Modeling and Fuzzy Adaptive Sliding Mode Control Method for an Elastic Hypersonic Vehicle under Aerodynamic Heat Effects

Abstract

The present invention relates to a method for dynamic modeling and fuzzy adaptive sliding mode control of an elastic hypersonic vehicle under aerodynamic heat influence, including: establishing a longitudinal dynamic model of the elastic hypersonic vehicle; calculating the change values of the angle of attack and elevator deflection after the hypersonic vehicle undergoes elastic deformation; using curve fitting functions of rigid body states, control inputs, and elastic modes to replace aerodynamic forces and moments; adding the influence of parameter uncertainties and external disturbances to the dynamic model and performing linearization processing using the T-S fuzzy strategy; designing an adaptive sliding mode controller according to the T-S fuzzy dynamic model. In view of the situation where the hypersonic vehicle has control instability due to inaccurate modeling caused by elastic deformation, the present invention effectively solves the flight instability problem caused by elastic deformation caused by aerodynamic heat by using the elastic dynamics modeling and fuzzy adaptive sliding mode control method.

Description

Technical Field

[0001] The present invention relates to the field of hypersonic aircraft, and particularly to a method for modeling and fuzzy adaptive sliding mode control of an elastic hypersonic aircraft under the influence of aerodynamic heat. Background Technique

[0002] Due to the close integration of the fuselage-engine structure of hypersonic aircraft, the elastic airframe, propulsion system, and structural dynamics are highly coupled. In addition, hypersonic aircraft are often very light, the elastic effects of the structure are obvious, and the natural frequencies are very low. Elastic deformation will cause changes in the flow field, thus changing the pressure distribution of the aircraft, mainly manifested as the influence on thrust; while the low natural frequency will slow down the decay response of the system after being disturbed, resulting in significant aeroelastic effects. During high-speed flight, the "real gas" effect on the airframe will change the air flow pressures at the inlet and outlet of the engine, thereby causing changes in aerodynamic parameters such as the load distribution on the aircraft surface and the pitch moment coefficient; high-speed flight will also generate obvious aerodynamic heating phenomena. The high temperature will not only exacerbate the elastic deformation of the aircraft, but also change the elastic modulus, thus affecting the natural frequency and having an impact on the structural dynamics of the aircraft. In addition, the uncertainties of aerodynamic force and propulsion force, the change of mass during flight with fuel consumption, and the uncertainties of model parameters cannot be ignored in the controller design. When considering the elastic problem of hypersonic aircraft, there are mainly two methods. The first method is to consider it as a disturbance and use a disturbance observer to estimate its value; the second method is to simplify the aircraft as a free beam and conduct modal analysis on it, and add the elastic mode to the longitudinal dynamic equation. For the pressure distribution problem on the surface of hypersonic aircraft, some researchers directly obtain the expression of the pressure acting on the aircraft using Newton's impact theory, and some research scholars use oblique shock wave and Prandtl-Meyer expansion theory to calculate the changes in force and moment.

[0003] Due to the excessive complexity of the original non-linear dynamics model, when designing a controller, it is usually necessary to simplify the longitudinal dynamics model to obtain a control-oriented model. For the characteristic of the large variation range of the flight speed of hypersonic vehicles, some researchers have adopted a linear time-varying model, which can avoid the problem of small control range caused by designing a controller near a single linearization equilibrium point. There are also scholars who use the T-S fuzzy modeling technique to approximate a complex non-linear model by superimposing a series of local linear models according to fuzzy rules. This technique can effectively approximate non-linear systems with arbitrary precision and is applicable to systems with strong non-linearity and large parameter uncertainties in a wide range. The commonly used non-linear control methods for hypersonic vehicles mainly include backstepping method, linear quadratic regulator, dynamic inversion method, intelligent control method, etc. The sliding mode control method has robustness to parameter changes and external disturbances, and at the same time, the algorithm is simple to implement and suitable for engineering applications; the intelligent control method has a large on-line calculation amount, the dynamic inversion method is sensitive to modeling errors and highly dependent on an accurate model, and the backstepping method is cumbersome in design steps when the model order is very large. These methods are not applicable to complex hypersonic vehicles. Summary of the Invention

[0004] The present invention proposes a modeling and fuzzy adaptive sliding mode control method for an elastic hypersonic vehicle under the influence of aerodynamic heat, which is used to solve the problems of strong model uncertainty caused by elastic deformation and aerodynamic thrust coupling of hypersonic vehicles and the resulting control problems.

[0005] The technical solution adopted by the present invention is as follows: A modeling and fuzzy adaptive sliding mode control method for an elastic hypersonic vehicle under the influence of aerodynamic heat, comprising the following steps:

[0006] Step 1: Establish a rigid body longitudinal dynamics model of a hypersonic vehicle, analyze the elastic modes of the vehicle, and establish an elastic longitudinal dynamics model;

[0007] Step 2: Obtain the change values of the angle of attack and the elevator deflection angle according to the deformations at the nose and tail of the vehicle and the deformation of the elevator control surface;

[0008] Step 3: Analyze the aerodynamics of the hypersonic vehicle, simplify the aerodynamic force and moment parameters in the real longitudinal dynamics model; replace the parameters in the rigid body longitudinal dynamics model with the corrected angle of attack and elevator deflection angle;

[0009] Step 4: Add parameter uncertainties and external disturbances to the corrected rigid body longitudinal dynamics model to obtain a complete elastic hypersonic vehicle longitudinal dynamics model; express it in an affine non-linear form and linearize it according to the T-S fuzzy rules;

[0010] Step 5: Design an adaptive sliding mode controller according to the T-S fuzzy model to enable the aircraft to track the given altitude and speed commands.

[0011] In view of the characteristics of hypersonic aircraft with aerodynamic thermoelastic effects and strong aerodynamic-thrust coupling, this invention takes into account the elastic mode, parameter uncertainty and external interference of the aircraft, conducts dynamic modeling on it, and linearizes it using T-S fuzzy rules. This method overcomes the problem of inaccurate modeling caused by ignoring the influence of the elastic mode on the angle of attack and elevator deflection angle and the aerodynamic-thrust coupling effect in the prior art. At the same time, an adaptive sliding mode controller is designed to enable the aircraft to stably track the reference commands. Brief Description of the Drawings

[0012] Figure 1 It is a schematic diagram of the overall system framework of the implementation case of this invention. Detailed Embodiments

[0013] The following further elaborates and explains this invention in conjunction with the drawings and specific embodiments. The technical features of each embodiment in this invention can be combined accordingly without conflict.

[0014] The embodiment of this invention provides a method for elastic modeling and fuzzy adaptive sliding mode control of an elastic hypersonic aircraft under the influence of aerodynamic heat, as Figure 1 shown, including:

[0015] Step 1: First, derive the rigid body longitudinal dynamics and kinematics equations based on the principle of virtual work and Lagrange's equation. Secondly, conduct an elastic mode analysis on the hypersonic aircraft. It can be assumed as a free beam with variable cross-section. Use the assumed mode method to analyze its mode to obtain the natural frequency and vibration mode, and then the longitudinal dynamics model of the elastic hypersonic aircraft can be obtained.

[0016] Step 2: When calculating the change values of the angle of attack and elevator deflection angle after the hypersonic aircraft undergoes elastic deformation, conduct free vibration and elastic deformation analysis on the free beam with variable cross-section in Step 1. Regard the deflection angle occurring at the nose of the aircraft as the change Δα(s) of the angle of attack of the aircraft; regard the deflection angle occurring at the tail of the aircraft as the change Δδ e1 (s) of the elevator hinge. Simplify the elevator surface as a simply supported-free beam hinged at the elevator hinge, and superimpose the deformation Δδ e2 (s) at the tail of the elevator and the deformation Δδ e1 (s) at the elevator hinge to obtain the change Δδ e (s) of the elevator deflection angle.

[0017] Step 3: When calculating the aerodynamic force of the aircraft, the shock wave / expansion wave effect, viscosity effect and unsteady effect are considered. The oblique shock wave and Prandtl-Meyer expansion wave theory and Newton collision theory can be used to calculate the fuselage force of the aircraft. Since lift, drag, thrust, pitch moment and generalized force are complex functions of system state and input, the model needs to be simplified for easy application. When simplifying the force and moment expressions, the aerodynamic force and moment can be replaced by the curve fitting function of the rigid body state, control input and elastic mode. Finally, the corrected aerodynamic parameters are used to replace the parameters in the original rigid body model.

[0018] Step 4: Based on the nonlinear mathematical model of the longitudinal motion of the aircraft, an affine linearization model is obtained, and the elastic mode, parameter uncertainty influence and external disturbance are added to the dynamic model. The nonlinear model is divided into 9 fuzzy subsets using the TS fuzzy strategy and the fuzzy membership function is designed.

[0019] Step 5: Design an integral sliding surface based on the fuzzy model, and design a sliding mode control law to make the tracking error slide to the sliding surface and stay on the sliding surface. And design an adaptive law to obtain the parameters ρ0 and ρ1 in the sliding mode controller so that the aircraft can stably track the given reference instructions.

[0020] In a specific embodiment of the present invention, the longitudinal dynamic equation of the aircraft in step 1 is as follows:

[0021] Step 1.1: When performing elastic modal analysis on a hypersonic vehicle, simplify the vehicle to a variable cross-section free beam, use the assumed modal method to derive the frequency and vibration mode, and then derive the longitudinal dynamic equation based on the Lagrange equation, and ignore the weaker rigid-flexible coupling term, that is, the coupling of modal acceleration and rigid body acceleration. So far, rigid-flexible coupling only occurs through force and torque. Considering the first three modes that have a greater impact on the vehicle, the following longitudinal dynamic model can be obtained:

[0022]

[0023] Where h and V represent the altitude and speed respectively, L, T, D represent the lift, thrust and drag respectively, α and γ represent the angle of attack and track climb angle respectively, q represents the pitch rate, M yy and I yy denote the moment and moment of inertia of the pitch axis, ξ i is the damping coefficient of the i-th mode, ω i is the natural frequency of the i-th mode, η i is the i-th elastic mode, N i is the i-th order generalized modal force.

[0024] In a specific embodiment of the present invention, the change values of the aircraft angle of attack and the elevator deflection angle in step 2 are calculated as follows:

[0025] Step 2.1: Calculate the change values Δα(s) and Δδ e1 (s) of the angle of attack and the deflection angle at the elevator hinge.

[0026] Assume the aircraft as a free beam. The free vibration equation of the free beam is (2-1); the boundary conditions are that the shear force and bending moment are equal to 0, as shown in Equation (2-2), where x f = 0 or L, and L is the total length of the fuselage.

[0027]

[0028]

[0029] In the formula, E(x) is the elastic modulus at any point x, I(x) is the moment of inertia at any point x, m(x) is the mass function at any point x, and y(x,t) is the displacement function of any point x at time t.

[0030] For a non-uniform variable cross-section beam, it is difficult to obtain an analytical solution. Therefore, the assumed mode method is used to solve the natural frequency and modal vibration mode. According to the principle of separation of variables, the general solution can be obtained as:

[0031]

[0032] Among them, η i (t) is the generalized displacement of the i-th order mode, n is the order of the elastic mode, and φ i (x) should be the actual mode function of the i-th order mode of the system, but usually it is approximately replaced by the assumed mode.

[0033] For the free vibration problem, according to the Lagrange equation (2-4), the generalized mode φ and natural frequency ω of the free beam can be obtained. M and K in the formula are the mass matrix and stiffness matrix respectively, and the calculation methods are shown in (2-5)

[0034]

[0035]

[0036] The angular deformation of the hypersonic aircraft at any point x in the i-th order mode at time t can be approximated as:

[0037]

[0038] In the formula, φ(x) is the vibration mode function, and η(t) is the generalized mode displacement function.

[0039] Considering the first three-order elastic modes, the elastic deflection at the nose is mainly applied to the angle of attack of the aircraft. The local change magnitude of the angle of attack can be expressed as:

[0040]

[0041] In the formula, α r represents the angle of attack of the rigid aircraft, and x n represents the reference point position of the selected angle of attack perturbation.

[0042] The deflection angle of the elastic deflection acting at the elevator hinge can be expressed as:

[0043]

[0044] In the formula, x h represents the position where the elevator hinge is located.

[0045] Step 2.2: Calculate the change value Δδ e2 (s) of the elevator surface. Add Δδ e2 (s) to the deformation Δδ e1 (s) at the elevator hinge, and the change Δδ e (s) of the elevator deflection angle can be obtained.

[0046] Assume the elevator is a simply supported-free beam hinged at the hinge, with a length of r. Its free vibration equation is the same as that of the free beam, as shown in Equation (2-1). The boundary conditions are that the deflection and bending moment at the hinge are equal to 0, where x r = r.

[0047]

[0048] Then the deflection angle of the elevator can be expressed as:

[0049]

[0050] In the formula, δ er is the elevator deflection angle of the rigid aircraft.

[0051] In a specific embodiment of the present invention, when fitting the lift L, drag D, thrust T, and moment M in the nonlinear model in Step 3, the influence of the elastic mode on the parameters is considered, and the fitting result can be basically the same as the true value. The calculation formula of the fitting model considering the shock wave, expansion wave effect, viscous effect, and unsteady effect is as follows:

[0052]

[0053] In the formula, is the dynamic pressure, S is the aerodynamic reference area, z T is the engine thrust eccentricity, c is the mean aerodynamic chord length, Φ represents the equivalent engine fuel equivalence ratio, δ e is the elevator deflection angle, η is the elastic mode, and T, L, D, M, N iThe coefficients are respectively:

[0054]

[0055] In the formula,

[0056] In a specific embodiment of the present invention, the specific operation of step four is as follows:

[0057] Step 4.1: The non-linear equation obtained in the above step can be written in the following affine non-linear model form:

[0058]

[0059] Wherein, is the state variable, u(t) = [Φ, δ e T is the control input, y(t) = [V, h] T is the control output.

[0060] Add the unknown modeling parameters and external disturbances into the model, and use the T-S fuzzy model to approximate the non-linear model. The fuzzy rule is: If Then

[0061]

[0062] Where z(t) = [z1(t)…z p (t)] is the premise variable, is the fuzzy subset, A i , B i , C, D i are known constant matrices. ΔA i is the uncertainty of the unknown parameter of A i . Then the non-linear model of the hypersonic vehicle can be expressed as:

[0063]

[0064] In the formula, l is the number of fuzzy rules, μ i (z) is the fuzzy membership function.​

[0065] In the above T-S fuzzy strategy, each premise variable corresponds to one of three ranges: the upper bound, the equilibrium point, and the lower bound. Since there are two premise variables in the hypersonic nonlinear model, namely the velocity V and the altitude h, there are a total of 3 2 That is, 9 fuzzy subsets. The fuzzy membership function μ i (z) is defined as follows:

[0066]

[0067] In the formula, the subscripts S, M, and B of μ represent the upper bound, the equilibrium point, and the lower bound respectively, h and V represent the altitude and velocity in the premise variables respectively, and μ i (t) ≥ 0, i = 0,... 9 and The membership functions of velocity and altitude are defined respectively as:

[0068]

[0069] In the formula, the subscripts S, M, and B of V and h represent the lower bound, the equilibrium point, and the upper bound respectively.

[0070] Step 4.2: According to the T-S fuzzy model (Equation 4-2), and assuming The reference model to be tracked can then be obtained as

[0071]

[0072] where z(t) = [z1(t) … z p (t)] is the premise variable, is the fuzzy subset, x m (t) is the state variable of the reference model, r(t) is a piecewise continuous and bounded reference input, A mi and B mi are known constant matrices, and A mi is a stable matrix.

[0073] The tracking error can be expressed as:

[0074] e(t) = x(t) - x m (t) (4-7)

[0075] The dynamic equation of the tracking error can be expressed as: If Then:

[0076]

[0077] Then the global tracking error is:

[0078]

[0079] Among them, and there exist positive values ρ0 and ρ1 to be designed such that ‖χ i (t)‖ max ≤ρ0 + ρ1‖e(t)‖.

[0080] Step 5: To stabilize the tracking error, a fuzzy integral sliding mode controller (FISMC) is designed for the control objective. First, the integral type sliding surface is designed as follows:

[0081]

[0082] Among them, t0 is the starting time, G i and K i are constant matrices to be designed, and the matrix A mi + B i K i is a Hurwitz matrix, and the matrix G i B i is a non-singular matrix.

[0083] Therefore, the global sliding surface is:

[0084]

[0085] Among them, s[x(t0, t0)] = 0.

[0086] After designing the sliding surface, the sliding mode control law is designed to make the error reach and stay in the sliding mode state. Therefore, the upper bound of ‖χ i (t)‖ max , that is, the values of ρ0 and ρ1, are needed. Since it is difficult to obtain ρ0 and ρ1 based on experience, an adaptive law is designed to obtain the values of ρ0 and ρ1, and thus an adaptive sliding mode controller is synthesized. There exists a constant γ π to be designed such that 0 < γ π < [u π (t)] ≤ 1, where [u π (t)] is the input after non-linear and saturation processing, and Then γ ≤ [u π (t)] ≤ 1 always holds, and the subscript π represents the input state variables Φ and δ e .

[0087] Suppose are the estimated values of ρ0, ρ1, and γ respectively. The design of the adaptive sliding mode controller that makes the system dynamics reach the sliding surface is as follows:

[0088]

[0089] Among them, u π(t) is the input, and the subscript π represents the input state variables Φ and δ e , k π is a parameter to be designed and satisfies k π > 1 / λ π , is called the gain attenuation tolerance and is a known positive constant, and both are known constants.

[0090] The adaptive control law is designed as follows:

[0091]

[0092] where, q1 and q2 are adjustable positive constants. The value of is the solution of the following linear differential equation

[0093]

[0094] where, γ0 is the bounded initial value of, and Also, because k π > 1 / λ π , so always holds.

[0095] In summary, the present invention proposes a modeling and fuzzy adaptive sliding mode control method for an elastic hypersonic vehicle under aerodynamic heating. Considering that the hypersonic vehicle has a high flight speed, the aerodynamic heating phenomenon will seriously affect the structural dynamics of the aircraft. The frequency of the structure depends on the Young's modulus, and the Young's modulus is a function of temperature. The increase in temperature will cause changes in the natural frequency of the structure and obvious deformations, resulting in a rapid decrease in the control effectiveness of the rudder. In severe cases, it will cause flight instability. Since the angle of attack and the elevator deflection angle of the aircraft have a greater impact on flight stability, the present invention mainly calculates the change values of the angle of attack and the elevator deflection angle. In the past, when calculating the angle of attack and the elevator deflection angle of the aircraft, the aircraft was simplified as a free beam, and the deformation at the nose was regarded as the change value of the angle of attack, and the change value at the elevator hinge was regarded as the change value of the elevator deflection angle. On this basis, the present invention more fully considers the change value of the elevator deflection angle. It not only considers the deformation Δδ e1 (s) at the elevator hinge, but also considers the elevator alone as a simply supported-free beam, with the hinge position at the elevator hinge, and takes the deformation value at the tail of the simply supported-free beam as the deformation value Δδ e2 (s) of the elevator surface, which is superimposed with the deformation Δδ e1 (s) at the elevator hinge to obtain the complete change value Δδ e(s), and when performing free vibration analysis on the free beam and the simply supported-free beam, the first three elastic modes with greater influence on deformation are considered, and the reduction of the elevator effectiveness caused by the deformation due to aerodynamic heat is fully considered, providing a theoretical basis for subsequent controller design.

[0096] Subsequently, the change values of the angle of attack and the elevator deflection angle are added to the aerodynamic force and aerodynamic moment calculation formulas to obtain the changed force and moment values. Thus, a complete longitudinal dynamics model is obtained. Since the model is too complex and needs to be simplified for control, the nonlinear model obtained in the previous steps is rewritten in an affine nonlinear form, and external disturbances and unmodeled errors are added to the model. Then, the T-S fuzzy method is used to linearize the model to obtain a model for control. The T-S fuzzy model is characterized by using the superposition of a series of local linear models to approximate complex nonlinear models according to fuzzy rules, and is suitable for systems with strong nonlinearity and large parameter uncertainties in a wide range. For the model for control, an adaptive sliding mode controller is designed. The sliding mode controller is insensitive to model parameter uncertainties, external disturbances, and matching disturbances, and the control algorithm is simple to implement and suitable for engineering applications.

[0097] The above-described embodiments merely represent several implementation manners of the present invention, and the description thereof is relatively specific and detailed, but should not be construed as a limitation on the scope of the patent of the present invention. For those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A modeling and fuzzy adaptive sliding mode control method for an elastic hypersonic vehicle under aerodynamic heating effects, characterized in that, It includes the following steps: Step 1: Establish a rigid-body longitudinal dynamics model of a hypersonic vehicle, analyze the elastic modes of the vehicle, and establish an elastic longitudinal dynamics model; Step 2: Obtain the change values of the angle of attack and elevator deflection angle according to the deformations at the nose and tail of the vehicle and the deformation of the elevator control surface; Step 3: Analyze the aerodynamics of the hypersonic vehicle, simplify the aerodynamic force and moment parameters in the real longitudinal dynamics model; replace the parameters in the elastic longitudinal dynamics model with the corrected angle of attack and elevator deflection angle; Step 4: Add parameter uncertainties and external disturbances to the corrected elastic longitudinal dynamics model, express it in affine nonlinear form, and linearize it according to the T-S fuzzy rules; Step 5: Design an adaptive sliding mode controller according to the T-S fuzzy model to enable the vehicle to track the given altitude and speed commands.

2. The method for modeling and fuzzy adaptive sliding mode control of an elastic hypersonic vehicle under aerodynamic heat effects according to claim 1, wherein, The described Step 1 is: Derive the rigid-body longitudinal dynamics equation and kinematic equation according to the principle of virtual work and Lagrange's equation; conduct an elastic mode analysis on the hypersonic vehicle, assume it as a free beam with variable cross-section, and use the assumed mode method to conduct modal analysis to obtain the natural frequency and vibration mode, thus obtaining the elastic longitudinal dynamics model.

3. The modeling and fuzzy adaptive sliding mode control method of an elastic hypersonic vehicle under aerodynamic heating according to claim 2, characterized in that, Specifically, in Step 1: When conducting an elastic mode analysis on the hypersonic vehicle, simplify the vehicle to a free beam with variable cross-section, use the assumed mode method to derive the frequency and vibration mode, and then derive the longitudinal dynamics equation according to Lagrange's equation, and ignore the coupling between the modal acceleration and the rigid-body acceleration. At this point, the rigid-flexible coupling only occurs through forces and moments; consider the first three modes that have a greater impact on the vehicle, and obtain the following elastic longitudinal dynamics model: Wherein, h and V respectively represent height and speed, L, T, and D respectively represent lift, thrust, and drag, α and γ respectively represent angle of attack and flight path climb angle, q represents pitch rate, M yy and I yy respectively represent the moment and moment of inertia about the pitch axis, ξ i is the damping coefficient of the i-th order mode, ω i is the natural frequency of the i-th order mode, η i is the i-th order elastic mode, N i is the i-th order generalized modal force.

4. The modeling and fuzzy adaptive sliding mode control method of an elastic hypersonic vehicle under aerodynamic heat effects according to claim 2, characterized in that The said step 2 is as follows: When calculating the change values of the angle of attack and the elevator deflection angle after the hypersonic vehicle undergoes elastic deformation, perform free vibration and elastic deformation analysis on the variable cross-section free beam in step 1. Consider the deflection angle occurring at the aircraft nose as the change in the angle of attack of the aircraft, Δα(s); consider the deflection angle occurring at the aircraft tail as the change in the elevator hinge, Δδ e1 (s). Simplify the elevator flap as a simply supported-free beam hinged at the elevator hinge, and superimpose the deformation Δδ e2 (s) at the elevator tail and the deformation Δδ e1 (s) at the elevator hinge to obtain the change value of the elevator deflection angle, Δδ e (s).

5. The modeling and fuzzy adaptive sliding mode control method of an elastic hypersonic vehicle under aerodynamic heat effects according to claim 4, characterized in that The calculation of the change values of the angle of attack and elevator deflection angle of the vehicle in Step 2 is as follows: Step 2.1: Calculate the change values Δα(s) and Δδ e1 (s) of the angle of attack and the deflection angle at the elevator hinge; The aircraft is assumed to be a free beam, and the free vibration equation of the free beam is (2-1); the boundary conditions are that the shear force and bending moment are equal to 0, as shown in Equation (2-2), where x f = 0 or L, and L is the total length of the fuselage; In the formula, E(x) is the elastic modulus at any point x, I(x) is the moment of inertia at any point x, m(x) is the mass function at any point x, and y(x,t) is the displacement function of any point x at time t; Adopt the assumed mode method to solve the natural frequency and modal vibration mode. According to the principle of separation of variables, it can be obtained: where, η i (t) is the generalized displacement of the i-th order mode, n is the order of the elastic mode, φ i (x) should be the actual mode function of the i-th order mode of the system; For the free vibration problem, the generalized mode φ and natural frequency ω of the free beam can be obtained according to Lagrange's equation (2-4); M and K in the formula are the mass matrix and stiffness matrix respectively; The angular deformation of any point x of the hypersonic vehicle at the i-th mode at time t is approximately: In the formula, φ(x) is the vibration mode function, and η(t) is the generalized modal displacement function; Considering the first three elastic modes, the elastic deflection at the nose is mainly applied to the angle of attack of the aircraft, and the local change magnitude of the angle of attack is expressed as: where α r denotes the angle of attack of the rigid aircraft, and x n denotes the reference point position of the selected angle of attack perturbation; The deflection angle magnitude of the elastic deflection acting on the elevator hinge is expressed as: where x h represents the position of the elevator hinge; Step 2.2: Calculate the change value Δδ of the elevator flap e2 (s), and add Δδ e2 (s) to the deformation Δδ e1 (s) at the hinge of the elevator, then the change Δδ e (s) of the elevator deflection angle can be obtained; The elevator is assumed to be a simply supported-free beam hinged at the hinge, with a length of r. Its free vibration equation is the same as that of a free beam, as shown in Equation (2-1). The boundary conditions are that the deflection and bending moment at the hinge are equal to 0, where x r = r; Then the deflection angle magnitude of the elevator is expressed as: where δ er is the elevator deflection angle of the rigid aircraft.

6. The modeling and fuzzy adaptive sliding mode control method of an elastic hypersonic vehicle under aerodynamic heat effects according to claim 2, characterized in that, Step 3 is as follows: when calculating the aerodynamic force of the aircraft, consider the shock wave / detonation wave effect, viscous effect and unsteady effect, and use the oblique shock wave and Prandtl-Meyer detonation wave theory and Newton's collision theory to calculate the force on the fuselage of the aircraft; simplify the force and moment expressions, and use the curve fitting functions of the rigid body state, control input and elastic mode to replace the aerodynamic force and moment; finally, replace the parameters in the elastic longitudinal dynamics model with the corrected aerodynamic parameters.

7. The modeling and fuzzy adaptive sliding mode control method of an elastic hypersonic vehicle under aerodynamic heat effects according to claim 6, characterized in that After step 3 replaces the parameters in the original elastic longitudinal dynamics model with the corrected aerodynamic parameters, the obtained nonlinear mathematical model of the longitudinal motion of the aircraft, that is, the corrected elastic longitudinal dynamics model is: where q is the dynamic pressure, S is the aerodynamic reference area, z T is the engine thrust eccentricity, c is the mean aerodynamic chord length, Φ represents the engine equivalent fuel equivalence ratio, δ e is the elevator deflection angle, η is the elastic mode, C T,φ (α) and C T (α) are the thrust coefficients related to the angle of attack, C L (α,δ e ,η) is the lift coefficient related to the angle of attack and the elevator deflection angle, C D (α,δ e ,η) is the drag coefficient related to the angle of attack, the elevator deflection angle, and the elastic mode, C M (α,δ e ,η) is the moment coefficient related to the angle of attack, the elevator deflection angle, and the elastic mode, is the generalized force coefficient related to the angle of attack, the elevator deflection angle, and the elastic mode.

8. The modeling and fuzzy adaptive sliding mode control method of an elastic hypersonic vehicle under aerodynamic heat effects according to claim 6, characterized in that Step 4 is as follows: obtain the affine linearized model according to the nonlinear mathematical model of the elastic longitudinal motion of the aircraft in step 3, add the elastic mode, parameter uncertainty influence and external disturbance to the affine linearized model, and use the T-S fuzzy strategy to divide the affine linearized model into 9 fuzzy subsets and design the fuzzy membership function.

9. The modeling and fuzzy adaptive sliding mode control method for an elastic hypersonic vehicle under aerodynamic heating effects according to claim 8, characterized in that, The specific operation of step 4 is as follows: Step 4.1: Write the nonlinear mathematical model of the elastic longitudinal motion of the aircraft in the following affine nonlinear model form: Among them, is the state variable, u(t) = [Φ, δ e T is the control input, y(t) = [V, h] T is the control output;​ The unknown modeling parameters and external disturbances are incorporated into the model, and the T-S fuzzy model is used to approximate the nonlinear model. The fuzzy rules are: If then where \(z(t)=[z_1(t)\cdots z p (t)]\) is the premise variable, is a fuzzy subset, \(A i \), \(B i \), \(C\), \(D i are known constant matrices; \(\Delta A i is the uncertainty of the unknown parameters of \(A i Then the nonlinear model of the hypersonic vehicle is expressed as: where l is the number of fuzzy rules, and μ i (z) is the fuzzy membership function; In the above T-S fuzzy strategy, each premise variable corresponds to one of three ranges: the upper boundary, the equilibrium point, and the lower boundary. Since there are two premise variables, namely velocity V and altitude h, in the hypersonic nonlinear model, there are a total of 3 2 i.e., 9 fuzzy subsets; Step 4.2: According to the T-S fuzzy model in Equation (4-2), and assuming that the reference model to be tracked can be obtained as where \(z(t)=[z_1(t)\cdots z p (t)]\) is the premise variable, is a fuzzy subset, \(x m (t)\) is the state variable of the reference model, \(r(t)\) is piecewise continuous and bounded reference input, \(A mi and \(B mi are known constant matrices, and \(A mi is a stable matrix; The tracking error can be expressed as: e(t) = x(t) - x m (t) (4 - 7) The dynamic equation of the tracking error can be expressed as: If Then: Then the global tracking error is: Among them, and there exist positive values ρ0 and ρ1 to be designed such that ‖χ i (t)‖ max ≤ ρ0 + ρ1‖e(t)‖.

10. The modeling and fuzzy adaptive sliding mode control method for an elastic hypersonic vehicle under aerodynamic heat influence according to claim 9, characterized in that, Step 5 is specifically: Design a fuzzy integral sliding mode controller (FISMC) for the control target. First, design the integral type sliding surface as follows: where t is time, T0 is the starting moment, G i and K i are constant matrices to be designed, and the matrix A mi +B i K i is a Hurwitz matrix, and the matrix G i B i is a non-singular matrix; A mi and B i are known constant matrices, and A mi is a stable matrix; e(t) is the error function; So the global sliding surface is: where s[x(t0,t0)] = 0; μ i (t) is a fuzzy membership function; After designing the sliding mode surface, the sliding mode control law is designed to make the error reach the sliding mode state and stay; therefore, it is necessary to know ‖χ i (t)‖ max 's upper bound, that is, the values of ρ0 and ρ1; since it is difficult to obtain ρ0 and ρ1 based on experience, an adaptive law is designed to obtain the values of ρ0 and ρ1, and thus an adaptive sliding mode controller is synthesized; there is a constant γ π to be designed such that 0 < γ π < [u π (t)] ≤ 1, where [u π (t)] is the input after nonlinear and saturation processing. Let Then γ ≤ [u π (t)] ≤ 1 always holds, and the subscript π represents the input state variables Φ and δ e ; Hypothesis Let the estimated values of ρ0, ρ1, and γ be ρ̂0, ρ̂1, and γ̂ respectively. The design of the adaptive sliding mode controller to make the system dynamics reach the sliding mode surface is as follows: where, u π (t) is the input, and the subscript π represents the input state variables Φ and δ e , k π is the parameter to be designed and satisfies k π > 1 / λ π , is called the gain attenuation tolerance and is a known positive constant, and both are known constants; The adaptive control law is designed as follows: where q1 and q2 are adjustable positive constants; The value of is the solution of the following linear differential equation: Among them, γ0 is a bounded initial value of and

Images