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

Abstract

The application provides a high-speed aircraft time coordination guidance method and system based on a sliding mode control, and belongs to the field of aircraft guidance and control. In order to solve the problems of large calculation amount, insufficient real-time performance and poor coordination accuracy of the existing guidance method, the application quickly predicts the residual flight time of multiple aircrafts through a centralized coordination strategy, adjusts the time deviation of the aircrafts according to the principle of "who is slow, who is followed", designs a bottom time controllable guidance law based on the sliding mode control, introduces a saturation function to improve the chattering phenomenon and solve the singularity problem, realizes the bending of the lateral trajectory of the aircraft to adjust the flight time through a three-dimensional offset proportional guidance law, improves the accuracy and efficiency of the residual flight time calculation through a variable step numerical integration method, and completes the formation transformation of the multiple aircrafts at the end of the gliding stage to support the terminal guidance task. The application significantly improves the accuracy and robustness of the time coordination while reducing the calculation complexity, and provides reliable technical support for the multiple aircraft coordination guidance task.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft guidance and control technology, in particular to a high-speed aircraft time coordination guidance method and system based on a sliding mode control. BACKGROUND

[0002] In the application of high-speed aircraft cooperative combat, how to realize the time synchronization of multiple aircrafts in the terminal guidance stage is a key problem. Although the traditional open-loop guidance method can realize cooperative flight in an ideal environment by presetting the flight trajectory, its adaptability to environmental disturbances is poor, and once the external conditions change, the cooperative effect will decrease significantly. The closed-loop guidance method dynamically adjusts the guidance command through information interaction between aircrafts, which can improve the coordination accuracy to a certain extent, but its centralized architecture has high dependence on the communication center, and the distributed method faces the problem of excessive calculation amount, which is difficult to meet the real-time demand.

[0003] For the under-actuated flight state of the gliding segment, the traditional guidance method faces greater challenges in time coordination. This is mainly because the gliding segment aircraft speed gradually decays, the control resources are limited, and the aerodynamic parameters change dramatically. The time coordination guidance calculation amount is huge and not easy to stabilize under complex environmental conditions. In addition, the seeker of the gliding segment aircraft cannot directly obtain relative motion information, and the traditional trajectory optimization or prediction correction method has large calculation amount and is not flexible enough to effectively respond to large-range maneuvering scenarios in the terminal gliding segment.

[0004] Based on this, the present application reorganizes the time coordination guidance method, does not use the traditional trajectory optimization method, but proposes a time coordination guidance law based on a double-layer coordination architecture. By combining the top-layer centralized coordination strategy and the bottom-layer sliding mode control method, the flight time error is directly adjusted. Compared with the traditional method, the present application improves the chattering phenomenon through sliding mode control, optimizes the time error convergence efficiency, and combines the field of view angle constraint to correct the guidance command, greatly reducing the complexity of guidance calculation, so as to ensure that the aircraft can more efficiently realize time coordination in the gliding segment and adapt to the demand of complex battlefield environment. SUMMARY

[0005] The technical problem solved by the present application is:

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

[0007] The technical scheme adopted by the present application to solve the above technical problems is:

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

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

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

[0011] S300, designing a time-cooperative guidance law based on a double-layer cooperative framework, including a bottom-layer guidance control and a top-layer centralized coordination control, for giving guidance instructions of each aircraft to reach the specified position at the same time.

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

[0013] S111, establishing a coordinate system required for the relative motion model, the coordinate system including a reference coordinate system, a line-of-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 positive direction points to the target direction; the o1y1′ axis 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′, the origin o1 is located at the center of mass of the aircraft; the o1x1′ axis is consistent with the direction of the aircraft velocity; the o1y2′ axis 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, designing a conversion relationship among the 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 line-of-sight coordinate system o1x1′y1′z1′,

[0019] The reference coordinate system o1x′y′z′ is converted by rotating in the order of z-y, and rotating ψ L and θ L in turn; wherein ψ L is the line-of-sight deflection angle, which is the included 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 angle, which is the included angle between the line-of-sight and the x′o1y′ plane; the conversion matrix is as follows:

[0020]

[0021] When converting the 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 is the yaw plane velocity lead angle, which is the angle between the projection of the velocity vector in the x1′o1y1′ plane and the o1x1′ axis; θ 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 it into the line of sight coordinate system and establish the relative kinematic equation:

[0028] According to the vector derivative formula, we can 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 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 obtain the kinematic equations of relative motion in three scalar forms:

[0037]

[0038] The dynamic equation of the aircraft is established:

[0039]

[0040] wherein, represents the rotation angular velocity of the velocity vector of the aircraft relative to the reference coordinate system, represents the projection of the rotation angular velocity of the line-of-sight coordinate system relative to the reference coordinate system in the velocity coordinate system:

[0041]

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

[0043]

[0044] Two scalar form relative motion dynamic equations are obtained after solving, and the relative motion mathematical model is obtained by combining the above kinematic equations:

[0045]

[0046] wherein, R represents the distance between the aircraft and the terminal guidance handover, and 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 speed lead angle and the yaw plane speed lead angle; the control variables are the acceleration commands in the pitch and yaw planes, i.e. z and y .

[0047] Further, in step S100, a time-controllable guidance law based on a sliding mode control is designed, which includes,

[0048] On the basis of a three-dimensional proportional guidance law, a biased proportional guidance law is designed as:

[0049]

[0050] wherein, by and bz are the yaw and pitch acceleration command bias terms respectively satisfying the time constraint of the high-speed aircraft; N is a proportional coefficient;

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

[0052] s=t c -t-t go

[0053] where t is the desired time of flight, t is the time of flight already flown, t is the time of flight remaining for the aircraft to fly; c where t is the desired time of flight, t is the time of flight already flown, t is the time of flight remaining for the aircraft to fly; go where t is the desired time of flight, t is the time of flight already flown, t is the time of flight remaining for the aircraft to fly;

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

[0055]

[0056] where k represents the control gain coefficient;

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

[0058]

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

[0060]

[0061] where η represents the total speed pre-angle;

[0062] The derivative of η with respect to time t in the relative motion model is obtained as:

[0063]

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

[0065]

[0066] By combining and neglecting the high-order small terms, we obtain:

[0067]

[0068] Under the premise of not affecting the convergence of the sliding surface, the bias term is modified, and the acceleration command bias terms in the yaw plane and the pitch plane are obtained as:

[0069]

[0070] Further, in step S100, the singularities and chattering are improved,

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

[0072]

[0073] The acceleration command switching term is constructed to solve the singularity problem caused by zero pre-angle at the initial time:

[0074]

[0075] The acceleration command of the middle guidance yaw plane and the pitch plane is finally obtained as:

[0076]

[0077] When the flight time error s≠0 and the aircraft does not point to the target, the acceleration command bias item plays a role of time adjustment; when the aircraft points to the target at the initial moment, the acceleration command switching item plays a role of time adjustment, the lead angle is first increased, and then the time adjustment is performed 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] Further, in step S200, a variable step fast numerical integration method is used to predict the remaining flight time of the aircraft, the current state quantity is taken as the initial value, the pure proportional guidance method is taken as the guidance law, the integral calculation is performed, the integral is stopped when the specified position is reached, 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, the following steps are included.

[0080] S310, the remaining flight time of all aircrafts is predicted by the time fast integral predictor in step S200, and the coordination variable is given based on the centralized coordination strategy;

[0081] Suppose that n aircrafts participate in the cooperative midcourse guidance, and all aircrafts are required to reach the specified position at the same time; the bottom layer guidance law of each aircraft adopts a three-dimensional specified time guidance law, and the controlled variable is the remaining flight time t go of the aircraft, and the remaining flight time of each aircraft is taken as the coordination variable ξ:

[0082]

[0083] The coordination strategy of the missile group is to follow the one who lags behind:

[0084] ξ * =max(ξ i )

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

[0086] S330, the acceleration guidance command of the aircraft is obtained by calling step S100 based on step S310 and step S320,

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

[0088]

[0089] The application is a high-speed aircraft time coordination guidance system based on a sliding mode control, which has a program module corresponding to the above steps, and executes the steps of the high-speed aircraft time coordination guidance method based on the sliding mode control.

[0090] The application is a computer readable storage medium, which stores a computer program configured to realize the steps of the high-speed aircraft time coordination guidance method based on the sliding mode control when called by a processor.

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

[0092] In the time coordination task of the under-actuated gliding aircraft, the application can provide a high-precision and high-efficiency coordination guidance solution under the condition of limited computing resources, especially suitable for the complex battlefield environment of multiple aircraft coordination, and provides strong support for the successful execution of the terminal guidance task, specifically including:

[0093] Efficiency of time error convergence: the application optimizes the sliding mode control method, uses a saturation function to replace a switching function, and realizes the rapid convergence of the time error; compared with the traditional method, the control discontinuity problem caused by the chattering phenomenon is avoided, and the stability of the coordinated flight is ensured;

[0094] Effective solution to singularity problem: for the singularity problem caused by the zero pre-angle, the application designs an acceleration instruction switching term to ensure the normal operation of the guidance law in special cases; through this improvement, the adaptability and robustness of the guidance system in complex environments are greatly improved;

[0095] Reduction of computational complexity: the application uses a variable step numerical integration method at the top level, quickly predicts the remaining flight time by dynamically adjusting the step size, reduces the calculation amount in the generation of the coordinated guidance instruction; at the same time, the lateral trajectory adjustment strategy delays the time error through the curved trajectory, without a large amount of complex trajectory optimization calculation, and is more suitable for flight tasks with high real-time requirements;

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

[0097] Adaptability of system modular design: the application modularizes the functions of the guidance system, including relative motion solving, guidance instruction generation, cooperative control and data communication modules, each module independently and efficiently operates, while cooperatively completes the time control task, has high scalability, and is suitable for various aircrafts and complex combat scenes;

[0098] Safety and stability: the application fully considers the field of view angle constraint of the terminal glide segment in the time cooperation process, avoids the aircraft entering a dangerous area, and at the same time, reduces large-scale maneuvering through lateral trajectory adjustment, guarantees the smoothness of the flight path of the aircraft, and improves the safety of task execution. BRIEF DESCRIPTION OF DRAWINGS

[0099] Figure 1 It is a coordinate system and relative motion relationship schematic diagram in the embodiment of the application;

[0100] Figure 2 It is a centralized cooperative framework diagram in the embodiment of the application;

[0101] Figure 3 It is a multi-scene simulation result comparison diagram in the embodiment of the application, wherein (a) is a flight trajectory comparison diagram of three aircrafts, (b) is a residual flight time error comparison diagram of three aircrafts, (c) is a pre-angle comparison diagram of three aircrafts, and (d) is an acceleration instruction comparison diagram of three aircrafts;

[0102] Figure 4 It is an anti-interference situation comparison diagram of different sliding mode approaching laws in the embodiment of the application, wherein (a) is an anti-interference situation comparison diagram of the sliding mode approaching law containing a saturation function sat, and (b) is an anti-interference situation comparison diagram of the sliding mode approaching law containing a switching function sgn;

[0103] Figure 5 It is a 100-time Monte Carlo test target shooting result schematic diagram in the embodiment of the application;

[0104] Figure 6 It is a cooperative flight scene comparison diagram in the embodiment of the application, wherein (a) is a flight trajectory comparison diagram of three aircrafts, (b) is a yaw plane trajectory comparison diagram of three aircrafts, (c) is a pre-angle comparison diagram of three aircrafts, and (d) is a roll angle comparison diagram of three aircrafts;

[0105] Figure 7 It is a process constraint curve comparison diagram in the cooperative flight scene in the embodiment of the application, wherein (a) is a heat flux density comparison diagram of three aircrafts, and (b) is a dynamic pressure comparison diagram of three aircrafts;

[0106] Figure 8The figure shows a flight trajectory comparison of seven aircrafts, and the figure (b) shows a yaw plane trajectory comparison of the seven aircrafts. DETAILED DESCRIPTION

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

[0108] Specific implementation scheme one: combined with Figure 1 and Figure 2 The present application provides a high-speed aircraft time coordination guidance method based on sliding mode control, which comprises the following steps:

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

[0110] S110, establishing a relative motion model of the aircraft and the target in a three-dimensional space, comprising,

[0111] S111, combined with Figure 1 The coordinate system required for establishing the relative motion model includes a reference coordinate system, a line-of-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′, and 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 positive direction points to the target direction; the o1y1′ axis is in the x′o1y′ plane and is perpendicular to the o1x1′ axis; and the o1z1′ axis is perpendicular to the x1′o1y1′ plane, forming a right-handed system;

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

[0115] S112, designing the conversion relationship between the 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 line-of-sight coordinate system o1x1′y1′z1′,

[0117] The reference coordinate system o1x′y′z′ is converted by rotating in the order of z-y, and rotating ψ L and θ L respectively; wherein ψ Lis the sight line angle, which is the angle between the projection of the sight line in the x' o1y' plane and the o1x' axis; θ L is the sight line inclination angle, which is the angle between the sight line and the x' o1y' plane; the conversion matrix is as follows:

[0118]

[0119] When the sight line coordinate system o1x1'y1'z1' is converted to the velocity coordinate system o1x2'y2'z2',

[0120] The sight line coordinate system o1x1'y1'z1' is rotated in the order of z-y, and is rotated by ψ m and θ m to complete the conversion; wherein ψ m is the yaw plane velocity lead angle, which is the angle between the projection of the velocity vector in the x1' o1y1' plane and the o1x1' axis; θ m is the pitch plane velocity lead angle, which is the angle between the velocity vector and the x1' o1y1' plane; the conversion matrix is as follows:

[0121]

[0122] S113, a kinematic equation of the aircraft is established,

[0123] The change relationship between the relative distance between the aircraft and the target position can be obtained as follows:

[0124]

[0125] wherein, represents the change rate of the relative vector between the aircraft and the target position with respect to the reference coordinate system, represents the velocity with respect to the reference coordinate system; now, they are all converted to the sight line coordinate system to establish the relative kinematic equation:

[0126] According to the vector derivation formula, the following can be obtained:

[0127]

[0128] wherein, represents the change rate of the aircraft-target relative vector with respect to the sight line coordinate system, which is expressed as:

[0129]

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

[0131]

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

[0133]

[0134] After solving the above formula, three scalar form kinematic equations of relative motion are obtained:

[0135]

[0136] The dynamics equation of the aircraft is established:

[0137]

[0138] Where, ω represents the rotation angular velocity of the velocity coordinate system relative to the line-of-sight coordinate system in the velocity coordinate system:

[0139]

[0140] ω represents the rotation 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 form relative motion dynamics equations are obtained, and the relative motion mathematical model is obtained by combining the above kinematic equations:

[0143]

[0144] Where, R represents the distance between the aircraft and the 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 speed lead angle and the yaw plane speed lead angle, and the control variables are the acceleration commands in the pitch and yaw planes, i.e. z and y ;

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

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

[0147]

[0148] Where, by and bzrespectively, are yaw and pitch acceleration command bias terms to meet the time constraint of high-speed vehicles; N is a proportional coefficient;

[0149] The aerodynamic parameters change dramatically in the glide phase, 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 by and a bz First, define the flight time error sliding mode surface as:

[0150] s = t c -t-t go

[0151] where t c is the desired flight time, t is the time that has flown, and t go is the remaining flight time of the vehicle;

[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 error and environmental disturbance, the use of switching function often causes chattering phenomenon, which may cause instability of hypersonic vehicles; therefore, by replacing the switching function sgn with the saturation function sat, the control command is continuous, thereby suppressing the chattering phenomenon of sliding mode control; the sliding mode reaching law is obtained as:

[0153]

[0154]

[0155] where k represents the control gain coefficient;

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

[0157]

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

[0159]

[0160] where η represents the total velocity pre-angle;

[0161] Differentiate η with respect to time t in the relative motion model to obtain:

[0162]

[0163] Due to the weak instantaneous maneuvering ability of high-speed vehicles, after performing an evasion maneuver in the glide phase, its pre-angle is usually small; therefore, based on the small angle assumption, we obtain:

[0164]

[0165] By combining and ignoring the high-order small terms, we get:

[0166]

[0167] In order to avoid the singularity problem of the preposition in the denominator, the bias term is modified 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:

[0168]

[0169] S130, improve for singularity and chattering,

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

[0171] Considering that the purpose of the guidance flight in the missile is to enter the mid- terminal guidance handover, and to create a favorable attack posture for terminal guidance attack; and in the process of terminal guidance, limited by the detection range of the missile seeker, there is usually a field of view angle constraint; therefore, in order to complete the smooth transition of mid- terminal guidance, when designing the acceleration command bias term of mid- guidance, it is necessary to improve the acceleration command bias term for 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 time, the bias term of this guidance law is always equal to zero in the process of guidance, and cannot play the role of time adjustment; therefore, an acceleration command switching term is constructed to solve the singularity problem caused by the zero preposition angle at the initial time:

[0174]

[0175] The final acceleration command of the mid- guidance in the yaw plane and the pitch plane is:

[0176]

[0177] When the flight time error s≠0, and the missile does not point to the target, the acceleration command bias term plays the role of time adjustment; when the missile points to the target at the initial time, the acceleration command switching term plays the role of time adjustment, first increasing the preposition angle, and then adjusting the time under the control of the bias term; when the flight time error s=0, the missile flies to the target under the action of the proportional guidance law;

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

[0179] The remaining flight time of the missile is predicted by using a variable step size fast numerical integration method, the current state quantity is taken as the initial value, the pure proportional guidance method is taken as the guidance law, the integral calculation is carried out, the integral stops when the specified position is reached, and the flight time required to reach the specified position at the current time is the remaining flight time;

[0180] S300, design a time coordination guidance law based on a double-layer coordination framework;

[0181] S310, predict the remaining flight time of all aircrafts by using the time fast integral predictor of step S200, and give the coordination variables based on the centralized coordination strategy;

[0182] For the problem of guidance in the coordination of hypersonic vehicles, a coordination guidance law based on a double-layer coordination framework is adopted, which includes bottom layer guidance control and upper layer coordination control. The bottom layer guidance control is realized by the guidance law set on each missile computer, and the upper layer coordination control is realized by the coordination strategy on the centralized information exchange platform, combined with Figure 2 As shown in the figure, consistent coordination variables are given according to the motion parameters of each missile, and are sent to each missile through the communication network;

[0183] Suppose that there are n missiles participating in the coordinated guidance, and all missiles are required to reach the specified position at the same time. The bottom layer guidance law of each missile adopts a three-dimensional specified time guidance law, and the controlled variable is the remaining flight time t 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 can reach the specified position at the same time. Therefore, the coordination strategy of the missile group is to follow the one who lags behind:

[0186] ξ * = max(ξ i )

[0187] S320, get the relative motion relationship according to the coordinate transformation of step S100;

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

[0189] Through the coordination strategy, the consistent coordination variable of all missiles is obtained 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 the guidance instruction is:

[0190]

[0191] Specific implementation two: the application is a kind of time cooperative guidance system of high-speed aircraft based on sliding mode control, the system has the program module corresponding to the above steps, when running, the steps in the above-mentioned time cooperative guidance method of high-speed aircraft based on sliding mode control are executed.

[0192] Other combinations and connection relationships of the present embodiment are the same as those of specific implementation one.

[0193] Specific implementation three: the application is a kind of computer readable storage medium, the computer readable storage medium stores a computer program, the computer program is configured to realize the steps of the time cooperative guidance method of high-speed aircraft based on sliding mode control when called by the processor.

[0194] Other combinations and connection relationships of the present embodiment are the same as those of specific implementation one.

[0195] According to the embodiment of the application, the effectiveness of the guidance method is verified by multi-target cooperative simulation experiment, and further optimization strategies are proposed, including:

[0196] 1. Monte Carlo shooting experiment: under random initial conditions, 100 Monte Carlo simulation experiments are carried out on multiple aircrafts. Assuming that the target area is a specific coordinate point (x, y, z), the initial state of multiple aircrafts is randomly generated, including speed, pre-angle and roll angle. The simulation results show that all aircrafts 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 cooperative mechanism under the condition of under-actuation is verified: the leading aircraft prolongs the flight time by increasing the trajectory curvature; the lagging aircraft keeps a low maneuvering amplitude to quickly approach the target area.

[0198] 3. Process constraint management: in order to ensure the safety of cooperative flight process, the dynamic pressure and heat flux density limit conditions of the aircraft are analyzed to ensure the safety of the guidance task.

[0199] In order to test the performance and mechanism of the underlying guidance law, simulation verification is carried out. The initial pre-angle and expected flight time of the three simulation cases are shown in Table 1.

[0200] Table 1 Simulation case parameter setting

[0201]

[0202] When the pre-angle is 0° and 40.1°, the flight time required by the aircraft using proportional guidance method is 33.94s and 35.67s respectively. In the guidance law parameter setting: N=3, k=20, η max= 45°. The simulation results are shown in Figure 3

[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 are 0.0002s, 0.0003s and 0.0005s different from the expected flight times, respectively. The error of the proposed guidance law is smaller than that of the reference, and the convergence is faster, so that the flight time control can be achieved.

[0204] As shown in Figure 3 From Figure 3 (a) and Figure 3 (b), it can be noted that the inherent mechanism of time coordination of the underactuated aircraft is that the leading aircraft increases the flight distance by bending the trajectory, thereby delaying the arrival of the midcourse guidance handover time, so as to achieve overall time coordination. The whole flight process is divided into three stages. In the initial stage, the aircraft adjusts the pre-angle with a large acceleration command, so that the pre-angle of the aircraft increases rapidly, so as to increase the bending degree of the trajectory; when the pre-angle reaches the maximum value, the acceleration command is quickly reduced, and the aircraft flies at the maximum field angle; finally, when the residual flight time error of the aircraft converges, the aircraft flies to the target position under the control of the proportional guidance command. The initial pre-angle of the aircraft in scenario 1 is zero degrees, and the guidance law can still be normally started, which proves that the improvement for the zero pre-angle singularity problem is effective.

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

[0206] The improved and unimproved sliding mode approaching law are compared, and the two guidance laws have some commonalities. When the noise is increased, the residual flight time error appears obvious chattering phenomenon, which is an inevitable drawback of the sliding mode control, but it can eventually converge to zero; when the inertia of the attitude control system is considered, the amplitude of the chattering phenomenon increases, and the convergence speed slows down, and there is obvious lag. However, since the inertia link is equivalent to a first-order low-pass filter, the chattering frequency is reduced. However, in any case, the frequency, amplitude and convergence time of the chattering phenomenon of the improved guidance law are superior to those of the traditional guidance law, and the chattering phenomenon is effectively improved.

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

[0208] ​When the cooperative guidance law is applied to the glide phase of a high-speed vehicle, in order to avoid excessive longitudinal maneuvering leading to dramatic changes in the external environment, the gain of the longitudinal bias term of the lower-level guidance law is set to 0, so that the vehicle only maneuvers in the yaw plane.

[0209] The effectiveness of the guidance law is verified by using three high-speed vehicles to perform 100 Monte Carlo shooting tests. The midcourse-to-terminal guidance handover is located at 121°45'E, 13°48'N, and an altitude of 27076 m. One vehicle is initially positioned at 120°17'E, 15°95'N, an altitude of 30386 m, a speed of 2403 m / s, a heading angle of 150°, and a flight path angle of 0.086°. The other two vehicles have random deviations in the east-west direction within a range of ±23000 m, in the north-south direction within a range of ±17000 m, in altitude within a range of ±200 m, and in heading angle within a range of ±10°. Figure 5 The distribution of the maximum errors of the three high-speed vehicles in reaching the midcourse-to-terminal guidance handover in 100 Monte Carlo shooting tests is shown.

[0210] In the 100 shooting results, the maximum error of the three high-speed vehicles reaching the midcourse-to-terminal guidance handover is about 1 s, and the average value is 0.289 s. The results show that under the condition of large deviations in the initial states of multiple high-speed vehicles, the guidance law proposed in this paper can also effectively coordinate the flight times.

[0211] One of the test groups is selected for detailed analysis, and the initial motion states of the three high-speed vehicles are shown in Table 2.

[0212] Table 2 Initial motion states of the vehicles

[0213] parameter aircraft 1 aircraft 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] Under the control of proportional guidance and cooperative guidance, the flight times of the three vehicles and the deviations of the maximum flight time and the minimum flight time are shown in Table 3.

[0215] Table 3 Flight times

[0216] parameter aircraft 1 aircraft 2 aircraft 3 time offset proportional guidance 141.1 146.5 136.3 10.2 cooperative guidance 146.4 146.5 146.2 0.3

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

[0218] Combined Figure 6 The simulation results of the three high-speed vehicles cooperatively reaching the midcourse-to-terminal guidance handover at the end of the glide phase are shown in FIG. 1. The blue curve represents vehicle 1, the red curve represents vehicle 2, and the yellow curve represents vehicle 3. From Figure 6(a) and Figure 6 (b)It can be seen that the trajectories of the aircraft 1 and 3 with shorter flight time are obviously curved. In combination with Figure 6 (c) and Figure 6 (d)Analysis shows that the flight time of the aircraft 2 is the longest, the acceleration command bias term is zero, and the trajectory and the pre-angle have no change. The flight times of the aircraft 1 and 3 are shorter, the roll angle direction is opposite to the proportional guidance term direction, the pre-angle increases, the trajectory is curved, and the remaining flight time increases. Finally, the three high-speed aircrafts arrive at the mid- terminal guidance handover at almost the same time. During the whole cooperative flight process, the roll angle is reversed only once, and the lateral maneuvering capability of the high-speed aircraft is fully utilized.

[0219] In combination with Figure 7 It can be seen that the process constraint curve in the cooperative flight process is shown. After the high-speed aircraft performs the evasion maneuver at the end of the glide segment, the speed decreases, and the heat flow constraint and the dynamic pressure constraint are no longer the main limitations. Therefore, during the cooperative flight process, the heat flow constraint and the dynamic pressure constraint do not break the maximum constraint limit, which ensures the safety of the cooperative guidance task, although the process constraint is not managed.

[0220] During the terminal guidance phase, the aircraft successfully intercepts the target by relying on the onboard seeker, which is the premise of successful attack. In order to improve the success probability of the mid- terminal guidance handover, the formation of multiple aircrafts at the handover is designed, and the search range of the seeker is expanded through field splicing and cooperative detection. In the following, taking seven high-speed aircrafts as an example, the formation at the handover is side-by-side and equidistantly expanded, and the interval is four kilometers.

[0221] In combination with Figure 8 It can be seen that the initial positions of the seven aircrafts are randomly allocated, and finally the seven aircrafts can simultaneously arrive at the mid- terminal guidance handover, and form a formation of side-by-side and equidistantly expanded, which provides a good initial condition for the cooperative detection and encircling attack in the terminal guidance phase.

[0222] Although the present disclosure is as above, the protection scope of the present disclosure is not limited to this. The person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present disclosure, and these changes and modifications will fall within the protection scope of the present disclosure.

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 three-dimensional space, and designing a time-controllable guidance law based on sliding mode control; S200, predicting the remaining flight time of the aircraft using a variable step-size fast numerical integration method; S300. Design a time-coordinated guidance law based on a two-layer collaborative framework, including bottom-layer guidance control and upper-layer centralized coordination control, to provide guidance instructions to each aircraft so that they arrive at the designated location simultaneously. include, S310, using the time fast integration predictor in step S200 to predict the remaining flight time of all aircraft, and providing coordination variables based on the centralized coordination strategy; Shared The aircraft participates in the coordinated guidance, requiring all aircraft 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 of the aircraft. , take the remaining flight time of each aircraft as the coordination variable : Adopt the coordinated strategy of the swarm to follow whoever lags behind: S320, obtaining a relative motion relationship according to the coordinate conversion in step S100; S330: Based on steps S310 and S320, call 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: in, and represent the control variables as acceleration commands on the pitch and yaw planes, respectively; and are the yaw and pitch acceleration command switching items that meet the time constraints of the high-speed aircraft; N is the proportional coefficient; is the yaw plane velocity lead angle; is the velocity lead angle in the pitch plane; Indicates the distance between the aircraft and the mid-terminal guidance handover. Indicates the speed of the aircraft; k represents the control gain coefficient; η represents the total velocity lead angle.

2. The time-coordinated guidance method for a 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 the coordinate system required for the relative motion model, the coordinate system including the reference coordinate system, the sight coordinate system and the velocity coordinate system, The reference coordinate system is ; The line of sight coordinate system is ,origin Located at the center of mass of the aircraft; Axis at center of mass In the direction of the line to the target position, the direction pointing to the target is positive; exist In the plane, with axis vertical; Axis vertical plane, forming a right-handed system; The velocity coordinate system is ,origin Located at the center of mass of the aircraft; The axis is consistent with the direction of the aircraft's speed; exist In the plane, with axis vertical; Axis vertical 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, Reference coordinate system Convert to the line of sight coordinate system hour, Reference coordinate system according to The rotation order is rotated in sequence and Complete the conversion; is the line of sight deflection angle, which is the line of sight in Projection within the plane and The angle between the axes; is the line of sight inclination angle, which is the line of sight and Angle between faces; transformation matrix as follows: The line of sight coordinate system Convert to velocity coordinate system hour, Line of sight coordinate system according to The rotation order is rotated in sequence and Complete the conversion; is the yaw plane velocity lead angle, which is the velocity vector in Projection within the plane and The angle between the axes; is the velocity lead angle of the pitch plane, which is the velocity vector and Angle between faces; 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 it into the line of sight coordinate system and establish the relative kinematic equation: According to the vector derivative formula, we can 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 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 obtain the kinematic equations of relative motion in three scalar forms: Establish the dynamic equations of the aircraft: in, It 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, we get two scalar relative motion dynamic equations. By combining the above kinematic equations, we get the relative motion mathematical model: in, Indicates the distance between the aircraft and the mid-terminal guidance handover. Indicates 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 leading angle and the yaw plane velocity leading angle, and the control variables are the acceleration instructions on the pitch and yaw planes, that is, and .

3. The time-coordinated guidance method for a 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: in, and 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: in, is the expected flight time, The time that has been flown, The remaining flight time of the aircraft; Through the saturation function Replace the switch function , make the control instructions continuous, and get the sliding mode reaching law as: Where k represents the control gain coefficient; The derivative of the sliding surface with respect to time is: The first-order derivative of the remaining flight time is: Where η represents the total velocity lead angle; The relative motion model About time Taking the derivative, we get: Based on the small angle assumption, we get: Combining and omitting 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 terms of the yaw plane and pitch plane: 。 4. The sliding mode control-based time-coordinated guidance method for a high-speed aircraft according to claim 3, characterized in that: In step S100, it also includes improving singularity and chattering. In order to achieve a smooth transition between mid- and terminal guidance, the acceleration command bias term of the field of view angle constraint is improved when designing the acceleration command bias term of mid-range guidance: Construct an acceleration command switching term to solve the singularity problem caused by the zero lead angle at the initial moment: The final acceleration instructions for the yaw and pitch planes of the mid-range guidance are: When the time-of-flight error , and the aircraft is not pointing to the target, the acceleration command bias item plays the role of time adjustment; when the aircraft is pointing to the target at the initial moment, the acceleration command switch item plays the role of time adjustment, first increasing the lead angle, and then adjusting the time under the control of the bias item; when the flight time error When , the aircraft flies towards the target under the action of the proportional guidance law.

5. The time-coordinated guidance method for a 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 flight time required to reach the specified position at the current moment is output as the remaining flight time.

6. A time-coordinated guidance system for high-speed aircraft based on sliding mode control, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 5, and executes the steps of the above-mentioned high-speed aircraft time-coordinated guidance method based on sliding mode control when running.

7. 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 5 when called by a processor.

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