Hydrodynamic Characteristics Analysis and Control Methods and Devices for Variable-Sweep Wing Transmedium Aircraft

Abstract

This invention discloses a method for hydrodynamic characteristic analysis and control of a variable-sweep wing cross-medium aircraft, comprising the following steps: Modeling stage of the variable-sweep wing cross-medium aircraft: acquiring the geometric model, structural parameters, shape parameters, and preset motion condition parameters of the variable-sweep wing cross-medium aircraft during underwater navigation, and performing equivalent simplification processing on the model. This method and apparatus for hydrodynamic characteristic analysis and control of a variable-sweep wing cross-medium aircraft, by combining steady and unsteady hydrodynamic numerical analysis in acquiring parameters related to the underwater longitudinal motion of the variable-sweep wing cross-medium aircraft, constructs a hydrodynamic calculation model in multiphysics simulation and computational fluid dynamics software, acquires steady-state force, torque, and unsteady response data of the aircraft under different operating conditions, and further identifies the hydrodynamic derivative coefficients related to longitudinal motion, thereby improving the efficiency of underwater hydrodynamic analysis and modeling of the variable-sweep wing cross-medium aircraft.

Description

Technical Field

[0001] This invention relates to the field of cross-medium aircraft modeling and control technology, specifically to a method and apparatus for analyzing and controlling the hydrodynamic characteristics of variable-sweep wing cross-medium aircraft. Background Technology

[0002] With the development of unmanned systems technology and sea-air collaborative reconnaissance technology, cross-medium aircraft capable of continuous operation in both underwater and air environments have gradually become a research hotspot. These aircraft possess both underwater and airborne capabilities, enabling transitions between different media, and have high application value in mission scenarios such as integrated sea-air reconnaissance, rapid deployment, and multi-domain collaboration. Variable-sweep wing cross-medium aircraft, by changing the wing sweep angle, can adjust the aerodynamic and hydrodynamic characteristics of the aircraft under different operating conditions, thus providing a new technical approach for performance optimization during underwater cruise, waterborne transition, and airborne flight phases.

[0003] For variable-sweep wing configurations, changes in the sweep angle significantly affect lift, drag, and pitching moment. Therefore, it is necessary to obtain corresponding aerodynamic or hydrodynamic parameters under different sweep angles, angles of attack, and motion conditions to provide a basis for subsequent dynamic modeling and control design. Meanwhile, in the underwater phase, the longitudinal motion of the aircraft involves both steady and unsteady hydrodynamic characteristics. Obtaining these parameters typically requires a combination of numerical simulation, parameter identification, and dynamic modeling, which is labor-intensive and makes it difficult to directly form a unified model suitable for control system design. Existing research often focuses on analyses of single phases, single media, or single problems, while integrated solutions that consider rapid underwater hydrodynamic analysis, longitudinal dynamic modeling, underwater cruise control, and pre-surface attitude control are relatively insufficient.

[0004] Furthermore, during the terminal phase of underwater cruise and the pre-emergence phase, the aircraft typically needs to simultaneously meet multiple control requirements, including speed, depth, and attitude. If the control is inadequate, the aircraft may experience problems such as large pitch angles, poor attitude, and insufficient stability when approaching the free surface. This can lead to increased additional drag when crossing the surface, and even adverse phenomena such as water plunging, anti-nose pitching, or sudden attitude changes, affecting the smoothness of the cross-medium transition and the mission execution effect. Therefore, how to establish a longitudinal dynamic model suitable for the underwater phase for variable-sweep wing cross-medium aircraft, quickly obtain and control-related hydrodynamic parameters, and achieve constant speed and depth control during the underwater cruise phase and attitude-velocity coordinated control before emergence remains an urgent problem to be solved in the existing technology. To this end, we propose a method and device for hydrodynamic characteristic analysis and control of variable-sweep wing cross-medium aircraft. Summary of the Invention

[0005] To address the shortcomings of existing methods and devices for hydrodynamic characteristic analysis and control of variable-sweep wing cross-medium aircraft, this invention provides such methods and devices. For the underwater cruise phase, a coordinated control strategy is designed to balance thrust and tail control surface deflection, achieving constant speed and depth control. Furthermore, for the pre-emergence phase, an attitude-velocity coordinated control method based on an extended state observer and backstepping is constructed. By estimating and compensating for disturbances and unmodeled dynamics online, the variable-sweep wing cross-medium aircraft can maintain good cruise stability in complex underwater environments and complete the pre-emergence transition with a stable attitude, thus solving the problems mentioned in the background art.

[0006] This invention provides the following technical solution: a method for analyzing and controlling the hydrodynamic characteristics of a variable-sweep wing transmedium aircraft, comprising the following steps: S1. Modeling stage of variable-sweep wing cross-medium aircraft: Obtain the geometric model, structural parameters, shape parameters and preset motion condition parameters of the variable-sweep wing cross-medium aircraft during the underwater navigation stage, and perform equivalent simplification processing on the model. Then, model it in 3D modeling software. Based on the 3D geometric model, construct the hydrodynamic numerical calculation domain in multiphysics simulation and computational fluid dynamics software and simulation software, set the inlet boundary, outlet boundary, external field boundary and wall boundary, select the turbulence model and generate the calculation mesh. S2. Steady hydrodynamic analysis stage of variable sweep wing transmedium aircraft: The hydrodynamic numerical solution of the aircraft is performed under steady motion conditions to obtain steady-state force and torque data related to longitudinal motion, and the data is fitted to obtain hydrodynamic coefficients. S3. Unsteady hydrodynamic analysis stage of variable sweep wing transmedium aircraft: The hydrodynamic numerical solution of the aircraft is performed under unsteady motion conditions to obtain unsteady force and torque data related to longitudinal motion and to fit the data to obtain hydrodynamic coefficients. S4. Mathematical Model Establishment and Control Problem Abstraction Stage of Variable-Sweep Wing Trans-medium Aircraft: Establish the mathematical model of the variable-sweep wing trans-medium aircraft and perform mathematical abstraction on the control problem of the variable-sweep wing trans-medium aircraft. S5. Underwater cruise control phase: During the underwater cruise phase, with the desired cruise speed and desired cruise depth as control targets, a coordinated control law for the thruster thrust and tail control surface deflection angle is designed to achieve constant speed and constant depth control. S6. Attitude control stage before water exit: In the stage before water exit, the control target is switched to pitch angle tracking, pitch angular velocity suppression and vertical velocity suppression to achieve coordinated attitude and velocity control, so that the aircraft can pass through the free liquid surface in a stable attitude.

[0007] Preferably, in step S1, the variable-sweep wing trans-medium aircraft undergoes 3D modeling and computational mesh generation, specifically including: S1.1. Establish an underwater three-dimensional geometric model of the variable-sweep wing cross-medium aircraft in three-dimensional modeling software. According to the requirements of underwater longitudinal motion analysis, set the working parameters of the three-dimensional geometric model. The working parameters include at least the sweep angle, the body attitude angle, the reference speed, and the immersion state. S1.2. The three-dimensional geometric model is simplified, retaining its volume influence and connection transition structure. The actual wing is replaced with an equal-length cuboid plate structure. The simplified three-dimensional geometric model is imported into multiphysics simulation and computational fluid dynamics software to generate a computational model for hydrodynamic analysis.

[0008] S1.3. Establish an external flow field computational domain around the underwater analysis model, and set the inlet boundary, outlet boundary, symmetry plane or far-field boundary, and wall boundary. Set the incoming flow medium as water, and input the corresponding fluid density, dynamic viscosity, and gravity parameters. Select SST. Turbulence model; S1.4. The computational domain is meshed using a structured mesh based on cut bodies, and local meshing is performed on the surface of the fuselage, the leading and trailing edges of the wings, the area near the tail, and the wake region. The computational domain range is 8–10 times the characteristic length of the aircraft. The boundary layer mesh in the near-wall region is controlled to meet the near-wall resolution requirements of turbulence solutions. Mesh independence is checked to obtain the final computational mesh that meets the accuracy requirements.

[0009] Preferably, in step S2, numerical calculations are performed on the steady-state hydrodynamics of the variable-sweep wing transmedium aircraft. The specific process includes: S3.1 Set the aircraft to a straight-line flight condition along the body axis x direction and obtain longitudinal drag data under different speed conditions; S3.2. Set the aircraft to a straight-ahead flight condition along the body axis z-direction, and rotate the aircraft nose 90 degrees. It also changes the mainstream direction to achieve numerical simulation of the vertical ascent or descent process and obtains vertical force data under different vertical velocity conditions; S3.3 Set the aircraft to slant flight in the longitudinal plane. By introducing a certain angle of attack on the basis of horizontal straight flight, the flow field has both horizontal and vertical velocity components, and obtain the vertical force and pitch moment data under different conditions. S3.4. Fit the obtained steady force and moment data to obtain the steady hydrodynamic derivatives related to longitudinal straight and oblique navigation.

[0010] Preferably, in step S3, numerical calculations are performed on the unsteady hydrodynamics of the variable-sweep wing transmedium aircraft. The specific process includes: S4.1. Using dynamic mesh technology, set the pure heave motion of the aircraft in the longitudinal plane, so that the aircraft moves periodically along the vertical direction at a preset frequency and preset amplitude, and record the time domain response data of the vertical force and pitch moment of the aircraft during the pure heave motion. S4.2. Using dynamic mesh technology, set the pure pitch motion of the aircraft around the lateral axis, so that the aircraft performs periodic pitch oscillations at a preset frequency and preset amplitude, and record the time domain response data of the vertical force and pitch moment on the aircraft during the pure pitch motion. S4.3 Fit the unsteady time-domain response data, identify dimensionless hydrodynamic coefficients related to vertical velocity and vertical acceleration based on pure heave motion data, and identify dimensionless hydrodynamic coefficients related to pitch angular velocity and pitch angular acceleration based on pure pitch motion data.

[0011] Preferably, in step S4, a dynamic model of the variable-sweep wing transmedium aircraft is constructed and the control problem is mathematically abstracted. The specific process includes: S4.1 Based on the identified steady and unsteady hydrodynamic derivative coefficients, select the coefficient terms related to longitudinal motion, ignore the lateral coupling terms that have little impact on longitudinal motion, and retain only the coupling terms related to speed, heave and pitch. Based on the equivalence relationship between the single-degree-of-freedom unsteady motion results and the longitudinal coupling coefficient, calculate the complete longitudinal coupling hydrodynamic coefficients. S4.2 The underwater external forces and moments acting on the variable-sweep wing transmedium aircraft are analyzed. These external forces mainly include gravity, buoyancy, propulsion, and hydrodynamic forces. The underwater longitudinal dynamic equations of the variable-sweep wing transmedium aircraft are obtained as follows: ; in, For the mass of the aircraft, The pitch inertia of the aircraft about the transverse axis of its body axis system; These represent the aircraft's body axis system. linear velocity in the direction, Representing the body axis system The angular velocity of the axis, where It is the pitch angular velocity; These are the time derivatives of the forward velocity, vertical velocity, and pitch angular velocity, respectively. The pitch angle is taken at the vehicle's center of mass. The axis points towards the front of the fuselage. The axis points to the right. The axis points downwards.

[0012] Here are the dimensionless hydrodynamic derivative coefficients, where The class coefficient corresponds to the forward hydrodynamic force along the body axis. The coefficient corresponds to the vertical hydrodynamic force of the body axis. The class coefficients correspond to the pitching hydrodynamic moment; the subscripts indicate the motion variables or coupling variables corresponding to the hydrodynamic term. For example, This represents the forward hydrodynamic coefficient caused by forward acceleration. This represents the forward hydrodynamic coefficient caused by the coupling term. This represents the vertical hydrodynamic coefficient caused by vertical acceleration. Indicates by The vertical hydrodynamic coefficient caused by the coupling term, This represents the pitch hydrodynamic moment coefficient caused by pitch angular acceleration. Indicates by The pitching moment coefficient caused by the coupling term.

[0013] The density of the water medium, Let be the characteristic length of the aircraft. In the formula, each hydrodynamic term is multiplied by according to the dimensionless transformation rule. and different levels This is used to convert dimensionless hydrodynamic derivatives into dimensional forces or torques. Generally, it includes... The item reflects the added mass or added inertia effect; containing The terms reflect steady or quasi-steady hydrodynamic effects; including The terms of equal product reflect the nonlinear coupling hydrodynamic effects between motions with different degrees of freedom.

[0014] and These represent the propulsion system on the body axis. and Thrust component in the direction, This indicates the applied control torque or equivalent pitch control torque acting on the pitch channel; For the aircraft's gravity, This is buoyancy. and These represent the components of the resultant force of gravity and buoyancy in the forward and vertical directions along the body axis, respectively. Since the directions of gravity and buoyancy are determined in the inertial frame, while the dynamic equations are established in the body axis frame, their projection along the body axis and the pitch angle are respectively... related.

[0015] The dynamic equation can be understood as follows: when an aircraft moves underwater, its forward, vertical, and pitch motion changes are not only determined by the difference between thrust and buoyancy, but also by the combined effects of hydrodynamic damping, added mass, and longitudinal motion coupling terms.

[0016] S4.3 Mathematical abstraction of the underwater cruise control problem, considering the control of speed and depth of the aircraft during the underwater cruise phase, mainly targeting... and Then the mathematical model for control can be written as: ; in, Indicates the spacecraft in the Earth-fixed coordinate system Position in direction Indicates the rate of change of the vertical position of the Earth-fixed system; This represents the equivalent mass of the longitudinal velocity channel. This refers to the control thrust acting on the longitudinal velocity channel, which is usually generated by the underwater propeller during the underwater cruise phase. , This is a modelable hydrodynamic nonlinear term, and , This represents the external disturbances and dynamics during the underwater phase that are modeled. This represents the equivalent moment of inertia of the pitch channel. This represents the equivalent control torque acting on the pitch channel, typically generated by the deflection of the tail elevator. By adjusting the propeller thrust, the longitudinal speed is increased. It can gradually approach the desired speed At the same time, adjust the elevator deflection angle. Suppressing vertical velocity and adjusting pitch attitude to increase operating depth It can gradually approach the desired depth The underwater cruise control problem is described as follows: ; in, Indicates time, Indicates that the aircraft is in The forward velocity of the body axis at any given moment, i.e., the underwater cruising speed; Indicates the desired cruising speed; Indicates that the aircraft is in The depth of operation at any given moment This indicates the desired cruising depth.

[0017] Similarly, the attitude control before emerging from the water is mathematically abstracted. Following the mathematical model of underwater cruise control, the pitch angle of the aircraft is gradually brought closer to the desired small upward pitch angle by adjusting the tail elevator. This involves suppressing pitch velocity to smooth attitude changes, and simultaneously eliminating vertical velocity to gradually align the aircraft's velocity direction with its longitudinal axis, thus enabling a smooth ascent along a pre-defined straight path. In essence, the attitude control problem before water exit can be summarized as follows: .

[0018] in, Indicates that the aircraft is in The pitch angle at any given moment; This indicates the desired pitch angle, which is usually a small upward pitch angle set before the vessel emerges from the water. Indicates that the aircraft is in The pitch angular velocity at any given moment; Indicates that the aircraft is in At all times along the body axis Vertical velocity in the direction of travel.

[0019] Preferably, in step S5, a speed and depth controller for the underwater cruising phase is designed using a backstepping method. The specific process includes: S5.1, For the longitudinal velocity subsystem of the aircraft Uncertain disturbance term in ,in, Indicates the equivalent mass of the longitudinal velocity channel; This represents the thrust generated by the propeller, i.e., the control input. Represents the modelable hydrodynamic terms. This represents the total disturbance term in the longitudinal velocity channel. Construct an extended state observer. For real-time estimation, the structure is designed as follows: ; in, Used to estimate longitudinal velocity , Used to estimate the disturbance term; This represents a nonlinear error feedback function used for individual tragic observation errors. The perturbation estimate is corrected, with 0.5 representing the convergence order parameter of the nonlinear function. This is a threshold parameter for the small error range, used to avoid excessive feedback when the error is close to zero.

[0020] In virtual thrust Compared with actual thrust input A control filter is constructed between the two to impose dual constraints on its amplitude and rate. The control filter can be expressed as a state equation: ; in, This indicates the actual thrust command after processing by the control filter. This indicates the rate of change of the thrust command after filtering; This represents the auxiliary state variable controlling the filter, which can also be understood as the thrust rate of change state inside the filter; This represents the time derivative of the auxiliary state variable. This indicates the damping ratio of the underwater velocity channel control filter; This indicates the inherent frequency of the underwater velocity channel control filter; Indicates the internal variables of the filter; This represents the thrust rate limiting function, used to constrain the rate of change of thrust command; This represents the output of the filter's internal variables after rate limiting.

[0021] In the formula This is the damping adjustment coefficient for the second-order filter, used to control the dynamic response speed and oscillation degree of the filter; This represents the deviation between the target rate of change after rate constraint and the current auxiliary state.

[0022] The virtual thrust command obtained by designing a backstepping controller based on ESO is as follows: ; in, This represents the equivalent control gain between the thrust input and the longitudinal acceleration in the underwater velocity channel; This represents the speed tracking error feedback gain, and is usually taken as a positive value. This represents the corrected longitudinal velocity tracking error, used to characterize the deviation between the actual velocity and the desired velocity, and taking into account the compensation effect caused by the control filter or thrust saturation. This represents the estimate of the total disturbance term in the velocity channel by the extended state observer; This represents the dynamic compensation amount for the perturbation estimation error, used to further correct the error caused by incomplete ESO perturbation estimation; Indicates the compensation state feedback gain; This indicates an auxiliary compensation state used to compensate for the effects of thrust filtering, thrust saturation, or actuator hysteresis.

[0023] S5.2, For the trajectory angle dynamics model and pitch angular velocity subsystem Design separate ESOs to estimate the disturbances. The structural design of the ESOs is as follows:

[0024] ; in, This indicates the trajectory angle of the aircraft in the longitudinal plane underwater. Indicates the rate of change of the track angle; This indicates the desired combined velocity or the reference velocity used in the control design; This represents the modelable nonlinear terms in the track angle channel, which mainly include the deterministic hydrodynamic effects caused by the coupling of velocity, track angle, and pitch angular velocity. Indicates pitch angle The equivalent influence coefficient on the rate of change of track angle; Indicates elevator deflection angle Equivalent control gain for the rate of change of track angle; This represents the equivalent external disturbance and unmodeled dynamics in the track angle channel.

[0025] This represents the nonlinear dynamics terms that can be modeled in the pitch angular velocity channel, mainly including the effects of hydrodynamic torque, added mass, Coriolis force, damping, and attitude coupling on pitch motion; Indicates elevator deflection angle The equivalent control gain for pitch acceleration; This represents the equivalent external disturbance and unmodeled dynamics in the pitch angular velocity channel.

[0026] Indicates the track angle Observed or estimated values; Indicates the total disturbance of the track angle channel The estimated value; This represents the observer gain of the track angle spread state observer, and is usually taken as a positive value; Indicates the error in track angle observation; Represents pitch angular velocity Observed or estimated values; Represents the total disturbance of the pitch angular velocity channel. The estimated value; This represents the observer gain of the pitch angular velocity extended state observer, and is usually taken as a positive value; This indicates the observation error of pitch angular velocity, usually corresponding to Compared with actual pitch angular velocity Deviation between; Construct a control filter for pitch angular velocity commands elevator angle command The filtering process is designed as follows: ; in, This indicates a virtual pitch rate command that is not processed by the filtered wave. This indicates the pitch rate command after processing by the control filter; This represents the auxiliary state variables of the filter. This indicates the pitch rate command for the unfiltered pitch angle. The result after applying amplitude constraints; Indicates the internal variable The result after applying rate constraints; This indicates the maximum permissible pitch rate command amplitude. This indicates the maximum permissible rate of change of the pitch angular velocity command. This filter is used to ensure that the pitch angular velocity command that ultimately enters the control law meets the amplitude and rate constraints of the actuator.

[0027] ; in, This indicates the elevator deflection angle command without filtering the wave. This indicates the executable elevator deflection angle command after processing by the control filter. This represents the time derivative of the elevator deflection command after filtering. Represents the auxiliary state variables of the filter; This represents the result after limiting the amplitude of the unfiltered elevator deflection command; Represents the internal variables of the filter The result after rate limiting; Indicates the maximum allowable amplitude of the elevator deflection angle; This indicates the maximum permissible rate of change of the elevator deflection angle. This filter is used to ensure that elevator control commands meet the amplitude and rate constraints of the actuator.

[0028] Based on ESO, an inverse stepping controller is designed, and the virtual control law and adaptive law of the elevator are obtained: ; in, This represents the equivalent control gain of the elevator deflection angle on the pitch acceleration. This represents the pitch angular velocity error feedback gain, and ; This indicates the corrected pitch rate tracking error; This indicates the corrected pitch tracking error; This represents the total disturbance of the pitch angular velocity channel by the extended state observer. The estimated value; This indicates an auxiliary compensation state used to compensate for the effects of elevator actuator saturation, control filter lag, or command deviation. This represents the compensation state feedback gain, which is usually taken as a positive value.

[0029] Preferably, in step S6, the attitude of the variable-sweep wing transmedium aircraft before exiting the water is controlled, and the specific process includes: S6.1 To further achieve pitch attitude adjustment during the underwater phase, considering the dynamic model of the pitch angle-pitch angular velocity subsystem under underwater cruise conditions, it can be written as: ; in, The modelable nonlinear terms in the pitch angular velocity channel mainly include deterministic dynamic effects caused by factors such as hydrodynamic torque, added mass, damping, and attitude coupling. Indicates elevator deflection angle The equivalent control gain for pitch acceleration; This represents the equivalent external disturbance and unmodeled dynamics in the pitch angular velocity channel.

[0030] S6.2. Following the ESO observer construction method described in S5.2, online estimation is performed on the unknowns in the pitch angle attitude channel, so that hydrodynamics, damping errors, and additional forces can be uniformly represented as the total disturbance in the modeling. Construction of pitch angular velocity observation error The ESO structure is designed as follows: ; in, This indicates that the extended state observer has a certain relationship with the pitch angular velocity. The estimated value; This represents the time derivative of the estimate; This represents the total disturbance of the pitch angular velocity channel by the extended state observer. The estimated value; This represents the time derivative of the disturbance estimate.

[0031] For pitch angular velocity virtual control quantity and elevator deflection virtual control quantity Construct a control filter, design a constrained backstepping controller based on ESO, and select the elevator control law and adaptive law as follows: .

[0032] in, This represents the estimate of the total disturbance in the pitch angular velocity channel by the extended state observer; This represents the residual or compensation error term of the disturbance estimation error in the pitch angular velocity channel; This indicates the pitch rate command after passing through the control filter. The time derivative. This represents the dynamic compensation amount used to compensate for ESO estimation errors; This represents the time derivative of the compensation amount; This represents the adaptive gain of the perturbation estimation error compensation law, and is usually taken as a positive value.

[0033] A control system for a variable-sweep wing cross-medium aircraft based on a hydrodynamic model includes a hydrodynamic analysis module for performing hydrodynamic analysis on the variable-sweep wing cross-medium aircraft. The module includes: constructing a hydrodynamic numerical computation domain, setting boundary conditions, fluid parameters, and a turbulence model, and generating a computational grid for numerical calculations; performing hydrodynamic numerical calculations on the aircraft under steady and unsteady motion conditions to obtain steady-state force and torque data related to longitudinal motion; identifying the hydrodynamic derivative coefficients related to the longitudinal motion of the aircraft based on the steady-state force and torque data and the unsteady force and torque time history data, and constructing the hydrodynamic parameter set required for the longitudinal dynamics model. The model establishment and control problem abstraction module is used for the establishment and control of mathematical models of variable-sweep wing cross-medium aircraft, including establishing the mathematical model of the variable-sweep wing cross-medium aircraft and mathematically abstracting the control problem of the variable-sweep wing cross-medium aircraft. The design module is used for controller design. It addresses the issues of large pitch angles, poor attitude, and instability in the underwater cruise and pre-emergence phases of variable-sweep wing transmedium aircraft. It designs an extended state observer (ESO) to observe disturbances and nonlinearities of the model. Based on this, an inverse stepping controller is designed to control the attitude of the variable-sweep wing transmedium aircraft, enabling it to cruise or emerge stably.

[0034] A control device for a variable-sweep wing transmedium aircraft based on a hydrodynamic model includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a method for rapid analysis of the underwater hydrodynamic characteristics of the variable-sweep wing transmedium aircraft, as well as a control method for the underwater cruise and pre-surface-out stages.

[0035] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements a method for rapid analysis of the underwater hydrodynamic characteristics of a variable-sweep wing transmedium aircraft, as well as a method for control during underwater cruise and pre-surface stages.

[0036] Compared with existing methods and devices for analyzing and controlling the hydrodynamic characteristics of variable-sweep wing transmedium aircraft, the present invention has the following advantages: 1. The method and device for hydrodynamic characteristic analysis and control of variable-sweep wing transmedium aircraft adopt a combination of steady and unsteady hydrodynamic numerical analysis in the acquisition of underwater longitudinal motion-related parameters of the variable-sweep wing transmedium aircraft. By constructing a hydrodynamic calculation model in multiphysics simulation and computational fluid dynamics software, the steady-state force, torque and unsteady response data of the aircraft under different operating conditions are obtained. Furthermore, the hydrodynamic derivative coefficients related to longitudinal motion are identified, and a longitudinal dynamic model suitable for control design is established, thereby improving the efficiency of underwater hydrodynamic analysis and modeling of variable-sweep wing transmedium aircraft.

[0037] 2. The hydrodynamic characteristics analysis and control method and device of the variable-sweep wing transmedium aircraft, by adopting an extended state observer in the control aspect, performs online observation and estimation of external disturbances, model uncertainties and unmodeled dynamics in the underwater cruise and pre-emergence stages of the aircraft. Compared with the processing method that relies on complex learning models or a large amount of prior information, it has the characteristics of clear structure, convenient implementation and low computational burden, which is conducive to improving the real-time performance and engineering application efficiency of the control system.

[0038] 3. The hydrodynamic characteristics analysis and control method and device of the variable-sweep wing cross-medium aircraft adopts a backstepping control strategy based on an extended state observer to achieve constant speed and depth control during the underwater cruise phase and attitude-velocity coordination control before the aircraft emerges from the water. This enables the aircraft to maintain good navigation stability in complex underwater environments and complete the transition before emerging from the water with a relatively stable pitch attitude, thereby improving the stability and reliability of the cross-medium process. Attached Figure Description

[0039] Figure 1 This is a flowchart of an embodiment of the hydrodynamic analysis and attitude stabilization control of the variable-sweep wing aircraft of the present invention; Figure 2 This is a simplified underwater model diagram of the variable-sweep wing aircraft of this invention; Figure 3 This is a background and transition mesh effect diagram of the variable sweep wing aircraft of this invention; Figure 4 This is a rendering of the underwater longitudinal cross-sectional grid of the variable-sweep wing aircraft of this invention; Figure 5 This invention relates to the grid effect of the transverse cross section of the wing of the variable sweep wing aircraft. Figure 6 This invention describes the lateral cross-sectional grid effect of the rudder of the variable-sweep wing aircraft. Figure 7 This is a graph showing the variation of vertical force and pitching moment at different frequencies of pure heave motion when V = 1.5 m / s, based on the numerical calculation of pure heave motion in this invention. Figure 8This is a graph showing the variation of vertical force and pitching moment at different frequencies of pure heave motion when V = 2.0 m / s, based on the numerical calculation of pure heave motion in this invention. Figure 9 This is a graph showing the variation of vertical force and pitch moment at different frequencies of pure pitch motion when V = 1.5 m / s, based on the numerical calculation of pure pitch motion in this invention. Figure 10 This is a graph showing the variation of vertical force and pitch moment at different frequencies of pure pitch motion when V = 2m / s, based on the numerical calculation of pure pitch motion in this invention. Figure 11 This is a depth tracking error curve of the underwater cruise phase controller of the variable-sweep wing aircraft of the present invention. Figure 12 This is a speed tracking error curve of the controller for the underwater cruise phase of the variable-sweep wing aircraft of this invention; Figure 13 This is a diagram illustrating the ESO disturbance estimation effect of the underwater cruise phase of the variable-sweep wing aircraft of this invention. Figure 14 This is a pitch angle tracking curve of the variable sweep wing aircraft before it emerges from the water. Figure 15 This is a diagram showing the disturbance observation and system input for the variable-sweep wing aircraft before it emerges from the water. Detailed Implementation

[0040] The technical solution of the present invention will be clearly and completely described below with reference to preferred embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. 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.

[0041] like Figure 1 As shown, the hydrodynamic characteristics analysis and control method of a variable-sweep wing cross-medium aircraft includes the following steps: S1. Modeling stage of the variable-sweep wing cross-medium aircraft: Obtain the geometric model, structural parameters, shape parameters, and preset motion condition parameters of the variable-sweep wing cross-medium aircraft during underwater navigation, and perform equivalent simplification on the model. Then, model the aircraft in 3D modeling software. Based on the 3D geometric model, perform simulation and computational fluid dynamics using the STAR multiphysics simulation and computational fluid dynamics software. In the CCM+ simulation software, a hydrodynamic numerical computation domain is constructed, inlet boundary, outlet boundary, external field boundary and wall boundary are set, a turbulence model is selected and a computational grid is generated; S2. Steady hydrodynamic analysis stage of variable sweep wing transmedium aircraft: The hydrodynamic numerical solution of the aircraft is performed under steady motion conditions to obtain steady-state force and torque data related to longitudinal motion, and the data is fitted to obtain hydrodynamic coefficients. S3. Unsteady hydrodynamic analysis stage of variable sweep wing transmedium aircraft: The hydrodynamic numerical solution of the aircraft is performed under unsteady motion conditions to obtain unsteady force and torque data related to longitudinal motion and to fit the data to obtain hydrodynamic coefficients. S4. Mathematical Model Establishment and Control Problem Abstraction Stage of Variable-Sweep Wing Trans-medium Aircraft: Establish the mathematical model of the variable-sweep wing trans-medium aircraft and perform mathematical abstraction on the control problem of the variable-sweep wing trans-medium aircraft. S5. Underwater cruise control phase: During the underwater cruise phase, with the desired cruise speed and desired cruise depth as control targets, a coordinated control law for the thruster thrust and tail control surface deflection angle is designed to achieve constant speed and constant depth control. S6. Pre-emergence Attitude Control Stage: In the pre-emergence stage, the control objectives are switched to pitch angle tracking, pitch rate suppression, and vertical velocity suppression to achieve coordinated attitude-velocity control, enabling the aircraft to traverse the free surface with a stable attitude. Based on step S1, the variable-sweep wing cross-medium aircraft is modeled in 3D modeling software and simulated in the multiphysics simulation and computational fluid dynamics software STAR. The specific steps for setting up and meshing hydrodynamic numerical simulations in CCM+ include: S1.1 The aircraft is modeled in 3D modeling software. The fuselage adopts an axisymmetric arrangement of "front dome - middle cylinder - rear small dome". The middle cylinder section is about 825 mm long and the cabin radius is 55 mm. The front end is designed as a spherical dome that smoothly transitions with the nose. The tail end adopts a smaller dome to reduce unnecessary drainage volume. At the same time, in order to ensure that the horizontal tail and elevator have sufficient lever arm, a slender tail boom with a length of about 0.75 m is attached to the tail end.

[0042] refer to Figure 2 S1.2. During the underwater navigation phase, the wings of the variable-sweep wing transmedium aircraft are in a fully retracted state, resulting in a very small lift surface area and limited impact on the overall force. Based on this, the wing section was simplified: its volume influence and connecting transition structures were retained, and the actual wing was replaced with a rectangular flat plate structure. The simplified underwater model of the variable-sweep wing transmedium aircraft is shown below. Figure 2 As shown.

[0043] refer to Figure 3 , Figure 4 , Figure 5 and Figure 6S1.3. The simplified model is imported into STAR-CCM+ to construct a k-ω SST turbulence model to solve the Reynolds-averaged Navier-Stokes equations in a closed loop. Mesh generation is performed using a partitioned overlapping network. During mesh generation, the cut-body mesh generator of STAR-CCM+ software is used for mesh generation. In order to improve the smoothness of the geometric surface and the calculation accuracy, the surface of the key area is reconstructed. Prismatic layer meshes are arranged on the fuselage and tail fin walls to accurately analyze the boundary layer flow and ensure the effectiveness of the turbulence model in the near-wall region. The computational domain is taken as 8-10 times the characteristic length of the aircraft to eliminate boundary reflections and inlet interference.

[0044] According to step S2, the specific steps for numerically solving the hydrodynamics of a variable-sweep wing aircraft under steady motion conditions include: S2.1 Numerical calculations were performed on the straight-line motion in the x-direction, with the nose facing the oncoming flow. Simulations of different flight speeds were achieved by applying different inlet velocity boundary conditions. The k-ω SST model was used as the turbulence model, and a pressure-based steady-state solver was selected. A second-order upwind discretization scheme was used, and the SIMPLE method was employed as the pressure-velocity coupling algorithm. The inlet velocities were set as follows: and The final steady-state drag results at various speeds are shown in Table 1: Table 1 Numerical results of the aircraft's straight-line flight in the x-direction.

[0045] According to the fitting equation The least-squares fit was performed on the calculated data to obtain the dimensionless drag coefficient. .

[0046] S2.2. Perform numerical calculations on the straight-line motion in the z-direction, rotating the entire aircraft model 90 degrees along the x-axis. Orient the flow path towards the top boundary of the computational domain, setting the top boundary as the velocity inlet and the bottom boundary as the pressure outlet, while maintaining symmetrical boundaries for the other four side boundaries. The turbulence model, discretization scheme, and convergence criterion remain consistent with step S2.1. Five different inlet velocity conditions are set: , , , , The steady-state drag results at various speeds after numerical calculation convergence are shown in Table 2.

[0047] Table 2 Numerical results of the aircraft's straight-line flight in the z-direction.

[0048] According to the resistance formula The least-squares fit was performed on the calculated data to obtain the dimensionless drag coefficient. .

[0049] S2.3 Numerical calculation of vertical plane oblique motion, rotating the aircraft around the body axis y-axis by a certain angle (angle of attack). To create different inflow directions, the influence of angle-of-attack variation on hydrodynamic characteristics in the vertical plane was studied. The angle-of-attack range was set to... Every Take one operating condition and set the incoming flow velocity to... and The entry conditions are consistent with those in step S1. The calculated values ​​for different angles of attack at different speeds are shown in Table 3. The speeds are shown in Table 4.

[0050] Table 3 Calculated values ​​of different angles of attack for different speeds

[0051] Table 4 Calculated values ​​of different angles of attack for different speeds

[0052] Least square linear fitting was performed on the vertical force and pitching moment data under different speed conditions to obtain dimensionless hydrodynamic parameters, as shown in Table 5.

[0053] Table 5 Vertical Plane Hydrodynamic Coefficients

[0054] According to step S3, the specific steps for numerically solving the hydrodynamics of a variable-sweep wing aircraft under unsteady motion conditions include: S3.1 Calculate the hydrodynamic coefficients in the longitudinal and transverse directions to obtain the hydrodynamic coefficients of the added mass of the variable-sweep wing transverse aircraft in the longitudinal and transverse directions. The calculation employed dynamic mesh technology and a custom acceleration function was written in STAR-CCM+ to simulate the unsteady force characteristics of the aircraft under actual longitudinal acceleration and deceleration during uniform acceleration and deceleration along the x-direction in the flow field. The dimensionless results of the added mass coefficients in the longitudinal and transverse directions were ultimately obtained. .

[0055] refer to Figure 7 and Figure 8 S3.2. Perform numerical calculations of pure heave motion to obtain the unsteady hydrodynamic coefficients of the variable-sweep wing transmedium aircraft in the vertical plane, including the vertical velocity correlation coefficient. Pitch speed correlation coefficient and the coefficient of inertia related to vertical acceleration. and The calculations were performed using STAR-CCM+ software for numerical simulation, employing dynamic mesh technology combined with a custom-designed function to control the heave and sway motion of the aircraft. To ensure flow field stability and computational accuracy, a turbulence model was selected. Model. The heave amplitude is set to a = 0.04 m, and the inflow velocities are set to V = 1.5 m / s and V = 2.0 m / s respectively. The heave frequency... Hz was set to 0.2, 0.4, 0.6, 0.8, and 1.0 Hz respectively. The calculation time for each frequency was 25 s. After selecting 3 complete cycles, the average amplitude was taken. The changes in vertical force and pitching moment of pure heave motion at different frequencies were calculated when V=1.5 m / s and when V=2.0 m / s. Curve fitting was performed on the data to obtain the dimensionless heave hydrodynamic coefficients, as shown in Table 6 below.

[0056] Table 6 Dimensionless Heating and Sinking Hydrodynamic Coefficients

[0057] refer to Figure 9 and Figure 10 S3.3, Perform numerical calculations of pitch motion to obtain the hydrodynamic derivative coefficients in the pitch direction within the vertical plane of the aircraft. , , and When simulating pure pitch motion of an aircraft in STAR-CCM+, the pitch amplitude is taken as... The inlet velocities are set to V = 1.5 m / s and V = 2.0 m / s respectively, and the angular frequency is taken as... Each set of calculations ran for approximately 25 seconds. Monitoring results from three cycles after stabilization were selected to obtain the changes in vertical force and pitching moment at different frequencies of pure pitching motion when V = 1.5 m / s, and the changes in vertical force and pitching moment at different frequencies of pure pitching motion when V = 2 m / s. Curve fitting was performed on the data to obtain the dimensionless heave hydrodynamic coefficients shown in Table 7 below.

[0058] Table 7 Calculation results of hydrodynamic coefficients for pure pitch motion

[0059] According to step S4, the mathematical model of the variable-sweep wing trans-medium aircraft is established, and the control problem of the variable-sweep wing trans-medium aircraft is mathematically abstracted. The specific process includes: S4.1 Based on the steady and unsteady hydrodynamic derivative coefficients identified in steps S2 and S3, select coefficient terms related to longitudinal motion, ignore lateral coupling terms that have little impact on longitudinal motion, retain only coupling terms related to speed, heave and pitch, and calculate the complete longitudinal coupling hydrodynamic coefficients based on the equivalence relationship between the single-degree-of-freedom unsteady motion results and the longitudinal coupling coefficients.

[0060] S4.2 Define the position and attitude of the aircraft in the Earth-fixed system. , The linear velocity and angular velocity vectors of the aircraft in the body axis are respectively , The rate of change of the aircraft's position in the Earth-fixed coordinate system can be obtained by transforming the body axis velocity through the attitude rotation matrix. The relationship between the rate of change of Euler angles and the angular velocity of the body axis can be written as: .

[0061] Variable-sweep wing aircraft exhibit structural characteristics symmetrical about the longitudinal plane underwater. For ease of subsequent dynamic modeling and control design, only considering... In planar motion, the lateral velocity, roll, and yaw of the aircraft can be ignored, i.e. , , The kinematic relationships of the variable-sweep wing aircraft in the underwater longitudinal plane are obtained as follows: ; in, Indicates the spacecraft in the Earth-fixed coordinate system Position in direction Indicates the spacecraft in the Earth-fixed coordinate system Position in the direction.

[0062] S4.3 The underwater forces acting on the variable-sweep wing aircraft are analyzed, mainly including gravity, buoyancy, propulsion, and hydrodynamic forces. In volume coordinates, the resultant force of gravity and buoyancy can be expressed as: ; in, This indicates that the resultant force of gravity and buoyancy lies in the body axis system. Components in direction; This indicates that the resultant force of gravity and buoyancy lies in the body axis system. Components in direction; The force of gravity acting on an aircraft is usually expressed as: ; This indicates the buoyancy force acting on the aircraft.

[0063] The thrust model of a propeller in water can be expressed as: ; in, This indicates the thrust generated by an underwater propeller. It represents the propeller thrust coefficient, which is usually a dimensionless parameter. Its magnitude is related to the propeller geometry, blade parameters and operating conditions. Indicates the density of the water medium; The propeller speed is usually expressed in units of 1000 rpm. ; This indicates the diameter of the propeller.

[0064] The hydrodynamics of the longitudinal motion of a variable-sweep wing aircraft can be expressed as: The expression for inertial hydrodynamic forces in the longitudinal plane can be written as: ; in, This represents the vector of inertial hydrodynamic / added mass terms caused by acceleration during the underwater motion of an aircraft. Indicates body axis system Inertial hydrodynamic components in the direction; Indicates body axis system Inertial hydrodynamic components in the direction; Indicates the body axis system The inertial hydrodynamic torque component of the axis.

[0065] Near the equilibrium point, viscous hydrodynamics can be expressed as a function of velocity and angular velocity, i.e. ; The final longitudinal hydrodynamic force can be expressed as: ; in, For the mass of the aircraft, The pitch inertia of the aircraft about the transverse axis of its body axis system; These represent the aircraft's body axis system. linear velocity in the direction, Representing the body axis system The angular velocity of the axis, where It is the pitch angular velocity; These are the time derivatives of the forward velocity, vertical velocity, and pitch angular velocity, respectively. The pitch angle is taken at the vehicle's center of mass. The axis points towards the front of the fuselage. The axis points to the right. The axis points downwards.

[0066] Here are the dimensionless hydrodynamic derivative coefficients, where The class coefficient corresponds to the forward hydrodynamic force along the body axis. The coefficient corresponds to the vertical hydrodynamic force of the body axis. The class coefficients correspond to the pitching hydrodynamic moment; the subscripts indicate the motion variables or coupling variables corresponding to the hydrodynamic term. For example, This represents the forward hydrodynamic coefficient caused by forward acceleration. This represents the forward hydrodynamic coefficient caused by the coupling term. This represents the vertical hydrodynamic coefficient caused by vertical acceleration. Indicates by The vertical hydrodynamic coefficient caused by the coupling term, This represents the pitch hydrodynamic moment coefficient caused by pitch angular acceleration. Indicates by The pitching moment coefficient caused by the coupling term.

[0067] The density of the water medium, Let be the characteristic length of the aircraft. In the formula, each hydrodynamic term is multiplied by according to the dimensionless transformation rule. and different levels This is used to convert dimensionless hydrodynamic derivatives into dimensional forces or torques. Generally, it includes... The item reflects the added mass or added inertia effect; containing The terms reflect steady or quasi-steady hydrodynamic effects; including The terms of equal product reflect the nonlinear coupling hydrodynamic effects between motions with different degrees of freedom.

[0068] and These represent the propulsion system on the body axis. and Thrust component in the direction, This indicates the applied control torque or equivalent pitch control torque acting on the pitch channel; S4.4 Mathematical abstraction of the underwater cruise control problem, considering the control of speed and depth of the aircraft during the underwater cruise phase, mainly targeting... and Then the mathematical model for control can be written as: ; in, Indicates the spacecraft in the Earth-fixed coordinate system Position in direction Indicates the rate of change of the vertical position of the Earth-fixed system; This represents the equivalent mass of the longitudinal velocity channel. This refers to the control thrust acting on the longitudinal velocity channel, which is usually generated by the underwater propeller during the underwater cruise phase. , This is a modelable hydrodynamic nonlinear term, and , This represents the external disturbances and dynamics during the underwater phase that are modeled. This represents the equivalent moment of inertia of the pitch channel. This represents the equivalent control torque acting on the pitch channel, typically generated by the deflection of the tail elevator. By adjusting the propeller thrust, the longitudinal speed is increased. It can gradually approach the desired speed At the same time, adjust the elevator deflection angle. Suppressing vertical velocity and adjusting pitch attitude to increase operating depth It can gradually approach the desired depth The underwater cruise control problem is described as follows: ; in, Indicates time, Indicates that the aircraft is in The forward velocity of the body axis at any given moment, i.e., the underwater cruising speed; Indicates the desired cruising speed; Indicates that the aircraft is in The depth of operation at any given moment This indicates the desired cruising depth.

[0069] Similarly, the attitude control before emerging from the water is mathematically abstracted. Following the mathematical model of underwater cruise control, the pitch angle of the aircraft is gradually brought closer to the desired small upward pitch angle by adjusting the tail elevator. This involves suppressing pitch velocity to smooth attitude changes, and simultaneously eliminating vertical velocity to gradually align the aircraft's velocity direction with its longitudinal axis, thus enabling a smooth ascent along a pre-defined straight path. In essence, the attitude control problem before water exit can be summarized as follows: ; in, Indicates that the aircraft is in The pitch angle at any given moment; This indicates the desired pitch angle, which is usually a small upward pitch angle set before the vessel emerges from the water. Indicates that the aircraft is in The pitch angular velocity at any given moment; Indicates that the aircraft is in At all times along the body axis Vertical velocity in the direction of travel.

[0070] According to step S5, the specific process of controlling the underwater cruise phase of the variable-sweep wing aircraft includes: S5.1. For the longitudinal velocity subsystem during the underwater cruise phase, considering the parameter uncertainties in the hydrodynamic model and the influence of free flow field disturbances, a constrained backstepping velocity controller based on ESO is designed under disturbance compensation and actuator constraints to achieve longitudinal velocity response to the desired command. The precise tracking process includes: S5.1.1, The longitudinal velocity subsystem during the underwater cruise phase is represented as... For the uncertain disturbance terms ,structure Perform real-time estimation and define observation error. Then the velocity subsystem The structural design is as follows: ; in, Used to estimate longitudinal velocity , Used to estimate the disturbance term; This represents a nonlinear error feedback function used for individual tragic observation errors. The perturbation estimate is corrected, with 0.5 representing the convergence order parameter of the nonlinear function. This is a threshold parameter for the small error range, used to avoid excessive feedback when the error is close to zero.

[0071] S5.1.2 Virtual thrust command derived by backstepping method The thrust cannot be directly input to the propeller actuator; a control filter needs to be built between the virtual thrust command and the actual thrust. First, the... Introduce a second-order filter with amplitude and rate constraints, and define the filter's internal variables: Based on this, the control filter can be expressed as the following state equation: ; in, This indicates the actual thrust command after processing by the control filter. This indicates the rate of change of the thrust command after filtering; This represents the auxiliary state variable controlling the filter, which can also be understood as the thrust rate of change state inside the filter; This represents the time derivative of the auxiliary state variable. This indicates the damping ratio of the underwater velocity channel control filter; This indicates the inherent frequency of the underwater velocity channel control filter; Indicates the internal variables of the filter; This represents the thrust rate limiting function, used to constrain the rate of change of thrust command; This represents the output of the filter's internal variables after rate limiting.

[0072] S5.1.3 Design an ESO-based backstepping controller. First, define the speed tracking error as... If based directly on error Backstepping control can easily lead to error accumulation when the actuator enters the restricted area; therefore, a compensation state is introduced. The corrected error is defined as , Dynamic selection as ,in, This represents the attenuation gain of the compensation state, which is usually taken as a positive value to ensure that the compensation state is bounded and gradually decays. This represents the equivalent gain associated with the thrust filter dynamics or the thrust input channel, used to adjust the impact of thrust command deviation on the compensation state. The intensity of the impact.

[0073] The synthesized disturbance term in the velocity channel can be obtained from the aforementioned constructed ESO. The estimated value is Let the disturbance error be denoted as To further improve the disturbance compensation performance, dynamic variables are introduced. Approaching And define the estimation error .

[0074] Selecting Lyapunov functions Underwater velocity dynamics, considering the effect of the filter, can be written as: ; According to the definition of error, the dynamic correction error can be obtained as follows: ; The disturbance is decomposed into ESO estimates and their errors: Substituting the values, we get: ; Differentiating the Lyapunov function yields: ; To eliminate the disturbance estimation error term, make Convergence, select adaptive law ,therefore, Substituting into the Lyapunov derivative, we get: ; Select virtual thrust command as .

[0075] in, This represents the equivalent control gain between the thrust input and the longitudinal acceleration in the underwater velocity channel; This represents the speed tracking error feedback gain, and is usually taken as a positive value. This represents the corrected longitudinal velocity tracking error, used to characterize the deviation between the actual velocity and the desired velocity, and taking into account the compensation effect caused by the control filter or thrust saturation. This represents the estimate of the total disturbance term in the velocity channel by the extended state observer; This represents the dynamic compensation amount for the perturbation estimation error, used to further correct the error caused by incomplete ESO perturbation estimation; Indicates the compensation state feedback gain; This indicates an auxiliary compensation state used to compensate for the effects of thrust filtering, thrust saturation, or actuator hysteresis.

[0076] S5.2 Design an underwater depth-attitude coordination controller. Explicitly introduce a pitch angle subsystem into the depth control link. By constructing reasonable virtual pitch angle commands, achieve coordinated control of depth adjustment and attitude stability. The specific process includes: S5.2.1 The underwater depth-attitude subsystem is simplified as follows: ; in, Indicates depth, This indicates the trajectory angle of the aircraft in the longitudinal plane underwater. Indicates the rate of change of the track angle; This indicates the desired combined velocity or the reference velocity used in the control design; This represents the modelable nonlinear terms in the track angle channel, which mainly include the deterministic hydrodynamic effects caused by the coupling of velocity, track angle, and pitch angular velocity. Indicates pitch angle The equivalent influence coefficient on the rate of change of track angle; Indicates elevator deflection angle Equivalent control gain for the rate of change of track angle; This represents the equivalent external disturbance and unmodeled dynamics in the track angle channel.

[0077] Design an ESO observer to monitor the track angle disturbance term. The total disturbance is defined by jointly estimating other uncertainties: Let the observation error of ESO be ; The ESO (Electronic Track Angle) is then selected as: ; in, Indicates the track angle Observed or estimated values; Indicates the total disturbance of the track angle channel The estimated value; This represents the observer gain of the track angle spread state observer, and is usually taken as a positive value; This indicates the error in the observation of the track angle.

[0078] S5.2.2 To address the uncertainties and disturbances in the pitch angle dynamics, an extended state observer is designed for estimation. A second ESO is designed using the exact same architecture as the longitudinal velocity ESO in step S5.2.1, to estimate... This total disturbance introduces an error in the pitch angular velocity observation. The ESO structure of the pitch angular velocity subsystem is then taken as follows: ; in, Represents pitch angular velocity Observed or estimated values; Represents the total disturbance of the pitch angular velocity channel. The estimated value; This represents the observer gain of the pitch angular velocity extended state observer, and is usually taken as a positive value; This indicates the observation error of pitch angular velocity, usually corresponding to Compared with actual pitch angular velocity Deviation between; S5.2.3 Constructing a control filter for pitch angular velocity commands elevator angle command The filtering process is designed as follows:

[0079] ; in, This indicates a virtual pitch rate command that is not processed by the filtered wave. This indicates the pitch rate command after processing by the control filter; This represents the auxiliary state variables of the filter. This indicates the pitch rate command for the unfiltered pitch angle. The result after applying amplitude constraints; Indicates the internal variable The result after applying rate constraints; This indicates the maximum permissible pitch rate command amplitude. This indicates the maximum permissible rate of change of the pitch angular velocity command. This filter is used to ensure that the pitch angular velocity command that ultimately enters the control law meets the amplitude and rate constraints of the actuator.

[0080] This indicates the elevator deflection angle command without filtering the wave. This indicates the executable elevator deflection angle command after processing by the control filter. This represents the time derivative of the elevator deflection command after filtering. Represents the auxiliary state variables of the filter; This represents the result after limiting the amplitude of the unfiltered elevator deflection command; Represents the internal variables of the filter The result after rate limiting; Indicates the maximum allowable amplitude of the elevator deflection angle; This indicates the maximum permissible rate of change of the elevator deflection angle. This filter is used to ensure that elevator control commands meet the amplitude and rate constraints of the actuator.

[0081] S5.2.4 Design an ESO-based backstepping controller. First, define the depth tracking error as... Based on the hierarchical structure of backstep control, the track angle, pitch angle, and pitch rate errors are defined sequentially as follows: , , ,in, , and These are the virtual control values ​​for the track angle, the virtual control value for the pitch angle, and the pitch rate command processed by the control filter.

[0082] Choose Lyapunov functions ,right Taking the derivative, Define the track angle error Substituting into the equation yields... The first term in the formula introduces a new error. This needs to be further addressed in the next step of the reverse step design.

[0083] Unknown disturbances and modeling errors are uniformly represented as Then the track angle subsystem can be further simplified to Combining the track angle error, the error dynamics can be derived as follows: ; To further mitigate the impact of ESO estimation errors on stability, a dynamic compensation amount for track angle disturbances is introduced. Used to compensate for the error of the extended state observer, its estimated error is: Construct new Lyapunov functions Its derivative is: ; The virtual control law and adaptive law for the track angle are selected as follows: ; Substituting, we can obtain ; S5.2.5 Construct two compensation variables in the current underwater depth-attitude control structure. , This is used to compensate for the saturation effect of the actuator and the deviation caused by the filter; the corrected error is defined as: ; Based on the corrected error , Lyapunov function for constructing pitch subsystem: Differentiating it, we get: ; A virtual control law for pitch angular velocity can be constructed: ,in The pitch angle control gain is used; to further eliminate pitch rate error and suppress the influence of model uncertainty and external disturbances, pitch rate ESO estimation error is introduced. To further mitigate the impact of ESO estimation errors on stability, a dynamic compensation amount for pitch angular velocity perturbation is introduced. Used to compensate for the error of the extended state observer, the estimated error is: .

[0084] Correcting errors Based on this, a Lyapunov function is constructed that incorporates pitch angular velocity error and ESO estimation error: ,right Differentiation yields: ; The elevator virtual control law and adaptive law are selected as follows: .

[0085] in, This represents the equivalent control gain of the elevator deflection angle on the pitch acceleration. This represents the pitch angular velocity error feedback gain, and ; This indicates the corrected pitch rate tracking error; This indicates the corrected pitch tracking error; This represents the total disturbance of the pitch angular velocity channel by the extended state observer. The estimated value; This indicates an auxiliary compensation state used to compensate for the effects of elevator actuator saturation, control filter lag, or command deviation. This represents the compensation state feedback gain, which is usually taken as a positive value.

[0086] refer to Figure 11 , Figure 12 and Figure 13 S5.3 To verify the effectiveness of the control method, a simulation analysis of the controller during the underwater cruise phase was performed. The initial state of the aircraft was set as follows: initial depth Initial pitch angle Initial flight speed .

[0087] According to step S6, the controller design for the pre-water exit stage of the variable-sweep wing is carried out, and the specific process includes: S6.1 Based on the design process in step S5, to further realize pitch attitude adjustment in the underwater phase, a dynamic model of the pitch angle-pitch angular velocity subsystem of the aircraft under underwater cruise conditions is constructed: ; in, The modelable nonlinear terms in the pitch angular velocity channel mainly include deterministic dynamic effects caused by factors such as hydrodynamic torque, added mass, damping, and attitude coupling. Indicates elevator deflection angle The equivalent control gain for pitch acceleration; This represents the equivalent external disturbance and unmodeled dynamics in the pitch angular velocity channel.

[0088] S6.2. Using the same ESO construction method as in step S5, online estimation of unknowns in the pitch angle attitude channel is performed, unmodeled hydrodynamics, damping errors, and additional forces are uniformly represented as the total disturbance. Construction of pitch angular velocity observation error , for From the estimation, the pitch angular velocity ESO structure can be obtained: ; in, This indicates that the extended state observer has a certain relationship with the pitch angular velocity. The estimated value; This represents the time derivative of the estimate; This represents the total disturbance of the pitch angular velocity channel by the extended state observer. The estimated value; This represents the time derivative of the disturbance estimate.

[0089] The control filters for the virtual control quantities of pitch rate and elevator deflection are constructed in the same way as those in step S5.

[0090] S6.3, define pitch angle error and pitch angular velocity error as... , Introducing dynamic compensation variables , Define the correction error: ; Constructing Lyapunov functions And differentiate it: In order to For negative constant, a virtual control law of pitch angular velocity is introduced: Substituting, we can get .

[0091] To suppress disturbances and ESO estimation errors, a dynamic compensation amount is introduced. Construct the global Lyapunov function: ,right Differentiate, combine with pitch angular velocity dynamics, and substitute into ESO decomposition. After sorting, we get: .

[0092] The final elevator control law and adaptive law are selected as follows: .

[0093] in, This represents the estimate of the total disturbance in the pitch angular velocity channel by the extended state observer; This represents the residual or compensation error term of the disturbance estimation error in the pitch angular velocity channel; This indicates the pitch rate command after passing through the control filter. The time derivative. This represents the dynamic compensation amount used to compensate for ESO estimation errors; This represents the time derivative of the compensation amount; This represents the adaptive gain of the perturbation estimation error compensation law, and is usually taken as a positive value.

[0094] refer to Figure 14 and Figure 15 S6.4 To verify the effectiveness of the proposed control method in the pre-water exit stage, numerical simulation analysis was conducted. The initial state of the aircraft was set as follows: initial pitch angle .

[0095] This invention constructs an underwater hydrodynamic numerical analysis method based on computational fluid dynamics to systematically analyze the longitudinal hydrodynamic characteristics of a variable-sweep wing cross-medium aircraft under steady and unsteady conditions. It obtains steady-state force, torque, and unsteady response data, further identifies hydrodynamic derivative coefficients, and establishes a longitudinal dynamic model for control design. Based on the hydrodynamic analysis and modeling, a unified mathematical abstraction is applied to the underwater cruise control problem and the pre-emergence attitude control problem. For the abstract model, an extended state observer is designed to perform online observation and compensation for external disturbances, model uncertainties, and unmodeled dynamics. Combined with backstepping, a velocity-depth coordinated controller and an attitude-velocity coordinated controller are constructed, enabling the variable-sweep wing cross-medium aircraft to achieve constant velocity and depth control during the underwater cruise phase and effectively suppress pitch attitude fluctuations before emergence, allowing for a stable approach and smooth passage across the free surface. This method has a clear structure, high analytical efficiency, and strong anti-disturbance capability, and has significant engineering application value for improving the underwater navigation stability and cross-medium transition performance of variable-sweep wing cross-medium aircraft.

Claims

1. A method for analyzing and controlling the hydrodynamic characteristics of a variable-sweep wing transmedium aircraft, characterized in that, Includes the following steps: S1. Modeling stage of variable-sweep wing cross-medium aircraft: Obtain the geometric model, structural parameters, shape parameters and preset motion condition parameters of the variable-sweep wing cross-medium aircraft during the underwater navigation stage, and perform equivalent simplification processing on the model. Then, model it in 3D modeling software. Based on the three-dimensional geometric model, a hydrodynamic numerical computation domain is constructed in multiphysics simulation and computational fluid dynamics software and simulation software. Inlet boundary, outlet boundary, external field boundary and wall boundary are set, turbulence model is selected and computational mesh is generated. S2. Steady hydrodynamic analysis stage of variable sweep wing transmedium aircraft: The hydrodynamic numerical solution of the aircraft is performed under steady motion conditions to obtain steady-state force and torque data related to longitudinal motion, and the data is fitted to obtain hydrodynamic coefficients. S3. Unsteady hydrodynamic analysis stage of variable sweep wing transmedium aircraft: The hydrodynamic numerical solution of the aircraft is performed under unsteady motion conditions to obtain unsteady force and torque data related to longitudinal motion and to fit the data to obtain hydrodynamic coefficients. S4. Mathematical Model Establishment and Control Problem Abstraction Stage of Variable-Sweep Wing Trans-medium Aircraft: Establish the mathematical model of the variable-sweep wing trans-medium aircraft and perform mathematical abstraction on the control problem of the variable-sweep wing trans-medium aircraft. S5. Underwater cruise control phase: During the underwater cruise phase, with the desired cruise speed and desired cruise depth as control targets, a coordinated control law for the thruster thrust and tail control surface deflection angle is designed to achieve constant speed and constant depth control. S6. Attitude control stage before water exit: In the stage before water exit, the control target is switched to pitch angle tracking, pitch angular velocity suppression and vertical velocity suppression to achieve coordinated attitude and velocity control, so that the aircraft can pass through the free liquid surface in a stable attitude.

2. The method for hydrodynamic characteristic analysis and control of a variable-sweep wing transmedium aircraft according to claim 1, characterized in that: In step S1, the variable-sweep wing transmedium aircraft is modeled in three dimensions and its computational mesh is generated. The specific process includes: S1.

1. Establish an underwater three-dimensional geometric model of the variable-sweep wing cross-medium aircraft in three-dimensional modeling software. According to the requirements of underwater longitudinal motion analysis, set the working parameters of the three-dimensional geometric model. The working parameters include at least the sweep angle, the body attitude angle, the reference speed, and the immersion state. S1.2 The three-dimensional geometric model is simplified, retaining its volume influence and connection transition structure. The actual wing is replaced with an equal-length cuboid plate structure. The simplified three-dimensional geometric model is imported into multiphysics simulation and computational fluid dynamics software to generate a computational model for hydrodynamic analysis. S1.

3. Establish an external flow field computational domain around the underwater analysis model, and set the inlet boundary, outlet boundary, symmetry plane or far-field boundary, and wall boundary. Set the incoming flow medium as water, and input the corresponding fluid density, dynamic viscosity, and gravity parameters. Select SST. Turbulence model; S1.

4. The computational domain is meshed using a structured mesh based on cut bodies, and local meshing is performed on the surface of the fuselage, the leading and trailing edges of the wings, the area near the tail, and the wake region. The computational domain range is 8–10 times the characteristic length of the aircraft. The boundary layer mesh in the near-wall region is controlled to meet the near-wall resolution requirements of turbulence solutions. Mesh independence is checked to obtain the final computational mesh that meets the accuracy requirements.

3. The method for hydrodynamic characteristic analysis and control of a variable-sweep wing transmedium aircraft according to claim 1, characterized in that, In step S2, numerical calculations are performed on the steady-state hydrodynamics of the variable-sweep wing transmedium aircraft. The specific process includes: S3.1 Set the aircraft to a straight-line flight condition along the body axis x direction and obtain longitudinal drag data under different speed conditions; S3.

2. Set the aircraft to a straight-ahead flight condition along the body axis z-direction, and rotate the aircraft nose 90 degrees. It also changes the mainstream direction to achieve numerical simulation of the vertical ascent or descent process and obtains vertical force data under different vertical velocity conditions; S3.3 Set the aircraft to slant flight in the longitudinal plane. By introducing a certain angle of attack on the basis of horizontal straight flight, the flow field has both horizontal and vertical velocity components, and obtain the vertical force and pitch moment data under different conditions. S3.

4. Fit the obtained steady force and moment data to obtain the steady hydrodynamic derivatives related to longitudinal straight and oblique navigation.

4. The method and apparatus for hydrodynamic characteristic analysis and control of a variable-sweep wing transmedium aircraft according to claim 1, characterized in that, In step S3, numerical calculations are performed on the unsteady hydrodynamics of the variable-sweep wing transmedium aircraft. The specific process includes: S4.

1. Using dynamic mesh technology, set the pure heave motion of the aircraft in the longitudinal plane, so that the aircraft moves periodically along the vertical direction at a preset frequency and preset amplitude, and record the time domain response data of the vertical force and pitch moment of the aircraft during the pure heave motion. S4.

2. Using dynamic mesh technology, set the pure pitch motion of the aircraft around the lateral axis, so that the aircraft performs periodic pitch oscillations at a preset frequency and preset amplitude, and record the time domain response data of the vertical force and pitch moment on the aircraft during the pure pitch motion. S4.3 Fit the unsteady time-domain response data, identify dimensionless hydrodynamic coefficients related to vertical velocity and vertical acceleration based on pure heave motion data, and identify dimensionless hydrodynamic coefficients related to pitch angular velocity and pitch angular acceleration based on pure pitch motion data.

5. The method for hydrodynamic characteristic analysis and control of a variable-sweep wing transmedium aircraft according to claim 1, characterized in that, In step S4, a dynamic model of the variable-sweep wing transmedium aircraft was constructed and the control problem was mathematically abstracted. The specific process includes: S4.1 Based on the identified steady and unsteady hydrodynamic derivative coefficients, select the coefficient terms related to longitudinal motion, ignore the lateral coupling terms that have little impact on longitudinal motion, and retain only the coupling terms related to speed, heave and pitch. Based on the equivalence relationship between the single-degree-of-freedom unsteady motion results and the longitudinal coupling coefficient, calculate the complete longitudinal coupling hydrodynamic coefficients. S4.2 The underwater external forces and moments acting on the variable-sweep wing transmedium aircraft are analyzed. These external forces mainly include gravity, buoyancy, propulsion, and hydrodynamic forces. The underwater longitudinal dynamic equations of the variable-sweep wing transmedium aircraft are obtained as follows: ； S4.3 Mathematical abstraction of the underwater cruise control problem, considering the control of speed and depth of the aircraft during the underwater cruise phase, mainly targeting... and Then the mathematical model for control can be written as: ； in, , This is a modelable hydrodynamic nonlinear term, and , This represents the external disturbances and modeling dynamics during the underwater phase, and the longitudinal velocity is adjusted by regulating the propeller thrust. It can gradually approach the desired speed At the same time, adjust the elevator deflection angle. Suppressing vertical velocity and adjusting pitch attitude to increase operating depth It can gradually approach the desired depth The underwater cruise control problem is described as follows: ； Similarly, the attitude control before emerging from the water is mathematically abstracted. Following the mathematical model of underwater cruise control, the pitch angle of the aircraft is gradually brought closer to the desired small upward pitch angle by adjusting the tail elevator. This involves suppressing pitch velocity to smooth attitude changes, and simultaneously eliminating vertical velocity to gradually align the aircraft's velocity direction with its longitudinal axis, thus enabling a smooth ascent along a pre-defined straight path. In essence, the attitude control problem before water exit can be summarized as follows: 。 6. The method for hydrodynamic characteristic analysis and control of a variable-sweep wing transmedium aircraft according to claim 1, characterized in that, In step S5, a speed and depth controller for the underwater cruising phase is designed using the backstepping method. The specific process includes: S5.1, For the longitudinal velocity subsystem of the aircraft Uncertain disturbance term in Construct an extended state observer For real-time estimation, the structure is designed as follows: ； in, Used to estimate longitudinal velocity , Used to estimate the disturbance term; In virtual thrust Compared with actual thrust input A control filter is constructed between the two to impose dual constraints on its amplitude and rate. The control filter can be expressed as a state equation: ； The virtual thrust command obtained by designing a backstepping controller based on ESO is as follows: ； S5.2, For the trajectory angle dynamics model and pitch angular velocity subsystem Design separate ESOs to estimate the disturbances. The structural design of the ESOs is as follows: ； Construct a control filter for pitch angular velocity commands elevator angle command The filtering process is designed as follows: ； Based on ESO, an inverse stepping controller is designed, and the virtual control law and adaptive law of the elevator are obtained: 。 7. The control method for a variable-sweep wing transmedium aircraft based on a hydrodynamic model according to claim 6, characterized in that, In step S6, the attitude of the variable-sweep wing transmedium vehicle before it exits the water is controlled. The specific process includes: S6.1 To further achieve pitch attitude adjustment during the underwater phase, considering the dynamic model of the pitch angle-pitch angular velocity subsystem under underwater cruise conditions, it can be written as: ； S6.

2. Following the ESO observer construction method described in S5.2, online estimation is performed on the unknowns in the pitch angle attitude channel, so that hydrodynamics, damping errors, and additional forces can be uniformly represented as the total disturbance in the modeling. Construction of pitch angular velocity observation error The ESO structure is designed as follows: ； For pitch angular velocity virtual control quantity and elevator deflection virtual control quantity Construct a control filter, design a constrained backstepping controller based on ESO, and select the elevator control law and adaptive law as follows: 。 8. A control system for a variable-sweep wing transmedium aircraft based on a hydrodynamic model, used to execute the method described in any one of claims 1-7, characterized in that: The system includes a hydrodynamic analysis module for performing hydrodynamic analysis on a variable-sweep wing transmedium aircraft. This includes: constructing a hydrodynamic numerical computation domain, setting boundary conditions, fluid parameters, and a turbulence model, and generating a computational grid for numerical calculations; performing hydrodynamic numerical calculations on the aircraft under steady and unsteady motion conditions to obtain steady-state force and torque data related to longitudinal motion; identifying the hydrodynamic derivative coefficients related to the longitudinal motion of the aircraft based on the steady-state force and torque data and the unsteady force and torque time history data, and constructing the hydrodynamic parameter set required for the longitudinal dynamics model. The model establishment and control problem abstraction module is used for the establishment and control of mathematical models of variable-sweep wing cross-medium aircraft, including establishing the mathematical model of the variable-sweep wing cross-medium aircraft and mathematically abstracting the control problem of the variable-sweep wing cross-medium aircraft. The design module is used for controller design. It addresses the issues of large pitch angles, poor attitude, and instability in the underwater cruise and pre-emergence phases of variable-sweep wing transmedium aircraft. It designs an extended state observer (ESO) to observe disturbances and nonlinearities of the model. Based on this, an inverse stepping controller is designed to control the attitude of the variable-sweep wing transmedium aircraft, enabling it to cruise or emerge stably.

9. A control device for a variable-sweep wing transmedium aircraft based on a hydrodynamic model, used to execute the method described in any one of claims 1-7, characterized in that: It includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a method for rapid analysis of the underwater hydrodynamic characteristics of a variable-sweep wing transmedium aircraft, as well as a method for underwater cruise and pre-surface-out control.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed, performs the method described in any one of claims 1-7. When the computer program is executed by a processor, it implements a method for rapid analysis of the underwater hydrodynamic characteristics of a variable-sweep wing transmedium aircraft, as well as a method for control during underwater cruise and pre-surface-out stages.

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