A non-singular finite-time fault-tolerant formation cooperative control method

Abstract

The present invention relates to a non-singular finite-time fault-tolerant formation cooperative control method, and belongs to the technical field of intelligent cooperative control of formation systems. The method includes 1) establishing a velocity layer and an attitude layer in a six-degree-of-freedom dynamic model of a fixed-wing formation system; 2) establishing an actuator fault model of the thrust actuator and the rudder actuator contained in the six-degree-of-freedom dynamic model; 3) establishing a topological relationship of a fixed-wing formation system including multiple models in step one; 4) solving the adjacency error of the attitude and velocity layers; 5) designing a thrust control law and an adaptive law in a velocity layer finite-time controller; 6) designing a virtual control law, a rudder control law and an adaptive law in an attitude layer finite-time controller. The present invention can make up for the gap in the research of the six-degree-of-freedom fixed-wing model of the formation system, overcome the instability problem caused by actuator failure, and overcome the potential singular value problem in the attitude layer controller.

Description

Technical Field

[0001] The invention relates to a non-singular finite-time fault-tolerant formation cooperative control method, belonging to the technical field of formation system intelligent cooperative control. Background Art

[0002] Formation collaborative control technology has significant advantages in mission execution and cost reduction, so this field has developed rapidly. Research mainly focuses on maintaining and changing the shape, speed and attitude synchronization of the formation. Existing formation system models usually use a three-degree-of-freedom model or only consider a single attitude / longitudinal model, which is different from the six-degree-of-freedom model actually required. Therefore, there is an urgent need for more in-depth research on the six-degree-of-freedom fixed-wing formation system.

[0003] Current conditions show that actuator failures occur frequently due to the aging of formation system components and potential collisions. Researchers enhance the robustness of the system and ensure flight safety by applying fault-tolerant control methods. In addition, due to the rapidly changing actual mission environment, the formation system needs to achieve rapid convergence of attitude and speed to improve system performance. Although some progress has been made in finite-time control methods in the field of multi-agent and formation systems, there is a lack of comprehensive research on six-degree-of-freedom fixed-wing formation systems. At the same time, the negative power terms in the controller will cause singular value problems (non-differentiable), which is a challenge that needs to be addressed urgently. Summary of the invention

[0004] In view of the deficiencies in the above-mentioned prior art, the present invention provides a non-singular finite-time fault-tolerant formation collaborative control method, which can fill the gap in the research of six-degree-of-freedom fixed-wing models of formation systems, overcome the instability problem caused by actuator failure, and overcome the potential singular value problem in the attitude layer controller while ensuring that the speed and attitude of the formation system converge within a finite time.

[0005] A non-singular finite-time fault-tolerant formation cooperative control method of the present invention is special in that it comprises the following steps:

[0006] Step 1: Establish the velocity layer and attitude layer in the six-degree-of-freedom dynamics model of the fixed-wing formation system;

[0007] Step 2: establishing an actuator fault model of the thrust actuator and the rudder actuator included in the six-degree-of-freedom dynamic model established in step 1;

[0008] Step 3: Establish a topological relationship of a fixed-wing formation system including multiple models in step 1;

[0009] Step 4: Based on the topological relationship in step 3, solve the adjacency error of the attitude and velocity layers;

[0010] Step 5: Based on the adjacent error of the velocity layer in step 4, the thrust control law and the adaptive law in the velocity layer finite time controller are designed;

[0011] Step 6: Based on the attitude adjacency error in step 4, design the virtual control law, rudder control law and adaptive law in the attitude layer finite time controller.

[0012] Preferably, the velocity layer of the six-degree-of-freedom dynamics model established in step 1 is:

[0013]

[0014] Among them, m i Indicates the mass of the drone, p i =[x i ,y i ,z i ] T represents the position vector in the ground coordinate system, represents the attitude angle vector, ω i =[p i ,q i ,r i ] T Represents the attitude angular velocity vector, T i =[T xi ,0,0] T represents the thrust vector, g = [0,0,g] T is the gravitational acceleration, S(ω i )v i Represents ω i ×v i , d vi For external disturbance.

[0015] R 1 is the transformation matrix between the body coordinate system and the ground coordinate system:

[0016]

[0017] Where s a and c a Represent sin(a) and cos(a), F i is the aerodynamic parameter, and its expression is:

[0018]

[0019] Where C Di ,C Yi ,C Li They are drag coefficient, sideslip coefficient and lift coefficient respectively.

[0020] Preferably, the six-degree-of-freedom dynamics model posture layer established in step 1 is:

[0021]

[0022] Where S(ω i )J i ω i Represents ω i ×J i ω i , d ωi is the external disturbance, J i is the inertia tensor of the body coordinate system xz plane, and its expression is:

[0023]

[0024] R 2 is the transformation matrix of angular velocity and attitude angle projection, and its expression is:

[0025]

[0026] C(δ i ) is the control effectiveness matrix, and its expression is:

[0027]

[0028] N i is the dynamic vector, and its expression is:

[0029]

[0030] Where S i is the wing area, is the air pressure, ρ is the air density, b i is the wingspan length, c nδri ,c mδei ,c lδai are the chord lengths along the x, y, and z axes of the fuselage coordinate system, is the average chord length, C′ ni ,C′ mi ,C′ li are the aerodynamic coefficients corresponding to the x, y, and z axes of the aircraft coordinate system respectively.

[0031] Preferably, the thrust actuator and rudder actuator actuator fault models in step 2 include effectiveness loss and bias fault, which are respectively:

[0032] T xi =ρ Ti T xi0 +T xif , δ i =ρ δiδ i0 +δ if

[0033] Where 0≤ρ Ti ≤1 represents the thrust actuator efficiency, T xif represents the bias fault size; ρ δi =diag{ρ δai ,ρ δei ,ρ δri} represents the thrust actuator efficiency, δ if =[δ aif ,δ eif ,δ rif ] T Indicates the bias fault size;

[0034] Considering the influence of actuator failure, the velocity and attitude layer dynamics model of the fixed-wing formation system is expressed as:

[0035]

[0036] in, represents the combined speed of the drone, △ vi and △′ ωi represents the modeling error.

[0037] Preferably, the specific steps of step three are as follows:

[0038] Establishing topological relationships in, Represents each fixed-wing system node; represents the connection between the i-th and j-th fixed-wing systems, i.e., the edge set; represents the weight of the corresponding edge set; if a ij =a ji ≠0 indicates that the i-th and j-th fixed-wing systems are connected, otherwise a ij =a ji =0; the adjacency matrix of the i-th fixed-wing system is expressed as

[0039] V r and is the speed and posture to be tracked, and the adjacency error of the posture and speed layers in step 4 satisfies:

[0040]

[0041] in, is the tracking error, λ i1 ,λ i2 ,λ i3 ,λ i4 is a positive constant, V r and are the expected speed and attitude respectively, and satisfy

[0042]

[0043] Preferably, in step three, vi +d vi The uncertain terms are approximated by RBF neural network:

[0044]

[0045] in, Meets the boundedness condition.

[0046] Preferably, the thrust control law in the speed layer finite time controller in step 5 is:

[0047]

[0048] in,

[0049] Preferably, the adaptive law in the speed layer finite time controller in step 5 is:

[0050]

[0051] Among them, the adaptive parameters satisfy θ vi =β vi sup t≥0 |T xif |,β vi =1 / ρ Ti , the estimated error is γ vi1 ,γ vi2 ,γ vi3 ,σ vi1 ,σ vi2 ,σ vi3 is a positive number; preferably, in step 2, △′ ωi +d ωi The uncertain terms are approximated by RBF neural network:

[0052]

[0053] in, Meet the boundedness condition;

[0054] Preferably, the attitude layer finite time controller in step 6 has a singular value problem, and the switching function is introduced as follows:

[0055]

[0056] Among them, τ 1 is a small positive constant, m = {φ,θ,ψ},

[0057] Preferably, the virtual control law in the attitude layer finite time controller in step 6 is:

[0058]

[0059] in, m={φ,θ,ψ},

[0060] Preferably, the control law of the rudder surface in the attitude layer finite time controller in step 6 is as follows:

[0061]

[0062] in, n={1,2,3},e ωi =diag{e ωi1 ,e ωi2 ,e ωi3}.

[0063] Preferably, the adaptive law in the speed layer finite time controller of step six is ​​as follows:

[0064]

[0065] Among them, the adaptive parameters satisfy β ωi =1 / g ωi The estimated error is γ ωi1 ,γ ωi2 ,σ ωi1 ,σ ωi2 Is a normal number.

[0066] The present invention designs a non-singular finite-time fault-tolerant formation cooperative control method, which solves the cooperative control problem of a six-degree-of-freedom fixed-wing formation system, and has the following beneficial effects:

[0067] 1. For the speed and attitude layers of the fixed-wing formation system, the speed and attitude finite-time formation collaborative control strategies are designed respectively. By flexibly switching between fractional and exponential functions, the singular value (non-differentiable) problem in the controller is eliminated, and the finite-time control of the fixed-wing formation system is realized;

[0068] 2. Considering the actuator failures in the system, an adaptive update law for fault parameters is designed to solve the actuator failure problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of the present invention;

[0070] Figure 2 is the roll-on angle tracking response diagram;

[0071] Figure 3 is the pitch angle tracking response diagram;

[0072] Figure 4 is the heading angle tracking response diagram;

[0073] Figure 5 is the speed tracking response plot. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0075] Example 1

[0076] A non-singular finite-time fault-tolerant formation cooperative control method of this embodiment is shown in the attached flowchart. Figure 1 , including the following steps:

[0077] Step 1: Establish the velocity layer and attitude layer in the six-degree-of-freedom dynamics model of the fixed-wing formation system;

[0078] The velocity layer in the six-degree-of-freedom dynamic model of the fixed-wing formation system established in step 1 is:

[0079]

[0080] Among them, m i Indicates the mass of the drone, p i =[x i ,y i ,z i ] T represents the position vector in the ground coordinate system, represents the attitude angle vector, ω i =[p i ,q i ,r i ] T Represents the attitude angular velocity vector, T i =[T xi ,0,0] T represents the thrust vector, g = [0,0,g] T is the gravitational acceleration, S(ω i )v i Represents ω i ×vi , d vi is the external disturbance. 1 is the transformation matrix between the body coordinate system and the ground coordinate system:

[0081]

[0082] Where s a and c a Represent sin(a) and cos(a), F i is the aerodynamic parameter, and its expression is:

[0083]

[0084] Where C Di ,C Yi ,C Li are the drag coefficient, sideslip coefficient and lift coefficient respectively;

[0085] The attitude layer in the six-degree-of-freedom dynamics model of the fixed-wing formation system established in step 1 is:

[0086]

[0087] Where S(ω i )J i ω i Represents ω i ×J i ω i , d ωi is the external disturbance, J i is the inertia tensor of the body coordinate system xz plane, and its expression is:

[0088]

[0089] R 2 is the transformation matrix of angular velocity and attitude angle projection, and its expression is:

[0090]

[0091] C(δ i ) is the control effectiveness matrix, and its expression is:

[0092]

[0093] N i is the dynamic vector, and its expression is:

[0094]

[0095] Where S i is the wing area, is the air pressure, ρ is the air density, b i is the wingspan length, c nδri ,c mδei ,c lδai are the chord lengths along the x, y, and z axes of the fuselage coordinate system, is the average chord length, C′ ni ,C′ mi ,C′ li are the aerodynamic coefficients corresponding to the x, y, and z axes of the aircraft coordinate system respectively.

[0096] Step 2: establishing an actuator fault model of the thrust actuator and the rudder actuator included in the six-degree-of-freedom dynamic model established in step 1;

[0097] The thrust actuator and rudder actuator actuator fault models in step 2 include effectiveness loss and bias failure, which are:

[0098] T xi =ρ Ti T xi0 +T xif , δ i =ρ δi δ i0 +δ if

[0099] Where 0≤ρ Ti ≤1 represents the thrust actuator efficiency, T xif represents the bias fault size; ρ δi =diag{ρ δai ,ρ δei ,ρ δri} represents the thrust actuator efficiency, δ if =[δ aif ,δ eif ,δ rif ] T Indicates the bias fault magnitude.

[0100] Considering the influence of actuator failure, the velocity and attitude layer dynamics model of the fixed-wing formation system is expressed as:

[0101]

[0102] in, represents the combined speed of the drone, △ vi and △′ ωi represents the modeling error.

[0103] Step 3: Establish a topological relationship for the actuator fault model in step 2;

[0104] Step 3 Topological relationship The meaning is as follows:

[0105] Nodes representing each fixed-wing system; represents the connection between the i-th and j-th fixed-wing systems, i.e., the edge set; represents the weight of the corresponding edge set. ij =a ji ≠0 indicates that the i-th and j-th fixed-wing systems are connected, otherwise a ij =a ji = 0. The adjacency matrix of the i-th fixed-wing system is expressed as

[0106] Step 4: Based on the topological relationship in step 3, solve the adjacency error of the velocity and attitude layers;

[0107] In step 4, V r and is the speed and attitude to be tracked, and the adjacency error solution of the speed and attitude layer is:

[0108]

[0109] in, is the tracking error, λ i1 ,λ i2 ,λ i3 ,λ i4 is a positive constant, V r and are the expected speed and attitude respectively, and satisfy

[0110] Step 5: Design a velocity layer finite time controller for the velocity layer adjacency error in step 4;

[0111] In step 5, the speed layer finite time controller design process is:

[0112] Use RBF neural network to approximate the uncertainty term △ in step 4 vi :

[0113]

[0114] in, Meets the boundedness condition.

[0115] The thrust control law in the speed layer finite time controller in the design step 5 is:

[0116]

[0117] in,

[0118] The adaptive law in the speed finite time controller described in the design step 5 is as follows:

[0119]

[0120] Step 6: Design an attitude layer finite time controller for the speed layer finite time controller in step 5;

[0121] In step 6, the design process of the attitude layer finite time controller is:

[0122] Approximating the Uncertain Term △′ in Step 2 Using RBF Neural Network ωi :

[0123]

[0124] in, Meets the boundedness condition.

[0125] The attitude finite time controller has a singular value problem, and the switching function is introduced as follows:

[0126]

[0127] Among them, τ 1 is a small positive constant, m = {φ,θ,ψ},

[0128] The virtual control law in the attitude layer finite time controller described in the design step six is:

[0129]

[0130] in, m={φ,θ,ψ},

[0131] The control law of the rudder surface in the attitude layer finite time controller described in design step 6 is as follows:

[0132]

[0133] in, n={1,2,3},e ωi =diag{e ωi1 ,e ωi2 ,e ωi3}.

[0134] The adaptive law in the attitude layer finite time controller described in design step 6 is as follows:

[0135]

[0136] Among them, the adaptive parameters satisfy β ωi =1 / g ωi The estimated error is γ ωi1 ,γ ωi2 ,σ ωi1 ,σ ωi2 Is a normal number.

[0137] Example 2

[0138] Considering that the six-degree-of-freedom fixed-wing system is a more common system than the fixed-wing system, a six-degree-of-freedom fixed-wing formation composed of three fixed-wing systems is taken as an example to further prove the effectiveness of the proposed non-singular finite-time fault-tolerant formation cooperative control method. The adjacency matrix of the model can be expressed as:

[0139]

[0140] The initial states of the three fixed-wing systems can be expressed as:

[0141] V 1 =V 2 =V 2 =40m / s, ω 1 =ω 2 =ω 3 =[0,0,0] T deg / s.

[0142] The tasks to be performed are:

[0143] Three six-degree-of-freedom fixed-wing systems perform a maneuvering rotation climb mission. On the one hand, they ensure that the speed is quickly increased to 50m / s, and on the other hand, their attitude is required to achieve attitude tracking for a limited time. The tracking trajectory is as follows:

[0144] Actuator faults are:

[0145] Assume that Wingman 2 encounters an actuator failure after 5 seconds: δi =[1,0.9,1], and the fault is eliminated after 10 seconds.

[0146] Considering the actual performance of the fixed-wing system, the following constraints are made:

[0147] V i ∈[0,80]m / s,φ i ∈[-60,60]deg, ψ i ∈[-180,180]deg,θ i ∈[-60,60]deg, and the angular acceleration cannot exceed 10deg / s.

[0148] The attitude tracking response of the fixed-wing system is shown in Figure 2-4 , speed tracking response see Figure 5 , the dotted line in the attitude tracking response represents the trajectory to be tracked. Figure 2-5 It can be seen that after adding the actuator failure, the fixed-wing system can still ensure the finite time convergence and the attitude angles and velocities do not exceed the allowable range. However, due to the uncertainty of the finite time convergence time, the accurate convergence time cannot be guaranteed. In addition, when the error of the attitude layer converges to near 0, there is no singularity problem, which shows that the singularity problem has been effectively solved.

[0149] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A non-singular finite-time fault-tolerant formation cooperative control method, characterized in that The following steps are involved: Step 1: Establish the velocity layer and attitude layer in the six-degree-of-freedom dynamics model of the fixed-wing formation system; Step 2: establishing an actuator fault model of the thrust actuator and the rudder actuator included in the six-degree-of-freedom dynamic model established in step 1; Step 3: Establish a topological relationship of a fixed-wing formation system including multiple models in step 1; Step 4: Based on the topological relationship in step 3, solve the adjacency error of the attitude and velocity layers; Step 5: Based on the adjacent error of the velocity layer in step 4, the thrust control law and the adaptive law in the velocity layer finite time controller are designed; Step 6: Based on the attitude adjacency error in step 4, design the virtual control law, the rudder control law and the adaptive law in the attitude layer finite time controller; The thrust control law in the speed layer finite time controller in step 5 is: in, The adaptive law in the speed layer finite time controller in step 5 is: Among them, the adaptive parameters satisfy θ vi =β vi sup t≥0 T xif , β vi =1 / ρ Ti , the estimated error is γ vi1 ,γ vi2 ,γ vi3 ,σ vi1 ,σ vi2 ,σ vi3 is a positive constant; In step 6, the attitude layer finite time controller has a singular value problem, and the switching function is introduced as follows: Among them, τ1 is a very small positive constant, m = {φ,θ,ψ}, The virtual control law in the attitude layer finite time controller in step 6 is: Among them, m={φ,θ,ψ}, The control law of the rudder surface in the attitude layer finite time controller in step 6 is as follows: Among them, n = {1,2,3}, e ωi =diag{e ωi1 ,e ωi2 ,e ωi3 }; The adaptive law in the attitude layer finite time controller in step 6 is as follows: Among them, the adaptive parameters satisfy β ωi =1 / g ωi The estimated error is γ ωi1 ,γ ωi2 ,σ ωi1 ,σ ωi2 Is a normal number.

2. A non-singular finite-time fault-tolerant formation cooperative control method according to claim 1, characterized in that The velocity layer of the six-degree-of-freedom dynamics model established in step 1 is: Among them, m i Indicates the mass of the drone, p i =[x i ,y i ,z i ] T represents the position vector in the ground coordinate system, represents the attitude angle vector, ω i =[p i ,q i ,r i ] T Represents the attitude angular velocity vector, T i =[T xi ,0,0] T represents the thrust vector, g = [0,0,g] T is the gravitational acceleration, S(ω i )v i Represents ω i ×v i , d vi is the external disturbance, and R1 is the transformation matrix between the body coordinate system and the ground coordinate system: Among them, s a and c a Represent sin(a) and cos(a), F i is the aerodynamic parameter, and its expression is: Among them, C Di ,C Yi ,C Li are the drag coefficient, sideslip coefficient and lift coefficient respectively; The six-degree-of-freedom dynamics model posture layer established in step 1 is: Among them, S(ω i )J i ω i Represents ω i ×J i ω i , d ωi is the external disturbance, J i is the inertia tensor of the body coordinate system xz plane, and its expression is: R2 is the transformation matrix of angular velocity and attitude angle projection, and its expression is: C(δ i ) is the control effectiveness matrix, and its expression is: N i is the dynamic vector, and its expression is: Among them, S i is the wing area, is the air pressure, ρ is the air density, b i is the wingspan length, c nδri ,c mδei ,c lδai are the chord lengths along the x, y, and z axes of the fuselage coordinate system, is the average chord length, C n ' i ,C′ mi ,C l ' i are the aerodynamic coefficients corresponding to the x, y, and z axes of the aircraft coordinate system respectively.

3. A non-singular finite-time fault-tolerant formation cooperative control method according to claim 1, characterized in that The thrust actuator and rudder actuator actuator fault models in step 2 include effectiveness loss and bias failure, which are: T xi =ρ Ti T xi0 +T xif ,d i =ρ δi d i0 +d if Where 0≤ρ Ti ≤1 represents the thrust actuator efficiency, T xif represents the bias fault size; ρ δi =diag{ρ δai ,ρ δei ,ρ δri } represents the thrust actuator efficiency, δ if =[δ aif ,δ eif ,δ rif ] T Indicates the bias fault size; Considering the influence of actuator failure, the velocity and attitude layer dynamics model of the fixed-wing formation system is expressed as: in, represents the combined speed of the drone, △ vi and △′ ωi represents the modeling error.

4. A non-singular finite-time fault-tolerant formation cooperative control method according to claim 1, characterized in that The specific steps of step three are as follows: Establishing topological relationships in, Represents each fixed-wing system node; represents the connection between the i-th and j-th fixed-wing systems, i.e., the edge set; represents the weight of the corresponding edge set; if a ij =a ji ≠0 indicates that the i-th and j-th fixed-wing systems are connected, otherwise a ij =a ji =0; the adjacency matrix of the i-th fixed-wing system is expressed as V r and is the speed and posture to be tracked, and the adjacency error of the posture and speed layers in step 4 satisfies: in, is the tracking error, λ i1 ,λ i2 ,λ i3 ,λ i4 is a positive constant, V r and are the expected speed and attitude respectively, and satisfy 5. A non-singular finite-time fault-tolerant formation cooperative control method according to claim 4, characterized in that: In step three, vi +d vi The uncertain terms are approximated by RBF neural network: in, Meets the boundedness condition.

6. A non-singular finite-time fault-tolerant formation cooperative control method according to claim 3, characterized in that In step 2, △′ ωi +d ωi The uncertain terms are approximated by RBF neural network: in, Meets the boundedness condition.

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