Flexible spacecraft attitude inner-loop control method under external disturbance

Abstract

The application relates to a flexible spacecraft attitude inner mode control method under external interference, in particular to a flexible spacecraft attitude tracking method, and particularly relates to a flexible spacecraft attitude maneuver control method in space operation under unknown frequency disturbance, and belongs to the technical field of spacecraft attitude control. In the case that unknown external disturbance exists and uncertain parameters exist in inertial information, a compound attitude controller based on the combination of an inner mode principle and an adaptive control method is provided, on the basis of realizing high-precision attitude control, asymptotic modal vibration suppression and unknown external disturbance suppression can be realized, the size of a control moment can be adjusted through corresponding parameters, and the compound attitude controller has actual engineering application value and theoretical research value.

Description

TECHNICAL FIELD

[0001] The present application relates to a flexible spacecraft attitude inner mode control method under external interference, in particular to a flexible spacecraft attitude tracking method, and particularly relates to a flexible spacecraft attitude maneuver control method under unknown frequency disturbance in space operation, and belongs to the technical field of spacecraft attitude control. BACKGROUND

[0002] The attitude control of a spacecraft is a very important part of spacecraft control, and normal attitude maneuver is the basis for the spacecraft to perform complex tasks, such as space rendezvous, orbit change, and docking, which all require high-precision attitude control to ensure the completion of complex tasks of the spacecraft.

[0003] In recent years, with the active development of space activities in various countries around the world, various series of spacecraft have emerged in an endless stream. China's "Long March" launch vehicle series, "Shenzhou" spacecraft series, "Chang'e" lunar probe series, etc. The United States' "Columbia", "Challenger", "Discovery", etc. These modern spacecraft carry many flexible devices to perform more complex tasks, such as flexible solar panels, antennas for remote sensing, command, and data transmission functions, and flexible landing plates for preventing rebound during the attachment landing process. Therefore, the attitude control of flexible spacecraft has very important application value.

[0004] Compared with rigid spacecraft, the complexity of flexible spacecraft lies in that the attitude control of flexible spacecraft will inevitably cause modal vibration of flexible devices, and the spacecraft modal vibration is highly coupled with the rigid body matrix, and the modal vibration will affect the control performance and steady state of the system, so the attitude control of flexible spacecraft is much more complex than that of rigid spacecraft. In addition, during space flight, the spacecraft will inevitably be subjected to external disturbances, and these external disturbances often have the characteristics of various forms and parameter positions. For flexible spacecraft, it is a very challenging task to eliminate external disturbances and suppress the influence of modal vibration to achieve high-precision attitude control. SUMMARY

[0005] The technical problem solved by the present application is to provide a flexible spacecraft attitude control method under external interference with uncertain inertia matrix information, and to provide an adaptive attitude control method based on the inner mode principle, which can actively eliminate external interference and uncertain parameters, and can also suppress the modal vibration of flexible devices.

[0006] The technical solution of the present application is as follows:

[0007] A flexible spacecraft attitude inner mode control method under external interference, the method comprising the following steps:

[0008] Step 1, the attitude kinematics model, the attitude dynamics model and the flexible modal vibration model of the flexible spacecraft are established, wherein:

[0009] The attitude kinematics model of the flexible spacecraft is:

[0010] The attitude dynamics model of the flexible spacecraft is:

[0011]

[0012] wherein q(t) = [q1(t), q2(t), q3(t), q4(t)] T is the attitude quaternion of the flexible spacecraft in the body coordinate system, the right upper corner T represents the transpose of the matrix, ω(t) = [ω1(t), ω2(t), ω3(t)] T is the angular velocity of the flexible spacecraft in the body coordinate system; q(ω(t)) = [ω(t), 0] T = [ω1(t), ω2(t), ω3(t), 0] T ; χ(t) is the modal variable caused by the vibration of the flexible device in the flexible spacecraft, is the coupling matrix between the flexible device and the rigid body, is a symmetric positive definite mass inertia matrix with uncertain parameters, ⊙ is a quaternion multiplication operator, ω(t) × is the skew-symmetric matrix of ω(t), u(t) is the control torque to be designed, is an external unknown disturbance, i represents the dimension of the D(t) vector; N i is the number of sinusoidal function disturbances, j = 1, 2, 3…, N i ; C i0 is a step disturbance with unknown parameters, C ij and r ij are the amplitude and phase of the sinusoidal disturbance with unknown parameters, b ij is the frequency of the sinusoidal disturbance with known parameters, and t is time; it should be pointed out that when the disturbance D is not in the above form, the D can be expanded into the form of Fourier series, and our method can still be used;

[0013] The flexible modal vibration model of the flexible spacecraft is:

[0014] wherein, represents the modal variable of the flexible device, is a diagonal damping matrix, is a rigid diagonal matrix, P represents the number of modes, ξ h and ω hrespectively are the damping coefficient and the natural frequency of the flexible device;

[0015] Step 2, the attitude control problem of establishing the attitude kinematics model, the dynamics model and the flexible modal vibration model of the flexible spacecraft established in step 1 is converted into a stabilization problem, specifically:

[0016] Define the attitude error: Where q d (t) = [q d1 (t), q d2 (t), q d3 (t), q d4 (t)] is the desired attitude, q d -1 (t) = [-q d1 (t), -q d2 (t), -q d3 (t), q d4 (t)], then

[0017] Let the desired angular velocity be 0, then the angular velocity error: ω e = ω, then the error closed loop model of the stabilization problem is:

[0018]

[0019]

[0020]

[0021] Step 3, linearize the uncertain parameters J in the error closed loop model of the stabilization problem obtained in step 2, specifically:

[0022] For any vector Since the inertia matrix is symmetric and positive definite, Jz = L(z) [J 11 , J 22 , J 33 , J 23 , J 13 , J 12 ] T Where For the uncertain parameters in J, there is an unknown vector μ, whose dimension is n μ Where 0 ≤ n μ ≤ 6, such that Where And are intermediate variable matrices obtained by calculation, whose dimensions are uniquely determined by the dimensions of the unknown vector μ, let Get Jz = L1(z) μ + L0(z);

[0023] Step 4, design the external disturbance dynamic compensator based on the internal model principle for the uncertainty parameter D in the error closed-loop model of the stabilization problem obtained in step 2, to obtain an external disturbance dynamic compensator, specifically:

[0024] For the disturbance There is a positive integer r i And real number Where i = 1, 2, 3, i represents the dimension of the D(t) vector, so that

[0025]

[0026] Construct the intermediate variable matrix

[0027]

[0028] According to the observability PBH criterion, (Φ i ,Ψ i ) is observable;

[0029] Select an arbitrary nonsingular matrix Let the intermediate variable matrix Then

[0030]

[0031] Take any Hurwitz matrix Select So that (M i ,N i ) is controllable, then the nonsingular matrix Y i satisfies the following Sylvester equation: Y i Φ i -M i Y i =N i Ψ i

[0032] Let θ = [θ1, θ2, θ3] T Then

[0033] M = diag(M1, M2, M3),

[0034] N = diag(N1, N2, N3),

[0035] Y = diag(Y1, Y2, Y3),

[0036] Φ = diag(Φ1, Φ2, Φ3),

[0037] Ψ = diag(Ψ1, Ψ2, Ψ3)

[0038] Constructing the corresponding inner model dynamic disturbance compensator: Wherein, is the inner membrane variable, is a parameter constructed according to the actual situation;

[0039] Step 5, according to the uncertainty parameter J after linearization processing in step 3 and the dynamic disturbance compensator constructed in step 4, design the adaptive control torque u, the specific method is:

[0040] Design the adaptive update law:

[0041]

[0042]

[0043] Wherein, used to estimate the uncertainty parameter μ in J, is the designed auxiliary variable,

[0044]

[0045] is the matrix calculated according to the actual situation in step 3, ρ(ω e , ζ) = [F1(ω e ) + ΨT -1 ζ + G1(ω e )], G1(ω e ) = ΨT -1 NL1(ω e ), Λ is an arbitrary diagonal matrix with positive diagonal elements, which modifies the adaptive update rate;

[0046] The specific form of the designed control torque u is as follows:

[0047]

[0048] Wherein q ev = [q e1 , q e2 , q e3 ] T ,G0(ω e ) = ΨT -1 NL0(ω e ), k1, k2 are parameters that can be designed.

[0049] Compared with the prior art, the present application has the following beneficial effects:

[0050] (1) The application proposes a kinematic model and a dynamic model of a flexible spacecraft with a kind of external unknown disturbance and unknown system parameters, adopts a coordinate conversion method to convert the attitude control problem into a stabilization problem, and obtains an error closed-loop model;

[0051] (2) The application adopts two different control methods to process the above two kinds of unknown parameters, first adopts an internal model principle to process the external unknown disturbance, establishes a dynamic internal model compensator for eliminating the external disturbance, adopts an adaptive control method to process the unknown parameters of the system for estimating the unknown inertia matrix of the system, and based on the internal model compensator and the adaptive control law, designs an adaptive internal model controller for controlling the attitude of the flexible spacecraft, which is different from an ordinary robust controller;

[0052] (3) The controller proposed by the application completely eliminates the influence of unknown external disturbance, realizes true disturbance elimination, simultaneously realizes active suppression of flexible modal vibration, and guarantees the progressive stability of the closed-loop system.

[0053] (4) The application discloses a flexible space probe attitude internal model control method under external disturbance, proposes a composite attitude controller based on the combination of the internal model principle and the adaptive control method in the case that unknown external disturbance and inertia information have uncertain parameters, realizes asymptotic modal vibration suppression and unknown external disturbance suppression on the basis of realizing high-precision attitude control, can adjust the size of the control torque through corresponding parameters, and has practical engineering application value and theoretical research value. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 is a controller structure block diagram of the application;

[0055] Figure 2 is an attitude error four-element change curve in the specific embodiment of the application;

[0056] Figure 3 is an angular velocity error change curve in the specific embodiment of the application;

[0057] Figure 4 is a flexible modal variable change curve in the specific embodiment of the application;

[0058] Figure 5 is a flowchart of the method of the application. DETAILED DESCRIPTION

[0059] The following is a specific embodiment of the application, but it should be understood that the protection scope of the application is not limited by the specific embodiment.

[0060] As Figure 5As shown, the specific control method of the application comprises the following steps:

[0061] P1, establish the kinematics, dynamics model and flexible modal vibration equation of the flexible spacecraft, in this example, the external unknown disturbance is a combination of unknown step disturbance and unknown sinusoidal disturbance.

[0062] The attitude kinematics model of the flexible spacecraft is:

[0063] The attitude dynamics model of the flexible spacecraft is:

[0064]

[0065] Wherein, q(t) = [q1(t), q2(t), q3(t), q4(t)] T is the attitude quaternion of the flexible spacecraft in the body coordinate system, and the right upper corner T represents the transpose of the matrix. ω(t) = [ω1(t), ω2(t), ω3(t)] T is the angular velocity of the flexible spacecraft in the body coordinate system; q(ω(t)) = [ω(t), 0] T = [ω1(t), ω2(t), ω3(t), 0] T ; χ(t) is the modal variable caused by the vibration of the flexible device in the flexible spacecraft, is the coupling matrix between the flexible device and the rigid body, is a symmetric positive definite mass inertia matrix with uncertain parameters, and is a quaternion multiplication operator, ω(t) × is the skew-symmetric matrix of ω(t), u(t) is the control torque to be designed, is an external unknown disturbance, i represents the dimension of the D(t) vector; N i is the number of sinusoidal function disturbances, j = 1, 2, 3…, N i ; C i0 is a step disturbance with unknown parameters, C ij and r ij are the amplitude and phase of the sinusoidal disturbance with unknown parameters, b ij is the frequency of the sinusoidal disturbance with known parameters, and t is time; It should be pointed out that when D is not the form of the above disturbance, D can be expanded into the form of Fourier series, and our method can still be used;

[0066] The flexible modal vibration model of the flexible spacecraft is:

[0067] Wherein, represents the modal variable of the flexible device, is a diagonal damping matrix, is a rigid diagonal matrix, P denotes the number of modes, ξ h and ω h are the damping coefficient and natural frequency of the flexible device, respectively;

[0068] In this embodiment, the inertia matrix contains an unknown parameter J 11 , the damping diagonal matrix is a rigid diagonal matrix the coupling matrix Consider unknown disturbance D i (t) = C i sin(ω i t + l i ), i = 1, 2, 3, where ω1= 0.1, ω2= 0.2, ω3= 0.2, C1= 1, C2= 2, C3= 0.6, l1= 0.1, l2= 0.2, l3= 0.3, Note that the internal model controller in the following only needs to use ω i in the disturbance, that is, C i , l i can be any value, in this embodiment, C i , l i are selected as the above values. The initial attitude quaternion q(0) = [0.3, -0.2, -0.3, 0.8832] T , the initial angular velocity ω(0) = [0, 0, 0] T , the initial flexible vibration mode χ(0) = [0, 0, 0, 0] T , the desired attitude quaternion q d = [-0.24, -0.57, -0.18, 0.77] T

[0069] P2, transformation of the control problem to the stabilization problem

[0070] Define the attitude error: where q d (t) = [q d1 (t), q d2 (t), q d3 (t), q d4 (t)] is the desired attitude, q d -1 (t) = [-q d1 (t), -q d2 (t), -q d3 (t), q d4 (t)], then

[0071] Let the desired angular velocity be 0, then the angular velocity error: ω e = ω, the error closed-loop model of the stabilization problem is:

[0072]

[0073]

[0074]

[0075] P3, linearization is performed on the uncertain parameters in J

[0076] For any vector Since the inertia matrix is symmetric and positive definite, Jz = L(z) [J 11 , J 22 , J 33 , J 23 , J 13 , J 12 T where For the uncertain parameters in J, there is an unknown vector μ with dimension n μ , where 0 ≤ n μ ≤ 6, such that where and are intermediate variable matrices obtained by calculation, whose dimensions are uniquely determined by the dimensions of the unknown vector μ, let Jz = L1(z) μ + L0(z) is obtained;

[0077] In this embodiment, there is an unknown parameter μ = J 11 , then n μ = 1,

[0078] P4, design of internal model compensator for unknown disturbance d

[0079] For the disturbance there is a positive integer r i and a real number where i = 1, 2, 3, i represents the dimension of the D(t) vector, such that

[0080]

[0081] An intermediate variable matrix is constructed

[0082]

[0083] According to the observability PBH criterion, (Φ i ​,Ψ i ) is observable;

[0084] Choose an arbitrary nonsingular matrix Let the intermediate variable matrix Then

[0085]

[0086] Choose an arbitrary Hurwitz matrix Choose such that (M i , N i ) is controllable, then the nonsingular matrix Y i satisfies the following Sylvester equation: Y i Φ i - M i Y i = N i Ψ i

[0087] Let θ = [θ1, θ2, θ3] T Then

[0088] M = diag(M1, M2, M3),

[0089] N = diag(N1, N2, N3),

[0090] Y = diag(Y1, Y2, Y3),

[0091] Φ = diag(Φ1, Φ2, Φ3),

[0092] Ψ = diag(Ψ1, Ψ2, Ψ3)

[0093] Construct the corresponding internal model dynamic disturbance compensator: where, is the internal membrane variable, is a parameter constructed according to the actual situation;

[0094] In this embodiment, D i (t) = C i sin(ω i t + l i ), i = 1, 2, 3, where ω1= 0.1, ω2= 0.2, ω3= 0.2, C1= 1, C2= 2, C3= 0.6, l1= 0.1, l2= 0.2, l3= 0.3, construct Ψ i = [1 0], Then Therefore:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] P5 Design of adaptive control torque u:

[0101] Design of adaptive update law:

[0102]

[0103]

[0104] wherein, is used to estimate the uncertainty parameter μ in J, is a designed auxiliary variable, is a matrix calculated according to actual conditions in step 3, ρ(ω e ,ζ)=[F1(ω e )+ΨT -1 ζ+G1(ω e )],G1(ω e )=ΨT -1 NL1(ω e ),Λ is an arbitrary diagonal matrix with positive diagonal elements, which modifies the adaptive update rate;

[0105] The specific form of the designed control torque u is as follows:

[0106]

[0107] wherein q ev =[q e1 ,q e2 ,q e3 ] T ,G0(ω e )=ΨT -1 NL0(ω e ), k1,k2 are parameters available for design.

[0108] In the embodiment, k1=10, k2=40 are selected.

[0109] Figure 2 Figure 3 ,​​Figure 4 It is shown that, under the corresponding simulation parameters, the designed comprehensive controller can achieve high-precision attitude control and effectively suppress the corresponding flexible mode variable. Figure 1 As shown in the figure, the attitude error, angular velocity error and the change curve of the flexible mode variable. It can be found that the attitude control can be completed with high precision and the corresponding flexible mode variable can be effectively suppressed.

[0110] The advantages of the present application are that: the present application proposes a kinematic model and a dynamic model of a flexible spacecraft with a class of external unknown disturbances and unknown system parameters, uses the method of coordinate transformation to convert the attitude control problem into a stabilization problem, obtains an error closed-loop model, and uses two different control methods to process the above two unknown parameters. First, the internal model principle is used to process the external unknown disturbance, and a dynamic internal model compensator is established to eliminate the external disturbance. An adaptive control method is used to process the unknown parameters of the system to estimate the unknown inertia matrix of the system. Based on the internal membrane compensator and the adaptive control law, an adaptive internal model controller for controlling the attitude of the flexible spacecraft is designed. Unlike ordinary robust controllers, the controller proposed in the present application completely eliminates the influence of unknown external disturbances, realizes true disturbance elimination, simultaneously realizes active suppression of flexible mode vibration, and ensures the asymptotic stability of the closed-loop system. The present application discloses a flexible space probe attitude internal model control method under external disturbance. In the presence of unknown external disturbances and uncertain parameters in the inertia information, a composite attitude controller based on the combination of internal model principle and adaptive control method is proposed. On the basis of realizing high-precision attitude control, asymptotic mode vibration suppression and unknown external disturbance suppression can be realized. The size of the control torque can be adjusted through the corresponding parameters, and it has practical engineering application value and theoretical research value.

[0111] To sum up, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A flexible spacecraft attitude inner-loop control method under external disturbances, characterized in that The method comprises the following steps: Step 1, establishing an attitude kinematics model, a dynamics model and a flexible modal vibration model of the flexible spacecraft; Step 2, converting the attitude control problem of the attitude kinematics model, the dynamics model and the flexible modal vibration model of the flexible spacecraft established in step 1 into a stabilization problem; Step 3, performing linearization processing on the uncertain parameter J in the error closed loop model of the stabilization problem obtained in step 2; Step 4, performing external disturbance dynamic compensator design on the uncertain parameter D in the error closed loop model of the stabilization problem obtained in step 2, to obtain an external disturbance dynamic compensator; Step 5, designing an adaptive control torque u according to the linearized uncertain parameter J in step 3 and the disturbance dynamic compensator constructed in step 4, to complete the attitude internal model control of the flexible spacecraft; In step 1, the established attitude kinematics model of the flexible spacecraft is: The established attitude dynamics model of the flexible spacecraft is: where q(t) = [q1(t), q2(t), q3(t), q4(t)] T is the attitude quaternion of the flexible spacecraft in the body coordinate system, the right upper corner T represents the transpose of the matrix, ω(t) = [ω1(t), ω2(t), ω3(t)] T is the angular velocity of the flexible spacecraft in the body coordinate system; q(ω(t)) = [ω(t), 0] T = [ω1(t), ω2(t), ω3(t), 0] T ; χ(t) is the modal variable caused by the vibration of the flexible device in the flexible spacecraft, is the coupling matrix between the flexible device and the rigid body, is the symmetric positive definite mass inertia matrix with uncertain parameters, ⊙ is the quaternion multiplication operator, ω(t) × is the skew-symmetric matrix of ω(t), u(t) is the control torque to be designed, is the external unknown disturbance, i represents the dimension of the D(t) vector; N i is the number of sinusoidal function disturbances, j = 1, 2, 3…, N i i0 is a step disturbance with unknown parameters, C ij ij is the amplitude and phase of the sinusoidal disturbance with unknown parameters, b ij is the frequency of the sinusoidal disturbance with known parameters, and t is time;​​ The flexible modal vibration model of the flexible spacecraft established is: wherein, denotes the flexible device modal variable, is a damping diagonal matrix, is a stiffness diagonal matrix, P denotes the number of modes, ξ h and ω h are the damping coefficient and natural frequency of the flexible device, respectively; In step 2, the attitude control problem of the attitude kinematics model, the dynamics model and the flexible modal vibration model of the flexible spacecraft is converted into a stabilization problem, specifically as follows: Define the pose error as: where q d (t) = [q d1 (t), q d2 (t), q d3 (t), q d4 (t)] is the desired pose, q d -1 (t) = [-q d1 (t), -q d2 (t), -q d3 (t), q d4 (t)], then Let the desired angular velocity be 0, then the angular velocity error: ω e = ω, then the error closed-loop model of the stabilization problem is: In step 3, the uncertain parameter J in the error closed loop model of the stabilization problem is linearized, specifically as follows: For any vector Since the inertia matrix is symmetric and positive definite, Jz=L(z)[J 11 ,J 22 ,J 33 ,J 23 ,J 13 ,J 12 ] T where For the uncertainty parameter in J, there is an unknown vector μ, whose dimension is n μ where 0≤n μ ≤6, so that where and is an intermediate variable matrix obtained by calculation, whose dimension is uniquely determined by the dimension of the unknown vector μ, let get Jz=L1(z)μ+L0(z); In step 4, the uncertain parameter D in the error closed loop model of the stabilization problem is designed into an external disturbance dynamic compensator based on the internal model principle, to obtain an external disturbance dynamic compensator, specifically as follows: For perturbations there exists a positive integer r i and real numbers where i = 1, 2, 3, i denotes the dimension of the D(t) vector, such that An intermediate variable matrix is constructed According to the observability PBH criterion, (Φ i , Ψ i ) is observable; select any nonsingular matrix Let the intermediate variable matrix then D i (t) = -Ψ i Y i -1 θ i (t) Let H be an arbitrary Hurwitz matrix selecting such that (M i ,N i ) is controllable, then the nonsingular matrix Y i satisfies the Sylvester equation Y i Φ i -M i Y i = N i Ψ i Let θ = [θ1, θ2, θ3] T then M = diag (M1, M2, M3), N = diag (N1, N2, N3), Y = diag (Y1, Y2, Y3), Φ = diag (Φ1, Φ2, Φ3), Ψ = diag (Ψ1, Ψ2, Ψ3) A corresponding inner model dynamic disturbance compensator is constructed: wherein is the intima variable, is a parameter constructed according to the actual situation; In step 5, the adaptive control torque u is designed according to the linearized uncertain parameter J and the disturbance dynamic compensator, specifically as follows: An adaptive updating law is designed as follows: wherein, used to estimate the uncertainty parameters in J are auxiliary variables of the design, is a matrix calculated according to the actual situation, p(ω e , ζ) = [F1(ω e ) + ΨT -1 ζ + G1(ω e )], G1(ω e ) = ΨT -1 NL1(ω e ), Λ is an arbitrary diagonal matrix with positive diagonal elements, which functions to modify the adaptive update rate; The specific form of the control torque u is as follows: where q ev = [q e1 ,q e2 ,q e3 ] T G0(ω e ) = ΨT -1 NL0(ω e ), k1,k2 are parameters available for design.

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