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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dynamic pressure
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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

The invention discloses a three-dimensional track scheduling method based on cylinder position discretization. Compared with the traditional track scheduling method of the space shuttle in the tail end energy management section, the method determines three fixed calibration cylinders, and when the space shuttle reaches the tail end energy management window, the calibration cylinders are determined according to the initial energy to obtain the return track. The method inhibits the influence of the perturbation of the initial parameters on the track, realizes the accurate dissipation of energy, and enables the aircraft to stably enter the automatic landing window with expected energy. In addition, the method greatly reduces the calculation complexity and has high engineering practical value.

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. A three-dimensional track scheduling method based on cylinder position discretization is characterized by comprising 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 profile of the typical energy point in the step 1;
and step 3: constructing nominal flight intervals with different energies on the basis of the altitude-flight profile in the step 2;
and 4, step 4: designing a two-dimensional track generation method, and determining three calibration cylinder/cone parameters when the aircraft returns with maximum energy, nominal energy and minimum energy at a nominal release position based on the method and by combining 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 columns/cones in the course and position scattering space, and constructing an off-line track library according to the distances;
step 6: and comparing the flight interval under the current energy with the actual flight distances when returning along the three calibration columns/cones under the current position and the current course, and returning along the calibration columns/cones corresponding to the actual flight distances when the actual flight distances fall within the nominal interval to obtain the complete three-dimensional track scheduling method.
2. The three-dimensional trajectory scheduling method based on the cylinder position discretization according to claim 1, wherein the step 1 specifically comprises:
aircraft glide according to quasi-equilibrium conditions
Figure FDA0003092110000000011
The dynamic pressure of the aircraft and its rate of change of the dynamic pressure are calculated as follows:
Figure FDA0003092110000000012
in the formula
Figure FDA0003092110000000013
Is dynamic pressure, rhoaIs the atmospheric density, SrefIs wing area, g is gravitational acceleration, CL,CDRespectively representing lift coefficient and drag coefficient, m representing aircraft mass, gamma representing glide angle and H representing altitude;
in order to ensure that the aircraft meets the dynamic pressure constraint in the returning process, a first section 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 first section function is represented by the following formula:
Figure FDA0003092110000000014
in the formula
Figure FDA0003092110000000015
Represents the dynamic pressure of a given profile at this height node, ai,biFor the parameters to be designed, i is 0,1,2, 3; h isALIAnd hTEPRespectively representing the heights of the starting points of the automatic landing segment and the tail end energy management segment, hM1And hM2Respectively representing the upper limit and the lower limit of a height interval flying along a constant dynamic pressure section;
Figure FDA0003092110000000021
the dynamic pressure of the constant dynamic pressure section is represented;
designing a track design method based on a dynamic pressure profile: setting
Figure FDA0003092110000000022
Has an initial value of qTEPCorresponding to a dynamic pressure change rate of
Figure FDA0003092110000000023
Introduction of performance index J to iterate attack angle to obtainCalculating the current energy to obtain the current predicted voyage by the attack angle and the glide angle when the performance index is minimum, wherein
Figure FDA0003092110000000024
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；
When the certain predicted voyage is the middle value of the maximum voyage and the minimum voyage, the corresponding dynamic pressure profile is the optimal dynamic pressure profile;
and (3) adopting a second piecewise function combined by the primary curve and the cubic curve to fit the relation between the height and the predicted flight to construct an optimal height-flight profile, wherein the second piecewise function is shown as the following formula:
Figure FDA0003092110000000025
in the formula SsubRepresenting the flight of the aircraft into the subsonic phase, c0,…,c4Representing a parameter;
five typical discrete energy points E are selectedmax、Emid_max、Enor、Emid_minAnd EminThe energy states are respectively (H)nor+ΔH,Vnor+ΔV)、(Hnor-ΔH,Vnor+ΔV)、(Hnor,Vnor)、(Hnor+ΔH，Vnor- Δ V) and (H)nor-ΔH，Vnor- Δ V), wherein Hnor,VnorRepresenting an initial desired altitude and speed of the aircraft entering the terminal energy management section, Δ H, Δ V representing fluctuating values of the aircraft altitude and speed;
further, obtaining the height-voyage section of the hypersonic section under different energy states:
Figure FDA0003092110000000026
in the formula, amnFor the undetermined coefficients of the altitude-range profile, m is 1,2,3,4,5, n is 1,2,3,4, EmaxDenotes the maximum energy, Emid_maxRepresenting the energy at the lower boundary of altitude, the upper boundary of velocity, EnorDenotes the nominal energy, Emid_minEnergy, E, representing the upper boundary of altitude, the lower boundary of velocityminRepresenting the minimum energy.
3. The three-dimensional trajectory scheduling method based on cylindrical position discretization of claim 1, wherein step 2 is performed when the aircraft is in an arbitrary energy state E based on the typical energy points determined in step 10Upon entering the end energy management segment, according to E0And fitting the corresponding height-range profile by adopting a linear interpolation mode between different typical energy points.
4. The three-dimensional track scheduling method based on cylinder position discretization according to claim 1, wherein in step 4, the two-dimensional track voyage S is adoptedtotalAs shown in the following formula:
Stotal＝SPF+SHAC+SAC+SS
in the formula SPF，SHAC,SAC,SSRespectively representing the voyage 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 S turning is not needed, after the aircraft reaches a capture section window of the tail end energy management section, 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/cone, so that the course is finally aligned to the airport runway, and after the HAC section is finished, the aircraft enters the approach front flight section to further adjust the course; in conclusion, the adjustment of the course can be realized by adjusting the position of the course calibration cylinder/cone and the entrance radius;
the cylinder/cone position is iteratively calculated for the heading calibration by:
Figure FDA0003092110000000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003092110000000032
and
Figure FDA0003092110000000033
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 and StotalA difference of (d);
the iterative calculation is performed for the approach radius by:
Figure FDA0003092110000000034
in the formula (I), the compound is shown in the specification,
Figure FDA0003092110000000035
and
Figure FDA0003092110000000036
respectively the entrance radius of the (k + 1) th and k times of iteration, RfCalibrating the radius of the cylinder/cone for the flying course of the aircraft;
when the aircraft enters the field indirectly, the course calibration section adopts a spiral line, and the spiral rate R of the spiral line2The relationship with the approach radius is shown as follows:
Figure FDA0003092110000000037
in the formula, RHACIs the approach radius, psi is the angle that the aircraft flies through along the course calibration cylinder/cone, i.e. the helix; radius R of spiral line and radius R of arc turningρThe relationship is shown as follows:
R＝Rρsinλ
in the formula, lambda is the included angle between the vector radius and the arc direction,
Figure FDA0003092110000000038
omega represents the central angle corresponding to the current position of the aircraft; and is
Figure FDA0003092110000000039
V represents the velocity, phimaxRepresenting the maximum roll angle;
when the aircraft enters the end energy management section window in a specific energy state, according to the initial energy E0Forecast voyage S0(ii) a Then, assuming that the aircraft enters the field in an indirect approach mode, ensuring that the course calibration position is coincident with the position of the automatic landing window, and calculating S at the momenttotalIf S istotal＞S0The aircraft enters the field by selecting an indirect approach mode, or else, the aircraft enters the field by selecting a direct approach mode; adjusting the entrance radius, the tail end radius and the position of the course calibration cylinder/cone by continuous iteration to enable the S0＝StotalFinally, three calibration cylinder/cone parameters are obtained for the return at maximum energy, nominal energy, and minimum energy.
5. The method as claimed in claim 1, wherein the calibration of the cylinder/cone parameters with the three heading directions of maximum energy, minimum energy and nominal energy are represented by HAC1, HAC2 and HAC3 in step 6, and S is used to calibrate the cylinder/cone parameters1，S2，S3Respectively representing the actual flight distance of the aircraft when the aircraft returns along three course calibration columns/cones, and using Snor_down，Snor_upThe upper and lower boundaries of the flight interval at the current energy, respectively, along which course calibration cylinder/cone the aircraft returns, are determined according to the position of the nominal interval:
(1) when S isnor_up＜S1In time, the aircraft cannot return to a preset airport due to insufficient energy, and an emergency landing scheme needs to be 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_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.
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