A flexible spacecraft attitude control method and system

Abstract

The application discloses a flexible spacecraft attitude control method and system, and the method comprises the following steps: establishing a flexible spacecraft attitude control model and a flexible accessory model; according to the homogeneous system theory, the flexible spacecraft attitude control model and the flexible accessory model are simplified for multiple times to obtain a simplified flexible spacecraft attitude control model and a simplified flexible accessory model; according to the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible accessory model, a full drive model is obtained; the output equation in the flexible accessory model is combined to design an observer, the modal variable in the flexible accessory model is estimated through the observer, the full drive model is combined, and a controller is designed based on a high-order full drive system method; the controller is substituted into the full drive model to obtain a linear closed-loop system; according to a parameterized design method, a parameterized controller is obtained, and a stable linear closed-loop system is obtained. The application can stabilize the flexible spacecraft attitude control system.

Description

Technical Field

[0001] This invention relates to the field of attitude control technology for flexible spacecraft, specifically to a method and system for attitude control of flexible spacecraft. Background Technology

[0002] The performance of a spacecraft's attitude control system directly impacts the success of a space mission. This system must possess high precision and high reliability, making spacecraft attitude control a highly valued and extensively researched task. To effectively reduce spacecraft weight and launch costs, and minimize energy consumption, spacecraft commonly incorporate flexible accessories such as foldable solar panels and flexible communication antennas. These flexible accessories are characterized by low damping and high flexibility. During spacecraft attitude maneuvers, these accessories are prone to oscillations. Influenced by external disturbances and temperature changes, they are easily stimulated to produce sustained oscillations. These oscillations are difficult to decay, and due to the coupling between the flexible accessories and the spacecraft's central rigid body, their oscillations can severely impact the spacecraft's attitude control, even compromising stability and leading to loss of control.

[0003] On the one hand, current research on attitude control of flexible spacecraft primarily employs first-order state-space methods to describe and design the system. This requires transforming the original high-order model into a first-order form, resulting in the loss of corresponding physical properties and the retention of nonlinearities, which significantly complicates the design of control methods. On the other hand, the application of high-order all-drive system methods in spacecraft attitude control leads to overly complex all-drive models and control methods. These methods incorporate substantial nonlinearities, causing large variations in the actual control torque and making convergence difficult in a short time.

[0004] In existing technologies, Li Kun et al. published "Research on Active Vibration Suppression and Attitude Control Methods for Flexible Spacecraft," which, by combining active vibration suppression and applying a preset performance control method, can ensure that the flexible spacecraft meets attitude control requirements within a preset time and enables rapid decay of flexible vibrations. However, this method retains nonlinearity. Summary of the Invention

[0005] The technical problem to be solved by this invention is that most current attitude control methods for flexible spacecraft are designed under state-space methods, which retain the nonlinearity of the model.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] A method for attitude control of a flexible spacecraft includes the following steps:

[0008] Establish attitude control models and flexible attachment models for flexible spacecraft;

[0009] Based on homogeneous system theory, the attitude control model of the flexible spacecraft and the flexible attachment model are simplified multiple times to obtain a simplified attitude control model of the flexible spacecraft and a simplified flexible attachment model.

[0010] Based on the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible attachment model, the all-drive model is obtained;

[0011] The output equation is incorporated into the flexible attachment model to design an observer, and the modal variables in the flexible attachment model are estimated using the observer. Combined with the all-drive model and based on a high-order all-drive system method, a controller is designed. The controller is then substituted into the all-drive model to obtain a linear closed-loop system.

[0012] Based on the parametric design method, a parametric controller is obtained, as well as a stable linear closed-loop system.

[0013] Advantages: Flexible attachments are prone to oscillations, which can affect the stability of a spacecraft's attitude control system. Attitude control techniques within a first-order state-space framework retain significant nonlinearities in the system model while losing the physical context of full-drive systems. Current attitude control techniques based on higher-order full-drive systems suffer from complex full-drive models and controller structures, making it difficult for control variables to converge quickly. This invention simplifies the model using homogeneous system theory and employs a higher-order full-drive model for design, preserving the physical context of full-drive systems. Simultaneously, it incorporates active suppression methods for flexible attachment oscillations, resulting in rapid decay of these oscillations. The resulting full-drive model and controller structure are simple, the controller does not contain system nonlinearities, and the control variables converge rapidly, making it more practically significant in engineering. When applied to specific systems, the controller parameters can be determined using parametric design methods according to actual needs, solving the attitude stability problem of flexible spacecraft while simultaneously enabling rapid decay of flexible attachment oscillations.

[0014] In one embodiment of the present invention, the flexible spacecraft attitude control model and the flexible attachment model are simplified by introducing expansion operators multiple times until the flexible spacecraft attitude control model and the flexible attachment model no longer contain nonlinear terms, thereby obtaining the simplified flexible spacecraft attitude control model and the simplified flexible attachment model.

[0015] In one embodiment of the present invention, the simplified attitude control model for the flexible spacecraft is obtained by the following formula:

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, z represents the angle from the reference coordinate system to the intermediate coordinate system during the first rotation under the (w,z) parameters, w1 and w2 are the relevant angle variables from the intermediate coordinate system to the body coordinate system during the second rotation under the (w,z) parameters, and ω = [ω x ,ω y ,ω z ] T Let J represent the three-axis angular velocities of the spacecraft in its body coordinate system, J∈R 3×3 Represented as the moment of inertia matrix, R 3×3 Represented as a 3×3 dimensional real space, J0=J-δ T δ, δ∈R n×3 R is represented as the coupling matrix between the rigid body at the spacecraft's center and the flexible appendages. n ×3 Represented as an n×3 dimensional real space, where n represents the number of flexible modes considered, u = [u x ,u y ,u z ] T ∈R 3 The three-axis control torque of the spacecraft, R 3 Represented as a 3-dimensional real number space;

[0021] The simplified flexible attachment model is obtained through the following formula:

[0022]

[0023]

[0024] In the formula, η∈R n and ψ∈R n Represented as two different modes of the flexible attachment, and Let η∈R be the respective values. n and ψ∈R n The derivative of u a ∈R n R represents the active suppression control quantity for flexible attachment oscillations. n It is represented as an n-dimensional real space, where n represents the number of flexible modes considered.

[0025] In one embodiment of the present invention, based on the coupling relationship, the derivatives of the attitude variables of the flexible spacecraft and the derivatives of the modal variables of the flexible attachments are derived again to obtain the all-drive model;

[0026] The all-drive model is obtained through the following formula:

[0027]

[0028]

[0029] In the formula, M = [w1, w2, z] T ∈R 3 This is represented by the attitude of a flexible spacecraft. diag is represented as a diagonal matrix.

[0030] In one embodiment of the present invention, the observer is represented by the following formula:

[0031]

[0032] in, C = [I 0 n×n ]∈R n×2n ;

[0033] In the formula, Let η and ψ be the observer's estimates of the unsimplified modal variables of the flexible attachment, respectively, and I be the identity matrix of the corresponding dimension, y∈R. n The output is represented as the flexible attachment model. Let L represent the estimated output of the flexible attachment model, C represent the damping matrix, K represent the stiffness matrix, and 0 represent the value of L. n×n It is represented as an n×n dimensional zero matrix, where n represents the number of flexible modes considered.

[0034] In one embodiment of the present invention, the controller is obtained by the following formula:

[0035]

[0036] In the formula, A1, A0, It is represented as a constant matrix.

[0037] In one embodiment of the present invention, the linear closed-loop system is obtained by the following formula:

[0038]

[0039] By appropriately setting the constant matrices A1, A0, To obtain a stable linear closed-loop system.

[0040] In one embodiment of the present invention, the constant matrices A1, A0, The selection criteria are obtained through the following methods:

[0041] Obtain the state-space equations of the linear closed-loop system:

[0042]

[0043] Among them, A 0～1 =[A0 A1], Φ(A 0～1 )and The system matrix is ​​represented as that of a linear closed-loop system, and Φ(A) 0～1 )and The following relationship must be satisfied:

[0044]

[0045] F1 and F2 represent the desired Jordan canonical form in the parametric design method, and V1 and V2 represent the corresponding eigenvector matrices of the desired Jordan canonical form; then we have Here, Z1 and Z2 are real matrices, and Z1∈R 3×6 ,Z2∈R 3×6 The selection criteria for Z1 and Z2 are: detV1(Z1,F1)≠0, detV2(Z2,F2)≠0; where det represents the value of the corresponding determinant.

[0046] The present invention also provides a flexible spacecraft attitude control system, based on the above-described flexible spacecraft attitude control method, comprising:

[0047] The flexible model module is used to build attitude control models and flexible attachment models for flexible spacecraft;

[0048] The simplification module is used to simplify the attitude control model of the flexible spacecraft and the flexible attachment model multiple times according to the homogeneous system theory to obtain a simplified attitude control model of the flexible spacecraft and a simplified flexible attachment model.

[0049] The all-drive model module is used to obtain the all-drive model based on the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible attachment model;

[0050] The linear closed-loop system module is used to combine the output equations of the flexible attachment model to design an observer, and to estimate the modal variables in the flexible attachment model through the observer. Combined with the all-drive model, and based on the high-order all-drive system method, a controller is designed. The controller is then substituted into the all-drive model to obtain the linear closed-loop system.

[0051] The stabilization module is used to obtain a parameterized controller and a stable linear closed-loop system based on the parametric design method.

[0052] In one embodiment of the present invention, the linear closed-loop system is obtained by the following formula:

[0053]

[0054] In the formula, M = [w1, w2, z] T ∈R 3 Let η ∈ R represent the attitude of a flexible spacecraft. n Represented as the simplified flexible attachment mode, Let A1, A0, and A1 be the observer's estimate of the pre-simplification flexible attachment modal variable η. It is represented as a constant matrix.

[0055] By appropriately setting the constant matrices A1, A0, To obtain a stable linear closed-loop system;

[0056] Obtain the state-space equations of the linear closed-loop system:

[0057]

[0058] Among them, A 0～1 =[A0 A1], Φ(A 0～1 )and The system matrix is ​​represented as that of a linear closed-loop system, and Φ(A) 0～1 )and The following relationship must be satisfied:

[0059]

[0060] F1 and F2 represent the desired Jordan canonical form in the parametric design method, and V1 and V2 represent the corresponding eigenvector matrices of the desired Jordan canonical form; then we have Here, Z1 and Z2 are real matrices, and Z1∈R 3×6 ,Z2∈R 3×6 The selection criteria for Z1 and Z2 are: detV1(Z1,F1)≠0, detV2(Z2,F2)≠0; where det represents the value of the corresponding determinant.

[0061] Compared with existing technologies, the advantages of this invention are: it provides a flexible spacecraft attitude control method based on a high-order all-drive system approach. The high-order model preserves the physical characteristics of the system, and the all-drive characteristics of the system facilitate controller design. By applying homogeneous system theory, the homogeneity of the model is observed, simplifying the model. The all-drive model and controller are simple in form, do not contain nonlinearity, the control quantity does not change over a large range, converges rapidly, and is more convenient to use. Active suppression of oscillations in the flexible attachments is employed, causing the oscillations to decay rapidly. When the flexible spacecraft's attitude is stable, the flexible attachments no longer oscillate, thus broadening its practical application range. Attached Figure Description

[0062] Figure 1 This is a flowchart of a flexible spacecraft attitude control method according to an embodiment of the present invention.

[0063] Figure 2 This is a diagram showing the attitude change of the flexible spacecraft attitude control system according to an embodiment of the present invention.

[0064] Figure 3 This is a graph showing the angular velocity variation of a flexible spacecraft according to an embodiment of the present invention.

[0065] Figure 4 This is a graph showing the change in attitude control torque of a flexible spacecraft according to an embodiment of the present invention.

[0066] Figure 5 and Figure 6 This is a graph showing the changes between the estimated and actual values ​​of the modal variable observer for the flexible attachments of a flexible spacecraft according to an embodiment of the present invention.

[0067] Figure 7 This is a graph showing the change in the active suppression control quantity of the flexible attachment in an embodiment of the present invention.

[0068] Figure 8 This is a block diagram of a flexible spacecraft attitude control system according to an embodiment of the present invention. Detailed Implementation

[0069] To facilitate understanding of the technical solution of the present invention by those skilled in the art, the technical solution of the present invention will now be further described in conjunction with the accompanying drawings.

[0070] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0071] Please see Figure 1 As shown, the present invention provides a flexible spacecraft attitude control method, comprising the following steps:

[0072] S100, establish the attitude control model and flexible attachment model of the flexible spacecraft.

[0073] S200, based on homogeneous system theory, the attitude control model of the flexible spacecraft and the flexible attachment model are simplified multiple times to obtain a simplified attitude control model of the flexible spacecraft and a simplified flexible attachment model.

[0074] S300, based on the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible accessory model, obtain the all-drive model.

[0075] S400, Integrate the output equations into the flexible attachment model to design an observer, and use the observer to estimate the modal variables in the flexible attachment model. Combine this with the all-drive model and design a controller based on a high-order all-drive system method. Substitute the controller into the all-drive model to obtain a linear closed-loop system.

[0076] S500, based on the parametric design method, obtains a parametric controller and a stable linear closed-loop system.

[0077] In step S100, a geocentric inertial coordinate system O is defined. i -X i Y i Z i The origin O is located at the Earth's center. i O i X i The positive direction of the axis points towards the vernal equinox along the intersection of the ecliptic plane and the equatorial plane. i Z i Pointing to the North Pole, O i Y i With O i X i O i Z i Establish a right-handed coordinate system. Define the orbital coordinate system OX. o Y o Z o Where the origin O is the spacecraft's center of mass, and OZ o The positive direction points to the Earth's center, OX o Axis and OZ o The velocity direction perpendicular to the spacecraft, O i Y i Define a coordinate system that is right-handed and orthogonal to the other two axes. Define the body coordinate system OX. b Y b Z b The origin O of the coordinate system is located at the center of mass of the spacecraft, and the direction of flight is OX. b (Roller axis) Positive direction, OZ b (Yaw axis) positive direction is perpendicular to the planet's ground-mounted surface, OY b The pitch axis forms a right-handed orthogonal coordinate system with the other two axes.

[0078] A flexible spacecraft attitude control model is established using (w,z) parameters:

[0079]

[0080] In the formula, z represents the angle from the reference coordinate system to the intermediate coordinate system during the first rotation under the (w,z) parameters, w1 and w2 are the relevant angle variables from the intermediate coordinate system to the body coordinate system during the second rotation under the (w,z) parameters, and ω = [ω x ,ω y ,ω z ] T This represents the three-axis angular velocities of the spacecraft in its body coordinate system. The (w,z) parameters, i.e., the w-z parameterization, have the fewest possible parameters; singularities can be avoided simply by preventing w1 and w2 from approaching infinity.

[0081] The dynamic equations for the flexible spacecraft can be obtained as follows:

[0082]

[0083] In the formula, ω × The antisymmetric matrix is ​​denoted as the antisymmetric matrix of ω, δ∈R. n×3 R is represented as the coupling matrix between the rigid body at the spacecraft's center and the flexible appendages. n×3 Let R be an n×3 dimensional real space, where n represents the number of flexible modes considered, and J∈R. 3×3 Represented as the moment of inertia matrix, R 3×3 Represented as a 3×3 dimensional real space, η∈R n The modes are represented as flexible structures.

[0084] To ensure the active suppression of oscillations in flexible attachments, the following assumption is introduced: the number of piezoelectric actuators is equal to the number of vibration modes of the system to be controlled. Modeling the flexible attachment yields the following model:

[0085]

[0086] In the formula, u a ∈R n Let K represent the active suppression control quantity for oscillations of flexible attachments, and let C represent the stiffness matrix and C represent the damping matrix.

[0087] The number of modal variables in a flexible attachment is infinite. The lower the modal order, the greater its impact on vibration; generally, only the first few modes are considered for control. Considering the first N modes, ω... ni ,i=1,...,N are the vibration frequencies of the flexible structure, ζ i Let i = 1, ..., N be the damping coefficients. Then the expressions for the damping matrix C and the stiffness matrix K are:

[0088]

[0089] The lower the order of the mode, the greater the impact on the oscillation of the flexible attachment. Generally, only the low-order modes are controlled, so the first three modes are considered.

[0090] Pick The flexible attachment model can be written in state-space equation form as follows:

[0091]

[0092] in,

[0093] In the formula, and Represented as η∈R n and ψ∈R n The modal variable derivative, η∈R n and ψ∈R n Let I represent two different modes of the flexible attachment, where I is the identity matrix of the corresponding dimension, and A and D are matrices, 0 n×n It is represented as an n×n dimensional zero matrix.

[0094] Combining the flexible attachment model and the flexible spacecraft dynamics model, the flexible spacecraft dynamics model can be written in the following form:

[0095]

[0096] In the formula, u=[u x ,u y ,u z ] T ∈R 3 The three-axis control torque of the spacecraft is J0 = J - δ T δ.

[0097] In step S200, using homogeneous system theory, the flexible spacecraft attitude control model and the flexible attachment model are simplified by repeatedly introducing an expansion operator until no nonlinear terms are found in either model, thus obtaining the simplified flexible spacecraft attitude control model and the simplified flexible attachment model. Specifically, the expansion operator δ is introduced. λ :

[0098] δ λ (ω z ,w1,w2,ω x ,ω y z,η,ψ,u,u a )=(λ 2 ω z ,λw1,λw2,λω x ,λω y ,λz,λη,λψ,λu,λua );

[0099] In the formula, λ represents a parameter in homogeneous system theory, used to calculate the degree of the homogeneous system.

[0100] The attitude control model for a flexible spacecraft can then be written in the following form:

[0101]

[0102] in,

[0103] After adding the expansion operator, we have:

[0104]

[0105] In the formula, lim represents the limit.

[0106] In spacecraft dynamics models, In and ω z The homogeneity of the relevant term is 3, higher than other terms, and can be ignored. In the flexible attachment model, the homogeneity with ω... z The homogeneity of the relevant term is 2, higher than that of the other terms, and can be ignored. Using homogeneous system theory, ignoring l1, l2, and l3 yields a simplified model:

[0107]

[0108] in, ω * Represented as not containing ω z Related items.

[0109] Further, we introduce an expansion operator into the above model:

[0110] δ λ (w1,w2,ω,η,ψ,u,u a )=(λw1,λw2,λω,λη,λψ,λu,λu a );

[0111] Furthermore, for ease of identification, the following symbols are introduced:

[0112]

[0113] The attitude control model and flexible attachment model of the flexible spacecraft can then be written in the following form:

[0114]

[0115] After adding the expansion operator, we have:

[0116]

[0117] By neglecting g1 to g6 using homogeneous system theory, the following simplified model can be obtained:

[0118]

[0119] Further, we introduce an expansion operator into the above model:

[0120] δ λ (ω,η,ψ,u,u a )=(λ 2 ω,λ 2 η,λ 2 ψ,λu,λu a );

[0121] For ease of representation, the following symbols are introduced:

[0122]

[0123] The attitude control model and flexible attachment model of the flexible spacecraft can then be written in the following form:

[0124]

[0125] After adding the expansion operator, we have:

[0126]

[0127] Using homogeneous system theory, neglecting g1, g2, g7, g8, g5, and g9, we obtain a simplified model:

[0128]

[0129] Further, we introduce an expansion operator into the above model:

[0130] δ λ (ω,ψ,u a ,u)=(λ 2 ω,λψ,λ 2 u a ,λu);

[0131] For ease of representation, the following symbols are introduced:

[0132]

[0133] The model can be represented in the following form:

[0134]

[0135] Add an expansion operator to the operation:

[0136]

[0137] Using the theory of homogeneous systems, neglecting g1, g2, g7, g 10 ,g 11 ,g 12 This yields the simplified final model:

[0138]

[0139] In step S200, f1~f3, l1~l3, h1~h 12 and g1~g 12 Symbols used only for convenience of representation.

[0140] In step S300, based on the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible appendage model, the derivatives of the attitude variables of the flexible spacecraft and the modal variables of the flexible appendages are differentiated again to obtain the full-drive model, i.e., the model obtained from ... Taking the first derivative, the all-drive model is:

[0141]

[0142] In the formula, M = [w1, w2, z] T ∈R 3 This is represented by the attitude of a flexible spacecraft. diag is represented as a diagonal matrix. It is a constant matrix, is invertible, and satisfies the all-drive conditions of the high-order all-drive system method.

[0143] In step S400, the observer estimates the modal variables of the flexible attachment, which are difficult to measure directly in practice. To facilitate the design of the observer, the following assumption is introduced: a sufficient number of piezoelectric sensors are installed on the flexible attachment to measure the modal displacement during vibration. The observer is then designed by incorporating the output equation into the flexible attachment model, where the incorporation of the output equation into the flexible attachment model has the following expression:

[0144]

[0145] Where, C = [I 0 n×n ]∈R n×2n y∈R n The output is represented as the flexible attachment model, which is actually the modal displacement.

[0146] The flexible attachment model is a linear system, and a Romberg observer can be designed to estimate the modal variables. The designed observer takes the following form:

[0147]

[0148] In the formula, Let η and ψ be the observer's estimates of the unsimplified modal variables of the flexible attachment, respectively. Let L represent the estimated output of the flexible attachment model, and let L represent the observer matrix.

[0149] The observation error is defined as The observation error system can be obtained as follows:

[0150]

[0151] By appropriately selecting the value of the observer matrix L, it can be ensured that the observation error converges rapidly, and the estimated value of the observer is consistent with the actual value.

[0152] Because the all-drive model satisfies the all-drive condition of the higher-order all-drive system method, and combined with the observer, a controller can be designed based on the higher-order all-drive system method. The controller then has the following characteristics:

[0153]

[0154] Among them, A1, A0, This is a constant matrix, which can be selected as needed to optimize the performance of the linear closed-loop system. Adding a controller, the final linear closed-loop system is:

[0155]

[0156] In the formula, 03 represents the 3-dimensional zero vector, 0 n Represented as an n-dimensional zero vector, the resulting closed-loop system is a linear time-invariant system. This can be achieved through proper design of A1, A0, ... The eigenvalues ​​of a linear system can be configured arbitrarily to optimize its performance.

[0157] In step S500, the linear closed-loop system is written in state-space form:

[0158]

[0159] Among them, A 0～1 =[A0 A1], Φ(A 0～1 )and The system matrix is ​​represented as that of a linear closed-loop system, and Φ(A) 0～1 )and The following relationship must be satisfied:

[0160]

[0161] F1 and F2 represent the desired Jordan canonical form in the parametric design method, and V1 and V2 represent the corresponding eigenvector matrices of the desired Jordan canonical form.

[0162] It can be further written as:

[0163]

[0164] Here, Z1 and Z2 are real matrices, and Z1∈R 3×6 ,Z2∈R 3×6 V1(Z1,F1) and V2(Z2,F2) are specifically as follows:

[0165]

[0166] The selection criteria for Z1 and Z2 are as follows:

[0167] detV1(Z1,F1)≠0,detV2(Z2,F2)≠0;

[0168] det represents the value of the corresponding determinant.

[0169] The Jordan canonical form F1, F2 and matrices Z1, Z2 of a linear closed-loop system provide the degrees of freedom for controller design, which can be used to further optimize the stability performance of the linear closed-loop system.

[0170] Please see Figures 1 to 7 As shown, in one embodiment of the present invention, the effectiveness of the controller obtained in this embodiment will be demonstrated below in conjunction with a specific system model. The relevant parameters of the verification system are as follows:

[0171] The final linear closed-loop system has a pole of -1, and F1 and F2 can be designed as follows:

[0172]

[0173] Choose Z1 and Z2 as:

[0174] Z1 = Z2 = [I 3×3 I 3×3 ];

[0175] The corresponding constant matrices A1, A0, can be obtained. Value: Where I represents a 3×3 identity matrix.

[0176] Then we have the rotational inertia matrix:

[0177] By controlling the first three modal variables, the coupling matrix between the spacecraft's central rigid body and flexible appendages is as follows:

[0178] The corresponding vibration frequency in the flexible attachment model: [ω n1 ωn2 ω n3 ] = [0.7681 1.1038 1.8733].

[0179] The damping coefficients corresponding to the flexible attachment model are: [ζ1 ζ2 ζ3] = [0.005607 0.00862 0.01283].

[0180] Observer matrix in the observer: L1=diag(500,300,100), L2=diag(2000,2000,2000).

[0181] The initial values ​​for the spacecraft attitude, modal variables, and observer estimates are set as follows:

[0182]

[0183] Based on the above, we can obtain the following: Figures 2 to 7 The diagram shown illustrates the state changes of the attitude control system for the flexible spacecraft. Figure 2 The graph shows the attitude variation curves w1, w2, z of a flexible spacecraft. The controller based on the high-order all-drive system method can ensure that the attitude of the flexible spacecraft stabilizes rapidly within a certain range. Figure 3 ω is the angular velocity of the flexible spacecraft. x ,ω y ,ω z The change curve shows that the controller can ensure that the angular velocity of the flexible spacecraft stabilizes rapidly during the attitude stabilization process. Figure 4 The graph shows the change in attitude control torque of a flexible spacecraft. Compared with the current spacecraft attitude stabilization control methods in high-order all-drive systems, the control method of this invention does not contain nonlinearity, and the control quantity does not need to compensate for large-scale changes in nonlinearity in the system, and can converge in a short time. Figure 5 and Figure 6 The graph shows the changes between the estimated and actual values ​​of the modal variables of the flexible appendages of a flexible spacecraft. The observer matrix L ensures that the observation error of the observer converges rapidly. Compared with robust control methods, this invention actively suppresses the oscillations of the flexible appendages, causing the oscillations of the flexible appendages to decay rapidly. While the attitude of the flexible spacecraft is stable, the flexible appendages no longer oscillate. Figure 7 The graph shows the change in the active suppression control quantity of the flexible attachment. The active suppression control method does not contain nonlinearity, and the control quantity can converge in a short time.

[0184] Please see Figure 8As shown, the present invention also provides a flexible spacecraft attitude control system, including a flexible model module 10, a simplified module 20, a full-drive model module 30, a linear closed-loop system module 40, and a stabilization module 50. The system comprises the following modules: Flexible Model 10, which establishes a flexible spacecraft attitude control model and a flexible attachment model; Simplification Module 20, which simplifies the flexible spacecraft attitude control model and the flexible attachment model multiple times based on homogeneous system theory to obtain simplified flexible spacecraft attitude control models and simplified flexible attachment models; Full-Drive Model 30, which obtains a full-drive model based on the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible attachment model; Linear Closed-Loop System Module 40, which combines the output equations of the flexible attachment model to design an observer, estimates the modal variables in the flexible attachment model through the observer, designs a controller based on the high-order full-drive system method, substitutes the controller into the full-drive model, and obtains a linear closed-loop system; and Stability Module 50, which obtains a parameterized controller and a stable linear closed-loop system based on a parameterized design method.

[0185] Please see Figure 8 As shown, in one embodiment of the present invention, the linear closed-loop system is obtained through the following formula:

[0186]

[0187] In the formula, M = [w1, w2, z] T ∈R 3 Let η ∈ R represent the attitude of a flexible spacecraft. n Represented as the simplified flexible attachment mode, Let A1, A0, and A0 be the observer's estimates of the pre-simplification flexible attachment modal variable η. It is represented as a constant matrix.

[0188] By appropriately setting the constant matrices A1, A0, To obtain a stable linear closed-loop system.

[0189] Wherein, the constant matrices A1, A0, The selection criteria are:

[0190] Obtain the state-space equations of the linear closed-loop system:

[0191]

[0192] Among them, A 0～1 =[A0 A1], Φ(A 0～1 )and The system matrix is ​​represented as that of a linear closed-loop system, and Φ(A)0～1 )and The following relationship must be satisfied:

[0193]

[0194] F1 and F2 represent the desired Jordan canonical form in the parametric design method, and V1 and V2 represent the corresponding eigenvector matrices of the desired Jordan canonical form; then we have Here, Z1 and Z2 are real matrices, and Z1∈R 3×6 ,Z2∈R 3×6 The selection criteria for Z1 and Z2 are: detV1(Z1,F1)≠0, detV2(Z2,F2)≠0. Here, det represents the value of the corresponding determinant.

[0195] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0196] The above embodiments are merely examples of implementation methods of the invention. The scope of protection of the present invention is not limited to the above embodiments. For those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for attitude control of a flexible spacecraft, characterized in that, Includes the following steps: Establish attitude control models and flexible attachment models for flexible spacecraft; Based on homogeneous system theory, the attitude control model and the flexible attachment model of the flexible spacecraft are simplified multiple times, and the simplified attitude control model and the simplified flexible attachment model of the flexible spacecraft are obtained through the following formulas: ； In the formula, Represented as The angle of the first rotation from the reference coordinate system to the intermediate coordinate system under the given parameters. for The relevant angle variables for the second rotation from the intermediate coordinate system to the body coordinate system under the parameters. Expressed as the three-axis angular velocities of the spacecraft in its body coordinate system. Represented as the moment of inertia matrix, It can be represented as a 3×3-dimensional real number space. , Represented as the coupling matrix between the rigid body at the spacecraft's center and the flexible appendages. Represented as The real space of dimension 1 This represents the number of flexible modes considered. The three-axis control torque of the spacecraft It is represented as a 3-dimensional real number space; The simplified flexible attachment model is obtained through the following formula: ； In the formula, and Represented as two different modes of the flexible attachment, and They are respectively represented as and The derivative, This represents the active suppression control quantity for oscillations of flexible attachments; Based on the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible attachment model, the derivatives of the attitude variables of the flexible spacecraft and the modal variables of the flexible attachments are derived again, and the all-drive model is obtained through the following formula: ； In the formula, This is represented by the attitude of a flexible spacecraft. , Represented as a diagonal matrix; The output equation is incorporated into the flexible attachment model to design an observer, and the modal variables in the flexible attachment model are estimated using the observer. Combined with the all-drive model and based on a high-order all-drive system method, a controller is designed. The controller is then substituted into the all-drive model to obtain a linear closed-loop system. The observer is represented by the following formula: ； in, ; ; In the formula, These represent the observer's modal variables of the flexible attachment before simplification. The estimated value, Represented as an identity matrix of the corresponding dimension. The output is represented as the flexible attachment model. This is represented as an estimate of the output of the flexible attachment model. L Represented as the observer matrix, Represented as a damping matrix, Represented as a stiffness matrix, Represented as A zero matrix of dimension; The controller is obtained through the following formula: ； In the formula, Represented as a constant matrix; The linear closed-loop system is obtained through the following formula: ； By properly setting the constant matrix To obtain a stable linear closed-loop system; Based on the parametric design method, a parametric controller is obtained, as well as a stable linear closed-loop system.

2. The flexible spacecraft attitude control method according to claim 1, characterized in that, By introducing expansion operators multiple times, the attitude control model of the flexible spacecraft and the flexible attachment model are simplified until no nonlinear terms are found in the attitude control model of the flexible spacecraft and the flexible attachment model, and the simplification is stopped to obtain the simplified attitude control model of the flexible spacecraft and the simplified flexible attachment model.

3. The flexible spacecraft attitude control method according to claim 1, characterized in that, The constant matrix The selection criteria were obtained through the following methods: Obtain the state-space equations of the linear closed-loop system: ； in, , and The system matrix is ​​represented as that of a linear closed-loop system, and and The following relationship must be satisfied: ； and Represented as the desired Jordan canonical form in the parametric design method. and Let the eigenvector matrix be the eigenvector matrix corresponding to the expected Jordan canonical form; then we have ;in, and Represented as a real matrix, and ;but and The selection criteria are: ; where det represents the value of the corresponding determinant.

4. A flexible spacecraft attitude control system, based on the flexible spacecraft attitude control method according to any one of claims 1-3, characterized in that, include: The flexible model module is used to build attitude control models and flexible attachment models for flexible spacecraft. The simplification module is used to simplify the attitude control model of the flexible spacecraft and the flexible attachment model multiple times according to the homogeneous system theory to obtain a simplified attitude control model of the flexible spacecraft and a simplified flexible attachment model. The all-drive model module is used to obtain the all-drive model based on the coupling relationship between the simplified flexible spacecraft attitude control model and the simplified flexible attachment model; The linear closed-loop system module is used to combine the output equations of the flexible attachment model to design an observer, and to estimate the modal variables in the flexible attachment model through the observer. Combined with the all-drive model, and based on the high-order all-drive system method, a controller is designed. The controller is then substituted into the all-drive model to obtain the linear closed-loop system. The stabilization module is used to obtain a parameterized controller and a stable linear closed-loop system based on the parametric design method.

5. The flexible spacecraft attitude control system according to claim 4, characterized in that, By properly setting the constant matrix To obtain a stable linear closed-loop system; wherein, the constant matrix The selection criteria are: Obtain the state-space equations of the linear closed-loop system: ; in, , and The system matrix is ​​represented as that of a linear closed-loop system, and and The following relationship must be satisfied: ； and Represented as the desired Jordan canonical form in the parametric design method. and Let the eigenvector matrix be the eigenvector matrix corresponding to the expected Jordan canonical form; then we have ;in, and Represented as a real matrix, and ;but and The selection criteria are: ; where det represents the value of the corresponding determinant.

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