An integrated design method for optimal fault-tolerant guidance and control of non-minimum phase hypersonic vehicles

Abstract

The present invention discloses an optimal fault-tolerant guidance and control integrated design method for a non-minimum phase hypersonic aircraft. Aiming at the six-degree-of-freedom model of the hypersonic aircraft, the present invention considers the state constraints and proposes an adaptive fault-tolerant guidance and control integrated method based on adaptive dynamic programming (ADP). Firstly, the state constraints are handled by introducing the obstacle Lyapunov function, and a basic feedback controller based on Backstepping control is designed to transform the tracking control problem into an equivalent optimal control problem. Subsequently, an adaptive optimal control strategy is designed using the ADP technology to provide a compensatory control behavior. An execution-evaluation structure is constructed to solve the HJB equation online. The present invention combines Backstepping control with ADP control to construct a total control input to improve the tracking performance and fault tolerance of the control system, thereby realizing the approximate tracking of the height, speed and lateral displacement, and providing a powerful reference for the specific implementation of engineering practice.

Description

Technical Field

[0001] The invention relates to an optimal fault-tolerant guidance and control integrated design method for a non-minimum phase hypersonic aircraft, and belongs to the technical field of automatic control. Background Art

[0002] As a new type of fast, large-area, fast-response aerospace vehicle, the dynamic model of hypersonic vehicle has strong coupling, including aerodynamic coupling, motion coupling, inertial and control coupling, etc., which is particularly significant when flying at a large angle of attack. These coupling effects will cause nonlinear and non-minimum phase characteristics in the vehicle kinematic model. Aerodynamic control surfaces are key components for adjusting the attitude and lift of the aircraft, but their movement will have a coupling effect on the lift, resulting in negative overshoot in the system. The main reason for this phenomenon is that there is an aerodynamic control surface coupling term in the lift model, which makes the input signal of the system appear in the low-order derivative of the output signal in advance, reducing the relative order of the system and leading to the emergence of unstable internal dynamics. Therefore, the longitudinal dynamic model of the hypersonic vehicle is a typical nonlinear non-minimum phase system. Compared with the minimum phase system, the control and output tracking of the non-minimum phase system are more complicated. It is necessary to ensure the stability of the internal state while achieving system output tracking, otherwise the closed-loop system will diverge. For the output tracking control problem of non-minimum phase hypersonic vehicles, traditional nonlinear control theory and output tracking control methods are no longer applicable. In order to overcome these challenges, it is necessary to explore new control methods and technologies to stabilize the internal dynamics to ensure the safe operation of hypersonic vehicles. In addition, the flight environment of hypersonic vehicles is harsh, the flight conditions vary greatly, and failures and damage will cause structural mutations in the aircraft. Therefore, the design of the aircraft control system must consider the impact of possible aerodynamic control surface failures during flight to achieve higher safety and reliability.

[0003] At present, there have been some research results on the integrated design of guidance and control for hypersonic vehicles. Tang Jian et al. proposed a new three-dimensional guidance and control integrated algorithm combining cascade control method and control obstacle function, which realizes the three-dimensional tracking control of the aircraft while satisfying the constraints of the hypersonic aircraft ascending phase process (Integrated design of guidance and control for hypersonic aircraft considering constraints. Journal of Astronautics, 2022, 43(05): 649-664.). However, this document ignores many couplings of hypersonic aircraft and does not consider the non-minimum phase characteristics of the aircraft. Wang et al. proposed an adaptive fault-tolerant guidance and control integrated strategy based on the extended loop backstepping method, which realized the approximate tracking of altitude, speed and lateral displacement (Integrated design of adaptive fault-tolerant control for non-minimum phase hypersonic flight vehicle system with input saturation and state constraints. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2022, 236(11): 2281-2301.). However, this paper assumes that all couplings between aerodynamic control surfaces and aerodynamic forces are system uncertainties, which can only be used for the control of weak non-minimum phase systems. In addition, although the adaptive fault tolerance problem has been studied in this paper, the method does not consider the optimal guidance control performance of hypersonic vehicles. Summary of the invention

[0004] Purpose of the invention: In view of the problems pointed out in the background technology, the present invention provides an integrated design method for optimal fault-tolerant guidance and control of non-minimum phase hypersonic aircraft, which makes the non-minimum phase hypersonic aircraft boundedly stable under aerodynamic control surface failure by outputting a redefinition and backstepping method designed guidance control signal. Subsequently, the compensation control signal designed based on adaptive dynamic programming technology is used to provide supplementary adjustment in the case of aerodynamic control surface failure to improve tracking performance and fault tolerance.

[0005] Technical solution: The present invention discloses an optimal fault-tolerant guidance and control integrated design method for a non-minimum phase hypersonic vehicle, comprising the following steps:

[0006] Step 1: Establish a six-degree-of-freedom model of a non-minimum phase hypersonic vehicle;

[0007] Step 2: Establish the fault model of the aerodynamic control surface and introduce the state constraint function;

[0008] Step 3: Based on the six-degree-of-freedom model of the hypersonic vehicle established in step 1, its internal dynamic characteristics are inferred by analyzing the zero-dynamic behavior;

[0009] Step 4: Convert the six-degree-of-freedom model of the hypersonic aircraft established in step 1 into the guidance and attitude subsystem and the velocity subsystem;

[0010] Step 5: For the system converted in step 4, combined with the aerodynamic control surface fault model and state constraint function established in step 2, design the speed subsystem controller, redefine the guidance subsystem guidance law based on the output, preliminarily design the attitude subsystem controller and its feedback controller and optimal compensation controller, further determine the feedback virtual controller, design the fault compensation controller according to the aerodynamic control surface fault, and realize the bounded stability of the hypersonic vehicle under fault based on the designed feedback controller and fault compensation controller;

[0011] Step 6: Introduce the optimal control performance index into the attitude subsystem, and design the optimal compensation controller through the adaptive dynamic programming iterative solution method, so that the closed-loop signal of the hypersonic aircraft control system can be quickly stabilized, ensuring its flight safety in the event of aerodynamic control surface failure and external interference.

[0012] Furthermore, the six-degree-of-freedom model of the hypersonic aircraft in step 1 is:

[0013]

[0014]

[0015]

[0016]

[0017] Among them, x, y, h, V, χ, γ, α, β, μ, p, q, r are the aircraft system states, which respectively represent the forward position, lateral position, altitude, speed, heading angle, track angle, angle of attack, sideslip angle, bank angle, roll angle rate, pitch angle rate, and yaw angle rate; m, g, T represent the mass, gravity constant, and engine thrust of the aircraft respectively; I xx ,I yy ,I zz is the moment of inertia; L, D, and Y are lift, drag, and lateral force, respectively; M xx 、M yy 、M zz To control the components of the torque in the three directions of the body axis system; the expressions of force and torque are:

[0018]

[0019]

[0020] in,

[0021]

[0022]

[0023] In the formula, δ=[δ LI δ LO δ RI δ RO δ rL δ rR ] T is the six rudder surface deflection matrix, δ LI is the left inner elevator, δ RI is the right inner elevator, δ LO is the left outer elevator, δ RO is the right outer elevator, δ rL is the left rudder, δ rR is the right rudder; S is the reference area, is the dynamic pressure, ρ is the atmospheric density, b is the wing span chord length, and c is the average aerodynamic chord length.

[0024] Furthermore, the fault model of the pneumatic control surface in step 2 is:

[0025]

[0026] In the formula, δ c Expressing the control input signal, σ = diag (σ1 σ2 … σ6) represents the rudder efficiency loss of the six aerodynamic control surfaces, Indicates the stuck position of the rudder surface; σ i ∈[0,1],τ i ={0,1}i=1,2,…,6, all working states of the aerodynamic control surfaces are:

[0027] 4) When 0<σ i <1 and τ i =1,δ i (t)=(1-σ i )δ ci (t) indicates that a partial failure of the aerodynamic control surface occurs;

[0028] 5) When σ i =1 and τ i =1, Indicates that the pneumatic control surface is stuck;

[0029] 6) When σ i = 0 and τ i =0, δ i (t) = δ ci (t) indicates that the corresponding aerodynamic control surface is working normally without any fault;

[0030] Select the state constraint function:

[0031]

[0032] Where log(·) is the natural logarithm function, k b >0 is the bound on which the hypersonic vehicle attitude error z is constrained, that is, |z|≤k b .

[0033] Furthermore, in step 3, the internal dynamic stability analysis: the system output vector is selected as Y = [h, y, V] T , the input is the scramjet engine thrust T and the rudder deflection angle vector δ of the aerodynamic control surface. Based on the feedback linearization method, the system output vector Y is continuously differentiated to obtain:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] For the output vector Y = [h, y, V] T , the relative order vector is [2,2,1], and the relative order of the system is r = 2 + 2 + 1 = 5, then the system has a 6th-order internal dynamic η = [α, β, μ, p, q, r] T :

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] The internal dynamics is a 6th order nonlinear system. By analyzing its zero dynamics at the equilibrium point [α, β, μ, p, q, r] = [α * The stability of the internal dynamics is judged by the local stability at ,0,0,0,0,0]

[0047] Furthermore, the guidance and attitude subsystem and speed subsystem converted in step 4 are:

[0048] The speed subsystem is:

[0049]

[0050] in, The thrust T is the control input of this subsystem;

[0051] The guidance and attitude subsystem is:

[0052]

[0053]

[0054]

[0055] in, and is the tracking error, χ r and γ r is the expected value, Ω=[α,β,μ] T ,ω=[p,q,r] T , Δf Ω is a coupling term, and the remaining nonlinear functions of the guidance and attitude subsystem are as follows:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] M=A+Bδ,

[0062]

[0063] Furthermore, the step 5 includes the following sub-steps:

[0064] Step 51: Speed ​​Subsystem Controller Design: Designing an Auxiliary Dynamic System To deal with the thrust saturation problem, the velocity tracking error is defined as Expressed as the state of the auxiliary system, the controller T is designed as:

[0065]

[0066] In the formula, k V Indicates the speed tracking error The boundary of Γ V is the normal number to be designed, is the parameter Θ V The estimated value of is, and the estimation error is defined as Its update law is:

[0067]

[0068] In the formula, is a positive constant;

[0069] Step 52: Design the guidance law of the guidance subsystem based on the output redefinition, redefine the system output as Ω, and the corresponding internal dynamics are:

[0070]

[0071] In the formula,

[0072]

[0073] In order to eliminate the direct influence of the system control input on the internal dynamics, the coordinate transformation is defined based on the definition of Lie derivatives and differential homeomorphism transformation:

[0074]

[0075] In the formula,

[0076]

[0077] Define the augmentation vector and in, and The dynamics are as follows:

[0078]

[0079] Using small gain control theory, the following coordinate transformation is given:

[0080]

[0081] In the formula, k i1 ∈(0,1](i=γ,χ) is a positive constant to be designed. and The local asymptotic stability along the desired output trajectory is designed as:

[0082]

[0083] Step 53: Attitude Subsystem Controller Designed as U=U a +U * , where U * is the optimal compensation controller, the feedback controller Feedback virtual control law Designed for:

[0084]

[0085] In the formula, is the diagonal positive definite matrix to be designed;

[0086] Design feedback virtual controller M a for:

[0087]

[0088] In the formula, is the diagonal positive definite matrix to be designed;

[0089] Step 54: Design of control allocation and fault-tolerant strategy. In order to compensate for unknown aerodynamic control surface failures, a fault compensation controller is designed as follows:

[0090]

[0091] In the formula, and Represent the estimated values ​​of k1 and k2 respectively, and their adaptive update law is designed as follows:

[0092]

[0093]

[0094] In the formula, Γ k1 and Γ k2 All are symmetric positive definite matrices to be designed;

[0095] Step 55: Feedback Based Controller and fault-tolerant strategy design to achieve bounded stability of hypersonic vehicles under faults:

[0096]

[0097] Where Z = [z T ,ω T ] T ,

[0098] Furthermore, the step 6 includes the following sub-steps:

[0099] Step 61: Convert the tracking error of the hypersonic vehicle attitude subsystem and Rewritten to optimize the affine nonlinear form:

[0100]

[0101] Among them, U * is the optimal compensation controller;

[0102] Step 62: Design a performance index function, optimize the performance index function through the Hamiltonian function, and obtain the optimal control strategy U through optimal admissible control * , the performance indicator function is:

[0103]

[0104] Where Q(Z) represents a semi-positive definite penalty function, R is a symmetric positive definite matrix; the Hamiltonian function defined is

[0105]

[0106] in, represents the partial derivative of V(Z) with respect to Z,

[0107] The optimal compensation controller U * for:

[0108]

[0109] Step 63: Based on the adaptive dynamic programming iterative solution method, a neural network is constructed to approximate the optimal cost function V online c * (Z), the neural network estimator is gradient-informed to obtain the optimal control strategy. The neural network estimator is:

[0110] V c * (Z) = W c T σ(Z)+ε c (Z)

[0111] Where W c ∈R l represents the ideal weight vector, σ(Z)∈R l is the activation function of the evaluation network, ε c(Z) is the approximate error of the evaluation network, and there is a positive constant satisfy

[0112] The true output of the evaluation network is Informatize the gradient of the neural network estimator The optimal control strategy is:

[0113]

[0114] Combined with optimal control strategy The Hamiltonian function error is formed as follows:

[0115]

[0116] Step 64: Define the following quadratic objective function:

[0117]

[0118] Based on the gradient descent method, the weight update law of the evaluation network is designed:

[0119]

[0120] in, α c >0 indicates the evaluation network learning rate, m s =1+φ T φ, F1 and F2 are the adjustment parameters of the corresponding dimensions that need to be designed.

[0121]

[0122] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0123] 1. The present invention proposes a new adaptive fault-tolerant guidance and control integration strategy by using output redefinition and Backstepping method, which provides a new idea for the approximate tracking control of complex strong nonlinear and strong non-minimum phase systems.

[0124] 2. The present invention adopts the optimal guidance control strategy based on adaptive dynamic technology as the compensation controller, thereby improving the transient performance of the system and enhancing the fault tolerance of the controller. In addition, the designed fault-tolerant guidance control method also considers the state constraints to ensure that the system state remains within a certain range. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 Block diagram of the integrated method for optimal fault-tolerant guidance and control.

[0126] Figure 2 This is the geometric configuration diagram of the six-degree-of-freedom model of the hypersonic aircraft.

[0127] Figure 3 is the output response curve.

[0128] Figure 4 are the heading angle and track angle response curves.

[0129] Figure 5 is the attitude angle response curve.

[0130] Figure 6 is the attitude angular velocity response curve.

[0131] Figure 7 is the deflection angle of the aerodynamic control surface.

[0132] Figure 8 The thrust curve.

[0133] Fig. 9 is the optimal compensation control law curve.

[0134] Fig.10 Overload curve. DETAILED DESCRIPTION

[0135] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0136] like Figure 1 As shown, the present invention provides an optimal fault-tolerant guidance and control integrated design method for a non-minimum phase hypersonic vehicle. For a six-degree-of-freedom model of a non-minimum phase hypersonic vehicle with actuator failure and state constraints, a new optimal fault-tolerant guidance and control integrated design method is proposed by using adaptive dynamic programming technology and output redefinition method, including the following steps:

[0137] Step 1: Establish a six-degree-of-freedom model of a non-minimum phase hypersonic vehicle. Its geometric configuration diagram is as follows: Figure 2 As shown, the nonlinear equation of motion is:

[0138]

[0139]

[0140]

[0141]

[0142] Among them, x, y, h, V, χ, γ, α, β, μ, p, q, r are the aircraft system states, which respectively represent the forward position, lateral position, altitude, speed, heading angle, track angle, angle of attack, sideslip angle, bank angle, roll angle rate, pitch angle rate, and yaw angle rate; m, g, T represent the mass, gravity constant, and engine thrust of the aircraft respectively; I xx ,I yy ,I zz is the moment of inertia; L, D, and Y are lift, drag, and lateral force, respectively; M xx 、M yy 、M zz To control the components of the torque in the three directions of the body axis system; the expressions of force and torque are:

[0143]

[0144]

[0145] in,

[0146]

[0147]

[0148] In the formula, δ=[δ LI δ LO δ RI δ RO δ rL δ rR ] T is the six rudder surface deflection matrix, δ LI is the left inner elevator, δ RI is the right inner elevator, δ LO is the left outer elevator, δ RO is the right outer elevator, δ rL is the left rudder, δ rR is the right rudder; S is the reference area, is the dynamic pressure, ρ is the atmospheric density, b is the wing span chord length, and c is the average aerodynamic chord length.

[0149] Step 2: Establish the fault model of the aerodynamic control surface:

[0150]

[0151] In the formula, δ c Expressing the control input signal, σ = diag (σ1 σ2 … σ6) represents the rudder efficiency loss of the six aerodynamic control surfaces, Indicates the stuck position of the rudder surface. i ∈[0,1],τi ={0,1}(i=1,2,…,6). Based on this fault model, all working states of the aerodynamic control surfaces can be described as follows:

[0152] 1) When 0<σ i <1 and τ i =1,δ i (t)=(1-σ i )δ ci (t) indicates that a partial failure of the aerodynamic control surface has occurred.

[0153] 2) When σ i =1 and τ i =1, Indicates that the pneumatic control surface is stuck.

[0154] 3) When σ i = 0 and τ i =0, δ i (t) = δ ci (t) indicates that the corresponding aerodynamic control surface works normally and no fault occurs.

[0155] In addition, the following state constraint functions are selected:

[0156]

[0157] Where log(·) is the natural logarithm function, k b >0 is the bound on which the hypersonic vehicle attitude error z is constrained, that is, |z|≤k b .

[0158] Step 3: Based on the six-degree-of-freedom model of the hypersonic vehicle established in step 1, its internal dynamic characteristics are inferred by analyzing the behavior of zero dynamics. Specifically, the system output vector is selected as Y = [h, y, V] T , the input is the scramjet engine thrust T and the rudder deflection vector δ of the aerodynamic control surface. Based on the feedback linearization method, the system output vector Y is continuously differentiated to obtain:

[0159]

[0160]

[0161]

[0162]

[0163]

[0164] For the output vector Y = [h, y, V] T, the relative order vector is [2,2,1], and the relative order of the system is r = 2 + 2 + 1 = 5, then the system has a 6th-order internal dynamic η = [α, β, μ, p, q, r] T :

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171] The internal dynamics is a 6th order nonlinear system. By analyzing its zero dynamics at the equilibrium point [α, β, μ, p, q, r] = [α * The stability of the internal dynamics is judged by the local stability at ,0,0,0,0,0]

[0172] Step 4: Convert the six-degree-of-freedom model of the hypersonic vehicle established in step 1 into the guidance and attitude subsystem and the velocity subsystem. The velocity subsystem is:

[0173]

[0174] in, The thrust T is the control input of this subsystem.

[0175] The guidance and attitude subsystem is:

[0176]

[0177]

[0178]

[0179] in, and is the tracking error, χ r and γ r is the expected value, Ω=[α,β,μ] T ,ω=[p,q,r] T , Δf Ω is a coupling term. The remaining nonlinear functions of the guidance and attitude subsystem are as follows:

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] M=A+Bδ,

[0186]

[0187] Step 5: For the system converted in step 4, combined with the aerodynamic control surface fault model and state constraint function established in step 2, an optimal fault-tolerant guidance and control integration strategy is designed by using output redefinition, Backstepping method and adaptive dynamic programming technology to achieve bounded stability of the internal dynamics of non-minimum phase hypersonic aircraft and approximate tracking effect of output. It includes the following sub-steps:

[0188] Step 51: Speed ​​subsystem controller design. Design auxiliary dynamic system To deal with the thrust saturation problem, the velocity tracking error is defined as Represents the state of the auxiliary system. The controller T is designed as:

[0189]

[0190] In the formula, k V Indicates the speed tracking error The boundary of Γ V is the normal number to be designed, is the parameter Θ V The estimated value of is, and the estimation error is defined as Its update law is:

[0191]

[0192] In the formula, Is a normal number.

[0193] Step 52: Design the guidance law of the guidance subsystem based on the output redefinition. Redefine the system output as Ω, and the corresponding internal dynamics are

[0194]

[0195] In the formula,

[0196]

[0197] In order to eliminate the direct influence of the system control input on the internal dynamics, the coordinate transformation is defined based on the definition of Lie derivatives and differential homeomorphism transformation:

[0198]

[0199] In the formula,

[0200]

[0201] Define the augmentation vector and in, and The dynamics are as follows:

[0202]

[0203] Using small gain control theory, the following coordinate transformation is given:

[0204]

[0205] In the formula, k i1 ∈(0,1](i=γ,χ) is a positive constant to be designed. and It is locally asymptotically stable along the desired output trajectory, and the design reference instruction is

[0206]

[0207] Step 53: Attitude Subsystem Controller Designed as U=U a +U * , where U * is the optimal compensation controller, the feedback controller Feedback virtual control law Designed for:

[0208]

[0209] In the formula, is the diagonal positive definite matrix to be designed.

[0210] Design feedback virtual controller M a for

[0211]

[0212] In the formula, is the diagonal positive definite matrix to be designed.

[0213] Step 54: Design of control allocation and fault-tolerance strategy. In order to compensate for unknown aerodynamic control surface failures, a fault compensation controller is designed as follows:

[0214]

[0215] In the formula, and Represent the estimated values ​​of k1 and k2 respectively, and their adaptive update law is designed as follows:

[0216]

[0217]

[0218] In the formula, Γ k1 and Γ k2 are all symmetric positive definite matrices to be designed.

[0219] Step 55: Feedback Based Controller and fault-tolerant strategy design to achieve bounded stability of hypersonic vehicles under faults:

[0220]

[0221] Where Z = [z T ,ω T ] T ,

[0222] Step 6: Introduce the optimal control performance index in the attitude subsystem, and design the compensation controller through adaptive dynamic programming optimization technology to make the closed-loop signal of the hypersonic aircraft control system quickly and stabilize, ensuring its flight safety in the case of aerodynamic control surface failure and external interference. It includes the following sub-steps:

[0223] Step 61: Convert the tracking error of the hypersonic vehicle attitude subsystem and Rewritten to optimize the affine nonlinear form:

[0224]

[0225] Among them, U * is the optimal compensation controller.

[0226] Step 62: Design a performance index function, optimize the performance index function through the Hamiltonian function, and obtain the optimal control strategy U through optimal admissible control * The performance indicator function is

[0227]

[0228] Where Q(Z) represents a semi-positive definite penalty function and R is a symmetric positive definite matrix. The Hamiltonian function defined is

[0229]

[0230] in, represents the partial derivative of V(Z) with respect to Z,

[0231] The optimal compensation controller U * for

[0232]

[0233] Step 63: Based on the adaptive dynamic programming iterative solution method, a neural network is constructed to approximate the optimal cost function V online c * (Z), the gradient of the neural network estimator is informatized to obtain the optimal control strategy.

[0234] The neural network estimator is

[0235] V c * (Z) = W c T σ(Z)+ε c (Z)

[0236] Where W c ∈R l represents the ideal weight vector, σ(Z)∈R l is the activation function of the evaluation network, ε c (Z) is the approximate error of the evaluation network, and there is a positive constant satisfy

[0237] The true output of the evaluation network is Informatize the gradient of the neural network estimator The optimal control strategy is:

[0238]

[0239] Combined with optimal control strategy The Hamiltonian function error is formed as follows:

[0240]

[0241] Step 64: Define the following quadratic objective function:

[0242]

[0243] Based on the gradient descent method, the weight update law of the evaluation network is designed:

[0244]

[0245] in, α c >0 indicates the evaluation network learning rate, m s =1+φ T φ, F1 and F2 are the adjustment parameters of the corresponding dimensions that need to be designed.

[0246]

[0247] The effectiveness of the ADP-based non-minimum phase HSV guidance and control integration method proposed in the present invention is verified by numerical simulation experiments. The simulation parameters are as follows:

[0248] The initial state values ​​are set to h(0) = 98400ft, y(0) = 0ft, V(0) = 3900ft / s, γ(0) = 0deg, χ(0) = 0deg, α(0) = -1.72deg, β(0) = 0deg, μ(0) = 0deg, p(0) = 0deg / s, q = 0deg / s, r = 0deg / s. The HSV output reference trajectory is generated by the following filter:

[0249]

[0250]

[0251]

[0252] Basic feedback guidance and control integrated strategy parameter setting: The speed subsystem controller parameters are set to Γ V =0.5, l = 2; the coordinate transformation parameter is set to k γ =5 and k χ =8; the attitude subsystem controller parameters are Γ1 = diag{0.1, 0.1, 0.1} and Γ2 = diag{0.12, 0.15, 0.1}; the neural network weight update law parameters are designed as Adaptive law parameter Γ k1 and Γ k2 Choose Γ k1 =diag{3×10 2} 6×6 and Γ k2 =diag{50} 6×6 .

[0253] Optimal compensation controller parameter setting: The initial weight of the evaluation network is The activation function is The weight matrix in the cost function is set to and R = 1; the learning rate is l c =0.8, the adjustment parameter is selected as F1=165[1 1 … 1] 1×9 and F2=3×[I] 1×9 , Lyapunov candidate function J s (Z) is defined as

[0254] In order to test the control effect of the control system under different combinations of rudder working modes, the present invention designs the following three working conditions:

[0255] 1)(0≤t<200s)All aerodynamic control surfaces of the system work normally, that is, σ=diag{0,0,0,0,0,0}, τ=diag{1,1,1,1,1,1}.

[0256] 2) (200≤t<350s) The system’s aerodynamic control surfaces partially fail. At this time, the left inner and left outer elevons only provide 75% and 60% of their saturation values, that is, σ=diag{0.25,0,0.4,0,0,0}, τ=diag{1,1,1,1,1,1}.

[0257] 3) (350≤t<500s) The system aerodynamic control surface is stuck. At this time, the left outer elevator deflection angle is stuck at 5 degrees, and the right rudder is stuck at 2 degrees, that is, σ=diag{0,0,1,0,0,1}, τ=diag{1,1,0,1,1,0},

[0258] The simulation results of the control system under the failure of the aerodynamic control surface are as follows: Figure 3 shown.

[0259] Figure 3 The output response curve and tracking error response curve are displayed. It can be observed that when the aerodynamic control surface of the HSV system fails, the output response will oscillate slightly under its influence, but will gradually reach a steady state in a short time. This is the compensation effect of the adaptive fault-tolerant strategy on the aerodynamic control surface failure of the system.

[0260] from Figure 3 From the tracking error curves of height and lateral displacement in (a) and 3(b), it can be seen that there is a short-term negative overshoot in the system output response, which is consistent with the characteristics of non-minimum phase control systems and is an additional price paid for stabilizing the internal dynamic subsystem. Figure 4 The heading angle and track angle response curves are shown. Figure 5The attitude angle (attack angle α, sideslip angle β, roll angle μ) response curve is shown. It can be seen that the attack angle response curve is always within the allowable constraint range. The attitude angular velocity response curve is as follows Figure 6 shown.

[0261] Figure 7-8 The aerodynamic control surface deflection angle and engine thrust response curve are shown. Figure 7 It can be seen from the figure that at 200s and 350s, when two of the system's pneumatic control surfaces fail, the remaining four pneumatic control surfaces can automatically compensate for the failed control surfaces according to the designed adaptive update law to ensure the total control torque (M xx ,M yy ,M zz ) remains unchanged, thereby maintaining the stability of the control system and ensuring that the deflection angle of each aerodynamic control surface is within the constraint range. Figure 8 The engine thrust response curve is given. Since the fault occurred on the aerodynamic control surface, the impact on the engine thrust is small.

[0262] Fig. 9 The optimal compensation control law U is designed based on ADP technology. * The response curve of the system aerodynamic control surface is * The ability to respond quickly allows the system to transition smoothly and improves its transient response performance. Fig.10 The overload variation curve is shown, from which it can be seen that it remains within the permissible overload constraint range.

[0263] In summary, no matter the aerodynamic control surfaces of the HSV system suffer from partial failure or stuck failure, the fault-tolerant guidance and control integrated strategy designed in the present invention has faster convergence speed and better transient performance.

[0264] The above embodiments are only for illustrating the technical idea of ​​the present invention, and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. An optimal fault-tolerant guidance and control integrated design method for a non-minimum phase hypersonic vehicle, characterized in that: The steps include: Step 1: Establish a six-degree-of-freedom model of a non-minimum phase hypersonic vehicle; The six-degree-of-freedom model of a hypersonic vehicle is: Among them, x, y, h, V, χ, γ, α, β, μ, p, q, r are the aircraft system states, which respectively represent the forward position, lateral position, altitude, speed, heading angle, track angle, angle of attack, sideslip angle, bank angle, roll angle rate, pitch angle rate, and yaw angle rate; m, g, T represent the mass, gravity constant, and engine thrust of the aircraft respectively; I xx ,I yy ,I zz is the moment of inertia; L, D, and Y are lift, drag, and lateral force, respectively; M xx 、M yy 、M zz To control the components of the torque in the three directions of the body axis system; the expressions of force and torque are: in, In the formula, δ=[δ LI δ LO δ RI δ RO δ rL δ rR ] T is the six rudder surface deflection matrix, δ LI is the left inner elevator, δ RI is the right inner elevator, δ LO is the left outer elevator, δ RO is the right outer elevator, δ rL is the left rudder, δ rR is the right rudder; S is the reference area, is the dynamic pressure, ρ is the atmospheric density, b is the wing span length, and c is the average aerodynamic chord length; Step 2: Establish the fault model of the aerodynamic control surface and introduce the state constraint function; The fault model of the aerodynamic control surface is: In the formula, δ c Expressing the control input signal, σ = diag (σ1σ2…σ6) represents the rudder efficiency loss of the six aerodynamic control surfaces, Indicates the stuck position of the rudder surface; σ i ∈[0,1],τ i ={0,1}i=1,2,…,6, all working states of the aerodynamic control surfaces are: 1) When 0<σ i <1 and τ i =1,δ i (t) = (1-σ i )δ ci (t) indicates that a partial failure of the aerodynamic control surface occurs; 2) When σ i =1 and τ i =1, Indicates that the pneumatic control surface is stuck; 3) When σ i = 0 and τ i =0, δ i (t) = δ ci (t) indicates that the corresponding aerodynamic control surface is working normally without any fault; Select the state constraint function: Where log(·) is the natural logarithm function, k b >0 is the bound on which the hypersonic vehicle attitude error z is constrained, that is, |z|≤k b ; Step 3: Based on the six-degree-of-freedom model of the hypersonic vehicle established in step 1, its internal dynamic characteristics are inferred by analyzing the zero-dynamic behavior; Internal dynamic stability analysis: The system output vector is selected as Y = [h, y, V] T , the input is the scramjet engine thrust T and the rudder deflection angle vector δ of the aerodynamic control surface. Based on the feedback linearization method, the system output vector Y is continuously differentiated to obtain: For the output vector Y = [h, y, V] T , the relative order vector is [2,2,1], and the relative order of the system is r = 2 + 2 + 1 = 5, then the system has a 6th-order internal dynamic η = [α, β, μ, p, q, r] T : The internal dynamics is a 6th order nonlinear system. By analyzing its zero dynamics at the equilibrium point [α, β, μ, p, q, r] = [α * ,0,0,0,0,0] to judge the stability of the internal dynamics; Step 4: Convert the six-degree-of-freedom model of the hypersonic aircraft established in step 1 into the guidance and attitude subsystem and the velocity subsystem; The guidance and attitude subsystem and velocity subsystem obtained by conversion are: The speed subsystem is: in, The thrust T is the control input of this subsystem; The guidance and attitude subsystem is: in, and is the tracking error, χ r and γ r is the expected value, Ω=[α,β,μ] T ,ω=[p,q,r] T , Δf Ω is a coupling term, and the remaining nonlinear functions of the guidance and attitude subsystem are as follows: Step 5: For the system converted in step 4, combined with the aerodynamic control surface fault model and state constraint function established in step 2, design the speed subsystem controller, redefine the guidance subsystem guidance law based on the output, preliminarily design the attitude subsystem controller, feedback controller and optimal compensation controller, design a fault compensation controller according to the aerodynamic control surface fault, and realize the bounded stability of the hypersonic vehicle under fault based on the designed feedback controller and fault compensation controller; Step 51: Speed ​​Subsystem Controller Design: Designing an Auxiliary Dynamic System To deal with the thrust saturation problem, the velocity tracking error is defined as Expressed as the state of the auxiliary system, the controller T is designed as: In the formula, k V Indicates the speed tracking error The boundary of Γ V is the normal number to be designed, is the parameter Θ V The estimated value of is, and the estimation error is defined as Its update law is: In the formula, is a positive constant; Step 52: Design the guidance law of the guidance subsystem based on the output redefinition, redefine the system output as Ω, and the corresponding internal dynamics are: In the formula, In order to eliminate the direct influence of the system control input on the internal dynamics, the coordinate transformation is defined based on the definition of Lie derivatives and differential homeomorphism transformation: In the formula, Define the augmentation vector and in, and The dynamics are as follows: Using small gain control theory, the following coordinate transformation is given: In the formula, k i1 ∈(0,1] is a positive constant to be designed, i=γ,χ, to make the internal dynamic and The local asymptotic stability along the desired output trajectory is designed as: Step 53: Attitude Subsystem Controller Designed as U=U a +U * , where U * is the optimal compensation controller, the feedback controller Feedback virtual control law Designed for: In the formula, is the diagonal positive definite matrix to be designed; Design feedback virtual controller M a for: In the formula, is the diagonal positive definite matrix to be designed; Step 54: Design of control allocation and fault-tolerant strategy. In order to compensate for unknown aerodynamic control surface failures, a fault compensation controller is designed as follows: In the formula, and Represent the estimated values ​​of k1 and k2 respectively, and their adaptive update law is designed as follows: In the formula, Γ k1 and Γ k2 All are symmetric positive definite matrices to be designed; Step 55: Feedback Based Controller and fault-tolerant strategy design to achieve bounded stability of hypersonic vehicles under faults: Where Z = [z T ,ω T ] T , Step 6: Introduce the optimal control performance index into the attitude subsystem, solve the optimal compensation controller through the adaptive dynamic programming iterative solution method, and build an execution-evaluation structure to solve the HJB equation online, so that the closed-loop signal of the hypersonic vehicle control system can be quickly stabilized to ensure its flight safety in the case of aerodynamic control surface failure and external interference; Step 61: Convert the tracking error of the hypersonic vehicle attitude subsystem and Rewritten to optimize the affine nonlinear form: Among them, U * is the optimal compensation controller; Step 62: Design a performance index function, optimize the performance index function through the Hamiltonian function, and obtain the optimal compensation controller U through optimal admissible control * , the performance indicator function is: Where Q(Z) represents a semi-positive definite penalty function, R is a symmetric positive definite matrix; the Hamiltonian function defined is in, represents the partial derivative of V(Z) with respect to Z, The optimal compensation controller U * for: Step 63: Based on the adaptive dynamic programming iterative solution method, a neural network is constructed to approximate the optimal cost function online The gradient of the neural network estimator is informatized to obtain the optimal control strategy. The neural network estimator is: Where W c ∈R l represents the ideal weight vector, σ(Z)∈R l is the activation function of the evaluation network, ε c (Z) is the approximate error of the evaluation network, and there is a positive constant satisfy The true output of the evaluation network is Informatize the gradient of the neural network estimator The optimal control strategy is: Combined with optimal control strategy The Hamiltonian function error is formed as follows: Step 64: Define the following quadratic objective function: Based on the gradient descent method, the weight update law of the evaluation network is designed: in, α c >0 indicates the evaluation network learning rate, m s =1+φ T φ, F1 and F2 are the adjustment parameters of the corresponding dimensions that need to be designed.

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