Distributed fault-tolerant control method and system for multi-spacecraft formation attitude system based on fractional-order sliding mode

Abstract

The present invention discloses a distributed fault-tolerant control system for a multi-spacecraft formation attitude system based on a fractional-order sliding mode, belonging to the field of automatic control. The method comprises: first, constructing a multi-spacecraft formation attitude system model, including a spacecraft mixed fault model and a multi-spacecraft formation flight attitude error system. Based on the constructed multi-spacecraft formation attitude system model, a distributed finite state observer is designed based on finite time theory, so that each observer can timely observe its own concentrated interference value and perform effective compensation. Finally, a new distributed collaborative fault-tolerant controller for the multi-spacecraft formation attitude system is designed based on fractional-order sliding mode theory, which can realize fault-tolerant control of the spacecraft formation attitude system, thereby ensuring the stability and reliability of the multi-spacecraft formation attitude system during mission execution.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed fault-tolerant control of a multi-spacecraft formation attitude system, and in particular to a distributed fault-tolerant control method and system for a multi-spacecraft formation attitude system based on a fractional-order sliding mode. Background Art

[0002] With the rapid development of space technology and the continuous expansion of aerospace applications, the missions undertaken by multi-spacecraft formations in orbit are becoming increasingly complex and diverse. However, prolonged exposure to the extreme space environment of alternating high and low temperatures and intense radiation inevitably causes aging of spacecraft components, which can lead to partial or complete failure of actuators. To ensure the stable and reliable operation of multi-spacecraft formation control systems and improve their safety and fault tolerance, it is necessary to fully consider potential actuator failures during the control system design process and design a fault-tolerant control system with targeted fault handling capabilities. This is crucial for improving overall spacecraft performance and ensuring mission success.

[0003] Existing distributed fault-tolerant control methods for multi-spacecraft formation attitude systems typically employ distributed observers to estimate the concentrated disturbances and design controllers to compensate for them. For example, high-order sliding mode fault-tolerant control [Qi Wennian, Wu Aiguo, Zhang Jie. Distributed Fault-Tolerant Attitude Cooperative Control Method for Multi-Spacecraft with Directed Communication [P]. Guangdong Province: CN202311335572.0, 2024-07-02.] first designs a high-order sliding mode disturbance observer to ensure that the integrated disturbance in the control system can be estimated. Based on this, a fault-tolerant attitude control strategy is designed using high-order sliding mode control theory, ensuring that the attitude of each follower spacecraft tracks the estimated attitude and angular velocity of the leader spacecraft output by the distributed observer, and achieving asymptotic convergence of the tracking error to zero. However, traditional sliding mode control suffers from chattering and long settling times, which hinder control performance.

[0004] Therefore, given the multiple interferences that current multi-spacecraft formation attitude systems face when performing complex missions, such as external disturbances, parameter uncertainty, and actuator failures, there is an urgent need for a distributed, collaborative, fault-tolerant control method for multi-spacecraft formation attitude systems that can achieve efficient control under complex, concentrated interference conditions. This novel control method not only ensures rapid attitude stabilization of the multi-spacecraft formation attitude system under complex, concentrated interference conditions, but also improves control accuracy and mission success rate in the ever-changing space environment, further promoting the application of spacecraft in real-world mission environments. Summary of the Invention

[0005] In order to overcome the above-mentioned deficiencies in the prior art, the present invention designs a new distributed fault-tolerant control method and system for a multi-spacecraft formation attitude system based on the non-smooth finite time theory. A new distributed state observer is designed based on the finite time theory, and each observer can timely observe its own concentrated interference value and perform effective compensation. At the same time, a distributed collaborative fault-tolerant controller for the multi-spacecraft formation attitude system is designed based on the fractional-order sliding mode theory, which realizes the consistency of attitude and angular velocity of the spacecraft formation flight system within a finite time. The designed fault-tolerant control system still maintains stable and robust operation of the multi-spacecraft formation attitude system under interference such as actuator failure, external interference, and parameter uncertainty. This technology can meet the requirements of rapidity and robustness of collaborative control of the attitude of multiple spacecraft formations.

[0006] To achieve the above object, the present invention includes the following technical solutions:

[0007] In the first aspect, the present invention provides a distributed fault-tolerant control method for a multi-spacecraft formation attitude system based on a fractional-order sliding mode, comprising the following steps:

[0008] S1. Construct a spacecraft formation attitude dynamics model;

[0009] S11, construct the attitude kinematics and dynamics model of the i-th spacecraft in the rigid spacecraft formation system based on attitude quaternion;

[0010] Consider a spacecraft formation flying system with 1 leading spacecraft and N following spacecraft. The attitude quaternion of the i-th spacecraft is: [q iv ,q i0 ] T , where q iv =[q i1 ,q i2 ,q i3 ] T is the vector part of the quaternion; q i0 is the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics model of the i-th spacecraft is obtained by the following formula:

[0011]

[0012] In the above formula, is the angular velocity of the i-th spacecraft in the rigid body coordinate system, q i0 The derivative of for q iv The derivative of is the identity matrix; ω i The derivative with respect to time; J i0 is the moment of inertia of the i-th spacecraft, τic =[τ i1 ,τ i2 ,τ i3 ] T is the control input of the i-th spacecraft; Represented by the following matrix

[0013]

[0014] S12, introduction of concentrated disturbance variables;

[0015] When certain changes occur in the system parameters, these changes will cause changes in the fault signal, and this change is closely related to the input signal; therefore, the control output signal τ of the i-th spacecraft i (t) F The mathematical expression of With the input signal τ i (t) The result of multiplication; that is:

[0016]

[0017] When an unknown input acts on the system, the change of the fault signal is not affected by the input signal; therefore, the output signal τ(t) F The mathematical description of is equivalent to the input signal τ(t) and the fault signal τ b The sum of (t); its mathematical expression is:

[0018]

[0019] When multiplicative faults and additive faults occur simultaneously in the actuator, this may cause a "stuck" phenomenon, where the actuator does not respond to the control signal and completely loses control. The mathematical expression for the mixed fault is:

[0020]

[0021] definition is the expected value of the control command of the attitude control system of the i-th spacecraft, then the actual output control command of the i-th spacecraft actuator τ i for:

[0022] τ i =Γ i (t)+P i (t)τ ic

[0023] In the above formula, is the bias fault of the i-th spacecraft, is the failure factor matrix, and satisfies in The smaller the value of , the more serious the actuator failure is, and the smaller the actual control torque that can be output is. i When (t) = 0, it means that the actuator has completely failed and will not be able to provide any control torque;

[0024] In the design of the spacecraft formation attitude control system, the influence of the uncertainty of the moment of inertia must be fully considered to ensure effective compensation and the smooth completion of the flight mission; the inertia matrix J of the i-th spacecraft is i By the standard inertia matrix J i0 and the uncertain part of the inertia matrix ΔJ i Composition, namely J i =J i0 +ΔJ i ;get:

[0025]

[0026] make have to:

[0027] Based on the mixed fault actuator model of the i-th spacecraft and the uncertain part model of the inertia matrix, and considering the external interference d0 of the i-th spacecraft, the angular acceleration of the i-th spacecraft in the rigid body coordinate system is for:

[0028]

[0029] In the above formula, τ ia =Γ i (t)+(P i (t)-I i )τ ic , is the angular velocity of the i-th spacecraft in the rigid body coordinate system, ω i The antisymmetric matrix of ;

[0030] Based on the above analysis, under the conditions of external disturbance, uncertainty of inertia matrix and mixed failure of actuator, the kinematic and dynamic models of the i-th spacecraft are rewritten as:

[0031]

[0032] in, is the concentrated interference of the i-th spacecraft. S13, introduces the multi-spacecraft formation flight attitude error system;

[0033] For a multi-spacecraft formation system with a leader, the expected attitude of the leader spacecraft is denoted as The desired angular velocity of the navigator or virtual navigator is ω0. Next, the attitude error quaternion and angular velocity error will be used to describe the spacecraft formation attitude coordination control system, and the error will be defined as:

[0034]

[0035] ω ie =ω i -R i ω0

[0036] Then the kinematic and dynamic equations of attitude tracking error are:

[0037]

[0038] in, is the attitude tracking error quaternion of the i-th spacecraft, ω ie is the angular velocity tracking error of the i-th spacecraft, R i is the rotation matrix from the navigator’s rigid body coordinate system to the i-th spacecraft’s rigid body coordinate system, and and ||R i ||=1 holds.

[0039] S2, distributed observer design based on finite time theory;

[0040] A finite-time disturbance observer is designed for each spacecraft. The designed observer can estimate the concentrated disturbance value d of each spacecraft in the system within a finite time. i , and can effectively compensate for actuator failures, external interference and moment of inertia uncertainty. and They are the spacecraft angular velocity ω i and concentrated disturbance d i The estimated value of ζ is introduced, and two auxiliary variables ζ are introduced. Design a distributed finite state observer of the following form:

[0041]

[0042] In the above formula, d i is the concentrated interference of the i-th spacecraft, d i The derivative of , sign represents the sign function, which is defined as follows:

[0043]

[0044] For the multi-spacecraft formation attitude system under the conditions of actuator failure, external disturbance and uncertainty of rotational inertia, the observer can effectively estimate the unknown concentrated disturbance value in a finite time; that is, when t>t0, Therefore, the observer can be used to effectively estimate the unknown concentrated interference in a limited time, where:

[0045] According to the finite-time non-smooth theory, the designed finite-time disturbance observer can accurately estimate the concentrated disturbance value d received by each spacecraft within a finite time. i .

[0046] S3, Design of a distributed attitude fault-tolerant controller for multiple spacecraft based on fractional-order integral sliding mode;

[0047] S31, design fractional sliding surface;

[0048] First, the tracking error associated with the attitude angle and angular velocity is defined as follows:

[0049]

[0050] In the above formula, is the vector part of the desired attitude quaternion of the i-th spacecraft, is the expected angular velocity of the i-th spacecraft;

[0051] For the spacecraft formation tracking error system, the following fractional-order sliding mode surface is defined for the i-th following spacecraft:

[0052]

[0053] Where i = 1, 2, 3...N, μ1, μ2 are positive constants, p, q are positive odd numbers and satisfy α i is a fractional order and satisfies 0<α i <1, is a fractional differential operator;

[0054] S32, Design of a finite-time fault-tolerant controller for distributed systems;

[0055] According to the fractional-order sliding surface designed above, the following fault-tolerant controller is designed for the i-th spacecraft:

[0056]

[0057] Among them, m i , b i are all positive numbers, η=diag(η1,η2,η3) is a positive real number matrix, β iis the designed adaptive parameter, β i β i The estimated value of parameter β i The adaptive rate is designed as follows:

[0058]

[0059] The controller can ensure that the formation flight attitude error system can asymptotically converge to the origin. That is, the multi-spacecraft formation attitude system can ultimately achieve consistency in attitude and angular velocity.

[0060] S4, inputting the kinematic and dynamic models of the spacecraft in step S1 into the controller in step S3, and obtaining a closed-loop system, namely, a distributed fault-tolerant control system for the multi-spacecraft formation attitude system.

[0061] In a second aspect, the present invention provides a spacecraft fault-tolerant control system based on a fractional-order sliding mode, comprising:

[0062] Spacecraft attitude dynamics model construction module: used to build the attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternions, and introduce the concentrated perturbation model;

[0063] Disturbance observer design module: used to design distributed finite state observers based on finite time theory;

[0064] Distributed Fault-Tolerant Controller Design Module: used to design a distributed cooperative fault-tolerant controller for spacecraft formation attitude systems based on fractional-order sliding mode theory;

[0065] Distributed fault-tolerant control system construction module for multi-spacecraft formation attitude system: used to input the designed distributed fault-tolerant controller of multi-spacecraft formation attitude system into the constructed spacecraft kinematic and dynamic models to obtain a closed-loop system.

[0066] The present invention also provides a computer storage medium and an electronic device, wherein the computer storage medium stores a computer program that, when executed by a processor, implements the steps of the method of the present invention. The electronic device includes a memory and one or more processors, wherein the memory is used to store one or more programs; when the one or more programs are executed by one or more processors, the method of the present invention is implemented.

[0067] Compared with the prior art, the advantages of the present invention are:

[0068] Based on non-smooth finite-time theory, this paper designs a novel distributed fault-tolerant control method and system for a multi-spacecraft formation attitude system. A distributed finite state observer, based on finite-time theory, accurately estimates concentrated disturbances caused by actuator failures, parameter uncertainty, and external disturbances, and provides effective compensation.

[0069] 2. The present invention designs a new distributed collaborative fault-tolerant controller for the attitude system of multiple spacecraft formations based on the fractional-order sliding mode theory, which realizes the consistency of attitude and angular velocity of the spacecraft formation flight system within a limited time. The designed fault-tolerant control system still maintains the stable and robust operation of the multi-spacecraft formation attitude system under interference such as actuator failure, external interference, and parameter uncertainty. Compared with traditional sliding mode control, the proposed fractional-order sliding mode controller has a faster system state convergence speed and can effectively suppress the chattering phenomenon. This technology can meet the requirements of rapidity and robustness of the collaborative control of the attitude of multiple spacecraft formations. This method has high accuracy, the controller does not require complex calculations, and is relatively friendly to the software and hardware cost requirements of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Flowchart of the present invention,

[0071] Figure 2 This is the communication topology diagram of the spacecraft formation system in this example.

[0072] Figure 3 is the control torque response curve of the spacecraft formation system in this example,

[0073] Figure 4 is the finite-time distributed observer disturbance estimation error response curve of the spacecraft formation system in this embodiment,

[0074] Figure 5 is the angular velocity tracking error response curve of the spacecraft formation system in this embodiment,

[0075] Figure 6 This is the attitude angle tracking error response curve of the spacecraft formation system in this embodiment. DETAILED DESCRIPTION

[0076] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0077] Depend on Figure 1 As shown, the spacecraft fault-tolerant control method based on fractional-order sliding mode of the present invention includes the following specific steps:

[0078] S1, constructing a spacecraft formation attitude dynamics model; including:

[0079] S11, construct attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternion;

[0080] S12, introduction of concentrated disturbance variables;

[0081] S13, introduces a multi-spacecraft formation flying attitude error system;

[0082] S2, distributed observer design based on finite time theory; including:

[0083] S21, Design of distributed finite state observer;

[0084] S3, Design of a distributed attitude fault-tolerant controller for multiple spacecraft based on fractional-order integral sliding mode; including:

[0085] S31, design fractional sliding surface;

[0086] S32, Design of finite-time distributed cooperative controller;

[0087] S4, inputting the control protocol in step S3 into the open-loop system controller in step S1, and the resulting closed-loop system is a distributed fault-tolerant control system for the multi-spacecraft formation attitude system.

[0088] In this embodiment, MATLAB 2021b is used as the simulation software to simulate the attitude motion of a multi-spacecraft formation under the interference of actuator failure, external interference, parameter uncertainty, etc. The simulation time is 50 seconds. In order to verify the effectiveness of the proposed fault-tolerant control method, a system consisting of four spacecraft with the following characteristics is designed. Figure 2 Topologically structured spacecraft formation system.

[0089] In this formation system, there are three follower spacecraft, of which the first and third follower spacecraft can directly obtain information from the leading spacecraft, and the second spacecraft cannot obtain information from the leading spacecraft, but can obtain information from the first and third follower spacecraft.

[0090] The inertia matrices J1, J2, J3 and the uncertain parts of the inertia matrices ΔJ1, ΔJ2, ΔJ3 of the three following spacecraft are selected as

[0091]

[0092] The external disturbances suffered by the three following spacecraft are

[0093]

[0094] The initial values ​​of the angular velocities of the three following spacecraft are

[0095] ω1=[0.1,0.2,0.3]T rad / s

[0096] ω2=[0.2,0.2,0.2] T rad / s

[0097] ω3=[0.3,0.2,0.1] T rad / s

[0098] The initial values ​​of the attitude angles of the three following spacecraft are

[0099] q1=[0.8832,0.3,-0.2,0.3] T

[0100] q2=[-0.806,0.5587,0.105,-0.1647] T

[0101] q3=[0.8832,-0.2,0.3,0.3] T

[0102] The angular velocity and attitude angle of the leading spacecraft are

[0103] ω0=[0,0,0] T rad / s,q0=[1,0,0,0] T

[0104] The failure factor matrix and bias failure of the first spacecraft are set as

[0105] P1(t)=diag(0.5,0.4,0.3)

[0106] Γ1(t)=[0.6sin(0.2t),0.6cos(0.3t),0.6sin(0.4t)] T

[0107] The failure factor matrix and bias fault setting of the second spacecraft are:

[0108] P2(t)=diag(0.6,0.4,0.5)

[0109] Γ2(t)=[0.5sin(1.2t),0.5cos(0.2t),0.5sin(0.3t)] T

[0110] The failure factor matrix and bias fault setting of the third spacecraft are:

[0111] P3(t)=diag(0.5,0.4,0.6)

[0112] Γ3(t)=[0.66sin(0.3t),0.65cos(0.4t),0.65sin(0.5t)] T

[0113] The parameters of the finite time observer are selected as: α=1, α=0.5. For each follower spacecraft, the parameters of the sliding surface are selected as

[0114] μ 11 =0.5,μ 12 =0.3,p=5,q=7,α1=0.2

[0115] μ 21 =0.4,μ 22 =0.5,p=5,q=7,α2=0.4

[0116] μ 31 =0.6,μ 32 =0.5,p=5,q=7,α3=0.6

[0117] For each follower spacecraft, the controller parameters are selected as

[0118] m1=20,γ 11 =6,γ 12 =40,

[0119] m2=15,γ 21 =3,γ 22 =35,

[0120] m3=20γ 31 =4,γ 32 =30.

[0121] Figure 3 The control torque response curves of the spacecraft formation system are shown. The black solid line in the figure is the control torque response curve of the leader output by the controller designed by the present invention, the black dotted line is the control torque response curve of follower 1 output by the controller designed by the present invention, the black dotted line is the control torque response curve of follower 2 output by the controller designed by the present invention, and the black dashed line is the control torque response curve of follower 3 output by the controller designed by the present invention.

[0122] Figure 4The figure shows the interference estimation error of a finite-time distributed observer in a spacecraft formation system. The solid black line shows the interference estimation error curve for the leader using the finite-time distributed observer designed by the present invention, the dashed black line shows the interference estimation error curve for follower 1 using the finite-time distributed observer designed by the present invention, the dotted black line shows the interference estimation error curve for follower 2 using the finite-time distributed observer designed by the present invention, and the dashed black line shows the interference estimation error curve for follower 3 using the finite-time distributed observer designed by the present invention. The figure shows that the concentrated interference experienced by the spacecraft can be accurately estimated at approximately 0.1 seconds, and the angular velocity of the virtual spacecraft can also be estimated. Figure 5 The angular velocity tracking error response curves for the spacecraft formation system are shown. The solid black line represents the angular velocity tracking error curve for the leader, the dashed black line represents the angular velocity tracking error curve for follower 1, the dotted black line represents the angular velocity tracking error curve for follower 2, and the dashed black line represents the angular velocity tracking error curve for follower 3. Figure 6 The attitude angle tracking error response curves of the spacecraft formation system are shown. The solid black line represents the leader's attitude angle tracking error curve, the dashed black line represents the attitude angle tracking error curve of Follower 1, the dotted black line represents the attitude angle tracking error curve of Follower 3, and the dashed black line represents the attitude angle tracking error curve of Follower 3. As can be seen from the simulation diagram, although the spacecraft formation has certain attitude errors in the initial stage and is also affected by multiple adverse factors such as external interference, inertia uncertainty, and possible actuator failure, within approximately 15 seconds, the angular velocity tracking errors and attitude quaternion vector tracking errors of each spacecraft in the spacecraft flight formation system converge to the attitude and angular velocity of the leader spacecraft, thus demonstrating the effectiveness of the designed fractional-order fault-tolerant controller.

[0123] It can be clearly seen from the above simulation results that the finite-time observer designed in the present invention can accurately observe and effectively compensate for the concentrated interference value of each following spacecraft, and the controller of the present invention can significantly enhance the stability of the spacecraft formation attitude system.

[0124] In summary, the present invention has a faster convergence speed, can effectively weaken the chattering phenomenon, and improve the control performance of the spacecraft.

[0125] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A distributed fault-tolerant control method for a multi-spacecraft formation attitude system based on fractional-order sliding mode, characterized by: The following steps are involved: S1. Construct a spacecraft formation attitude dynamics model; S2. Design of distributed observer based on finite time theory; S3. Design of a distributed attitude fault-tolerant controller for multiple spacecraft based on fractional-order integral sliding mode; S4, inputting the kinematic and dynamic models of the spacecraft in step S1 into the controller in step S3, and obtaining a closed-loop system, namely, a distributed fault-tolerant control system for the multi-spacecraft formation attitude system; Wherein, step S1 specifically includes the following steps: S11, construct the attitude kinematics and dynamics model of the i-th spacecraft in the rigid spacecraft formation system based on attitude quaternion; Consider a spacecraft formation flying system with 1 leading spacecraft and N following spacecraft. The attitude quaternion of the i-th spacecraft is: [q iv ,q i0 ] T , where q iv =[q i1 ,q i2 ,q i3 ] T is the vector part of the quaternion; q i0 is the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics model of the spacecraft is obtained by the following formula: In the above formula, is the angular velocity of the i-th spacecraft in the rigid body coordinate system, q i0 The derivative of for q iv The derivative of is the identity matrix; ω i The derivative with respect to time; J i0 is the moment of inertia of the i-th spacecraft; τ ic =[τ i1 ,τ i2 ,τ i3 ] T is the control torque of the spacecraft; Represents the following matrix S12, introduction of concentrated disturbance variables; When certain changes occur in the system parameters, these changes will cause changes in the fault signal, and this change is closely related to the input signal; therefore, the control output signal τ of the i-th spacecraft i (t) F The mathematical expression of With the input signal τ i (t) The result of multiplication; that is: When an unknown input acts on the system, the change of the fault signal is not affected by the input signal; therefore, the output signal τ(t) F The mathematical description of is equivalent to the input signal τ(t) and the fault signal τ b The sum of (t); its mathematical expression is: When multiplicative faults and additive faults occur simultaneously in the actuator, this may cause a "stuck" phenomenon, where the actuator does not respond to the control signal and completely loses control. The mathematical expression for the mixed fault is: definition is the expected value of the control command of the attitude control system of the i-th spacecraft, then the actual output control command of the i-th spacecraft actuator τ i for: t i =C i (t)+P i (t)t ic In the above formula, is the bias fault of the i-th spacecraft, is the failure factor matrix, and satisfies in The smaller the value of , the more serious the actuator failure is, and the smaller the actual control torque that can be output is. i When (t) = 0, it means that the actuator has completely failed and cannot provide any control torque; In the design of the spacecraft formation attitude control system, the influence of the uncertainty of the moment of inertia must be fully considered to ensure effective compensation and the smooth completion of the flight mission; the inertia matrix J of the i-th spacecraft is i By the standard inertia matrix J i0 and the uncertain part of the inertia matrix ΔJ i Composition, namely J i =J i0 +ΔJ i ;get: make have to: Based on the mixed fault actuator model of the i-th spacecraft and the uncertain part model of the inertia matrix, and considering the external interference d0 of the i-th spacecraft, the angular acceleration of the i-th spacecraft in the rigid body coordinate system is for: In the above formula, τ ia =Γ i (t)+(P i (t)-I i )τ ic , is the angular velocity of the i-th spacecraft in the rigid body coordinate system, ω i The antisymmetric matrix of ; Based on the above analysis, under the conditions of external disturbance, uncertainty of inertia matrix and mixed failure of actuator, the kinematic and dynamic models of the i-th spacecraft are rewritten as: in, is the concentrated interference of the i-th spacecraft, S13, introduces a multi-spacecraft formation flying attitude error system; For a multi-spacecraft formation system with a leader, the expected attitude of the leader spacecraft is denoted as The desired angular velocity of the navigator or virtual navigator is ω0. Next, the attitude error quaternion and angular velocity error will be used to describe the spacecraft formation attitude coordination control system. The error is defined as: Then the kinematic and dynamic equations of the spacecraft formation attitude tracking error are: in, is the attitude tracking error quaternion of the i-th spacecraft, ω ie is the angular velocity tracking error of the i-th spacecraft, R i is the rotation matrix from the navigator’s rigid body coordinate system to the i-th spacecraft’s rigid body coordinate system, and and ||R i ||=1 holds; In step S2, the distributed finite state observer design specifically includes: A finite-time disturbance observer is designed for each spacecraft. The designed observer can estimate the concentrated disturbance value d of each spacecraft in the system within a finite time. i , and can effectively compensate for actuator failures, external interference and uncertainty in rotational inertia. and They are the spacecraft angular velocity ω i and concentrated disturbance d i The estimated value of ζ is introduced, and two auxiliary variables ζ are introduced. Design a distributed finite state observer of the following form: In the above formula, d i is the concentrated interference of the i-th spacecraft, d i The derivative of , sign represents the sign function, which is defined as follows: For the multi-spacecraft formation attitude system under the conditions of actuator failure, external disturbance and uncertainty of rotational inertia, the observer can effectively estimate the unknown concentrated disturbance value in a finite time; that is, when t>t0, Therefore, the observer is used to achieve effective estimation of unknown concentrated interference in a finite time, where: According to the finite-time non-smooth theory, the designed finite-time disturbance observer can accurately estimate the concentrated disturbance value d received by each spacecraft within a finite time. i .

2. The distributed fault-tolerant control method for a multi-spacecraft formation attitude system based on fractional-order sliding mode according to claim 1 is characterized in that: Step S3 specifically includes the following steps: S31, design fractional sliding surface; First, the tracking error associated with the attitude angle and angular velocity is defined as follows: In the above formula, is the vector part of the desired attitude quaternion of the i-th spacecraft, is the expected angular velocity of the i-th spacecraft; For the spacecraft formation tracking error system, the following fractional-order sliding mode surface is defined for the i-th following spacecraft: Where i = 1, 2, 3...N, μ1, μ2 are positive constants, p, q are positive odd numbers and satisfy α i is a fractional order and satisfies 0<α i <1, is a fractional differential operator; S32, Design of finite-time distributed cooperative fault-tolerant controller; According to the fractional-order sliding surface designed above, the following fault-tolerant controller is designed for the i-th spacecraft: Among them, m i , b i are all positive numbers, η=diag(η1,η2,η3) is a positive real number matrix, β i is the designed adaptive parameter, β i β i The estimated value of parameter β i The adaptive rate is designed as follows: Among them, 0<γ1<γ2<1 is a positive constant, This controller can ensure that the formation flight attitude error system can asymptotically converge to the origin. That is, the multi-spacecraft formation flight system can ultimately achieve consistency in attitude and angular velocity.

3. A spacecraft fault-tolerant control system based on fractional-order sliding mode, characterized by: A method for implementing a distributed fault-tolerant control system of a multi-spacecraft formation attitude system based on a fractional-order sliding mode according to any one of claims 1 to 2, wherein the fault-tolerant control system comprises: Multi-spacecraft formation attitude dynamics model construction module: used to build the attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternions, and introduce the mixed fault model and multi-spacecraft formation flight attitude error system; Disturbance Observer Design Module: used to design a distributed finite state observer based on finite time theory; Distributed Fault-Tolerant Controller Design Module: used to design a distributed cooperative fault-tolerant controller for spacecraft formation attitude systems based on fractional-order sliding mode theory; Distributed fault-tolerant control system construction module for multi-spacecraft formation attitude system: used to input the designed distributed fault-tolerant controller of multi-spacecraft formation attitude system into the constructed spacecraft kinematic and dynamic models to obtain a closed-loop system.

4. A computer storage medium, characterized in that A computer program is stored thereon, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 2 are implemented.

5. An electronic device, characterized in that: The method comprises a memory and one or more processors, wherein the memory is used to store one or more programs; when the one or more programs are executed by the one or more processors, the method according to any one of claims 1 to 2 is implemented.

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