A high-speed gliding vehicle reentry guidance method based on high-precision analytical solution

Abstract

The present invention provides a high-speed gliding aircraft reentry guidance method based on a high-precision analytical solution. Based on the prediction-correction guidance method, a longitudinal guidance law is designed to compensate for the effects of the Earth's rotation and improve the accuracy of reentry range prediction. A lateral guidance law with a "course corridor + predicted reversal point" is designed to control the number of roll angle reversals, reduce the burden on the aircraft attitude control system, and improve the accuracy of the reentry landing point. Compared with the existing technology, the present invention adds a range prediction compensation term to the range prediction of the longitudinal guidance law to improve the range prediction accuracy. The lateral guidance law uses a lateral range formula to accurately predict the roll angle reversal point and reduce the number of roll angle reversals. The present invention has the advantages of higher landing point accuracy and fewer roll angle reversals.

Description

Technical Field

[0001] The present 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 phases of a high-speed glide vehicle can be divided into a boost ascent phase, a reentry glide phase, and a terminal guidance phase. The reentry glide phase accounts for over 90% of the total flight time, maintaining a speed above 5 Ma and reaching a maximum speed of 20 Ma. High-speed glide vehicles offer high speeds, wide coverage, and strong maneuverability. They are a promising new type of aircraft and will become a hot research topic in the 21st century aerospace field.

[0003] During the reentry glide phase, high-speed gliders face a complex flight environment with unknown interference, a large flight airspace span, and high uncertainty in aerodynamic parameters. Furthermore, high-speed gliders must simultaneously meet three process constraints: heat flux density, overload, and dynamic pressure, while also ensuring the safety of their reentry flight. This poses a significant challenge to their reentry guidance.

[0004] Reentry guidance is a key technology for high-speed aircraft, primarily divided into standard trajectory guidance and predictive correction guidance. The standard trajectory guidance method, an early and commonly used reentry guidance method, pre-plans a reference flight trajectory that satisfies all constraints offline based on a known flight target and stores this reference trajectory in an onboard computer. However, during actual flight, high-speed aircraft often experience discrepancies between the actual and reference flight trajectories due to complex flight environments, unknown interference, the large span of the flight airspace, and high uncertainty in aerodynamic parameters. Therefore, control variables must be adjusted to eliminate these discrepancies and bring the actual flight trajectory closer to the reference trajectory. However, the standard trajectory guidance method requires extensive offline calculations and reference trajectory storage, resulting in a high workload. Furthermore, the guidance process relies heavily on the reference trajectory, making it suitable only for specific missions and flight targets, lacking universal applicability and flexibility.

[0005] The predictive-correction guidance method is a real-time reentry guidance algorithm. The onboard computer calculates the predicted terminal impact point in real time based on the vehicle's current state. Based on the deviation between the actual and predicted impact points, it obtains bank angle guidance commands, modifies the flight trajectory in real time, and ultimately reduces the impact point error. This guidance method eliminates the need for a standard trajectory as a reference and offers high impact point accuracy, addressing the shortcomings of the standard trajectory guidance method. It is currently becoming a trend in the development of reentry guidance technology. Scholars at home and abroad have conducted in-depth research on the predictive-correction guidance method, achieving significant results.

[0006] The existing analytical prediction and correction guidance method introduces many assumptions in range prediction, resulting in low prediction accuracy and re-entry point accuracy. The lateral guidance law generally adopts a 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 re-entry guidance method for high-speed gliding vehicles with high range prediction accuracy and fewer bank angle reversals is of great engineering significance. Summary of the Invention

[0008] The existing analytical prediction-correction method has low prediction accuracy and landing point precision, and the number of bank angle reversals is large. To overcome the shortcomings of the existing technology, a high-speed gliding vehicle reentry guidance method based on a high-precision analytical solution is proposed. Taking into account the influence of the earth's rotation, a longitudinal range prediction compensation term is added to design a longitudinal reentry guidance law to improve the accuracy of reentry range prediction. A lateral guidance law with a "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 objectives, the technical solutions provided by the present invention are:

[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 of the high-speed glider reentry process, open-loop guidance is performed using a set constant bank angle.

[0012] Step 2: Determine whether the high-speed gliding aircraft has entered the glide phase based on its altitude change rate. If so, proceed to Step 3. If not, continue open-loop guidance based on the set constant bank angle. The basis for determining whether the aircraft has entered the glide phase is that the moment when the altitude change rate first reaches zero is used as the handover moment between the initial descent phase and the steady glide phase.

[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 tilt angle command amplitude, α cmdis the angle of attack command, α is the angle of attack of the high-speed gliding aircraft, 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 first calculated, 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 as follows, where D and L are the drag and lift of the high-speed gliding aircraft, 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 according to the heat flux density constraint, overload constraint and dynamic pressure constraint of the high-speed gliding aircraft through the following process:

[0030] High-speed gliding vehicle 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] Where ρ0 is the atmospheric density at sea level, β is an atmospheric constant;

[0038] Based on the reentry corridor, the maximum atmospheric density boundary ρ can be obtained 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 met during balanced gliding, the maximum roll angle boundary is calculated to be

[0039]

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

[0041]

[0042] Among them, α1 is the initial value of the reentry attack angle, α2 is the maximum lift-to-drag ratio attack angle, 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 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 segment point, k1, k2, l1 and l2 are set constants.

[0051] Beneficial effects

[0052] The present invention is a high-speed gliding aircraft reentry guidance method based on a high-precision analytical solution. The advantages provided by the present invention are as follows: based on the 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 existing technology, such as the document (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 present invention adds a range prediction compensation term in the range prediction of the longitudinal guidance law to improve the range prediction accuracy, and uses the 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 present 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 : Statistics 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 and comparison thereof in the examples of the present invention;

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

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

[0062] Figure 10 : Angle of attack curves under standard conditions in examples of the present invention and their comparison;

[0063] Figure 11 : Heat flux density variation curve under standard conditions in the examples of the present invention;

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

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

[0066] Figure 14 : The rolling angle variation curve under disturbance conditions in the example of the present invention;

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

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

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

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

[0071] Combine 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 bank angle command.

[0073] (2) Convert the heat flux density constraint, overload constraint, and dynamic pressure constraint of the high-speed gliding aircraft into a 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 bank 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 velocity 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, respectively. 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 the initial descent phase and the steady glide phase; the moment when the altitude change rate reaches 0 for the first time is regarded 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 low, and the aerodynamic force is weak, so a constant bank 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] Where ρ0 is the atmospheric density at sea level, β is an atmospheric constant;

[0094] Based on the reentry corridor, the maximum atmospheric density boundary ρ can be obtained 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 the 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 constraint, speed constraint, and longitude and latitude constraints, which can be expressed as

[0097]

[0098] Among them, H f 、V f ,λ f 、φ f are the corresponding terminal altitude, speed, longitude and latitude respectively; among them, 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, i.e. 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] Substitute equation (19) into equation (26), and 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 realize the process 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 the output of a fully connected neural network. First, an input and output data set containing the current state and predicted track angle is established. The data is then randomly divided into a training set and a test set. The neural network performs backpropagation 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 a preset value, the neural network is considered to have converged, and a neural network that can quickly predict the 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 equations, we can determine that the variables that affect the track angle include speed V, altitude H, and roll angle σ, and determine that the input layer dimension is 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 in the neural network, on the one hand, the smaller the fitting error and the better the effect. On the other hand, the more network parameters, the longer the training time and call time. 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 dataset. 100 state points are randomly selected from each trajectory, for a total of 80,000 state points. Data from 500 trajectories are selected as the training set, and data from 300 trajectories are selected as the test set.

[0121] Table 1 Dataset generation

[0122]

[0123]

[0124] The neural network training was performed according to the above method. Figure 3The statistical graph of the average relative error between the predicted and true values ​​of the track angles 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 a high-speed glider vehicle indicate that the Earth's rotation has 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. The compensation terms for the drag, vertical component of lift, and horizontal component of lift are denoted 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 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 assumed that they do not change with E. Substituting Eq. (36) into Eq. (21), the analytical formula of the reentry 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 reentry phase, aerodynamic heating is severe, so it is suitable to fly at a high angle of attack to reduce aerodynamic heating. In the latter part of the flight, in order to meet the range requirements, it is suitable to fly at a 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 attack angle, α2 is the maximum lift-to-drag ratio attack angle, E a and E b is the energy value of the segment point;

[0144] (4) In lateral guidance, the sign of the bank angle is obtained to eliminate lateral errors; 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 bank angle reversal point is predicted by the lateral range analytical formula in the latter stage of flight. The number of bank 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, the 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 segmentation point speed values;

[0153] During the second half of the flight, the cross-range formula is used to predict the bank angle reversal point; it is assumed that during this process, the bank 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 the 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, and Newton's method can be used to solve E REV1 and E REV2

[0160]

[0161] Where,

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

[0163]

[0164] (5) High-speed gliding aircraft have a highly periodic oscillation phenomenon during flight, which can easily lead to a serious deterioration of the aircraft's external stress, thus having a serious impact on the lightweight structure and thermal protection system. Therefore, it is necessary to add a compensation term 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] During the initial reentry phase, the trajectory oscillation is severe and a larger compensation is required to suppress the oscillation. During the latter part of the flight, in order to ensure the guidance accuracy, the compensation amount needs to be reduced. Therefore, k and l are designed to be 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, with an aircraft mass of 907.2 kg and an aerodynamic reference area of ​​0.4836 m 2 , the maximum lift-to-drag ratio is 3. The simulation verifies the accuracy of the analytical solution of longitudinal and transverse ranges and compares it with the analytical solution 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 = 50km, V0 = 6000ms, 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 range. The range analytical solution of the present invention is closer to the true value than the Yu-Chen analytical solution. The trend of the mid-to-front range prediction results is closer to the actual situation. The prediction accuracy is improved by 45.79%, with high analytical accuracy. The 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° and 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 this invention (denoted as Method 1), it is compared with Method 2 under standard conditions. Method 2: In the longitudinal guidance law, Equation (21) is used to predict the longitudinal reentry range, and in the lateral guidance law, Equation (42) is used 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. Figure 9 and Figure 10 The figure shows the roll angle and angle of attack curve under standard conditions. Open-loop guidance is performed with a constant roll angle in the initial descent phase. It can be seen from the figure that the guidance law of the present invention has fewer roll angle reversals than the traditional method. The cross-range analytical formula can accurately predict the roll angle reversal point, reducing the burden on the aircraft attitude control system. Figure 11-13 This is the path constraint change curve of a high-speed gliding aircraft. The heat flux density, dynamic pressure, and overload do not exceed the maximum limit, and the changes are relatively smooth without periodic oscillations, making it easier for the aircraft to withstand.

[0182] Table 5 Terminal landing point error

[0183]

[0184] To verify the robustness of the proposed method, 500 Monte Carlo simulations were performed. The deviations in the simulations all conformed to the normal distribution, as shown in Table 6. Figure 14 and Figure 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 the relevant constraints. In the first half of the flight, the control command is mainly affected by the oscillation suppression term. As the target point is approached, the influence of the suppression term becomes smaller and smaller. Figure 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. Figure 17 This 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°, meeting the re-entry guidance requirements.

[0185] Table 6 Monte Carlo simulation parameter deviation

[0186]

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

Claims

1. A high-speed gliding vehicle reentry guidance method based on a high-precision analytical solution, characterized in that: The following steps are involved: Step 1: During the initial descent of the high-speed glider reentry process, open-loop guidance is performed using a set constant bank angle. Step 2: Determine whether the high-speed gliding aircraft has entered the glide phase based on its altitude change rate. If so, proceed to Step 3. If not, continue open-loop guidance based on the set constant bank angle. The basis for determining whether the aircraft has entered the glide phase is that the moment when the altitude change rate first reaches zero is used as the handover moment between the initial descent phase and the steady glide phase. 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 tilt angle command amplitude, α cmd is the angle of attack command, α is the angle of attack of the high-speed gliding aircraft, 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 first calculated, 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. The high-speed gliding vehicle reentry guidance method based on a high-precision analytical solution according to claim 1, characterized in that: The tilt angle amplitude |σ| is calculated according to the formula It is calculated as follows, where D and L are the drag and lift of the high-speed gliding aircraft, and L1 is the vertical component of the lift.

3. The high-speed gliding vehicle reentry guidance method based on high-precision analytical solution according to 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. The high-speed gliding vehicle reentry guidance method based on high-precision analytical solution according to claim 3, characterized in that: The maximum roll angle amplitude |σ max |The calculation is based on the heat flux density constraint, overload constraint and dynamic pressure constraint of the high-speed glider aircraft through the following process: High-speed gliding vehicle 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 Where ρ0 is the atmospheric density at sea level, β is an atmospheric constant; Based on the reentry corridor, the maximum atmospheric density boundary ρ can be obtained 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 met during balanced gliding, the maximum roll angle boundary is calculated to be 5. The high-speed gliding vehicle reentry guidance method based on high-precision analytical solution according to claim 1, characterized in that: The angle of attack of high-speed gliding aircraft adopts the form of piecewise quadratic function Among them, α1 is the initial value of the reentry attack angle, α2 is the maximum lift-to-drag ratio attack angle, E a and E b is the energy value of the segment point, and E is the current energy value.

6. The high-speed gliding vehicle reentry guidance method based on high-precision analytical solution according to 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. The high-speed gliding vehicle reentry guidance method based on high-precision analytical solution according to 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 according to 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 segment point, k1, k2, l1 and l2 are set constants.

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