A method for modeling the dynamics of an aircraft with a multi-degree of freedom actuator

Abstract

The application provides a kind of aircraft dynamics modeling method containing multi-degree-of-freedom actuator, the modeling method returns general mechanics and advanced theory and thought of mechanics basic disciplines, aircraft is regarded as multi-rigid body system, based on virtual power principle and multi-body system topological configuration recursive modeling method, the deformation multi-body system dynamics model suitable for aircraft containing multi-actuator is established, and the motion characteristics of multi-degree-of-freedom, strong coupling between the motion characteristics of aircraft external body attitude motion and internal component relative motion are accurately described.

Description

Technical Field

[0001] This invention belongs to the field of high-speed flight technology, specifically relating to a method for modeling the dynamics of an aircraft containing multi-degree-of-freedom actuators. Background Technology

[0002] Aircraft with multi-degree-of-freedom actuators are a type of aircraft whose internal components have a large range of relative motion. These aircraft can continuously deform in space and time according to a pre-designed program based on different flight environments to obtain optimal aerodynamic performance, complete various types of flight missions, and have better maneuverability and flexibility. They are currently a hot research topic in the field of high-speed flight.

[0003] Compared to traditional fixed-shape aircraft, aircraft with multi-degree-of-freedom actuators face more complex dynamic problems. On the one hand, during deformation, the aerodynamic parameters, center of mass, and moment of inertia of the aircraft all exhibit significant time-varying characteristics, rendering traditional assumptions such as the "coefficient freezing method" inapplicable. On the other hand, complex interaction forces and torques exist between the moving parts inside the aircraft, introducing multi-degree-of-freedom and strongly nonlinear characteristics into the dynamic model, which greatly affects the stability and maneuverability of the aircraft, and may even lead to instability.

[0004] Traditional flight mechanics modeling methods treat aircraft as controlled rigid bodies, establishing six-degree-of-freedom (DOF) dynamic equations based on the Newton-Euler method of classical theoretical mechanics. However, this approach is insufficient to meet the urgent need for a refined description of the relative motion of aircraft components with multi-DOF actuators. Therefore, whether from the perspective of accurately characterizing dynamic behavior or from the need for precise design of high-performance control algorithms, there is a pressing need to research dynamic modeling methods for aircraft with multi-DOF actuators. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art or related art.

[0006] To address this, the present invention provides a dynamics modeling method for aircraft with multi-degree-of-freedom actuators. This modeling method returns to the advanced theories and ideas of general mechanics and fundamental mechanical disciplines, treating the aircraft as a multi-rigid-body system. Based on the principle of virtual power and the recursive modeling method of multi-body system topology, it establishes a dynamics model of a deformable multi-body system suitable for aircraft with multiple actuators, accurately describing the multi-degree-of-freedom and strongly coupled motion characteristics between the attitude motion of the aircraft's external fuselage and the relative motion of its internal components.

[0007] The technical solution of the present invention is as follows:

[0008] According to one aspect, a method for modeling the dynamics of an aircraft containing multi-degree-of-freedom actuators is provided, the modeling method comprising:

[0009] Step 1: Obtain the relative motion between the rigid bodies of the aircraft containing multi-degree-of-freedom actuators, and perform kinematic description of each rigid body and the center of pressure position of the aircraft based on the vector transfer relationship and the principle of angular velocity superposition. The aircraft includes two types of actuators: one is a sliding actuator, which controls component A to move along the axial direction with a displacement s; the other is a rotary actuator, which controls components B1 and B2 to rotate around the rudder axis along the fuselage to change the aerodynamic layout. The rigid bodies of the aircraft include the fuselage, component B1, component B2 and component A.

[0010] Step 2: Based on the kinematic description obtained in Step 1, establish the transformation relationship matrix between the kinematic parameters and system state variables involved in the virtual power principle;

[0011] Step 3: Based on the principle of virtual power and the transformation relation matrix obtained in Step 2, obtain the virtual power equations of each rigid body with virtual velocity as the virtual variation of the system state variable. The virtual power equations of each rigid body are superimposed to obtain the virtual power equation of the system.

[0012] Step 4: Based on the virtual power equation of the system obtained in Step 3, derive the free-flight simulation dynamic equation and the virtual flight test dynamic equation of the multi-body system of the aircraft to construct a multi-body dynamic model.

[0013] Step 5: Incorporate the multibody dynamics model obtained in Step 4 into the original flight mechanics description framework to complete the aircraft dynamics modeling.

[0014] Furthermore, in step one, the fuselage dynamics are described as follows:

[0015] The transformation relationship between the fuselage coordinate system and the ground coordinate system is expressed as follows:

[0016]

[0017] Where x1, y1, and z1 are the three basis vectors of the fuselage coordinate system; x, y, and z are the three basis vectors of the ground coordinate system; the rotation of the fuselage coordinate system relative to the ground coordinate system is decomposed into three fixed-axis rotations: ① the first rotation rotates about the y-axis of the ground coordinate system by a yaw angle ψ; ② the second rotation rotates about the z′ axis corresponding to the original z-axis after one rotation by a pitch angle θ; ③ the third rotation rotates about the x″ axis corresponding to the x-axis after two rotations by a roll angle γ; the x″ axis is the x1 axis of the fuselage coordinate system; R1 is the rotation matrix;

[0018]

[0019] According to the principle of angular velocity superposition, the angular velocity ω1 is the sum of the product of the rate of change of rotation angle and the axis of rotation, as shown in the following formula:

[0020]

[0021] Furthermore, in step one, components B1 and B2 are both described dynamically in the following manner:

[0022] 1) The transformation relationship between the component B1 / B2 coordinate system and the ground coordinate system is expressed as follows:

[0023]

[0024] Where x2, y2, and z2 are the three basis vectors of the B1 / B2 coordinate system, respectively; the variable sweep motion of the aircraft is achieved by the rotation of the B1 / B2 components around the rotation axis. The B1 / B2 coordinate system can be regarded as the body coordinate system rotated around the y-axis by an angle χ, where the rotation angle χ of the B1 component is positive and the rotation angle χ of the B2 component is negative, and the two are opposites of each other; R2 is the rotation matrix;

[0025]

[0026] 2) According to the principle of superposition of angular velocities, the rotational angular velocity ω2 of components B1 / B2 is:

[0027]

[0028] 3) The components of the centroid of parts B1 / B2 in the ground coordinate system are expressed as follows:

[0029]

[0030] Its time derivative is expressed as:

[0031]

[0032] Among them, component B1 / B2 is connected to the fuselage at hinge point A, and the body hinge vector component fixed in the fuselage coordinate system is... The body hinge vector components fixed in the B1 / B2 coordinate system of the component are: The component of the fuselage's center of mass in the ground coordinate system is r1.

[0033] Furthermore, in step one, component A is dynamically described in the following manner:

[0034] The real-time position of the centroid of component A in the ground coordinate system is represented by the following components:

[0035]

[0036] Its time derivative can be:

[0037]

[0038] In the initial state, the component of the centroid of component A in the fuselage coordinate system is: Then it moves in a straight line along the axis at a velocity v, with a linear displacement s; during the movement, the coordinate system of component A is always consistent with the coordinate system of the fuselage, and its rotational angular velocity and angular acceleration are the same as those of the fuselage.

[0039] Furthermore, in step one, the pressure core is kinetically described in the following manner:

[0040] Let the coordinates of the center of gravity relative to the fuselage coordinate system be... Its components in the ground coordinate system are

[0041]

[0042] Its time derivative is expressed as

[0043]

[0044] Furthermore, in step two, the transformation relationships between the various rigid body kinematic parameters and the system description variables are as follows:

[0045] 1) Relationship between fuselage virtual angular velocity and attitude virtual angular velocity

[0046]

[0047] 2) Relationship between fuselage angular acceleration and attitude angular acceleration

[0048]

[0049] 3) Relationship between the virtual angular velocity of component B1 and the virtual angular velocity of attitude and virtual rotation angular velocity

[0050]

[0051] 4) The relationship between the virtual center of mass velocity of component B1 and the virtual center of mass velocity, attitude virtual angular velocity, and virtual rotation angular velocity of the fuselage.

[0052] relation

[0053]

[0054] 5) Relationship between the angular acceleration of component B1 and its attitude angular acceleration and rotational acceleration

[0055]

[0056] 6) Relationship between the center-of-gravity acceleration of component B1 and the center-of-gravity acceleration, attitude angular acceleration, and rotation angular acceleration of the fuselage.

[0057]

[0058] 7) Relationship between the virtual angular velocity of component B2 and the virtual angular velocity of attitude and virtual rotation angular velocity

[0059] 8) Relationship between the virtual center of mass velocity of component B2 and the virtual center of mass velocity of the fuselage, the virtual angular velocity of attitude, and the virtual angular velocity of rotation.

[0060]

[0061] 9) Relationship between the angular acceleration of component B2 and its attitude angular acceleration and rotational acceleration

[0062] 10) Relationship between the center-of-gravity acceleration of component B2 and the center-of-gravity acceleration, attitude angular acceleration, and rotation angular acceleration of the fuselage.

[0063]

[0064] 11) Relationship between the virtual angular velocity of component A and the virtual angular velocity of attitude

[0065]

[0066] 12) Relationship between the virtual center of mass velocity of component A and the virtual center of mass velocity of the fuselage, virtual angular velocity of attitude, and virtual slip velocity.

[0067]

[0068] 13) Relationship between angular acceleration and attitude angular acceleration of component A

[0069]

[0070] 14) Relationship between the center-of-mass acceleration of component A and the center-of-mass acceleration, attitude angular acceleration, and slip acceleration of the fuselage.

[0071]

[0072] The transformation matrix and acceleration margin matrix involved are defined as follows:

[0073] Table 1. Definition of the transformation matrix between rigid body kinematic parameters and system description variables.

[0074] Transformation matrix between fuselage virtual angular velocity and attitude virtual angular velocity <![CDATA[T 1ω ]]> Transformation matrix between virtual angular velocity and virtual rotational angular velocity of component B1 <![CDATA[T χ,R ]]> Transformation matrix between virtual angular velocity and virtual rotational angular velocity of component B2 <![CDATA[T χ,L ]]> The transformation matrix between the virtual center-of-mass velocity and the virtual angular velocity and virtual rotation angular velocity of component B1 <![CDATA[T 2r,R ,T 2χ,R ]]> The transformation matrix between the virtual center-of-mass velocity and the virtual angular velocity and virtual rotation angular velocity of component B2 <![CDATA[T 2r,L ,T 2χ,L ]]> The transformation matrix between the virtual center-of-mass velocity and the virtual angular velocity and virtual slip velocity of component A <![CDATA[T 3r ,T 3s ]]> Residual matrix between fuselage angular acceleration and attitude angular acceleration <![CDATA[α 1ω ]]> Residual matrix of angular acceleration of component B1 <![CDATA[α 2ω,R ]]> The residual matrix of angular acceleration of component B2 <![CDATA[α 2ω,L ]]> The residual matrix of the acceleration of the center of mass of component B1 <![CDATA[α 2r,R ]]> The residual matrix of the acceleration of the center of mass of component B2 <![CDATA[α 2r,L ]]> The residual matrix of the acceleration of the center of mass of component A <![CDATA[α 3r ]]>

[0075] Furthermore, in step three, the system's virtual power equation is obtained using the following formula:

[0076]

[0077] In the formula, M1 and F1 are the generalized mass matrix and force matrix of the fuselage, respectively. 2,R ,F 2,R M represents the generalized mass matrix and force matrix of component B1. 2,L ,F 2,LLet M2 be the generalized mass matrix and force matrix of component B2, and M3 and F3 be the generalized mass matrix and force matrix of component A, respectively. The specific representation is as follows:

[0078]

[0079]

[0080] Where m1 is the fuselage mass, m2 is the mass of components B1 and B2, and J1 is the fuselage moment of inertia. 2,R For the moment of inertia of component B1, J 2,L Let F be the moment of inertia of component B2, J3 be the moment of inertia of component A, and F be the moment of inertia of component A. air M is the aerodynamic vector borne by the fuselage. χ,R M is the control torque for component B1. χ,L F is the control torque for component B2. s The control thrust of component A is g, where g is the acceleration due to gravity, and T is the acceleration due to gravity. sr E is the transformation matrix between the virtual velocity at the center of pressure position and the virtual angular velocity at the attitude. 3×3 It is a 3×3 identity matrix.

[0081] Furthermore, step four specifically includes:

[0082] 4.1 Determine whether the aircraft is constrained. If the aircraft is not constrained, proceed to step 4.2; if the aircraft is constrained, proceed to step 4.3.

[0083] 4.2 Based on the system's virtual power equation, the virtual variation is removed to obtain the system's free-flight simulation dynamic equation;

[0084] 4.3 According to the specific constraint form, constraint processing is performed, in which the state variables are divided into independent terms and non-independent terms, the transformation relationship between independent terms and non-independent terms is established, and the terms are substituted into the system virtual power equation to obtain the system virtual power equation corresponding to the virtual variation of independent terms. The virtual variation of independent terms is removed to obtain the system virtual flight test dynamic equation.

[0085] According to another aspect, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described prediction method.

[0086] Compared with the prior art, the present invention has the following advantages:

[0087] 1) This invention fully leverages the advantages of combining the basic principles of dynamic modeling with the dynamic modeling method of multibody systems. On the one hand, it utilizes the universality of the virtual power principle, and on the other hand, it introduces the mathematical description of the topological configuration of multibody systems. By utilizing the vector transfer relationship between components, the modeling becomes more systematic.

[0088] 2) This invention not only considers the external variable configuration of conventional variable sweepback (i.e., components B1\B2), but also the internal variable configuration of internal objects (i.e., component A), as well as the dynamic effects of their mutual coupling. The variants are more complex and the factors considered are more comprehensive.

[0089] 3) From the perspective of overall coordination and engineering application, this invention re-incorporates the constructed multibody dynamics model into the traditional flight mechanics description framework, forming a dynamics model of deformable aircraft multibody system under the traditional flight mechanics description framework, which is more applicable.

[0090] 4) This invention can balance the detailed characterization of numerical simulation with the simplified description of engineering applications, avoiding the errors caused by the decoupling of the translational and rotational coupling terms of the mass matrix in the rigid body dynamics model under the traditional flight mechanics description framework. Attached Figure Description

[0091] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0092] Figure 1 This is a schematic diagram of an aircraft with a multi-degree-of-freedom actuator.

[0093] Figure 2 This is a topology diagram of a multibody system for an aircraft with multiple degrees of freedom actuators. Detailed Implementation

[0094] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0095] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0096] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0097] like Figure 1 As shown, in one embodiment of the present invention, a method for modeling the dynamics of an aircraft containing multi-degree-of-freedom actuators is provided. This modeling method includes:

[0098] Step 1: Obtain the relative motion between the rigid bodies of the aircraft containing multi-degree-of-freedom actuators, and perform kinematic descriptions of each rigid body and the center of pressure position based on vector transfer relationships and the principle of angular velocity superposition. The aircraft includes two types of actuators: a sliding actuator that controls component A to move axially by a displacement s; and a rotary actuator that controls components B1 and B2 to rotate around the rudder axis along the fuselage, changing the aerodynamic layout. The rigid bodies of the aircraft include the fuselage, component B1, component B2, and component A, and their topological structure is shown in the diagram below. Figure 2 As shown;

[0099] Step 2: Based on the kinematic description obtained in Step 1, establish the transformation relationship matrix between the kinematic parameters and system state variables involved in the virtual power principle;

[0100] Step 3: Based on the principle of virtual power and the transformation relation matrix obtained in Step 2, obtain the virtual power equations of each rigid body with virtual velocity as the virtual variation of the system state variable. The virtual power equations of each rigid body are superimposed to obtain the virtual power equation of the system.

[0101] Step 4: Based on the virtual power equation of the system obtained in Step 3, obtain the free flight simulation dynamic equation and the virtual flight test dynamic equation of the multibody system of the aircraft to construct a multibody dynamic model.

[0102] Step 5: Incorporate the multibody dynamics model obtained in Step 4 into the original flight mechanics description framework to complete the aircraft dynamics modeling.

[0103] The embodiments of this invention are based on the principle of virtual power and graph theory of multibody system topology. For a multi-rigid-body system, the principle of virtual power can be stated as follows: the virtual power of translational inertial force plus the virtual power of rotational inertial force equals the virtual power of external force. The specific expression is as follows:

[0104]

[0105] In the formula, r c,i ,ω i For the radius vector and angular velocity vector of the rigid body's center of mass; F a,i M a,i m represents the external forces and torques acting on a rigid body. i J is the mass of a rigid body; i is the moment of inertia; g is the gravitational acceleration vector; n is the number of rigid bodies.

[0106] The steps of each embodiment of the present invention will be described in detail below:

[0107] The kinematic description in step one is as follows:

[0108] The aircraft can be viewed as a 4-rigid-body system consisting of the fuselage, component B1, component B2, and component A. The kinematics of the rigid bodies and the center of pressure are described respectively.

[0109] 1.1 Fuselage

[0110] According to the traditional framework of flight mechanics, the rotation of the fuselage coordinate system relative to the ground coordinate system can be decomposed into three fixed-axis rotations: ① The first rotation involves a yaw angle ψ about the y-axis of the ground coordinate system; ② The second rotation involves a pitch angle θ about the z′ axis corresponding to the original z-axis after the first rotation; ③ The third rotation involves a roll angle γ about the x″ axis (i.e., the x1 axis of the fuselage coordinate system) corresponding to the x-axis after the second rotation. The transformation relationship between the fuselage coordinate system and the ground coordinate system can be expressed as follows:

[0111]

[0112] Where x1, y1, and z1 are the three basis vectors of the fuselage coordinate system; the rotation matrix is...

[0113]

[0114] According to the principle of angular velocity superposition, angular velocity is the sum of the product of the rate of change of rotation angle and the axis of rotation.

[0115]

[0116] 1.2 Components B1 or B2

[0117] The variable sweep motion of the aircraft is achieved by the rotational motion of components B1 / B2 around the axis of rotation. The coordinate system of components B1 / B2 can be regarded as obtained by rotating the body coordinate system around the y-axis by an angle χ. Therefore, the transformation relationship between the coordinate system of components B1 / B2 and the ground coordinate system can be expressed as follows:

[0118]

[0119] Where x2, y2, and z2 are the three basis vectors of the B1 / B2 coordinate system of component; the rotation matrix is...

[0120]

[0121] Similarly, according to the principle of superposition of angular velocities, the rotational angular velocity is...

[0122]

[0123] Among them, the rotation angle χ of component B1 is positive, and the rotation angle χ of component B2 is negative, and the two are opposites of each other.

[0124] The hinge point between components B1 / B2 and the fuselage is A, and the body hinge vector components are fixed in the fuselage coordinate system. The body hinge vector components fixed in the coordinate system of component B are: Based on the vector transfer relationship, the components of the centroid of component B in the ground coordinate system can be expressed as follows:

[0125]

[0126] Its time derivative can be expressed as

[0127]

[0128] 1.3 Component A

[0129] In the initial state, the component of the center of mass of part A in the fuselage coordinate system is: Then, it moves linearly along the axial direction with a velocity v (linear displacement s); the components of the real-time position of the center of mass of component A in the ground coordinate system can be expressed as:

[0130]

[0131] Its time derivative can be expressed as

[0132]

[0133] Among them, the component of the fuselage center of mass in the ground coordinate system is r1; during the movement of component A, the coordinate system is always consistent with the fuselage coordinate system, and its rotational angular velocity and angular acceleration are the same as those of the fuselage.

[0134] 1.4 Core Pressure

[0135] During virtual flight testing, the aircraft is primarily affected by gravity and aerodynamic forces. Gravity acts directly on the center of mass, vertically downwards; aerodynamic forces act on the center of pressure. Let the coordinates of the center of pressure relative to the fuselage coordinate system be... Its components in the ground coordinate system are

[0136]

[0137] Its time derivative can be expressed as

[0138]

[0139] This completes the kinematic description of each rigid body.

[0140] In step two of this embodiment of the invention:

[0141] Based on the motion characteristics of deformable aircraft, the radius vector r1 of the fuselage center of mass, pitch angle θ, yaw angle ψ, roll angle γ, translational displacement s of component A, and rotation angle χ of component B are selected as system description variables. For ease of description, vectors are defined.

[0142]

[0143] Based on the above kinematic description, the transformation relationship between kinematic parameters and descriptive variables can be obtained, summarized in the following table (where the definition of the transformation matrix is ​​shown in Table 1).

[0144] Table 2. Relationship Matrix between Kinematic Parameters and Descriptive Variables of the Deformable Aircraft

[0145]

[0146] In step three of this embodiment of the invention:

[0147] Substituting the kinematic relationships in the table above into the virtual power principle equation, and considering the force characteristics of the aircraft, we obtain the virtual power equations for the fuselage, component B1, component B2, and component A respectively. Superimposing these equations yields the system's virtual power equation, in the following form:

[0148]

[0149] In the formula, M1 and F1 are the generalized mass matrix and force matrix of the fuselage, respectively. 2,R ,F 2,R M represents the generalized mass matrix and force matrix of component B1.2,L ,F 2,L Let M2 be the generalized mass matrix and force matrix of component B2, and M3 and F3 be the generalized mass matrix and force matrix of component A, as shown in the following specific representation:

[0150]

[0151]

[0152] Where m1 is the fuselage mass, m2 is the mass of components B1 and B2, and J1 is the fuselage moment of inertia. 2,R For the moment of inertia of component B1, J 2,L Let F be the moment of inertia of component B2, J3 be the moment of inertia of component A, and F be the moment of inertia of component A. air M is the aerodynamic vector borne by the fuselage. χ,R M is the control torque for component B1. χ,L F is the control torque for component B2. s The control thrust of component A is g, where g is the acceleration due to gravity, and T is the acceleration due to gravity. sr E is the transformation matrix between the virtual velocity at the center of pressure position and the virtual angular velocity at the attitude. 3×3 It is a 3×3 identity matrix.

[0153] Thus, the virtual power equation of the system is obtained by superimposing the virtual power equations of each rigid body.

[0154] In step four of this embodiment of the invention, the dynamic equations for free flight simulation and virtual flight test of the deformable multibody system are given respectively.

[0155] 4.1 Equations of Free Flight Dynamics

[0156] In actual free flight, the aircraft is unconstrained and has 6+2 independent degrees of freedom. The radius vector r1 of the fuselage center of mass, pitch angle θ, yaw angle ψ, roll angle γ, translational displacement s of component A, and rotation angle χ of component B1 / B2 are independent of each other. Therefore, the dynamic equations can be directly written as follows:

[0157]

[0158] In the formula, M1 and F1 are the generalized mass matrix and force matrix of the fuselage, respectively. 2,R ,F 2,R M represents the generalized mass matrix and force matrix of component B1. 2,L ,F 2,L Let M1 and M2 be the generalized mass matrix and force matrix of component B2, and M3 and F3 be the generalized mass matrix and force matrix of component A.

[0159] 4.2 Virtual Flight Dynamics Equations

[0160] During virtual flight testing, the aircraft is fixed by a support system and has a clamping point. The three translational degrees of freedom at this point are constrained and fixed, and the independent degrees of freedom of the system become 3+2. The radius vector of the fuselage center of mass r1, pitch angle θ, yaw angle ψ, roll angle γ, translational displacement of component A s, and rotation angle χ of component B1 / B2 are not independent, and the independence of the descriptive variables needs to be tested.

[0161] 1) Constraint handling

[0162] Let the components of the clamping point relative to the fuselage coordinate system be... The constraint equations are then expressed as follows:

[0163] ① Displacement constraint equations

[0164]

[0165] ② Velocity constraint equations

[0166]

[0167] ③Acceleration constraint equations

[0168]

[0169] Where, r jx These are the coordinates of the clamping point.

[0170] 2) Dynamic equations

[0171] Based on the above constraint equations, the relationship matrix between the virtual velocities and accelerations describing the variables can be obtained, which can be represented as follows:

[0172]

[0173] Among them, T jr Let α be the matrix relating the fuselage center-of-gravity velocity and attitude angular velocity. jr T is the residual matrix between the fuselage center-of-mass acceleration and the attitude angular acceleration. c Let α be the transformation matrix between the first-order time derivatives of the system describing variables and the first-order time derivatives of the independent describing variables. c E is the residual matrix between the second-order time derivatives of the system describing variables and the second-order time derivatives of the independent describing variables. 3×3 It is a 3×3 identity matrix.

[0174] By combining the system's virtual power equation and the constraint matrix, the independent descriptive variables can be obtained. The corresponding virtual power equation leads to the system dynamics equation, as follows:

[0175]

[0176] In the formula, M1 and F1 are the generalized mass matrix and force matrix of the fuselage, respectively. 2,R ,F 2,R M represents the generalized mass matrix and force matrix of component B1. 2,L ,F 2,L Let M1 and M2 be the generalized mass matrix and force matrix of component B2, and M3 and F3 be the generalized mass matrix and force matrix of component A.

[0177] The acceleration term, which describes the variable, can be obtained from the formula. This forms a closed second-order dynamic differential equation, which satisfies the completeness of the dynamic solution.

[0178] In this embodiment of the invention, for step five:

[0179] The constructed multibody dynamics model is incorporated into the traditional flight mechanics description framework; therefore, the system description variables are reselected as...

[0180] ① Radius of the fuselage center of mass r1;

[0181] ② Velocity magnitude V, angle of attack α, sideslip angle β;

[0182] ③ Pitch angle θ, yaw angle ψ, roll angle γ;

[0183] ④ Pitch angle time derivative Yaw angle time derivative Roll angle time derivative

[0184] ⑤ Translation s, rotation angle χ;

[0185] ⑥ Translation speed angular velocity

[0186] According to the traditional framework of flight mechanics, the velocity coordinate system can be viewed as the fuselage coordinate system first rotating around the y1 axis by a sideslip angle β, and then rotating around the z1′ axis corresponding to the original z1 axis after the first rotation by an angle of attack α. The relationship between the two can be described as follows:

[0187]

[0188] in, Let x1, y1, and z1 be the three basis vectors of the velocity coordinate system; and x1, y1, and z1 be the three basis vectors of the fuselage coordinate system. Then the first-order time derivative of the fuselage center of mass can be expressed as:

[0189]

[0190] The second-order time derivative can be expressed as...

[0191]

[0192] In turn, one can obtain

[0193]

[0194] In the formula

[0195] b1=-V(sinαcosβx1+cosαcosβy1)

[0196] b2=V(sinαsinβy1-cosαsinβx1+cosβz1)

[0197] As can be seen, the above content presents the following important relationship: Given the velocity magnitude V, angle of attack α, and sideslip angle β, find the first-order time derivative of the fuselage center-of-mass radius vector. Given the second time derivative of the radius vector of the fuselage center of mass. Find the magnitude of the acceleration. time derivative of angle of attack Sideslip angle time derivative Combining the dynamic equations and the aforementioned relationships, the first-order time derivatives of the descriptive variables can be obtained. Thus, the first-order solution model for the dynamic equations of free flight and virtual flight experiments within the traditional framework of flight mechanics is complete.

[0198] The above technical solution differs from traditional fixed-shape aircraft dynamics modeling methods and general variant aircraft dynamics modeling methods, mainly in the following aspects: 1) This invention fully leverages the advantages of combining the basic principles of dynamics modeling with multibody system dynamics modeling methods. On the one hand, it utilizes the universality of the virtual power principle, and on the other hand, it introduces a mathematical description of the topological configuration of multibody systems, utilizing the vector transfer relationships between components, making the modeling more systematic. 2) This invention not only considers the external variant configuration of conventional variable sweep (i.e., components B1\B2), but also the internal variant configuration of internal objects (i.e., component A), as well as the dynamic influence of their mutual coupling. The variants are more complex, and the factors considered are more comprehensive. 3) From the perspective of overall coordination and engineering application, this invention re-incorporates the constructed multibody dynamics model into the traditional flight mechanics description framework, forming a variant aircraft multibody system dynamics model under the traditional flight mechanics description framework, which is more applicable. 4) This invention can balance the refined characterization of numerical simulation and the simplified description of engineering applications, avoiding the errors caused by the decoupling of the translational and rotational coupling terms of the mass matrix in the rigid body dynamics model under the traditional flight mechanics description framework.

[0199] The features described and / or illustrated above with respect to one embodiment may be used in the same or similar manner in one or more other embodiments, and / or in combination with or in lieu of features in other embodiments.

[0200] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, whole, step, or component, but does not exclude the presence or addition of one or more other features, wholes, steps, components, or combinations thereof.

[0201] The methods described above in this invention can be implemented in hardware or in combination with software. This invention relates to computer-readable programs that, when executed by a logic component, enable the logic component to implement the aforementioned apparatus or constituent parts, or to implement the various methods or steps described above. This invention also relates to storage media for storing the above programs, such as hard disks, magnetic disks, optical disks, DVDs, flash memory, etc.

[0202] Many features and advantages of these embodiments are apparent from this detailed description, and therefore the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. Furthermore, since many modifications and alterations will readily occur to those skilled in the art, the embodiments of the invention are not intended to be limited to the precise structures and operations illustrated and described, but rather to encompass all suitable modifications and equivalents falling within their scope.

[0203] The parts of this invention not described in detail are techniques known to those skilled in the art.

Claims

1. A method for modeling the dynamics of an aircraft containing multi-degree-of-freedom actuators, characterized in that, The modeling method includes: Step 1: Obtain the relative motion between the rigid bodies of the aircraft containing multi-degree-of-freedom actuators, and perform kinematic description of each rigid body and the center of pressure position of the aircraft based on the vector transfer relationship and the principle of angular velocity superposition. The aircraft includes two types of actuators: one is a sliding actuator, which controls component A to move along the axial direction with a displacement s; the other is a rotary actuator, which controls components B1 and B2 to rotate around the rudder axis along the fuselage to change the aerodynamic layout. The rigid bodies of the aircraft include the fuselage, component B1, component B2 and component A. Step 2: Based on the kinematic description obtained in Step 1, establish the transformation relationship matrix between the kinematic parameters and system state variables involved in the virtual power principle; Step 3: Based on the principle of virtual power and the transformation matrix obtained in Step 2, obtain the virtual power equations for each rigid body with virtual velocities as virtual variations of the system state variables. The virtual power equations of each rigid body are superimposed to obtain the system virtual power equation, as shown in the following equation: In the formula, For the generalized mass and force arrays of the fuselage, For the generalized mass matrix and force matrix of component B1, For the generalized mass matrix and force matrix of component B2, Let A be the generalized mass matrix and force matrix of component A; For the velocity of the fuselage's virtual center of mass, The virtual velocity of the fuselage attitude angle. Let the rotational velocity be the imaginary velocity. The virtual slip velocity, For the acceleration of the fuselage's center of gravity, For the fuselage attitude angular acceleration, For angular acceleration, It is the slip acceleration; Step 4: Based on the virtual power equation of the system obtained in Step 3, obtain the free flight simulation dynamic equation and the virtual flight test dynamic equation of the multibody system of the aircraft to construct a multibody dynamic model; Step 5: Incorporate the multibody dynamics model obtained in Step 4 into the original flight mechanics description framework to complete the aircraft dynamics modeling.

2. The method for modeling aircraft dynamics with multi-degree-of-freedom actuators according to claim 1, characterized in that, In step one, the fuselage dynamics are described as follows: The transformation relationship between the fuselage coordinate system and the ground coordinate system is expressed as follows: ,in, , , These are the three basis vectors of the fuselage coordinate system; , , These are the three basis vectors of the ground coordinate system; the rotation of the fuselage coordinate system relative to the ground coordinate system is decomposed into three fixed-axis rotations, ① the first rotation around the ground coordinate system. Shaft rotation yaw angle ② The second rotation around the original position after one rotation axis corresponding Axis rotation pitch angle ③ After the third rotation around the second rotation axis corresponding Shaft rotation roll angle ; The axis is the fuselage coordinate system. axis; Here is the rotation matrix; According to the principle of superposition of angular velocities, angular velocity The sum of the product of the rate of change of rotation angle and the axis of rotation is shown in the following formula: .

3. The method for modeling aircraft dynamics with multi-degree-of-freedom actuators according to claim 2, characterized in that, In step one, components B1 and B2 are both described dynamically in the following manner: 1) The transformation relationship between the component B1 / B2 coordinate system and the ground coordinate system is expressed as follows: ， in, , , These are the three basis vectors of the component B1 / B2 coordinate system; the variable sweep motion of the aircraft is achieved by the rotational motion of component B1 / B2 around the rotation axis, and the component B1 / B2 coordinate system is regarded as the body coordinate system around the rotation axis. The shaft rotated The angle is obtained, where the rotation angle of component B1 is... Positive, component B2 corner The result is negative, and the two are opposites of each other; Here is the rotation matrix; ； 2) According to the principle of angular velocity superposition, the rotational angular velocity of components B1 / B2 for: ； 3) The components of the centroid of parts B1 / B2 in the ground coordinate system are expressed as follows: ， Its time derivative is expressed as: ， Among them, the hinge point for the rotational connection between components B1 / B2 and the fuselage is The body hinge vector components fixed in the fuselage coordinate system are The body hinge vector components fixed in the B1 / B2 coordinate system of the component are: The component of the fuselage's center of mass in the ground coordinate system is .

4. The method for modeling aircraft dynamics with multi-degree-of-freedom actuators according to claim 3, characterized in that, In step one, component A is described dynamically in the following manner: The real-time position of the centroid of component A in the ground coordinate system is represented by the following components: ， Its time derivative is: , In the initial state, the component of the centroid of component A in the fuselage coordinate system is: Then along the axial direction at a velocity To move in a straight line, linear displacement During the movement, the coordinate system of component A remains consistent with the coordinate system of the fuselage, and its rotational angular velocity and angular acceleration are the same as those of the fuselage.

5. The method for modeling aircraft dynamics with multi-degree-of-freedom actuators according to claim 4, characterized in that, In step one, the pressure core is kinetically described in the following manner: Let the coordinates of the center of gravity relative to the fuselage coordinate system be... Its components in the ground coordinate system are ， Its time derivative is expressed as .

6. The method for modeling aircraft dynamics with multi-degree-of-freedom actuators according to claim 5, characterized in that, In step two, the transformation relationships between the various rigid body kinematic parameters and the system description variables are as follows: 1) Virtual angular velocity of the fuselage With attitude angular virtual velocity Interrelationship ， 2) Fuselage angular acceleration With attitude angular acceleration Interrelationship ， 3) Virtual angular velocity of component B1 With attitude angular virtual velocity , Rotational virtual velocity Interrelationship ， 4) Velocity of virtual center of mass of component B1 With the speed of the fuselage's virtual center of mass Attitude angular virtual velocity , Rotational virtual velocity Interrelationship ， 5) Angular acceleration of component B1 With attitude angular acceleration Angular acceleration Interrelationship ， 6) Acceleration of the center of mass of component B1 With the acceleration of the fuselage center of mass Attitude angular acceleration Angular acceleration Interrelationship ， 7) Virtual angular velocity of component B2 With attitude angular virtual velocity , Rotational virtual velocity Interrelationship ， 8) Velocity of virtual center of mass of component B2 With the speed of the fuselage's virtual center of mass Attitude angular virtual velocity , Rotational virtual velocity Interrelationship ， 9) Angular acceleration of component B2 With attitude angular acceleration Angular acceleration Interrelationship ， 10) Acceleration of the center of mass of component B2 With the acceleration of the fuselage center of mass Attitude angular acceleration Angular acceleration Interrelationship ， 11) Virtual angular velocity of component A With attitude angular virtual velocity Interrelationship ， 12) Velocity of virtual center of mass of component A With the speed of the fuselage's virtual center of mass Attitude angular virtual velocity Virtual slip velocity Interrelationship ， 13) Angular acceleration of component A With attitude angular acceleration Interrelationship ， 14) Acceleration of the center of mass of component A With the acceleration of the fuselage center of mass Attitude angular acceleration Slip acceleration Interrelationship The transformation matrix and acceleration margin matrix involved are defined as follows: Table 1. Definition of the transformation matrix between rigid body kinematic parameters and system description variables. 。 7. The method for modeling aircraft dynamics with multi-degree-of-freedom actuators according to claim 6, characterized in that, The specific form of the system's virtual power equation is as follows: ， ， ， ， ， ， ， ， in, For the weight of the fuselage, For the mass of components B1 and B2, For the moment of inertia of the fuselage, For the moment of inertia of component B1, For the moment of inertia of component B2, Let A be the moment of inertia of component A. The aerodynamic vector borne by the fuselage. The control torque for component B1, The control torque for component B2, For the control thrust of component A, It is the acceleration due to gravity. This is the transformation matrix between the virtual velocity at the center of pressure position and the virtual velocity at the attitude angle. It is a 3×3 identity matrix.

8. A method for modeling the dynamics of an aircraft containing a multi-degree-of-freedom actuator according to any one of claims 1-7, characterized in that, Step four specifically includes: 4.1 Determine whether the aircraft is constrained. If the aircraft is not constrained, proceed to step 4.2; if the aircraft is constrained, proceed to step 4.

3. 4.2 Based on the system's virtual power equation, the virtual variation is removed to obtain the system's free-flight simulation dynamic equation; 4.3 According to the specific constraint form, constraint processing is performed, in which the state variables are divided into independent terms and non-independent terms, the transformation relationship between independent terms and non-independent terms is established, and the terms are substituted into the system virtual power equation to obtain the system virtual power equation corresponding to the virtual variation of independent terms. The virtual variation of independent terms is removed to obtain the system virtual flight test dynamic equation.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1-8.

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