Predefined time fault-tolerant control method for rigid spacecraft system

Abstract

The invention discloses a predefined time fault-tolerant control method for a rigid spacecraft system, and relates to the technical field of aerospace flight control, and the method comprises the following steps: S1, building kinematics and dynamics models of a fault-tolerant control system for attitude tracking errors of a rigid spacecraft, and initializing a system state and control parameters; s2, designing a non-singular predefined time sliding mode surface based on an attitude error tracking control system of the rigid spacecraft; and S3, designing a non-singular adaptive fault-tolerant predefined time controller, and effectively solving the potential buffeting problem in the design process of the controller based on the predefined time preset performance function and the non-singular adaptive fault-tolerant predefined time control method. Under the condition that controller faults, inertia uncertainty and external interference exist at the same time, the steady-state performance and state constraint of attitude tracking errors are guaranteed, and system predefined time convergence is guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of aerospace flight control technology, and in particular to a predefined time fault-tolerant control method for a rigid spacecraft system. Background Art

[0002] In recent years, rigid spacecraft have received extensive attention in the development of control algorithms and practical mission applications. Attitude control performance is the key to ensuring the stability and safety of rigid spacecraft. The safety and reliability of spacecraft are particularly important. A small fault in the rigid spacecraft system may lead to significant performance degradation or even instability.

[0003] There are many control methods for the problem of fault-tolerant control in attitude tracking of rigid spacecraft systems, among which sliding mode control is particularly widely used in various fields. Sliding mode control is considered to be an effective robust control method in solving system uncertainties and external disturbances. The sliding mode control method has the advantages of simple algorithm, fast response speed, strong robustness to external interference and parameter perturbations. Therefore, the sliding mode control method is widely used in various fields. However, the singularity problem in the sliding mode control method has become an obstacle to the application of sliding mode control in practical systems. In order to solve this problem, many methods to avoid singularities have been proposed one after another, such as virtual control input, introduction of piecewise functions, etc. Among these methods, virtual control input will increase the complexity of the control algorithm, and the introduction of piecewise functions will destroy the integrity of the controller, resulting in an increase in the uncertainty of the system; a control method of non-singular sliding surface is proposed, which can directly avoid the singularity problem of the controller and ensure the integrity of the controller.

[0004] The attitude tracking control of rigid spacecraft systems also needs to consider the rapid convergence of the system. For some spacecraft missions, such as earth observation, near-space monitoring and on-orbit servicing, the spacecraft needs to achieve rapid attitude stabilization. The finite time and fixed time theories can achieve rapid attitude stabilization, but the finite time theory is heavily dependent on the initial conditions of the system state, and the fixed time theory is usually difficult to calculate the exact upper bound of the convergence time, which limits their practical applications. Therefore, a predefined time fault-tolerant control method for rigid spacecraft systems is proposed. Summary of the invention

[0005] The purpose of the present invention is to solve the problems in the prior art and to propose a predefined time fault-tolerant control method for a rigid spacecraft system.

[0006] A predefined time fault tolerant control method for a rigid spacecraft system comprises the following steps:

[0007] S1. Establish the kinematic and dynamic models of the fault-tolerant control system of the rigid spacecraft attitude tracking error, and initialize the system state and control parameters;

[0008] S2. Design of non-singular predefined time sliding surface based on attitude error tracking control system of rigid spacecraft;

[0009] S3. Design a non-singular adaptive fault-tolerant predefined time controller.

[0010] Preferably, in step S1, the dynamic model of the rigid spacecraft angular velocity error tracking control system is expressed as:

[0011]

[0012] Among them, ω and are the angular velocity and angular acceleration of the rigid spacecraft, ω e and are the angular velocity error and the time derivative of the angular velocity error of the rigid spacecraft, ω d and are the expected angular velocity of the rigid spacecraft and the time derivative of the expected angular velocity, respectively, Ω is the angular velocity of the reaction flywheel, × is an operator. × Applied to ω × and ω e × , expressed as follows: × =[0,-ω3,ω2;ω3,0,-ω1;-ω2,ω1,0] and ω e × =[0,-ω e3 ,ω e2 ;ω e3 ,0,-ω e1 ; -ω e2 ,ω e1 ,0],J ω =diag([J ω1 ,J ω2 ,J ω3 ,J ω4 ]) is the rotational inertia matrix of the reaction flywheel, J0 and ΔJ represent the nominal part and the uncertain part of the rotational inertia matrix respectively, D is the control torque distribution matrix of the reaction flywheel, C represents the corresponding rotation matrix, u is the reaction flywheel input, E(t) = diag([e1(t), e2(t), e3(t), e4(t)]) is the actuator control efficiency matrix, 0≤e i (t)≤1, i=1,2,3,4 represents the effective coefficient of the i-th reaction flywheel, is the additional fault input of the reaction flywheel, d(t) is the external disturbance;

[0013] The kinematic model of the rigid spacecraft attitude tracking error system is expressed as:

[0014]

[0015] in, I3=diag([1,1,1]),q ve =[q 1e ,q 2e ,q 3e ] T The vector part representing the attitude tracking error, q 4e represents the scalar part of the attitude tracking error, and They are q ve and q 4e The time derivative of .

[0016] Preferably, in step S2, the design process is as follows:

[0017] The design performance function is:

[0018]

[0019] Among them, 0<c<1, ρ0 and ρ T is i The initial and final values ​​of (t), is the upper bound of the convergence time of the predefined performance function;

[0020] The design standardized tracking error is:

[0021]

[0022] The non-singular predefined time sliding surface s is designed as:

[0023]

[0024] Where ε=[ε1,ε2,ε3] T , sign(·) is the sign function, sig(·) is the vector form of sign(·), and the function sig 1+α (ε)=[|ε1| 1+α sign(ε1),|ε2| 1+α sign(ε2),|ε3| 1+α sign(ε3)] T , is the first-order derivative of ε; 0<α<1; is the upper bound of the convergence time of the predefined non-singular predefined time sliding surface;

[0025] Derivative of ε with respect to time:

[0026]

[0027] in, γ=diag([γ1,γ2,γ3]), Yes * The first-order derivative of , ρ(t)=diag([ρ1,ρ2,ρ3]), ρ -1 (t) is the inverse matrix of ρ(t).

[0028] Preferably, in step S2, the design process is as follows:

[0029] The design function φ is:

[0030]

[0031] Among them, μ=(1-α) / (1+α);

[0032] Design a non-singular adaptive fault-tolerant predefined time controller as:

[0033]

[0034] Among them, ||b|| is the norm of b, ||D|| is the norm of D, is the predefined upper bound of the convergence time of the attitude tracking error, λ max is the maximum value of the eigenvalue of the inertia matrix, and are the estimated parameters, and yes and Adaptive law, Φ=1+||ω|+||ω|| 2 , 0<β<1;

[0035] The update law of the designed adaptive parameters is:

[0036]

[0037] in, p0>0,p1>0, ||g|| is the norm form of g;

[0038] Design Lyapunov functions V1 and V2:

[0039]

[0040] Among them, s T is the transpose of s, and is the error value of the estimated parameter;

[0041] Derivative of formula (6) yields:

[0042]

[0043] Substituting the rigid spacecraft dynamics model equations (1), (2) and (3) into equation (7), we obtain:

[0044]

[0045] in, is the second-order derivative of ε, B(t,q ve ) = bDE(t),

[0046] Differentiating equation (13) yields:

[0047]

[0048] Substituting formula (14) into formula (16) we obtain:

[0049]

[0050] Substituting formula (15) into formula (17), we obtain:

[0051]

[0052] Substituting equations (9), (10) and (11) into equation (18), we obtain:

[0053]

[0054] Since g exists in two cases: 0<g<1 and g>1, if equation (19) is written as , then the system is determined to be convergent in a predefined time; where,

[0055] It can be concluded that the attitude tracking error q in the rigid spacecraft system ve It can converge to a sufficiently small area, and its convergent area is:

[0056]

[0057] in, T max T P The time upper bound of ′.

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] Based on preset performance functions, non-singular predefined time sliding surfaces and adaptive parameters, the present invention designs a control method based on preset performance functions and non-singular adaptive fault-tolerant predefined time, which effectively solves the potential chattering problem in the controller design process. In the presence of controller failure, inertial uncertainty and external interference, the steady-state performance and state constraints of the attitude tracking error are guaranteed, and the system convergence within the predefined time is guaranteed. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a control flow diagram of the present invention.

[0061] Figure 2 It is a schematic diagram of the posture tracking error effect of the present invention.

[0062] Figure 3 Schematic diagram of the angular velocity error effect of the present invention.

[0063] Figure 4 It is a schematic diagram of the non-singular predefined time sliding surface of the present invention.

[0064] Figure 5 Enter the schematic diagram for the controller of the present invention.

[0065] Figure 6 It is a schematic diagram comparing the effects of the posture tracking error of the present invention and the posture tracking error under the finite time controller solution.

[0066] Figure 7 It is a schematic diagram comparing the effects of the angular velocity error of the present invention and the angular velocity error under the finite time controller solution.

[0067] Figure 8 It is a schematic diagram comparing the performance of the controller of the present invention with that of the finite time controller. DETAILED DESCRIPTION

[0068] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0069] Reference Figure 1 As shown, a predefined time fault-tolerant control method for a rigid spacecraft system comprises the following steps:

[0070] S1. Establish the kinematic and dynamic models of the fault-tolerant control system of the rigid spacecraft attitude tracking error, and initialize the system state and control parameters;

[0071] S2. Considering the uncertainty of moment of inertia and external disturbance, a non-singular predefined time sliding surface is designed based on the attitude error tracking control system of a rigid spacecraft, which can avoid the singular problem in the controller and ensure the integrity of the controller through a design function;

[0072] S3. Design a non-singular adaptive fault-tolerant predefined time controller.

[0073] In step S1, the dynamic model of the rigid spacecraft angular velocity error tracking control system is expressed as:

[0074]

[0075] Among them, ω and are the angular velocity and angular acceleration of the rigid spacecraft, ω e and are the angular velocity error and the time derivative of the angular velocity error of the rigid spacecraft, ω d and are the expected angular velocity of the rigid spacecraft and the time derivative of the expected angular velocity, respectively, Ω is the angular velocity of the reaction flywheel, × is an operator. × Applied to ω × and ω e × , expressed as follows: × =[0,-ω3,ω2;ω3,0,-ω1;-ω2,ω1,0] and ω e × =[0,-ω e3 ,ω e2 ;ω e3 ,0,-ω e1 ; -ω e2 ,ω e1 ,0],J ω =diag([J ω1 ,J ω2 ,J ω3 ,J ω4 ]) is the rotational inertia matrix of the reaction flywheel, J0 and ΔJ represent the nominal part and the uncertain part of the rotational inertia matrix respectively, D is the control torque distribution matrix of the reaction flywheel, C represents the corresponding rotation matrix, u is the reaction flywheel input, E(t) = diag([e1(t), e2(t), e3(t), e4(t)]) is the actuator control efficiency matrix, 0≤e i(t)≤1, i=1,2,3,4 represents the effective coefficient of the i-th reaction flywheel, is the additional fault input of the reaction flywheel, d(t) is the external disturbance;

[0076] The kinematic model of the rigid spacecraft attitude tracking error system is expressed as:

[0077]

[0078]

[0079] in, I3=diag([1,1,1]),q ve =[q 1e ,q 2e ,q 3e ] T The vector part representing the attitude tracking error, q 4e represents the scalar part of the attitude tracking error, and They are q ve and q 4e The time derivative of .

[0080] In step S2, the design process is as follows:

[0081] The design performance function is:

[0082]

[0083] Among them, 0<c<1, ρ0 and ρ T is i The initial and final values ​​of (t), is the upper bound of the convergence time of the predefined performance function;

[0084] The design standardized tracking error is:

[0085]

[0086] The non-singular predefined time sliding surface s is designed as:

[0087]

[0088] Where ε=[ε1,ε2,ε3] T , sign(·) is the sign function, sig(·) is the vector form of sign(·), and the function sig 1+α (ε)=[|ε1| 1+α sign(ε1),|ε2| 1+αsign(ε2),|ε3| 1+α sign(ε3)] T , is the first-order derivative of ε; 0<α<1; is the upper bound of the convergence time of the predefined non-singular predefined time sliding surface;

[0089] Derivative of ε with respect to time:

[0090]

[0091] in, γ=diag([γ1,γ2,γ3]), Yes * The first-order derivative of , ρ(t)=diag([ρ1,ρ2,ρ3]), ρ -1 (t) is the inverse matrix of ρ(t).

[0092] In step S2, the design process is as follows:

[0093] The design function φ is:

[0094]

[0095] Among them, μ=(1-α) / (1+α);

[0096] Design a non-singular adaptive fault-tolerant predefined time controller as:

[0097]

[0098] Among them, ||b|| is the norm of b, ||D|| is the norm of D, is the predefined upper bound of the convergence time of the attitude tracking error, λ max is the maximum value of the eigenvalue of the inertia matrix, and are the estimated parameters, and yes and Adaptive law, Φ=1+||ω|+||ω|| 2 , 0<β<1;

[0099] The update law of the designed adaptive parameters is:

[0100]

[0101] in, p0>0,p1>0, ||g|| is the norm form of g;

[0102] Design Lyapunov functions V1 and V2:

[0103]

[0104] Among them, s T is the transpose of s, and is the error value of the estimated parameter;

[0105] Derivative of formula (6) yields:

[0106]

[0107] Substituting the rigid spacecraft dynamics model equations (1), (2) and (3) into equation (7), we obtain:

[0108]

[0109] in, is the second-order derivative of ε, B(t,q ve ) = bDE(t),

[0110] Differentiating equation (13) yields:

[0111]

[0112] Substituting formula (14) into formula (16) we obtain:

[0113]

[0114] Substituting formula (15) into formula (17), we obtain:

[0115]

[0116] Substituting equations (9), (10) and (11) into equation (18), we obtain:

[0117]

[0118] Since g exists in two cases: 0<g<1 and g>1, if equation (19) is written as , then the system is determined to be convergent in a predefined time; where,

[0119] It can be concluded that the attitude tracking error q in the rigid spacecraft system ve It can converge to a sufficiently small area, and its convergent area is:

[0120]

[0121] in, T max T P The time upper bound of ′.

[0122] Based on the above analysis, the attitude tracking error, angular velocity error and non-singular predefined time sliding surface of the rigid spacecraft system converge within the predefined time.

[0123] To verify the effectiveness of the proposed method, the present invention provides a comparison between the non-singular adaptive fault-tolerant predefined time control (NPFPTC) method and the finite time control (FTC) method:

[0124] In order to make a more effective comparison, all system parameters are consistent, that is: q(0) = [0.3, -0.2, -0.3, 0.8832] T ,ω(0)=[1,0,-1] T rad / s,J ω =0.015I4 kg·m 2 , E=diag([0.6,0.8,0.7,0.5]), J0=[20,1.2,0.9;1.2,17,1.4;0.9,1.4,15]kg·m 2 , Ω=[50,50,50,50] T kg·m 2 ,q d (0) = [0,0,0,1] T ,ω d (0) = [0,0,0] T rad / s, the inertial uncertainty of the given system is: ΔJ = 0.1J0 kg·m 2 , and the given controller fault input is: Occurs at 15 seconds. Occurs at 16 seconds, Given the external disturbance of the system is: d = 0.3 [sin (0.8t), cos (0.5t), cos (0.3t)] N m, the system control signal parameters are: α = 0.015, β = 0.015, λ max =20,ρ0(t)=5,ρ ∞ (t) = 0.05, c = 0.4, p0=0.01,p1=0.01.

[0125] from Figure 2 and Figure 3We see that the attitude tracking error and angular velocity error of the rigid spacecraft system converge within a predefined time and under the preset performance function, the attitude tracking error constraint;

[0126] from Figure 4 It can be seen that the non-singular predefined time sliding surface converges at the predefined time;

[0127] from Figure 5 It can be seen that the non-singular adaptive fault-tolerant predefined time controller converges in the predefined time when controller fault, external disturbance and inertia uncertainty matrix exist simultaneously;

[0128] from Figure 6 and Figure 7 We can see that the NPFPTC method and the FTC method can achieve similar tracking performance in terms of attitude error and angular velocity error, but Figure 8 By comparison, it can be seen that the NPFPTC method requires less input than the FTC method, and when the controller is in the steady-state stage, the FTC method has obvious chattering phenomenon, while the NPFPTC method effectively solves the potential chattering problem in the controller design process.

[0129] In summary, compared with the FTC method, the NPFPTC method has stronger stability to the simultaneous existence of controller failure, external disturbance and inertial uncertainty matrix, and guarantees the steady-state performance and state constraints of the attitude tracking error.

[0130] It is known from common technical knowledge that the present invention can be implemented by other embodiments that do not deviate from its spirit or essential features. Therefore, the above disclosed embodiments are only illustrative in all respects and are not exclusive. All changes within the scope of the present invention or within the scope equivalent to the present invention are included in the present invention.

Claims

1. A predefined time fault-tolerant control method for a rigid spacecraft system, characterized in that: The following steps are involved: S1. Establish the kinematic and dynamic models of the fault-tolerant control system of the rigid spacecraft attitude tracking error, and initialize the system state and control parameters; S2. Design of non-singular predefined time sliding surface based on attitude error tracking control system of rigid spacecraft; S3. Design a non-singular adaptive fault-tolerant predefined time controller.

2. A predefined time fault-tolerant control method for a rigid spacecraft system according to claim 1, characterized in that: In step S1, the dynamic model of the rigid spacecraft angular velocity error tracking control system is expressed as: Among them, ω and are the angular velocity and angular acceleration of the rigid spacecraft, ω e and are the angular velocity error and the time derivative of the angular velocity error of the rigid spacecraft, ω d and are the expected angular velocity of the rigid spacecraft and the time derivative of the expected angular velocity, Ω is the angular velocity of the reaction flywheel, and × is the operator. × Applied to ω × and ω e × , expressed as follows: × =[0,-ω3,ω2;ω3,0,-ω1;-ω2,ω1,0] and ω e × =[0,-ω e3 ,ω e2 ;ω e3 ,0,-ω e1 ; -ω e2 ,ω e1 ,0],J ω =diag([J ω1 ,J ω2 ,J ω3 ,J ω4 ]) is the rotational inertia matrix of the reaction flywheel, J0 and ΔJ represent the nominal part and the uncertain part of the rotational inertia matrix respectively, D is the control torque distribution matrix of the reaction flywheel, C represents the corresponding rotation matrix, u is the reaction flywheel input, E(t) = diag([e1(t), e2(t), e3(t), e4(t)]) is the actuator control efficiency matrix, 0≤e i (t)≤1, i=1,2,3,4 represents the effective coefficient of the i-th reaction flywheel, is the additional fault input of the reaction flywheel, d(t) is the external disturbance; The kinematic model of the rigid spacecraft attitude tracking error system is expressed as: in, I3=diag([1,1,1]),q ve =[q 1e ,q 2e ,q 3e ] T The vector part representing the attitude tracking error, q 4e represents the scalar part of the attitude tracking error, and They are q ve and q 4e The time derivative of .

3. A predefined time fault-tolerant control method for a rigid spacecraft system according to claim 2, characterized in that: In step S2, the design process is as follows: The design performance function is: Among them, 0<c<1, ρ0 and ρ T is i The initial and final values ​​of (t), is the upper bound of the convergence time of the predefined performance function; The design standardized tracking error is: The non-singular predefined time sliding surface s is designed as: Where ε=[ε1,ε2,ε3] T , sign(·) is the sign function, sig(·) is the vector form of sign(·), and the function sig 1+α (ε)=[|ε1| 1+α sign(ε1),|ε2| 1+α sign(ε2),|ε3| 1+α sign(ε3)] T , is the first-order derivative of ε; 0<α<1; is the upper bound of the convergence time of the predefined non-singular predefined time sliding surface; Derivative of ε with respect to time: in, γ=diag([γ1,γ2,γ3]), Yes * The first-order derivative of , ρ(t)=diag([ρ1,ρ2,ρ3]), ρ -1 (t) is the inverse matrix of ρ(t).

4. A predefined time fault-tolerant control method for a rigid spacecraft system according to claim 3, characterized in that: In step S2, the design process is as follows: The design function φ is: Among them, μ=(1-α) / (1+α); Design a non-singular adaptive fault-tolerant predefined time controller as: Among them, ||b|| is the norm of b, ||D|| is the norm of D, is the predefined upper bound of the convergence time of the attitude tracking error, λ max is the maximum value of the eigenvalue of the inertia matrix, and are the estimated parameters, and yes and Adaptive law, Φ=1+||ω||+||ω|| 2 , 0<β<1; The update law of the designed adaptive parameters is: in, p0>0,p1>0, ||g|| is the norm form of g; Design Lyapunov functions V1 and V2: Among them, s T is the transpose of s, and is the error value of the estimated parameter; Derivative of formula (6) yields: Substituting the rigid spacecraft dynamics model equations (1), (2) and (3) into equation (7), we obtain: in, is the second-order derivative of ε, B(t,q ve ) = bDE(t), Differentiating equation (13) yields: Substituting formula (14) into formula (16) we obtain: Substituting formula (15) into formula (17), we obtain: Substituting equations (9), (10) and (11) into equation (18), we obtain: Since g exists in two cases: 0<g<1 and g>1, if equation (19) is written as , then the system is determined to be convergent in a predefined time; where, It can be concluded that the attitude tracking error q in the rigid spacecraft system ve It can converge to a sufficiently small area, and its convergent area is: in, T max T P The time upper bound of ′.

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