Fractional order sliding mode-based spacecraft fault-tolerant control method and system

Abstract

The invention discloses a spacecraft fault-tolerant control method and system based on a fractional order sliding mode, and belongs to the field of automatic control. The method comprises the following steps: firstly, constructing a spacecraft attitude dynamics model, including spacecraft mixed fault actuator modeling, spacecraft inertia matrix uncertainty part modeling and spacecraft external disturbance modeling; and designing a centralized disturbance observer of the spacecraft based on a finite time theory according to the constructed spacecraft attitude dynamic model, and compensating centralized disturbance of the spacecraft. Secondly, a novel spacecraft attitude finite time fault-tolerant controller is designed based on the fractional order sliding mode theory, it is ensured that the spacecraft can stably reach and maintain the expected attitude and angular velocity state within the finite time, finally, the fault-tolerant controller is combined with the event triggering technology, a spacecraft attitude system event triggering mechanism is designed, and the fault-tolerant controller is used for controlling the attitude of the spacecraft. The updating frequency of the controller is reduced, and the consumption of communication resources between the control center and the spacecraft is avoided, so that the efficiency and reliability of the spacecraft in the task execution process are improved.

Description

Technical Field

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

[0002] The spacecraft attitude control system is a core component of aerospace technology. It is responsible for accurately controlling the directional attitude of the spacecraft in the space environment. The system is mainly composed of key components such as attitude sensors, controllers and actuators, forming a tight working mechanism. The attitude sensor is responsible for real-time monitoring of the attitude information of the spacecraft, and the controller efficiently processes this information and instructions from the navigation or guidance system to generate precise control signals. Subsequently, the actuator generates the necessary control torque based on these control signals to ensure that the spacecraft can stably and accurately maintain or adjust its attitude. Therefore, the spacecraft attitude control system plays a vital role in ensuring the stability and operability of the spacecraft during flight, and is an indispensable technical support in the aerospace field.

[0003] In the existing spacecraft fault-tolerant control methods, for the spacecraft fault-tolerant control under concentrated interference, the observer is generally used to estimate the concentrated interference of the spacecraft and compensate it by designing a controller, such as adaptive fault-tolerant sliding mode control [Yang Yuxuan, Chen Ming. Finite-time adaptive fault-tolerant sliding mode control for spacecraft attitude tracking [J]. Journal of Liaoning University of Science and Technology, 2023, 46(02): 120-126.], firstly, an adaptive fixed-time interference observer is designed to ensure that the comprehensive disturbance in the control system can be estimated within a fixed time; on this basis, the sliding mode control theory is used to design a fixed-time attitude fault-tolerant control strategy. However, the jitter problem and long stabilization time of traditional sliding mode control limit the improvement of control performance. In addition, the limited resources faced by spacecraft during operation, such as energy and computing power, have an impact on communication and computing power, further leading to a decline in spacecraft control performance.

[0004] Therefore, in view of the various interferences faced by current on-orbit spacecraft under limited communication resources, such as external interference, parameter uncertainty, actuator failure, etc., there is an urgent need for a spacecraft fault-tolerant control system that can achieve efficient control under complex concentrated interference conditions. This new control system can not only ensure the rapid attitude stabilization of the spacecraft under complex concentrated interference, but also improve the control accuracy and mission success rate in a changing space environment, while reducing the waste of spacecraft energy under limited communication resources, and further promote the application of spacecraft in real mission environments. Summary of the invention

[0005] In order to overcome the defects in the above-mentioned prior art, the present invention designs a new spacecraft fault-tolerant control method and system based on the non-smooth finite time theory. A new disturbance observer is designed based on the finite time theory to accurately estimate the concentrated disturbance caused by factors such as actuator failure, parameter uncertainty and external disturbance, and provide effective compensation. A spacecraft finite time fault-tolerant controller is designed based on the fractional order sliding mode theory, so that the attitude angle and angular velocity of the spacecraft reach the desired state within a limited time. On this basis, an event trigger mechanism is designed to reduce the update frequency of the control input and reduce the waste of spacecraft energy. The designed spacecraft fault-tolerant control system still maintains stable and robust operation of the spacecraft under the conditions of limited communication resources, actuator failure, external disturbance, parameter uncertainty, etc. This technology can meet the requirements of rapidity and robustness of spacecraft attitude control.

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

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

[0008] S1. Construct spacecraft attitude dynamics model;

[0009] S11, construct attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternion;

[0010] Consider the quaternion part of the spacecraft's attitude as: [q v ,q0] T , where q v =[q1,q2,q3] T is the vector part of the quaternion; q0 is the scalar part of the quaternion; based on the defined attitude quaternion, the attitude kinematics and dynamics model of the spacecraft can be obtained by the following formula:

[0011]

[0012] In the above formula, is the angular velocity of the spacecraft in the rigid body coordinate system, is the derivative of q0, for q v The derivative of is the identity matrix. is the time derivative of ω; J0 is the moment of inertia of the ith satellite, τ=[τ1,τ2,τ3] T is the control torque of the spacecraft; ω × The following matrix is ​​represented

[0013]

[0014] S12, introduction of concentrated disturbance variables;

[0015] When certain changes occur in system parameters, these changes will cause changes in the fault signal, and this change is closely related to the input signal. Therefore, the output signal τ(t) F The mathematical expression of can be regarded as a fault signal The result of multiplying the input signal τ(t). 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 can be equivalently expressed as 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 lead to a "stuck" phenomenon, where the actuator does not respond to the control signal and completely loses control. The mixed fault is expressed by a mathematical expression, namely:

[0020]

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

[0022] τ=Γ(t)+P(t)τ c

[0023] In the above formula, is the spacecraft bias fault, is the failure factor matrix,

[0024] And meet in The smaller the value, the more serious the actuator failure is, and the smaller the actual control torque that can be output is. When P(t) = 0, it means that the actuator has completely failed and will not be able to provide any control torque.

[0025] In the design of the spacecraft 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 spacecraft inertia matrix J is composed of the standard inertia matrix J0 and the uncertain part of the inertia matrix ΔJ, that is, J = J0 + ΔJ. It can be obtained:

[0026]

[0027] make We can get:

[0028] Based on the spacecraft mixed fault actuator model and the uncertain part model of the inertia matrix, and considering the external disturbance d0 of the spacecraft, the angular acceleration of the spacecraft in the rigid body coordinate system is for:

[0029]

[0030] In the above formula, τ a =Γ(t)+(P(t)-I)τ c , is the angular velocity of the spacecraft in the rigid body coordinate system, ω × is the antisymmetric matrix of ω.

[0031] Based on the above analysis, under the conditions of external disturbance, uncertain part of inertia matrix and mixed failure of actuator, the kinematic and dynamic model of a single spacecraft can be rewritten as:

[0032]

[0033] To concentrate interference.

[0034] S2. Design of disturbance observer based on finite time theory;

[0035] For the spacecraft, considering multiple interference factors such as actuator failure, external disturbance and uncertain part of inertia matrix, we assume and are the estimated values ​​of the spacecraft angular velocity ω and the concentrated disturbance d, respectively. The finite-time disturbance observer is designed as follows:

[0036]

[0037] In the above formula, d is the concentrated interference. is the derivative of d, sign represents the sign function, and is defined as follows:

[0038]

[0039] The observer can effectively estimate the unknown concentrated interference value in a finite time. That is, when t>t0,

[0040] It can be known from the finite-time non-smoothness theory that the finite-time disturbance observer designed in the present invention can accurately estimate the concentrated disturbance value d suffered by the spacecraft within a finite time.

[0041] S3. Design of finite-time fault-tolerant controller for spacecraft attitude based on fractional-order sliding mode theory;

[0042] S31, design fractional sliding surface;

[0043] First, the tracking error associated with the attitude angle and angular velocity is defined as follows:

[0044] q e =q ν -q r

[0045] ω e =J0ω-J0ω r

[0046] In the above formula, is the vector part of the desired attitude quaternion, is the desired angular velocity.

[0047] Select the following fractional sliding surface:

[0048]

[0049] Where, μ1=diag(μ 11 ,μ 12 ,μ 13 ), μ2=diag(μ 21 ,μ 22 ,μ 23 ) are two constant diagonal matrices, each component of which is a positive number greater than zero. α1, α2 are fractional orders and satisfy 0<α1, α2<1. γ1, γ2 are exponentials and satisfy 0<γ1, γ2<1. D a (x) is a fractional differential operator.

[0050] S32, design a finite-time fault-tolerant controller;

[0051] According to the fractional-order sliding surface designed above, the following controller form is given:

[0052]

[0053] Among them, 0<λ<1, |s| 1-λ =diag(|s1| 1-λ ,|s2| 1-λ ,|s3| 1-λ ), η=diag(η1,η2,η3) is a positive real matrix. And

[0054] is an adaptive time-varying matrix and is defined as follows:

[0055]

[0056] In the above formula, η max yes An upper bound for , positive parameter The saturation function sat(x) is defined as:

[0057]

[0058] The controller can ensure that the expected tracking errors of the spacecraft's attitude and angular velocity converge to a domain within a finite time. That is, the attitude and angular velocity of the spacecraft will approach the expected value within a finite time. S4. Design of event trigger mechanism for spacecraft attitude system;

[0059] S41, design event triggering mechanism;

[0060] First, define the error equation of the trigger control torque and the current event control torque as follows:

[0061]

[0062] In the above formula, τ c (t) represents the control torque when the kth event is triggered, t∈[t k ,t k+1 ],k=0,1,2...,n,t0=0,where t k and t k+1 are two adjacent triggering time instants, with τ c (t) remains constant. The triggering time t under this scheme k+1 Evaluated by:

[0063]

[0064] in, These are the parameters to be designed in the event triggering mechanism.

[0065] In the designed event trigger mechanism, the value τ is transmitted through the wireless network only when the predefined trigger condition is violated. c (t) is updated to the actuator. Therefore, the spacecraft receives aperiodic updates τ of the control input c (t k ), instead of updating τ in continuous time c (t). Therefore, under the designed event trigger mechanism, the control input is expressed as:

[0066]

[0067] S5. Input the control protocol in step S4 into the system controller in step S1. The resulting closed-loop system is the spacecraft fault-tolerant control system.

[0068] In a second aspect, the present invention provides a spacecraft fault-tolerant control system based on fractional-order sliding mode, comprising:

[0069] Spacecraft attitude dynamics model construction module: used to construct the attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternion, and introduce the concentrated perturbation model;

[0070] Disturbance observer design module: used to design disturbance observer based on finite time theory;

[0071] Finite-time fault-tolerant controller design module: used to design a finite-time fault-tolerant controller for spacecraft attitude based on fractional-order sliding mode theory;

[0072] Event trigger mechanism design module: used to reduce the communication frequency between the spacecraft and the control center;

[0073] Spacecraft fault-tolerant control system construction module: used to input the designed spacecraft fault-tolerant control system into the constructed spacecraft kinematic and dynamic models to obtain a closed-loop system.

[0074] In addition, the present invention also provides a computer storage medium and an electronic device, wherein a computer program is stored on the computer storage medium, and when the computer program is executed by a processor, the steps of the method of the present invention are implemented. The electronic device includes a memory and one or more processors, and 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.

[0075] Compared with the prior art, the advantages of the present invention are:

[0076] 1. Based on the non-smooth finite time theory, this paper designs a new fault-tolerant control method and system for spacecraft. Based on the finite time theory, a new disturbance observer is designed to accurately estimate the concentrated disturbance caused by actuator failure, parameter uncertainty, external disturbance and other factors, and provide effective compensation.

[0077] 2. The present invention designs a finite-time fault-tolerant controller for spacecraft based on fractional-order sliding mode theory, which enables the attitude angle and angular velocity of the spacecraft to reach the desired state within a finite time. The designed fault-tolerant control system can still maintain stable and robust operation of the spacecraft under interferences 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 method has high accuracy, the controller does not require complex calculations, and is more friendly to the system's software and hardware cost requirements.

[0078] 3. The present invention designs a dynamic event-triggered control strategy for spacecraft based on event-triggered theory, which can reduce the update frequency of control input and the waste of spacecraft energy when the spacecraft has limited communication resources, thereby further improving the control performance of the spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flow chart of the present invention.

[0080] Figure 2 This is the control torque response curve of the spacecraft attitude system in this example.

[0081] Figure 3 : is the finite time observer disturbance estimation error response curve of the spacecraft in this embodiment.

[0082] Figure 4 This is the tracking error response curve of the spacecraft angular velocity in this embodiment.

[0083] Figure 5 4 is the tracking error response curve of the spacecraft quaternion component in this embodiment.

[0084] Figure 6 This is the execution interval diagram under the event-triggered control strategy. DETAILED DESCRIPTION

[0085] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0086] like Figure 1 As shown, the spacecraft fault-tolerant control method based on fractional order sliding mode of the present invention comprises the following specific steps:

[0087] S1, spacecraft concentrated interference modeling; including:

[0088] S11, Modeling of hybrid fault actuators in spacecraft;

[0089] S12, modeling of the uncertain part of the spacecraft inertial matrix and modeling of the external disturbance of the spacecraft;

[0090] S2, Disturbance Observer Design Based on Finite Time Theory; including:

[0091] S21, design disturbance observer;

[0092] S22, Stability analysis of finite-time disturbance observer;

[0093] S3, Design of finite-time fault-tolerant controller for spacecraft attitude based on fractional-order sliding mode theory; including:

[0094] S31, Design of a finite-time fault-tolerant controller for spacecraft attitude;

[0095] S32, stability analysis of finite-time fault-tolerant controller;

[0096] S4, design of event trigger mechanism for spacecraft attitude system;

[0097] S41, design event triggering mechanism;

[0098] S5, input the control protocol in step S4 into the open-loop system controller in step S1, and the resulting closed-loop system is the spacecraft fault-tolerant control system.

[0099] In this embodiment, MATLAB 2021b is used as the simulation calculation software to simulate the attitude motion of the spacecraft under interference such as actuator failure, external interference, parameter uncertainty, etc., and the spacecraft fault-tolerant control method and system based on fractional-order sliding mode are output to output the attitude value during the attitude motion process.

[0100] In order to prove the effectiveness and superiority of the control algorithm proposed in the invention, this example chooses to compare with an integer-order sliding mode controller:

[0101]

[0102] Set the initial attitude angle and initial angular velocity to:

[0103] q=[0.8832,0.3,-0.2,0.3] T ,ω=[0.1,0.2,0.3] T rad / s.

[0104] Select the desired attitude angle and desired angular velocity values ​​as:

[0105] q r =[1,0,0,0] T ,ω r =[0,0,0] T rad / s.

[0106] The failure factor matrix is ​​defined as:

[0107]

[0108] Select the spacecraft's inertia matrix to be:

[0109]

[0110] The uncertain part of the spacecraft's moment of inertia is selected as:

[0111]

[0112] The event triggering mechanism parameters are:

[0113] β=0.95,δ=1×10 -5 ,

[0114] Select the parameters of the fractional sliding surface and controller η1=η2=η3=0.1,μ1=μ2=0.05,α1=α2=0.75,γ1=γ2=0.5,d0=[3sin(0.1t),2sin(0.2t),3sin(0.2t)] T . The simulation duration is 50 seconds;

[0115] Figure 2 The control torque response curve of the spacecraft is shown, where from top to bottom are the control torque component τ1 response curve, the control torque component τ2 response curve, and the control torque component τ3 response curve. The black solid line in the figure is the control torque response curve output by the fractional-order sliding mode controller designed by the present invention, and the black dotted line is the control torque response curve output by the integer-order sliding mode controller. Figure 3 The observation error curve of the spacecraft finite time observer is shown. From top to bottom, the observation error components e 21 Response curve diagram, observation error component e 22 Response curve diagram, observation error component e 23 Response curve diagram: The black solid line in the figure is the error response curve of the output of the finite time observer designed in the present invention. Figure 4 The response curve of the angular velocity of the spacecraft is shown. From top to bottom, there are the response curve of the angular velocity component w1, the response curve of the angular velocity component w2, and the response curve of the angular velocity component w3. The black solid line in the figure is the angular velocity response curve output by the fractional-order sliding mode controller designed by the present invention, and the black dotted line is the angular velocity response curve output by the integer-order sliding mode controller. Figure 5 The response curve of the spacecraft attitude quaternion is shown. Among them, from top to bottom are the attitude quaternion component q0 response curve, attitude quaternion q1 response curve, attitude quaternion q2 response curve, attitude quaternion component q3 response curve. The black solid line in the figure is the attitude quaternion response curve output by the fractional-order sliding mode controller designed by the present invention, and the black dotted line is the attitude quaternion response curve output by the integer-order sliding mode controller. Figure 5The response curve of the spacecraft attitude quaternion is shown. As can be seen from the figure, the spacecraft cannot reach the desired attitude in the initial state due to the interference of actuator failure, external interference, and uncertainty of rotational inertia, but in about 20 seconds, the spacecraft's attitude quaternion and angular velocity can converge to the desired attitude in a limited time. Figure 6 It is the execution interval diagram under the event-triggered control strategy, where from top to bottom are the execution time interval diagram of the control torque component τ1, the execution time interval diagram of the control torque component τ2, and the execution time interval diagram of the control torque component τ3. The black circle horizontal line is t k+1 The black solid line is t k The control strategy has higher communication efficiency under resource constraints, and the interval update time during the entire simulation run is positive, which means that there is no Zeno behavior under this event-triggered control strategy.

[0116] It can be clearly seen from the above simulation results that the present invention can quickly and stably control the attitude of the spacecraft, and its convergence speed and stabilization time are significantly better than those of the traditional integer-order sliding mode fault-tolerant controller.

[0117] In summary, the present invention has a faster convergence speed, can effectively weaken the chattering phenomenon, reduce the energy waste of the spacecraft, and improve the control performance of the spacecraft.

[0118] 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 protection scope of the present invention.

Claims

1. A spacecraft fault-tolerant control method based on fractional-order sliding mode, characterized in that: The following steps are involved: S1. Construct attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternion, and introduce concentrated disturbance model; S2. Design a disturbance observer based on finite time theory; S3. Design a finite-time fault-tolerant controller for spacecraft attitude based on fractional-order sliding mode theory; S4. Design the event triggering mechanism of the spacecraft attitude system; S5. Input the controller in step S3 into the kinematic and dynamic models of the spacecraft in step S1, and the obtained closed-loop system is the spacecraft fault-tolerant control system.

2. The spacecraft fault-tolerant control method based on fractional order sliding mode according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S11, construct attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternion; Consider the quaternion part of the spacecraft's attitude as: [q v ,q0] T , where q v =[q1,q2,q3] T is the vector part of the quaternion; q0 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 spacecraft in the rigid body coordinate system, is the derivative of q0, for q v The derivative of is the identity matrix; is the time derivative of ω; J0 is the moment of inertia of the ith satellite, τ=[τ1,τ2,τ3] T is the control torque of the spacecraft; ω × The following matrix is ​​represented 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 output signal τ(t) F The mathematical expression of The result of multiplying the input signal τ(t); 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 (t); its mathematical expression is: When multiplicative faults and additive faults occur in the actuator at the same time, 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 spacecraft attitude control system, then the actual output control command τ of the spacecraft actuator is: τ=Γ(t)+P(t)τ c In the above formula, is the bias fault of the spacecraft, P(t)=diag(ρ1,ρ2,ρ3) is the fault failure factor matrix, And satisfy 0≤ρ i ≤1(i=1,2,3), where The smaller the value, the more serious the actuator failure is, and the smaller the actual control torque that can be output is. When P(t) = 0, it means that the actuator has completely failed and will not be able to provide any control torque. In the design of the spacecraft 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 spacecraft inertia matrix J is composed of the standard inertia matrix J0 and the uncertain part of the inertia matrix ΔJ, that is, J = J0 + ΔJ; get: make have to: Based on the spacecraft mixed fault actuator model and the uncertain part model of the inertia matrix, and considering the external disturbance d0 of the spacecraft, the angular acceleration of the spacecraft in the rigid body coordinate system is for: In the above formula, is the angular velocity of the spacecraft in the rigid body coordinate system, ω × is the antisymmetric matrix of ω; Based on the above analysis, under the conditions of external disturbance, uncertain part of inertia matrix and mixed failure of actuator, the kinematic and dynamic model of a single spacecraft is rewritten as: in, To concentrate interference.

3. The spacecraft fault-tolerant control method based on fractional order sliding mode according to claim 2 is characterized in that: Step S2 specifically includes: For the spacecraft, considering the multiple interference factors of actuator failure, external disturbance and the uncertain part of the inertia matrix, we assume and are the estimated values ​​of the spacecraft angular velocity ω and the concentrated disturbance d, respectively. The finite-time disturbance observer is designed as follows: In the above formula, d is the concentrated interference. is the derivative of d, sign represents the sign function, and is defined as follows: The observer can effectively estimate the unknown concentrated disturbance value in a finite time; that is, when t>t0, It can be known from the finite-time non-smooth theory that the designed finite-time disturbance observer can accurately estimate the concentrated disturbance value d suffered by the spacecraft within a finite time.

4. The spacecraft fault-tolerant control method based on fractional order sliding mode according to claim 3 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: q e =q ν -q r oh e =J0ω-J0ω r In the above formula, is the vector part of the desired attitude quaternion, is the desired angular velocity; Select the following fractional sliding surface: Where, μ1=diag(μ 11 ,μ 12 ,μ 13 ), μ2=diag(μ 21 ,μ 22 ,μ 23 ) are two constant diagonal matrices, each component of which is a positive number greater than zero; α1, α2 are fractional orders and satisfy 0<α1, α2<1; γ1, γ2 are exponentials and satisfy 0<γ1, γ2<1; D a (x) is a fractional differential operator; S32, design a finite-time fault-tolerant controller; According to the fractional-order sliding surface designed above, the following controller form is given: Among them, 0<λ<1, |s| 1-λ =diag(|s1| 1-λ ,|s2| 1-λ ,|s3| 1-λ ), η=diag(η1,η2,η3) is a positive real matrix; and is an adaptive time-varying matrix and is defined as follows: In the above formula, η max yes An upper bound for , positive parameter The saturation function sat(x) is defined as: The controller can ensure that the desired tracking errors of the spacecraft's attitude and angular velocity converge to a region within a finite time; that is, the spacecraft's attitude and angular velocity will approach the desired values ​​within a finite time.

5. The spacecraft fault-tolerant control method based on fractional order sliding mode according to claim 4 is characterized in that: Step S4 specifically includes the following steps: S41, design event trigger mechanism; First, define the error equation of the trigger control torque and the current event control torque as follows: In the above formula, τ c (t) represents the control torque when the kth event is triggered, t∈[t k ,t k+1 ],k=0,1,2...,n,t0=0,where t k and t k+1 are two adjacent triggering time instants, with τ c (t) remains constant; trigger time t k+1 Evaluated by: Among them, β>0, δ>0 is the parameter to be designed in the event trigger mechanism; In the designed event trigger mechanism, the value τ is transmitted through the wireless network only when the predefined trigger condition is violated. c (t) is updated to the actuator; thus, the spacecraft receives aperiodic updates τ of the control input c (t k ), instead of updating τ in continuous time c (t); therefore, under the designed event trigger mechanism, the control input is expressed as:

6. A spacecraft fault-tolerant control system based on fractional-order sliding mode, characterized in that: include: Spacecraft attitude dynamics model construction module: used to construct the attitude kinematics and dynamics model of rigid spacecraft based on attitude quaternion, and introduce the concentrated perturbation model; Disturbance observer design module: used to design disturbance observer based on finite time theory; Finite-time fault-tolerant controller design module: used to design a finite-time fault-tolerant controller for spacecraft attitude based on fractional-order sliding mode theory; Event trigger mechanism design module: used to reduce the communication frequency between the spacecraft and the control center; Spacecraft fault-tolerant control system construction module: used to input the designed spacecraft fault-tolerant control system into the constructed spacecraft kinematic and dynamic models to obtain a closed-loop system.

7. 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 5 are implemented.

8. An electronic device, characterized in that: It 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 5 is implemented.

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