A quad-rotor turbojet hybrid unmanned aerial vehicle dynamics modeling method

Abstract

A dynamic modeling method for a quadrotor-turbojet hybrid unmanned aerial vehicle (UAV) is presented, belonging to the field of UAV dynamic modeling technology. The method includes establishing coordinate systems: an inertial coordinate system, a body coordinate system, and a turbojet engine coordinate system; defining the turbojet engine attitude angles; establishing coordinate transformation relationships; calculating the system's time-varying moment of inertia; establishing a quadrotor dynamic model, calculating the force and torque vectors generated by the four rotors based on their positions and dynamic parameters; establishing a turbojet engine dynamic model, calculating the turbojet engine's thrust vector, eccentric torque, anti-torque, and gyroscopic torque; establishing complete time-varying dynamic equations, including translational and rotational dynamic equations; establishing incremental comparative analysis, defining the increments of moment of inertia, torque, and thrust; and establishing an incremental comparison relationship between the hybrid power system and the original quadrotor system. Experiments verify the necessity of establishing the complete time-varying dynamic model presented in this paper.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) dynamics modeling technology, specifically to a precise dynamics modeling method for a quadcopter UAV and a turbojet engine hybrid power system. This technology belongs to the interdisciplinary field of aircraft design and control, and multibody dynamics analysis. The dynamic model proposed in this invention can accurately describe the influence mechanism of turbojet engine attitude adjustment on the overall aircraft dynamics characteristics, providing a rigorous theoretical foundation for the design of flight controllers, trajectory planning algorithms, and flight performance optimization of hybrid-powered UAVs. This technology can be widely applied to long-endurance reconnaissance UAVs, high-speed cargo UAVs, emergency rescue UAVs, and other unmanned aerial vehicle systems that require both hovering capability and high-speed cruise performance. Background Technology

[0002] While traditional multi-rotor drones possess excellent hovering and maneuverability, their limitations in battery energy density and rotor propulsion efficiency make them unsuitable for long-distance, long-duration flight missions. To address this issue, various hybrid-powered drone solutions have emerged in recent years. Among them, the technology of adding a turbojet engine to a quadcopter has attracted considerable attention due to its ability to significantly improve endurance and cruising speed. However, existing hybrid-powered drone designs primarily rely on empirical tuning and simplified control strategies, lacking precise modeling and in-depth understanding of the overall aircraft's dynamic characteristics.

[0003] The main problems with existing technologies include: First, the addition of a turbojet engine alters the system's mass distribution and rotational inertia characteristics, but current research often simplifies the turbojet engine as a fixed thrust source, neglecting the complex impact of its attitude adjustment on system dynamics. Second, turbojet engines are typically installed off-center from the airframe's center of mass, and their thrust and counter-torque generate significant coupled moments, but rigorous mathematical descriptions and quantitative analysis methods are lacking. Finally, most existing control algorithms are designed based on traditional quadrotor dynamic models, failing to fully leverage the performance advantages of hybrid power systems, leading to low flight efficiency and poor stability.

[0004] These technical deficiencies severely restrict the development and application of turbojet hybrid unmanned aerial vehicle (UAV) technology, and there is an urgent need to establish a complete and accurate dynamic modeling theory to provide a scientific basis for the design optimization and control system development of hybrid UAVs. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a dynamic modeling method for a quadcopter-turbojet hybrid unmanned aerial vehicle (UAV), comprising:

[0006] Step 1: Establishing the inertial coordinate system and the body coordinate system

[0007] Establish an inertial coordinate system ,origin Fixed at a ground reference point, The axis points north. The axis points eastward. The axis points vertically downwards towards the Earth's center, which conforms to the right-hand rule.

[0008] Establish the body coordinate system ,origin Located at the geometric center of the quadcopter fuselage, The shaft points forward along the longitudinal axis of the fuselage. The shaft points to the right along the transverse axis of the aircraft body. The axes point downwards along the body's normal axis, and the three axes form a right-handed coordinate system. The Euler angles of the body coordinate system relative to the inertial coordinate system are: roll angle. (around) (axis rotation), pitch angle (around) (axis rotation), yaw angle (around) (Axis rotation). The following is a simplified version, showing the Euler angles of the machine body. , , Abbreviated as , , And the positive direction of the angle is determined by the right-hand rule.

[0009] Establish the coordinate system of the turbojet engine ,origin Located at the center of mass of the turbojet engine The shaft points in the thrust direction along the axis of the turbojet engine. shaft and The axes point radially towards the turbojet engine. The position vector of the turbojet engine's center of mass in the body coordinate system is... ,in For along Distance between axes For along Distance between axes For along Distance between axes (usually) ).

[0010] Step 2: Definition of Turbojet Engine Attitude Angles and Dynamic Parameters

[0011] Define two attitude angles of the turbojet engine relative to the airframe coordinate system:

[0012] Pitch angle Turbojet engines in the airframe The angle of rotation in a plane is defined as from Shaft to turbojet axis The angle between the projections onto this plane. This indicates that the turbine axis is deflected downwards. Pitch angle. The corresponding angular velocity is .

[0013] Yaw angle Turbojet engines on the fuselage plane The rotation angle within is defined as from Shaft to turbojet axis The angle between the projections onto this plane. This indicates that the turbine axis is deflected to the right. Yaw angle. The corresponding angular velocity is .

[0014] The angular velocity limit for a turbojet engine is: , , ,in , For the maximum deflection angle, This represents the maximum angular velocity.

[0015] Step 3: Establish time-varying coordinate transformation relationship

[0016] use If the rotation matrix is ​​defined by internal rotation, then the direction cosine matrix from the inertial coordinate system to the body coordinate system is defined as follows:

[0017]

[0018] The direction cosine matrix from the body coordinate system to the inertial coordinate system is:

[0019]

[0020] in Indicates circling Shaft rotation The rotation matrix of the angle. Indicates circling Shaft rotation The rotation matrix of the angle. Indicates circling Shaft rotation The rotation matrix of the angle. For the Euler angle sequence, the exact relationship between the body angular velocity and the Euler angle derivative in the body coordinate system is:

[0021]

[0022] in Indicates circling angular velocity components of the axis, Indicates circling angular velocity components of the axis, Indicates circling Angular velocity components of the axis.

[0023] The column vector notation is adopted uniformly. Indicates the coordinate system Transform the column vectors into a coordinate system The column vectors below, that is, any vector satisfies Therefore, for the composite transformation from the engine body to the turbojet engine, the transformation matrix from the inertial coordinate system to the turbojet engine coordinate system is:

[0024]

[0025] The inverse transformation from the turbojet engine coordinate system to the inertial coordinate system is: .

[0026] Directional cosine matrix from body coordinate system to turbojet coordinate system for:

[0027]

[0028] According to the above column vector convention, the unit vector of the nozzle axis in the body coordinate system is determined by... e j = R J B [1,0,0 ] ⊤ Given the direction cosine matrix that transforms the body coordinate system to the turbojet coordinate system. Substituting, we get:

[0029]

[0030] Step 4: Calculation of system mass characteristics and time-varying moment of inertia

[0031] Define the total mass of the system ,in For the mass of a quadcopter fuselage, Let the mass be the turbojet engine mass. The moment of inertia matrix of the quadrotor fuselage about its center of mass is:

[0032]

[0033] in , , The moment of inertia of the main shaft. , , , , , It is the inertia product.

[0034] The moment of inertia matrix of a turbojet engine in its own coordinate system is:

[0035]

[0036] in This represents the moment of inertia of the turbojet engine about its own axis. Let be the moment of inertia of the turbojet engine about its radial axis. The moment of inertia matrix of the turbojet engine in the body coordinate system is:

[0037]

[0038] Considering the effect of the turbojet engine's center of mass shift, according to the parallel axis theorem, the rotational inertia matrix of the turbojet engine about the engine's center of mass is:

[0039]

[0040] in Represents the tensor product. It is a 3×3 identity matrix. for:

[0041]

[0042] The overall rotational inertia matrix of the system is: .

[0043] Due to the rigid body of the quadcopter Since the body coordinate system remains constant, the time change of the system's moment of inertia is only generated by the turbojet component.

[0044]

[0045] For the inertia term of the turbojet in the machine system, we have Its time derivative can be written in strict matrix derivative form as follows:

[0046]

[0047] If we denote the angular velocity of the turbojet relative to the aircraft (in the aircraft coordinate system) as... Using the equation of the derivative of the rotation matrix (in (Indicating an antisymmetric matrix), the above expression is equivalent to a more compact form. If the centroid offset vector of the vortex jet With changes in posture, i.e. The time derivative of the parallel axis terms additionally includes If the turbojet's center of mass is a fixed assembly in the body coordinate system, then its time derivative term is zero, i.e. .

[0048] To facilitate numerical implementation, it is necessary to... Using attitude angle derivative Mapping representation; based on the nozzle rotation sequence of "yaw first, then pitch," that is, relative to the body coordinate system, first yaw... Axis yaw rotation , then go around Axis pitch and rotation The final synthesized relative angular velocity in the body coordinate system is expressed as follows:

[0049]

[0050] This Substitute the above The expression can be used to obtain the time-varying derivative of the inertia in the rotation equation. item.

[0051] Step 5: Quadrotor Dynamics Modeling

[0052] The position vectors of the four rotors are as follows: Rotor 1, Rotor 2, Rotor 3, Rotor 4 .

[0053] in The longitudinal wheelbase of the aircraft. This refers to the transverse wheelbase of the aircraft. The height of the rotor plane above the center of mass of the fuselage.

[0054] Define rotor dynamic parameters: Represents the rotor lift constant. Represents the rotor's anti-torque constant. Indicates the first One rotor speed, This represents the polar moment of inertia of a single rotor. The lift and counter-torque generated by each rotor are as follows:

[0055]

[0056] The direction of lift generated by a single rotor is defined in the airframe coordinate system as follows: The total lift of the quadcopter is: The torque generated by the rotor can be given by the cross product of the position vector and the thrust:

[0057]

[0058] Expand the cross product and merge the gyrocoupling. Anti-yawing torque Then, the resultant torque of the quadrotor under the machine system can be written as:

[0059]

[0060] in This is the total angular momentum of the rotor. For the first The rotation factor of each rotor This indicates a positive rotation according to the right-hand rule. The yaw moment term is expressed as a weighted sum of inverse torques in the direction of rotation: .

[0061] Step Six: Dynamic Modeling of Turbojet Engine

[0062] Define the thrust parameters of a turbojet engine: Indicates the thrust of a turbojet engine, along Positive direction of the axis. This indicates the magnitude of the axial counter-torque of a turbojet engine. This represents the angular velocity of the turbojet engine rotor.

[0063] The time-varying vector representation of turbojet thrust in the body coordinate system is as follows:

[0064]

[0065] For ease of verification and implementation, the eccentric torque can be simultaneously expressed in vector form as follows: .

[0066] Detailed breakdown of each component:

[0067]

[0068] in The position vector of the turbojet's center of mass relative to the body's center of mass in the body coordinate system , , Projection on the axis; , , yes In the body coordinate system , , Projection on the axis.

[0069] The time-varying torque of the turbojet engine in the body coordinate system is expressed as:

[0070]

[0071] in Indicates along The reverse torque in the direction.

[0072] turbojet engine in its own coordinate system The rotor angular momentum is:

[0073]

[0074] in This represents the moment of inertia of the turbojet engine about its own axis. Represent this in the body coordinate system:

[0075]

[0076] The angular velocity of the nozzle relative to the fuselage in the fuselage coordinate system is expressed as follows:

[0077]

[0078] If you need to use the vortex jet coordinate system The text indicates that it is available for use:

[0079]

[0080] The gyroscopic torque generated by the turbojet's attitude adjustment should include two types of coupling terms: the coupling between the airframe angular velocity and the rotor angular momentum, and the influence of the nozzle's own attitude change on the angular momentum. These two types of terms can be expressed together in the airframe coordinate system as follows:

[0081]

[0082] in The first term is the body angular velocity vector (represented in body coordinates), and the second term is the sum of the relative gyroscopic torques within the turbojet system after transformation to the body coordinates. When When doing so, one can choose to retain the dominant term or provide an approximation based on the magnitude comparison.

[0083] The total torque vector generated by the turbojet engine is:

[0084]

[0085] Step 7: Detailed Establishment of Complete Time-Varying Dynamic Equations

[0086] Define the position vector of the system's center of mass in the inertial coordinate system. ,in This indicates that the center of mass is in the inertial coordinate system. Position coordinates along the axis This indicates that the center of mass is in the inertial coordinate system. Position coordinates along the axis This indicates that the center of mass is in the inertial coordinate system. Position coordinates along the axis. Define the acceleration vector of the system's center of mass in the inertial coordinate system. ,in Indicates that the center of mass is at axial acceleration components, Indicates that the center of mass is at axial acceleration components, Indicates that the center of mass is at The acceleration component in the axial direction.

[0087] According to Newton's second law, the translational equation of the system's center of mass is given in vector form:

[0088]

[0089] in The resultant force vector in the airframe coordinate system (including the total lift of the quadrotor and the turbojet component; the aerodynamic forces of the airframe are ignored in this paper). Let be the gravitational vector in the inertial frame, and take . g E =[0,0, g ] ⊤ .

[0090] The total thrust in the body coordinate system is:

[0091]

[0092] Therefore, the total force in the inertial frame is: .

[0093] Therefore, the complete equations of translational motion are:

[0094]

[0095] Define the body angular acceleration vector ω ̇ B =[ p ̇ , q ̇ , r ̇ ] ⊤ ,in Indicates circling Angular acceleration components of the axis, Indicates circling Angular acceleration components of the axis, Indicates circling The angular acceleration components of the axis. According to Euler's equations of motion, considering the time-varying moment of inertia, the general form of the rotational dynamics equations is:

[0096]

[0097] in Represents the moment of inertia matrix The derivative with respect to time, This represents the vector of total torque in the body coordinate system.

[0098] To simplify the expression, the rotational inertia matrix is... The components are defined as follows: Representing the moment of inertia matrix element, Representing the moment of inertia matrix element, Representing the moment of inertia matrix Elements, and so on.

[0099] Define the time derivative matrix of the moment of inertia The components: express The derivative with respect to time, express The derivative with respect to time, express The derivative with respect to time follows the same principle.

[0100] The complete rotational dynamics equations can be expanded as follows:

[0101] Roll direction:

[0102]

[0103] Pitch direction:

[0104]

[0105] Yaw direction:

[0106]

[0107] Define the mass increment introduced by a turbojet engine: Define the components of the moment of inertia increment matrix introduced by the turbojet engine: Represents the matrix of rotational inertia increment The elements are defined as follows, and the remaining elements are defined similarly. The components of the time derivative increment of the moment of inertia introduced by the turbojet engine are defined as follows: express The derivative with respect to time, and so on for the remaining elements. Define the components of the torque increment introduced by the turbojet engine: Indicates turbojet engine in The increase in torque generated in the axial direction, Indicates turbojet engine in The increase in torque generated in the axial direction, Indicates turbojet engine in The increase in torque generated in the axial direction.

[0108] The translational motion equations expressed in increments are as follows:

[0109]

[0110] in Expanded by components:

[0111]

[0112] The rotational dynamics equation expressed in increments is:

[0113]

[0114] in ,and ( When fixed, the time derivative of the parallel axis term is zero.

[0115] Note: Quadrotor airframe inertia matrix In the body coordinate system, it is a constant matrix ( Therefore, in the equation Introduced from turbojet .

[0116] The beneficial effects of this invention are:

[0117] To address the problems of simplistic and distorted modeling, incomplete gyro coupling mechanisms, and disconnect between design and flight control implementation in existing quadrotor-two-DOF turbojet hybrid UAV modeling technologies, this invention proposes a closed-loop solution from modeling to application for the first time: First, unified modeling with dual-channel gyro coupling, simultaneously characterizing the coupling between the airframe rotation and the high-speed rotor, as well as the coupling between the nozzle relative oscillation and the high-speed rotor, under the same airframe system and unified coordinate convention, ensuring stable and reliable torque prediction under rapid yaw / pitch superposition conditions; Second, analytical sensitivity of time-varying inertia / inertia product caused by nozzle attitude and installation offset, using a recalculated and traceable design process to transform the impact of attitude and assembly changes on the overall mass distribution and coupling terms into decision-making basis that can be directly used for structural optimization, achieving model-driven engineering optimization; Third, turbojet incremental injection path for existing flight control, seamlessly embedding incremental interfaces of mass, resultant force, resultant torque, and time-varying inertia effects into the existing quadrotor control loop, maintaining the main control structure and real-time characteristics unchanged, significantly reducing the difficulty of porting and parameter tuning threshold, and shortening the development cycle from simulation to actual aircraft. Based on this closed-loop scheme, the installation position of the turbojet can be optimized, the controller can be designed in a refined manner and its performance can be quantitatively analyzed. This effectively solves problems such as low efficiency and poor control stability of UAVs. It can be widely used in hybrid UAV systems for reconnaissance, cargo transport, and emergency rescue, laying the foundation for their industrialization. Attached Figure Description

[0118] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0119] Figure 1 This is a front view of the UAV structure described in an embodiment of the present invention.

[0120] Figure 2 This is a side view of the UAV structure according to an embodiment of the present invention.

[0121] Figure 3 This is a bottom view of the UAV structure described in an embodiment of the present invention. Detailed Implementation

[0122] Example 1: Parameter Calculation Method for Hybrid Unmanned Aerial Vehicle System Based on Dynamic Model

[0123] Taking a practical quadcopter-turbojet hybrid unmanned aerial vehicle (UAV) as an example, the specific implementation process of the dynamic modeling method of this invention is explained in detail. The UAV's airframe mass... quadcopter wheelbase The height of the rotor from the center of mass of the fuselage Turbojet engine mass Maximum thrust Installed on the underside of the machine body, position parameters .

[0124] First, determine the basic system parameters. Quadrotor fuselage moment of inertia matrix. Calculated using 3D modeling software: , , Inertia product The moment of inertia of the turbojet engine in its own coordinate system is obtained from the manufacturer's technical data. , Rotor parameters are obtained from the manufacturer's technical data: lift constant. reverse torque constant Rotor extreme moment of inertia .

[0125] When the turbojet engine is at a specific attitude angle First, calculate the transformation matrix from the turbojet coordinate system to the body coordinate system. .

[0126] Calculate the transformation matrix according to the formula in step three:

[0127]

[0128] when At that time, the unit vector of the nozzle axis and the thrust in the computer system:

[0129] e j = R J B [1,0,0 ] ⊤ = &0.9811 &0.0858 &0.1736

[0130]

[0131] Then, according to step four, the time-varying moment of inertia of the turbojet engine in the body coordinate system is calculated:

[0132]

[0133] The total moment of inertia matrix of the system is:

[0134]

[0135] If the turbojet engine is in a steady state and there is no accessory power take-off or jet vortex, then If at the same time and ,but Calculate the torque generated by the turbojet engine according to step six:

[0136]

[0137] Complete the translational modeling of the entire machine according to step seven:

[0138]

[0139]

[0140] When the quadcopter is in a horizontal attitude ( ), quadcopter combined force ,at this time:

[0141]

[0142] Because only around The yaw of the axis will not change Components, therefore Only The plane rotates the first two terms of this vector, therefore:

[0143]

[0144] As can be seen from the numerical examples above, turbojet engines introduce significant horizontal acceleration into quadcopters.

[0145] In the machine system, when Then, complete the rotational modeling of the entire machine according to step seven:

[0146]

[0147] Quadrotor torque:

[0148]

[0149] To facilitate direct numerical calculations, the numerical formula for triaxial component-by-component expansion is given below:

[0150] Roll (X):

[0151] Pitch (Y):

[0152] Yaw (Z):

[0153] Example 2: Sensitivity Analysis Method for Dynamic Model Parameters

[0154] To evaluate the impact of nozzle attitude angle on the overall dynamic characteristics of the aircraft, based on the parameters of Example 1, the following was conducted. Static sensitivity scanning. Scanning domain taken... , Within the range, parameter scanning calculations are performed at certain intervals. The calculations employ ZYX internal rotation and passive transformation of column vectors, while the nozzle rotation relative to the fuselage maintains the convention from step three. , , ,therefore , , Other parameters remain the same as in Example 1.

[0155] Moment of inertia about the spindle Perform sensitivity analysis and fixation ,analyze Changes Impact:

[0156] when hour:

[0157]

[0158] when hour:

[0159]

[0160] when hour:

[0161]

[0162] when hour:

[0163]

[0164] Product of inertia Sensitivity analysis, fixation ,analyze Changes Impact:

[0165] when hour:

[0166]

[0167]

[0168] when hour:

[0169]

[0170] when hour:

[0171]

[0172]

[0173] Torque sensitivity analysis: This study analyzes the influence of the turbojet attitude angle on the eccentric torque, with a fixed... :

[0174] when exist arrive When changing within the range, Axial eccentricity moment Changes:

[0175]

[0176] Sensitivity analysis results:

[0177] Spindle moment of inertia Follow Significant changes: θ J ∈[- 30 ∘ ,+ 15 ∘ ] Inside, From the agreement Change to approximately The relative rate of change is approximately .

[0178] Product of inertia right It is oddly symmetrical. from arrive hour, By Change to approximately Amplitude approximately .

[0179] Eccentric torque right Most sensitive: Within the above scanning domain, the variation range is approximately This is equivalent to approximately [amount] of the maximum value of the component within the scanned domain. .

[0180] The above results show that the nozzle attitude angle has a significant impact on the overall dynamic characteristics of the aircraft, especially the inertia product and eccentric moment, which verifies the necessity of establishing a complete time-varying dynamic model in this paper.

Claims

1. A dynamic modeling method for a quadcopter-turbojet hybrid unmanned aerial vehicle, characterized in that, include: Step 1: Establish the inertial coordinate system, the body coordinate system, and the turbojet engine coordinate system; Step 2: Definition of turbojet engine attitude angles and their dynamic parameters; Step 3: Establish time-varying coordinate transformation relationships; Step 4: Calculation of system mass characteristics and time-varying moment of inertia; Step 5: Quadrotor dynamics modeling; Step Six: Dynamic Modeling of Turbojet Engine; Step 7: Establish the complete time-varying dynamic equations.

2. The method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to claim 1, characterized in that, Step one is described in detail as follows: Establish an inertial coordinate system ,origin Fixed at a ground reference point, The axis points north. The axis points eastward. The axis points vertically downwards towards the Earth's center, which conforms to the right-hand rule; Establish the body coordinate system ,origin Located at the geometric center of the quadcopter fuselage, The shaft points forward along the longitudinal axis of the fuselage. The shaft points to the right along the transverse axis of the aircraft body. The axes point downwards along the body's normal axis, and the three axes form a right-handed coordinate system; the Euler angles of the body coordinate system relative to the inertial coordinate system are: roll angle. (around) (axis rotation), pitch angle (around) (axis rotation), yaw angle (around) (axis rotation); the following is a simplified version, Euler angles of the machine body. , , Abbreviated as , , And the positive direction of the angle is determined by the right-hand rule; Establish the coordinate system of the turbojet engine ,origin Located at the center of mass of the turbojet engine The shaft points in the thrust direction along the axis of the turbojet engine. shaft and The axes point to the radial direction of the turbojet engine; the position vector of the turbojet engine's center of mass in the body coordinate system is... ,in For along Distance between axes For along Distance between axes For along Distance between axes.

3. The method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to claim 2, characterized in that, Step two is as follows: Define two attitude angles of the turbojet engine relative to the airframe coordinate system: Pitch angle Turbojet engines in the airframe The angle of rotation in a plane is defined as from Shaft to turbojet axis The angle between the projections onto this plane. This indicates that the turbine axis is deflected downwards; pitch angle The corresponding angular velocity is ; Yaw angle Turbojet engines on the fuselage plane The rotation angle within is defined as from Shaft to turbojet axis The angle between the projections onto this plane. This indicates that the turbine axis is deflected to the right; yaw angle. The corresponding angular velocity is ; The angular velocity limit for a turbojet engine is: , , ,in , For the maximum deflection angle, This represents the maximum angular velocity.

4. The method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to claim 3, characterized in that, Step three is described in detail below: use If the rotation matrix is ​​defined by internal rotation, then the direction cosine matrix from the inertial coordinate system to the body coordinate system is defined as follows: The direction cosine matrix from the body coordinate system to the inertial coordinate system is: in Indicates circling Shaft rotation The rotation matrix of the angle. Indicates circling Shaft rotation The rotation matrix of the angle. Indicates circling Shaft rotation The rotation matrix of the angle; for the Euler angle sequence, the precise relationship between the body angular velocity and the Euler angle derivative in the body coordinate system is: in Indicates circling angular velocity components of the axis, Indicates circling angular velocity components of the axis, Indicates circling Angular velocity components of the axis; The column vector notation is adopted uniformly. Indicates the coordinate system Transform the column vectors into a coordinate system The column vectors below, that is, any vector satisfies Therefore, for the composite transformation from the engine body to the turbojet engine, the transformation matrix from the inertial coordinate system to the turbojet engine coordinate system is: The inverse transformation from the turbojet engine coordinate system to the inertial coordinate system is: ; Directional cosine matrix from body coordinate system to turbojet coordinate system for: According to the above column vector convention, the unit vector of the nozzle axis in the body coordinate system is determined by... Given the direction cosine matrix that transforms the body coordinate system to the turbojet coordinate system. Substituting, we get: 。 5. The method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to claim 4, characterized in that, Step four is described in detail below: Define the total mass of the system ,in For the mass of a quadcopter fuselage, The mass of the turbojet engine; the rotational inertia matrix of the quadcopter fuselage about its center of mass is: in , , The moment of inertia of the main shaft. , , , , , It is the product of inertia; The moment of inertia matrix of a turbojet engine in its own coordinate system is: in This represents the moment of inertia of the turbojet engine about its own axis. Let be the moment of inertia of the turbojet engine about its radial axis; the moment of inertia matrix of the turbojet engine in the body coordinate system is: Considering the effect of the turbojet engine's center of mass shift, according to the parallel axis theorem, the rotational inertia matrix of the turbojet engine about the engine's center of mass is: in Represents the tensor product. It is a 3×3 identity matrix. for: The overall rotational inertia matrix of the system is: ; Due to the rigid body of the quadcopter Since the body coordinate system remains constant, the time change of the system's moment of inertia is only generated by the turbojet component. For the inertia term of the turbojet in the machine system, we have Its time derivative, in strict matrix derivative form, is written as: If we denote the angular velocity of the turbojet relative to the fuselage as... Using the equation of the derivative of the rotation matrix ,in If we represent an antisymmetric matrix, then the above expression is equivalent to a more compact form. ; If the centroid offset vector of the vortex jet With changes in posture, i.e. The time derivative of the parallel axis terms additionally includes If the turbojet's center of mass is fixed in the body coordinate system, then its time derivative term is zero, i.e. ; To facilitate numerical implementation, it is necessary to... Using attitude angle derivative The mapping representation is based on the nozzle rotation sequence of "yaw first, then pitch," meaning it rotates around the body coordinate system first. Axis yaw rotation , then go around Axis pitch and rotation The final synthesized relative angular velocity in the body coordinate system is expressed as follows: This Substitute the above The expression, that is, the time-varying derivative of the inertia, is used in the rotation equation. item.

6. The method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to claim 5, characterized in that, Step five is described in detail below: The position vectors of the four rotors are as follows: Rotor 1, Rotor 2, Rotor 3, Rotor 4 ; in The longitudinal wheelbase of the aircraft. This refers to the transverse wheelbase of the aircraft. The height of the rotor plane from the center of mass of the fuselage; Define rotor dynamic parameters: Represents the rotor lift constant. Represents the rotor's anti-torque constant. Indicates the first One rotor speed, Represents the polar moment of inertia of a single rotor; the... The lift and counter-torque generated by each rotor are as follows: The direction of lift generated by a single rotor is defined in the airframe coordinate system as follows: The total lift of the quadcopter is: The torque generated by the rotor is given by the cross product of the position vector and the thrust: Expand the cross product and merge the gyrocoupling. Anti-yawing torque Then, the resultant moment of the quadrotor under the machine system is written as: in This is the total angular momentum of the rotor. For the first The rotation factor of each rotor The right-hand rule indicates positive rotation; the yaw moment term is expressed as a weighted sum of inverse torques in the direction of rotation. .

7. The method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to claim 6, characterized in that, Step six is ​​described in detail below: Define the thrust parameters of a turbojet engine: Indicates the thrust of a turbojet engine, along Positive direction of the axis; Indicates the magnitude of the axial counter-torque of a turbojet engine; This represents the angular velocity of the turbojet engine rotor; The time-varying vector representation of turbojet thrust in the body coordinate system is as follows: For ease of verification and implementation, the eccentric torque is also represented in vector form as follows: ; Detailed breakdown of each component: in The position vector of the turbojet's center of mass relative to the body's center of mass in the body coordinate system , , Projection on the axis; , , yes In the body coordinate system , , Projection on the axis; The time-varying torque of the turbojet engine in the body coordinate system is expressed as: in Indicates along Reverse torque in the direction; turbojet engine in its own coordinate system The rotor angular momentum is: in The moment of inertia of the turbojet engine about its own axis is represented; it is expressed in the body coordinate system: The angular velocity of the nozzle relative to the fuselage in the fuselage coordinate system is expressed as follows: If you need to use the vortex jet coordinate system The expression in the middle is represented by the following formula: The gyroscopic torque generated by the turbojet attitude adjustment should include two types of coupling terms: the coupling between the airframe angular velocity and the rotor angular momentum, and the influence of the nozzle's own attitude change on the angular momentum; these two types of terms can be expressed together in the airframe coordinate system as: in The first term is the body angular velocity vector, and the second term is the sum of the relative gyroscopic torques within the turbojet system after being transformed into the body system. The total torque vector generated by the turbojet engine is: 。 8. The method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to claim 7, characterized in that, Step seven is described in detail below: Define the position vector of the system's center of mass in the inertial coordinate system. ,in This indicates that the center of mass is in the inertial coordinate system. Position coordinates along the axis This indicates that the center of mass is in the inertial coordinate system. Position coordinates along the axis This indicates that the center of mass is in the inertial coordinate system. Position coordinates along the axis; define the acceleration vector of the system's center of mass in the inertial coordinate system. ,in Indicates that the center of mass is at axial acceleration components, Indicates that the center of mass is at axial acceleration components, Indicates that the center of mass is at Components of acceleration in the axial direction; According to Newton's second law, the translational equation of the system's center of mass is given in vector form: in This is the resultant force vector in the airframe coordinate system, including the total lift of the quadrotor and the turbojet component, while neglecting airframe aerodynamic forces. Let be the gravitational vector in the inertial frame, and take . ; The total thrust in the body coordinate system is: Therefore, the total force in the inertial frame is: ; Therefore, the complete equations of translational motion are: Define the body angular acceleration vector ,in Indicates circling Angular acceleration components of the axis, Indicates circling Angular acceleration components of the axis, Indicates circling The angular acceleration components of the axis; according to Euler's equations of motion, considering the time-varying moment of inertia effect, the general form of the rotational dynamics equations is: in Represents the moment of inertia matrix The derivative with respect to time, This represents the vector of total torque in the body coordinate system; To simplify the expression, the rotational inertia matrix is... The components are defined as follows: Representing the moment of inertia matrix element, Representing the moment of inertia matrix element, Representing the moment of inertia matrix Elements, and so on; Define the time derivative matrix of the moment of inertia The components: express The derivative with respect to time, express The derivative with respect to time, express The derivative with respect to time, and so on; The complete rotational dynamics equations can be expanded as follows: Roll direction: Pitch direction: Yaw direction: Define the mass increment introduced by a turbojet engine: Define the components of the moment of inertia increment matrix introduced by the turbojet engine: Represents the matrix of rotational inertia increment Elements, and so on for the remaining elements; define the components of the time derivative increment of the moment of inertia introduced by the turbojet engine: express The derivative with respect to time, and so on for the remaining elements; define the components of the torque increment introduced by the turbojet engine: Indicates turbojet engine in The increase in torque generated in the axial direction, Indicates turbojet engine in The increase in torque generated in the axial direction, Indicates turbojet engine in The increase in torque generated in the axial direction; The translational motion equations expressed in increments are as follows: in Expanded by components: The rotational dynamics equation expressed in increments is: in ,and , When fixed, the time derivative of the parallel axis term is zero; Note: Quadrotor airframe inertia matrix In the body coordinate system, it is a constant matrix. Therefore, in the equation Introduced from turbojet .

9. A method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to any one of claims 1-8, characterized in that, This method can be applied to the flight performance analysis, overall design optimization, or flight simulation of hybrid-powered unmanned aerial vehicles (UAVs).

10. A method for dynamic modeling of a quadcopter-turbojet hybrid unmanned aerial vehicle according to any one of claims 1-8, characterized in that, By calculating the turbojet engine attitude angle in real time and The corresponding system rotational inertia distribution and torque distribution provide accurate dynamic model parameters for the design of hybrid-powered UAV control systems.

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