A long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation

Abstract

The application relates to the technical field of aircraft flight dynamics, and discloses a long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation, which comprises the following steps: establishing wing flexible deformation structure dynamics and flight dynamics coupling equations; based on the coupling equations, solving an initial accurate equilibrium point according to a Newton-Raphson iteration method; based on the initial accurate equilibrium point, solving a parameter variation equilibrium curve according to a pseudo-arc length continuation method; and based on the parameter variation equilibrium curve, establishing a bifurcation diagram according to a bifurcation theory to analyze long-endurance unmanned aerial vehicle global stability. The long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation can deeply analyze system nonlinearities and coupling properties and the like by establishing structure dynamics and flight dynamics coupling nonlinear dynamics equations considering wing flexible deformation, and can clearly show global system stability changes caused by parameter variation, so that the method is more comprehensive and effective.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft flight dynamics, in particular to a long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation. BACKGROUND

[0002] The long-endurance unmanned aerial vehicle generally refers to the unmanned aerial vehicle capable of continuously flying in the atmosphere for more than 24 hours, and has the advantages of high task height and long loitering time. In order to meet the task requirements, the long-endurance unmanned aerial vehicle generally adopts a large aspect ratio wing design, which has a high lift-drag ratio characteristic. However, this design makes the wing structure insufficient in rigidity, and brings about a significant wing flexible deformation problem. On the one hand, the wing structure has a passive flexible deformation under the action of the aerodynamic load, and the scale of the flexible deformation is large, which cannot meet the small deformation assumption in the linear structure analysis, and the structure nonlinear analysis must be carried out. On the other hand, in order to solve the aeroelastic problem caused by the wing flexible deformation, the long-endurance unmanned aerial vehicle will take some active deformation means to enhance the task adaptability. Therefore, the wing flexible deformation is an important problem commonly existing in the long-endurance unmanned aerial vehicle.

[0003] The wing flexible deformation will cause the change of the local aerodynamic parameter, thereby affecting the stability of the aircraft motion. The change of the flight stability will cause the fluctuation of the flight state, and will also affect the degree of the local aerodynamic load and the wing flexible deformation. The coupling of the wing flexible deformation and the motion stability is a complex nonlinear stability problem.

[0004] At present, the traditional method is to separately simplify and analyze the wing flexible deformation and the motion stability, but the existing technology does not consider the motion stability problem under the wing flexible deformation, and cannot be applied to the nonlinear dynamic analysis of the structure and flight dynamics coupling. SUMMARY

[0005] The purpose of the present application is to provide a long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation, which couples the structure dynamics equation and the flight dynamics equation of the wing flexible deformation, and solves the nonlinear stability analysis problem of the wing flexible deformation and the motion stability coupling based on the bifurcation theory.

[0006] The present application provides a long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation, comprising:

[0007] S1, establishing a wing flexible deformation structure dynamics and flight dynamics coupling equation;

[0008] S2, based on the coupling equation, solving the initial accurate equilibrium point according to the Newton-Raphson iteration method;

[0009] S3, based on the initial precise equilibrium point, solving the parameter variation equilibrium curve according to the pseudo-arc length continuation method;

[0010] S4, based on the parameter variation equilibrium curve, establishing a bifurcation diagram according to bifurcation theory, and analyzing the global stability of the long-haul unmanned aerial vehicle.

[0011] Preferably, in step S1, the coupled equations of wing flexible deformation structure dynamics and flight dynamics are established, including:

[0012] ;

[0013] wherein, is a modal coefficient vector, representing the flexible deformation modal of the wing;

[0014] , , represent the mass matrix, damping matrix and stiffness matrix of the wing structure, represent the flight state parameters of the unmanned aerial vehicle, represent the control parameters of the unmanned aerial vehicle, represent the wing geometric parameters, represent other characteristic parameters of the unmanned aerial vehicle, represent the projection of aerodynamic force on the flexible deformation modal, represent the flight dynamics equation considering the flexible deformation of the wing.

[0015] Preferably, the flight state parameters of the unmanned aerial vehicle are ;

[0016] wherein, represent the flight speed, represent the angle of attack, represent the sideslip angle, represent the Euler roll angle, represent the Euler pitch angle, , and represent the body axis roll angular velocity, pitch angular velocity and yaw angular velocity;

[0017] The control parameters of the unmanned aerial vehicle are , represent the elevator deflection angle, represent the throttle amount, represent the aileron deflection angle, represent the rudder deflection angle;

[0018] The projection of aerodynamic force on the flexible deformation modal is ;

[0019] wherein, is a modal function, is air density, is wing area integral microelement.

[0020] Preferably, the wing flexible deformation structure dynamics equation is expressed as:

[0021] ;

[0022] The component form of the wing flexible deformation structure dynamics equation is:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] wherein m represents the mass of the unmanned aerial vehicle, represents the combined external force in the body coordinate system, represents the combined external moment in the body coordinate system, represents the rotational inertia of the inertia principal axis, represents the inertia product.

[0032] Preferably, in step S2, the initial accurate equilibrium point is solved according to the Newton-Raphson iteration method based on the coupling equation, including:

[0033] Based on a fuzzy initial solution , the Newton-Raphson iteration formula is used,

[0034] ;

[0035] to obtain a solution satisfying that the time derivative of the coupling equation is zero, that is, satisfying:

[0036] ;

[0037] wherein the state variable is , the control input is , the parameters are and , is Jacobian matrix, is a natural number representing the number of iteration steps.

[0038] Preferably, when solving for the initial exact equilibrium point, the iteration error is set to... When the iteration error is less than the error threshold, the initial precise equilibrium point is determined to have been found.

[0039] Preferably, in step S3, based on the initial precise equilibrium point, the parameter variation equilibrium curve is solved according to the pseudo-arc length extension method, including:

[0040] Starting from the initial precise equilibrium point, predict the next solution based on the tangent direction of the initial precise equilibrium point. The next solution satisfies the arc length constraint and the equilibrium point constraint, that is:

[0041] ;

[0042] ;

[0043] in, and These represent the equilibrium point to be determined and the initial precise equilibrium point, respectively. and These represent the extension parameters and the initial extension parameters, respectively. This is the increment of arc length;

[0044] The prediction results are corrected using the Newton-Raphson method to obtain the final state variables. With parameters The equilibrium curve of changing parameters.

[0045] Preferably, the specific method for predicting the next solution is as follows:

[0046] Let the equilibrium solution obtained in the previous step be... Predict the next solution along the tangent direction of the equilibrium point. The formula for calculating the prediction point is as follows:

[0047] ;

[0048] The specific method for correcting the prediction results is as follows:

[0049] The predicted point is adjusted to the actual equilibrium point using the Newton-Raphson iterative formula until the tolerance condition is met. Obtain state variables With parameters The equilibrium curve of changing parameters.

[0050] Preferably, in step S4, based on the parameter variation equilibrium curve, a bifurcation diagram is established according to bifurcation theory to analyze the global stability of the long-endurance unmanned aerial vehicle, including:

[0051] Based on the parameter variation equilibrium curve of step S3, at each equilibrium point, linearization is performed to obtain a Jacobian matrix as follows:

[0052] ;

[0053] The stability of the equilibrium point is judged by calculating the eigenvalues of .

[0054] Preferably, the stability of the equilibrium point is judged by the following method:

[0055] If all the real parts of the eigenvalues are negative, the corresponding equilibrium point is judged to be a stable equilibrium point.

[0056] If there is an eigenvalue with a positive real part, the corresponding equilibrium point is judged to be an unstable equilibrium point.

[0057] If there is an eigenvalue that crosses zero from the real axis, the corresponding equilibrium point is judged to be a saddle-node bifurcation point.

[0058] If there is a conjugate eigenvalue that crosses the imaginary axis, the corresponding equilibrium point is judged to be a Hopf bifurcation point.

[0059] Compared with the prior art, the present application has the following advantages:

[0060] (1) The method of the present application couples the structural dynamics equation of wing flexible deformation and the flight dynamics equation for analysis. Compared with the traditional simplified analysis method, the present application fully considers the coupling factors of wing flexible deformation on the motion stability of the long-endurance unmanned aerial vehicle. The research method is more in line with the real situation in essence, is more accurate, and is more suitable for the stability analysis of the long-endurance unmanned aerial vehicle.

[0061] (2) The present application uses a nonlinear analysis method based on parameter continuation and bifurcation analysis. Compared with the traditional reduced-order model analysis method, the present application fully analyzes the high-order nonlinear dynamics system equation considering wing flexible deformation, can deeply analyze the nonlinear and coupling characteristics of the system, and clearly shows the global change of the system stability caused by parameter variation, which is more comprehensive and effective. BRIEF DESCRIPTION OF DRAWINGS

[0062] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only aim to explain part of the embodiments of the present application, and not all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present application.

[0063] Figure 1 is a flowchart of a long-endurance unmanned aerial vehicle stability analysis method considering flexible deformation of a wing. DETAILED DESCRIPTION

[0064] The technical solutions in the embodiments of the present application will be clearly and completely described in combination with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, and not all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present application.

[0065] The present application discloses a long-endurance unmanned aerial vehicle stability analysis method considering flexible deformation of a wing, comprising:

[0066] S1, a wing flexible deformation structure dynamics and flight dynamics coupling equation is established.

[0067] Firstly, the structural dynamics behavior of the flexible deformable wing can be approximately expressed by the modal superposition method, and the structural dynamics equation is:

[0068]

[0069] Specifically, is a modal coefficient vector, representing the flexible deformation mode of the wing.

[0070] , are the mass matrix, the damping matrix and the stiffness matrix of the wing structure respectively. is an unmanned aerial vehicle flight state parameter, wherein is the flight speed, and are the angle of attack and the sideslip angle respectively, and are the Euler roll angle and the Euler pitch angle respectively, , and are the body axis roll angular velocity, the pitch angular velocity and the yaw angular velocity respectively. is an unmanned aerial vehicle control parameter, and is the elevator deflection angle, the throttle amount, the aileron deflection angle and the rudder deflection angle respectively. ​​are wing geometry parameters.

[0071] is the projection of aerodynamic force on the flexible deformation mode, in the form of:

[0072] ;

[0073] where, is the modal function, is the air density, is the wing area integral infinitesimal.

[0074] The rigid body flight dynamics equation of the UAV considering the wing deformation parameters can be expressed as a set of differential equations, that is:

[0075] ;

[0076] In the above equation, are other characteristic parameters of the UAV, such as mass, inertia, etc.

[0077] Further, the rigid body flight dynamics differential equation of the UAV is written in the form of components as follows:

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] where m represents the mass of the UAV, represents the total external force in the body coordinate system, represents the total external moment in the body coordinate system, represents the rotational inertia of the principal axis of inertia, represents the inertia product.

[0087] The total external force and the total external moment in the body coordinate system are mainly composed of aerodynamic force, gravity and engine thrust.

[0088] By integrating the above structural dynamics equation and flight dynamics equation, the complete coupled equation can be obtained as:

[0089] ;

[0090] Let the state variable be , the control input be , and the parameters be and . The whole system is a high-dimensional nonlinear dynamic system.

[0091] S2, based on the coupling equation, an initial accurate equilibrium point is solved according to the Newton-Raphson iteration method.

[0092] The stability of the unmanned aerial vehicle generally refers to the stability at the equilibrium point, and the definition of the equilibrium point is that the time derivative of the state variable is zero, that is, the system dynamics equation is satisfied:

[0093] ;

[0094] In order to obtain an accurate initial solution, a fuzzy initial solution is first estimated, and then the Newton-Raphson iteration method is used for solution. Let the fuzzy initial solution be , and the Newton-Raphson iteration solution formula is as follows:

[0095] ;

[0096] wherein, is the Jacobian matrix of . is a natural number, representing the number of iteration steps.

[0097] When solving the initial accurate equilibrium point, let the iteration error be , and when the iteration error is less than the error threshold, it is determined that the initial accurate equilibrium point is found.

[0098] The error threshold is set to in the application.

[0099] S3, based on the initial accurate equilibrium point, a parameter variation equilibrium curve is solved according to the pseudo-arc length continuation method.

[0100] After an accurate initial solution is obtained, the equilibrium curve of the system under parameter variation can be tracked, and the arc length continuation method is used to solve the equilibrium curve. Let be the parameter to be analyzed, which can be a parameter in the control variable, a wing geometric parameter or other unmanned aerial vehicle characteristic parameter. The selected parameter is the continuation variable, and other parameters need to be fixed. Therefore, during the parameter variation process, the system dynamics equation needs to satisfy the equilibrium point constraint:

[0101] ;

[0102] Simultaneously satisfying the arc length constraint:

[0103] ;

[0104] where, and are the equilibrium point to be solved and the initial accurate equilibrium point, respectively, and are the continuation parameter and the initial continuation parameter, respectively, is the arc length increment.

[0105] The continuation curve is solved by a predictor-corrector algorithm, where the steps in the predictor phase are:

[0106] Assuming the equilibrium point solution obtained in the previous step is , the next solution is predicted in the direction of the equilibrium point tangent . The calculation formula of the predicted point is as follows:

[0107] ;

[0108] The correction phase adjusts the predicted point to the actual equilibrium point by the Newton-Raphson iteration formula until the tolerance condition is met.

[0109] After a series of continuation calculations, the equilibrium curve of the state variable with the parameter can be obtained.

[0110] S4, based on the parameter variation equilibrium curve, a bifurcation diagram is established according to the bifurcation theory, and the global stability of the long-haul unmanned aerial vehicle is analyzed.

[0111] Based on the parameter variation equilibrium curve of S3, the system is linearized at each equilibrium point, and the Jacobian matrix is obtained as:

[0112] ;

[0113] By calculating the eigenvalues of , the stability of the equilibrium point is determined. If all the real parts of the eigenvalues are negative, the equilibrium point is a stable equilibrium point. If there is a real part of the eigenvalue that is positive, the point is an unstable equilibrium point. If there is an eigenvalue that crosses zero from the real axis, the point is a saddle node bifurcation point. If there is a conjugate eigenvalue that crosses from the imaginary axis, the point is a Hopf bifurcation point.

[0114] By adding different marks to the equilibrium points and bifurcation points, a balance curve diagram containing the information of equilibrium points, called bifurcation diagram, can be reconstructed. By looking at the bifurcation diagram, the global change process of the stability of the system equilibrium points under the influence of parameters can be analyzed. The bifurcation point means that the stability changes suddenly, and under certain specific parameters, the system appears unstable behavior or oscillation behavior.

[0115] Compared with the prior art, the long-endurance unmanned aerial vehicle stability analysis method considering the flexible deformation of the wing of the application couples the structural dynamics equation of the flexible deformation of the wing with the flight dynamics equation, fully considers the influence of the flexible deformation of the wing on the motion stability of the long-endurance unmanned aerial vehicle, is more in line with the real physical principle, and the analysis result is more accurate and reliable. The nonlinear analysis method based on numerical continuation calculation and bifurcation theory used in the application fully considers the influence of parameters on the stability change of the dynamic system, can deeply analyze the nonlinear and coupling nonlinear dynamic characteristics of the system caused by the parameter change, and is more comprehensive and effective.

[0116] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the application and not to limit them, although the application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: it can still modify or equivalently replace the technical solutions of the application, and these modifications or equivalent replacements also cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the application.

[0117] The system provided by the above examples is only illustrated by the division of the above functional modules, and in actual application, the above functions can be completed by different functional modules according to needs, that is, the modules or steps in the embodiments of the application are further decomposed or combined, for example, the modules of the above examples can be combined into one module, or can be further split into multiple sub-modules to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the application are only for distinguishing the modules and steps, and are not considered as improper limitation of the application.

[0118] Those skilled in the art should clearly understand that the modules and method steps of each example described in combination with the embodiments disclosed herein can be realized by electronic hardware, computer software or a combination of both. The programs corresponding to the software modules and method steps can be placed in a random access memory (RAM), a memory, a read-only memory (ROM), an electrically erasable programmable ROM, a register, a hard disk, a removable disk, a CD-ROM or any other form of storage medium known in the art. In order to clearly illustrate the interchangeability of electronic hardware and software, the components and steps of each example have been described in the above description in general terms. Whether the functions are performed in electronic hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

Claims

1. A stability analysis method for long-endurance unmanned aerial vehicles (UAVs) considering wing flexibility deformation, characterized in that, include: S1, establish the coupled equations of wing flexible deformation structure dynamics and flight dynamics; S2, Based on the coupling equation, the initial precise equilibrium point is solved using the Newton-Raphson iterative method; S3, Based on the initial precise equilibrium point, solve the equilibrium curve of parameter variation according to the pseudo-arc length extension method; S4. Based on the parameter variation equilibrium curve, a bifurcation diagram is established according to bifurcation theory to analyze the global stability of the long-endurance UAV. In step S1, the coupled equations of the wing's flexible deformable structure dynamics and flight dynamics are established, including: ;in, It is a modal coefficient vector, representing the flexible deformation modes of the wing; , , This represents the mass matrix, damping matrix, and stiffness matrix of the wing structure. Indicates the flight status parameters of the drone. Indicates control input, Indicates the wing's geometric parameters, Indicates other characteristic parameters of the drone, This represents the projection of aerodynamic forces onto the flexible deformation mode. The equations of flight dynamics considering the flexible deformation of the wing are given. In step S2, based on the coupling equation, the initial exact equilibrium point is solved using the Newton-Raphson iterative method, including: Based on a fuzzy initial solution Using the Newton-Raphson iterative formula, We obtain a solution that satisfies the coupling equation with zero time derivative, i.e., satisfies: Among them, the state variables are The control input is The parameters are and , for Jacobian matrix, is a natural number representing the number of iteration steps.

2. The stability analysis method for long-endurance UAVs considering wing flexibility deformation according to claim 1, characterized in that, The flight status parameters of the UAV are: ; in, Indicates flight speed. Indicates the angle of attack. Indicates the sideslip angle. Indicates Euler roll angle, Indicates Euler pitch angle, , and This indicates the roll rate, pitch rate, and yaw rate of the airframe shaft system; The control input is , Indicates elevator deflection angle, Indicates throttle position, Indicates the aileron deflection angle. Indicates the rudder deflection angle; The projection of the aerodynamic force onto the flexible deformation mode is as follows: ; in, It is a modal function. It is air density. It is the integral element of the wing area.

3. The stability analysis method for long-endurance UAVs considering wing flexibility deformation according to claim 2, characterized in that, The dynamic equation of the flexible deformable structure of the wing is expressed as: ； The component form of the dynamic equation for the flexible deformable structure of the wing is: ; ; ; ; ； ； ； ； Where m represents the mass of the drone. This represents the net external force in the body coordinate system. This represents the net external torque in the body coordinate system. The moment of inertia represents the rotational inertia of the principal axis of inertia. It represents the product of inertia.

4. The stability analysis method for long-endurance UAVs considering wing flexibility deformation according to claim 1, characterized in that, When solving for the initial exact equilibrium point, let the iteration error be... When the iteration error is less than the error threshold, the initial precise equilibrium point is determined to have been found.

5. The stability analysis method for long-endurance UAVs considering wing flexibility deformation according to claim 1, characterized in that, In step S3, based on the initial precise equilibrium point, the parameter variation equilibrium curve is solved according to the pseudo-arc length extension method, including: Starting from the initial precise equilibrium point, predict the next solution based on the tangent direction of the initial precise equilibrium point. The next solution satisfies the arc length constraint and the equilibrium point constraint, that is: ; ; in, and These represent the equilibrium point to be determined and the initial precise equilibrium point, respectively. and These represent the extension parameters and the initial extension parameters, respectively. This is the increment of arc length; The prediction results are corrected using the Newton-Raphson method to obtain the final state variables. With parameters The equilibrium curve of changing parameters.

6. The stability analysis method for long-endurance UAVs considering wing flexibility deformation according to claim 5, characterized in that, The specific method for predicting the next solution is as follows: Let the equilibrium solution obtained in the previous step be... Predict the next solution along the tangent direction of the equilibrium point. The formula for calculating the prediction point is as follows: ; The specific method for correcting the prediction results is as follows: The predicted point is adjusted to the actual equilibrium point using the Newton-Raphson iterative formula until the tolerance condition is met. Obtain state variables With parameters The equilibrium curve of changing parameters.

7. The stability analysis method for long-endurance UAVs considering wing flexibility deformation according to claim 1, characterized in that, In step S4, based on the parameter variation equilibrium curve, a bifurcation diagram is established according to bifurcation theory to analyze the global stability of the long-endurance UAV, including: Based on the parameter change equilibrium curve from step S3, linearization is performed at each equilibrium point to obtain the Jacobian matrix: ; Through calculation The eigenvalues ​​are used to determine the stability of the equilibrium point.

8. The stability analysis method for long-endurance UAVs considering wing flexibility deformation according to claim 7, characterized in that, The specific method for determining the stability of an equilibrium point is as follows: If the real part of all eigenvalues ​​is negative, then the corresponding equilibrium point is determined to be a stable equilibrium point; If there exists an eigenvalue with a positive real part, then the corresponding equilibrium point is determined to be an unstable equilibrium point. If an eigenvalue passes through the zero point from the real axis, then the corresponding equilibrium point is determined to be a saddle point or bifurcation point. If a conjugate eigenvalue passes through the imaginary axis, then the corresponding equilibrium point is determined to be a Hopf bifurcation point.

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