A close formation anti-disturbance control method and system considering eddy current effect

Abstract

This invention belongs to the field of aerospace flight control technology, specifically disclosing a close formation disturbance rejection control method and system considering the influence of vortices. The method includes numerical simulation of the aerodynamic coupling effect of wingtip vortices in close formation of two aircraft, analysis of the influence of wingtip vortices on the aerodynamic characteristics of the following aircraft, and determination of the correspondence between the relative position of the formation and the aerodynamic effect of wingtip vortices. A predefined time-dilation state observer is designed to perform real-time online estimation of the total system disturbance, including wingtip vortices, and to ensure that the observation error converges to zero within a predefined time. A nonlinear dynamic inverse control law based on the predefined time-dilation state observer is constructed, and then the angular rate loop control law and airflow angle loop control law of the aircraft are designed to achieve precise tracking control of the aircraft state. This invention solves the problems of traditional nonlinear dynamic inverse control relying on accurate models and the adverse interference of wingtip vortices.

Description

Technical Field

[0001] This invention belongs to the field of aviation flight control technology, specifically relating to a close formation anti-disturbance control method and system that takes into account the influence of eddy currents. Background Technology

[0002] In close formation flying, the wingtip vortices generated by the leading aircraft have a dual impact on the following aircraft. On the one hand, under specific relative position conditions, these vortices can provide a beneficial aerodynamic effect of "increasing lift and reducing drag," helping to improve the overall fuel economy and range of the formation. On the other hand, wingtip vortices also constitute a strongly nonlinear, spatiotemporally variable external disturbance, posing a serious threat to the flight safety and stability control of the following aircraft. Therefore, systematically analyzing the vortex effectiveness between aircraft in formation is not only important for optimizing the relative position of the formation and fully utilizing the beneficial aerodynamic effects, but also lays a necessary foundation for designing a flight control system with disturbance resistance capabilities.

[0003] In existing technologies, computational fluid dynamics (CFD) methods have been widely used to simulate the aerodynamic coupling effects of wake vortices in formation flight, enabling quantitative analysis of key aerodynamic characteristics experienced by the trailing aircraft, such as increased lift, reduced induced drag, induced roll moment, and stability changes. However, in flight control under vortex disturbance environments, wingtip vortices are characterized by high model uncertainty, complex spatiotemporal evolution, and difficulty in accurate prediction. Although conventional methods such as robust control and adaptive control have achieved disturbance suppression to some extent, traditional nonlinear dynamic inverse (NDI) control methods still heavily rely on the accurate mathematical model of the controlled object, exhibiting significantly insufficient online estimation and compensation capabilities for unknown disturbances. This limits their control performance and engineering practicality under strong vortex disturbance scenarios. Summary of the Invention

[0004] The purpose of this invention is to address the problems of traditional nonlinear dynamic inverse control relying on accurate models and the adverse interference of wingtip vortices. It proposes a close formation anti-disturbance control method and system that considers the influence of vortices, aiming to overcome the strong dependence of dynamic inverse control on accurate models, thereby improving the robustness of the dynamic inverse control system to vortex interference and enhancing the safety and stability of formation aircraft.

[0005] The technical solution of the present invention is as follows: Firstly, a method for close formation anti-disturbance control considering eddy current effects, comprising the following steps: Computational fluid dynamics was used to numerically simulate the aerodynamic coupling effect of wingtip vortex in close formation of two aircraft, analyze the influence of wingtip vortex on the aerodynamic characteristics of the following aircraft, and determine the correspondence between the relative position of the formation and the aerodynamic effect of wingtip vortex. Based on the correspondence between the relative positions of the formation and the vortex aerodynamic effects, a predefined time-dilation state observer is designed to perform real-time online estimation of the total system disturbance, including wingtip vortices, and to make the observation error converge to zero within a predefined time. A predefined time-extended state observer is integrated into the nonlinear dynamic inverse control framework to construct a nonlinear dynamic inverse control law based on the predefined time-extended state observer. The disturbance estimate output by the predefined time-extended state observer is used to feedforward compensation of the nonlinear dynamic inverse control quantity to suppress the interference of wingtip vortices on the aircraft control system. Based on the nonlinear dynamic inverse control law based on the predefined time-dilation state observer, the angular rate loop control law and the airflow angle loop control law of the aircraft are designed respectively to achieve precise tracking control of the aircraft state.

[0006] Preferably, the numerical simulation is based on the Navier-Stokes equation coupled with the SST turbulence model and solved using the finite volume method. By changing the relative lateral distance between the two aircraft, the influence of eddies on the lift coefficient, drag coefficient, lift-to-drag ratio and rolling torque of the rear aircraft under different formation positions is calculated and analyzed.

[0007] As a preferred option, the specific correspondence between the relative positions of the formation and the wingtip vortex aerodynamic effects is as follows: When the lateral distance between the two aircraft is 0.5 times the wingspan, the wingtip vortex has a drag-increasing and lift-reducing effect on the rear aircraft; when the lateral distance is greater than 0.5 times the wingspan, the wingtip vortex has a lift-increasing and drag-reducing effect on the rear aircraft; when the lateral distance is 1 times the wingspan, the rear aircraft achieves the maximum lift-increasing and drag-reducing efficiency.

[0008] As a preferred option, the predefined time-extended state observer is specifically:

[0009] in, express The differential, For the aircraft system state vector The estimated value, This represents the nonlinear dynamic term of the aircraft system that is independent of the control input. This represents the control input matrix of the aircraft system. Represents the control input vector. , , express The differential, Integrated disturbances to aircraft systems The estimated value; and Indicates tracking error. , , This represents the state vector of the aircraft system. This indicates the overall disturbance to the aircraft system. and They are respectively and The estimated value, , , and For positive integers, , , Indicates the predefined convergence time. It is a positive number, and .

[0010] As a preferred embodiment, the nonlinear dynamic inverse control law based on the predefined time-extended state observer is as follows:

[0011] in, Represents the control input vector. The generalized inverse of the control input matrix of the aircraft system is represented. This represents the nonlinear dynamic term of the aircraft system that is independent of the control input. This represents the perturbation obtained from a predefined time-dilated state observer. To represent virtual control variables, we have:

[0012] in, express The differential, Indicates control commands. Indicates tracking error. Indicates control commands. Indicates the status value of the aircraft system. Represents gain, satisfying .

[0013] As a preferred option, the angular rate loop control law Specifically:

[0014] in, This represents the control effectiveness matrix of the aircraft system. , This represents the derivative of the rolling moment coefficient caused by aileron deflection. Denotes the derivative of the yaw moment coefficient caused by aileron deflection. This represents the derivative of the rolling moment coefficient caused by rudder deflection. This represents the derivative of the yaw moment coefficient caused by rudder deflection. This represents the derivative of the pitch moment coefficient caused by elevator deflection. Indicates the mean aerodynamic chord length. Indicates dynamic pressure. Indicates the wing reference area. Indicates the span of the aircraft. This represents the nonlinear term of the aircraft system. , Indicates the yaw rate. Indicates pitch rate, Indicates the roll rate. This indicates the roll moment excluding control surface maneuvers. This indicates pitch moment excluding control surface maneuvers. This indicates the yaw moment excluding control surface maneuvers. , , , , , , , and This represents the inertial coupling coefficient related to the aircraft's moment of inertia. , This represents the control gain of the angular rate loop. Represents the angular velocity state vector. express The differential, The angular rate control command is derived from the external loop control law. The perturbation estimate output by the predefined time-dilation state observer is as follows:

[0015] in, Represents the state estimate The differential, Indicates the disturbance estimate The differential, This indicates the error in angular rate state estimation. This indicates the error in perturbation estimation. , , , , , , , .

[0016] As a preferred option, the airflow angle loop control law is as follows:

[0017] in, This represents the airflow angle loop control matrix. , Indicates the angle of attack. Indicates the sideslip angle. Represents the sine function. Represents the cosine function. Represents the tangent function. This represents the nonlinear term of the airflow angle loop. , For state vectors, Indicates the airflow angle loop control gain. express The differential, Angle control commands for the external loop control law. For the perturbation estimate output by the predefined time-dilation state observer, we have:

[0018] in, Represents the angular velocity state vector. This indicates the error in the airflow angle state estimation. This indicates the error in perturbation estimation. , , , , , , , , , .

[0019] Preferably, the method further includes performing stability analysis on the predefined time-extended state observer and the nonlinear dynamic inverse control law based on the predefined time-extended state observer.

[0020] The beneficial effects of this invention are: This invention first employs CFD software to perform vortex aerodynamic coupling analysis on a formation of two identical aircraft, obtaining the influence of vortices on the aerodynamic characteristics of the following aircraft under typical formation positions. Second, a predefined time observer is introduced to perform rapid and accurate online estimation of unknown disturbances such as wingtip vortices. This observer can achieve high-precision estimation of modeling errors and vortex disturbances within a set predefined time, effectively overcoming the dependence of traditional NDI methods on accurate models and achieving active suppression and compensation for the adverse effects of vortices. The method proposed in this invention can fully utilize the beneficial aerodynamic effects brought by vortices, while significantly improving the flight safety and stability of formation aircraft in complex disturbance environments, providing a practical technical solution for close formation flight control.

[0021] Secondly, a close-formation anti-disturbance control system considering eddy current effects includes: The first module is used to numerically simulate the aerodynamic coupling effect of wingtip vortex in close formation of two aircraft using computational fluid dynamics methods, analyze the influence of wingtip vortex on the aerodynamic characteristics of the following aircraft, and determine the correspondence between the relative position of the formation and the aerodynamic effect of wingtip vortex. The second module is used to design a predefined time-dilation state observer based on the correspondence between the relative positions of the formation and the vortex aerodynamic effects, to perform real-time online estimation of the total system disturbance, including wingtip vortices, and to make the observation error converge to zero within a predefined time. The third module is used to integrate the predefined time-extended state observer into the nonlinear dynamic inverse control framework, construct the nonlinear dynamic inverse control law based on the predefined time-extended state observer, and use the disturbance estimate output by the predefined time-extended state observer to perform feedforward compensation on the nonlinear dynamic inverse control quantity in order to suppress the interference of wingtip vortices on the aircraft control system. The fourth module is used to design the aircraft's angular rate loop control law and airflow angle loop control law based on the nonlinear dynamic inverse control law based on the predefined time-dilation state observer, so as to achieve precise tracking control of the aircraft's state.

[0022] Thirdly, a computer-readable storage medium stores computer instructions, and in response to a computer reading the computer instructions in the storage medium, the computer executes the close formation disturbance rejection control method considering eddy current effects as described in the first aspect. Attached Figure Description

[0023] Figure 1 The diagram shows a flowchart of a close formation disturbance rejection control method that takes into account the effects of eddy currents.

[0024] Figure 2 The figure shows the lift coefficient variation curves of the front and rear engines obtained from numerical simulation calculations.

[0025] Figure 3 The figure shows the drag coefficient variation curves of the front and rear engines obtained from numerical simulation calculations.

[0026] Figure 4 The figure shows the lift-to-drag ratio curves of the front and rear engines obtained from numerical simulation calculations.

[0027] Figure 5 The figure shows the rolling torque variation curves of the front and rear engines obtained from numerical simulation calculations.

[0028] Figure 6 The diagram shown is a block diagram of an angle loop control structure.

[0029] Figure 7The figure shows the angle-of-attack response of the aircraft under the influence of eddies.

[0030] Figure 8 The figure shows the pitch rate response of the aircraft under the influence of eddies.

[0031] Figure 9 The figure shows the aircraft's roll angle response under the influence of eddies.

[0032] Figure 10 The figure shows the aircraft's roll rate response under the influence of eddies.

[0033] Figure 11 The figure shows the sideslip angle response of the aircraft under the influence of eddies.

[0034] Figure 12 The figure shows the aircraft's yaw rate response under the influence of eddies. Detailed Implementation

[0035] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.

[0036] Example 1: like Figure 1 As shown, a close formation disturbance rejection control method considering eddy current effects includes the following steps: S1. Computational fluid dynamics was used to numerically simulate the aerodynamic coupling effect of wingtip vortex in close formation of two aircraft, analyze the influence of wingtip vortex on the aerodynamic characteristics of the following aircraft, and determine the correspondence between the relative position of the formation and the aerodynamic effect of wingtip vortex. S2. Based on the correspondence between the relative positions of the formation and the vortex aerodynamic effects, a predefined time-dilation state observer is designed to perform real-time online estimation of the total system disturbance, including wingtip vortices, and to make the observation error converge to zero within a predefined time. S3. Integrate the predefined time-extended state observer into the nonlinear dynamic inverse control framework, construct a nonlinear dynamic inverse control law based on the predefined time-extended state observer, and use the disturbance estimate output by the predefined time-extended state observer to feedforward compensate the nonlinear dynamic inverse control quantity in order to suppress the interference of wingtip vortices on the aircraft control system. S4. Based on the nonlinear dynamic inverse control law based on the predefined time-expanded state observer, design the aircraft's angular rate loop control law and airflow angle loop control law respectively to achieve precise tracking control of the aircraft's state.

[0037] In this embodiment, step S1 specifically includes: To address the impact of formation vortices, a steady aerodynamic numerical simulation of a two-aircraft formation was conducted using the CFX-Solver solver. A hybrid meshing strategy was employed: an unstructured mesh generated using ICEM was used for the aircraft surface and its vicinity, while a structured mesh was used for the background flow field. The Navier-Stokes equations were selected as the governing equations and coupled with an SST turbulence model for solution. The numerical method was based on the finite volume method of the finite element method, and the accuracy of the convergence residuals was controlled within a certain range. .

[0038] In the numerical simulation calculation of the eddy current effect of the two engines, the angle of attack of both engines is 1. The two aircraft remain at the same altitude, meaning their relative altitude distance is zero. Only the vortex effect on performance caused by changes in the lateral formation parameters of the two aircraft is considered. The selected lateral distance is... ( (For the length of the aircraft).

[0039] In close formation flying, the relative lateral distance between two aircraft indicates whether and to what extent their wings overlap, which causes the vortices from the leading aircraft to have different effects on the aerodynamic characteristics of the trailing aircraft. With a fixed relative longitudinal distance between the two aircraft, changing the relative lateral distance... The aerodynamic performance of the two engines under different relative lateral distances was calculated and analyzed.

[0040] The specific results of lift coefficient, drag coefficient, lift-to-drag ratio, and rolling moment of the front and rear engines obtained through numerical simulation calculations are as follows: Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown in the diagram, graphical analysis reveals that the aerodynamics of the leading aircraft remains essentially unchanged when the two aircraft are in different lateral relative positions. For the trailing aircraft, when the lateral distance between the two aircraft is 0.5 times the wingspan, the vortex effect on the wingman exhibits a "drag increase, lift decrease" phenomenon. This is because the trailing aircraft is located in the downwash region of the leading aircraft's wingtip vortex, resulting in reduced surface pressure and thus reduced lift. However, when the lateral distance between the two aircraft is greater than 0.5 times the wingspan, the vortex effect on the trailing aircraft exhibits a "lift increase, drag decrease" phenomenon. This is because the trailing aircraft is located in the upwash region of the leading aircraft's wingtip vortex, resulting in increased lower surface pressure and thus increased lift. As the lateral distance between the two aircraft continues to increase, the trailing aircraft gradually moves out of the leading aircraft's vortex influence zone, and therefore, the aerodynamic influence of the leading aircraft's wingtip vortex on the trailing aircraft gradually decreases. In the embodiment of this invention, with a lateral distance of 1 times the wingspan, the trailing aircraft achieves the maximum "lift increase, drag decrease" efficiency and has the highest lift-to-drag ratio at this distance. It can also be seen that the lateral distance between the two machines is at... In between, the rear aircraft can obtain a relatively large "lift increase and drag reduction" benefit.

[0041] Meanwhile, the wingtip vortices of the leading aircraft also affect the roll moment of the trailing aircraft. This is because the wingtip vortices of the leading aircraft have different effects on the lift of the left and right wings of the trailing aircraft. When the roll moment of the trailing aircraft is at 0.5 times the wingspan, the wingtip vortices cause a left roll effect. This is because the left wing is in the downwash region of the wingtip vortex, while the right wing is in the upwash region, resulting in less lift for the left wing compared to the right wing, thus causing left roll. When the roll moment is greater than 0.5 times the wingspan, the wingtip vortices cause a right roll effect on the trailing aircraft. This is because the right wing of the trailing aircraft is farther from the upwash region than the left wing, resulting in greater lift for the left wing than the right wing, thus generating a right roll moment.

[0042] In this embodiment, to achieve rapid and accurate estimation of unknown disturbances such as wingtip vortices, and to overcome the shortcomings of traditional observers whose convergence time depends on initial errors and cannot be set as needed, this invention designs a predefined time-extended state observer (PTESO). This observer extends the unmodeled dynamics of the system and external disturbances into new state variables. By designing a predefined time-convergent error dynamic, it ensures that the observation error converges to zero within a user-defined time. The design of the predefined time-extended state observer is as follows: Under external disturbance conditions, the system equations are:

[0043] in, and These represent the system state vector and output vector, respectively. Represents the control input vector; This represents a bounded disturbance to the system, and the existence of positive constants. , making . This represents the nonlinear dynamic term of the system, which is independent of the control input. This represents the control input matrix of the system.

[0044] Extended State Observer (ESO) can ensure system stability while guaranteeing that the tracking error is consistently bounded. ESO extends the perturbation into a new state, where the system equations are expressed as:

[0045] in, Represents the state vector of the system, extended-dimensional state Indicates the overall disturbance .

[0046] make , They represent , The estimated value. The system tracking error can be denoted as... By incorporating a predefined time concept into ESO, the proposed PTESO structure is as follows:

[0047] in, ; It is a positive number, and ; ; ; It is a positive number; ; ; The convergence time is predefined.

[0048] In this embodiment, the nonlinear dynamic inverse control law based on the predefined time-extended state observer consists of two parts: dynamic inverse control and the predefined time-extended state observer.

[0049] For the system equations under external disturbance conditions Based on the dynamic inverse control method, the designed PTESO-NDI is shown in the following equation:

[0050] Among them, disturbance The virtual control quantity is estimated by the PTESO designed in step S2. The design is as follows:

[0051] in, Indicates control commands; Indicates tracking error; gain satisfy .

[0052] In this embodiment, the angle loop control law consists of a two-layer cascade structure: an outer loop for airflow angle and an inner loop for angular velocity. PTESO is introduced into both the inner and outer loops to improve the anti-interference capability of the NDI. The angle loop control structure block diagram is shown below. Figure 6 As shown.

[0053] The angular rate control law is designed as follows: Considering the influence of eddies on aerodynamic torque, the aircraft torque equations can be rearranged into an affine nonlinear form:

[0054] in, The angular velocity state vector; Input for the system; To model the effects of errors and disturbances on the aircraft, the system's nonlinear terms and control performance matrix can be expressed as:

[0055]

[0056] in, These are the roll moment, pitch moment, and yaw moment, excluding control surface manipulation. It is dynamic pressure.

[0057] Based on the PTESO-NDI method designed in step S3, the angular rate control law with observer can be obtained as follows:

[0058] in, , The angular rate control command is calculated from the external loop control law. The perturbation estimated for PTESO is specifically designed as follows:

[0059] in, ; ; ; ; ; ; ; .

[0060] The airflow angle control rate is designed as follows: Considering the influence of vortices on aerodynamic forces, angular state The differential equation can be rearranged into an affine nonlinear form:

[0061] in, It is a state vector; To model the effects of errors and disturbances on the aircraft, the nonlinear terms of the airflow angle loop and the control matrix are as follows:

[0062]

[0063] Based on the PTESO-NDI method designed in step S3, the outer loop control law with the observer can be obtained as follows:

[0064] in, , Angle control commands for the external loop control law; The perturbation estimated for PTESO is specifically designed as follows:

[0065] in, ; ; ; ; ; ; ; .

[0066] In this embodiment, the relevant theories used in proving the stability of the control system are given as follows: Lemma 1 (Uniform Stability Theorem): Consider a nonlinear system ,choose For Lyapunov functions, This is the initial value of the function. If Established, among which If the value is a positive constant, then the trajectory of the system state will eventually stabilize consistently, and the following inequality holds:

[0067] Lemma 2 (Predefined Time Stability Theorem): Consider a nonlinear system Define a continuous Lyapunov function if the following inequalities hold:

[0068] Among them, positive numbers satisfy Then the system is said to be in a predefined time. Internal stability.

[0069] Lemma 3: Consider nonlinear systems Define a continuous Lyapunov function if the following inequalities hold:

[0070] in, Therefore, the system is stable within a predefined time, and the system will remain stable within the specified time. Internally, converges to Inside.

[0071] Lemma 4: For any positive constant , The following inequalities hold:

[0072] Lemma 5: .

[0073] The specific method for PTESO stability analysis is as follows: The dynamic error of PTESO is as follows:

[0074] The following proves that the state observation error of PTESO can converge to the following region within a predefined time:

[0075] Choose Lyapunov functions , , .but The differential can be derived as:

[0076] Applying Young's inequality, the above equation becomes:

[0077] Combined with the bounded perturbation and And with Lemma 5, it can be further transformed into:

[0078] Will Substituting, we get:

[0079] According to the inequality in Lemma 4, it can be further transformed into:

[0080] It can be further transformed into:

[0081] According to Lemma 3, it can be deduced from the above equation that the designed PTESO is predefined in terms of time uniformity and stability. Specifically, the observation error of the PTESO... and It will be within the predefined time. Internal convergence, and the observation error of PTESO will converge to the following region within a predefined time:

[0082] The specific method for stability analysis of the PTESO-NDI closed-loop system is as follows: Choose Lyapunov functions Its differential form can be expressed as Combining the control law, the state extension system, and the virtual control variable, the tracking dynamic error of the closed-loop system is:

[0083] Furthermore, it can be deduced that:

[0084] Applying Young's inequality, the above equation can be further transformed into:

[0085] The stability analysis of PTESO has proven that the error of PTESO converges within a predefined time. Therefore, according to Lemma 1, when the controller parameters satisfy... If this holds true at all times, then the control law of the PTESO-NDI closed-loop system is eventually uniformly stable, and the control tracking error will converge to the following bounded region:

[0086] in, , .

[0087] In this embodiment, considering the influence of wingtip vortices, a dynamic inverse (PTESO-NDI) anti-airflow disturbance control simulation verification is conducted based on a predefined time-spreading state observer, given an airflow angle command. A traditional NDI control is set as a control group. The aircraft's state information under vortex disturbance is recorded and analyzed to verify the anti-interference performance of the proposed control method. The simulation results are as follows: Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 and Figure 12 As shown.

[0088] Example 2: Based on Embodiment 1, this embodiment of the invention provides a close formation anti-disturbance control system that considers eddy current effects, which can be used to implement the close formation anti-disturbance control method considering eddy current effects as described in the foregoing embodiments. The system includes: The first module is used to numerically simulate the aerodynamic coupling effect of wingtip vortex in close formation of two aircraft using computational fluid dynamics methods, analyze the influence of wingtip vortex on the aerodynamic characteristics of the following aircraft, and determine the correspondence between the relative position of the formation and the aerodynamic effect of wingtip vortex. The second module is used to design a predefined time-dilation state observer based on the correspondence between the relative positions of the formation and the vortex aerodynamic effects, to perform real-time online estimation of the total system disturbance, including wingtip vortices, and to make the observation error converge to zero within a predefined time. The third module is used to integrate the predefined time-extended state observer into the nonlinear dynamic inverse control framework, construct the nonlinear dynamic inverse control law based on the predefined time-extended state observer, and use the disturbance estimate output by the predefined time-extended state observer to perform feedforward compensation on the nonlinear dynamic inverse control quantity in order to suppress the interference of wingtip vortices on the aircraft control system. The fourth module is used to design the aircraft's angular rate loop control law and airflow angle loop control law based on the nonlinear dynamic inverse control law based on the predefined time-dilation state observer, so as to achieve precise tracking control of the aircraft's state.

[0089] According to embodiments of the present invention, the present invention also provides an electronic device, a readable storage medium, and a computer program product.

[0090] In an exemplary embodiment, an electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method as described in Embodiment 1 above.

[0091] In an exemplary embodiment, the readable storage medium may be a non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the method described in Embodiment 1 above.

[0092] In an exemplary embodiment, the computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1 above.

[0093] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0094] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0095] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0096] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0097] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0098] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A close formation disturbance rejection control method considering eddy current effects, characterized in that, Includes the following steps: Computational fluid dynamics was used to numerically simulate the aerodynamic coupling effect of wingtip vortex in close formation of two aircraft, analyze the influence of wingtip vortex on the aerodynamic characteristics of the following aircraft, and determine the correspondence between the relative position of the formation and the aerodynamic effect of wingtip vortex. Based on the correspondence between the relative positions of the formation and the vortex aerodynamic effects, a predefined time-dilation state observer is designed to perform real-time online estimation of the total system disturbance, including wingtip vortices, and to make the observation error converge to zero within a predefined time. A predefined time-extended state observer is integrated into the nonlinear dynamic inverse control framework to construct a nonlinear dynamic inverse control law based on the predefined time-extended state observer. The disturbance estimate output by the predefined time-extended state observer is used to feedforward compensation of the nonlinear dynamic inverse control quantity to suppress the interference of wingtip vortices on the aircraft control system. Based on the nonlinear dynamic inverse control law based on the predefined time-dilation state observer, the angular rate loop control law and the airflow angle loop control law of the aircraft are designed respectively to achieve precise tracking control of the aircraft state.

2. The close formation disturbance rejection control method considering eddy current effects according to claim 1, characterized in that, The numerical simulation is based on the Navier-Stokes equation coupled with the SST turbulence model and solved using the finite volume method. By changing the relative lateral distance between the two aircraft, the influence of eddies on the lift coefficient, drag coefficient, lift-to-drag ratio and rolling torque of the rear aircraft under different formation positions is calculated and analyzed.

3. The close formation disturbance rejection control method considering eddy current effects according to claim 2, characterized in that, The specific relationship between the relative positions of the formation and the aerodynamic effects of wingtip vortices is as follows: When the lateral distance between the two aircraft is 0.5 times the wingspan, the wingtip vortex has a drag-increasing and lift-reducing effect on the rear aircraft; when the lateral distance is greater than 0.5 times the wingspan, the wingtip vortex has a lift-increasing and drag-reducing effect on the rear aircraft; when the lateral distance is 1 times the wingspan, the rear aircraft achieves the maximum lift-increasing and drag-reducing efficiency.

4. The close formation disturbance rejection control method considering eddy current effects according to claim 1, characterized in that, The predefined time-dilation state observer is as follows: in, express The differential, For the aircraft system state vector The estimated value, This represents the nonlinear dynamic term of the aircraft system that is independent of the control input. This represents the control input matrix of the aircraft system. Represents the control input vector. , , express The differential, Integrated disturbances to aircraft systems The estimated value; and Indicates tracking error. , , This represents the state vector of the aircraft system. This indicates the overall disturbance to the aircraft system. and They are respectively and The estimated value, , , and For positive integers, , , Indicates the predefined convergence time. It is a positive number, and .

5. The close formation disturbance rejection control method considering eddy current effects according to claim 1, characterized in that, The nonlinear dynamic inverse control law based on the predefined time-extended state observer is: in, Represents the control input vector. The generalized inverse of the control input matrix of the aircraft system is represented. This represents the nonlinear dynamic term of the aircraft system that is independent of the control input. This represents the perturbation obtained from a predefined time-dilated state observer. To represent virtual control variables, we have: in, express The differential, Indicates control commands, Indicates tracking error. Indicates control commands, Indicates the status value of the aircraft system. Represents gain, satisfying .

6. The close formation disturbance rejection control method considering eddy current effects according to claim 1, characterized in that, Angular rate loop control law Specifically: in, This represents the control effectiveness matrix of the aircraft system. , This represents the derivative of the rolling moment coefficient caused by aileron deflection. Denotes the derivative of the yaw moment coefficient caused by aileron deflection. This represents the derivative of the rolling moment coefficient caused by rudder deflection. This represents the derivative of the yaw moment coefficient caused by rudder deflection. This represents the derivative of the pitch moment coefficient caused by elevator deflection. Indicates the mean aerodynamic chord length. Indicates dynamic pressure. Indicates the wing reference area. Indicates the span of the aircraft. This represents the nonlinear term of the aircraft system. , Indicates the yaw rate. Indicates pitch rate, Indicates the roll rate. This indicates the roll moment excluding control surface maneuvers. This indicates pitch moment excluding control surface maneuvers. This indicates the yaw moment excluding control surface maneuvers. , , , , , , , and This represents the inertial coupling coefficient related to the aircraft's moment of inertia. , This represents the control gain of the angular rate loop. Represents the angular velocity state vector. express The differential, The angular rate control command is derived from the external loop control law. The perturbation estimate output by the predefined time-dilation state observer is as follows: in, Represents the state estimate The differential, Indicates the disturbance estimate The differential, This indicates the error in angular rate state estimation. This indicates the error in perturbation estimation. , , , , , , , .

7. The close formation disturbance rejection control method considering eddy current effects according to claim 1, characterized in that, The specific airflow angle loop control law is as follows: in, This represents the airflow angle loop control matrix. , Indicates the angle of attack. Indicates the sideslip angle. Represents the sine function. Represents the cosine function. Represents the tangent function. This represents the nonlinear term of the airflow angle loop. , For state vectors, Indicates the airflow angle loop control gain. express The differential, Angle control commands for the external loop control law. For the perturbation estimate output by the predefined time-dilation state observer, we have: in, Represents the angular velocity state vector. This indicates the error in the airflow angle state estimation. This indicates the error in perturbation estimation. , , , , , , , , , .

8. The close formation disturbance rejection control method considering eddy current effects according to claim 1, characterized in that, The method further includes stability analysis of the predefined time-extended state observer and the nonlinear dynamic inverse control law based on the predefined time-extended state observer.

9. A close formation disturbance rejection control system considering eddy current effects, characterized in that, include: The first module is used to numerically simulate the aerodynamic coupling effect of wingtip vortex in close formation of two aircraft using computational fluid dynamics methods, analyze the influence of wingtip vortex on the aerodynamic characteristics of the following aircraft, and determine the correspondence between the relative position of the formation and the aerodynamic effect of wingtip vortex. The second module is used to design a predefined time-dilation state observer based on the correspondence between the relative positions of the formation and the vortex aerodynamic effects, to perform real-time online estimation of the total system disturbance, including wingtip vortices, and to make the observation error converge to zero within a predefined time. The third module is used to integrate the predefined time-extended state observer into the nonlinear dynamic inverse control framework, construct the nonlinear dynamic inverse control law based on the predefined time-extended state observer, and use the disturbance estimate output by the predefined time-extended state observer to perform feedforward compensation on the nonlinear dynamic inverse control quantity in order to suppress the interference of wingtip vortices on the aircraft control system. The fourth module is used to design the aircraft's angular rate loop control law and airflow angle loop control law based on the nonlinear dynamic inverse control law of the predefined time-dilation state observer, so as to achieve precise tracking control of the aircraft's state.

10. A computer-readable storage medium, characterized in that, The storage medium stores computer instructions. In response to the computer reading the computer instructions in the storage medium, the computer executes the close formation anti-disturbance control method considering eddy current effects as described in any one of claims 1-8.

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