High-speed aircraft time cooperative guidance method and system based on sliding mode control

Abstract

The invention provides a high-speed aircraft time cooperative guidance method and system based on sliding mode control, and belongs to the field of aircraft guidance and control. The problems that an existing guidance method is large in calculation amount, insufficient in real-time performance and poor in cooperation precision are solved. According to the method, the residual flight time of multiple aircrafts is quickly predicted through a centralized collaborative strategy, and the time deviation of the aircrafts is adjusted according to the principle that who follows the aircrafts slowly; designing a bottom layer time controllable guide law based on sliding mode control, and introducing a saturation function to improve a buffeting phenomenon and solve a singular point problem; realizing transverse trajectory bending of the aircraft through a three-dimensional offset proportional guidance law so as to adjust the flight time; the precision and efficiency of residual flight time calculation are improved by using a variable step size numerical integration method; and completing formation transformation of multiple aircrafts at the tail end of the gliding section to support a terminal guidance task. According to the method, the calculation complexity is reduced, meanwhile, the precision and robustness of time cooperation are remarkably improved, and reliable technical support is provided for a multi-aircraft cooperative guidance task.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft guidance and control, and in particular to a time-coordinated guidance method and system for a high-speed aircraft based on sliding mode control. Background Art

[0002] In the application of high-speed aircraft cooperative combat, how to achieve time synchronization of multiple aircraft in the terminal guidance stage is a key issue. Although the traditional open-loop guidance method can achieve cooperative flight in an ideal environment by presetting the flight trajectory, its adaptability to environmental disturbances is poor. Once the external conditions change, the cooperative effect will be significantly reduced. The closed-loop guidance method dynamically adjusts the guidance instructions through information interaction between aircraft, which can improve the coordination accuracy to a certain extent, but its centralized architecture is highly dependent on the communication center, and the distributed method faces the problem of excessive computational complexity and is difficult to meet real-time requirements.

[0003] For the under-actuated flight state of the gliding phase, traditional guidance methods face greater challenges in time coordination. This is mainly because the speed of the aircraft gradually decays during the gliding phase, the control resources are limited, and the aerodynamic parameters change dramatically. The time coordination guidance under complex environmental conditions is computationally intensive and difficult to achieve stably. In addition, the seeker of the aircraft during the gliding phase cannot directly obtain relative motion information. Traditional methods based on trajectory optimization or prediction correction are computationally intensive and not flexible enough, and cannot effectively cope with the large-scale maneuvering scenarios at the end of the gliding phase.

[0004] Based on this, the present invention re-examines the method of time-cooperative guidance. Instead of using the traditional trajectory optimization method, it proposes a time-cooperative guidance law based on a two-layer collaborative architecture. By combining the top-level centralized coordination strategy and the bottom-level sliding mode control method, the flight time error is directly adjusted. Compared with the traditional method, the present invention improves the jitter phenomenon through sliding mode control, optimizes the time error convergence efficiency, and combines the field of view angle constraint to correct the guidance instructions, which greatly reduces the complexity of the guidance calculation, thereby ensuring that the aircraft can achieve time coordination more efficiently in the gliding phase and adapt to the needs of complex battlefield environments. Summary of the invention

[0005] The technical problems to be solved by the present invention are:

[0006] In order to solve the problems of large computational complexity, insufficient real-time performance and poor coordination accuracy in existing guidance methods.

[0007] The present invention adopts the following technical solutions to solve the above technical problems:

[0008] The present invention provides a time-coordinated guidance method for a high-speed aircraft based on sliding mode control, comprising the following steps:

[0009] S100, establishing a relative motion model between the aircraft and the target in a three-dimensional space, and designing a time-controllable guidance law based on sliding mode control;

[0010] S200, predicting the remaining flight time of the aircraft by using a variable step-size fast numerical integration method;

[0011] S300. Design a time-coordinated guidance law based on a double-layer collaborative framework, including the bottom-level guidance control and the upper-level centralized coordination control, which is used to give guidance instructions to each aircraft so that they arrive at the specified position at the same time.

[0012] Furthermore, in step S100, establishing a relative motion model between the aircraft and the target in three-dimensional space specifically includes:

[0013] S111, establishing a coordinate system required for a relative motion model, wherein the coordinate system includes a reference coordinate system, a sight coordinate system, and a velocity coordinate system.

[0014] The reference coordinate system is o1x′y′z′;

[0015] The line of sight coordinate system is o1x1′y1′z1′, the origin o1 is located at the center of mass of the aircraft; the o1x1′ axis is in the direction of the line connecting the center of mass o1 to the target position, and the direction pointing to the target is positive; o1y1′ is in the x′o1y′ plane and is perpendicular to the o1x1′ axis; the o1z1′ axis is perpendicular to the x1′o1y1′ plane, forming a right-handed system;

[0016] The velocity coordinate system is o1x2′y2′z2′, with the origin o1 located at the center of mass of the aircraft; the o1x1′ axis is consistent with the direction of the aircraft velocity; o1y2′ is in the x1′o1y1′ plane and is perpendicular to the o1x′2 axis; the o1z′2 axis is perpendicular to the x′2o1y′2 plane, forming a right-handed system;

[0017] S112, the conversion relationship between the design coordinate system, the line of sight coordinate system and the velocity coordinate system,

[0018] When converting the reference coordinate system o1x′y′z′ to the sight coordinate system o1x1′y1′z1′,

[0019] The reference coordinate system o1x′y′z′ rotates ψ in the order of rotation of zy L and θ L Complete the conversion; where ψ L is the line of sight deflection angle, which is the angle between the projection of the line of sight in the x′o1y′ plane and the o1x′ axis; θ L is the line of sight inclination, which is the angle between the line of sight and the x′o1y′ plane; the transformation matrix as follows:

[0020]

[0021] When converting the line of sight coordinate system o1x1′y1′z1′ to the velocity coordinate system o1x2′y2′z2′,

[0022] The line of sight coordinate system o1x1′y1′z1′ rotates ψ in the order of rotation of zy m and θ m Complete the conversion; where ψ m θ is the velocity lead angle in the yaw plane, which is the angle between the projection of the velocity vector in the x1′o1y1′ plane and the o1x1′ axis; m is the velocity lead angle of the pitch plane, which is the angle between the velocity vector and the x1′o1y1′ plane; the transformation matrix as follows:

[0023]

[0024] S113, establish the kinematic equations of the aircraft,

[0025] The relationship between the relative distance between the aircraft and the target position is obtained:

[0026]

[0027] in, It represents the rate of change of the relative vector between the aircraft and the target position relative to the reference coordinate system. Represents the velocity relative to the reference coordinate system; transform them all into the line of sight coordinate system and establish the relative kinematic equation:

[0028] According to the vector derivation formula, we get:

[0029]

[0030] in, It represents the rate of change of the aircraft-target relative vector relative to the line of sight coordinate system, expressed as:

[0031]

[0032] The rotation angular velocity of the line of sight coordinate system is expressed in the line of sight coordinate system as:

[0033]

[0034] speed In the line of sight coordinate system it is expressed as:

[0035]

[0036] After solving the above formula, we can get the kinematic equations of relative motion in three scalar forms:

[0037]

[0038] Establish the dynamic equation of the aircraft:

[0039]

[0040] in, represents the angular velocity of the aircraft's velocity vector relative to the reference coordinate system, Represents the projection of the angular velocity of the sight coordinate system relative to the reference coordinate system in the velocity coordinate system:

[0041]

[0042] Represents the projection of the angular velocity of the velocity coordinate system relative to the line of sight coordinate system in the velocity coordinate system:

[0043]

[0044] After solving, two scalar relative motion dynamics equations are obtained, and the relative motion mathematical model is obtained by combining the above kinematic equations:

[0045]

[0046] Among them, R represents the distance between the aircraft and the mid-terminal guidance handover, V represents the speed of the aircraft; the state variables are the relative distance between the aircraft and the target, the line of sight inclination angle, the line of sight deflection angle, the pitch plane velocity lead angle and the yaw plane velocity lead angle, and the control variables are the acceleration instructions on the pitch and yaw planes, that is, a z and a y .

[0047] Further, in step S100, designing a time controllable guiding law based on sliding mode control includes:

[0048] Based on the three-dimensional proportional guidance law, a biased proportional guidance law is designed as follows:

[0049]

[0050] Among them, a by and a bz are the yaw and pitch acceleration command bias terms that meet the time constraints of the high-speed aircraft; N is the proportional coefficient;

[0051] The flight time error sliding surface is defined as:

[0052] s=t c -tt go

[0053] Among them, t c is the expected flight time, t is the time already flown, and t go The remaining flight time of the aircraft;

[0054] By replacing the switching function sgn with the saturation function sat, the control instruction is made continuous, and the sliding mode reaching law is obtained as follows:

[0055]

[0056] Where k represents the control gain coefficient;

[0057] The derivative of the sliding surface with respect to time is obtained as:

[0058]

[0059] The first-order derivative of the remaining flight time is:

[0060]

[0061] Among them, η represents the total speed lead angle;

[0062] Derivative η in the relative motion model with respect to time t yields:

[0063]

[0064] Based on the small angle assumption, we get:

[0065]

[0066] Combining and ignoring the higher-order terms, we get:

[0067]

[0068] Under the premise of not affecting the convergence of the sliding surface, the bias term is corrected to obtain the acceleration command bias term of the yaw plane and the pitch plane:

[0069]

[0070] Furthermore, in step S100, it also includes improving singularity and chattering.

[0071] In order to complete the smooth transition of mid-terminal guidance, the acceleration command bias item of the field of view angle constraint is improved when designing the acceleration command bias item of mid-term guidance:

[0072]

[0073] Construct the acceleration command switching term to solve the singularity problem caused by the zero lead angle at the initial moment:

[0074]

[0075] Finally, the acceleration instructions for the yaw and pitch planes of the mid-range guidance are:

[0076]

[0077] When the flight time error s≠0 and the aircraft is not pointing to the target, the acceleration command bias item plays a role in time adjustment; when the aircraft is pointing to the target at the initial moment, the acceleration command switching item plays a role in time adjustment, first increasing the lead angle, and then performing time adjustment under the control of the bias item; when the flight time error s=0, the aircraft flies to the target under the action of the proportional guidance law.

[0078] Furthermore, in step S200, a variable step-size fast numerical integration method is used to predict the remaining flight time of the aircraft. The current state quantity is used as the initial value, and the pure proportional guidance method is used as the guidance law to perform integral calculation. When the specified position is reached, the integration stops, and the flight time required to reach the specified position at the current moment is output as the remaining flight time.

[0079] Further, in step S300, it includes:

[0080] S310, predicting the remaining flight time of all aircrafts using the time fast integration predictor in step S200, and providing coordination variables based on the centralized coordination strategy;

[0081] Assume that there are n aircraft participating in the coordinated mid-range guidance, and all aircraft are required to arrive at the designated position at the same time; the underlying guidance law of each aircraft adopts the three-dimensional specified time guidance law, and its controlled variable is the remaining flight time t of the aircraft go , take the remaining flight time of each aircraft as the coordination variable ξ:

[0082]

[0083] Adopt the coordinated strategy of the swarm to decide who lags behind and who follows:

[0084] ξ * =max(ξ i )

[0085] S320, obtaining a relative motion relationship according to the coordinate conversion in step S100;

[0086] S330, based on step S310 and step S320, calling step S100 to obtain the aircraft acceleration guidance instruction,

[0087] The consistent coordination variable of all aircraft is obtained through this coordination strategy as the maximum value of the remaining flight time, which is sent to each aircraft through the communication network; each aircraft flies under the control of the specified time guidance law, and its guidance instruction is:

[0088]

[0089] The present invention discloses a high-speed aircraft time cooperative guidance system based on sliding mode control. The system has a program module corresponding to the above steps and executes the steps in the high-speed aircraft time cooperative guidance method based on sliding mode control during operation.

[0090] The present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a high-speed aircraft time-coordinated guidance method based on sliding mode control when called by a processor.

[0091] Compared with the prior art, the present invention has the following beneficial effects:

[0092] The present invention can provide a high-precision and high-efficiency collaborative guidance solution in the aircraft time coordination task in the underactuated gliding phase under the condition of limited computing resources; it is particularly suitable for complex battlefield environments where multiple aircraft cooperate in combat, and provides strong support for the successful execution of the terminal guidance task, specifically including:

[0093] High efficiency of time error convergence: The present invention optimizes the sliding mode control method and uses a saturation function instead of a switching function to achieve rapid convergence of the time error. Compared with the traditional method, it avoids the control discontinuity problem caused by the buffeting phenomenon and ensures the stability of the coordinated flight.

[0094] Effective solution to the singularity problem: In view of the singularity problem caused by the zero lead angle, the present invention designs an acceleration command switching item to ensure the normal operation of the guidance law under special circumstances; through this improvement, the adaptability and robustness of the guidance system in complex environments are greatly improved;

[0095] Reduction of computational complexity: The present invention adopts a variable step-size numerical integration method at the top level, and quickly predicts the remaining flight time by dynamically adjusting the step-size, thereby reducing the amount of calculation in the generation of collaborative guidance instructions; at the same time, the lateral trajectory adjustment strategy delays the time error by bending the trajectory, without the need for a large number of complex trajectory optimization calculations, and is more suitable for flight missions with high real-time requirements;

[0096] Flexibility of collaborative strategy: The present invention combines the field of view angle constraint to correct the guidance trajectory, ensuring that the aircraft can enter the terminal guidance handover at the best attitude and speed state at the end of the gliding phase; compared with the traditional trajectory optimization method and prediction correction method, the present invention has better flexibility and adaptability;

[0097] Adaptability of modular system design: The present invention modularizes the guidance system functions, including relative motion solution, guidance instruction generation, collaborative control and data communication modules. Each module operates independently and efficiently, and simultaneously collaborates to complete the time control task. It has high scalability and is suitable for a variety of aircraft and complex combat scenarios.

[0098] Safety and stability: The present invention fully considers the field of view angle constraints at the end of the gliding phase during the time coordination process to prevent the aircraft from entering a dangerous area. At the same time, it reduces large-scale maneuvers through lateral trajectory adjustments, ensures the smoothness of the aircraft's flight path, and improves the safety of mission execution. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 A schematic diagram of the coordinate system and relative motion relationship in an embodiment of the present invention;

[0100] Figure 2 This is a centralized collaborative framework diagram in an embodiment of the present invention;

[0101] Figure 3 1 is a comparison diagram of multi-scenario simulation results in an embodiment of the present invention, wherein (a) is a comparison diagram of flight trajectories of three aircraft, (b) is a comparison diagram of remaining flight time errors of three aircraft, (c) is a comparison diagram of lead angles of three aircraft, and (d) is a comparison diagram of acceleration instructions of three aircraft;

[0102] Figure 4 1 is a comparison diagram of the anti-interference conditions of different sliding mode reaching laws in the embodiments of the present invention, wherein (a) is a comparison diagram of the anti-interference conditions of the sliding mode reaching law including the saturation function sat, and (b) is a comparison diagram of the anti-interference conditions of the sliding mode reaching law including the switching function sgn;

[0103] Figure 5 Schematic diagram of the results of 100 Monte Carlo test shots in an embodiment of the present invention;

[0104] Figure 6 1 is a comparison diagram of cooperative flight scenarios in an embodiment of the present invention, wherein (a) is a comparison diagram of the flight trajectories of three aircraft, (b) is a comparison diagram of the yaw plane trajectories of three aircraft, (c) is a comparison diagram of the lead angles of three aircraft, and (d) is a comparison diagram of the roll angles of three aircraft;

[0105] Figure 7 1 is a comparison diagram of process constraint curves in a collaborative flight scenario in an embodiment of the present invention, wherein (a) is a comparison diagram of heat flux densities of three aircrafts, and (b) is a comparison diagram of dynamic pressures of three aircrafts;

[0106] Figure 81 is a scene diagram of the aircraft formation transformation in an embodiment of the present invention, wherein (a) is a comparison diagram of the flight trajectories of seven aircraft, and (b) is a comparison diagram of the yaw plane trajectories of seven aircraft. DETAILED DESCRIPTION

[0107] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0108] Specific implementation plan 1: Combine Figure 1 and Figure 2 As shown, the present invention provides a high-speed aircraft time coordinated guidance method based on sliding mode control, comprising the following steps:

[0109] S100, establishing a relative motion model between the aircraft and the target in three-dimensional space, and designing a time-controllable guidance law based on sliding mode control, specifically including:

[0110] S110, establishing a relative motion model between the aircraft and the target in three-dimensional space, including:

[0111] S111, Combination Figure 1 As shown, the coordinate system required for establishing the relative motion model includes a reference coordinate system, a sight coordinate system and a velocity coordinate system.

[0112] The reference coordinate system is o1x′y′z′;

[0113] The line of sight coordinate system is o1x1′y1′z1′, the origin o1 is located at the center of mass of the aircraft; the o1x1′ axis is in the direction of the line connecting the center of mass o1 to the target position, and the direction pointing to the target is positive; o1y1′ is in the x′o1y′ plane and is perpendicular to the o1x1′ axis; the o1z1′ axis is perpendicular to the x1′o1y1′ plane, forming a right-handed system;

[0114] The velocity coordinate system is o1x2′y2′z2′, with the origin o1 located at the center of mass of the aircraft; the o1x1′ axis is consistent with the direction of the aircraft velocity; o1y2′ is in the x1′o1y1′ plane and is perpendicular to the o1x2′ axis; the o1z2′ axis is perpendicular to the x2′o1y2′ plane, forming a right-handed system;

[0115] S112, the conversion relationship between the design coordinate system, the line of sight coordinate system and the velocity coordinate system,

[0116] When converting the reference coordinate system o1x′y′z′ to the sight coordinate system o1x1′y1′z1′,

[0117] The reference coordinate system o1x′y′z′ rotates ψ in the order of rotation of zy L and θ L Complete the conversion; where ψ Lis the line of sight deflection angle, which is the angle between the projection of the line of sight in the x′o1y′ plane and the o1x′ axis; θ L is the line of sight inclination, which is the angle between the line of sight and the x′o1y′ plane; the transformation matrix as follows:

[0118]

[0119] When converting the line of sight coordinate system o1x1′y1′z1′ to the velocity coordinate system o1x2′y2′z2′,

[0120] The line of sight coordinate system o1x1′y1′z1′ rotates ψ in the order of rotation of zy m and θ m Complete the conversion; where ψ m θ is the velocity lead angle in the yaw plane, which is the angle between the projection of the velocity vector in the x1′o1y1′ plane and the o1x1′ axis; m is the velocity lead angle of the pitch plane, which is the angle between the velocity vector and the x1′o1y1′ plane; the transformation matrix as follows:

[0121]

[0122] S113, establish the kinematic equations of the aircraft,

[0123] From the changing relationship of the relative distance between the aircraft and the target position, we can get:

[0124]

[0125] in, It represents the rate of change of the relative vector between the aircraft and the target position relative to the reference coordinate system. Represents the velocity relative to the reference coordinate system; now transform them all into the sight coordinate system and establish the relative kinematic equation:

[0126] According to the vector derivative formula, we can get:

[0127]

[0128] in, It represents the rate of change of the aircraft-target relative vector relative to the line of sight coordinate system, expressed as:

[0129]

[0130] The rotation angular velocity of the line of sight coordinate system can be expressed in the line of sight coordinate system as:

[0131]

[0132] speed In the line of sight coordinate system it can be expressed as:

[0133]

[0134] After solving the above formula, we can get the kinematic equations of relative motion in three scalar forms:

[0135]

[0136] Establish the dynamic equation of the aircraft:

[0137]

[0138] in, represents the angular velocity of the aircraft's velocity vector relative to the reference coordinate system, Represents the projection of the angular velocity of the sight coordinate system relative to the reference coordinate system in the velocity coordinate system:

[0139]

[0140] Represents the projection of the angular velocity of the velocity coordinate system relative to the line of sight coordinate system in the velocity coordinate system:

[0141]

[0142] After solving, two scalar forms of relative motion dynamics equations are obtained, and the relative motion mathematical model is obtained by combining the above kinematic equations:

[0143]

[0144] Among them, R represents the distance between the aircraft and the mid-terminal guidance handover, V represents the speed of the aircraft; the state variables are the relative distance between the aircraft and the target, the line of sight inclination angle, the line of sight deflection angle, the pitch plane velocity lead angle and the yaw plane velocity lead angle, and the control variables are the acceleration instructions on the pitch and yaw planes, that is, a z and a y ;

[0145] S120, design a time controllable guide law based on sliding mode control,

[0146] In order to meet the guidance requirements of designated time flight in three-dimensional space, a biased proportional guidance law is designed based on the three-dimensional proportional guidance law:

[0147]

[0148] Among them, a by and a bzare the yaw and pitch acceleration command bias terms that meet the time constraints of the high-speed aircraft; N is the proportional coefficient;

[0149] The aerodynamic parameters in the gliding stage change dramatically, and the nonlinear sliding mode control method is insensitive to parameter uncertainty and internal / external disturbances; therefore, in order to achieve attack time control in three-dimensional space, a sliding mode control method is designed based on the sliding mode control concept. by and a bz , we need to first define the flight time error sliding surface as:

[0150] s=t c -tt go

[0151] Among them, t c is the expected flight time, t is the time already flown, and t go The remaining flight time of the aircraft;

[0152] The traditional sliding mode reaching law contains a switching function, and the control command is discontinuous. Due to the existence of inertia, hysteresis and other factors, the attitude control link cannot perfectly track the guidance command; at the same time, when observing the state quantity, due to the existence of sensor errors and environmental interference, the use of switching functions often causes jitter, which may cause instability of the hypersonic aircraft; therefore, the switching function sgn is replaced by the saturation function sat, and the control command is continuous, thereby suppressing the sliding mode control jitter phenomenon; the sliding mode reaching law is obtained as:

[0153]

[0154]

[0155] Where k represents the control gain coefficient;

[0156] The derivative of the sliding surface with respect to time is obtained as:

[0157]

[0158] The first-order derivative of the remaining flight time is:

[0159]

[0160] Among them, η represents the total speed lead angle;

[0161] Derivative η in the relative motion model with respect to time t yields:

[0162]

[0163] Since the instantaneous maneuverability of high-speed aircraft is weak, its lead angle is usually small after performing evasive maneuvers in the gliding phase; therefore, based on the small angle assumption, we get:

[0164]

[0165] Combining and ignoring the higher-order terms, we get:

[0166]

[0167] In order to avoid the singularity problem caused by the pre-position on the denominator, the bias term is corrected without affecting the convergence of the sliding surface, and the acceleration command bias terms of the yaw plane and the pitch plane are obtained as follows:

[0168]

[0169] S130, Improvements for singularity and chattering,

[0170] Two improvements are made based on the above formula:

[0171] Considering that the purpose of the missile's mid-range guidance flight is to enter the mid-range and terminal guidance handover and create a favorable strike situation for the terminal guidance strike; and in the terminal guidance process, it is usually subject to the field of view angle constraint due to the detection range of the missile seeker; therefore, in order to complete the smooth transition of mid-range and terminal guidance, when designing the mid-range guidance acceleration command bias item, it is necessary to improve the acceleration command bias item according to the field of view angle constraint:

[0172]

[0173] It is worth noting that when the flight time error s≠0, but the missile points to the target at the initial moment, the bias term of the guidance law is always equal to zero during the guidance process and cannot play a role in time adjustment; therefore, an acceleration command switching term is constructed to solve the singularity problem caused by the zero lead angle at the initial moment:

[0174]

[0175] Finally, the acceleration instructions for the yaw and pitch planes of the mid-range guidance are:

[0176]

[0177] When the flight time error s≠0 and the missile is not pointing to the target, the acceleration command bias item plays a role in time adjustment; when the missile is pointing to the target at the initial moment, the acceleration command switching item plays a role in time adjustment, first increasing the lead angle, and then adjusting the time under the control of the bias item; when the flight time error s=0, the missile flies to the target under the action of the proportional guidance law;

[0178] S200, design a fast integral prediction algorithm for remaining flight time;

[0179] The variable step-size fast numerical integration method is used to predict the remaining flight time of the missile. The current state quantity is used as the initial value, and the pure proportional guidance method is used as the guidance law. The integration calculation is performed. When the missile reaches the specified position, the integration stops, and the output is the flight time required to reach the specified position at the current moment, which is the remaining flight time.

[0180] S300, design a temporal cooperative guidance law based on a two-layer cooperative framework;

[0181] S310, predicting the remaining flight time of all aircrafts using the time fast integration predictor in step S200, and providing coordination variables based on the centralized coordination strategy;

[0182] In order to solve the problem of coordinated guidance of hypersonic vehicles, a coordinated guidance law based on a two-layer coordination architecture is adopted, which is: bottom-level guidance control and upper-level coordination control. The bottom-level guidance control is realized by the guidance law pre-set on the onboard computer of each missile, and the upper-level coordination control is realized by the coordination strategy on the centralized information exchange platform. Figure 2 As shown, consistent coordination variables are given according to the motion parameters of each missile and sent to each missile through the communication network;

[0183] Assume that there are n missiles participating in the coordinated mid-course guidance, and all missiles are required to arrive at the designated position at the same time; the underlying guidance law of each missile adopts the three-dimensional specified time guidance law, and its controlled quantity is the remaining flight time t of the missile go , therefore, the remaining flight time of each missile is taken as the coordination variable ξ:

[0184]

[0185] Obviously, if the remaining flight time of each missile can converge to the same value, then under the control of the specified time guidance law, all missiles must arrive at the specified position at the same time; therefore, the coordination strategy of the missile group is adopted to follow who lags behind:

[0186] ξ * =max(ξ i )

[0187] S320, obtaining a relative motion relationship according to the coordinate conversion in step S100;

[0188] S330, based on step S310 and step S320, calling step S100 to obtain the aircraft acceleration guidance instruction,

[0189] The consistent coordination variable of all missiles is obtained through this coordination strategy as the maximum value of the remaining flight time, which is sent to each missile through the communication network. Each missile flies under the control of the specified time guidance law, and its guidance instruction is:

[0190]

[0191] Specific implementation scheme 2: The present invention provides a high-speed aircraft time coordinated guidance system based on sliding mode control. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned high-speed aircraft time coordinated guidance method based on sliding mode control during operation.

[0192] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0193] Specific implementation scheme three: The present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a high-speed aircraft time-coordinated guidance method based on sliding mode control when called by a processor.

[0194] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0195] According to the embodiment of the present invention, the effectiveness of the guidance method is verified through a multi-objective collaborative simulation experiment, and a further optimization strategy is proposed, including:

[0196] 1. Monte Carlo target shooting experiment: 100 Monte Carlo simulation tests were conducted on multiple aircraft under random initial conditions. Assuming that the target area is a specific coordinate point (x, y, z), the initial states of multiple aircraft are randomly generated, including speed, lead angle and roll angle. The simulation results show that all aircraft can reach the target area with a time error of less than 1 second.

[0197] 2. Target distribution analysis: By analyzing the trajectory of the aircraft, the time coordination mechanism under under-actuated conditions was verified: the leading aircraft extended the flight time by increasing the curvature of the trajectory; the lagging aircraft maintained a low maneuvering amplitude and quickly approached the target area.

[0198] 3. Process constraint management: In order to ensure the safety during collaborative flight, the dynamic pressure and heat flux density constraints of the aircraft are analyzed to ensure the safety of the guidance mission.

[0199] In order to verify the performance and mechanism of the underlying guidance law, simulation verification is carried out. The initial lead angles and expected flight times of the three simulation cases are shown in Table 1.

[0200] Table 1 Simulation case parameter settings

[0201]

[0202] When the leading angle is 0° and 40.1°, the flight time required for the aircraft to use proportional guidance is 33.94s and 35.67s respectively. In the guidance law parameter setting: N = 3, k = 20, η max=45°. The simulation results are as follows Figure 3 shown.

[0203] When the simulation step is 0.0001s, the actual flight times in the three scenarios are 37.9998s, 40.9997s and 34.9995s, respectively, which differ from the expected flight times by 0.0002s, 0.0003s and 0.0005s, respectively. The guidance law error proposed in the present invention is smaller than that in the reference, converges faster, and can achieve flight time control.

[0204] Combination Figure 3 As shown, from Figure 3 (a) and Figure 3 It can be noted in (b) that the internal mechanism for the underactuated aircraft to achieve time coordination is that the leading aircraft increases the flight distance by bending the trajectory, thereby delaying the arrival time of the mid-terminal guidance handover and achieving overall time coordination. The entire flight process is divided into three stages. In the initial stage, the aircraft adjusts the lead angle with a larger acceleration command, so that the lead angle of the aircraft increases rapidly to increase the curvature of the trajectory; when the lead angle reaches the maximum value, the acceleration command decreases rapidly, and the aircraft maintains the maximum field of view angle for flight; finally, when the remaining flight time error of the aircraft converges, the aircraft flies to the target position under the control of the proportional guidance command. In scenario 1, the initial lead angle of the aircraft is zero degrees, and the guidance law can still be started normally, proving that the improvement of the zero lead angle singularity problem is effective.

[0205] In scenario 1, the first-order inertial link is used to simulate the hysteresis effect of the attitude control link, and an anti-interference simulation test is carried out while considering noise interference. Figure 4 As shown, Type 1 is an ideal case, Type 2 considers noise but not inertia, and Type 3 considers both noise and inertia.

[0206] Comparing the sliding film approach law before and after the improvement, the two guidance laws have some similarities. When the noise is increased, the remaining flight time error shows obvious jitter phenomenon, which is an inevitable drawback of sliding mode control, but it can eventually converge to zero; when the inertia of the attitude control system is considered, the amplitude of the jitter phenomenon increases, the convergence speed slows down, and there is an obvious lag phenomenon. However, since the inertial link is equivalent to a first-order low-pass filter, the jitter frequency decreases. But in either case, the frequency, amplitude, and convergence time of the jitter phenomenon of the improved guidance law are better than those of the traditional guidance law, which effectively improves the jitter phenomenon.

[0207] Simulation verification of centralized dual-layer cooperative guidance law

[0208] When the collaborative guidance law is applied to the gliding phase of a high-speed aircraft, in order to avoid the problems of excessive longitudinal maneuvers leading to drastic changes in the external environment, insufficient available overload, and poor handover conditions, the gain of the longitudinal bias term of the underlying guidance law is set to 0, so that the aircraft can only maneuver in the yaw plane.

[0209] The effectiveness of the guidance law was verified by conducting 100 Monte Carlo target shooting tests using three high-speed aircraft. The mid-terminal guidance handover was located at 121°45′ east longitude, 13°48′ north latitude, and 27076m altitude. The initial position of one aircraft was fixed at 120°17′ east longitude, 15°95′ north latitude, and 30386m altitude, with a speed of 2403m / s, a heading angle of 150°, and a flight path angle of 0.086°. The other two aircraft had certain random deviations from the aircraft within the range of ±23000m in the east-west direction, ±17000m in the north-south direction, ±200m in the altitude, and ±10° in the heading angle. Figure 5 The distribution of the maximum errors of three high-speed aircraft arriving at the mid-terminal guidance handover in 100 Monte Carlo target shooting tests is shown.

[0210] In the results of 100 target shootings, the maximum error of the three high-speed aircraft in reaching the mid-terminal guidance handover was about 1s, and the average was 0.289s. The results show that when there are large deviations in the initial states of multiple high-speed aircraft, the guidance law proposed in this paper can also achieve effective coordination of flight time.

[0211] One set of experiments was selected for detailed analysis, and the initial motion states of the three high-speed aircraft are shown in Table 2.

[0212] Table 2 Initial motion state of aircraft

[0213] parameter Aircraft 1 Flying Machine 2 Aircraft 3 h / m 30386 30232 30320 θ / ° 120.0936 120.0899 120.0970 φ / ° 15.8964 15.9257 15.8199 <![CDATA[V / m·s -1 ]]> 2403 2403 2403 γ / ° 0.086 0.086 0.086 ψ / ° 149.4894 139.3804 148.3227

[0214] The flight time of the three aircraft and the deviations of the maximum and minimum flight times under proportional guidance and collaborative guidance control are shown in Table 3.

[0215] Table 3 Flight time

[0216] parameter Aircraft 1 Flying Machine 2 Aircraft 3 Time deviation Proportional navigation 141.1 146.5 136.3 10.2 Cooperative Guidance 146.4 146.5 146.2 0.3

[0217] Under the control of the proportional guidance method, the flight time deviation is 10.2s, while under the cooperative guidance control, the flight time deviation is shortened to 0.3s.

[0218] Combination Figure 6 As shown in the figure, the simulation results of three high-speed aircrafts coordinating to achieve mid-terminal guidance handover at the end of the glide phase are shown. The blue curve represents aircraft 1, the red curve represents aircraft 2, and the yellow curve represents aircraft 3. Figure 6(a) and Figure 6 (b) It can be seen that the trajectories of aircraft 1 and aircraft 3, which originally had shorter flight times, have obvious curvature. Figure 6 (c) and Figure 6 (d) Analysis shows that the flight time of aircraft 2 is the longest, its acceleration command bias term is zero, and the trajectory and lead angle are basically unchanged. However, the flight time of aircraft 1 and aircraft 3 is shorter, the direction of the bank angle is opposite to the direction of the proportional guidance term, the lead angle increases, the trajectory is curved, and the remaining flight time increases. In the end, the three high-speed aircraft arrived at the mid-terminal guidance handover almost at the same time. During the entire coordinated flight process, the bank angle was reversed only once, making full use of the lateral maneuverability of the high-speed aircraft.

[0219] Combination Figure 7 As shown in the figure, the process constraint curve during the cooperative flight is displayed. After the high-speed aircraft performs an evasive maneuver at the end of the gliding phase, the speed decreases, and its thermal flow constraint and dynamic pressure constraint are no longer the main constraints. Therefore, during the cooperative flight, although the process constraints are not managed, the thermal flow constraint and dynamic pressure constraint do not exceed the maximum constraint limit, ensuring the safety of the cooperative guidance mission.

[0220] The successful interception of the target by the aircraft's onboard seeker during the terminal guidance phase is a prerequisite for a successful strike. In order to increase the success rate of the mid-terminal guidance handover, it is necessary to design the formation of multiple aircraft in the handover, and expand the seeker search range by means of field of view splicing and collaborative detection. In the following, taking seven high-speed aircraft as an example, the handover formation is to be deployed side by side with equal distances, with a spacing of four kilometers.

[0221] Combination Figure 8 As shown, the initial positions of the seven aircraft are randomly assigned, and they can eventually arrive at the mid-terminal guidance handover at the same time, forming a row of equidistantly deployed formations, providing good initial conditions for coordinated detection and encirclement and attack in the terminal guidance stage.

[0222] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A time-coordinated guidance method for high-speed aircraft based on sliding mode control, characterized in that: The following steps are involved: S100, establishing a relative motion model between the aircraft and the target in a three-dimensional space, and designing a time-controllable guidance law based on sliding mode control; S200, predicting the remaining flight time of the aircraft by using a variable step-size fast numerical integration method; S300. Design a time-coordinated guidance law based on a double-layer collaborative framework, including the bottom-level guidance control and the upper-level centralized coordination control, which is used to give guidance instructions to each aircraft so that they arrive at the specified position at the same time.

2. The time-coordinated guidance method for high-speed aircraft based on sliding mode control according to claim 1, characterized in that: In step S100, establishing a relative motion model between the aircraft and the target in three-dimensional space specifically includes: S111, establishing a coordinate system required for a relative motion model, wherein the coordinate system includes a reference coordinate system, a sight coordinate system, and a velocity coordinate system. The reference coordinate system is o1x′y′z′; The line of sight coordinate system is o1x1′y1′z1′, the origin o1 is located at the center of mass of the aircraft; the o1x1′ axis is in the direction of the line connecting the center of mass o1 to the target position, and the direction pointing to the target is positive; o1y1′ is in the x′o1y′ plane and is perpendicular to the o1x1′ axis; the o1z1′ axis is perpendicular to the x1′o1y1′ plane, forming a right-handed system; The velocity coordinate system is o1x′2y′2z′2, with the origin o1 located at the center of mass of the aircraft; the o1x1′ axis is consistent with the direction of the aircraft velocity; o1y′2 is in the x1′o1y1′ plane and is perpendicular to the o1x2′ axis; the o1z2′ axis is perpendicular to the x2′o1y2′ plane, forming a right-handed system; S112, the conversion relationship between the design coordinate system, the line of sight coordinate system and the velocity coordinate system, When converting the reference coordinate system o1x′y′z′ to the sight coordinate system o1x1′y1′z1′, The reference coordinate system o1x′y′z′ rotates ψ in the order of rotation of zy L and θ L Complete the conversion; Among them, ψ L is the line of sight deflection angle, which is the angle between the projection of the line of sight in the x′o1y′ plane and the o1x′ axis; θ L is the line of sight inclination, which is the angle between the line of sight and the x′o1y′ plane; the transformation matrix as follows: When converting the line of sight coordinate system o1x1′y1′z1′ to the velocity coordinate system o1x2′y2′z2′, The line of sight coordinate system o1x1′y1′z1′ rotates ψ in the order of rotation of zy m and θ m Complete the conversion; where ψ m θ is the velocity lead angle in the yaw plane, which is the angle between the projection of the velocity vector in the x1′o1y1′ plane and the o1x1′ axis; m is the velocity lead angle of the pitch plane, which is the angle between the velocity vector and the x1′o1y1′ plane; the transformation matrix as follows: S113, establish the kinematic equations of the aircraft, The relationship between the relative distance between the aircraft and the target position is obtained: in, It represents the rate of change of the relative vector between the aircraft and the target position relative to the reference coordinate system. Represents the velocity relative to the reference coordinate system; transform them all into the sight coordinate system and establish the relative kinematic equation: According to the vector derivation formula, we get: in, It represents the rate of change of the aircraft-target relative vector relative to the line of sight coordinate system, expressed as: The rotation angular velocity of the line of sight coordinate system is expressed in the line of sight coordinate system as: speed In the line of sight coordinate system it is expressed as: After solving the above formula, we can get the kinematic equations of relative motion in three scalar forms: Establish the dynamic equation of the aircraft: in, represents the angular velocity of the aircraft's velocity vector relative to the reference coordinate system, Represents the projection of the angular velocity of the sight coordinate system relative to the reference coordinate system in the velocity coordinate system: Represents the projection of the angular velocity of the velocity coordinate system relative to the line of sight coordinate system in the velocity coordinate system: After solving, two scalar forms of relative motion dynamics equations are obtained, and the relative motion mathematical model is obtained by combining the above kinematic equations: Among them, R represents the distance between the aircraft and the mid-terminal guidance handover, V represents the speed of the aircraft; the state variables are the relative distance between the aircraft and the target, the line of sight inclination angle, the line of sight deflection angle, the pitch plane velocity lead angle and the yaw plane velocity lead angle, and the control variables are the acceleration instructions on the pitch and yaw planes, that is, a z and a y .

3. The time-coordinated guidance method for high-speed aircraft based on sliding mode control according to claim 2, characterized in that: In step S100, designing a time controllable guiding law based on sliding mode control includes: Based on the three-dimensional proportional guidance law, a biased proportional guidance law is designed as follows: Among them, a by and a bz are the yaw and pitch acceleration command bias terms that meet the time constraints of the high-speed aircraft; N is the proportional coefficient; The flight time error sliding surface is defined as: s=t c -t-t go Among them, t c is the expected flight time, t is the time already flown, and t go The remaining flight time of the aircraft; By replacing the switching function sgn with the saturation function sat, the control instruction is made continuous, and the sliding mode reaching law is obtained as follows: Where k represents the control gain coefficient; The derivative of the sliding surface with respect to time is obtained as: The first-order derivative of the remaining flight time is: Among them, η represents the total speed lead angle; Derivative η in the relative motion model with respect to time t yields: Based on the small angle assumption, we get: Combining and ignoring the higher-order terms, we get: Under the premise of not affecting the convergence of the sliding surface, the bias term is corrected to obtain the acceleration command bias term of the yaw plane and the pitch plane:

4. The time-coordinated guidance method for high-speed aircraft based on sliding mode control according to claim 3 is characterized in that: In step S100, it also includes improving singularity and chattering. In order to complete the smooth transition of mid-terminal guidance, the acceleration command bias item of the field of view angle constraint is improved when designing the acceleration command bias item of mid-term guidance: Construct the acceleration command switching term to solve the singularity problem caused by the zero lead angle at the initial moment: Finally, the acceleration instructions for the yaw and pitch planes of the mid-range guidance are: When the flight time error s≠0 and the aircraft is not pointing to the target, the acceleration command bias item plays a role in time adjustment; when the aircraft is pointing to the target at the initial moment, the acceleration command switching item plays a role in time adjustment, first increasing the lead angle, and then performing time adjustment under the control of the bias item; when the flight time error s=0, the aircraft flies to the target under the action of the proportional guidance law.

5. The time-coordinated guidance method for high-speed aircraft based on sliding mode control according to claim 4, characterized in that: In step S200, the variable step-size fast numerical integration method is used to predict the remaining flight time of the aircraft. The current state quantity is used as the initial value, and the pure proportional guidance method is used as the guidance law to perform integral calculation. When the specified position is reached, the integration stops, and the output flight time required to reach the specified position at the current moment is the remaining flight time.

6. The time-coordinated guidance method for high-speed aircraft based on sliding mode control according to claim 5, characterized in that: In step S300, it includes: S310, predicting the remaining flight time of all aircrafts using the time fast integration predictor in step S200, and providing coordination variables based on the centralized coordination strategy; Assume that there are n aircraft participating in the coordinated mid-range guidance, and all aircraft are required to arrive at the designated position at the same time; the underlying guidance law of each aircraft adopts the three-dimensional specified time guidance law, and its controlled variable is the remaining flight time t of the aircraft go , take the remaining flight time of each aircraft as the coordination variable ξ: Adopt the coordinated strategy of the swarm to decide who lags behind and who follows: x * =max(ξ i ) S320, obtaining a relative motion relationship according to the coordinate conversion in step S100; S330, based on step S310 and step S320, calling step S100 to obtain the aircraft acceleration guidance instruction, The consistent coordination variable of all aircraft is obtained through this coordination strategy as the maximum value of the remaining flight time, which is sent to each aircraft through the communication network; each aircraft flies under the control of the specified time guidance law, and its guidance instruction is:

7. A high-speed aircraft time-coordinated guidance system based on sliding mode control, characterized in that: The system has a program module corresponding to the steps of any one of claims 1 to 6, and executes the steps of the above-mentioned high-speed aircraft time-coordinated guidance method based on sliding mode control when running.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the high-speed aircraft time-coordinated guidance method based on sliding mode control according to any one of claims 1 to 6 when called by a processor.

Images