High-speed aircraft online real-time energy management guidance method and system and medium

Abstract

The invention provides a high-speed aircraft online real-time energy management guidance method and system and a medium, and relates to the technical field of high-speed aircraft guidance, and the method comprises the steps: determining a flight sub-stage of an energy management stage; determining an energy corridor, and planning a low-energy nominal longitudinal track based on a Gaussian pseudo-spectral method; when the aircraft enters the energy management section, judging whether the current actual energy exceeds the energy upper boundary of the energy corridor, adding the S turning section if the current actual energy exceeds the energy upper boundary, otherwise, entering the capture section; predicting the to-fly distance of the aircraft, and obtaining an expected energy state by interpolating the energy profile of the longitudinal trajectory; obtaining an attack angle and a speed brake guidance instruction through a longitudinal guidance law according to the deviation between the current energy state and the expected energy state; outputting a heeling angle guidance instruction according to the flight sub-stage through a transverse lateral guidance law; and circularly executing until the aircraft successfully enters the pre-landing section. According to the strategy, online energy management is realized, and the aircraft is ensured to safely enter the landing section.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed aircraft guidance, and in particular to a high-speed aircraft online real-time energy management guidance method, system and medium. Background Art

[0002] High-speed aircraft, generally referring to aircraft with a flight speed exceeding Mach 5 (i.e. 6,120 kilometers per hour), have important strategic and technological significance. In the military field, high-speed aircraft can cover the entire globe in a short period of time, significantly improving rapid response and strike capabilities. Due to their high-speed flight characteristics, existing air defense systems find it difficult to effectively intercept high-speed aircraft, which enhances their penetration capabilities. The existence of high-speed aircraft poses a deterrent to potential adversaries and affects their strategic decision-making. In the civilian field, high-speed aircraft can be used for ultra-high-speed passenger transport, shortening long-distance travel time and improving global transportation efficiency. High-speed aircraft have important applications in space exploration, and can quickly enter and return space, reducing the cost and risk of space missions.

[0003] The energy management segment (TAEM) refers to the flight phase of the aircraft from the end of the reentry segment to the end of the approach and landing segment. It is mainly used to eliminate the energy and position deviations of the aircraft at the end of the reentry segment, and to guide the aircraft into the landing segment in a flight state that meets the initial window of the approach and landing segment. During the energy management flight process, the aircraft's altitude, speed, heading, and position relative to the airport runway need to be adjusted in real time to ensure that the aircraft can smoothly enter the initial window of approach and landing. If the aircraft's energy or position control effect is poor and exceeds the maximum tolerance of the approach and landing segment, flight safety cannot be guaranteed. Therefore, in the energy management segment, it is necessary to design a suitable energy management strategy and a supporting trajectory design plan to meet the mission requirements of the aircraft.

[0004] The guidance system design for the energy management phase is generally divided into two parts: longitudinal guidance and lateral guidance. During flight, guidance commands are implemented by tracking the nominal trajectory profile. The longitudinal guidance strategy uses tracking a two-dimensional trajectory profile to control energy, ensuring that the vehicle's energy state meets the requirements when entering the approach and landing phase. The lateral guidance strategy primarily controls the vehicle's position by changing the vehicle's roll angle, thereby changing the ground trajectory, ensuring that the vehicle's heading and position relative to the airport runway meet the requirements when entering the approach and landing phase.

[0005] Scholars at home and abroad have also conducted relevant research on the energy management segment guidance problem. Sun Chunzhen proposed an online trajectory guidance technology that improves the adaptability of the trajectory profile to the initial conditions. In view of the uncertainty of the initial window of energy management, the concept of aircraft energy management is combined with trajectory generation to enhance the robustness of the reference trajectory. Hu Mengquan proposed a real-time guidance algorithm for the terminal trajectory of the aircraft. Considering the trajectory constraints of the terminal flight process, the initial and final conditions of the terminal trajectory are given, and the distance to be flown is changed by adjusting the position and radius of the heading calibration cone, thereby generating a reference trajectory that meets the constraints in real time. In order to track the dynamic pressure profile and meet the path constraints, Ni Xiaobin adopted the SNAKE technology of the Drapper Laboratory and introduced a three-dimensional trajectory online generation method, which provides a trajectory that meets the actual application conditions for the terminal trajectory control.

[0006] However, due to experimental limitations, these algorithms have high requirements for onboard computer performance and poor timeliness, making them difficult to implement in practical applications. Therefore, these technologies are still in the theoretical analysis stage, and their engineering practicality still needs to be improved. Summary of the Invention

[0007] The purpose of the present invention is to provide a method, system and medium for online real-time energy management guidance of a high-speed aircraft. By adopting a low-energy trajectory tracking strategy, the guidance system's adaptability to the low-energy state of the aircraft is improved. At the same time, an S-turn strategy is used to handle high-energy states. For normal energy states, the low-energy trajectory can be tracked normally. The above strategy realizes online energy management and ensures that the aircraft enters the landing phase safely.

[0008] The present invention adopts the following technical solutions:

[0009] In one aspect, a high-speed aircraft online real-time energy management guidance method comprises:

[0010] S1, determine the energy management segment, including the flight sub-phases of the S-turn segment, the capture segment, the heading calibration segment, and the pre-landing segment; determine the energy corridor based on the energy upper boundary and the low-energy trajectory composition, and plan the low-energy nominal longitudinal trajectory based on the Gaussian pseudospectral method;

[0011] S2, when the aircraft enters the energy management phase, determines whether the current actual energy exceeds the upper energy boundary of the energy corridor. If so, an S-turn phase is added; otherwise, the aircraft enters the capture phase. The aircraft's distance to be flown is predicted in real time based on the geometric characteristics of the trajectory of each flight sub-phase and the position of the aircraft.

[0012] S3: Determine the current flight subphase of the aircraft in real time and obtain the desired energy state, including the altitude and velocity profiles, by interpolating the energy profile of the longitudinal trajectory. Determine the angle of attack and speed brake guidance commands based on the deviation between the current energy state and the desired energy state using the longitudinal guidance law. Based on the distance to be flown, output the bank angle guidance command according to the flight subphase using the lateral guidance law.

[0013] S4: Continuously adjust the state of the aircraft according to the real-time obtained angle of attack, speed brake guidance instructions, and roll angle guidance instructions until the aircraft successfully enters the pre-landing phase.

[0014] Preferably, in S1, the method for obtaining the upper energy boundary is as follows:

[0015] When the aircraft does not make an S-turn and the speed brakes are fully deployed, and the end state of the trajectory can still meet the window range of entering the landing phase, the maximum acceptable initial energy state is used as the upper energy boundary;

[0016] The method for obtaining the low-energy trajectory is as follows:

[0017] The state distribution of the initial window of the energy management segment is obtained based on the Monte Carlo shooting simulation results, and the lowest energy state in the initial state of the energy management segment is determined, and this state is used as the initial energy state of the low-energy trajectory;

[0018] The full trajectory is designed without external disturbances, aerodynamic deviations and while satisfying the end constraints of the trajectory to obtain a low-energy trajectory.

[0019] Preferably, in S1, planning the low-energy nominal longitudinal trajectory based on the Gaussian pseudospectral method specifically includes:

[0020] Initialize the longitudinal trajectory angle of attack, longitudinal trajectory altitude, and longitudinal trajectory speed, using the angle of attack as the control variable as input, and the output state variables include altitude, speed, trajectory angle, and range;

[0021] Select Legendre Gauss point;

[0022] Using Lagrange interpolation polynomials and taking Legendre Gauss points as nodes, the time history of state and control variables is approximately represented, and the continuous state and control variables are converted into discrete numerical sequences.

[0023] Construct the kinematic equations of the aircraft, discretize the dynamic equations at Gaussian points, and determine the motion state of the aircraft at discrete time points;

[0024] Determine the dynamic constraints, initial condition constraints, terminal constraints, process constraints, and control constraints of the aircraft; wherein the dynamic constraints are the constraints of the dynamic equations; the initial condition constraints are the constraints on the altitude, speed, and trajectory angle of the aircraft at the beginning of the energy management phase; the terminal constraints are the constraints on the altitude, speed, trajectory angle, and range of the aircraft at the end of the energy management phase; the process constraints are the dynamic pressure constraints and the overload constraints; and the control constraints are the constraints on the range and rate of change of the angle of attack;

[0025] Since the range of the longitudinal trajectory matches the range of the actual ground trajectory, the range is used as the optimization target. At the same time, in order to take into account the overall smoothness of the reentry trajectory, the integral of the square of the trajectory angular rate is used as the optimization index to construct the final performance index.

[0026] While satisfying the constraints of the dynamic equations, initial condition constraints, terminal constraints, process constraints and control constraints, the state variables, control variables, initial moments and terminal moments at discrete nodes are solved to minimize the performance indicators and finally obtain the longitudinal trajectory of the aircraft after planning.

[0027] Preferably, in said S2, the distance to be flown S varies with the flight phase. tg The real-time calculation steps include:

[0028] After the aircraft enters the energy management phase, it makes an energy judgment. If the energy is excessive, it enters the S-turn phase, otherwise it directly enters the capture phase. If it enters the S-turn phase, it calculates the positions of the two tangent points B and T in real time and calculates the distance S to be flown for each flight sub-phase based on the current position A of the aircraft. tg , including the S-turn section S AB , capture segment S BT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances, that is, S tg =S AB +S BT +S HAC +S PFL If the capture phase is entered, the position of the tangent point T is calculated in real time and the distance to be flown S for each flight sub-phase is calculated based on the current position A of the aircraft. tg , including the capture segment S AT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances, that is, S tg =S AT +S HAC +S PFL ;

[0029] After entering the S-turn section, it is determined in real time whether the aircraft has reached the two tangent points B and T. If S ABIf the distance is less than or equal to the threshold, it is determined that the aircraft has reached the tangent point B. At this time, the S-turn segment ends and enters the capture segment. The distance to be flown is S tg Transformed into the distance to be flown S calculated based on the current position A and the real-time position of the tangent point T tg , waiting distance S tg Include capture segment S AT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances;

[0030] After entering the capture phase, if S AT If the distance is less than or equal to the threshold, the aircraft is judged to have reached the tangent point T, the capture phase ends and enters the heading calibration phase, and an initial value of 0 is set for the integral range L. s , S HAC and S PFL The sum of the range minus the integral range L s Get the distance to fly S tg ;

[0031] With the integral range L s Continuously increasing, waiting distance S tg It will continue to decrease until it decreases to meet the condition S tg ≤S PFL The heading calibration phase ends and the aircraft enters the pre-landing phase;

[0032] When the aircraft meets the conditions for entering the landing phase, that is, it successfully hits the line, the aircraft's height from the ground is lower than the set height or S tg ≤0When any of the three conditions is met, the online waiting distance prediction is terminated;

[0033] Wherein, the integral range L s By integrating the local horizontal velocity, the velocity of the aircraft in the geographic coordinate system is V N =[v Nx ,v Ny ,v Nz ] T , where v Nx 、v Ny and v Nz Represent the speed in the X, Y and Z directions respectively, then the local horizontal speed V level for:

[0034]

[0035] Calculate the integral range L by trapezoidal integration method s :

[0036]

[0037] Among them, Δt is the calculation step size, k is the current calculation step size, L s (k) represents the integrated range at the current moment, L s (k-1) represents the integrated range at the previous moment, V level (k) represents the local horizontal velocity at the current moment, V level (k-1) represents the local horizontal velocity at the previous moment.

[0038] Preferably, the aircraft does not perform an S-turn maneuver to directly capture the return distance S tg =S AT +S HAC +S PFL The specific calculation process is as follows:

[0039] Determine the center position of the heading calibration cylinder HAC in the heading calibration section (x HAC ,y HAC ), radius R HAC and the tangent point C(x c ,y c ); Obtain the straight ground track S based on the current position of the aircraft point A (x, y), the center position of the HAC circle, and the distance OA between point O and point A AT The flight distance is as follows:

[0040]

[0041] Among them, x represents the horizontal coordinate value of point A, y represents the vertical coordinate value of point A, and x HAC Indicates the horizontal coordinate value of the HAC center position, y HAC Indicates the vertical coordinate value of the HAC center position;

[0042] Draw an auxiliary line DN through point A parallel to the x-axis. AT , OA and DA lengths, first determine ∠AOT and ∠DOA, and then calculate ∠TOE using the following formula:

[0043]

[0044] ∠TOE=π-∠DOA-∠AOT;

[0045] Then, the turning angle Δψ around the HAC circle is obtained HAC , get the heading calibration segment S HAC The itinerary is as follows:

[0046] Δψ HAC =∠TOE;

[0047] S HAC =R HAC Δψ HAC;

[0048] Finally, the remaining range S before the landing phase PFL defined as the straight-line distance between the tangent point C and the landing point ALI, is calculated by the following formula:

[0049]

[0050] where x c represents the horizontal coordinate value of the point C, y c represents the vertical coordinate value of the point C, x ALI represents the horizontal coordinate value of the point ALI, and y ALI represents the vertical coordinate value of the point ALI.

[0051] Preferably, the aircraft has a distance S to fly to perform the S-turn maneuver tg = S AB + S BT + S HAC + S PFL The specific calculation process is as follows:

[0052] In the S-turn segment, the aircraft maintains a constant roll angle σ s = 35° to form a circular arc trajectory; in order to calculate the arc length of the S-turn, the positions of the center O s and the tangent point B need to be determined; the S-turn circular arc radius R s is obtained according to the current position and speed of the aircraft, as follows:

[0053]

[0054] where γ is the trajectory angle of the aircraft;

[0055] Draw an auxiliary line AN parallel to the x-axis through the point A(x, y); let ∠NAOs be the included angle between the line segment AN and AO s , then the coordinate position of the center O s (x s , y s ) is obtained by the following formula:

[0056]

[0057] x s = x + R s cos ∠NAO s ;

[0058] y s = y + R s sin ∠NAO s ;

[0059] where x represents the horizontal coordinate value of the point A, and y represents the vertical coordinate value of the point A.s Indicates O s The horizontal coordinate value of the point, y s Indicates O s The ordinate value of the point, χ is the azimuth of the aircraft;

[0060] According to ΔO s The geometric relationship of OD, ∠BO s The size of O is calculated by the following formula:

[0061] OD=R HAC +R s ;

[0062]

[0063] Among them, R HAC Indicates the radius of the heading calibration cylinder HAC of the heading calibration section; OD indicates the distance between points O and D; OO s Indicates point O and O s The distance between the points;

[0064] Draw a line segment O through point O parallel to the x-axis s E, determine the angle ∠EO s The size of O, from which we get the angle

[0065] ∠EO s The size of B is as follows:

[0066]

[0067] ∠EO s B=∠EO s O-∠BO s O;

[0068] Among them, x HAC Indicates the horizontal coordinate value of the HAC center position, y HAC Indicates the vertical coordinate value of the HAC center position;

[0069] Therefore, the tangent point B(x b ,y b ) is calculated using the following formula:

[0070] x b =x s -R s cos∠EO s B;

[0071] y b =y s +R s sin∠EO s B;

[0072] Among them, x b Indicates the horizontal coordinate value of point B, y b Indicates the vertical coordinate value of point B;

[0073] According to the center O s , the position of the tangent point B and the angle ∠AO s The size of B, calculate the S turn S AB The arc length is as follows:

[0074]

[0075] S AB =R s ∠AO s B;

[0076] Among them, AB represents the distance between point A and point B;

[0077] Draw a line segment OF through point O, parallel to the x-axis, given the angle ∠O s OF and ∠O s The size of OD determines the size of the angle ∠DOF as follows:

[0078] ∠O s OF=∠EO s O;

[0079] ∠DOF=∠O s OF-∠O s OD;

[0080] Then, the tangent point T(x t ,y t ) is obtained by the following formula:

[0081] x t =x HAC +R HAC cos∠DOF;

[0082] y t =y HAC -R HAC sin∠DOF;

[0083] Among them, x t Indicates the horizontal coordinate value of point T, y t Indicates the vertical coordinate value of point T;

[0084] After determining the tangent points B and T, the straight-line flight distance S of the capture segment is BT Calculated by the following formula:

[0085]

[0086] Finally, the heading calibration segment SHAC and the remaining range before the landing phase S PFL The range calculation method is the same as that for the return method without S-turn maneuver, so it will not be repeated here.

[0087] Preferably, in S3, the angle of attack and speed brake guidance instructions are obtained according to the deviation between the current energy state and the desired energy state through the longitudinal guidance law, as follows:

[0088] Determine the current flight subphase of the aircraft in real time and obtain the desired energy state by interpolating the energy profile of the longitudinal trajectory, including the altitude profile and velocity profile;

[0089] After the aircraft enters the energy management phase, the altitude guidance law α is determined. c ,as follows:

[0090]

[0091] Among them, h and Respectively represent the altitude and ascent and descent speed of the aircraft; α * They represent the expected angle of attack of the longitudinal trajectory being tracked; h * and They represent the desired altitude and ascent and descent speed, respectively, both derived from the tracked trajectory; and is the gain coefficient;

[0092] When the aircraft's Mach number is lower than 0.8, the speed brake is activated to control the speed. The proportional and integral controllers are used to adjust the speed brake opening to achieve speed control. The guidance law of the speed control loop is expressed as δ sbc ,as follows:

[0093]

[0094] Where V is the speed of the aircraft, V * is the desired speed of the aircraft, is the deflection angle when the speed brake is in the center position, and is the gain coefficient.

[0095] Preferably, in S3, the roll angle guidance instruction is output according to the flight sub-stage through the lateral guidance law, specifically as follows:

[0096] According to the track characteristics of different sub-stages, corresponding lateral guidance methods are adopted:

[0097] In the S-turn section, the open-loop fixed roll angle control mode is adopted, and the corresponding roll angle command is:

[0098]

[0099] wherein, Flag S = 1 indicates that the aircraft enters the S-turn section to start the roll to increase the range to consume energy, and Flag S = 0 indicates that after a period of S-turn flight, the energy of the aircraft is less than the nominal energy corresponding to the real-time distance to be flown, and the roll in the opposite direction needs to be started;

[0100] In the capture section, the heading tracking control strategy is adopted, and the guidance law based on the heading angle deviation is adopted:

[0101] σ c = K χ (χ-χ * );

[0102] wherein, χ is the current flight heading of the aircraft, χ * is the desired heading, and K χ is the gain coefficient;

[0103] In the heading calibration section, the aircraft tracks the circular arc trajectory of the heading calibration cylinder HAC of the preset heading calibration section, adopts a proportional-derivative controller, generates a roll angle command according to the lateral deviation distance and deviation rate of the aircraft from the circular arc, and adopts a nonlinear L1 guidance method, including the following steps:

[0104] According to the point B corresponding to the current position A of the aircraft on the circular arc path and the tangent line drawn from the point B, a virtual reference point C is determined on the tangent line, and the distance from the current position to the reference point C is taken as L1, and the angle between the speed direction of the aircraft and the AC line is taken as η, and the lateral overload command N zc is obtained according to the centripetal force formula, as follows:

[0105]

[0106] wherein, V is the speed of the aircraft;

[0107] In actual flight, the lift component generated by the roll of the aircraft provides this part of the lateral overload, as follows:

[0108] N zc = g tanσ c ;

[0109] The corresponding roll angle command is obtained as follows:

[0110]

[0111] wherein, η1 is determined according to the lateral deviation distance d of the current position of the aircraft and the target path, and η2 is determined by the heading deviation Δψ of the speed direction of the aircraft and the target path;

[0112] The solution method for parameter L1 is as follows:

[0113] Assuming that η is a very small value, sinη is approximately sinη≈η=η1+η2, where Approximately:

[0114]

[0115] in, is the first-order derivative of d;

[0116] make The following second-order system is obtained:

[0117]

[0118] in, is the second-order derivative of d;

[0119] The above formula shows that the L1 guidance algorithm is an approximate linear model, which can be regarded as a simple second-order system with a damping ratio of The natural frequency is Take the period T = 2π / ω n , we get:

[0120]

[0121] In actual arc path tracking, the distance OA between the current position A of the aircraft and the center O of the heading calibration cylinder HAC is used to obtain the side deviation distance d = OA - R HAC , that is, the lateral deviation of the aircraft relative to the target arc; η2 is obtained according to the angle between the aircraft's velocity direction and the target arc's tangent direction, that is, the heading deviation Δψ between the velocity direction and the target tangent BC; the heading of the target tangent BC is the azimuth angle ψ of the line connecting the center O and the current position A of the aircraft OA Subtract 90° to obtain the roll angle command:

[0122]

[0123] During the pre-landing phase, the aircraft is aligned with the runway centerline and the L1 guidance algorithm is used to correct the heading and lateral offset. The corresponding roll angle command is obtained based on the lateral offset d between the aircraft's current position and the target straight path and the heading deviation Δψ between the velocity direction and the target straight direction:

[0124]

[0125] In another aspect, an online real-time energy management and guidance system for a high-speed aircraft is provided, the system comprising:

[0126] processor;

[0127] a memory having stored thereon a computer program executable on the processor;

[0128] Wherein, when the computer program is executed by the processor, the steps of the high-speed aircraft online real-time energy management guidance method are implemented.

[0129] On the other hand, a computer-readable storage medium stores a data processing program, which, when executed by a processor, implements the steps of the high-speed aircraft online real-time energy management guidance method.

[0130] Compared with the prior art, the present invention has the following beneficial effects:

[0131] (1) By tracking low-energy trajectories and combining them with an S-turn energy management strategy, the present invention can flexibly cope with the uncertainty of initial energy, enabling the aircraft to safely enter the landing phase under various circumstances;

[0132] (2) The present invention cleverly connects the prediction range algorithms of each stage based on the real-time flight position and combined with the ground track, and can obtain a continuously changing and accurate distance to be flown;

[0133] (3) Compared with other complex trajectory optimization methods, the Gaussian pseudospectral method of the present invention has higher computational efficiency and good convergence, can find the global optimal solution more quickly, can achieve rapid iterative optimization in actual engineering applications, complete ground trajectory generation and flight distance prediction online, can ensure real-time operation, and can meet the requirements of engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0134] Figure 1 This is a flow chart of a high-speed aircraft online real-time energy management and guidance method according to an embodiment of the present invention;

[0135] Figure 2 This is a schematic diagram of an energy corridor according to an embodiment of the present invention;

[0136] Figure 3 This is a flow chart of Gaussian pseudospectral trajectory planning according to an embodiment of the present invention;

[0137] Figure 4 This is a schematic diagram of the TAEM segment ground track according to an embodiment of the present invention;

[0138] Figure 5 The normal return voyage prediction for the TAEM segment according to an embodiment of the present invention;

[0139] Figure 6 This is a range prediction for a TAEM segment containing an S-turn return according to an embodiment of the present invention;

[0140] Figure 7 A flow chart of real-time calculation of the distance to fly for an embodiment of the present application;

[0141] Figure 8 A circular arc tracking linear model for an embodiment of the present application. DETAILED DESCRIPTION

[0142] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0143] As shown in Figure 1 The present embodiment provides an online real-time energy management guidance method for a high-speed aircraft, specifically comprising the following steps.

[0144] S1, determining an energy management section, including flight sub-phases of an S-turn section, a capture section, a heading calibration section and a pre-landing section; determining an energy corridor according to an upper energy boundary and a low-energy trajectory group, and planning a low-energy nominal longitudinal trajectory based on a Gauss pseudospectral method.

[0145] Specifically, the position and energy state of the aircraft at the initial time of entering the energy management section have certain uncertainties, so the energy management section must be guided by an effective and feasible guidance strategy to achieve energy management and control, thereby guiding the aircraft to have a desired speed and height when reaching the landing section window.

[0146] In view of the uncertainty of the initial window energy state, a low-energy trajectory tracking strategy is proposed to improve the adaptability of the guidance system to low energy. When the aircraft enters the energy management section with low energy, the longitudinal trajectory can still be tracked to ensure that the speed and height of the aircraft entering the landing section meet the window requirements. However, the adaptability of this strategy to high energy is also reduced, so the S-turn strategy is added to compensate for the shortcomings of the low-energy trajectory tracking strategy. The S-turn increases the distance to fly to consume energy, and when the real-time energy of the aircraft is less than or equal to the low-energy trajectory profile, the S-turn is ended and the aircraft safely enters the landing section according to the normal guidance strategy.

[0147] Based on the above-mentioned strategic requirements, an energy corridor consisting of an upper energy boundary (EnS) and a low-energy trajectory (EnL) is indispensable for the energy management segment. The upper energy boundary is used to determine whether to make an S-turn, and the low-energy trajectory is used for trajectory tracking to obtain the desired instructions. In the design of the low-energy trajectory, the state distribution of the end of the reentry segment, i.e., the initial window of the TAEM, is first obtained based on the results of the Monte Carlo target shooting simulation, so as to determine the lowest energy situation in the initial state of the TAEM, and use this state as the initial energy state of the low-energy trajectory. Then, the full trajectory is designed without external disturbances, aerodynamic deviations, and while satisfying the terminal constraints. The upper energy boundary refers to the maximum initial energy state that the aircraft can accept when it does not make an S-turn and the speed brake is fully open, and the terminal state of the trajectory can also meet the window range of entering the landing segment.

[0148] The energy corridor determined by the energy distribution at the end of the reentry segment and the TAEM end constraint is as follows: Figure 2 As shown, when the aircraft enters the TAEM, it begins to calculate the distance to be flown at its current position in real time. By interpolating the trajectory energy profile, the corresponding upper and lower energy bounds can be obtained. When the aircraft's actual energy at this time is between the corridors, it flies along the desired longitudinal trajectory profile according to the conventional guidance process. If the aircraft's actual energy exceeds the upper bound, it is determined that there is excess energy and an S-turn is required to dissipate energy. During the S-turn process, when the aircraft's real-time energy returns to the corridors and is less than or equal to the lower energy bound, the S-turn ends and the aircraft begins to capture the heading calibration circle, adjusting the heading and aligning with the runway centerline.

[0149] To summarize, if the aircraft enters TAEM in a low-energy state, the low-energy trajectory is tracked to ensure that its terminal state meets the initial landing window requirements; for a high-energy state, energy is dissipated through S-turn maneuvers to bring the aircraft's energy state within the energy corridor range to achieve subsequent safe landing; if it is in a conventional energy state, the low-energy trajectory profile can be tracked according to the normal guidance process.

[0150] Furthermore, the Gauss pseudo-spectral method (GPM) is used to solve the longitudinal trajectory of the energy management segment. The state and control variables of the continuous optimal control problem are discretized at Legendre Gauss points. Then, using the discrete points as nodes, full-interval Lagrange interpolation polynomials are used to approximate the state and control variables. In this way, the optimal control problem is transformed into a nonlinear programming problem, thus achieving trajectory design.

[0151] This method does not require complex optimization algorithms and can quickly obtain a trajectory that meets the constraints of initial and final states, dynamic pressure, etc., while ensuring the actual engineering requirements such as trajectory design efficiency, re-entry trajectory smoothness, and smooth changes in control quantities. It has strong engineering practicality. The planning flow chart is as follows: Figure 3 As shown, the following steps are included:

[0152] Initialize the longitudinal trajectory angle of attack, longitudinal trajectory altitude, and longitudinal trajectory speed, using the angle of attack as the control variable as input, and the output state variables include altitude, speed, trajectory angle, and range;

[0153] Select Legendre Gauss point;

[0154] Using Lagrange interpolation polynomials and taking Legendre Gauss points as nodes, the time history of state and control variables is approximately represented, and the continuous state and control variables are converted into discrete numerical sequences.

[0155] Construct the kinematic equations of the aircraft, discretize the dynamic equations at Gaussian points, and determine the motion state of the aircraft at discrete time points;

[0156] Determine the dynamic constraints, initial condition constraints, terminal constraints, process constraints and control constraints of the aircraft.

[0157] Since the range of the longitudinal trajectory matches the range of the actual ground trajectory, the range is used as the optimization target. At the same time, in order to take into account the overall smoothness of the reentry trajectory, the integral of the square of the trajectory angular rate is used as the optimization indicator to construct the final performance index.

[0158] While satisfying the constraints of the dynamic equations, initial condition constraints, terminal constraints, process constraints and control constraints, the state variables, control variables, initial moments and terminal moments at discrete nodes are solved to minimize the performance indicators and finally obtain the longitudinal trajectory of the aircraft after planning.

[0159] Specifically:

[0160] (1) Dynamic constraints

[0161] If the unpowered aircraft is regarded as a point mass and the influence of the earth's rotation is not considered, and the earth is assumed to be flat, its kinematic equation can be expressed as:

[0162]

[0163] Where V is velocity, γ is trajectory angle, χ is azimuth, σ is the current bank angle of the aircraft, m is mass, g is constant gravity, h is altitude, x is the lateral position from the runway center, and y is the longitudinal position from the runway center. The symbols on the left represent first-order derivatives. The formulas for calculating lift L and drag D are as follows:

[0164]

[0165] in, is the dynamic pressure, ρ is the air density, S ref is the reference area. C L is the lift coefficient, C D is the drag coefficient, which is obtained by two-dimensional interpolation of aerodynamic data with Mach number and angle of attack α as independent variables.

[0166] (2) Initial and final constraints

[0167] The initial condition constraints include the altitude, velocity, and trajectory angle constraints at the initial time (t0) of entering the energy management phase:

[0168]

[0169] The terminal constraint refers to the time when the energy management phase switches to the landing phase, that is, the end of the energy management phase (t f )’s altitude, speed, trajectory angle, and range constraints:

[0170] h(t f )=h f ; V(t f )=V f ;γ(t f )=γ f ;

[0171] (3) Process constraints

[0172] To ensure the safety of the aircraft structure, the dynamic pressure constraints and overload constraints are:

[0173]

[0174] in, n ymax are the maximum values ​​of dynamic pressure and normal overload, which are 80kPa and 4G respectively.

[0175] (4) Control constraints

[0176] The range of the angle of attack α is defined according to aerodynamic data: -5°≤α≤15°. At the same time, in order to obtain a smooth, stable and feasible trajectory, the rate of change of the angle of attack is also constrained:

[0177] (5) Performance indicators

[0178] The longitudinal trajectory of the energy management section uses the distance to be flown as the independent variable. During the actual flight, the longitudinal trajectory data is interpolated based on the predicted distance to be flown to obtain the corresponding longitudinal guidance instructions. Therefore, the range of the longitudinal trajectory should match the range of the actual ground trajectory. Therefore, the range is used as the optimization target:

[0179] J1=L f ;

[0180] Secondly, in order to take into account the overall smoothness of the reentry trajectory, the integral of the square of the trajectory angular rate is used as a performance indicator:

[0181]

[0182] Taking into account the robustness and efficiency of the designed trajectory, the performance indicators shown in the above two equations are selected as the optimization objectives. By adjusting the weight coefficient, a trade-off is made between the range and trajectory smoothness to plan the most suitable trajectory. The final performance indicator formula is:

[0183]

[0184] Among them, w1 and w2 are weight coefficients, which are used to adjust the weight of each performance indicator in trajectory planning.

[0185] (6) Optimal control problem

[0186] The optimal control problem based on GPM is as follows: Under the condition of satisfying the dynamic equation constraints, initial and final constraints, process constraints and control constraints, solve the state quantity x at the discrete node i (i=0,1,...k), control quantity u i (i=0,1,...k), initial time t0 and final time t f , so that the performance index J is minimized, and the optimal control problem is transformed into a nonlinear programming problem:

[0187]

[0188] satisfy:

[0189]

[0190] φ(x(t0),t0,x(t f ),t f )=0;

[0191] C(x(t),μ(t),t)≤0;

[0192] Among them, the state variable x(t)∈R n , state variable μ(t)∈R m , t is the time.

[0193] The performance index function J includes the Mayer term Φ(x(t0), t0, x(t f ),t f ) and the Lagrangian term L(x(t),μ(t),t); is the constraint of the dynamic differential equation; φ(x(t0),t0,x(t f ),t f )=0 is the equality constraint determined by the initial and final constraints; C(x(t),μ(t),t)≤0 is the inequality constraint determined by the process constraints and control constraints.

[0194] S2: When the aircraft enters the energy management stage, it determines whether the current actual energy exceeds the upper energy boundary of the energy corridor. If it exceeds, an S-turn stage is added; otherwise, it enters the capture stage; the aircraft's waiting distance to fly is predicted in real time based on the geometric characteristics of the trajectory of each flight sub-stage and the position of the aircraft.

[0195] Specifically, the designed ground track is as follows Figure 4 As shown in the figure, it is divided into four sub-phases: S-turn phase, capture phase, heading calibration phase, and pre-landing phase. If the aircraft has excess energy when entering the TAEM, an S-turn is performed to increase the distance to be flown to consume the excess energy. If there is no excess energy, the aircraft directly enters the capture phase. The flight mission of the capture phase is to fly toward and tangent to the pre-set heading calibration circle. After reaching the tangent point of the heading calibration cylinder (HAC), the heading calibration phase begins, tracking the HAC arc. After appropriate heading adjustments, the aircraft is basically aligned with the runway centerline. Then, the pre-landing phase begins, tracking the extended runway centerline, and further adjusting the heading and lateral position to ensure that the aircraft enters the landing phase with high alignment accuracy.

[0196] Furthermore, the normal return trajectory, such as Figure 5 If the aircraft enters the capture phase directly, the ground track will be as follows: Figure 5 As shown in the figure, in actual flight, the flight trajectory during the capture phase should consist of an arc followed by a straight line. Because the arc trajectory during the capture phase has a large turning radius, its flight trajectory is approximately consistent with the straight line, and the deviation between the two ranges is small. To simplify the calculation, the actual flight range of the capture phase is directly approximated using a straight line trajectory.

[0197] Figure 5 The distance to be flown in the flight trajectory S tg Include capture segment S AT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground range is calculated as follows:

[0198] S tg =S AT +S HAC+S PFL ;

[0199] This embodiment adopts fixed heading alignment circle position and radius, and the position of landing point ALI is also determined. The heading alignment cylinder HAC center position (x HAC ,y HAC ), radius R HAC and the tangent point C (x c ,y c ) of HAC and pre-landing section are determined; the distance of straight ground track S AT is obtained according to the current position A (x, y) of the aircraft, HAC center position and the distance OA between O and A, as follows:

[0200]

[0201] Wherein, x represents the horizontal coordinate value of A, y represents the vertical coordinate value of A, x HAC represents the horizontal coordinate value of HAC center position, and y HAC represents the vertical coordinate value of HAC center position;

[0202] An auxiliary line DN parallel to the x-axis is drawn through A, and according to the lengths of S AT , OA and DA, ∠AOT and ∠DOA are determined first, and then ∠TOE is calculated, and the calculation formula is as follows:

[0203]

[0204] ∠TOE = π - ∠DOA - ∠AOT;

[0205] Then, the turning angle Δψ HAC around HAC circle is obtained, and the distance of heading alignment section S HAC is obtained, as follows:

[0206] Δψ HAC = ∠TOE;

[0207] S HAC = R HAC Δψ HAC ;

[0208] Finally, the remaining range S PFL before the landing stage is defined as the straight line distance between the tangent point C and the landing point ALI, which is calculated by the following formula:

[0209]

[0210] Wherein, x c represents the horizontal coordinate value of C, and y c represents the vertical coordinate value of C.ALI Indicates the horizontal coordinate value of the ALI point, y ALI Indicates the vertical coordinate value of the ALI point.

[0211] Furthermore, the S-turn return trajectory, such as Figure 6 If the aircraft enters the energy management phase with excess energy, the ground range calculation of the S-turn phase needs to be increased. Figure 6 As shown in the flight trajectory, when the S turn is triggered, the ground waiting distance S tg Including S-turn section S AB , capture segment S BT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground range is calculated as follows:

[0212] S tg =S AB +S BT +S HAC +S PFL ;

[0213] During the S-turn, the aircraft maintains a constant roll angle σ s = 35° to form an arc trajectory; in order to calculate the arc length of the S turn, it is necessary to determine the center O s and the position of the tangent point B; calculate the S-turn arc radius R based on the current position and speed of the aircraft s ,as follows:

[0214]

[0215] Where γ is the trajectory angle of the aircraft;

[0216] Draw an auxiliary line AN through point A (x, y) parallel to the x-axis; let ∠NAOs be the line segment AN and AO s The angle between the center of the circle O s (x s ,y s ) is obtained from the following formula:

[0217]

[0218] x s =x+R s cos∠NAO s ;

[0219] y s =y+R s sin∠NAO s ;

[0220] Among them, x represents the horizontal coordinate value of point A, y represents the vertical coordinate value of point A, and x s Indicates O s The horizontal coordinate value of the point, y s Indicates O s The ordinate value of the point, χ is the azimuth of the aircraft;

[0221] According to ΔO s The geometric relationship of OD, ∠BO s The size of O is calculated by the following formula:

[0222] OD=R HAC +R s ;

[0223]

[0224] Among them, R HAC Indicates the radius of the heading calibration cylinder HAC of the heading calibration section; OD indicates the distance between points O and D; OO s Indicates point O and O s The distance between the points;

[0225] Draw a line segment O through point O parallel to the x-axis s E, determine the angle ∠EO s The size of O, from which we get the angle

[0226] ∠EO s The size of B is as follows:

[0227]

[0228] ∠EO s B=∠EO s O-∠BO s O;

[0229] Among them, x HAC Indicates the horizontal coordinate value of the HAC center position, y HAC Indicates the vertical coordinate value of the HAC center position;

[0230] Therefore, the tangent point B(x b ,y b ) is calculated using the following formula:

[0231] x b =x s -R s cos∠EO s B;

[0232] y b =y s +R s sin∠EOs B;

[0233] Among them, x b Indicates the horizontal coordinate value of point B, y b Indicates the vertical coordinate value of point B;

[0234] According to the center O s , the position of the tangent point B and the angle ∠AO s The size of B, calculate the S turn S AB The arc length is as follows:

[0235]

[0236] S AB =R s ∠AO s B;

[0237] Among them, AB represents the distance between point A and point B;

[0238] Draw a line segment OF through point O, parallel to the x-axis, given the angle ∠O s OF and ∠O s The size of OD determines the size of the angle ∠DOF as follows:

[0239] ∠O s OF=∠EO s O;

[0240] ∠DOF=∠O s OF-∠O s OD;

[0241] Then, the tangent point T(x t ,y t ) is obtained by the following formula:

[0242] x t =x HAC +R HAC cos∠DOF;

[0243] y t =y HAC -R HAC sin∠DOF;

[0244] Among them, x t Indicates the horizontal coordinate value of point T, y t Indicates the vertical coordinate value of point T;

[0245] After determining the tangent points B and T, the straight-line flight distance S of the capture segment is BT Calculated by the following formula:

[0246]

[0247] Finally, the heading calibration segment S HAC and the remaining range before the landing phase S PFL The range calculation method is the same as that for the return method without S-turn maneuver, so it will not be repeated here.

[0248] Through the above derivation process, we can get the geometric calculation method of the flight range in each flight phase of the energy management section. In order to predict the distance to be flown in real time during each guidance cycle, it is necessary to calculate the distance to be flown S in real time based on the real-time position of the aircraft and the geometric algorithm of the phase. tg , Figure 7 The real-time calculation process of the distance to be flown that changes with the flight phase is given.

[0249] After the aircraft enters the energy management phase, it makes an energy judgment. If the energy is excessive, it enters the S-turn phase, otherwise it directly enters the capture phase. If it enters the S-turn phase, it calculates the positions of the two tangent points B and T in real time and calculates the distance S to be flown for each flight sub-phase based on the current position A of the aircraft. tg , including the S-turn section S AB , capture segment S BT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances, that is, S tg =S AB +S BT +S HAC +S PFL If the capture phase is entered, the position of the tangent point T is calculated in real time and the distance to be flown S for each flight sub-phase is calculated based on the current position A of the aircraft. tg , including the capture segment S AT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances, that is, S tg =S AT +S HAC +S PFL ;

[0250] After entering the S-turn section, it is determined in real time whether the aircraft has reached the two tangent points B and T. If S AB If the distance is less than or equal to the threshold, it is determined that the aircraft has reached the tangent point B. At this time, the S-turn segment ends and enters the capture segment. The distance to be flown is S tg Transformed into the distance to be flown S calculated based on the current position A and the real-time position of the tangent point T tg , waiting distance S tg Include capture segment S AT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances;

[0251] After entering the capture phase, if S AT If the distance is less than or equal to the threshold, the aircraft is judged to have reached the tangent point T, the capture phase ends and enters the heading calibration phase, and an initial value of 0 is set for the integral range L. s , S HAC and S PFL The sum of the range minus the integral range L s Get the distance to fly S tg ;

[0252] With the integral range L s Continuously increasing, waiting distance S tg It will continue to decrease until it decreases to meet the condition S tg ≤S PFL The heading calibration phase ends and the aircraft enters the pre-landing phase;

[0253] When the aircraft meets the conditions for entering the landing phase, that is, it successfully hits the line, the aircraft is ≤4000m above the ground or S tg ≤0When any of the three conditions is met, the online waiting distance prediction is terminated;

[0254] Wherein, the integral range L s By integrating the local horizontal velocity, the velocity of the aircraft in the geographic coordinate system is V N =[v Nx ,v Ny ,v Nz ] T , where v Nx 、v Ny and v Nz Represent the speed in the X, Y and Z directions respectively, then the local horizontal speed V level for:

[0255]

[0256] Calculate the integral range L by trapezoidal integration method s :

[0257]

[0258] Among them, Δt is the calculation step size, k is the current calculation step size, L s (k) represents the integrated range at the current moment, L s (k-1) represents the integrated range at the previous moment, V level (k) represents the local horizontal velocity at the current moment, V level (k-1) represents the local horizontal velocity at the previous moment.

[0259] Introducing the integral range Ls In the calculation process of the waiting-to-fly distance in some stages, the distance between fixed positions is subtracted from the integrated range to ensure that the waiting-to-fly distance keeps changing continuously throughout the whole process, avoiding step jumps that cause sudden changes in the longitudinal reference instructions and thus affect the guidance effect.

[0260] S3 determines the current flight sub-stage of the aircraft in real time, obtains the desired energy state by interpolating the energy profile of the longitudinal trajectory, including the altitude profile and velocity profile; obtains the angle of attack and speed brake guidance instructions based on the deviation between the current energy state and the desired energy state through the longitudinal guidance law; and outputs the bank angle guidance instructions according to the flight sub-stage based on the distance to be flown through the lateral guidance law.

[0261] The longitudinal guidance strategy achieves energy control by tracking a two-dimensional trajectory profile, including both altitude and velocity profiles. During the supersonic phase, an altitude control loop outputs angle-of-attack commands to adjust the vehicle's altitude, ensuring it tracks the predetermined altitude profile. In the subsonic phase, a velocity control loop is added to the altitude control loop, controlling speed via the airbrakes. This integrated control of altitude and velocity ensures the vehicle's energy remains within the energy corridor, while achieving stable trajectory tracking.

[0262] After the aircraft enters TAEM, in order to achieve accurate altitude tracking, the altitude guidance law shown below is adopted:

[0263]

[0264] Among them, h and Respectively represent the altitude and ascent and descent speed of the aircraft; α * They represent the expected angle of attack of the longitudinal trajectory being tracked; h * and They represent the desired altitude and ascent and descent speed, respectively, both derived from the tracked trajectory; and is the gain coefficient;

[0265] When the aircraft's Mach number is lower than 0.8, the speed brake can be activated to control the speed. The proportional integral (PI) controller is used to adjust the speed brake opening to achieve speed control. The guidance law of the speed control loop can be expressed as:

[0266]

[0267] Where V is the speed of the aircraft, V * is the desired speed of the aircraft, is the deflection angle when the speed brake is in the center position, and is the gain coefficient.

[0268] The lateral guidance law in S3:

[0269] The task of lateral guidance is to adjust the distance to go and solve the problem of excess energy, and to adjust the flight heading to make the aircraft fly along the predetermined ground trajectory, so as to ensure that it is aligned with the runway centerline and prepare for subsequent approach and landing. Figure 4 The ground trajectory of the TAEM segment is given, including the S-turn segment, the capture segment, the heading alignment segment, and the pre-landing segment. According to the characteristics of the flight path in different sub-phases, appropriate guidance methods will be used.

[0270] (1) S-turn segment

[0271] The S-turn segment is a phase of energy consumption, and the purpose is to consume excess energy by increasing flight distance. It should be noted that the S-turn segment is not a necessary flight phase of TAEM, and it will only be performed in the case of excess energy.

[0272] If the energy of the aircraft exceeds the maximum energy boundary, the S-turn segment will be entered to start the S-type lateral maneuver. In this process, the flight range gradually increases, and at the same time, the excess energy is consumed. When the real-time energy of the aircraft is less than the nominal energy corresponding to the current distance to go, the heading will be adjusted in the opposite direction by tilting, and the flight will continue along the S-turn circular arc trajectory. When the aircraft reaches the intersection point of the S-turn circular arc and the capture segment trajectory, the S-turn is ended and the capture segment is entered. This phase adopts an open-loop fixed bank angle control mode, and the corresponding bank angle command is:

[0273]

[0274] Where Flag S = 1 indicates that the aircraft enters the S-turn segment to start tilting to increase the range to consume energy, and Flag S = 0 indicates that after a period of S-turn flight, the energy of the aircraft is less than the nominal energy corresponding to the real-time distance to go, and the opposite direction tilting needs to be started.

[0275] (2) Capture segment

[0276] The task of the capture segment is to guide the aircraft to the pre-set HAC and make it tangent to it. During the flight of this phase, the heading will be continuously adjusted to align with the intersection point, so the heading tracking control strategy is directly adopted, and the guidance law based on the heading angle deviation is designed as follows:

[0277] σ c = K χ (χ-χ * );

[0278] Where χ is the current flight heading of the aircraft, and χ * is the desired heading.

[0279] (3) Heading calibration section

[0280] In the heading calibration section, the aircraft tracks the preset HAC arc trajectory and gradually adjusts its heading to align with the runway centerline. Arc tracking usually uses a proportional differential controller to generate a roll angle instruction based on the lateral deviation distance and deviation rate of the aircraft from the arc. However, this type of linear controller often has limited adaptability to wind interference in actual flight, and TAEM happens to be in a strong wind area at an atmospheric altitude of about 10km. Therefore, in order to improve the adaptability of the aircraft to wind interference during high-speed circular movements, the present invention particularly adopts a nonlinear L1 guidance method during the energy management section flight process, thereby improving the arc tracking accuracy and subsequent more accurate alignment with the runway centerline. The corresponding arc tracking linear model is as follows: Figure 8 shown.

[0281] Draw a tangent line from point B on the arc path corresponding to the current position A of the aircraft. Determine the virtual reference point C on this tangent line. Take the distance from the current position to the reference point C as L1. The angle between the aircraft's velocity direction and the line connecting AC is η. According to the centripetal force formula, the lateral overload command can be obtained as:

[0282]

[0283] In actual flight, this part of the lateral overload can be provided by the lift component generated by the aircraft's tilt:

[0284] N zc =g tanσ c ;

[0285] It can be seen that the corresponding roll angle command is:

[0286]

[0287] Among them, η1 is determined according to the lateral deviation between the current position of the aircraft and the target path, that is, η2 can be determined by the heading deviation Δψ between the aircraft velocity direction and the target path.

[0288] The solution for parameter L1 is as follows: Assuming that η is a very small value, sinη can be approximated as sinη≈η=η1+η2, where It can be approximated as:

[0289]

[0290] make The following second-order system can be obtained:

[0291]

[0292] The above formula shows that the L1 guidance algorithm is an approximate linear model and can be regarded as a simple second-order system with a damping ratio of The natural frequency is Take the period T = 2π / ω n , we can get:

[0293]

[0294] In actual arc path tracking, the distance OA between the current position A of the aircraft and the center O of the heading calibration cylinder HAC is used to obtain the side deviation distance d = OA - R HAC , that is, the lateral deviation of the aircraft relative to the target arc; η2 is obtained according to the angle between the aircraft's velocity direction and the target arc's tangent direction, that is, the heading deviation Δψ between the velocity direction and the target tangent BC; the heading of the target tangent BC is the azimuth angle ψ of the line connecting the center O and the current position A of the aircraft OA Subtract 90° to obtain the roll angle command:

[0295]

[0296] (4) Pre-landing phase

[0297] During the pre-landing phase, the aircraft further precisely calibrates its heading to align it with the runway centerline in preparation for landing. When the flight status (such as altitude, speed, position, etc.) meets the requirements of the landing window, the aircraft smoothly transitions to the landing phase. In this phase, the L1 guidance algorithm is also used to correct the heading and lateral deviation. Based on the lateral deviation d between the current position of the aircraft and the target straight path, and the heading deviation Δψ between the velocity direction and the target straight direction, the corresponding roll angle command can be obtained:

[0298]

[0299] During the actual guidance process, S4 loops through steps S1 to S3, with a guidance cycle of 0.005 seconds, continuously adjusting the aircraft's state until it successfully enters the pre-landing phase, ensuring it can ultimately reach the landing point safely and accurately.

[0300] The above is a high-speed aircraft online real-time energy management and guidance method provided by one embodiment of this embodiment. Based on the same idea, this embodiment also provides a corresponding high-speed aircraft online real-time energy management and guidance system. For the specific definition of the high-speed aircraft online real-time energy management and guidance system, please refer to the definition of the high-speed aircraft online real-time energy management and guidance method above, which will not be repeated here. The various modules in the above-mentioned high-speed aircraft online real-time energy management and guidance system can be fully or partially implemented by software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the corresponding operations of the above-mentioned modules.

[0301] This embodiment also provides a computer-readable storage medium, which stores a computer program that can be used to execute the above Figure 1 An online real-time energy management guidance method for high-speed aircraft is provided.

[0302] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A high-speed aircraft online real-time energy management guidance method, characterized in that: include: S1, determine the energy management segment, including the flight sub-phases of the S-turn segment, the capture segment, the heading calibration segment, and the pre-landing segment; determine the energy corridor based on the energy upper boundary and the low-energy trajectory composition, and plan the low-energy nominal longitudinal trajectory based on the Gaussian pseudospectral method; S2, when the aircraft enters the energy management stage, it determines whether the current actual energy exceeds the upper energy boundary of the energy corridor. If it exceeds, an S-turn stage is added; otherwise, it enters the capture stage; Predict the distance to be flown of the aircraft in real time based on the geometric characteristics of the trajectory of each flight sub-stage and the position of the aircraft; S3: Determine the current flight subphase of the aircraft in real time and obtain the desired energy state, including the altitude and velocity profiles, by interpolating the energy profile of the longitudinal trajectory. Determine the angle of attack and speed brake guidance commands based on the deviation between the current energy state and the desired energy state using the longitudinal guidance law. Based on the distance to be flown, output the bank angle guidance command according to the flight subphase using the lateral guidance law. S4: Continuously adjust the state of the aircraft according to the real-time obtained angle of attack, speed brake guidance instructions, and roll angle guidance instructions until the aircraft successfully enters the pre-landing phase.

2. The high-speed aircraft online real-time energy management guidance method according to claim 1, characterized in that: In S1, the method for obtaining the upper energy boundary is as follows: When the aircraft does not make an S-turn and the speed brakes are fully deployed, and the end state of the trajectory can still meet the window range of entering the landing phase, the maximum acceptable initial energy state is used as the upper energy boundary; The method for obtaining the low-energy trajectory is as follows: The state distribution of the initial window of the energy management segment is obtained based on the Monte Carlo shooting simulation results, and the lowest energy state in the initial state of the energy management segment is determined, and this state is used as the initial energy state of the low-energy trajectory; The full trajectory is designed without external disturbances, aerodynamic deviations and while satisfying the end constraints of the trajectory to obtain a low-energy trajectory.

3. The high-speed aircraft online real-time energy management guidance method according to claim 1, characterized in that: In S1, planning a low-energy nominal longitudinal trajectory based on the Gaussian pseudospectral method specifically includes: Initialize the longitudinal trajectory angle of attack, longitudinal trajectory altitude, and longitudinal trajectory speed, using the angle of attack as the control variable as input, and the output state variables include altitude, speed, trajectory angle, and range; Select Legendre Gauss point; Using Lagrange interpolation polynomials and taking Legendre Gauss points as nodes, the time history of state and control variables is approximately represented, and the continuous state and control variables are converted into discrete numerical sequences. Construct the kinematic equations of the aircraft, discretize the dynamic equations at Gaussian points, and determine the motion state of the aircraft at discrete time points; Determine the dynamic constraints, initial condition constraints, terminal constraints, process constraints, and control constraints of the aircraft; wherein the dynamic constraints are the constraints of the dynamic equations; the initial condition constraints are the constraints on the altitude, speed, and trajectory angle of the aircraft at the beginning of the energy management phase; the terminal constraints are the constraints on the altitude, speed, trajectory angle, and range of the aircraft at the end of the energy management phase; the process constraints are the dynamic pressure constraints and the overload constraints; and the control constraints are the constraints on the range and rate of change of the angle of attack; Since the range of the longitudinal trajectory matches the range of the actual ground trajectory, the range is used as the optimization target. At the same time, in order to take into account the overall smoothness of the reentry trajectory, the integral of the square of the trajectory angular rate is used as the optimization index to construct the final performance index. While satisfying the constraints of the dynamic equations, initial condition constraints, terminal constraints, process constraints and control constraints, the state variables, control variables, initial moments and terminal moments at discrete nodes are solved to minimize the performance indicators and finally obtain the longitudinal trajectory of the aircraft after planning.

4. The high-speed aircraft online real-time energy management guidance method according to claim 1, characterized in that: In S2, the distance to be flown S varies with the flight phase. tg The real-time calculation steps include: After the aircraft enters the energy management phase, it makes an energy judgment. If the energy is excessive, it enters the S-turn phase, otherwise it directly enters the capture phase. If it enters the S-turn phase, it calculates the positions of the two tangent points B and T in real time and calculates the distance S to be flown for each flight sub-phase based on the current position A of the aircraft. tg , including the S-turn section S AB , capture segment S BT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances, that is, S tg =S AB +S BT +S HAC +S PFL If the capture phase is entered, the position of the tangent point T is calculated in real time and the distance to be flown S for each flight sub-phase is calculated based on the current position A of the aircraft. tg , including the capture segment S AT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances, that is, S tg =S AT +S HAC +S PFL ; After entering the S-turn section, it is determined in real time whether the aircraft has reached the two tangent points B and T. If S AB If the distance is less than or equal to the threshold, it is determined that the aircraft has reached the tangent point B. At this time, the S-turn segment ends and enters the capture segment. The distance to be flown is S tg Transformed into the distance to be flown S calculated based on the current position A and the real-time position of the tangent point T tg , waiting distance S tg Include capture segment S AT , heading calibration segment S HAC and pre-landing segment S PFL The sum of the ground distances; After entering the capture phase, if S AT If the distance is less than or equal to the threshold, the aircraft is judged to have reached the tangent point T, the capture phase ends and enters the heading calibration phase, and an initial value of 0 is set for the integral range L. s , S HAC and S PFL The sum of the range minus the integral range L s Get the distance to fly S tg ; With the integral range L s Continuously increasing, waiting distance S tg It will continue to decrease until it decreases to meet the condition S tg ≤S PFL The heading calibration phase ends and the aircraft enters the pre-landing phase; When the aircraft meets the conditions for entering the landing phase, that is, it successfully hits the line, the aircraft's height from the ground is lower than the set height or S tg ≤0When any of the three conditions is met, the online waiting distance prediction is terminated; Wherein, the integral range L s By integrating the local horizontal velocity, the velocity of the aircraft in the geographic coordinate system is V N =[v Nx ,v Ny ,v Nz ] T , where v Nx 、v Ny and v Nz Represent the speed in the X, Y and Z directions respectively, then the local horizontal speed V level for: Calculate the integral range L by trapezoidal integration method s : Among them, Δt is the calculation step size, k is the current calculation step size, L s (k) represents the integrated range at the current moment, L s (k-1) represents the integrated range at the previous moment, V level (k) represents the local horizontal velocity at the current moment, V level (k-1) represents the local horizontal velocity at the previous moment.

5. The high-speed aircraft online real-time energy management guidance method according to claim 4, characterized in that: The aircraft does not perform an S-turn maneuver and directly captures the return distance S tg =S AT +S HAC +S PFL The specific calculation process is as follows: Determine the center position of the heading calibration cylinder HAC in the heading calibration section (x HAC ,y HAC ), radius R HAC and the tangent point C(x c ,y c ); Obtain the straight ground track S based on the current position of the aircraft point A (x, y), the center position of the HAC circle, and the distance OA between point O and point A AT The flight distance is as follows: Among them, x represents the horizontal coordinate value of point A, y represents the vertical coordinate value of point A, and x HAC Indicates the horizontal coordinate value of the HAC center position, y HAC Indicates the vertical coordinate value of the HAC center position; Draw an auxiliary line DN through point A parallel to the x-axis. AT , OA and DA lengths, first determine ∠AOT and ∠DOA, and then calculate ∠TOE using the following formula: ∠TOE=π-∠DOA-∠AOT; Then, the turning angle Δψ around the HAC circle is obtained HAC , get the heading calibration segment S HAC The itinerary is as follows: Dp HAC =∠TOE; S HAC =R HAC Δψ HAC ; Finally, the remaining range before the landing phase S PFL It is defined as the straight-line distance between the tangent point C and the landing point ALI and is calculated using the following formula: Among them, x c Indicates the horizontal coordinate value of point C, y c Indicates the vertical coordinate value of point C, x ALI Indicates the horizontal coordinate value of the ALI point, y ALI Indicates the vertical coordinate value of the ALI point.

6. The high-speed aircraft online real-time energy management guidance method according to claim 4, characterized in that: The aircraft has a waiting distance S for S-turn maneuvers tg =S AB +S BT +S HAC +S PFL The specific calculation process is as follows: During the S-turn, the aircraft maintains a constant roll angle σ s = 35° to form an arc trajectory; in order to calculate the arc length of the S turn, it is necessary to determine the center O s and the position of the tangent point B; calculate the S-turn arc radius R based on the current position and speed of the aircraft s ,as follows: Where γ is the trajectory angle of the aircraft; Draw an auxiliary line AN through point A (x, y) parallel to the x-axis; let ∠NAOs be the line segment AN and AO s The angle between the center of the circle O s (x s ,y s ) is obtained from the following formula: x s =x+R s cos∠NAO s ; y s =y+R s sin∠NAO s ; Among them, x represents the horizontal coordinate value of point A, y represents the vertical coordinate value of point A, and x s Indicates O s The horizontal coordinate value of the point, y s Indicates O s The ordinate value of the point, χ is the azimuth of the aircraft; According to ΔO s The geometric relationship of OD, ∠BO s The size of O is calculated by the following formula: OD=R HAC +R s ; Among them, R HAC Indicates the radius of the heading calibration cylinder HAC of the heading calibration section; OD indicates the distance between points O and D; OO s Indicates point O and O s The distance between the points; Draw a line segment O through point O parallel to the x-axis s E, determine the angle ∠EO s The size of O, from which we get the angle ∠EO s The size of B is as follows: ∠EO s B=∠EO s O-∠BO s HE; Among them, x HAC Indicates the horizontal coordinate value of the HAC center position, y HAC Indicates the vertical coordinate value of the HAC center position; Therefore, the tangent point B(x b ,y b ) is calculated using the following formula: x b =x s -R s cos∠EO s B; y b =y s +R s sin∠EO s B; Among them, x b Indicates the horizontal coordinate value of point B, y b Indicates the vertical coordinate value of point B; According to the center O s , the position of the tangent point B and the angle ∠AO s The size of B, calculate the S turn S AB The arc length is as follows: S AB =R s ∠AO s B; Among them, AB represents the distance between point A and point B; Draw a line segment OF through point O, parallel to the x-axis, given the angle ∠O s OF and ∠O s The size of OD determines the size of the angle ∠DOF as follows: ∠O s OF=∠EO s O; ∠DOF=∠O s OF-∠O s OF; Then, the tangent point T(x t ,y t ) is obtained by the following formula: x t =x HAC +R HAC cos∠DOF; y t =y HAC -R HAC sin∠DOF; Among them, x t Indicates the horizontal coordinate value of point T, y t Indicates the vertical coordinate value of point T; After determining the tangent points B and T, the straight-line flight distance S of the capture segment is BT Calculated by the following formula: Finally, the heading calibration segment S HAC and the remaining range before the landing phase S PFL The range calculation method is the same as that for the return method without S-turn maneuver, so it will not be repeated here.

7. The high-speed aircraft online real-time energy management guidance method according to claim 1, characterized in that: In S3, the angle of attack and speed brake guidance instructions are obtained according to the deviation between the current energy state and the desired energy state through the longitudinal guidance law, as follows: Determine the current flight subphase of the aircraft in real time and obtain the desired energy state by interpolating the energy profile of the longitudinal trajectory, including the altitude profile and velocity profile; After the aircraft enters the energy management phase, the altitude guidance law α is determined. c ,as follows: Among them, h and Respectively represent the altitude and ascent and descent speed of the aircraft; α * They represent the expected angle of attack of the longitudinal trajectory being tracked; h * and They represent the desired altitude and ascent and descent speed, respectively, both derived from the tracked trajectory; and is the gain coefficient; When the aircraft's Mach number is lower than 0.8, the speed brake is activated to control the speed. The proportional and integral controllers are used to adjust the speed brake opening to achieve speed control. The guidance law of the speed control loop is expressed as δ sbc ,as follows: Where V is the speed of the aircraft, V * is the desired speed of the aircraft, is the deflection angle when the speed brake is in the center position, and is the gain coefficient.

8. The high-speed aircraft online real-time energy management guidance method according to claim 1, characterized in that: In S3, the bank angle guidance command is output according to the flight sub-phase through the lateral guidance law, as follows: According to the track characteristics of different sub-stages, corresponding lateral guidance methods are adopted: In the S-turn section, the open-loop fixed roll angle control mode is adopted, and the corresponding roll angle command is: Among them, Flag S =1 means the aircraft enters the S-turn segment and begins to tilt to increase the range to consume energy, while Flag S =0 means that after a period of S-turn flight, the aircraft energy is less than the nominal energy corresponding to the real-time distance to fly, and it is necessary to start bank in the opposite direction; During the capture phase, a heading tracking control strategy is adopted, using a guidance law based on heading angle deviation: s c =K χ (h-h * ); Among them, χ is the current flight direction of the aircraft, χ * is the desired heading, K χ is the gain coefficient; During the heading calibration phase, the aircraft tracks the arc trajectory of the heading calibration cylinder HAC in the preset heading calibration phase. A proportional differential controller is used to generate a roll angle command based on the aircraft's side deviation distance and deviation rate from the arc. The nonlinear L1 guidance method is used, including the following steps: Draw a tangent line from the point B on the arc path corresponding to the current position A of the aircraft and the heading calibration cylinder HAC, determine the virtual reference point C on this tangent line, and take the distance from the current position to the reference point C as L1, the angle between the aircraft speed direction and the AC line as η, and obtain the lateral overload command N according to the centripetal force formula zc ,as follows: Where V is the speed of the aircraft; In actual flight, the lift component generated by the aircraft's tilt provides this part of the lateral overload, as follows: N zc =g tanσ c ; The corresponding roll angle command is: Where η1 is determined by the lateral deviation d between the current position of the aircraft and the target path, and η2 is determined by the heading deviation Δψ between the aircraft's velocity direction and the target path; The solution method for parameter L1 is as follows: Assuming that η is a very small value, sinη is approximately sinη≈η=η1+η2, where Approximately: in, is the first-order derivative of d; make The following second-order system is obtained: in, is the second-order derivative of d; The above formula shows that the L1 guidance algorithm is an approximate linear model, which can be regarded as a simple second-order system with a damping ratio of The natural frequency is Take the period T = 2π / ω n , we get: In actual arc path tracking, the distance OA between the current position A of the aircraft and the center O of the heading calibration cylinder HAC is used to obtain the side deviation distance d = OA - R HAC , that is, the lateral deviation of the aircraft relative to the target arc; η2 is obtained according to the angle between the aircraft's velocity direction and the target arc's tangent direction, that is, the heading deviation Δψ between the velocity direction and the target tangent BC; the heading of the target tangent BC is the azimuth angle ψ of the line connecting the center O and the current position A of the aircraft OA Subtract 90° to obtain the roll angle command: During the pre-landing phase, the aircraft is aligned with the runway centerline and the L1 guidance algorithm is used to correct the heading and lateral offset. The corresponding roll angle command is obtained based on the lateral offset d between the aircraft's current position and the target straight path and the heading deviation Δψ between the velocity direction and the target straight direction:

9. A high-speed aircraft online real-time energy management and guidance system, characterized in that: The system comprises: processor; a memory having stored thereon a computer program executable on the processor; Wherein, when the computer program is executed by the processor, the steps of the high-speed aircraft online real-time energy management guidance method as described in any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a data processing program, which, when executed by a processor, implements the steps of the high-speed aircraft online real-time energy management and guidance method according to any one of claims 1 to 8.

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