Anti-unwinding flexible spacecraft attitude tracking hybrid control method

Abstract

The application discloses an anti-unwinding flexible spacecraft attitude tracking composite control method, first, based on the quaternion method, a flexible spacecraft attitude tracking error kinematics and dynamics model is established; then, the flexible accessory vibration mode, external environmental disturbance and model uncertainty are regarded as a lumped disturbance, a generalized proportional integral observer is designed, and the lumped disturbance is observed and estimated; finally, a non-singular terminal sliding mode surface is constructed, the lumped disturbance observation and estimation compensation of the generalized proportional integral observer is taken as a feedforward signal, and a feedforward-feedback anti-unwinding attitude tracking composite controller is designed. Through determining appropriate control gain, the closed-loop attitude tracking error system is globally finite time stable, and the anti-unwinding effect can be realized. The application can realize finite time attitude tracking of the flexible spacecraft, has high attitude tracking precision and strong robustness.

Description

Technical Field

[0001] This invention relates to a composite control method for attitude tracking of spacecraft with anti-deflection and deflection resistance, belonging to the field of spacecraft attitude control technology. Background Technology

[0002] With the increasing complexity of space missions such as rendezvous and docking, satellite observation, and regional imaging, spacecraft attitude tracking control faces increasingly higher demands in terms of attitude tracking accuracy, dynamic response speed, and anti-interference capability. In recent years, experts and scholars both domestically and internationally have designed and implemented many different spacecraft attitude tracking control methods, including backstepping, preset performance, and sliding mode control, to address the spacecraft attitude control problem. Among these, sliding mode control has gained widespread application in the field of spacecraft attitude tracking control due to its strong robustness to external disturbances.

[0003] The literature (RQDong, AGWu, and Y. Zhang, “Anti-unwinding sliding-mode attitude maneuver control for rigid spacecraft,” IEEE Transactions on Automatic Control, vol. 67, no. 2, pp. 978-985, 2022.) achieved asymptotically bounded convergence of attitude tracking error for rigid spacecraft by constructing a linear sliding mode surface; furthermore, the literature (Z. Song, H. Li, and Sun, K, “Finite-time control for nonlinear spacecraft attitude based on terminal sliding-mode technique,” ​​ISA Transactions, vol. 53, no. 1, pp. 117-124, 2014.) designed a terminal sliding mode surface to achieve finite-time convergence of attitude tracking error for rigid spacecraft. However, considering the singularity problem of terminal sliding mode, which can limit engineering applications, some experts and scholars have proposed control methods based on non-singular terminal sliding mode for attitude tracking of rigid spacecraft. For example, the literature (D. Lee, “Fault-tolerant finite-time controller for attitude tracking of rigid spacecraft using intermediate quaternion,” IEEE Transactions on Aerospace Electronic Systems, vol.57, no.1, pp.540-553, 2021.) uses the non-singular terminal sliding mode control method to achieve finite-time convergence of attitude tracking error of rigid spacecraft.

[0004] However, on the one hand, the attitude tracking control methods mentioned above are only applicable to rigid spacecraft. In real space missions, spacecraft typically carry flexible attachments such as solar panels, large antennas, and robotic arms. The elastic vibrations of these flexible attachments can affect the spacecraft's attitude tracking accuracy and even cause instability. More importantly, the modal variables describing the vibrations of flexible attachments are difficult to measure directly. Furthermore, external environmental disturbances such as magnetic forces, solar radiation pressure, or gravitational perturbations, as well as model uncertainties, can also affect the tracking accuracy of flexible spacecraft. On the other hand, the attitude tracking control methods mentioned above do not consider the multi-equilibrium problem inherent in quaternion modeling itself, i.e., the attitude error quaternion q. e There are two equilibrium points, namely (1, 0, 0, 0). Tand (-1, 0, 0, 0) T Since it lacks the ability to unwind, the attitude tracking control method mentioned above results in unnecessary waste of control energy.

[0005] This invention addresses the attitude tracking control problem of flexible spacecraft, and designs a decoupling-resistant composite control method for flexible spacecraft attitude tracking under the condition of considering external environmental disturbances. On one hand, this control method treats the flexible appendage vibration modes, external environmental disturbances, and model uncertainties as lumped disturbances, and designs a generalized proportional-integral (PII) observer to effectively estimate these lumped disturbances. On the other hand, after using the lumped disturbance estimation compensation from the PPI observer as a feedforward signal, this control method designs a decoupling-resistant feedforward-feedback attitude tracking composite controller by constructing a non-singular terminal sliding surface. This ensures finite-time convergence of attitude tracking errors, while also possessing decoupling resistance, high tracking accuracy, and strong robustness. Summary of the Invention

[0006] To address the aforementioned problems, this invention discloses a composite control method for attitude tracking of flexible spacecraft with anti-decoupling capabilities. This method can track the reference attitude in finite time while simultaneously achieving anti-decoupling performance. First, a kinematic and dynamic model of the attitude tracking error of the flexible spacecraft is established based on the quaternion method. Then, the vibration modes of the flexible appendages, external environmental disturbances, and model uncertainties are considered as lumped disturbances. A generalized proportional-integral (PII) observer is designed to observe and estimate the lumped disturbances. Finally, a non-singular terminal sliding surface is constructed, and the lumped disturbance observation estimate compensation from the PII observer is used as a feedforward signal to design a feedforward-feedback anti-decoupling attitude tracking composite controller. By determining an appropriate control gain, the closed-loop attitude tracking error system achieves global finite-time stability and anti-decoupling performance. This invention enables finite-time attitude tracking of flexible spacecraft with high accuracy and strong robustness.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] A composite control method for attitude tracking of a spacecraft with anti-deflection and deflection resistance, comprising the following specific steps:

[0009] (1) Based on the quaternion method, establish the kinematics and dynamics model of the attitude of the flexible spacecraft, give the desired attitude trajectory, and then give the kinematics and dynamics model of the attitude tracking error of the flexible spacecraft.

[0010] (2) Based on the kinematic and dynamic model of attitude tracking error of flexible spacecraft in step (1), the vibration mode of flexible attachment, external environmental disturbance and model uncertainty are regarded as lumped disturbance. A generalized proportional integral observer is designed to observe and estimate the lumped disturbance.

[0011] (3) Construct a non-singular terminal sliding surface and, based on the lumped disturbance observation output of the generalized proportional integral observer in step (2), design a feedforward-feedback anti-decoupling attitude tracking composite controller to obtain the control torque input of the flexible spacecraft.

[0012] (4) Substitute the flexible spacecraft control torque input obtained in step (3) into the kinematic and dynamic model of the flexible spacecraft attitude tracking error established in step (1). By determining a suitable control gain, the closed-loop attitude tracking error system can be stabilized globally in finite time and can achieve anti-decoupling effect.

[0013] Furthermore, in step (1), a kinematic and dynamic model of the flexible spacecraft attitude is established based on the quaternion method:

[0014]

[0015]

[0016]

[0017] Where q is the attitude quaternion of the spacecraft's own system relative to the inertial frame. ω is the angular velocity of the spacecraft in the inertial frame. η is the vibration mode coordinate of the flexible attachment. N represents the number of vibration modes of the flexible attachments considered; δ represents the coupling matrix between the rigid body and the flexible attachments. C is the damping matrix. K is the stiffness matrix. d represents the environmental disturbance torque experienced by the spacecraft; J F J is the inertia matrix. F =J R +δ T δ;J R Here, u is the rigid body inertia matrix; u is the control input torque to be designed. right x × Indicates antisymmetric matrix

[0018] definition Let ω be the desired quaternion. d For the desired angular velocity, the attitude tracking error quaternion is... Defined as:

[0019]

[0020]

[0021] And the attitude tracking error quaternion q e and attitude error angular velocity ω ehave:

[0022]

[0023] ω e =ω-Rω d

[0024] Where R is the rotation matrix from the desired constitutive system to the actual constitutive system, and its calculation formula is:

[0025]

[0026] definition J represents the total velocity of the flexible attachment. R =J RN +ΔJ, where J RN Let ΔJ be the nominal inertia of the rigid body and ΔJ be the uncertain inertia of the rigid body. Then, the kinematic and dynamic system model of the attitude tracking error of the flexible spacecraft can be summarized as follows:

[0027]

[0028]

[0029] in,

[0030] Furthermore, in step (2), the vibration modes of the flexible attachment, external environmental disturbances, and model uncertainties are considered as lumped disturbances, and lumped disturbances are defined. Assume lumped disturbance D i The following conditions are met when i = 1, 2, 3:

[0031]

[0032] Among them, a i μ is the coefficient. i If (t) is the remainder term, then l is a positive integer, and Bounded, satisfied

[0033] To estimate the lumped disturbance D, the following generalized proportional-integral observer is designed:

[0034]

[0035] Where, ξ0=[ξ 0，1 ξ 0，2 ξ 0，3 ] T ξ1=[ξ 1，1 ξ 1，2 ξ 1，3 ]T , …, ξ l =[ξ l，1 ξ l，2 ξ l，3 ] T ω e D, ..., D (l-1) The estimate, β j j = 0, ..., l is the observer gain;

[0036] Define estimation error The estimation error system is then...

[0037]

[0038] in,

[0039] Select the observer gain β j If j = 0, ..., l, and A is a Hurwitz matrix, then the estimation error E is bounded and asymptotically converges to the region. Where P is a positive definite real symmetric matrix, and satisfies A T P + PA = -I 3(l+1) c = max{c1, c2, c3}.

[0040] Furthermore, in step (3), the non-singular terminal sliding surface is designed as follows:

[0041] s = sig α (ω e )+ρsgn(q e，0 (0))q e，v

[0042] Where ρ>0, 1<α<2, sig α (x)=|x| α sgn(x),

[0043] Based on the lumped disturbance observation output ξ1 of the generalized proportional-integral observer designed in step two, the feedforward-feedback anti-decoupling attitude tracking composite controller is designed as follows:

[0044]

[0045] in, These are adjustable control parameters.

[0046] Furthermore, in step (4), the torque input u calculated by the attitude tracking composite controller designed in step (3) is substituted into the attitude tracking error kinematics and dynamics model established in step one, so that the sliding mode variable s can reach 0 in a finite time.

[0047] Furthermore, the attitude tracking error q e and ω e It can converge to the equilibrium point in a finite time while effectively avoiding decoupling, that is, there exists a time T that satisfies:

[0048] 1) If q e0 (0)≥0, then

[0049] 2) If q e0 (0) < 0, then

[0050] Because the discontinuous sign function term sgn(s) in the controller can cause chattering, in practical engineering applications, a saturation function sat(s) = [sat(s1), sat(s2), sat(s3)] can be used. T Replace sgn(s) in the controller to obtain continuous control torque input. sat(s) i ), i = 1, 2, 3 are defined as:

[0051]

[0052] Where o represents the boundary layer to be designed;

[0053] Furthermore, the feedforward-feedback anti-decoupling attitude tracking composite controller is further modified as follows:

[0054]

[0055] At this point, the attitude tracking error q e and ω e It can converge to the neighborhood near the equilibrium point in a finite amount of time.

[0056] The beneficial effects of this invention are as follows:

[0057] 1. The anti-deflection flexible spacecraft attitude tracking composite control method proposed in this invention, after considering the vibration of flexible attachments, external environmental disturbances and model uncertainties as lumped disturbances, designs a generalized proportional-integral observer to observe and estimate the lumped disturbances, and uses the disturbance estimate as a feedforward signal to compensate in the controller, effectively improving the robustness of the attitude tracking error system.

[0058] 2. The anti-decoupling flexible spacecraft attitude tracking composite control method proposed in this invention, based on considering the anti-decoupling effect, designs a non-singular terminal sliding surface, and then designs a feedforward-feedback anti-decoupling attitude tracking composite controller, which can achieve finite-time convergence of attitude tracking error, high tracking accuracy, and effectively avoid decoupling at the same time. Attached Figure Description

[0059] Figure 1 This is a block diagram of the control system for the attitude tracking error of the flexible spacecraft of the present invention.

[0060] Figure 2 The first set of numerical simulation experimental results of this invention are shown in the figure, where: (a) is the attitude quaternion tracking error q e The time response curve, (b) shows the angular velocity tracking error ω. e (c) is the time response curve of the lumped disturbance estimation error e1, (d) is the time response curve of the sliding mode variable s, and (e) is the curve of the control torque input u changing with time.

[0061] Figure 3 The first set of numerical simulation experimental results of this invention are shown in the figure, where: (a) is the attitude quaternion tracking error q e The time response curve, (b) shows the angular velocity tracking error ω. e (c) is the time response curve of the lumped disturbance estimation error e1, (d) is the time response curve of the sliding mode variable s, and (e) is the curve of the control torque input u changing with time. Detailed Implementation

[0062] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0063] This embodiment of a spacecraft attitude tracking composite control method with anti-deflection and deflection includes the following steps:

[0064] Step 1: Establish the kinematic and dynamic model of attitude tracking error for flexible spacecraft

[0065] Based on the quaternion method, an attitude kinematics and dynamics model of a flexible spacecraft is established:

[0066]

[0067]

[0068]

[0069] Where q is the attitude quaternion of the spacecraft's own system relative to the inertial frame. ω is the angular velocity of the spacecraft in the inertial frame. η is the vibration mode coordinate of the flexible attachment. N represents the number of vibration modes of the flexible attachments considered; δ represents the coupling matrix between the rigid body and the flexible attachments. C is the damping matrix. K is the stiffness matrix. d represents the environmental disturbance torque experienced by the spacecraft; J F J is the inertia matrix. F =J R +δ T δ;J R Here, u is the rigid body inertia matrix; u is the control input torque to be designed. right x × Indicates antisymmetric matrix

[0070] definition Let ω be the desired quaternion. d For the desired angular velocity, the attitude tracking error quaternion is... Defined as:

[0071]

[0072]

[0073] And the attitude tracking error quaternion q e and attitude error angular velocity ω e have:

[0074]

[0075] ω e =ω-Rω d

[0076] Where R is the rotation matrix from the desired constitutive system to the actual constitutive system, and its calculation formula is:

[0077]

[0078] definition J represents the total velocity of the flexible attachment. R =J RN +ΔJ, where J RN Let ΔJ be the nominal inertia of the rigid body and ΔJ be the uncertain inertia of the rigid body. Then, the kinematic and dynamic system model of the attitude tracking error of the flexible spacecraft can be summarized as follows:

[0079]

[0080]

[0081] in,

[0082] Step 2: Treat the vibration modes of the flexible attachment, external environmental disturbances, and model uncertainties as lumped disturbances, and design a generalized proportional-integral observer to observe and estimate the lumped disturbances.

[0083] Define lumped interference Assume lumped disturbance D i The following conditions are met when i = 1, 2, 3:

[0084]

[0085] Among them, a i μ is the coefficient. i If (t) is the remainder term, then l is a positive integer, and Bounded, satisfied

[0086] To estimate the lumped disturbance D, the following generalized proportional-integral observer is designed:

[0087]

[0088] Where, ξ0=[ξ 0，1 ξ 0，2， ξ0 ，3] T ξ1=[ξ 1，1 ξ 1，2 ξ 1，3 ] T ,…,ξ l =[ξ l，1 ξ l，2 ξ l，3 ] T ω e D, ..., D (l-1) The estimate, β j j = 0, ..., l is the observer gain;

[0089] Define estimation error The estimation error system is then...

[0090]

[0091] in,

[0092] Select the observer gain β j If j = 0, ..., l, and A is a Hurwitz matrix, then the estimation error E is bounded and asymptotically converges to the region. Where P is a positive definite real symmetric matrix, and satisfies A T P + PA = -I 3(l+1) c = max{c1, c2, c3}.

[0093] Step 3: Construct a non-singular terminal sliding mode surface, design a feedforward-feedback anti-decoupling attitude tracking composite controller, and obtain the control torque input for the flexible spacecraft.

[0094] The non-singular terminal sliding surface is designed as follows:

[0095] s = sig α (ω e )+ρsgn(q e，0 (0))q e，v

[0096] Where ρ>0, 1<α<2, sig α (x)=|x| α sgn(x),

[0097] Based on the lumped disturbance observation output ξ1 of the generalized proportional-integral observer designed in step two, the feedforward-feedback anti-decoupling attitude tracking composite controller is designed as follows:

[0098]

[0099] in, These are adjustable control parameters.

[0100] Step 4: Substitute the flexible spacecraft control torque input u into the kinematic and dynamic model of the flexible spacecraft attitude tracking error.

[0101] Substituting the torque input u calculated by the attitude tracking composite controller designed in step (3) into the attitude tracking error kinematics and dynamics model established in step one, the sliding mode variable s can reach 0 in finite time;

[0102] Furthermore, the attitude tracking error q e and ω e It can converge to the equilibrium point in a finite time while effectively avoiding decoupling, that is, there exists a time f that satisfies:

[0103] 1) If q e0 (0)≥0, then

[0104] 2) If q e0 (0) < 0, then

[0105] Because the discontinuous sign function term sgn(s) in the controller can cause chattering, in practical engineering applications, a saturation function sat(s) = [sat(s1), sat(s2), sat(s3)] can be used. T Replace sgn(s) in the controller to obtain continuous control torque input. sat(s) i ), i = 1, 2, 3 are defined as:

[0106]

[0107] Where σ is the boundary layer to be designed;

[0108] Furthermore, the feedforward-feedback anti-decoupling attitude tracking composite controller is further modified as follows:

[0109]

[0110] At this point, the attitude tracking error q e and ω e It can converge to the neighborhood near the equilibrium point in a finite amount of time.

[0111] Numerical simulation experiment

[0112] To verify the effectiveness of the anti-deflection and deflection spacecraft attitude tracking composite control method proposed in this invention, two sets of numerical simulation experiments were designed.

[0113] In the simulation experiment, the spacecraft model and control parameters were set as follows: d=[sin(0.4t), 1.2cos(0.5t), 0.8cos(0.7t)] T N·m, α=1.2, ρ=1.2, k=0.2, β0=14, β1=69, β2=140, β3=100, σ=0.001, q d =[1, 0, 0, 0] T ω d = [0.1, -0.1, 0.2] T rad / s.

[0114] In the first group of numerical simulation experiments, the initial conditions were set as follows: q(0) = [0.7, 0.3, -0.2, 0.6164] T ω(0) = [0, 0, 0] T rad / s, η(0)=[-0.01, 0.02, 0.01] T rad / s, ξ i (0) = [0, 0, 0] T , i = 0, 1, 2, 3. Simulation results are as follows: Figure 2 As shown. Where (a) is the attitude quaternion tracking error q e The time response curve, (b) shows the angular velocity tracking error ω. e (c) is the time response curve of the lumped disturbance estimation error e1, (d) is the time response curve of the sliding mode variable s, and (e) is the curve of the control torque input u changing with time.

[0115] In the second group of numerical simulation experiments, the initial conditions were set as follows: q(0) = [-0.7, 0.3, -0.2, 0.6164] T ω(0) = [0, 0, 0] T rad / s, η(0)=[-0.01, 0.02, 0.01] T rad / s, ξ i (0) = [0, 0, 0] T , i = 0, 1, 2, 3. Simulation results are as follows: Figure 3 As shown. Where (a) is the attitude quaternion tracking error q e The time response curve, (b) shows the angular velocity tracking error ω. e (c) is the time response curve of the lumped disturbance estimation error e1, (d) is the time response curve of the sliding mode variable s, and (e) is the curve of the control torque input u changing with time.

[0116] It should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. For those skilled in the art, several improvements and modifications can be made on the basis of the above embodiments without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A composite control method for attitude tracking of a spacecraft with anti-descent and deflection resistance, characterized in that, The specific steps are as follows: (1) Based on the quaternion method, establish the kinematics and dynamics model of the attitude of the flexible spacecraft, give the desired attitude trajectory, and then give the kinematics and dynamics model of the attitude tracking error of the flexible spacecraft. (2) Based on the kinematic and dynamic model of attitude tracking error of flexible spacecraft in step (1), the vibration mode of flexible attachment, external environmental disturbance and model uncertainty are regarded as lumped disturbance. A generalized proportional integral observer is designed to observe and estimate the lumped disturbance. (3) Construct a non-singular terminal sliding surface, and based on the lumped disturbance observation output of the generalized proportional integral observer in step (2), design a feedforward-feedback anti-decoupling attitude tracking composite controller to obtain the control input torque of the flexible spacecraft. (4) Substitute the flexible spacecraft control input torque obtained in step (3) into the kinematic and dynamic model of the flexible spacecraft attitude tracking error established in step (1). By determining a suitable control gain, the closed-loop attitude tracking error system can be stabilized globally in finite time and achieve anti-decoupling effect.

2. The anti-deflection and deflection-resistant spacecraft attitude tracking composite control method according to claim 1, characterized in that, Step (1) specifically includes: First, based on the quaternion method, an attitude kinematics and dynamics model of the flexible spacecraft is established: ; in, Let be the attitude quaternion of the spacecraft's intrinsic system relative to the inertial frame. ; The angular velocity of the spacecraft in the inertial frame. ; For the vibration mode coordinates of the flexible attachment, ; The number of vibration modes of the flexible attachment to be considered; Let be the coupling matrix between the rigid body and the flexible attachment. ; Here is the damping matrix. ; Here is the stiffness matrix. ; The environmental disturbance torque experienced by the spacecraft; The inertia matrix, ; The inertia matrix of the rigid body; For the control input torque to be designed, ; ,right , Indicates antisymmetric matrix ; definition For the desired quaternion, For the desired angular velocity, the attitude tracking error quaternion is... Defined as: ; And attitude tracking error quaternion and attitude error angular velocity have: ; in, The rotation matrix from the desired system to the actual system is calculated using the following formula: ; definition Indicates the total velocity of the flexible attachment. ,in This represents the nominal inertia of the rigid body. Considering the uncertain inertia of the rigid body, the kinematic and dynamic model of the attitude tracking error of the flexible spacecraft can be summarized as follows: ; ; in, , .

3. The anti-deflection and deflection-resistant spacecraft attitude tracking composite control method according to claim 2, characterized in that: In step (2), the vibration modes of the flexible attachment, external environmental disturbances, and model uncertainties are considered as lumped disturbances, and lumped disturbances are defined. Assuming lumped interference satisfy: ; in, For coefficients, If the remainder is a term, then , It is a positive integer, and Bounded, satisfied ; To estimate lumped interference Design the following generalized proportional-integral observer: ; in, , ,…, They are respectively , ,…, The estimate, For observer gain; Define estimation error , ,…, Then the estimation error system is ; in, , , ; Selecting the observer gain ,make If it is a Hurwitz matrix, then the estimation error is... Bounded and asymptotically convergent to the region ,in It is a positive definite real symmetric matrix, and satisfies , .

4. The anti-deflection and deflection-resistant spacecraft attitude tracking composite control method according to claim 3, characterized in that: In step (3), the non-singular terminal sliding surface is designed as follows: ; in, , , , ; Lumped interference observation output based on the generalized proportional-integral observer designed in step two The feedforward-feedback anti-decoupling attitude tracking composite controller is designed as follows: ; in, These are adjustable control parameters.

5. The anti-deflection and deflection-resistant spacecraft attitude tracking composite control method according to claim 4, characterized in that: In step (4), the control input torque calculated by the feedforward-feedback anti-decoupling attitude tracking composite controller designed in step (3) is... Substituting the kinematic and dynamic model of attitude tracking error established in step one, the sliding mode variables are then... Limited time available ; Furthermore, attitude tracking error quaternions and attitude error angular velocity It can converge to the equilibrium point in a finite time while effectively avoiding decoupling, i.e., there exists a time interval... ,satisfy: 1) If ,but , ; 2) If ,but , ; Because the feedforward-feedback anti-unwinding attitude tracking composite controller contains discontinuous sign function terms. This can cause chattering; therefore, in practical engineering applications, a saturation function can be used. Replacing the feedforward-feedback anti-unwinding attitude tracking composite controller To obtain continuous control input torque; Defined as: ; in, For the boundary layer to be designed; Furthermore, the feedforward-feedback anti-decoupling attitude tracking composite controller is further modified as follows: ; At this point, the attitude tracking error quaternion and attitude error angular velocity It can converge to the neighborhood near the equilibrium point in a finite amount of time.

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