Method for analyzing and solving reentry trajectory of variable-structure hypersonic aircraft

Abstract

The invention provides an analytic solution method for a reentry trajectory of a variable-structure hypersonic flight vehicle. The analytic solution method comprises the following steps: modeling a reentry guidance problem of the variable-structure hypersonic flight vehicle; the reentry trajectory of the variable-structure hypersonic aircraft is analyzed and solved; and constructing a reentry trajectory compensation framework based on a physical information neural network, compensating the analytical solution of the reentry trajectory, and generating the reentry trajectory under aerodynamic disturbance. According to the method, the kinematic model is established, the analytic expression of the reentry trajectory of the variable-structure hypersonic aircraft is solved, parameter dependence is effectively reduced, and high solving precision is achieved under the non-disturbance condition; meanwhile, an extended state observer is used for estimating a dynamics simplification error and an aerodynamic disturbance error, a loss function based on the dynamics of the variable-structure hypersonic aircraft is designed, a physical information neural network is constructed to compensate an analytical solution, and high-precision track generation under aerodynamic disturbance is achieved.

Description

Technical Field

[0001] The present invention relates to the field of control technology for a variable-configuration hypersonic aircraft, and in particular to a method for analytically solving the re-entry trajectory of a variable-configuration hypersonic aircraft based on physical information neural network compensation. Background Art

[0002] In today's aerospace field, variable-state hypersonic vehicles (VVHVs) demonstrate significant strategic significance and broad application prospects, and their high-precision guidance command generation technology is attracting increasing attention. Analytical methods, as a traditional research approach, have been a key and challenging area for accurately generating reentry guidance commands for hypersonic vehicles. However, due to the highly nonlinear dynamics and complex aerodynamic characteristics of VVHVs, analytical methods cannot guarantee the accuracy of the resulting solutions. Furthermore, the actual flight environment is fraught with uncertainties, such as the unsteady aerodynamic changes caused by VVVs and the random fluctuations in atmospheric density. These factors expose analytical methods to certain limitations when applied to real-world flight scenarios.

[0003] Considering the above two shortcomings, it is necessary to generate high-precision guidance commands for variable-state hypersonic vehicles based on a completely new guidance command generation strategy and framework. First, an auxiliary spherical coordinate system is constructed based on the characteristics of the vehicle's reentry trajectory. The reentry dynamics are reasonably simplified using Taylor expansion, and then the analytical solution of the reentry trajectory is derived using the Lyapunov artificial small parameter method. Secondly, the information loss caused by the dynamic simplification and the external aerodynamic perturbations are estimated through an extended state observer, and training data is generated based on the observation results. Then, a physical information neural network compensation framework is constructed to compensate the analytical solution online. The reentry dynamics equations are simultaneously incorporated into the training as physical constraints to enhance the network's ability to capture complex nonlinear characteristics. Summary of the Invention

[0004] The purpose of the present invention is to address the deficiencies in the above-mentioned background technology and provide a new analytical solution for reentry trajectories of variable-state hypersonic vehicles, so as to maintain high-precision compensation under strong aerodynamic perturbations and improve the robustness of guidance command generation.

[0005] In order to achieve the above object, the present invention provides a method for analytically solving the reentry trajectory of a variable-configuration hypersonic vehicle, comprising the following steps:

[0006] S1, modeling the reentry guidance problem of a variable-configuration hypersonic vehicle;

[0007] Considering the Earth as a uniform sphere and taking into account its rotation, the aircraft's motion equations in a semi-velocity coordinate system are established with time t as the independent variable. Parameters involved include distance from the Earth's center, Earth's radius and altitude, longitude and latitude, velocity, velocity inclination, heading angle, roll angle, Earth's rotational angular velocity, gravitational acceleration, aircraft mass, aerodynamic lift, and aerodynamic drag. The aircraft's aerodynamics are modeled, including lift coefficient and drag coefficient.

[0008] S2, analytical solution of the reentry trajectory of the hypersonic vehicle;

[0009] The generalized equator is introduced, which includes the great circle tangent to the initial reentry velocity and contains the center of the Earth. An auxiliary spherical coordinate system is constructed based on the generalized equator. The origin of the auxiliary spherical coordinate system is located at the center of the Earth. The generalized equatorial plane is the zero latitude plane, and the zero longitude line passes through the initial sub-satellite point of the reentry point. The dynamic model in S1 is converted into a dynamic model with energy as the independent variable. The analytical solution of the reentry trajectory is obtained by solving the dynamic model.

[0010] S3, constructing a reentry trajectory compensation framework based on physical information neural network to compensate the analytical solution of the reentry trajectory and generate the reentry trajectory under aerodynamic disturbance;

[0011] Considering the scenario with aerodynamic disturbances, the dynamic model in S1 is transformed, the aerodynamic disturbance and the information loss caused in S2 are regarded as the total disturbance, and the total disturbance is converted into an expanded state variable; an expanded state observer is constructed; a reentry trajectory compensation framework based on a physical information neural network is constructed; a data loss function of the physical information neural network is designed to train the physical information neural network; the analytical solution of the reentry trajectory in S2 is compensated by the trained physical information neural network to obtain a reentry trajectory with improved accuracy.

[0012] The above solution of the present invention has the following beneficial effects:

[0013] The present invention provides a method for analytically solving the reentry trajectory of a variable hypersonic vehicle. Based on the technology of a variable hypersonic vehicle as the research object, a kinematic model is established and an analytical expression of the reentry trajectory of the variable hypersonic vehicle is solved. This method effectively reduces parameter dependence and has high solution accuracy in the absence of disturbances. At the same time, the present invention uses an extended state observer to estimate the dynamic simplification error and aerodynamic disturbance error, and designs a loss function based on the dynamics of the variable hypersonic vehicle. On this basis, a physical information neural network is constructed to compensate for the above analytical solution, thereby achieving high-precision trajectory generation under aerodynamic disturbances.

[0014] Other beneficial effects of the present invention will be described in detail in the subsequent specific implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a flow chart of the steps of the present invention;

[0016] Figure 2 In the embodiment of the present invention, K A =1.15,ψ0=60deg reentry trajectory solution result diagram;

[0017] Figure 3 In the embodiment of the present invention, K A =1.3,ψ0=70deg reentry trajectory solution result diagram;

[0018] Figure 4 In the embodiment of the present invention, K B =1.15,ψ0=80deg reentry trajectory solution result diagram;

[0019] Figure 5 In the embodiment of the present invention, K B =1.15,ψ0=80deg. DETAILED DESCRIPTION

[0020] The following describes the embodiments of the present disclosure through specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present disclosure.

[0021] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0022] It should also be noted that the diagrams provided in the following embodiments are merely schematic illustrations of the basic concepts of the present disclosure. The diagrams only show components relevant to the present disclosure and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the configuration, quantity, and proportion of each component may be varied at will, and the component layout may be more complex. Furthermore, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will appreciate that the described aspects may be practiced without these specific details.

[0023] like Figure 1 As shown, an embodiment of the present invention provides a method for analytically solving the reentry trajectory of a variable-configuration hypersonic vehicle, which specifically includes the following steps:

[0024] S1, Modeling the reentry guidance problem of a variable-configuration hypersonic vehicle.

[0025] In this example, a two-dimensional transformable hypersonic vehicle is studied. The vehicle consists of a waverider fuselage and morphing wings capable of varying sweep angles and telescopic deformation. The wings undergo synchronous and symmetrical deformation, with the sweep angle varying from 80° to 0°. At 80°, the wings are stowed, while at 0°, they are fully extended. The telescopic wings can extend from 0 mm to 200 mm. The wing length is dimensionless, and the range of the wing variation is uniformly represented using a [0, 1] expansion ratio.

[0026] At the same time, considering the earth as a uniform sphere and taking into account the earth's rotation, the motion equation of the aircraft with time t as the independent variable in the semi-velocity coordinate system (also called the ballistic coordinate system) is as follows:

[0027]

[0028] Where R is the distance from the center of the earth, R = R e +H,R e , H are the radius and height of the earth respectively, λ and φ are the longitude and latitude respectively, V is the velocity, θ is the velocity inclination, ψ is the heading angle (where north-east is defined as the positive direction), σ is the roll angle, ω e is the angular velocity of the Earth’s rotation, g = μ / R 2 is the acceleration due to gravity (μ is the earth's gravitational constant), m is the mass of the aircraft, L and D are the aerodynamic lift and aerodynamic drag respectively, and the calculation formula is:

[0029]

[0030] Where q is the dynamic pressure, ρ is the atmospheric density, S ref is the aerodynamic reference area of ​​the aircraft, C L is the lift coefficient, CD is the drag coefficient, which is a function of the angle of attack α, Mach number Ma, sweep angle δ and retraction rate η.

[0031] In this embodiment, the aircraft aerodynamics (lift coefficient, drag coefficient) is modeled using a polynomial model, as follows:

[0032]

[0033] in, These are aerodynamic fitting coefficients, and the other parameters are:

[0034]

[0035] S2, analytically solve the reentry trajectory of the variable-configuration hypersonic vehicle.

[0036] In this example, to simplify the highly nonlinear dynamic model, a generalized equator is introduced, defined as a great circle containing the Earth's center and tangent to the initial reentry velocity. Furthermore, an auxiliary spherical coordinate system is constructed based on the generalized equator: this coordinate system has its origin at the Earth's center, the generalized equatorial plane is the zero latitude plane, and the zero longitude line passes through the initial subsatellite point of the reentry point. Converting the dynamic model to a dynamic model with energy E as the independent variable yields:

[0037]

[0038] Among them, ~ represents the corresponding generalized state.

[0039] Since the altitude change of the aircraft during reentry is relatively small and the aircraft is almost flying horizontally, it can be assumed that θ≈0, cosθ≈1, and tanθ≈0. At the same time, we can obtain Therefore, formula (5) contains The term can be ignored. Based on the above assumptions, the following simplified dynamic model can be obtained:

[0040]

[0041] Among them, R * is the average of the initial and terminal altitudes, L1 / D and L2 / D are defined as the longitudinal lift-to-drag ratio and the lateral lift-to-drag ratio, respectively, that is:

[0042]

[0043] exist Performing Taylor expansion on formula (6) yields:

[0044]

[0045] Using Lyapunov's artificial small parameter method, we introduce a small parameter p into the nonlinear term of formula (8), and obtain:

[0046]

[0047] In order to obtain an analytical solution with sufficiently high accuracy, the generalized state is expanded into a second-order series:

[0048]

[0049] The subscripts 0, 1, and 2 represent different orders of the corresponding generalized states.

[0050] Substituting formula (10) into formula (9) yields:

[0051]

[0052] From this, the dynamic equations of the zero-order, first-order and second-order states can be obtained:

[0053]

[0054]

[0055] By solving the above three subsystems through simple integration and spectral decomposition method, the analytical solution of the reentry trajectory is obtained as follows:

[0056]

[0057] Where E0 is the initial energy, X is the integral variable, They are The initial value of .

[0058] S3, constructs a reentry trajectory compensation framework based on physical information neural network to compensate the analytical solution of the reentry trajectory and realize high-precision reentry trajectory generation under aerodynamic disturbances.

[0059] In this embodiment, considering the scenario with aerodynamic disturbance, the dynamic model in formula (5) under aerodynamic disturbance becomes:

[0060]

[0061] in, are respectively the longitude, latitude and heading angle under aerodynamic disturbance, are the disturbance lift and drag, respectively, defined as:

[0062]

[0063] Among them, K A ,K B is the disturbance coefficient.

[0064] Considering the aerodynamic disturbance and the information loss caused by the dynamic simplification in S2 as the total disturbance, and converting the total disturbance into an expanded state variable, we can obtain:

[0065]

[0066] Among them, z1, z2, z3 are the total disturbances of the three channels respectively, ξ1, ξ2, ξ3 are the differentials of the total disturbance, To set parameters and

[0067] Construct the following extended state observer:

[0068]

[0069] in, is the observer estimated state, β 11 ,β 12 ,β 21 ,β 22 ,β 31 ,β 32 is the feedback coefficient of the observer.

[0070] Based on the extended state observer, the reentry trajectory compensation framework based on physical information neural network is constructed as follows:

[0071]

[0072] in, is the reentry trajectory result after compensation, P is the physical information neural network F Output.

[0073] In order to P F Conduct training and design P F The data loss is:

[0074]

[0075] Among them, j is the number of training data in the data loss, N is the number of training data, is the output value of the physical information neural network for the training data numbered j, E j Represents the energy corresponding to the training data numbered j, The energy is E j The analytical solution of equation (15) is: j is the true compensation value generated by formula (20), and:

[0076]

[0077] Design PF The physical loss is:

[0078]

[0079] Among them, i is the number of the training data in the physical loss, is the output value of the physical information neural network for the training data numbered i, E i Represents the energy corresponding to the training data numbered i, The energy is E i The analytical solution of equation (15) is obtained.

[0080] Therefore, the total loss function is:

[0081] Γ=ζ p Γ p +ζ r Γ r (25)

[0082] Among them, p ,ζ r is a coefficient used to balance physical loss and data loss, and satisfies ζ p +ζ r =1.

[0083] Through the re-entry trajectory compensation framework of the physical information neural network and the setting of the loss function, the analytical solution of the re-entry trajectory in S2 can be compensated, thereby obtaining high-precision re-entry trajectory generation.

[0084] The following is a further explanation of the effect of the present invention through specific cases. Considering that the aerodynamic disturbance coefficients are K A =1.15,K A =1.3,K B =1.15,K B =1.3, taking the long-range trajectory as an example, the accuracy of the solutions of different methods is compared. The initial conditions are set as λ0 = 0 degrees, φ0 = 0 degrees, H0 = 60000m, V0 = 6000m / s, and ψ0 = 60 degrees, 70 degrees, 80 degrees, and 90 degrees, respectively. During the reentry process of the edge-configuration hypersonic vehicle, the intermediate state configuration is maintained, that is, δ = 40 degrees and η = 0.5.

[0085] Figure 2 K is shown A =1.15,ψ0=60deg reentry trajectory solution results (where TrajectorySimulation is the Runge-Kutta integration result, is the analytical solution obtained from formula (15) in this application, is the compensated result obtained by formula (21) in this application; Figure 3 K is shown A =1.3,ψ0=70deg reentry trajectory solution; Figure 4 K is shown B =1.15,ψ0=80deg reentry trajectory solution; Figure 5 K is shown B =1.15, ψ0 = 80 degrees. It can be seen that the compensation result in this application is closer to the value of the Runge-Kutta integral result, and it shows that this application takes into account the influence of disturbances such as gas disturbances.

[0086] Based on the same inventive concept, this embodiment further provides a device comprising at least one processor and a memory communicatively connected to the at least one processor. The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the aforementioned method for analyzing the reentry trajectory of a variable-configuration hypersonic vehicle.

[0087] Based on the same inventive concept, this embodiment also provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, it implements the aforementioned method for analyzing and solving the re-entry trajectory of a variable-configuration hypersonic aircraft.

[0088] The computer-readable medium includes, but is not limited to, any type of disk (including floppy disks, hard disks, optical disks, CD-ROMs, and magneto-optical disks), ROM, RAM, EPROM (Erasable Programmable Read-Only Memory), EEPROM, flash memory, magnetic cards, or optical cards. In other words, the computer-readable medium includes any medium that can store or transmit information in a form that can be read by a device (such as a printer).

[0089] The device, computer-readable storage medium, etc. provided in this embodiment have the same inventive concept and the same beneficial effects as the aforementioned method, and will not be described in detail here.

[0090] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0091] The above embodiments merely illustrate several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A method for solving the reentry trajectory of a hypersonic vehicle, characterized by: The steps include: S1, modeling the reentry guidance problem of a variable-configuration hypersonic vehicle; Considering the Earth as a uniform sphere and taking into account its rotation, the aircraft's motion equations in a semi-velocity coordinate system are established with time t as the independent variable. Parameters involved include distance from the Earth's center, Earth's radius and altitude, longitude and latitude, velocity, velocity inclination, heading angle, roll angle, Earth's rotational angular velocity, gravitational acceleration, aircraft mass, aerodynamic lift, and aerodynamic drag. The aircraft's aerodynamics are modeled, including lift coefficient and drag coefficient. S2, analytical solution of the reentry trajectory of the hypersonic vehicle; The generalized equator is introduced, which includes the great circle tangent to the initial reentry velocity and contains the center of the Earth. An auxiliary spherical coordinate system is constructed based on the generalized equator. The origin of the auxiliary spherical coordinate system is located at the center of the Earth. The generalized equatorial plane is the zero latitude plane, and the zero longitude line passes through the initial sub-satellite point of the reentry point. The dynamic model in S1 is converted into a dynamic model with energy as the independent variable. The analytical solution of the reentry trajectory is obtained by solving the dynamic model. S3, constructing a reentry trajectory compensation framework based on physical information neural network to compensate the analytical solution of the reentry trajectory and generate the reentry trajectory under aerodynamic disturbance; Considering the scenario with aerodynamic disturbances, the dynamic model in S1 is transformed, the aerodynamic disturbance and the information loss caused in S2 are regarded as the total disturbance, and the total disturbance is converted into an expanded state variable; an expanded state observer is constructed; a reentry trajectory compensation framework based on a physical information neural network is constructed; a data loss function of the physical information neural network is designed to train the physical information neural network; the analytical solution of the reentry trajectory in S2 is compensated by the trained physical information neural network to obtain a reentry trajectory with improved accuracy.

2. The method for analytically solving the reentry trajectory of a hypersonic vehicle according to claim 1, characterized in that: The motion equation of the aircraft in S1 with time t as the independent variable is: Where R is the distance from the center of the earth, R = R e +H,R e , H are the radius and height of the earth respectively, λ and φ are the longitude and latitude respectively, V is the speed, θ is the speed inclination, ψ is the heading angle, σ is the roll angle, ω e is the angular velocity of the Earth’s rotation, g = μ / R 2 is the acceleration due to gravity, μ is the gravitational constant of the earth, m is the mass of the aircraft, L and D are the aerodynamic lift and aerodynamic drag respectively.

3. The method for analytically solving the reentry trajectory of a variable-configuration hypersonic vehicle according to claim 2, characterized in that: The calculation formulas for aerodynamic lift and aerodynamic drag are: Where q is the dynamic pressure, ρ is the atmospheric density, S ref is the aerodynamic reference area of ​​the aircraft, C L is the lift coefficient, C D is the drag coefficient. The lift coefficient and the drag coefficient are both functions of the angle of attack α, Mach number Ma, sweep angle δ and retraction rate η.

4. The method for analytically solving the reentry trajectory of a hypersonic vehicle according to claim 3, characterized in that: In S1, the lift coefficient and drag coefficient are modeled using a polynomial model: in, are aerodynamic fitting coefficients, 5. The method for analytically solving the reentry trajectory of a hypersonic vehicle according to claim 4, characterized in that: In S2, the kinetic model is converted into a kinetic model with energy E as the independent variable: Among them, ~ represents the corresponding generalized state.

6. The method for analytically solving the reentry trajectory of a hypersonic vehicle according to claim 5, characterized in that: The kinetic model is simplified to obtain a simplified kinetic model: Among them, R * is the average of the initial altitude and the terminal altitude, L1 / D and L2 / D are the longitudinal lift-to-drag ratio and the lateral lift-to-drag ratio, respectively, that is:

7. The method for analytically solving the reentry trajectory of a hypersonic vehicle according to claim 6, characterized in that: exist Taylor expansion of the simplified dynamic model is performed, and we get: Using Lyapunov's artificial small parameter method, we introduce a small parameter p into the nonlinear term of the above equation and obtain: Expand the generalized state into a second-order series: Among them, the subscripts 0, 1, and 2 represent different orders of the corresponding generalized states; Bring in: This leads to the kinetic equations for the zero-order, first-order, and second-order states: By solving the problem through simple integration and spectral decomposition, we can obtain the analytical solution of the reentry trajectory: Where E0 is the initial energy, X is the integral variable, They are The initial value of .

8. The method for analytically solving the reentry trajectory of a variable-configuration hypersonic vehicle according to claim 7, characterized in that: The dynamic model under aerodynamic disturbance in S3 is: in, are respectively the longitude, latitude and heading angle under aerodynamic disturbance, are the disturbance lift and drag, respectively, defined as: Among them, K A ,K B is the disturbance coefficient.

9. The method for analytically solving the reentry trajectory of a hypersonic vehicle according to claim 8, characterized in that: In S3, the aerodynamic disturbance and the information loss caused by the dynamic simplification in S2 are regarded as the total disturbance, and the total disturbance is converted into an expanded state variable to obtain: Among them, z1, z2, z3 are the total disturbances of the three channels respectively, ξ1, ξ2, ξ3 are the differentials of the total disturbance, To set parameters and Construct the extended state observer: in, is the observer estimated state, β 11 ,β 12 ,β 21 ,β 22 ,β 31 ,β 32 is the feedback coefficient of the observer.

10. The method for analytically solving the reentry trajectory of a hypersonic vehicle according to claim 9, characterized in that: In S3, based on the extended state observer, a reentry trajectory compensation framework based on physical information neural network is constructed: in, is the reentry trajectory result after compensation, P is the physical information neural network F Output; Design P F Data loss Γ r and physical loss Γ p , the total loss function Γ is: C=g p C p +g r C r Among them, p ,ζ r is a coefficient used to balance physical loss and data loss, and satisfies ζ p +ζ r =1.

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