Spacecraft fault-tolerant control method and system based on fractional order sliding mode

Abstract

The application discloses a spacecraft fault-tolerant control method and system based on a fractional order sliding mode, and belongs to the automatic control field. The method comprises the following steps: firstly, a spacecraft attitude dynamics model is constructed, including spacecraft hybrid fault actuator modeling, spacecraft inertia matrix uncertain part modeling and spacecraft external disturbance modeling. According to the constructed spacecraft attitude dynamics model, a spacecraft centralized disturbance observer is designed based on the finite time theory, and the spacecraft centralized disturbance is compensated. Secondly, a novel spacecraft attitude finite time fault-tolerant controller is designed based on the fractional order sliding mode theory, so that the spacecraft can stably reach and maintain the expected attitude and angular velocity state in a limited time. Finally, the fault-tolerant controller is combined with an event triggering technology, a spacecraft attitude system event triggering mechanism is designed, the controller update frequency is reduced, the communication resource consumption between a control center and the spacecraft is avoided, and therefore the efficiency and reliability of the spacecraft in the task execution process are improved.

Description

TECHNICAL FIELD

[0001] The present application 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

[0002] The spacecraft attitude control system is a core component in aerospace technology, responsible for precisely regulating the directional attitude of the spacecraft in space. This 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 spacecraft's attitude information, and the controller efficiently processes these information and instructions from the navigation or guidance system to generate precise control signals. Subsequently, the actuator generates the necessary control torque according to 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 crucial role in ensuring the stability and maneuverability of the spacecraft during flight, and is an indispensable technical support in the aerospace field.

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

[0004] Therefore, in view of the various disturbances such as external disturbance, parameter uncertainty, and actuator failure faced by current on-orbit spacecraft under limited communication resources, there is an urgent need for a spacecraft fault-tolerant control system that can achieve efficient control under complex centralized disturbance. This new control system not only ensures rapid attitude stabilization of the spacecraft under complex centralized disturbance, but also improves control accuracy and mission success rate in a variable space environment, while reducing energy waste of the spacecraft under limited communication resources, further promoting the application of spacecraft in real task environments. SUMMARY

[0005] In order to overcome the defects in the prior art, the application designs a new spacecraft fault-tolerant control method and system based on non-smooth finite time theory. A new disturbance observer is designed based on finite time theory, which accurately estimates the centralized disturbance formed by actuator faults, parameter uncertainties and external disturbances, and provides effective compensation. And based on the fractional order sliding mode theory, a spacecraft finite time fault-tolerant controller is designed, which realizes that the attitude angle and angular velocity of the spacecraft reach the desired state in a finite time. On this basis, an event-triggered mechanism is designed, which can reduce the update frequency of the control input and reduce the waste of spacecraft energy. The designed spacecraft fault-tolerant control system can still maintain the stable and robust operation of the spacecraft under the conditions of limited communication resources, actuator faults, external disturbances and parameter uncertainties. This technology can meet the requirements of spacecraft attitude control speed and robustness.

[0006] To achieve the above object, the application comprises the following technical solutions:

[0007] The first aspect of the application provides a spacecraft fault-tolerant control method based on fractional order sliding mode, comprising the following steps

[0008] S1, constructing a spacecraft attitude dynamics model;

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

[0010] The attitude quaternion of the spacecraft is considered as: [q v ,q0] T Wherein, 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 rigid body coordinate system, is the derivative of q0, is the derivative of q v , and is a unit matrix. is the derivative of ω with respect to time; J0 is the moment of inertia of the i-th satellite, τ=[τ1,τ2,τ3] T is the control moment of the spacecraft; ω × represents the following matrix

[0013]

[0014] S12, introducing centralized interference variables;

[0015] When some changes occur in system parameters, these changes will cause the change of fault signal, and this change is closely related to the input signal. Therefore, the mathematical expression of output signal τ(t) F can be regarded as the result of multiplication of fault signal and input signal τ(t). That is:

[0016]

[0017] When unknown input acts on the system, the change of fault signal is not affected by the input signal. Therefore, the mathematical description of output signal τ(t) F can be equivalently expressed as the sum of input signal τ(t) and fault signal τ b (t). Its mathematical expression is:

[0018]

[0019] When multiplicative fault and additive fault occur in the actuator at the same time, this situation may cause "stuck" phenomenon, the actuator has no response to the control signal, and completely loses the control effect. The mixed fault is expressed by mathematical expression, that is:

[0020]

[0021] Definition is the expected value of the control command of the spacecraft attitude control system, and 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 bias fault of the spacecraft, is the fault failure factor matrix,

[0024] and satisfies where The smaller the value of P(t) is, the more serious the failure of the actuator is, and the smaller the actual control torque that can be output is. When P(t) = 0, it means that the actuator is completely failed and cannot provide any control torque.

[0025] In the design of spacecraft attitude control system, the influence of rotational inertia uncertainty should be fully considered to ensure effective compensation and ensure the smooth completion of the flight mission. The spacecraft inertia matrix J is composed of the standard inertia matrix J0 and the inertia matrix uncertainty part ΔJ, that is, J = J0 + ΔJ. It can be obtained:

[0026]

[0027] Let Available:

[0028] Based on spacecraft hybrid fault actuator model and inertia matrix uncertainty part model, and considering the existence of external disturbance d0 of spacecraft, the angular acceleration of spacecraft rigid coordinate system is :

[0029]

[0030] In the above formula, τ a = Γ(t) + (P(t)-I) τ c , The angular velocity of spacecraft rigid coordinate system is ω × , and the anti-symmetric matrix of ω is ω

[0031] Based on the above analysis, under the conditions of external disturbance, inertia matrix uncertainty part and actuator hybrid fault, the kinematics and dynamics model of single spacecraft can be rewritten as:

[0032]

[0033] The centralized disturbance is d.

[0034] S2, disturbance observer design based on finite time theory;

[0035] For spacecraft, considering multiple disturbance factors such as actuator fault, external disturbance and inertia matrix uncertainty part, let And The estimated value of the angular velocity ω of spacecraft and the centralized disturbance d is designed as follows:

[0036]

[0037] In the above formula, d is the centralized disturbance, The derivative of d is d, and sign represents the sign function, which is defined as follows:

[0038]

[0039] The observer can effectively estimate the unknown centralized disturbance value in a limited time. That is, when t>t0,

[0040] According to the finite time non-smooth theory, the finite time disturbance observer designed in the application can accurately estimate the centralized disturbance value d of spacecraft in a limited time.

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

[0042] S31, Design of fractional order sliding surface

[0043] Firstly, the tracking error related to 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] The fractional order sliding surface is selected as follows:

[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 is a positive number greater than zero. α1, α2 are fractional orders and satisfy 0 < α1, α2 < 1. γ1, γ2 are exponents and satisfy 0 < γ1, γ2 < 1. D a (x) is a fractional order differential operator.

[0050] S32, Design of finite-time fault-tolerant controller

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

[0052]

[0053] where 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 number matrix. And

[0054] is an adaptive time-varying matrix, and is defined as the following form:

[0055]

[0056] where η max is an upper bound of the positive parameter The saturation function sat(x) is defined as:

[0057]

[0058] The controller can ensure that the desired tracking error of the spacecraft's attitude and angular velocity converges to a region within a finite time. That is, the spacecraft's attitude and angular velocity will approach the desired value within a finite time. S4, spacecraft attitude system event-triggered mechanism design;

[0059] S41, design event-triggered mechanism;

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

[0061]

[0062] where τ c (t) represents the control torque at the kth event trigger, t∈[t k ,t k+1 ], k = 0, 1, 2,..., n, t0=0, where t k and t k+1 are two adjacent trigger time instants, and τ c (t) remains constant between them. The trigger time t k+1 under this scheme is evaluated by:

[0063]

[0064] where is the parameter to be designed in the event-triggered mechanism.

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

[0066]

[0067] S5, input the system controller of step S1 with the control protocol of step S4, and the resulting closed-loop system is the spacecraft fault-tolerant control system. ​

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

[0069] A spacecraft attitude dynamics model construction module: used for constructing the attitude kinematics and dynamics model of a rigid spacecraft based on attitude quaternion, and introducing a concentrated disturbance model;

[0070] A disturbance observer design module: used for designing a disturbance observer based on finite time theory;

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

[0072] An event-triggered mechanism design module: used for reducing the communication frequency between the spacecraft body and the control center;

[0073] A spacecraft fault-tolerant control system construction module: used for inputting the designed spacecraft fault-tolerant control system into the constructed spacecraft kinematics and dynamics model to obtain a closed-loop system.

[0074] In addition, the present application also provides a computer storage medium and an electronic device, wherein the computer storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of the method of the present application. The electronic device comprises a memory and one or more processors, 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 of the present application is implemented.

[0075] Compared with the prior art, the present application has the following advantages:

[0076] 1. The present application designs a new spacecraft fault-tolerant control method and system based on non-smooth finite time theory. A new disturbance observer is designed based on finite time theory, which accurately estimates the concentrated disturbance formed by actuator faults, parameter uncertainties and external disturbances, and provides effective compensation.

[0077] 2. The present application designs a spacecraft finite time fault-tolerant controller based on order sliding mode theory, which realizes that the attitude angle and angular velocity of the spacecraft reach the desired state in a finite time. The designed fault-tolerant control system still maintains the stable and robust operation of the spacecraft under the disturbance of actuator faults, external disturbances and parameter uncertainties. Compared with the 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 precision, and the controller does not require complex operation, and is friendly to the software and hardware cost requirements of the system.

[0078] 3、The spacecraft dynamic event-triggered control strategy is designed based on the event-triggering theory, and in the case that communication resources of the spacecraft are limited, the update frequency of the control input can be reduced, the waste of energy of the spacecraft is reduced, and the control performance of the spacecraft is further improved. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 The flowchart of the present application.

[0080] Figure 2 The control moment response curve of the spacecraft attitude system of the present example.

[0081] Figure 3 The disturbance estimation error response curve of the finite time observer of the spacecraft of the present example.

[0082] Figure 4 The tracking error response curve of the angular velocity of the spacecraft of the present example.

[0083] Figure 5 The tracking error response curve of the quaternion component of the spacecraft of the present example.

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

[0085] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

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

[0087] S1, spacecraft centralized disturbance modeling; comprising:

[0088] S11, spacecraft hybrid fault actuator modeling;

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

[0090] S2, disturbance observer design based on finite time theory; comprising:

[0091] S21, designing a disturbance observer;

[0092] S22, stability analysis of the finite time disturbance observer;

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

[0094] S31, design of spacecraft attitude finite time fault-tolerant controller;

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

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

[0097] S41, design of event-triggered mechanism;

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

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

[0100] In order to prove the effectiveness and superiority of the control algorithm proposed in the application, an integer order sliding mode controller is selected for comparison in this example:

[0101]

[0102] The values of the initial attitude angle and the initial angular velocity are set as:

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

[0104] The values of the desired attitude angle and the desired angular velocity are selected as:

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

[0106] The fault factor matrix is defined as:

[0107]

[0108] The inertia matrix of the spacecraft is selected as:

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

[0115] Figure 2 The spacecraft control torque response curves are shown, wherein the control torque component τ1 response curve, the control torque component τ2 response curve, and the control torque component τ3 response curve are sequentially shown from top to bottom. The black solid line in the figure is the control torque response curve output by the fractional order sliding mode controller designed in the application, and the black dashed line is the control torque response curve output by the integer order sliding mode controller. Figure 3 The observation error curves of the spacecraft finite time observer are shown. Wherein, the observation error component e 21 response curve, the observation error component e 22 response curve, and the observation error component e 23 response curve are sequentially shown from top to bottom. The black solid line in the figure is the error response curve output by the finite time observer designed in the application. Figure 4 The response curves of the angular velocity of the spacecraft are shown. Wherein, the angular velocity component w1 response curve, the angular velocity component w2 response curve, and the angular velocity component w3 response curve are sequentially shown from top to bottom. The black solid line in the figure is the angular velocity response curve output by the fractional order sliding mode controller designed in the application, and the black dashed line is the angular velocity response curve output by the integer order sliding mode controller. Figure 5 The response curves of the attitude quaternion of the spacecraft are shown. Wherein, the attitude quaternion component q0 response curve, the attitude quaternion q1 response curve, the attitude quaternion q2 response curve, and the attitude quaternion component q3 response curve are sequentially shown from top to bottom. The black solid line in the figure is the attitude quaternion response curve output by the fractional order sliding mode controller designed in the application, and the black dashed 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. It can be seen from the figure that the spacecraft cannot reach the desired attitude in the initial state under the disturbance of actuator failure, external disturbance and uncertain moment of inertia, but the attitude quaternion and angular velocity of the spacecraft can converge to the desired attitude in a limited time in about 20 seconds. Figure 6 The execution interval diagram under the event-triggered control strategy is shown, wherein, from top to bottom, 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 are sequentially arranged. The black horizontal line is the execution time interval of the control torque component τ1, the black horizontal line is the execution time interval of the control torque component τ2, and the black horizontal line is the execution time interval of the control torque component τ3. k+1 The black solid line is the execution time interval of the control torque component τ1 at the moment t k The black solid line is the execution time interval of the control torque component τ1 at the moment t. The control strategy has higher communication efficiency under resource limitation, and the interval update time is positive during the whole simulation running, which means that there is no Zeno behavior under the event-triggered control strategy.

[0116] It can be obviously seen from the simulation results that the spacecraft attitude can be quickly and stably controlled by the application, and the convergence speed and stable time are obviously better than those of the conventional integer-order sliding mode fault-tolerant controller.

[0117] In summary, the application has 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 is only the preferred embodiment of the application, and does not limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. A spacecraft fault-tolerant control method based on fractional order sliding mode, characterized in that, The method comprises the following steps: S1, constructing an attitude kinematics and dynamics model of a rigid spacecraft based on a quaternion, and introducing a concentrated disturbance model; Under the conditions of external disturbance, inertia matrix uncertainty, and mixed faults of actuators, the kinematics and dynamics model of a single spacecraft is rewritten as: where is the concentrated disturbance; q v = [q1, q2, q3] T is the vector part of the quaternion; q0is the scalar part of the quaternion; is the identity matrix; is the angular velocity in the spacecraft body coordinate system; is the derivative of q0; is the derivative of q v ; is the derivative of ω with respect to time; J0is the moment of inertia of the ith satellite; ω × is the skew-symmetric matrix of ω; is the desired value of the spacecraft attitude control system control command; d0represents the external disturbance; J is the spacecraft inertia matrix; J0is the inertia matrix; ΔJ is the uncertain part of the inertia matrix; τ a = Γ(t) + (P(t) - I)τ c ; is the bias fault of the spacecraft, and P(t) = diag(ρ1, ρ2, ρ3) is the fault failure factor matrix; S2, designing a disturbance observer based on finite time theory; For spacecraft, and considering the multiple disturbance factors of actuator faults, external disturbances and uncertain inertia matrix, we assume that and are the estimates of the spacecraft angular velocity ω and the concentrated disturbance d, respectively, and the finite-time disturbance observer is designed as follows: In the above equation, d is the concentrated interference, is the derivative of d, and sign denotes the sign function, which is defined as follows: The observer can effectively estimate the unknown centralized disturbance value in finite time; that is, when t > t0, According to the finite-time nonsmooth theory, the designed finite-time disturbance observer can accurately estimate the centralized disturbance value d suffered by the spacecraft in finite time. S3, designing a spacecraft attitude finite time fault-tolerant controller based on fractional order sliding mode theory; The controller has the following form: where μ1 = diag(μ 11 , μ 12 , μ 13 ), μ2 = diag(μ 21 , μ 22 , μ 23 ) are two constant diagonal matrices, each component is a positive number greater than zero; α1, α2 are fractional orders and satisfy 0 < α1, α2 < 1; γ1, γ2 are exponents and satisfy 0 < γ1, γ2 < 1; D a (x) is a fractional differential operator; 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; q e and ω e are the tracking errors related to the attitude angle and angular velocity, respectively; is an adaptive time-varying matrix and is defined as follows: In the above formula, η max is an upper bound of the positive parameter The saturation function sat(x) is defined as: The controller can ensure that the desired tracking error of the attitude and angular velocity of the spacecraft converges to a region in a finite time; that is, the attitude and angular velocity of the spacecraft will approach the desired value in a finite time; S4, design a spacecraft attitude system event trigger mechanism, when violating the predefined trigger condition, send the value τ c (t) update to the actuator; S5, inputting the controller in step S3 into the kinematics and dynamics model of the spacecraft in step S1 to obtain a closed-loop system, i.e., a spacecraft fault-tolerant control system.

2. The fractional order sliding mode based spacecraft fault-tolerant control method of claim 1, wherein, Step S1 specifically comprises the following steps: S11, constructing an attitude kinematics and dynamics model of a rigid spacecraft based on a quaternion; Consider the attitude quaternion of the spacecraft is partially given by: [q v , q0] T where q v = [q1, q2, q3] T is the vector part of the quaternion; q0is 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 body coordinate system, is the derivative of q0, is the derivative of q v is the derivative of q is the identity matrix; is the derivative of ω with respect to time; J0is the moment of inertia of the ith satellite, τ = [τ1, τ2, τ3] T is the control torque of the spacecraft; ω × denotes the matrix S12, introducing a concentrated disturbance variable; When the system parameters undergo certain changes, these changes will cause the change of the fault signal, and this change is closely related to the input signal τ(t); therefore, the mathematical expression of the output signal τ(t) F is considered as the result of the multiplication of the fault signal and the input signal τ(t); that is: When unknown inputs act on the system, the change in the fault signal is not affected by the input signal; thus, the output signal τ(t) F is mathematically described as the sum of the input signal τ(t) and the fault signal τ b (t). When multiplicative faults and additive faults occur simultaneously in actuators, the mixed faults are expressed as: Definitions is the desired value of the control command by the spacecraft attitude control system, and the actual output control command τ of the spacecraft actuator is: τ = Γ(t) + P(t)τ c In the above formula, P(t) = diag(ρ1, ρ2, ρ3) is a fault failure factor matrix for the bias fault of the spacecraft, and satisfies 0 ≤ ρ i ≤ 1, i = 1, 2, 3, wherein The smaller the value of P(t) is, the more serious the failure degree of the actuator is, and the smaller the actual control torque that can be output is; when P(t) = 0, the actuator is completely failed and cannot provide any control torque. In the design of a spacecraft attitude control system, the influence of rotational inertia uncertainty should be fully considered to ensure effective compensation and ensure the smooth completion of the flight mission; the spacecraft inertia matrix J is composed of a standard inertia matrix J0 and an inertia matrix uncertainty ΔJ, i.e., J = J0 + ΔJ; and the following is obtained: Let be: Based on the spacecraft hybrid fault actuator model and the inertia matrix uncertain part model, and considering the existence of external disturbance d0, the angular acceleration of the spacecraft in the rigid body coordinate system is : In the above equation, τ a = Γ(t) + (P(t) - I)τ c , is the angular velocity of the spacecraft in the body frame, ω × is the skew-symmetric matrix of ω.

3. The fractional order sliding mode based spacecraft fault-tolerant control method of claim 2, wherein, Step S3 specifically comprises the following steps: S31, designing a fractional order sliding surface; First, the tracking error related to the attitude angle and angular velocity is defined as follows: q e = q ν - q r ω e = J0ω - J0ω r In the above formulae, is the vector part of the desired attitude quaternion, is the desired angular velocity; The fractional order sliding surface is selected as follows: where μ1 = diag(μ1, μ2, μ3), μ2 = diag(μ4, μ5, μ6) are two constant diagonal matrices, each component is a positive number greater than zero; α1, α2 are fractional orders and satisfy 0 < α1, α2 < 1; γ1, γ2 are exponents and satisfy 0 < γ1, γ2 < 1; D(x) is a fractional differential operator; 11 12 13 21 22 23 a ​​​​​​​ S32, designing a finite time fault-tolerant controller according to the designed fractional order sliding surface.

4. The fractional order sliding mode based spacecraft fault-tolerant control method according to claim 3, characterized in that, Step S4 specifically comprises the following steps: S41, designing an event-triggered mechanism; First, the error equation of the trigger control torque and the current event control torque is defined as follows: In the above formula, τ c (t k ) represents the control torque at the kth event trigger, t ∈ [t k , t k+1 ], k = 0, 1, 2,..., n, t0= 0, where t k and t k+1 are two adjacent trigger time instants, between which τ c (t) remains constant; the trigger time t k+1 is evaluated by the following formula: wherein β > 0, δ > 0 is a parameter to be designed in the event-triggered mechanism; In the designed event-triggered mechanism, the value τ c (t) is transmitted through the wireless network when the predefined triggering condition is violated c (t k ), instead of continuous-time updates τ c (t); under the designed event-triggered mechanism, the control input is represented as:

5. A computer storage medium, characterized in that, A computer program is stored on the storage medium, and the computer program is executed by a processor to implement the steps of the method according to any one of claims 1 to 4.

6. An electronic device, comprising: The device comprises a memory and one or more processors, wherein the memory is used to store one or more programs; and the one or more programs are executed by the one or more processors to implement the method according to any one of claims 1 to 4.

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