in the time scale:

[0137] .

[0138] For the slow - varying attitude subsystem, the degenerate form of this equation can be obtained. Introduce the subscript slow to represent the three - axis attitude in the slow - varying attitude subsystem and physical quantities such as control torque. The expressions for the attitude variables are: etc.

[0139] ;

[0140] ;

[0141] Then, the real system is approximated by boundary layer correction. According to singular perturbation theory, the slow-varying attitude subsystem remains unchanged in the boundary layer, while the fast-varying vibration subsystem changes rapidly. The time scale of the fast-varying vibration subsystem is stretched to , where represents time, . Introduce fast to represent variables in the fast-varying vibration subsystem and physical quantities such as control torque etc., and the following equations are obtained:

[0142] ;

[0143] In step three, for the slow-varying attitude subsystem, a terminal sliding mode attitude controller with adaptive switching and input saturation is designed to achieve high-precision attitude stabilization in a finite time.

[0144] Define the terminal sliding mode surface as:

[0145] ;

[0146] In the formula: and represent positive definite diagonal matrices; is represented by a piecewise function as follows:

[0147] ;

[0148] In the formula: represents the row number of the matrix; , , respectively represent the specific elements of matrices , and ; represents the boundary layer thickness of the sliding mode surface; and represent the terminal sliding mode parameters, are both positive odd numbers; the control parameters , and the specific elements of the sliding mode surface are respectively expressed as:

[0149] , ,

[0150] ;

[0151] where: and respectively represent the specific elements of matrices and ; , , where represents the identity matrix of the corresponding dimension.

[0152] Combined with Step 2,

[0153] there is , substituting into the sliding surface to obtain:

[0154] .

[0155] To improve the attitude control performance, the following fixed-time adaptive reaching law is designed:

[0156] ;

[0157] where: and represent the diagonal matrices to be designed, similar to and ; and represent the power exponents; the sig function and the adaptive law are expressed as:

[0158] , ,

[0159] , ;

[0160] where: , represent the positive gains to be designed; is the specific element of matrix ; is 's maximum value, used to handle the chattering problem. sat represents the saturation function:

[0161] ;

[0162] Therefore, the attitude control law considering input saturation can be designed as:

[0163] .

[0164] In Step 4, for the fast-varying vibration subsystem, a vibration suppression method based on distributed piezoelectric actuators is designed. Combining consensus theory and negative feedback cooperative control, high-precision vibration suppression of super-large-scale flexible structures is achieved quickly.

[0165] The state-space equation of the fast-varying vibration subsystem is expressed as:

[0166] ;

[0167] where: ,

[0168] . Taking the flexible structure numbered 1 as an example, its state-space equation is:

[0169] ;

[0170] where: , , respectively represent the matrix modules corresponding to the first flexible structure; it is the same for other structures. For No. 2, only the matrix with subscript 11 in the formula needs to be changed to the matrix with subscript 22, and so on, without further elaboration.

[0171] The distributed piezoelectric actuators form a multi-agent system through the following communication topology:

[0172] ;

[0173] where, and respectively represent the node set and boundary set of the actuator; The adjacent matrix of . In the topological structure, there is a communication connection between the c i c -th and j -th actuators if , and self-communication of a single actuator is not considered, that is, . Given the undirected communication topology

[0174] The Laplacian matrix is introduced, where is expressed as:

[0175] , ;

[0176] The distributed cooperative control law with leader-follower consensus and negative feedback control is designed as:

[0177] ;

[0178] In the formula: represents the control force generated by the i-th piezoelectric actuator on the first flexible structure; c The control force generated by the i-th piezoelectric actuator on the first flexible structure; represents the modal shape matrix; and respectively represent the displacements of the flexible structure under the action of the i-th c and j-th c piezoelectric actuators; represents the first derivative of the vibration displacement ; , , represent the control parameters. is the inverse matrix of.

[0179] From the above formula, the control law applied by all actuators to the first flexible structure is expressed as:

[0180] ;

[0181] In the formula, represents the modal shape orthogonal matrix containing all execution nodes, represents the vibration displacement matrix of the execution nodes; represents the Laplacian matrix.

[0182] To illustrate the effectiveness of the proposed cooperative active control method, a numerical simulation is carried out using a certain ultra-large-scale flexible spacecraft as an example, and the sampling time is set to 0.1 s.

[0183] The simulation parameters of the ultra-large-scale flexible spacecraft are selected as shown in the following table:

[0184] Table 1

[0185] .

Claims

1. A method for coordinated attitude control and distributed vibration suppression of ultra-large-scale flexible spacecraft, characterized in that: The steps include: Step 1: Based on the Hamiltonian principle, a rigid-flexible coupling dynamic model of a super-large-scale spacecraft with multiple flexible structures under space disturbance is established; Step 2: Decomposing the coupled dynamics model by using a singular perturbation method to obtain a slowly varying attitude subsystem and a rapidly varying vibration subsystem on different time scales for subsequent active controller design; Step 3: In the slow-changing attitude subsystem, a terminal sliding mode controller with adaptive switching and input saturation is used to control the attitude of the ultra-large-scale flexible spacecraft; Step 4: In the fast-changing vibration subsystem, based on the leader-follower consistency theory, a vibration suppression method based on distributed piezoelectric actuators is designed. An undirected topological communication structure is adopted between the actuators, combined with a negative feedback collaborative controller for structural vibration suppression, to quickly achieve high-precision vibration suppression of ultra-large-scale flexible structures; The step one comprises: Based on the Hamiltonian principle, the rigid-flexible coupling dynamics model of ultra-large-scale flexible spacecraft is obtained: ； ； ； Where: , , are the total kinetic energy, strain energy and external work of the spacecraft respectively; is a variational operator, t1 and t2 are the start and end times respectively; the superscript T indicates the transpose of the matrix; J represents the moment of inertia matrix of the spacecraft; represents the modal vector of the spacecraft; represents the modal damping ratio of the spacecraft; represents the modal frequency matrix of the spacecraft; represents the attitude control torque applied to the spacecraft; represents the spatial disturbance composed of solar radiation moment and gravity gradient moment; represents the modal input force; Indicates the flexible structure number; is the coupling coefficient matrix between the rigid body and the flexible structure of the spacecraft: ； Where: is the vector from the kth flexible structure connection point p to the center of mass O; represents the vector from the jth node to the kth p of the flexible structure; is the mass of the jth node; is the orthogonal shape function of the kth flexible structure; represents the three-axis angular velocity of the spacecraft in the body coordinate system, and ； Represents the transformation matrix from the orbital coordinate system to the body coordinate system: ； The three-axis attitude angle of the spacecraft is defined by express: ， ； The final expression of the rigid-flexible coupling dynamics model of the ultra-large-scale flexible spacecraft is obtained: ， ； Where: is the first-order derivative of the attitude angle; is the second-order derivative of the attitude angle; is the resultant external torque; The step 2 is specifically as follows: S21, define the generalized coordinates including attitude angle and vibration mode as: ； The rigid-flexible coupling dynamic model is rewritten as: ； ； Where: , , are the positive definite mass, damping and stiffness matrices respectively; , , Respectively represent the corresponding matrices , , The module matrix of Indicated by the roll angle , Pitch angle and yaw angle The posture matrix composed of Represents generalized coordinates The vector consisting of the first four vibration modes in ; The formula with positive mass, damping, and stiffness matrix blocks can be written in the form of state-space equations: ； ； definition , based on singular perturbation theory, the following variables are introduced: ， ； Where: Express Find the minimum eigenvalue, represents the minimum eigenvalue obtained, ,in ; The vibration mode is determined by the variable It is expressed as: ； Where: represents the singular perturbation coefficient; S22 decomposes the state space equation into two time scale models: ； S23 For the slow attitude subsystem, set The degenerate form of the equation in step S22 is obtained, and the subscript slow is introduced to represent the three-axis attitude in the slow-changing attitude subsystem. , Control torque Physical quantity; the three-axis attitude is expressed as: ； ； S24 According to the singular perturbation theory, the time scale of the fast subsystem is stretched to ,in, Indicates time, , fast is introduced to represent the variables in the fast-changing vibration subsystem , Control torque , the form of the fast-changing vibration subsystem is obtained as: ； Where: Representation variables The first derivative of ; Express Ask about The first derivative of ; express Ask about The second derivative of .

2. The method for coordinated attitude control and distributed vibration suppression of a super-large-scale flexible spacecraft according to claim 1 is characterized in that: The step three is specifically as follows: S31 sets the sliding surface in the form of: ； Where: and represents the positive definite diagonal matrix to be designed; is the attitude angle Expression in the slow-changing subsystem; Represents a piecewise function as follows: ； Where: Represents the row number of the matrix; , , Respectively represent matrices , and specific elements of represents the boundary layer thickness of the sliding surface; and Represents the terminal sliding mode parameters; two control parameters , And the specific elements of the sliding surface Respectively expressed as: ， ， ； Where: and Respectively represent matrices and specific elements of , , represents the identity matrix of the corresponding dimension; Will Substitute the sliding surface , find the first-order derivative of the sliding surface : ； Design a fixed-time reaching law for adaptive switching and write the sliding surface into the following form: ； Where: and represents the diagonal matrix to be designed; and represents the power exponent; the sig function and the adaptive law are expressed as: ， ； ， ； Where: , Indicates the positive gain that needs to be designed; For the matrix specific elements of for The maximum value of sat represents the saturation function: ； The attitude control law considering input saturation is designed as: 。 3. The method for coordinated attitude control and distributed vibration suppression of a super-large-scale flexible spacecraft according to claim 1 is characterized in that: The step 4 is specifically as follows: S41, the dynamic equation of the fast-changing vibration subsystem and its required control input are expressed as: ； Where: , ； The state of the first flexible structure is expressed in the fast-changing vibration subsystem as: ； Where: , , Respectively represent the matrix modules corresponding to the first flexible structure; Multiple distributed piezoelectric actuators form a collaborative multi-agent system, and the communication topology is expressed as: ； In the formula, A set of nodes representing distributed piezoelectric actuators; represents the boundary set; The adjacent matrix is ​​expressed as: ； like , , then the i-th c and j c There is a communication connection between the actuators, and the self-communication of a single actuator is not considered, that is, ; Given that the communication graph is undirected, then Established; Introducing the Laplace matrix , It is expressed as: ， ； The distributed cooperative control law with consensus and feedback is designed as follows: ； Where: represents the i-th c Control force generated by a piezoelectric actuator; represents the mode shape matrix; and The i c and j c Displacement of the flexible structure under the action of a piezoelectric actuator; Represents vibration displacement The first derivative of ; , , Indicates control parameters; express The inverse matrix of .

Images