CN113589838A - Three-dimensional track scheduling method based on cylinder position discretization - Google Patents

Three-dimensional track scheduling method based on cylinder position discretization Download PDF

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CN113589838A
CN113589838A CN202110598604.0A CN202110598604A CN113589838A CN 113589838 A CN113589838 A CN 113589838A CN 202110598604 A CN202110598604 A CN 202110598604A CN 113589838 A CN113589838 A CN 113589838A
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aircraft
dynamic pressure
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profile
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CN113589838B (en
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李春涛
王震
戴飞
梁耀
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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Abstract

本发明公开了一种基于圆柱位置离散化的三维轨迹调度方法。和航天飞机在末端能量管理段中传统的轨迹调度方法相比，该方法确定三个固定校准圆柱，飞行器在到达末端能量管理窗口时根据初始能量确定校准圆柱，获得返回轨迹。该方法抑制了初始参数摄动对轨迹的影响，实现对能量的精确耗散，使飞行器以期望能量平稳进入自动着陆窗口。另外该方法极大地降低了计算复杂度，具有极高的工程实用价值。

Figure 202110598604

The invention discloses a three-dimensional trajectory scheduling method based on cylindrical position discretization. Compared with the traditional trajectory scheduling method in the terminal energy management section of the space shuttle, this method determines three fixed calibration cylinders. When the aircraft reaches the terminal energy management window, the calibration cylinder is determined according to the initial energy, and the return trajectory is obtained. The method suppresses the influence of the initial parameter perturbation on the trajectory, realizes the accurate dissipation of energy, and enables the aircraft to enter the automatic landing window smoothly with the expected energy. In addition, the method greatly reduces the computational complexity and has extremely high engineering practical value.

Figure 202110598604

Description

Three-dimensional track scheduling method based on cylinder position discretization
Technical Field
The invention relates to a trajectory scheduling method of a hypersonic aircraft in a tail end energy management section, in particular to a three-dimensional trajectory scheduling technology based on cylindrical position discretization, and belongs to the technical field of aerospace aircraft trajectory design
Background
At present, track design technologies of most tail end energy management sections adopt complex track guidance, and energy consumption is realized through multiple transverse lateral maneuvers. Its advantages are high guidance precision, simple design process and no need of large-scale simulation. The defects are that the complex track gives larger pressure to the control end, and provides larger challenge to the computing capacity of the onboard computer, and the complex track is not easy to realize in engineering.
The method is also reasonable for an aircraft that consumes energy without multiple lateral maneuvers for a small initial energy, but for an aircraft that has a large initial velocity and a large initial energy spread. When the aircraft is laterally maneuvered, the flight range of the aircraft is sharply increased due to the fact that the turning radius is large due to high speed, and the aircraft cannot be guaranteed to smoothly enter the automatic landing window in an expected state. Moreover, the rolling of the aircraft can cause the loss of lift force, thereby generating a rolling and diving phenomenon. Finally, the actual voyage is far smaller than the predicted voyage, and the energy is too large when the aircraft enters a landing window. Therefore, a trajectory scheduling method which has the advantages of large initial energy, wide spread of positions and headings and simple trajectory is urgently needed.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to design a track scheduling method, so that an aircraft can tolerate uncertainty of initial energy and position course, and the aircraft can be ensured to reach an automatic landing window in an expected state, and the safe return flight of the aircraft is ensured.
The technical scheme is as follows:
a three-dimensional track scheduling method based on cylinder position discretization comprises the following steps:
step 1: designing a track design method based on a dynamic pressure profile, and determining a predicted course and a height profile under a typical energy point by combining an optimal height-course profile selection principle;
step 2: determining the altitude-range profile of the aircraft entering the tail end energy management window with different energies based on a linear interpolation principle and in combination with the altitude profiles of different typical energy points in the step 1;
and step 3: establishing nominal flight intervals with different energies on the basis of the altitude-flight profile under different energies;
and 4, step 4: designing a two-dimensional track generation method, and determining three calibration cylinder (cone) parameters of the aircraft at a nominal release position by using maximum energy, nominal energy and minimum energy when the aircraft returns at the nominal release position based on the method and in combination with a predicted course under the typical energy point in the step 1;
and 5: according to the two-dimensional track generation method in the step 4, calculating the distances of the aircraft respectively returning along three calibration cylinders (cones) in the course and position scattering space, and accordingly constructing an off-line track library;
step 6: and comparing the flight interval under the current energy with the actual flight distance when returning along three calibration cylinders (cones) under the current position and the current course, and returning along the calibration cylinder (cone) corresponding to the flight distance when the actual flight distance falls within the nominal interval to obtain the complete three-dimensional track scheduling method.
Further, in step 1, it is assumed that the aircraft glides in a quasi-equilibrium condition
Figure BDA0003092110010000021
The dynamic pressure and the rate of change of the dynamic pressure are calculated as follows:
Figure BDA0003092110010000022
in the formula
Figure BDA0003092110010000023
Is dynamic pressure, rhoaIs the atmospheric density, SrefIs wing area, g is gravitational acceleration, CL,CDRespectively, lift coefficient and drag coefficient, m aircraft mass, gamma glide angle, and H altitude.
Figure BDA0003092110010000024
dρathe/dH represents the rate of change of dynamic pressure and air density with height, respectively.
In order to ensure that the aircraft meets dynamic pressure constraint in the returning process, a piecewise function consisting of two sections of cubic curves and one section of constant curve is designed to represent the dynamic pressure of a given section on the height node, and the specific functional relationship is shown as the following formula:
Figure BDA0003092110010000025
in the formula
Figure BDA0003092110010000026
Represents the dynamic pressure of a given profile at this height node, ai,biI ═ 0,1,2,3 are parameters to be designed, hALIAnd hTEPRespectively, the heights of the starting points of the automatic landing leg and the terminal energy management leg. [ h ] ofM2,hM1]It indicates the altitude interval flying along the constant pressure section,
Figure BDA0003092110010000027
it represents the dynamic pressure in the constant dynamic pressure section.
Designing a track design method based on a dynamic pressure profile: setting
Figure BDA0003092110010000028
Has an initial value of qTEPCorresponding to a dynamic pressure change rate of
Figure BDA0003092110010000029
Introducing performance index J to iterate the attack angle, obtaining the attack angle and the glide angle when the performance index is minimum, calculating the current energy, and further obtaining the current predicted flight, wherein
Figure BDA00030921100100000210
Figure BDA00030921100100000211
S represents the predicted voyage, EhRepresenting the current energy, D representing the resistance; thirdly, calculating the dynamic pressure and the dynamic pressure change rate on the next altitude node, and repeating the previous step to predict the voyage again until the altitude H of the initial point of the automatic landing segment is reachedALI。
Because the attack angle and the glide-angle on the nodes with different heights are known quantities, the flight to be flown is predicted according to the dissipation rate of the flight on the energy on the nodes with different heights. In the returning process, different dynamic pressure profiles are constructed by optimizing the constant dynamic pressure interval and the constant dynamic pressure value to adjust and predict the voyage, and when the voyage is in the middle value of the maximum voyage and the minimum voyage, the corresponding dynamic pressure profile is the optimal dynamic pressure profile.
Then, a piecewise function combined by a primary curve and a cubic curve is adopted to fit the relation between the height and the flight range to be flown, so as to construct a height-flight range profile, wherein the profile is the optimal height-flight range profile, and the fitting function is shown as the following formula:
Figure BDA0003092110010000031
in the formula SsubRepresenting the flight path of the aircraft into the subsonic phase, hALIIt indicates the altitude at which the aircraft reaches the end of the energy management segment, i.e., the automatic landing window.
As an aircraft enters the terminal energy management section, there is a wide spread in its altitude and speed due to its high altitude, high speed nature. Assume that the initial expected state of the aircraft entering the terminal energy management segment is (H)nor,Vnor) The fluctuation intervals of the height and the speed are (+/- Δ H and (+/- Δ V) respectively. The upper and lower boundaries of the height and the speed are combined to form the upper and lower boundaries of the energy, and a typical energy point is selected between the upper boundary of the energy and the nominal energy in order to ensure the tracking accuracy of the height profile. Similarly, a typical energy point is also selected between the lower energy boundary and the nominal energy. The energy states and expressions of these five typical discrete energy points are shown in table 1:
TABLE 1 typical discrete energy point energy states and expressions
Energy state Form of expression
(Hnor+ΔH,Vnor+ΔV) Emax
(Hnor-ΔH,Vnor+ΔV) Emid_max
(Hnor,Vnor) Enor
(Hnor+ΔH,Vnor-ΔV) Emid_min
(Hnor-ΔH,Vnor-ΔV) Emin
Therefore, according to the track design method based on the dynamic pressure profile, even if the initial energy states are different, the subsonic section height course profile is still the same, and the height-course profile of the supersonic section in different energy states is as shown in the formula:
Figure BDA0003092110010000032
in the formula, amnThe undetermined coefficients of the altitude-range profile are m ═ 1,2,3,4,5, and n ═ 1,2,3, 4; emaxRepresents the maximum energy; emid_maxRepresenting the energy below the lower boundary of altitude, the upper boundary of velocity; enorRepresents the nominal energy; emid_minRepresenting the energy at the lower boundary of the upper boundary velocity of the altitude; eminThe minimum energy is indicated.
Further, in step 2, when the aircraft is in the arbitrary energy state E, based on the typical energy point determined in step 10When entering the tail end energy management window, the energy is different according to the energyThe energy interval of the altitude flight curve is fitted in a linear interpolation mode.
Assume initial state E0Is located in (E)mid_max，Emax) The height voyage section coefficient is shown as the following formula:
Figure BDA0003092110010000041
in the formula (I), the compound is shown in the specification,
Figure BDA0003092110010000042
the undetermined coefficients representing the altitude-course profile of the aircraft at any energy entry into the terminal window are listed in the above equation as the initial energy state E0Is located in (E)mid_max，Emax) In the case of the above, the initial energy falls in the other energy intervals. And taking the five typical energy points as a reference, when the aircraft enters an end energy management window in any energy state, calculating an altitude profile in any energy state on line by using a linear fitting method, and taking the altitude profile as a reference altitude instruction profile returned by the aircraft.
Further, a two-dimensional track generation method is designed in the step 4, and two-dimensional track parameters under the maximum energy, the nominal energy and the minimum energy are determined. Wherein, the two-dimensional track voyage StotalThe main composition is shown as the following formula:
Stotal＝SPF+SHAC+SAC+SS
in the formula SPF,SHAC,SAC,SSRespectively representing the flight of a flying section before approach, a course calibration section, a capturing section and an S turning section.
After entering the tail end energy management section, if the energy is moderate and S-turn is not needed, after the aircraft reaches the tail end energy management section capturing section window, the aircraft starts to fly along the tangential direction of the course calibration section, after reaching the HAC tangent point, the aircraft flies along the calibration cylinder, the course is finally aligned to the airport runway, and after the HAC section is finished, the aircraft enters the approach front flying section to further adjust the course.
In summary, the course calibration cylinder position X is adjustedHACAnd the radius of approach RHACThe adjustment of the course can be realized, and the iterative calculation of the position of the course calibration cylinder is calculated by the following formula:
Figure BDA0003092110010000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003092110010000044
and
Figure BDA0003092110010000045
respectively the (k + 1) th iteration course calibration cylinder position and the (k) th iteration course calibration cylinder position, b is a weight factor, and Delta S is a predicted course S0Voyage S with two-dimensional tracktotalThe difference value. The cylinder position is iteratively calibrated by the above formula. And iterating by adopting the following formula as a basis for the iterative calculation of the approach radius.
Figure BDA0003092110010000046
In the formula (I), the compound is shown in the specification,
Figure BDA0003092110010000047
and
Figure BDA0003092110010000048
respectively the entrance radius of the (k + 1) th and k times of iteration, RfAnd selecting a weight factor b of 0.2 for the radius of the aircraft when the aircraft flies out of the course calibration cylinder (cone), namely adjusting the track mainly by adjusting the radius, and adjusting the position of the calibration cylinder as an auxiliary means. The situation that the distance between the course calibration cylinder and the automatic landing window is too far when the track is adjusted is prevented, and the turning capacity exceeds the maximum turning capacity when the vehicle enters the course calibration cylinder. The maximum turning capability of an aircraft is primarily related to the current speed and roll angle.
When the aircraft approaches indirectly, the course calibration section adopts a spiral line,helix ratio R of the helix2The relationship with the approach radius is shown as follows:
Figure BDA0003092110010000051
in the formula, RHACIs the radius, R, of the aircraft entry course calibration cylinder (cone)fThe radius at which the aircraft flies out of the heading calibration cylinder (cone) and ψ is the angle through which the aircraft flies along the heading calibration cylinder (cone), i.e., the helix. The radius of the spiral line and the radius R of the arc turningρThe relationship is shown as follows:
R＝Rρsinλ
in the formula, λ is an included angle between the vector radius and the arc direction, and the calculation formula is shown as the following formula:
Figure BDA0003092110010000052
in the formula, ω represents a central angle corresponding to the current position of the aircraft. According to the formula, when the aircraft flies along the spiral line, the radius of the aircraft is not too small and is not smaller than the minimum radius under the maximum rolling angle, and the relationship is shown as the following formula:
Figure BDA0003092110010000053
predicting the flight to be flown S according to the initial energy when the aircraft enters the terminal energy management section window in a specific energy state0. Then, assuming that the aircraft enters the field in an indirect approach mode, ensuring that the course calibration position and the automatic landing window position are coincided and calculating the distance S to be flown at the momenttotal. If S istotal＞S0And the aircraft enters the field by selecting an indirect approach mode, otherwise, the aircraft enters the field by selecting a direct approach mode. By continuously iteratively adjusting the radius and position of the calibration cylinder (cone) to make S0＝Stotal. Finally, obtaining the two-dimensional track parameters of the maximum energy state, the nominal energy state and the minimum energy state(i.e., three calibration cylinder (cone) parameters at maximum energy, nominal energy, minimum energy return).
Further, in step 6, the flight interval under the current energy and the actual flight distances when returning along the three calibration cylinders under the current position and heading are determined, and the calibration cylinders when returning are determined by comparing the flight interval with the actual flight distances. Three heading calibration cylinder (cone) parameters at maximum energy, minimum energy, nominal energy return are represented by HAC1, HAC2, and HAC3, respectively, with S1,S2,S3Representing the flight distance of the aircraft returning along the three calibration cylinders, denoted Snor_down,Snor_upRespectively representing the upper and lower boundaries of the flight space. And finally, determining the heading calibration cylinder along which the aircraft returns according to the position of the nominal interval on the number axis. The selection method comprises the following steps:
(1) when S isnor_up＜S1In time, the aircraft cannot return to a predetermined airport due to insufficient energy, and an emergency landing scheme needs to be implemented.
(2) When S isnor_down≤S1≤Snor_upThe aircraft is returned along HAC 1.
(3) When S isnor_down≤S2≤Snor_upThe aircraft is returned along HAC 2.
(4) When S isnor_down≤S3≤Snor_upThe aircraft is returned along HAC 3.
(5) When S is3＜Snor_downAnd then, the initial energy of the aircraft is overlarge, the aircraft needs to turn S, and the course when the aircraft returns along the HAC3 at the current position is calculated in real time until the current energy is matched with the predicted course.
Has the advantages that:
1. the three-dimensional trajectory scheduling method based on the cylindrical position discretization solves the problem that an aircraft cannot enter an automatic landing window in an expected state due to large-range perturbation of initial energy, position and course; the method obtains the optimal range under the maximum energy, the nominal energy and the minimum energy according to the optimal profile selection principle, and determines three fixed calibration cylinders (cones) by combining a two-dimensional track generation method; and finally, comparing the range returned along the fixed cylinder with the range interval under the current energy to determine the track parameter of the tail end energy management section. The safe return flight of the aircraft is ensured;
2. on the basis of ensuring the guidance precision, the height-range profile under the condition of any energy state is obtained by designing the height-range profile under five typical energy points and adopting a linear interpolation mode, so that the operation complexity in the design process of the track guidance method is reduced; meanwhile, the computing power requirement on the onboard computer is reduced, the aircraft can quickly determine the return track according to the current state, and the engineering practicability is strong;
3. compared with the traditional track guidance method of the tail end energy management section, the method can effectively inhibit the problems of large-range spread of the energy, position and course of the aircraft at the initial window, inhibit the influence of perturbation of the initial parameters on the track, improve the indexes of the success rate, reliability and the like of safe return of the aircraft, and has important application value;
4. the invention designs a two-dimensional track prediction correction algorithm, and aims at the problem of large initial position and course spread, the algorithm can plan a two-dimensional track course by optimizing the position and radius of a calibration cylinder (cone), so that the accurate dissipation of energy is realized while the position course meets the requirement when an aircraft reaches an automatic landing window;
5. the method comprises the steps of selecting three calibration columns (cones) with fixed radiuses and positions, calculating flight distances of an aircraft when the aircraft returns along the three calibration columns (cones) respectively, and selecting a reference track of the aircraft according to the relation between a nominal flight interval of the aircraft and the three flight distances when the aircraft enters a terminal window in different states; according to the method, the aircraft is designed to return along three fixed calibration cylinders (cones), so that the workload of a simulation task in the process of constructing a two-dimensional track database is greatly simplified, and the condition that the height, the speed, the position, the course and the like meet the terminal limit when the aircraft reaches a landing window can be ensured.
Drawings
FIG. 1 is a flow chart of trajectory design based on dynamic pressure profile;
FIG. 2 is a comparison of a fitted height profile and an original height profile;
FIG. 3 is a dynamic pressure-height profile at various typical energy points;
FIG. 4 is an energy-range profile at various exemplary energy points;
FIG. 5 is a velocity-course profile at various exemplary energy points;
FIG. 6 is a height-course profile at various typical energy points;
FIG. 7 is an angle of attack-height profile at various typical energy points;
FIG. 8 is a slip angle-height profile at various typical energy points;
FIG. 9 is a two-dimensional nominal trajectory flight segment;
FIG. 10 is a two-dimensional trajectory configuration diagram of an end energy management segment
FIG. 11 is a flow chart of a two-dimensional trajectory generation method;
FIG. 12 is a schematic view of a calibration cylinder flight distance axis;
FIG. 13 is a flow chart of a three-dimensional trajectory scheduling scheme;
FIG. 14 is a two-dimensional return trajectory plot based on cylinder position discretization;
FIG. 15 is a glide angle-height profile;
FIG. 16 is an angle of attack elevation profile;
FIG. 17 is a height-course section;
fig. 18 is a height-velocity profile.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The three-dimensional track scheduling method based on the cylinder position discretization comprises the following specific design steps:
step 1, designing a track design method based on dynamic pressure profile
The hypersonic vehicle is based on the standard flatness in the unpowered returning processCondition of constant glide
Figure BDA0003092110010000071
The dynamic pressure and the rate of change of the dynamic pressure are calculated as follows;
Figure BDA0003092110010000072
in the formula
Figure BDA0003092110010000073
Is dynamic pressure, rhoaIs the atmospheric density, SrefIs wing area, g is gravitational acceleration, CL,CDRespectively, lift coefficient and drag coefficient, m aircraft mass, gamma glide angle, and H altitude.
Figure BDA0003092110010000074
dρathe/dH represents the rate of change of dynamic pressure and air density with height, respectively.
The iterative angle of attack causes the dynamic pressure
Figure BDA0003092110010000079
Dynamic pressure at the height node corresponding to a given dynamic pressure profile
Figure BDA0003092110010000075
Comparing and then calculating the dynamic pressure change rate on the height node
Figure BDA0003092110010000076
And given dynamic pressure change rate at the node of the height
Figure BDA0003092110010000077
Compared with the prior art, the method has the advantages that the performance index J is introduced to continuously iterate the attack angle, when the performance index is minimum, the attack angle and the downward sliding angle are recorded, then the dynamic pressure and the dynamic pressure change rate on the next height node are calculated, the steps are repeated, and the performance index calculation formula is shown as the following formula;
Figure BDA0003092110010000078
fig. 1 shows a flow chart of trajectory design based on dynamic pressure profile. When the given dynamic pressure-height profile is known, the attack angle and the glide angle of each height node can be determined according to the track design flow. The following relationship exists for energy voyage:
Figure BDA0003092110010000081
in the formula EhRepresenting the current energy of the aircraft, S representing the range of the aircraft, D representing the resistance, and predicting the range to be flown according to the dissipation rates of the range to the energy on different height nodes because the attack angles and the glide angles on the different height nodes are known quantities. In the returning process, different dynamic pressure profiles are constructed by optimizing the constant dynamic pressure interval and the constant dynamic pressure value to adjust and predict the voyage, and when the voyage is in the middle value of the maximum voyage and the minimum voyage. At this time, the corresponding dynamic pressure profile is the optimal dynamic pressure profile.
With the initial height of 24km and the initial speed of mach 3.6 as the nominal energy, the dynamic pressure-height profile obtained by the method has the following relationship:
Figure BDA0003092110010000082
the relation between the fitting height and the flight range to be flown by a piecewise function combined by a primary curve and a tertiary curve is adopted to construct a height-flight range profile, the profile is an optimal height-flight range profile under nominal energy, the fitting function of the profile is shown as the following formula, and fig. 2 is a comparison graph of the fitting height profile and an original height profile.
Figure BDA0003092110010000083
When an aircraft enters the terminal energy management section, there is a wide spread in its altitude and speed due to its high altitude and high speed characteristics. Assuming that the initial expected state of the aircraft entering the terminal energy management section is (24km,3.6ma), the fluctuation ranges of the altitude and the speed are (+ -1 km, + -0.2 ma), the upper and lower boundaries of the altitude and the speed are combined to form the upper and lower boundaries of energy, and meanwhile, in order to ensure the tracking accuracy of the altitude profile, a typical energy point is selected between the upper boundary of the energy and the nominal energy. Similarly, a typical energy point is also selected between the lower energy boundary and the nominal energy. The energy states and expressions of these five typical discrete energy points are shown in table 2:
TABLE 2 exemplary discrete energy Point energy states and expressions
Energy state Form of expression
(25km,3.8ma) Emax
(23km，3.8ma) Emid_max
(24km，3.6ma) Enor
(25km,3.4ma) Emid_min
(23km，3.4ma) Emin
The dynamic pressure-altitude profile, the energy-voyage profile, the speed-voyage profile, the altitude-voyage profile, the attack angle-altitude profile and the glide angle altitude profile in five typical energy states can be obtained according to the method, and are respectively shown in fig. 3 to 8. After the height-range profiles at the different typical energy points are obtained, the height-profile at the five typical energy points is fitted by using a piecewise function combining a cubic curve and a linear curve. When the aircraft enters the function interval of the primary curve, the curves are completely overlapped and are not listed here, and the relationship of the cubic function curve segments of the altitude-flight distance under five typical energy points is shown as the following formula:
Figure BDA0003092110010000091
in step 2, aiming at the condition that the energy is arbitrary when the aircraft enters the tail end energy management window, the aircraft is in an arbitrary energy state E according to the combination of the five typical energy points in the step 1 according to the linear interpolation principle0And when the terminal energy management window is entered, fitting a height range curve in a linear interpolation mode according to the energy falling in different energy intervals. Assume initial state E0Is located in (E)mid_max，Emax) The height voyage section coefficient is shown as the following formula:
Figure BDA0003092110010000092
thus, a corresponding altitude-range profile may be obtained when the aircraft enters the end energy management window at any energy.
And 3, constructing nominal flight intervals with different energies, and tracking a given height profile by adopting height control in the process of unpowered return of the aircraft in the longitudinal control. When the actual height is greater than the given height during the flight, there is a height deviation when the elevator is rudders. The aircraft generates a low head moment and the aircraft dives at a steeper attitude. Conversely, when the actual height is less than the given height. The elevator controls the aircraft to generate a head-up moment. The aircraft approaches the given altitude profile at a relatively gradual attitude. Therefore, the aircraft has stronger robustness by adopting the height control, and has certain self-regulation capacity to external disturbance. Therefore, the nominal flight distance is expanded into a nominal flight interval, the tolerance to two-dimensional track errors can be increased, the fluctuation is up and down 10% on the basis of the nominal flight distance, and the nominal flight interval is constructed as shown in fig. 9.
And 4, designing a two-dimensional track generation method, wherein the two-dimensional track is formed as shown in FIG. 10, and the two-dimensional flight is adjusted mainly by adjusting the position and the radius of a course calibration cylinder (cone). A flow chart of a two-dimensional trajectory generation method is shown in fig. 11. When an aircraft enters a terminal energy management window, although the energy is widely dispersed, the maximum and minimum energy boundaries, namely E, still existmaxAnd Emin. Assuming that the aircraft enters the terminal energy management window at maximum energy, the nominal flight path of the aircraft can be determined according to the above altitude profile design method. Therefore, the maximum energy, the minimum energy and the nominal flight distance S under the nominal energy can be finally determined1,S2,S3Then, the radius and position of the calibration cylinders HAC1, HAC2 and HAC3 at three flight distances are obtained by a two-dimensional track generation algorithm, wherein the radius and position are (-10km,5.7km), (-19km,13km), (-14.5km, -10km), respectively.
And 5, calculating the distances of the aircraft when the aircraft returns along three calibration cylinders in the course and position scattering space respectively, wherein the aircraft takes (130 ) km as a nominal launching position and 56 degrees as a nominal course. A window of 10km is limited for the initial position and a window of 10 deg. is limited for the initial heading. In the position and course spread interval, the return is respectively returned along three calibration cylinders of (-10km,5.7km), (-19km,13km), (-14.5km, -10km) at different positions and different courses, a two-dimensional track database is constructed as shown in table 3, so that the return track can be found in the two-dimensional track database under any initial state in a space allowing position, course and energy walking.
TABLE 3 two-dimensional trajectory database
Figure BDA0003092110010000101
The table above lists the flight paths of the aircraft as they return along the three heading calibration columns at five typical positions with a range spread of 10 ° in heading angle. When the aircraft enters the tail end energy management window, the flight range at the typical position close to the aircraft is selected as the predicted range of the unpowered return of the aircraft according to the proximity principle aiming at the uncertainty of the position. The two-dimensional track database can determine the flight distance to be flown when the aircraft enters the tail energy management section in any state in the random dispersion space of the allowed position and heading.
In the step 6, a complete guidance scheme needs to be designed because the energy, the position, the course and the like are relatively arbitrary when the aircraft enters the tail end energy management window. So that it can enter the automatic landing window in the same flight state in any initial state. Firstly, the nominal flight distance and the flight interval of the aircraft under the energy are determined according to the initial energy. While determining the altitude profile of the aircraft. This profile is the profile for a given altitude during the return of the aircraft. Then, determining the flight distances of the aircraft returning along the three calibration cylinders to be S respectively in the two-dimensional track database according to the initial position and the heading1,S2,S3. For the purpose of visual presentation, the three flight distances are shown in the form of a number axis as shown in fig. 12. And finally, determining the heading calibration cylinder along which the aircraft returns according to the position of the nominal interval on the number axis. The selection method comprises the following steps:
(1) when S isnor_up＜S1In time, the aircraft cannot return to a preset airport due to insufficient energy, and an emergency landing scheme is implemented;
(2) when S isnor_down≤S1≤Snor_upWhile, the aircraft is returning along HAC 1;
(3) when S isnor_down≤S2≤Snor_upWhile, the aircraft is returning along HAC 2;
(4) when S isnor_down≤S3≤Snor_upWhile, the aircraft is returning along HAC 3;
(5) when S is3＜Snor_downAt the moment, the initial energy of the aircraft is too large, the aircraft needs to make an S turn, and the flight course of the aircraft at the current position when the aircraft returns along the HAC3 is calculated in real time until the current energy is matched with the predicted flight course. The flow chart of the scheduling scheme is shown in fig. 13.
Finally, aiming at the uncertainty of the initial position, the heading and the energy, the feasibility and the accuracy of the three-dimensional track guidance and scheduling method based on the discretization of the cylindrical position are verified by random dotting in the allowable scattering space range. The initial values of the simulation are shown in table 4:
TABLE 4 initial values of discretized guidance method for cylinder position
Figure BDA0003092110010000111
When the aircraft enters the tail end energy management section at any energy, a nominal flight interval and an altitude profile of the aircraft at the energy are obtained on the basis of the altitude profile of a typical energy point. And then selecting and judging the return track of the aircraft according to the two-dimensional track database. Ensuring that the aircraft lands safely in the desired state. Which returns a two-dimensional trajectory as shown in fig. 14. In order to intuitively explain the guidance effect of the invention, a state instruction of the task 1 is given, as shown in fig. 15-18, wherein the attack angle range is 3-4.5 degrees, the glide angle is-12 degrees when the glide angle is steepest, and the key physical signal quality in the returning process is good and meets the state limit of a landing window as can be seen from a height flight profile and a height speed profile.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (5)

1.一种基于圆柱位置离散化的三维轨迹调度方法，其特征在于，包括如下步骤：1. a three-dimensional trajectory scheduling method based on the discretization of cylindrical position, is characterized in that, comprises the steps: 步骤1：设计基于动压剖面的轨迹设计方法，结合最优高度-航程剖面选取原则，确定典型能量点下的预测航程及高度剖面；Step 1: Design the trajectory design method based on the dynamic pressure profile, and combine the optimal altitude-range profile selection principle to determine the predicted range and height profile under typical energy points; 步骤2：基于线性插值原理，结合步骤1中典型能量点下的高度剖面，确定飞行器以不同能量进入末端能量管理窗口时的高度-航程剖面；Step 2: Based on the principle of linear interpolation, combined with the altitude profile under the typical energy point in Step 1, determine the altitude-range profile when the aircraft enters the terminal energy management window with different energies; 步骤3：以步骤2中的高度-航程剖面为基础，构建不同能量的标称飞行区间；Step 3: Based on the altitude-range profile in Step 2, construct nominal flight zones with different energies; 步骤4：设计二维轨迹生成方法，基于此方法并结合步骤1典型能量点下的预测航程确定飞行器在标称投放位置处，以最大能量、标称能量、最小能量返回时的三个校准圆柱/锥参数；Step 4: Design a two-dimensional trajectory generation method. Based on this method and combined with the predicted range at the typical energy point in step 1, determine the three calibration cylinders when the aircraft returns at the nominal delivery position with maximum energy, nominal energy and minimum energy. /cone parameter; 步骤5：根据步骤4中的二维轨迹生成方法，计算飞行器在航向、位置散布空间内分别沿三个校准圆柱/锥返回时的距离，并据此构建离线轨迹库；Step 5: According to the two-dimensional trajectory generation method in Step 4, calculate the distance when the aircraft returns along the three calibration cylinders/cones in the heading and position dispersion space respectively, and build an offline trajectory library accordingly; 步骤6：比较当前能量下的飞行区间与当前位置和航向下沿三个校准圆柱/锥返回时的实际飞行距离，当实际飞行距离落在标称区间内，则沿此实际飞行距离对应的校准圆柱/锥返回，得到完整的三维轨迹调度方法。Step 6: Compare the flight interval under the current energy with the actual flight distance when returning along the three calibration cylinders/cones at the current position and heading. When the actual flight distance falls within the nominal interval, the calibration corresponding to the actual flight distance Cylinder/cone return to get a complete 3D trajectory scheduling method. 2.根据权利要求1所述的一种基于圆柱位置离散化的三维轨迹调度方法，其特征在于，步骤1具体为：2. a kind of three-dimensional trajectory scheduling method based on cylindrical position discretization according to claim 1, is characterized in that, step 1 is specifically: 飞行器依据准平衡下滑条件
Figure FDA0003092110000000011
飞行器的动压及其动压变化率计算如下式所示：The aircraft glides under quasi-equilibrium conditions
Figure FDA0003092110000000011
The dynamic pressure of the aircraft and its dynamic pressure change rate are calculated as follows:
Figure FDA0003092110000000012
Figure FDA0003092110000000012
 式中
Figure FDA0003092110000000013
为动压、ρa为大气密度、Sref为机翼面积、g为重力加速度、CL,CD分别代表升力系数和阻力系数、m代表飞行器质量、γ代表下滑角、H代表高度；in the formula
Figure FDA0003092110000000013
is the dynamic pressure, ρ a is the atmospheric density, S ref is the wing area, g is the gravitational acceleration, C L , C D are the lift coefficient and drag coefficient, m is the mass of the aircraft, γ is the glide angle, and H is the height; 为了保证飞行器在返回过程中满足动压约束，设计两段三次曲线和一段常值曲线组成的第一分段函数来表示给定剖面在此高度节点上的动压，第一分段函数如下式所示：In order to ensure that the aircraft satisfies the dynamic pressure constraint during the return process, a first piecewise function composed of two cubic curves and a constant curve is designed to represent the dynamic pressure of a given section at this height node. The first piecewise function is as follows shown:
Figure FDA0003092110000000014
Figure FDA0003092110000000014
 式中
Figure FDA0003092110000000015
表示给定剖面在此高度节点上的动压，ai,bi为待设计参数，i＝0，1,2,3；hALI和hTEP分别表示自动着陆段和末端能量管理段起始点的高度，hM1和hM2分别表示沿常值动压段飞行的高度区间的上下限；
Figure FDA0003092110000000021
表示常值动压段的动压；in the formula
Figure FDA0003092110000000015
Represents the dynamic pressure of a given profile at this height node, a i , b i are parameters to be designed, i=0, 1, 2, 3; h ALI and h TEP represent the starting point of the automatic landing section and the terminal energy management section, respectively The height of , h M1 and h M2 respectively represent the upper and lower limits of the altitude interval flying along the constant dynamic pressure section;
Figure FDA0003092110000000021
Indicates the dynamic pressure of the constant dynamic pressure section; 设计基于动压剖面的轨迹设计方法：①设定
Figure FDA0003092110000000022
的初值为qTEP，对应动压变化率为
Figure FDA0003092110000000023
②引入性能指标J迭代迎角，得到性能指标最小时的迎角与下滑角，计算当前能量，进而得到当前预测航程，其中
Figure FDA0003092110000000024
S表示预测航程，Eh表示当前能量，D表示阻力；③计算下一高度节点上动压以及动压变化率，并重复前一步骤重新进行航程预测，直至达到自动着陆段起始点的高度HALI；Design the trajectory design method based on the dynamic pressure profile: ① Setting
Figure FDA0003092110000000022
The initial value of q TEP , the corresponding dynamic pressure change rate is
Figure FDA0003092110000000023
②Introduce the performance index J to iterate the angle of attack, obtain the angle of attack and glide angle when the performance index is the smallest, calculate the current energy, and then obtain the current predicted range, where
Figure FDA0003092110000000024
S represents the predicted voyage, E h represents the current energy, and D represents the resistance; ③ Calculate the dynamic pressure and the dynamic pressure change rate at the next altitude node, and repeat the previous step to re-predict the voyage until it reaches the height H of the starting point of the automatic landing segment ali ; 当上述某一预测航程为最大航程和最小航程的中间值时，对应的动压剖面即为最优动压剖面；When one of the above predicted voyages is the middle value of the maximum voyage and the minimum voyage, the corresponding dynamic pressure profile is the optimal dynamic pressure profile; 采用由一次曲线和三次曲线组合的第二分段函数拟合高度与预测航程的关系，构建最优高度-航程剖面，第二分段函数如下式所示：The relationship between altitude and predicted range is fitted by a second piecewise function composed of a primary curve and a cubic curve, and the optimal altitude-range profile is constructed. The second piecewise function is shown in the following formula:
Figure FDA0003092110000000025
Figure FDA0003092110000000025
 式中Ssub表示飞行器进入亚音速阶段的航程，c0,…,c4表示参数；In the formula, S sub represents the voyage of the aircraft entering the subsonic stage, and c 0 ,…,c 4 represent the parameters; 选取五个典型离散能量点Emax、Emid_max、Enor、Emid_min和Emin，其能量状态分别为(Hnor+ΔH,Vnor+ΔV)、(Hnor-ΔH,Vnor+ΔV)、(Hnor,Vnor)、(Hnor+ΔH，Vnor-ΔV)和(Hnor-ΔH，Vnor-ΔV)，其中Hnor,Vnor表示飞行器进入末端能量管理段的初始期望高度和速度，ΔH,ΔV表示飞行器高度和速度的波动值；Five typical discrete energy points E max , E mid_max , E nor , E mid_min and E min are selected, and their energy states are (H nor +ΔH,V nor +ΔV), (H nor -ΔH,V nor +ΔV) respectively , (H nor ,V nor ), (H nor +ΔH, V nor -ΔV) and (H nor -ΔH, V nor -ΔV), where H nor ,V nor represent the initial desired altitude of the aircraft entering the terminal energy management section and speed, ΔH, ΔV represent the fluctuation value of aircraft altitude and speed; 进而，得到不同能量状态下超音速段的高度-航程剖面：Furthermore, the altitude-range profiles of the supersonic segment under different energy states are obtained:
Figure FDA0003092110000000026
Figure FDA0003092110000000026
 式中，amn为高度-航程剖面的待定系数，m＝1,2,3,4,5，n＝1,2,3,4，Emax表示最大能量，Emid_max表示高度下边界、速度上边界下的能量，Enor表示标称能量，Emid_min表示高度上边界、速度下边界下的能量、Emin表示最小能量。In the formula, a mn is the undetermined coefficient of the altitude-range profile, m=1, 2, 3, 4, 5, n= 1, 2, 3, 4, E max represents the maximum energy, E mid_max represents the lower boundary of altitude, speed The energy under the upper boundary, E nor is the nominal energy, E mid_min is the energy under the upper boundary of the height and the lower boundary of the velocity, and E min is the minimum energy. 3.根据权利要求1所述的一种基于圆柱位置离散化的三维轨迹调度方法，其特征在于，步骤2中以步骤1中确定的典型能量点为基准当飞行器以任意能量状态E0进入末端能量管理段时，根据E0落在不同的典型能量点之间，采取线性插值的方式拟合相应的高度-航程剖面。3. a kind of three-dimensional trajectory scheduling method based on the discretization of cylindrical position according to claim 1, it is characterized in that, in step 2, take the typical energy point determined in step 1 as the benchmark when the aircraft enters the terminal with any energy state E 0 During the energy management stage, according to E 0 falling between different typical energy points, the corresponding altitude-range profile is fitted by means of linear interpolation. 4.根据权利要求1所述的一种基于圆柱位置离散化的三维轨迹调度方法，其特征在于，步骤4中二维轨迹航程Stotal如下式所示：4. a kind of three-dimensional trajectory scheduling method based on cylindrical position discretization according to claim 1, is characterized in that, in step 4, two-dimensional trajectory range S total is as shown in the following formula: Stotal＝SPF+SHAC+SAC+SS S total =S PF +S HAC +S AC +S S 式中SPF，SHAC,SAC,SS分别代表进场前飞段、航向校准段、捕获段、S转弯段的航程；In the formula, S PF , S HAC , S AC , and S S represent the flight range of the pre-approach flight segment, the heading calibration segment, the capture segment, and the S turn segment, respectively; 进入末端能量管理段后，若不需要S转弯，那么在飞行器到达末端能量管理段捕获段窗口后，飞行器开始沿航向校准段的切线方向飞行，到达HAC切点后，沿着校准圆柱/锥飞行，使航向最终对准机场跑道，结束HAC段后进入进场前飞段进一步调整航向；综上所述，调节航向校准圆柱/锥位置与进场半径能够实现对航程的调整；After entering the end energy management segment, if the S turn is not required, after the aircraft reaches the capture segment window of the end energy management segment, the aircraft starts to fly along the tangent direction of the heading calibration segment, and after reaching the HAC tangent point, it flies along the calibration cylinder/cone , so that the heading is finally aligned with the airport runway, and after the HAC segment is completed, it enters the pre-approach flight segment to further adjust the heading; in summary, adjusting the heading calibration cylinder/cone position and approach radius can adjust the flight range; 对于航向校准圆柱/锥位置通过下式进行迭代计算：The cylinder/cone position for heading calibration is iteratively calculated by:
Figure FDA0003092110000000031
Figure FDA0003092110000000031
 式中，
Figure FDA0003092110000000032
和
Figure FDA0003092110000000033
分别为第k+1、k次迭代的航向校准圆柱位置，b为权重因子，ΔS为预测航程与Stotal的差值；In the formula,
Figure FDA0003092110000000032
and
Figure FDA0003092110000000033
are the heading calibration cylinder positions of the k+1 and k iterations, respectively, b is the weight factor, and ΔS is the difference between the predicted range and S total ; 对于进场半径通过下式进行迭代计算：The approach radius is iteratively calculated by:
Figure FDA0003092110000000034
Figure FDA0003092110000000034
 式中，
Figure FDA0003092110000000035
和
Figure FDA0003092110000000036
分别为第k+1、k次迭代的进场半径，Rf为飞行器飞出航向校准圆柱/锥时的半径；In the formula,
Figure FDA0003092110000000035
and
Figure FDA0003092110000000036
are the approach radius of the k+1 and kth iterations, respectively, and R f is the radius when the aircraft flies out of the heading calibration cylinder/cone; 当飞行器间接进场时航向校准段采用的是螺旋线，螺旋线的螺旋率R2与进场半径存在关系如下式所示：When the aircraft is approaching indirectly, the heading calibration section uses a helix. The helix rate R 2 of the helix has a relationship with the approach radius as shown in the following formula:
Figure FDA0003092110000000037
Figure FDA0003092110000000037
 式中，RHAC是进场半径，ψ为飞行器沿航向校准圆柱/锥即螺旋线飞过的角度；螺旋线的半径R与圆弧转弯半径Rρ关系如下式所示：In the formula, R HAC is the approach radius, ψ is the angle that the aircraft flies along the heading calibration cylinder/cone, that is, the helix; the relationship between the radius R of the helix and the arc turning radius R ρ is shown in the following formula: R＝RρsinλR=R ρ sinλ 式中，λ为矢量半径与弧线方向的夹角，
Figure FDA0003092110000000038
ω表示飞行器当前位置对应的圆心角；且
Figure FDA0003092110000000039
V表示速度，φmax表示最大滚转角；where λ is the angle between the radius of the vector and the direction of the arc,
Figure FDA0003092110000000038
ω represents the central angle corresponding to the current position of the aircraft; and
Figure FDA0003092110000000039
V represents the speed, φ max represents the maximum roll angle; 当飞行器以特定的能量状态进入末端能量管理段窗口时，根据初始能量E0预测航程S0；然后假设飞行器以间接进场的方式进场，确保航向校准位置与自动着陆窗口位置重合，计算此时的Stotal，如果Stotal＞S0飞行器选择间接进场方式进场，否则选择直接进场方式进场；通过不断迭代调整航向校准圆柱/锥的进场半径与末端半径及位置使S0＝Stotal，最后获得以最大能量、标称能量、最小能量返回时的三个校准圆柱/锥参数。When the aircraft enters the terminal energy management segment window with a specific energy state, the flight range S 0 is predicted according to the initial energy E 0 ; then, assuming that the aircraft approaches in an indirect approach, ensure that the heading calibration position coincides with the position of the automatic landing window, calculate this When S total , if S total > S 0 , the aircraft chooses the indirect approach approach, otherwise it chooses the direct approach approach; by continuously iteratively adjusting the approach radius, end radius and position of the heading calibration cylinder/cone to make S 0 =S total , and finally obtain three calibrated cylinder/cone parameters when returning at maximum energy, nominal energy, and minimum energy. 5.根据权利要求1所述的一种基于圆柱位置离散化的三维轨迹调度方法，其特征在于，步骤6中用HAC1、HAC2和HAC3分别表示以最大能量、最小能量、标称能量返回时的三个航向校准圆柱/锥参数，用S1，S2，S3分别表示飞行器沿三个航向校准圆柱/锥返回时的实际飞行距离，用Snor_down，Snor_up分别表示当前能量下的飞行区间的上下边界，根据标称区间的位置来确定飞行器沿哪个航向校准圆柱/锥返回：5. a kind of three-dimensional trajectory scheduling method based on cylindrical position discretization according to claim 1, is characterized in that, in step 6, use HAC1, HAC2 and HAC3 to represent respectively with maximum energy, minimum energy, when the nominal energy returns. Three heading calibration cylinder/cone parameters, S 1 , S 2 , S 3 respectively represent the actual flight distance when the aircraft returns along the three heading calibration cylinder/cone, S nor_down , S nor_up respectively represent the flight interval under the current energy The upper and lower bounds of , determine which heading calibration cylinder/cone returns to the aircraft based on the position of the nominal interval: (1)当Snor_up＜S1时，飞行器由于能量不足，无法返回预定机场，需实施应急着陆方案；(1) When S nor_up < S 1 , the aircraft cannot return to the intended airport due to insufficient energy, and an emergency landing plan needs to be implemented; (2)当Snor_down≤S1≤Snor_up时，飞行器沿着HAC1返回；(2) When S nor_down ≤S 1 ≤S nor_up , the aircraft returns along HAC1; (3)当Snor_down≤S2≤Snor_up时，飞行器沿着HAC2返回；(3) When S nor_down ≤S 2 ≤S nor_up , the aircraft returns along HAC2; (4)当Snor_down≤S3≤Snor_up时，飞行器沿着HAC3返回；(4) When S nor_down ≤S 3 ≤S nor_up , the aircraft returns along HAC3; (5)当S3＜Snor_down时，此时飞行器初始能量过大，飞行器需S转弯，实时计算当前位置处飞行器沿HAC3返回时航程，直到当前能量与预测航程相匹配。(5) When S 3 <S nor_down , the initial energy of the aircraft is too large, the aircraft needs to turn S, and the flight range when the aircraft returns along HAC3 at the current position is calculated in real time until the current energy matches the predicted range.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117112964A (en) * 2023-08-14 2023-11-24 中国科学院力学研究所 Method, device and medium for estimating remaining range of unpowered return of high-speed aircraft
CN117112964B (en) * 2023-08-14 2024-05-03 中国科学院力学研究所 Method, device and medium for estimating unpowered return-to-field residual range of high-speed aircraft

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