High-speed gliding aircraft reentry guidance method based on high-precision analytic solution

Abstract

The invention provides a high-speed gliding aircraft reentry guidance method based on a high-precision analytic solution, which compensates the influence generated by earth rotation and improves the reentry range prediction precision based on a prediction-correction guidance method and a designed longitudinal guidance law. Designing a transverse guidance law of a course corridor and a predicted reversal point, controlling the reversal times of a heeling angle, reducing the burden of an aircraft attitude control system, and improving the precision of a reentry point; compared with the prior art, in the course prediction of the longitudinal guidance law, the course prediction compensation item is added, the course prediction precision is improved, the roll angle reversal point is accurately predicted and the roll angle reversal frequency is reduced by using the transverse course formula in the transverse guidance law, and the method has the advantages of higher drop point precision and less roll angle reversal frequency.

Description

Technical Field

[0001] The invention belongs to the technical field of high-speed aircraft re-entry guidance, and in particular relates to a high-speed gliding aircraft re-entry guidance method based on a high-precision analytical solution. Background Art

[0002] The flight phase of a high-speed glider can be divided into the boost ascent phase, the reentry glide phase, and the terminal guidance phase. The reentry glide phase accounts for more than 90% of the entire flight time. The flight speed is maintained above 5 Ma, and the maximum speed can reach 20 Ma. High-speed gliders have fast flight speeds, wide coverage, and strong maneuverability. They are a new type of aircraft with broad prospects and will become a hot research direction in the development of the aerospace field in the 21st century.

[0003] During the re-entry glide stage, the flight environment of the high-speed glider is complex, with unknown interference, a large span of flight airspace, and strong uncertainty in aerodynamic parameters. In addition, the high-speed glider needs to simultaneously meet the three process constraints of heat flux density, overload, and dynamic pressure, and also ensure the safety of the high-speed glider's re-entry flight, which poses a great challenge to the re-entry guidance problem of the high-speed glider.

[0004] Reentry guidance technology is a key technology for high-speed aircraft, which is mainly divided into standard trajectory guidance method and prediction and correction guidance method. The standard trajectory guidance method is an early common reentry guidance method. According to the existing flight target, a reference flight trajectory that meets all constraints is planned offline in advance, and the reference flight trajectory is stored in the onboard computer. However, in the actual flight process of high-speed aircraft, due to the complex flight environment, unknown interference, large span of the flight sky and airspace, and strong uncertainty of aerodynamic parameters, the actual flight trajectory and the reference flight trajectory will produce errors. Therefore, it is necessary to eliminate the error by adjusting the control amount to make the actual flight trajectory closer to the reference flight trajectory. However, the standard trajectory guidance method requires a lot of offline calculations and storage of reference trajectories, which is a large workload. In addition, it relies too much on the reference flight trajectory during the guidance process. It is only for specific flight missions and flight targets, and is not universal and has poor flexibility.

[0005] The prediction-correction guidance method is a real-time reentry guidance algorithm. The onboard computer calculates the predicted terminal landing point in real time according to the current state of the aircraft, obtains the roll angle guidance command according to the deviation between the actual terminal landing point and the predicted terminal landing point, modifies the flight trajectory in real time, and finally reduces the landing point error. This guidance method does not require a standard trajectory as a reference, and the landing point accuracy is relatively high, which makes up for the shortcomings of the standard trajectory guidance method. It has gradually become the development trend of reentry guidance technology. Domestic and foreign scholars have conducted in-depth research on the prediction-correction guidance method and have achieved a lot of research results.

[0006] The existing analytical prediction and correction guidance method introduces many assumptions in range prediction, and the prediction accuracy is not high, and the re-entry point accuracy is also not high; the lateral guidance law generally adopts the heading corridor method, and when approaching the target area, the number of bank angle reversals is large, which puts a heavy burden on the aircraft attitude control system.

[0007] In summary, designing a high-speed gliding vehicle reentry guidance method with high range prediction accuracy and fewer roll angle reversal times has important engineering significance. Summary of the invention

[0008] The existing analytical prediction-correction method has low prediction accuracy and landing point accuracy, and the number of bank angle reversals is relatively large. In order to overcome the shortcomings of the existing technology, a high-speed gliding vehicle reentry guidance method based on high-precision analytical solution is proposed; considering the influence of the earth's rotation, a longitudinal range prediction compensation term is added, and the reentry longitudinal guidance law is designed to improve the reentry range prediction accuracy; a lateral guidance law of "heading corridor and predicted reversal point" is designed to control the number of bank angle reversals, reduce the burden on the aircraft attitude control system, and improve the accuracy of the reentry landing point.

[0009] To achieve the above purpose, the technical solution provided by the present invention is:

[0010] A high-speed gliding vehicle reentry guidance method based on a high-precision analytical solution comprises the following steps:

[0011] Step 1: During the initial descent phase of the high-speed glider reentry process, open-loop guidance is performed using a set constant roll angle;

[0012] Step 2: judging whether the high-speed gliding aircraft has entered the gliding stage according to the altitude change rate of the high-speed gliding aircraft, if it has entered the gliding stage, proceed to step 3, if it has not entered the gliding stage, continue to perform open-loop guidance according to the set constant roll angle; the basis for judging whether the aircraft has entered the gliding stage is: taking the moment when the altitude change rate is 0 for the first time as the handover moment between the initial descent stage and the stable gliding stage;

[0013] Step 3: Follow the formula

[0014] α cmd =α+k(γ QEGC -γ)

[0015] |σ cmd |=|σ|-l(γ QEGC -γ)

[0016] Provide glide phase guidance for high-speed gliding aircraft;

[0017] Where σ is the roll angle of the high-speed gliding aircraft, |σ| is the roll angle amplitude, |σ cmd | is the roll angle command amplitude, α cmdis the angle of attack command, α is the angle of attack of the high-speed glider, k and l are the corresponding compensation coefficients, γ QEGC is the flight path angle corresponding to the high-speed gliding aircraft during balanced gliding, and γ is the flight path angle of the high-speed gliding aircraft;

[0018] The roll angle command symbol in the first half is

[0019]

[0020] Among them, sign(σ i ) is the sign of the roll angle command in the current control cycle, sign(σ i-1 ) is the sign of the roll angle command in the previous control cycle, ΔΨ is the heading error threshold, and Δψ is the heading error.

[0021] The roll angle command symbol in the second half is

[0022]

[0023] Where E is the current energy value, E REV1 and E REV2 is the predicted roll angle reversal point, according to the formula

[0024]

[0025] Calculated, where x c1 is the terminal lateral distance when the reversal point is calculated for the first time, x c ′1 is the first-order derivative of energy, x c2 is the terminal lateral distance when calculating the reversal point for the second time, x c '2 is the first-order derivative of energy. Further, the roll angle amplitude σ is calculated according to the formula

[0026]

[0027] It is calculated that, where D and L are the drag and lift of the high-speed gliding vehicle, and L1 is the vertical component of the lift.

[0028] Furthermore, if the roll angle amplitude calculated according to the above formula is greater than the maximum roll angle amplitude σ max , then the roll angle amplitude is taken as the maximum roll angle amplitude.

[0029] Furthermore, the maximum roll angle amplitude σ max The calculation is done through the following process based on the heat flux constraint, overload constraint and dynamic pressure constraint of the high-speed gliding vehicle:

[0030] High-speed glider heat flux The constraints of dynamic pressure q and overload n are expressed as

[0031]

[0032] q=0.5ρV 2 q max

[0033]

[0034] in, is the heat flow correlation coefficient; q max and n max are the maximum constraint values ​​of heat flux, dynamic pressure and overload respectively;

[0035] The above heat flux constraint, dynamic pressure constraint and overload constraint are converted into the altitude-speed reentry corridor, which is expressed as

[0036]

[0037] Among them, ρ0 is the atmospheric density at sea level, β is the atmospheric constant;

[0038] Based on the reentry corridor, the maximum atmospheric density boundary ρ max The maximum lift L is obtained by using the lift calculation formula according to the law of change of speed V. max The law of change with speed V; considering that the quasi-balanced gliding condition is satisfied during balanced gliding, the maximum roll angle boundary is calculated as

[0039]

[0040] Furthermore, the angle of attack of the high-speed glider aircraft adopts a piecewise quadratic function form

[0041]

[0042] Among them, α1 is the initial value of the reentry angle of attack, α2 is the maximum lift-to-drag ratio angle of attack, E a and E b is the energy value of the segment point, and E is the current energy value.

[0043] Furthermore, the heading error threshold ΔΨ is set as a linear function of the speed:

[0044]

[0045] Among them, V1 and V2 are the set segment point speed values.

[0046] Furthermore, the corresponding track angle γ during balanced gliding QEGC for

[0047]

[0048] Furthermore, the compensation coefficients k and l are calculated according to the formula

[0049]

[0050] Calculated, where E k and E l is the energy value of the segmentation point, k1, k2, l1 and l2 are set constants.

[0051] Beneficial Effects

[0052] The invention discloses a high-speed gliding aircraft reentry guidance method based on a high-precision analytical solution. The invention provides the following advantages: based on a prediction-correction guidance method, a longitudinal guidance law is designed to compensate for the influence of the earth's rotation and improve the reentry range prediction accuracy; a lateral guidance law of "course corridor + predicted reversal point" is designed to control the number of roll angle reversals, reduce the burden of the aircraft attitude control system, and improve the reentry landing point accuracy; compared with the prior art, such as the literature (Yu WB, Chen WC. Entry guidance with real-time planning of reference based on analytical solutions [J]. Advances in Space Research, 2015, 55 (9): 2325-2345), the invention adds a range prediction compensation item in the range prediction of the longitudinal guidance law to improve the range prediction accuracy, and uses a lateral range formula in the lateral guidance law to accurately predict the roll angle reversal point and reduce the number of roll angle reversals. The invention has the advantages of higher landing point accuracy and fewer roll angle reversals. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 :Flowchart of the design of high-speed gliding vehicle reentry guidance method based on high-precision analytical solution;

[0054] Figure 2 :Design structure diagram of neural network for fast prediction of track angle;

[0055] Figure 3 : Statistical diagram of the average relative error between the predicted and true values ​​of the track angle;

[0056] Figure 4 :ΔL1D QEGC , ΔL2D QEGC , ΔDD QEGC , L1D and L2D change curves;

[0057] Figure 5 : Comparison of reentry results in examples of the present invention;

[0058] Figure 6 : Comparison of reentry process results in examples of the present invention;

[0059] Figure 7 : Altitude-speed variation curve under standard conditions in the examples of the present invention and its comparison;

[0060] Figure 8 : Two-dimensional ground trajectory under standard conditions and its comparison in the examples of the present invention;

[0061] Fig. 9 : The roll angle variation curve under standard conditions in the examples of the present invention and its comparison;

[0062] Fig.10 : Angle of attack curve under standard conditions in the examples of the present invention and its comparison;

[0063] Fig.11 : Heat flux density variation curve under standard conditions in the example of the present invention;

[0064] Fig.12 : Dynamic pressure variation curve under standard conditions in the example of the present invention;

[0065] Fig.13 : Overload variation curve under standard conditions in the example of the present invention;

[0066] Fig.14 : The roll angle variation curve under disturbance conditions in the example of the present invention;

[0067] Fig.15 : The angle of attack variation curve under disturbance conditions in the example of the present invention;

[0068] Fig.16 : Altitude-speed variation curve under disturbance conditions in the example of the present invention;

[0069] Fig.17 : Distribution diagram of falling points under disturbance conditions in an example of the present invention. DETAILED DESCRIPTION

[0070] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0071] Combination Figures 1 to 17 , the overall research idea of ​​the present invention is:

[0072] (1) During the initial descent phase of a high-speed gliding vehicle, open-loop guidance is performed using a constant roll angle command;

[0073] (2) Convert the heat flux density constraint, overload constraint and dynamic pressure constraint of the high-speed gliding vehicle into the roll angle amplitude constraint;

[0074] (3) Entering the steady glide phase, based on the prediction-correction guidance method, taking into account the influence of the earth's rotation, and according to the high-precision longitudinal range prediction expression, the roll angle amplitude and angle of attack command are obtained in the reentry longitudinal guidance law;

[0075] (4) Based on the analytical expression of the lateral range, the bank angle reversal point is predicted, and combined with the heading angle corridor, the bank angle sign is obtained in the reentry lateral guidance law;

[0076] (5) According to the expected value of the track angle during balanced gliding, a compensation term is added to the control quantity command to suppress the trajectory oscillation during the reentry process.

[0077] Specific research contents include:

[0078] (1) The kinematic equation of a high-speed gliding vehicle is:

[0079]

[0080]

[0081] Where λ and φ are longitude and latitude; H is the altitude; V is the speed of the aircraft relative to the Earth-fixed coordinate system; γ is the track angle; ψ is the heading angle, based on the local north direction; R e =6378135m is the radius of the earth; ω e is the angular velocity of the earth's rotation; m is the mass of the aircraft; g is the acceleration of gravity; σ is the roll angle; D and L are the drag and lift, and the specific expressions are as follows

[0082]

[0083] Where ρ is the atmospheric density; S ref is the aircraft reference area; C D and C L are the drag coefficient and lift coefficient;

[0084] According to the ballistic characteristics of the high-speed gliding vehicle during the re-entry glide phase, its flight process can be divided into an initial descent phase and a steady glide phase. The moment when the altitude change rate is 0 for the first time is taken as the handover moment between the initial descent phase and the steady glide phase. In the initial descent phase, the flight altitude is high, the air density is small, and the aerodynamic force is weak. A constant roll angle is usually used for open-loop guidance.

[0085] (2) Heat flux density of high-speed gliding aircraft The constraints of dynamic pressure q and overload n can be expressed as

[0086]

[0087] q=0.5ρV 2 q max (10)

[0088]

[0089] in, is the heat flow correlation coefficient; q max and n max are the maximum constraint values ​​of heat flux, dynamic pressure and overload respectively;

[0090] The above heat flux constraint, dynamic pressure constraint and overload constraint are converted into the altitude-speed reentry corridor, which is expressed as

[0091]

[0092]

[0093] Among them, ρ0 is the atmospheric density at sea level, β is the atmospheric constant;

[0094] Based on the reentry corridor, the maximum atmospheric density boundary ρ max The maximum lift L can be obtained by using the lift calculation formula according to the law of change of speed V. max The law of change with speed V; considering that in balanced gliding, the quasi-balanced gliding condition is approximately satisfied, the maximum roll angle boundary is calculated to be

[0095]

[0096] The terminal constraints of a high-speed glider include terminal altitude constraints, speed constraints, and longitude and latitude constraints, which can be expressed as

[0097]

[0098] Among them, H f 、V f , f ,φ f are the corresponding terminal altitude, speed, longitude and latitude respectively; among which, the terminal longitude and latitude constraints can be converted into range constraints

[0099] s(t f )=s f (17)

[0100] Among them, s(t f ) is the terminal reentry voyage; s f is the actual value of the reentry range, which can be expressed as

[0101] s f =arccos(sinφsinφ f +cosφcosφ f cos(λf -λ)) (18)

[0102] (3) After entering the steady glide phase, the roll angle amplitude and angle of attack command are obtained in the longitudinal guidance; the energy E is defined as

[0103]

[0104] Where μ is the gravitational constant; generally, the terminal energy E f As the simulation termination condition

[0105]

[0106] Define L1 and L2 as the vertical and horizontal components of lift, that is, L1 = Lcosσ, L2 = Lsinσ. Generally, L1D and L2D are expressed as low-order polynomial functions, L1D = a0 + a1x E +a2x E 2 , L2D=b0+b1x E +b2x E 2 , where a0, a1, a2, b0, b1, b2 are unknown coefficients; establish the longitudinal range x D , horizontal range x C Glide analytical formula

[0107]

[0108] Among them, E0 is the initial energy value, E is the current energy value, x C0 Initial range error, Δψ0 is the initial heading error, R * =R e +H * , H * is the average flight altitude; f1(x E ) is defined as

[0109]

[0110] If the rate of change of the track angle is not ignored, the kinematic equation of the track angle is:

[0111]

[0112] Then the rate of change of reentry distance with energy is deduced to be

[0113]

[0114] Define Δx D is the compensation term in the reentry course prediction. According to the chain rule of function derivation,

[0115]

[0116] Substituting equation (19) into equation (26), let C = μR * , according to the method of integration by parts, calculate the longitudinal compensation term Δx D

[0117]

[0118] In the present invention, a neural network prediction method is used to predict the track angle under different energies, and a function fitting function of a fully connected neural network is applied to achieve the transition from "current state" to "predicted track angle γ E "The fitting of the mapping function is to build a "predicted track angle γ" with "current state" as input. E " is a fully connected neural network with output. First, an input and output data set containing the current state and predicted track angle is established, and then the data is randomly divided into a training set and a test set. The neural network performs back propagation based on the data in the training set to update the network parameters; the neural network then performs forward propagation based on the data in the test set to obtain the neural network output. When the difference between the neural network output and the data set output is less than the preset value, the neural network is considered to have converged, and a neural network that can realize the function of fast prediction of track angle is obtained.

[0119] The dimension of the neural network input layer is determined by the number of inputs that can affect the output. By analyzing the kinematic equation, it can be determined that the variables that affect the track angle include speed V, altitude H, and roll angle σ, and the input layer dimension is determined to be 3. The dimension of the neural network output layer is determined by the output quantity. In the neural network model, only the predicted track angle γ is output. E , determine that the output layer dimension is 1. The more hidden layers the neural network has, on the one hand, the smaller the fitting error and the better the effect. On the other hand, the more network parameters there are, the longer the training time and call time are. The activation function uses the sigmoid function. Based on the above situation, the neural network model structure designed for fast prediction of track angle is as follows Figure 2 shown.

[0120] As shown in Table 1, there are 800 trajectories in the data set. 100 state points are randomly selected from each trajectory, with a total of 80,000 state points. Data from 500 trajectories are selected as training sets, and data from 300 trajectories are selected as test sets.

[0121] Table 1 Dataset generation

[0122]

[0123]

[0124] The neural network training is carried out according to the above method. Figure 3The statistical graph of the average relative error between the predicted and true values ​​of the track angle in the test set is displayed. The average relative error of most ballistic track angles is within 10%, which meets the prediction accuracy requirements and verifies the correctness of the track angle neural network model.

[0125] The kinematic equations of high-speed gliding vehicles show that the rotation of the earth will have a complex effect on the reentry process. When predicting the remaining flight range, the Taylor expansion method is used to compensate for the effect of the earth's rotation during the prediction process; the compensation terms of drag, vertical component of lift, and horizontal component of lift are recorded as ΔD, ΔL1, and ΔL2, respectively;

[0126]

[0127]

[0128]

[0129] The control variables after adding the compensation term are L1D and L2D

[0130]

[0131] Expand the above formula into the first-order Taylor formula

[0132]

[0133] Calculation of the vertical component of lift L during balanced gliding using quasi-balanced gliding conditions 1-QEGC and resistance D QEGC

[0134]

[0135] Then, equations (33) and (34) can be updated as

[0136]

[0137] During the reentry flight, ΔL1 / D QEGC , ΔL2 / D QEGC , ΔD / D QEGC The curves of L1 / D and L2 / D changing with E are as follows: Figure 4 As shown. Energy versus ΔL1 / D QEGC , ΔL2 / D QEGC , ΔD / D QEGC The influence of is very small. To simplify the calculation, it is approximately assumed that they do not change with E. Substituting equation (36) into equation (21), the analytical formula for the reentry longitudinal path considering the rotation of the Earth is:

[0138]

[0139] According to sf =x D (E f ,E) can quickly solve L1D and then get the roll angle amplitude

[0140]

[0141] In the initial stage of reentry, aerodynamic heating is serious, so it is suitable to fly at a high angle of attack to reduce aerodynamic heating; in the middle and later stages of flight, in order to meet the range requirements, it is suitable to fly at the maximum lift-to-drag ratio angle of attack; in the longitudinal guidance, a piecewise quadratic function angle of attack scheme is used

[0142]

[0143] Among them, α1 is the initial value of the reentry angle of attack, α2 is the maximum lift-to-drag ratio angle of attack, E a and E b is the energy value of the segment point;

[0144] (4) In lateral guidance, the sign of the roll angle is obtained to eliminate the lateral error; the guidance law of "heading corridor + predicted reversal point" is adopted. The heading angle corridor method is used in the early stage of flight, and the roll angle reversal point is predicted by the lateral range analytical formula in the latter stage of flight. The number of roll angle reversals is controlled to reduce the burden on the aircraft attitude control system;

[0145] It should be noted that, in this embodiment, after completing 2 to 3 reversals using the heading corridor (lateral guidance law) in the first half, the lateral guidance law in the second half is entered.

[0146] In the first half of the flight, the traditional heading angle corridor method is used, and ψ LOS The line of sight angle from the current aircraft to the target point

[0147]

[0148] Then, the roll angle reversal logic can be expressed as

[0149]

[0150] Wherein, heading error Δψ=ψ LOS -ψ, ΔΨ is the heading error threshold, which is generally set as a linear function of speed

[0151]

[0152] Among them, V1 and V2 are the set segment point speed values;

[0153] During the second half of the flight, the cross-range formula is used to predict the reversal point of the roll angle; it is assumed that during this process, the roll angle is at an energy of E REV1 and E REV2When E>E REV1 When E REV2 =E b Then use the cross-range formula to predict E REV1 ; Substitute equation (37) into equation (22), consider the roll angle reversal, and predict the terminal lateral distance

[0154]

[0155] When E REV1 >E>E REV2 When the terminal lateral distance is predicted

[0156]

[0157] Among them, k REV is the number of times the bank angle has reversed in the second half of flight, x C0 Take it as 0, sgn is the sign function, and the expression of f2 is as follows

[0158]

[0159] We hope that the terminal lateral distance x C (E f ,E)=0, Newton's method can be used to solve E REV1 and E REV2

[0160]

[0161] In the formula,

[0162] During the second half of the flight, the roll angle reversal logic is:

[0163]

[0164] (5) High-speed gliding vehicles have highly periodic oscillations during flight, which can easily lead to serious deterioration of the external stress of the vehicle, thus having a serious impact on the lightweight structure and thermal protection system. Therefore, it is necessary to add compensation terms to the control quantity to eliminate this periodic oscillation. According to formula (24), the corresponding track angle γ during balanced gliding is QEGC Approximately

[0165]

[0166] Generate and Gamma QEGC -γ proportional feedback signal and add it to the control quantity instruction

[0167]

[0168] In the initial stage of reentry, the trajectory oscillation is serious and a larger compensation is needed to suppress the oscillation; in the latter stage of flight, in order to ensure the guidance accuracy, the compensation amount needs to be reduced. Therefore, k and l are designed as quadratic functions of energy.

[0169]

[0170] Where: E k and E l is the energy value of the segment point, k1, k2, l1 and l2 are constants.

[0171] (6) The correctness of the derived analytical solutions of longitudinal and transverse ranges is verified by numerical simulation. The present invention uses a high-speed gliding aircraft CAV-H as the simulation object. The aircraft mass is 907.2 kg and the aircraft aerodynamic reference area is 0.4836 m 2 , the maximum lift-to-drag ratio is 3. The simulation verifies the accuracy of the analytical solutions for longitudinal and transverse ranges, and compares them with the analytical solutions in the literature (Yu W, Chen W. Entry guidance with real-time planning of reference based on analytical solutions [J]. Advances in Space Research, 2015, 55 (9): 2325-2345). The initial conditions of the aircraft are: λ0 = 0°, ψ0 = 0°, H0 = 50 km, V0 = 6000 ms, γ0 = 0°, ψ0 = 90°. The simulation termination condition is E f =-6×10 7 Jkg.

[0172] Within the energy variation range, 100 energy points are evenly selected, the longitudinal and transverse prediction errors of each energy point are calculated, and then the average error is obtained. Figure 5 Table 2 shows the comparison results of the reentry longitudinal range. The longitudinal range analytical solution of the present invention is closer to the true value than the Yu-Chen analytical solution. The trend of the longitudinal range prediction results in the middle and front sections is closer to the actual situation. The prediction accuracy is improved by 45.79%, with higher analytical accuracy. The longitudinal range compensation term improves the prediction accuracy. Figure 6 Table 3 shows the comparison results of the reentry range. Compared with the Yu-Chen analytical solution, the accuracy of the analytical solution of the present invention is improved by 7.37%, and the average range error is within 2.8 km, which meets the reentry guidance requirements.

[0173] Table 2 Comparison of the accuracy of analytical solutions for the reentry process

[0174]

[0175] Table 3 Comparison of the accuracy of analytical solutions for the reentry cross-section

[0176]

[0177] (7) The effectiveness of the reentry guidance law is verified by numerical simulation. The present invention uses the high-speed gliding aircraft CAV-H as the simulation object, and the aircraft process constraint q max =100kPa, n max =1.5, The initial state and terminal constraints of the aircraft are shown in Table 4. The angle of attack profile parameters are α1 = 20°, α2 = 10°.

[0178] Table 4 Aircraft initial state and terminal constraints

[0179]

[0180] In order to verify the effectiveness and superiority of the guidance method proposed in the present invention (denoted as method 1), it is compared with method 2 under standard conditions. Method 2: The longitudinal guidance law uses equation (21) to predict the longitudinal reentry range, and the lateral guidance law uses equation (42) to predict the traditional heading angle corridor.

[0181] Table 5 shows the terminal errors of the two methods. Compared with method 2, the landing point accuracy of the present invention is improved by 32.08%, and it has higher guidance accuracy. Figure 7 It is the height-speed curve under standard conditions. The trajectory is basically smooth and basically meets the quasi-balanced gliding conditions. Figure 8 is the two-dimensional trajectory on the ground under standard conditions. Fig. 9 and Fig.10 It is the roll angle and angle of attack curve under standard conditions. The initial descent stage performs open-loop guidance with a constant roll angle. It can be seen from the figure that the guidance law of the present invention has fewer roll angle reversal times than the traditional method. The roll angle reversal point can be predicted more accurately through the lateral analytical formula, reducing the burden on the aircraft attitude control system. Figure 11-13 It is the path constraint change curve of the high-speed gliding vehicle. The heat flux density, dynamic pressure and overload do not exceed the maximum limit, and the changes are relatively smooth without periodic oscillation, which is easier for the aircraft to withstand.

[0182] Table 5 Terminal landing error

[0183]

[0184] In order to verify the robustness of the method proposed in the present invention, 500 Monte Carlo simulations were performed. All deviations in the simulations conformed to the normal distribution, as shown in Table 6. Fig.14 and Fig.15For the roll angle and angle of attack curves under disturbance conditions, the present invention can reduce the number of roll angle reversals while ensuring the landing point accuracy. The roll angle and angle of attack meet relevant constraints. In the first half of the flight, the control command is mainly affected by the oscillation suppression term. As it approaches the target point, the influence of the suppression term becomes smaller and smaller. Fig.16 It is the height-speed curve under disturbance conditions. The trajectory is relatively smooth, without periodic oscillation, and basically meets the quasi-balanced gliding conditions. Fig.17 It is the landing point distribution under disturbance conditions. The average landing point error is 3.3691km, and the longitude and latitude errors are both less than 0.1°, which meets the re-entry guidance requirements.

[0185] Table 6 Monte Carlo simulation parameter deviation

[0186]

[0187] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be included in the protection scope of the present invention.

Claims

1. A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution, characterized in that: The following steps are involved: Step 1: During the initial descent phase of the high-speed glider reentry process, open-loop guidance is performed using a set constant roll angle; Step 2: judging whether the high-speed gliding aircraft has entered the gliding stage according to the altitude change rate of the high-speed gliding aircraft, if it has entered the gliding stage, proceed to step 3, if it has not entered the gliding stage, continue to perform open-loop guidance according to the set constant roll angle; the basis for judging whether the aircraft has entered the gliding stage is: taking the moment when the altitude change rate is 0 for the first time as the handover moment between the initial descent stage and the stable gliding stage; Step 3: Follow the formula a cmd =α+k(γ QEGC -c) |s cmd |=|σ|-l(γ QEGC -c) Provide glide phase guidance for high-speed gliding aircraft; Where σ is the roll angle of the high-speed gliding aircraft, |σ| is the roll angle amplitude, |σ cmd | is the roll angle command amplitude, α cmd is the angle of attack command, α is the angle of attack of the high-speed glider, k and l are the corresponding compensation coefficients, γ QEGC is the flight path angle corresponding to the high-speed gliding aircraft during balanced gliding, and γ is the flight path angle of the high-speed gliding aircraft; The roll angle command symbol in the first half is Among them, sign(σ i ) is the sign of the roll angle command in the current control cycle, sign(σ i-1 ) is the sign of the roll angle command in the previous control cycle, ΔΨ is the heading error threshold, and Δψ is the heading error; The roll angle command symbol in the second half is Where E is the current energy value, E REV1 and E REV2 is the predicted roll angle reversal point, according to the formula Calculated, where x c1 is the terminal lateral distance when the reversal point is calculated for the first time, x c ′1 is the first-order derivative of energy, x c2 is the terminal lateral distance when calculating the reversal point for the second time, x c '2 is the first-order derivative with respect to energy.

2. A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution as claimed in claim 1, characterized in that: The roll angle amplitude |σ| is calculated according to the formula It is calculated that, where D and L are the drag and lift of the high-speed gliding vehicle, and L1 is the vertical component of the lift.

3. A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution as claimed in claim 2, characterized in that: If the roll angle amplitude calculated according to the above formula is greater than the maximum roll angle amplitude |σ max |, then the roll angle amplitude is taken as the maximum roll angle amplitude.

4. A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution as claimed in claim 3, characterized in that: The maximum roll angle amplitude |σ max |According to the heat flux density constraint, overload constraint and dynamic pressure constraint of the high-speed gliding vehicle, it is calculated through the following process: High-speed glider heat flux The constraints of dynamic pressure q and overload n are expressed as q=0.5ρV 2 ≤q max in, is the heat flow correlation coefficient; q max and n max are the maximum constraint values ​​of heat flux, dynamic pressure and overload respectively; The above heat flux constraint, dynamic pressure constraint and overload constraint are converted into the altitude-speed reentry corridor, which is expressed as Among them, ρ0 is the atmospheric density at sea level, β is the atmospheric constant; Based on the reentry corridor, the maximum atmospheric density boundary ρ max The maximum lift L is obtained by using the lift calculation formula according to the law of change of speed V. max The law of change with speed V; considering that the quasi-balanced gliding condition is satisfied during balanced gliding, the maximum roll angle boundary is calculated as 5. A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution as claimed in claim 1, characterized in that: The angle of attack of high-speed glider aircraft adopts the form of piecewise quadratic function Among them, α1 is the initial value of the reentry angle of attack, α2 is the maximum lift-to-drag ratio angle of attack, E a and E b is the energy value of the segment point, and E is the current energy value.

6. A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution as claimed in claim 1, characterized in that: The heading error threshold ΔΨ is set as a linear function of speed: Among them, V1 and V2 are the set segment point speed values.

7. A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution as claimed in claim 1, characterized in that: The corresponding track angle γ during balanced gliding QEGC for 8. The high-speed gliding vehicle reentry guidance method based on high-precision analytical solution as claimed in claim 1, characterized in that: The compensation coefficients k and l are calculated according to the formula Calculated, where E k and E l is the energy value of the segmentation point, k1, k2, l1 and l2 are set constants.

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