Composite adaptive preset time attitude fault-tolerant control method for rigid aircraft

Abstract

The invention relates to a composite adaptive preset time attitude fault-tolerant control method for a rigid aircraft, which comprises the following steps of: constructing a rigid aircraft kinematics and dynamics model based on corrected Rodrigues parameters, and considering an actuator fault problem in the model; a virtual controller in a hyperbolic tangent form is constructed, so that the problem of singularity of the controller caused by derivation of the virtual controller is avoided; a fuzzy logic system is adopted to approach a nonlinear uncertain item of the system, and an adaptive law is designed to estimate the upper bound of composite interference of the system; on the basis, a composite self-adaptive preset time attitude fault-tolerant controller is designed. According to the method, under the conditions of uncertainty of rotational inertia, external interference and actuator faults, the rigid aircraft attitude is converged to the neighborhood near the original point within the preset time, and the upper bound of the minimum convergence time can be predetermined by adjusting a simple parameter.

Description

Technical Field

[0001] The present invention belongs to the technical field of rigid aircraft attitude control. Aiming at the problems of uncertain moment of inertia, external interference and actuator failure faced by rigid aircraft systems during long-term operation in complex space environments, a composite adaptive predetermined time attitude fault-tolerant control method for rigid aircraft is proposed. Background Art

[0002] Aerospace technology is one of the most rapidly developing and most influential cutting-edge scientific and technological fields in the 21st century. It is also an important manifestation of a country's scientific and technological level and comprehensive national strength. As a core component of the aerospace system, rigid aircraft is an important carrier of aerospace activities. Whether it is the docking of the "Shenzhou 11" spacecraft with the "Tiangong 2" space station or the construction of the global GPS positioning and navigation system, its carrier is inseparable from rigid aircraft. Aircraft attitude control is a prerequisite for the normal operation of aircraft payloads and is also the fundamental guarantee for the aircraft to accurately complete its mission.

[0003] Aircraft attitude control refers to the process of maintaining an aircraft in a given direction or maneuvering from an original direction to a target direction with a certain accuracy relative to a reference coordinate system. However, when a rigid aircraft operates for a long time in a complex space environment, it is inevitably affected by the uncertainty of the moment of inertia, external disturbances, and actuator failures, which poses a severe challenge to achieving high-speed and high-precision attitude control. In order to improve the control performance of the aircraft system, finite-time attitude control and fixed-time attitude control have been proposed and developed rapidly due to their excellent performance in fast convergence and high control accuracy. These two control strategies significantly improve the dynamic response performance by achieving system stability within a finite time, and have received widespread attention in high-speed and high-precision application fields such as aerospace. However, these two control strategies have the following two limitations: (i) The convergence time is highly dependent on the initial conditions of the system. The larger the initial value, the longer the convergence time, resulting in insufficient performance of the control system when dealing with a large range of initial errors; (ii) The convergence time is a complex function of multiple control parameters. It is difficult to intuitively establish a clear relationship between the convergence time and the control parameters, which increases the complexity of system parameter adjustment. For time-critical missions such as rendezvous and docking of spacecraft with space stations, these limitations may directly affect the efficiency and success of the mission.

[0004] In order to solve the limitations of finite time / fixed time control, scholars further proposed the concept of scheduled time stability, whose key advantage is that the minimum upper bound of the system convergence time can be accurately determined by adjusting only one control parameter. With this advantage, scholars have successfully applied scheduled time control to practical systems such as robotic arms, aircraft, unmanned vehicles, and servo motors. However, the existing scheduled time control research has the following two main problems: (i) overestimating the upper bound of the system convergence time, that is, or 2Ts, where Ts is a predetermined time constant; (ii) introducing some piecewise continuous functions to solve the controller singularity problem, thereby increasing the complexity of stability analysis. Recently, scholars have proposed several predetermined time criteria, with the upper limit of the convergence time being Ts instead of or 2Ts, which will be beneficial for practical applications.

[0005] On the other hand, rigid aircraft will inevitably experience actuator aging and failure problems when operating in harsh environments for a long time, especially failures in attitude control systems, which are often fatal. These problems may cause the failure of the pre-designed control law, seriously affecting the subsequent attitude adjustment and control of the aircraft. Therefore, in the design of the control scheme, fully considering the failure risk of the control system and the reliability of long-term operation is the key to ensuring the safety of the aircraft and the success of the mission. However, most of the existing aircraft attitude fault-tolerant control methods can only guarantee the asymptotic or finite time convergence of the attitude, and it is difficult to achieve high-speed and high-precision convergence of the attitude in the case of execution failure.

[0006] Therefore, in order to address the problems of uncertain moment of inertia, external interference, and actuator failure faced by rigid aircraft systems during long-term operation in complex space environments, a composite adaptive predetermined time attitude fault-tolerant control method for rigid aircraft is designed. This method can improve the steady-state control accuracy and transient response speed of the aircraft while ensuring the safety and reliability of the aircraft system. It has important academic value and good application prospects. Summary of the invention

[0007] In order to overcome the problems of uncertainty in moment of inertia, external interference and actuator failure in the existing rigid aircraft attitude control system, the present invention proposes a composite adaptive predetermined time attitude fault-tolerant control method. First, the kinematic and dynamic models of the rigid aircraft are constructed based on the modified Rodriguez parameters, and the actuator failure problem is considered in the model; secondly, a virtual controller in the form of hyperbolic tangent is constructed to avoid the controller singularity problem caused by the derivation of the virtual controller; then, a fuzzy logic system is used to approximate the nonlinear uncertainty of the system, and an adaptive law is designed to estimate the upper bound of the system's composite interference. On this basis, a composite adaptive predetermined time attitude fault-tolerant controller is designed to ensure that the aircraft attitude can converge to a neighborhood near the origin within a predetermined time, where the convergence time can be predetermined by adjusting a simple parameter.

[0008] The technical solutions proposed to solve the above technical problems are as follows:

[0009] A composite adaptive predetermined time attitude fault-tolerant control method for a rigid aircraft comprises the following steps:

[0010] Step 1: Establish the kinematic and dynamic models of the rigid aircraft and initialize the system state and control parameters. The process is as follows:

[0011] 1.1 The kinematic equation of the rigid aircraft system is:

[0012]

[0013] Where σ=[σ1,σ2,σ3] T Represents the attitude of the rigid aircraft; σ1, σ2, σ3 are the values ​​mapped on the x, y, and z axes of the spatial rectangular coordinate system respectively; is the derivative of σ; ω∈R 3 is the angular velocity of the rigid vehicle; G(σ)∈R 3×3 is the Jacobian matrix, defined as I3 is R 3×3 Identity matrix; σ T is the transpose of σ; × It is expressed as:

[0014]

[0015] 1.2 The dynamic equation of the rigid aircraft system is:

[0016]

[0017] Among them, J∈R 3×3 is the rotational inertia matrix of the aircraft; is the angular acceleration of the aircraft; d∈R 3represents external disturbance, satisfying ||d||≤d m , d m is an unknown positive constant; ||d|| represents the bi-norm of d; ω × It is expressed as:

[0018]

[0019] E(t)=diag{e1(t),e2(t),e3(t)} is a 3×3 diagonal matrix, representing the actuator efficiency matrix, e i (t)∈(0,1],i=1,2,3 represents the health status of the ith actuator: when e i (t) = 1 means the i-th actuator is normal, when 0 < e i (t)<1 indicates that the i-th actuator has partial failure. i (t) = 0 means that the i-th actuator has completely lost its control function; u = [u1,u2,u3] T is the control torque; For actuator bias fault, satisfy u m is an unknown positive constant; express The second norm of ;

[0020] 1.3 The rotational inertia matrix J satisfies J = J0 + ΔJ, where J0∈R 3×3 and ΔJ∈R 3×3 denote the nominal part and the uncertain part of J respectively, then equation (3) can be rewritten as:

[0021]

[0022] Further we get:

[0023]

[0024] definition The kinematic and dynamic equations of a rigid aircraft are reformulated as:

[0025]

[0026] in, is the nonlinear uncertain part of the system, Considered as part of the total interference of the system;

[0027]

[0028] Step 2, for the rigid aircraft system with inertial uncertainty, external disturbance and actuator failure, the required virtual controller is designed based on the inverse recursive idea;

[0029] Step 3, designing a predetermined time adaptive fuzzy controller. Further, the process of step 2 is as follows:

[0030] Design virtual controller α=[α1,α2,α3] T for:

[0031]

[0032]

[0033] in, T s >0 is a predetermined time constant, 0<γ<1,κ>0,b>1,β1>0,β2>0 are positive constants; sig γ (·)=|·| γ sgn(·), sgn(·) represents the sign function.

[0034] Furthermore, the process of step 3 is as follows:

[0035] 3.1 Define the fuzzy logic system as:

[0036] Λ i =W i T S i (Z n )+ε i ,i=1,2,3 (10)

[0037] in, is the total uncertainty of the system, is the input vector, S i (X n )∈R 3 is the basis function, W i T W i The transpose of W i ∈R 3 is the weight vector, ε i is the approximation error, satisfying |ε i |≤ε N ,i=1,2,3,ε N is a very small positive constant;

[0038] 3.2 Definition of composite interference D′=[D1′,D2′,D3′] T for:

[0039] D′=ε+D (11)

[0040] Where ε=[ε1,ε2,ε3] T, the composite interference D′ satisfies ||D′||≤d a , d a is an unknown positive constant;

[0041] 3.3 Considering the composite scheduled time controller is designed as:

[0042]

[0043] Where z = [z1, z2, z3] T =x2-α is the virtual error; is a 3×3 diagonal matrix, ||W1||,||W2||,||W3|| are the bi-norms of W1, W2, and W3 respectively, and θ=max{||W1|| 2 ,||W2|| 2 ,||W3|| 2} is ||W1|| 2 ,||W2|| 2 ,||W3|| 2 The maximum value of d l is a normal number, satisfying is the estimated value of θ, is d l An estimated value of are all positive numbers, and their values ​​satisfy: τ>0, h1=k1,

[0044] 3.4 Design and The adaptive update laws are:

[0045]

[0046] Among them, λ, m1, m2, c1, c2 are all positive numbers, and their values ​​satisfy: λ>0, They are The derivative of ; ||z|| represents the second norm of z.

[0047] Furthermore, the method further comprises the following steps:

[0048] Step 4, proof of stability over a predetermined period of time, the process is as follows:

[0049] 4.1 Based on the inversion recursive idea, the following Lyapunov function is designed:

[0050]

[0051] By taking the derivative of formula (15), we can obtain:

[0052]

[0053] 4.2 Based on the inversion recursive idea, the following Lyapunov function is designed:

[0054]

[0055] By taking the derivative of formula (17), we can obtain:

[0056]

[0057] in, and is the parameter estimation error, is a positive constant;

[0058] 4.3 Based on the inversion recursive idea, the following Lyapunov function is designed:

[0059]

[0060] Deriving equation (19) and substituting equations (13) and (14) into it, we obtain:

[0061]

[0062] in, is a positive constant, Θ(γ)=(γ / 2)·((2-γ) / 2) (2- γ ) / γ is a positive constant;

[0063] Based on the above analysis, the attitude of the rigid aircraft can be determined within a predetermined time T s Converges to a small enough neighborhood.

[0064] The present invention designs a composite adaptive predetermined time attitude fault-tolerant control method for a rigid aircraft, designs a virtual controller in the form of a hyperbolic tangent based on the inverse recursive idea, avoids the controller singularity problem caused by the derivation of the virtual controller, introduces a fuzzy logic system to estimate and compensate for the system nonlinear uncertainty items including the uncertainty of the moment of inertia, external interference and actuator failure, and designs an adaptive law to estimate the upper bound of the system composite interference including the external interference and the approximation error of the fuzzy logic system. On this basis, a composite adaptive predetermined time attitude fault-tolerant controller is designed to achieve the rigid aircraft attitude being able to converge to a neighborhood near the origin within a predetermined time, wherein the minimum convergence time upper bound can be predetermined by adjusting a simple parameter.

[0065] The technical concept of the present invention is as follows: for a rigid aircraft system with uncertain moment of inertia, external disturbance and actuator failure, firstly, a kinematic and dynamic model of the rigid aircraft is constructed based on the modified Rodriguez parameters, and the actuator failure problem is considered in the model; secondly, a virtual controller in the form of hyperbolic tangent is constructed to avoid the controller singularity problem caused by the derivation of the virtual controller; then, a fuzzy logic system is used to approximate the nonlinear uncertainty of the system, and an adaptive law is designed to estimate the upper bound of the system's composite disturbance. On this basis, a composite adaptive predetermined time attitude fault-tolerant controller is designed to ensure that the aircraft attitude can converge to a neighborhood near the origin within a predetermined time, where the convergence time can be predetermined by adjusting a simple parameter.

[0066] The beneficial effects of the present invention are: when a rigid aircraft has uncertain moment of inertia, external interference and actuator failure, the aircraft attitude converges within a predetermined time, and the minimum upper limit of the convergence time is only related to one control parameter. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a control flow chart of the present invention;

[0068] Figure 2 The attitude diagrams of the rigid aircraft at Ts = 10, 15, and 20 seconds;

[0069] Figure 3 Angular velocity diagram of the rigid aircraft at Ts = 10, 15, and 20 seconds;

[0070] Figure 4 is the virtual error diagram of the rigid aircraft under Ts = 10, 15, and 20 seconds;

[0071] Figure 5 The control torque diagram of the rigid aircraft at Ts = 10, 15, and 20 seconds;

[0072] Figure 6 The attitude diagram of the rigid aircraft under different κ values ​​at Ts = 15 seconds;

[0073] Figure 7 The control torque diagram of the rigid aircraft under different κ values ​​when Ts = 15 seconds. DETAILED DESCRIPTION

[0074] The present invention will be further described below in conjunction with the accompanying drawings.

[0075] Reference Figure 1-Figure 7 , a composite adaptive predetermined time attitude fault-tolerant control method for a rigid aircraft, comprising the following steps:

[0076] Step 1: Establish the kinematic and dynamic models of the rigid aircraft and initialize the system state and control parameters. The process is as follows:

[0077] 1.1 The kinematic equation of the rigid aircraft system is:

[0078]

[0079] Where σ=[σ1,σ2,σ3] T Represents the attitude of the rigid aircraft; σ1, σ2, σ3 are the values ​​mapped on the x, y, and z axes of the spatial rectangular coordinate system respectively; is the derivative of σ; ω∈R 3 is the angular velocity of the rigid vehicle; G(σ)∈R 3×3 is the Jacobian matrix, defined as I3 is R 3×3 Identity matrix; σ T is the transpose of σ; × It is expressed as:

[0080]

[0081] 1.2 The dynamic equation of the rigid aircraft system is:

[0082]

[0083] Among them, J∈R 3×3 is the rotational inertia matrix of the aircraft; is the angular acceleration of the aircraft; d∈R 3 represents external disturbance, satisfying ||d||≤d m , d m is an unknown positive constant; ||d|| represents the bi-norm of d; ω × It is expressed as:

[0084]

[0085] E(t)=diag{e1(t),e2(t),e3(t)} is a 3×3 diagonal matrix, representing the actuator efficiency matrix, e i (t)∈(0,1],i=1,2,3 represents the health status of the ith actuator: when e i (t) = 1 means the i-th actuator is normal, when 0 < e i (t)<1 indicates that the i-th actuator has partial failure. i (t) = 0 means that the i-th actuator has completely lost its control function; u = [u1,u2,u3] T is the control torque; For actuator bias fault, satisfy um is an unknown positive constant; express The second norm of ;

[0086] 1.3 The rotational inertia matrix J satisfies J = J0 + ΔJ, where J0∈R 3×3 and ΔJ∈R 3×3 denote the nominal part and the uncertain part of J respectively, then equation (3) can be rewritten as:

[0087]

[0088] Further we get:

[0089]

[0090] definition The kinematic and dynamic equations of a rigid aircraft are reformulated as:

[0091]

[0092] in, is the nonlinear uncertain part of the system, Considered as part of the total interference of the system;

[0093]

[0094] Step 2: For the rigid aircraft system with inertial uncertainty, external disturbance and actuator failure, the required virtual controller is designed based on the inverse recursive idea. The process is as follows:

[0095] Design virtual controller α=[α1,α2,α3] T for:

[0096]

[0097]

[0098] in, T s >0 is a predetermined time constant, 0<γ<1,κ>0,b>1,β1>0,β2>0 are positive constants; sig γ (·)=|·| γ sgn(·), sgn(·) represents the sign function;

[0099] Step 3, design the scheduled time adaptive fuzzy controller, the process is as follows:

[0100] 3.1 Define the fuzzy logic system as:

[0101] Λi =W i T S i (Z n )+ε i ,i=1,2,3 (10)

[0102] in, is the total uncertainty of the system, is the input vector, S i (X n )∈R 3 is the basis function, W i T W i The transpose of W i ∈R 3 is the weight vector, ε i is the approximation error, satisfying |ε i |≤ε N ,i=1,2,3,ε N is a very small positive constant;

[0103] 3.2 Definition of composite interference D′=[D1′,D2′,D3′] T for:

[0104] D′=ε+D (11)

[0105] Where ε=[ε1,ε2,ε3] T , the composite interference D′ satisfies ||D′||≤d a , d a is an unknown positive constant;

[0106] 3.3 Considering the composite scheduled time controller is designed as:

[0107]

[0108] Where z = [z1, z2, z3] T =x2-α is the virtual error; is a 3×3 diagonal matrix, ||W1||,||W2||,||W3|| are the bi-norms of W1, W2, and W3 respectively, and θ=max{||W1|| 2 ,||W2|| 2 ,||W3|| 2} is ||W1|| 2 ,||W2|| 2 ,||W3|| 2 The maximum value of d l is a normal number, satisfying is the estimated value of θ, is d l An estimated value of are all positive numbers, and their values ​​satisfy: τ>0, h1=k1,

[0109] 3.4 Design and The adaptive update laws are:

[0110]

[0111] Among them, λ, m1, m2, c1, c2 are all positive numbers, and their values ​​satisfy: λ>0, They are The derivative of ; ||z|| represents the second norm of z;

[0112] Step 4, proof of stability over a predetermined period of time, the process is as follows:

[0113] 4.1 Based on the inversion recursive idea, the following Lyapunov function is designed:

[0114]

[0115] By taking the derivative of formula (15), we can obtain:

[0116]

[0117] 4.2 Based on the inversion recursive idea, the following Lyapunov function is designed:

[0118]

[0119] By taking the derivative of formula (17), we can obtain:

[0120]

[0121] in, and is the parameter estimation error, is a positive constant;

[0122] 4.3 Based on the inversion recursive idea, the following Lyapunov function is designed:

[0123]

[0124] Deriving equation (19) and substituting equations (13) and (14) into it, we obtain:

[0125]

[0126] in, is a positive constant, Θ(γ)=(γ / 2)·((2-γ) / 2) (2- γ ) / γ is a positive constant;

[0127] Based on the above analysis, the attitude of the rigid aircraft can be determined within a predetermined time T s Converges to a small enough neighborhood.

[0128] To verify the effectiveness of the proposed method, this method is simulated for a rigid aircraft system. The system initialization conditions and control parameters are set as follows: the sampling step is 0.001 seconds; the system initial value is selected as: σ(0) = [0.2, 0.1, -0.1] T ,ω(0)=[-1,0,1] T Radians / second; the nominal part of the rotational inertia matrix J0 = [20, 1.2, 0.9; 1.2, 17, 1.4; 0.9, 1.4, 15] kg*m2, the uncertain part of the rotational inertia matrix ΔJ = diag[sin(0.1t), 2sin(0.2t), 3sin(0.3t)] kg*m2; external disturbance d(t) = [0.2sin(0.1t), 0.3sin(0.2t), 0.5sin(0.2t)] T Newton meter, actuator bias fault Newton meters, actuator efficiency matrix E(t) = diag[0.85,0.85,0.85]; virtual controller, actual controller and adaptive law parameters are set to In order to verify the scheduled time convergence performance of the proposed control method, three groups of different Ts values ​​were selected, namely Ts = 10 seconds, 15 seconds and 20 seconds.

[0129] Figure 2-Figure 7 The simulation results of the proposed rigid aircraft composite adaptive predetermined time attitude fault-tolerant control method on system (7) are shown in FIG. Figure 2 and Figure 3 They are the attitude effect diagram and angular velocity effect diagram of the rigid aircraft under Ts = 10, 15, and 20 seconds. Figure 2 and Figure 3 It can be seen that the aircraft attitude and angular velocity can converge quickly within the pre-given time Ts. Figure 4 and Figure 5 They are the virtual error effect diagram and control torque effect diagram of the rigid aircraft under Ts = 10, 15, and 20 seconds. Figure 4 and Figure 5 Similar conclusions can be drawn. Figure 2-Figure 5It can be seen that the smaller the value of Ts, the faster the aircraft system converges, but the greater the control torque. In order to further verify the influence of the control parameter κ on the system performance, we fixed Ts = 15 seconds, and the corresponding simulation results are as follows Figure 6 and 7 As shown. Figure 6 It can be seen that a smaller κ value can accelerate the convergence speed of the aircraft system, but it will also lead to a larger control torque. Therefore, the selection of Ts and κ should be based on the actual mission requirements to strike a balance between convergence speed and control torque. In summary, even when considering the uncertainty of the moment of inertia of the rigid aircraft system, external disturbances, and actuator failures, the proposed control method can still show good transient and steady-state performance.

[0130] The above is an excellent optimization effect of an embodiment of the present invention. Obviously, the present invention is not limited to the above embodiment, and various modifications can be made to it without departing from the basic spirit of the present invention and not exceeding the scope of the essential content of the present invention. The control method designed by the present invention has a good control effect on the rigid aircraft system with uncertain moment of inertia, external interference and actuator failure, and can effectively improve the attitude control accuracy and rapidity of the system.

Claims

1. A composite adaptive predetermined time attitude fault-tolerant control method for a rigid aircraft, characterized in that the method comprises the following steps: Step 1: Establish the kinematic and dynamic models of the rigid aircraft and initialize the system state and control parameters. The process is as follows: 1.1 The kinematic equation of the rigid aircraft system is: in, σ=[σ1,σ2,σ3] T Represents the attitude of the rigid aircraft; σ1, σ2, σ3 are the values ​​mapped on the x, y, and z axes of the spatial rectangular coordinate system respectively; is the derivative of σ; ω∈R 3 is the angular velocity of the rigid vehicle; G(σ)∈R 3×3 is the Jacobian matrix, defined as I3 is R 3×3 Identity matrix; σ T is the transpose of σ; × It is expressed as: 1.2 The dynamic equation of the rigid aircraft system is: Among them, J∈R 3×3 is the rotational inertia matrix of the aircraft; is the angular acceleration of the aircraft; d∈R 3 represents external disturbance, satisfying ||d||≤d m , d m is an unknown normal number; ||d|| represents the bi-norm of d; ω × It is expressed as: E(t)=diag{e1(t),e2(t),e3(t)} is a 3×3 diagonal matrix, representing the actuator efficiency matrix, e i (t)∈(0,1],i=1,2,3 represents the health status of the ith actuator: when e i (t) = 1 means the i-th actuator is normal, when 0 < e i (t)<1 indicates that the i-th actuator has partial failure. i (t) = 0 means that the i-th actuator has completely lost its control function; u = [u1,u2,u3] T is the control torque; For actuator bias fault, satisfy u m is an unknown positive constant; express The second norm of ; 1.3 The rotational inertia matrix J satisfies J = J0 + ΔJ, where J0∈R 3×3 and ΔJ∈R 3×3 denote the nominal part and the uncertain part of J respectively, then equation (3) can be rewritten as: Further we get: definition The kinematic and dynamic equations of a rigid aircraft are reformulated as: in, is the nonlinear uncertain part of the system, Considered as part of the total interference of the system; Step 2, for the rigid aircraft system with inertial uncertainty, external disturbance and actuator failure, the required virtual controller is designed based on the inverse recursive idea; Step 3, design a scheduled time adaptive fuzzy controller.

2. A composite adaptive predetermined time attitude fault-tolerant control method for a rigid aircraft as claimed in claim 1, characterized in that: The process of step 2 is as follows: Design virtual controller α=[α1,α2,α3] T for: α i =-k1sig 1-γ (x 1i )+k2sig 1+γ (x 1i )+k3x 1i (9) in, T s >0 is a predetermined time constant, 0<γ<1,κ>0,b>1,β1>0,β2>0 are positive constants; sig γ (·)=|·| γ sgn(·), sgn(·) represents the sign function.

3. A composite adaptive predetermined time attitude fault-tolerant control method for a rigid aircraft as claimed in claim 2, characterized in that: The process of step 3 is as follows: 3.1 Define the fuzzy logic system as: in, is the total uncertainty of the system, is the input vector, S i (X n )∈R 3 is the basis function, W i T W i The transpose of W i ∈R 3 is the weight vector, ε i is the approximation error, satisfying |ε i |≤ε N ,i=1,2,3,ε N is a very small positive constant; 3.2 Definition of composite interference D′=[D1′,D2′,D3′] T for: D′=ε+D (11) Where ε=[ε1,ε2,ε3] T , the composite interference D′ satisfies ||D′||≤d a , d a is an unknown positive constant; 3.3 Considering the composite scheduled time controller is designed as: Where z = [z1, z2, z3] T =x2-α is the virtual error; is a 3×3 diagonal matrix, ||W1||,||W2||,||W3|| are the bi-norms of W1, W2, and W3 respectively, and θ=max{||W1|| 2 ,||W2|| 2 ,||W3|| 2 } is ||W1|| 2 ,||W2|| 2 ,||W3|| 2 The maximum value of d l is a normal number, satisfying is the estimated value of θ, is d l The estimated value of τ,h1, h2, h3 are all positive numbers, and their values ​​satisfy: τ>0, 3.4 Design and The adaptive update laws are: Among them, λ, m1, m2, c1, c2 are all positive numbers, and their values ​​satisfy: λ>0, They are The derivative of ; ||z|| represents the second norm of z.

4. A composite adaptive predetermined time attitude fault-tolerant control method for a rigid aircraft as claimed in claim 1 or 2, characterized in that: The method further comprises the following steps: Step 4, proof of stability over a predetermined period of time, the process is as follows: 4.1 Based on the inversion recursive idea, the first step is to design the following Lyapunov function: By taking the derivative of formula (15), we can obtain: 4.2 Based on the inversion recursive idea, the second step is to design the following Lyapunov function: By taking the derivative of formula (17), we can obtain: in, and is the parameter estimation error, is a positive constant; 4.3 Based on the inversion recursive idea, the third step is to design the following Lyapunov function: Deriving equation (19) and substituting equations (13) and (14) into it, we obtain: in, is a positive constant, Θ(γ)=(γ / 2)·((2-γ) / 2) (2-γ) / γ is a positive constant; Based on the above analysis, the attitude of the rigid aircraft can be determined within a predetermined time T s Converges to a small enough neighborhood.

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