CN109977543B - Three-dimensional profile coverage area calculation method, system and medium based on lateral priority - Google Patents
Three-dimensional profile coverage area calculation method, system and medium based on lateral priority Download PDFInfo
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Abstract
The invention discloses a three-dimensional section coverage area calculation method, a system and a medium based on lateral priority, wherein the method comprises the steps of establishing a large boundary and a small boundary of a lateral flight corridor; setting lateral lift-drag ratio symbols of an initial terminal and a terminal, converting the size boundary of a lateral flight corridor into a complete lateral feasible section boundary and generating a reference lateral section; solving a longitudinal flight corridor according to the reference lateral profile and generating a reference longitudinal profile; solving a reference trajectory according to a three-dimensional profile formed by a reference lateral profile and a reference longitudinal profile, designing a tracking controller to verify the feasibility of the reference trajectory and storing a trajectory drop point; and iteratively executing the steps of setting the initial and terminal lateral lift-drag ratio symbols to obtain a three-dimensional section coverage area formed by a trajectory drop point set. The method can solve the problem of determining the inherent maneuvering capability of the hypersonic gliding aircraft after the constraint of the attack angle section is removed, and release the potential of the aircraft to adapt to large maneuvering in a long distance and a wide area.
Description
Technical Field
The invention relates to the field of aircraft dynamics and guidance, in particular to a three-dimensional profile coverage area calculation method, a three-dimensional profile coverage area calculation system and a three-dimensional profile coverage area calculation medium based on lateral priority. The method can be widely applied to the maneuverability analysis and the coverage area calculation of aircrafts such as hypersonic aircrafts, manned airships and the like, provides support for trajectory planning and guidance, and has wide application prospect and value.
Background
The determination of the target coverage area of a gliding aircraft is a relatively difficult problem. Although the key to the solution of the coverage area is the calculation of the flight trajectory, in order to obtain the trajectory meeting the flight mission, a plurality of rigorous equality and inequality constraint conditions need to be met simultaneously, and the influence of factors such as fast time variation, strong coupling and strong nonlinearity needs to be considered. Meanwhile, the calculation of the coverage area of the target area needs to be both fast and accurate. The method of purely numerical integration by exhaustively integrating all the control quantities is therefore forced to be abandoned by the fact that the calculation is too time-consuming.
In view of this, it was first thought by the scholars to convert this into an optimal control problem to solve, for example, without changing the initial speed direction, solving for the maximum traverse at a series of given strokes to produce this coverage area. However, this method is too rough to consider the constraints of dynamic pressure, overload and heat flow, and the error is relatively large. Later, learners research a coverage area calculation method based on the tracking guidance of the resistance acceleration profile by utilizing the characteristic that the voyage is approximately inversely proportional to the resistance acceleration. Because the coverage area is obtained by tracking the feasible section in the corridor, the solving process naturally meets the constraint requirement; the method can obtain higher precision only by tracking a small number of feasible profiles, thereby effectively meeting the requirements of accuracy and calculation speed. However, this method only takes into account two-dimensional longitudinal movements and does not take into account the coupling effect of lateral movements, and is developed in particular on the basis of a predetermined optimization of the angle of attack profile. Once the angle of attack scheme is determined in advance, which is a key control parameter for determining maneuverability, the actual maneuverability of the aircraft is greatly limited, even if the angle of attack scheme can be finely adjusted in actual flight. Therefore, the calculation of the coverage area of the three-dimensional profile for researching the constraint relief of the attack angle profile is of great significance for ballistic planning, and particularly for some limit targets, the coverage is difficult to achieve by the traditional method and the calculation can be easily achieved by the three-dimensional profile method.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the invention provides a three-dimensional section coverage area calculation method, a system and a medium based on lateral priority aiming at the problem that a given scheme of an attack angle section restricts the gliding maneuverability of a hypersonic aircraft.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a three-dimensional section coverage area calculation method based on lateral priority comprises the following implementation steps:
1) Comprehensively considering five constraint conditions of heat flux density, dynamic pressure, overload, attack angle and roll angle, and determining the size boundary of a lateral flight corridor with the lateral lift-drag ratio and energy as references;
2) Setting lateral lift-drag ratio symbols of an initial terminal and a terminal, converting the size boundary of a lateral flight corridor into a complete lateral feasible section boundary and generating a reference lateral section;
3) Solving a longitudinal flight corridor according to the reference lateral profile and generating a reference longitudinal profile;
4) A three-dimensional section is formed according to the reference lateral section and the reference longitudinal section; solving a reference trajectory according to the obtained three-dimensional profile, designing a tracking controller to verify the feasibility of the reference trajectory and storing a trajectory drop point;
5) Judging whether the iteration times are smaller than a preset threshold value, and if the iteration times are smaller than the preset threshold value, skipping to execute the step 2) to perform the next iteration; otherwise, skipping to execute the step 6);
6) And obtaining a three-dimensional section coverage area formed by a ballistic drop point set.
Preferably, the detailed steps of step 1) include: determining lift-drag ratio L according to the altitude range of the aircraft shown in the formula (1-9) under the condition of comprehensively considering five constraint conditions of heat flux density, dynamic pressure, overload, attack angle and inclination angle D The combined vertical type (1-12) and the combined vertical type (1-13) solve the variation range of the lateral lift-drag ratio corresponding to the current attack angle, and then traverse all the attack angles to determine the size boundary of the lateral flight corridor;
in the formulae (1-9), (1-12) and (1-13), h feamin Denotes the minimum safety height, h feamax Denotes the maximum feasible height, h min Representing the current minimum feasible altitude of the aircraft, h max Represents the current maximum feasible altitude of the aircraft, [ h ] f ,h 0 ]A value interval of a given height; l represents lift acceleration, upsilon represents a roll angle, E represents the energy of the aircraft at the current moment, mu represents an earth gravity constant, and r represents the distance from the earth center to the mass center of the aircraft; l is a radical of an alcohol z Denotes the lateral lift-to-drag ratio, L D The lift-to-drag ratio is shown.
Preferably, when the signs of the initial and terminal lateral lift-drag ratios are set in step 2), the initial and terminal lateral lift-drag ratios have four combinations of initial positive and terminal positive, initial positive and terminal negative, initial negative and terminal negative, and initial negative and terminal positive, and each iteration selects one combination, which includes 4 iterations.
Preferably, the functional expression for generating the reference lateral profile in the step 2) is shown in the formula (2-2);
L z (e)＝ω z L zup (e)+(1-ω z )L zdn (e) (2-2)
in the formula (2-2), L z (e) Lateral lift-to-drag ratio profile, ω, representing normalized energy z ∈[0,1]Representing the weight coefficient, e the normalized energy, L zup (e) Upper boundary, L, of lateral corridor representing normalized energy zdn (e) Representing the lower boundary of the lateral corridor of normalized energy.
Preferably, the detailed step of step 3) solving the longitudinal flight corridor from the reference lateral profile and generating the reference longitudinal profile comprises:
3.1 Solving maximum and minimum feasible longitudinal drag acceleration boundaries from the reference lateral profile;
3.2 On the basis of obtaining the maximum and minimum feasible longitudinal resistance acceleration boundaries, an initial longitudinal section D (e) can be obtained by interpolation by using the resistance acceleration range determined by the formula (3-1) as a reference longitudinal section;
D(e)＝ω D D fbmax +(1-ω D )D fbmin (3-1)
in the formula (3-1), ω is D Weight coefficient representing longitudinal drag acceleration profile, D fbmax And D fbmin Representing the maximum and minimum feasible longitudinal drag acceleration boundaries, respectively.
Preferably, the functional expression for solving the maximum and minimum feasible longitudinal resistance acceleration boundaries in step 3.1) is as shown in formula (3-2);
in the formula (3-2), D fbmax And D fbmin Denotes the maximum and minimum feasible longitudinal drag acceleration boundaries, respectively, V denotes the aircraft speed, h denotes the current altitude of the aircraft, g denotes the gravitational acceleration, r denotes the distance of the geocenter from the aircraft center of mass, L D Representing lift-to-drag ratio, υ representing roll angle, L representing lift acceleration, e being normalized energy, L z (e) Represents the lateral lift-to-drag ratio profile of the normalized energy.
Preferably, the function expression for solving the reference trajectory according to the obtained three-dimensional profile in the step 4) is shown in formulas (4-1) - (4-3);
in the expressions (4-1) to (4-3), σ represents the velocity azimuth, E represents the energy, φ represents the geocentric latitude, r represents the geocentric distance, D represents the resistive acceleration, V represents the aircraft velocity, L represents the aircraft velocity, and z denotes the lateral lift-drag ratio, ω e Representing the rotational angular velocity of the earth and lambda represents longitude.
The invention also provides a three-dimensional profile coverage area calculation system based on lateral precedence, comprising a computer device programmed to execute the steps of the aforementioned three-dimensional profile coverage area calculation method based on lateral precedence of the invention,
the invention also provides a three-dimensional profile coverage area calculation system based on lateral priority, which comprises a computer device, wherein a storage medium of the computer device is stored with a computer program which is programmed to execute the three-dimensional profile coverage area calculation method based on lateral priority.
The present invention also provides a computer readable storage medium having stored thereon a computer program programmed to execute the aforementioned three-dimensional profile coverage area calculation method based on lateral precedence of the present invention.
Compared with the prior art, the invention has the following advantages: aiming at the covering problem of a glider maneuvering target of a hypersonic aircraft, the invention comprehensively considers the reachable and lateral maneuvering task requirements of the aircraft target on the basis of a three-dimensional profile, combines a plurality of constraint conditions, traverses all feasible flight profiles in a three-dimensional flight corridor according to the sequence of designing the lateral profile and then solving the longitudinal profile, and solves the three-dimensional profile track falling points of four different initial and terminal strategies to complete the calculation of a covering area, thereby solving the constraint problem of the given scheme of an attack angle profile on the glider maneuvering capability of the hypersonic aircraft, further ensuring the integrity of dynamics information, releasing the inherent maneuvering capability of the aircraft to adapt to long-distance wide-area large maneuvering, and providing effective technical support for a trajectory planning and guidance method of the glider.
Drawings
FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.
Fig. 2 is a flowchart illustrating coverage area solution according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a lateral corridor according to an embodiment of the present invention.
Fig. 4 is a simulation result of a lateral feasible profile according to an embodiment of the present invention.
Fig. 5 shows a longitudinal corridor corresponding to a lateral profile according to an embodiment of the present invention.
FIG. 6 shows the results of the resistive acceleration tracking according to an embodiment of the present invention.
FIG. 7 shows the result of course angle tracking according to an embodiment of the present invention.
Fig. 8 is all possible lateral profiles of the initial positive-terminal negative case of an embodiment of the invention.
Fig. 9 is all possible lateral profiles for the initial positive terminal negative case of an embodiment of the present invention.
FIG. 10 is an initial positive-terminal negative corresponding resistive acceleration profile of an embodiment of the present invention.
Fig. 11 is a ground trace corresponding to the initial positive terminal negative of an embodiment of the invention.
FIG. 12 is a diagram illustrating a falling point outermost boundary for the positive counterpart of the initial negative terminal according to an embodiment of the present invention.
FIG. 13 is a diagram illustrating a negative-to-negative landing outermost boundary of an initial negative terminal, in accordance with an embodiment of the present invention.
Fig. 14 is a coverage area boundary corresponding to a three-dimensional profile in an embodiment of the present invention, where an inner dotted line is a drop point set boundary obtained by a conventional two-dimensional method, and a thick solid line is a drop point set outer boundary obtained by using a longitudinal resistance acceleration profile priority policy.
Fig. 15 is a cross-section of a reference angle of attack corresponding to the coverage area of the conventional method of fig. 14.
Detailed Description
As shown in fig. 1 and fig. 2, the implementation steps of the three-dimensional cross-sectional coverage area calculation method based on lateral priority in this embodiment include:
1) Comprehensively considering five constraint conditions of heat flux density, dynamic pressure, overload, attack angle and roll angle, and determining the size boundary of a lateral flight corridor based on the lateral lift-drag ratio and energy, as shown in fig. 3;
2) Setting lateral lift-drag ratio symbols of an initial terminal and a terminal, converting the size boundary of a lateral flight corridor into a complete lateral feasible section boundary and generating a reference lateral section; in the embodiment, a hypersonic glide vehicle conceptual model CAV-H designed by Lockheed-Martin corporation in 1999 is adopted as an object to carry out a simulation experiment. In this embodiment, the stagnation heat flux density, dynamic pressure and overload constraint are
q max ＝200kpa，n max =3g, the amplitude constraints of angle of attack and roll angle are respectively alpha epsilon [10 DEG, 20 DEG ]]，σ∈[-80°,80°]The resulting lateral feasible corridor and initial lateral profile is shown in fig. 4.
3) Solving a longitudinal flight corridor according to the reference lateral profile and generating a reference longitudinal profile; fig. 5 is a longitudinal resistive acceleration corridor corresponding to fig. 4.
4) A three-dimensional section is formed according to the reference lateral section and the reference longitudinal section; solving a reference trajectory according to the obtained three-dimensional profile, designing a tracking controller to verify the feasibility of the reference trajectory and storing a trajectory drop point;
5) Judging whether the iteration times are smaller than a preset threshold value, and if the iteration times are smaller than the preset threshold value, skipping to execute the step 2) to perform the next iteration; otherwise, skipping to execute the step 6);
6) And obtaining a three-dimensional section coverage area formed by a ballistic drop point set.
In the embodiment, the constraint and limitation of complex processes such as heat flux density, overload, dynamic pressure and the like on the gliding reentry aircraft in the flight process are shown as a formula (1-1);
in the formula (1-1), the compound,
q max and n max Respectively maximum heat flowDensity, maximum dynamic pressure and maximum overload, k h Is a constant coefficient, ρ is the atmospheric density, g 0 The sea level gravity acceleration, V the aircraft speed, D the aerodynamic drag acceleration and L the aerodynamic lift acceleration. Wherein, the calculation formula of the aerodynamic resistance acceleration D and the aerodynamic lift acceleration L is shown as the formula (1-2);
in the formula (1-2), C D And C L Respectively representing the aerodynamic drag and lift coefficients,
indicating dynamic head, S ref For the characteristic area, M is the aircraft mass. f. of D (α, V, h) represents a drag acceleration function, f L (α, V, h) represents the lift acceleration function.
The resistance acceleration D (E) with the energy E as an independent variable can be expressed as shown in the formula (1-3);
formula (1-3)
q max And n max Maximum heat flux density, maximum dynamic pressure, maximum overload, and resistance acceleration coefficient C D And lift-to-drag ratio L D Is a function of the angle of attack alpha and the Mach number Ma, S r M is the aircraft mass, M is a constant, with a value of 3.15 h Is a constant coefficient, V is the aircraft speed, g 0 Is sea level gravitational acceleration. When designing the flight trajectory of the glide flight, the aircraft is expected to be in the initial h 0 And terminal h f The quasi-balanced gliding flight is realized, and meanwhile, the stagnation heat flux density, the peak dynamic pressure, the maximum overload and the like in the flight process are limited not to exceed given constraint values. Thus, for each energy point,the minimum altitude that the aircraft is allowed to reach should ensure that the drag acceleration does not exceed a given constraint boundary.
in the formula (1-4), D max To represent
D q (E)、D n (E) The minimum value of the three.
The angle of attack α, angle of inclination θ constraints can be expressed as (1-5):
in the formula (1-5), α min ,α max Respectively a lower limit value and an upper limit value, upsilon, of the angle of attack alpha min ,υ max Respectively, a lower limit value and an upper limit value of the inclination angle v.
Different angles of attack correspond to different maximum resisting accelerations D for a given energy max And lift-to-drag ratio L D The formula (1-6) is assumed according to equilibrium glide:
in the formula (1-6), g is gravity acceleration, V is aircraft speed, r is geocentric distance, L is aerodynamic lift acceleration, theta is a speed inclination angle, and upsilon is an aircraft inclination angle. Since the glide slope velocity tilt angle is generally kept around 0, cos θ =1 is usually taken.
The formula is defined by the resistance acceleration, and is shown as the formula (1-7):
f D (α,V,h min )≤D max (1-7)
in the formula (1-7), f D (α,V,h min ) Representing the drag acceleration function, alpha representing the current angle of attack, V representing the aircraft speed, h min Representing the current minimum feasible altitude of the aircraft. Meanwhile, the upper boundary of the altitude is the altitude value of the aircraft for keeping quasi-balanced gliding flight, namely the altitude value has the formula (1-8):
in the formula (1-8), f L (α, V, h) represents a lift acceleration function, V represents aircraft velocity, h represents aircraft current altitude, g represents gravitational acceleration, and r represents the distance from the geocenter to the aircraft centroid. In solving for the maximum and minimum allowable heights, the angle of attack must be constrained within a given constraint.
At the same time, the height value is kept at the given [ h ] f ,h 0 ]I.e. of the formula (1-9):
in the formula (1-9), h feamin Denotes the minimum safety height, h feamax Denotes the maximum feasible height, h min Represents the current minimum feasible altitude of the aircraft, h max Represents the current maximum feasible altitude of the aircraft, [ h ] f ,h 0 ]The value interval of the given height. The definition of the binding energy allows the conditioning of quasi-equilibrium glide to be of the formula (1-10):
in the formula (1-10), L represents the lift acceleration, upsilon represents the inclination angle, and E represents the current state of the aircraftThe time of day energy, μ represents the earth's gravitational constant, and r represents the distance from the geocenter to the aircraft centroid. The value of the longitudinal lift acceleration Lcos v is determined by the quasi-equilibrium glide conditions: lcos upsilon = g-V 2 Where V represents the aircraft speed, h represents the current altitude of the aircraft, g represents gravitational acceleration, and r represents the distance from the Earth's center to the center of mass of the aircraft.
By definition, it can be established that:
in the formula, L z Is the lateral lift-to-drag ratio, L u = Lcos upsilon/D longitudinal lift-drag ratio, upsilon tilt angle, L lift acceleration D The lift-to-drag ratio is shown. Analysis shows that Lcos upsilon monotonically increases with height for each energy E. Again, defined by the lift acceleration, L monotonically decreases with height when given energy and angle of attack. Therefore, the right end of the expression (1-10) monotonically increases with the height. Thus, there are formulae (1-12):
in the formula (1-12), L represents lift acceleration, upsilon represents inclination angle, E represents energy of the aircraft at the current moment, mu represents an earth gravity constant, and r represents the distance from the earth center to the center of mass of the aircraft.
The function cos upsilon increases monotonically with height, so that in the definition domain of the roll angle [ - π/2, π/2]And the maximum value of the amplitude of the roll angle is obtained at the minimum safe height, and whether the minimum roll angle 0 can be obtained depends on the difference between the feasible height and the difference between the gravitational acceleration and the centrifugal acceleration and whether the lift acceleration can be just equal to the difference between the gravitational acceleration and the centrifugal acceleration in the value interval of the attack angle. Let L z The lateral lift-drag ratio is indicated. Thus, there are formulae (1-13):
in the formula (1-13), L z Denotes the lateral lift-to-drag ratio, L D Denotes the lift-to-drag ratio and υ denotes the roll angle.
Therefore, when the attack angle is given, the change range of the lift-drag ratio can be determined by the height range determined by the combination formula (1-9), and then the change range of the lateral lift-drag ratio corresponding to the current attack angle can be obtained by the joint type (1-12) and the joint type (1-13). Finally, all angles of attack are traversed, so that the size boundaries of the lateral flight corridor can be determined.
In this embodiment, the detailed steps of step 1) include: determining lift-drag ratio L according to the altitude range of the aircraft shown in the formula (1-9) under the condition of comprehensively considering five constraint conditions of heat flux density, dynamic pressure, overload, attack angle and inclination angle D The combined vertical type (1-12) and the combined vertical type (1-13) solve the variation range of the lateral lift-drag ratio corresponding to the current attack angle, and then traverse all the attack angles to determine the size boundary of the lateral flight corridor;
in this embodiment, when the signs of the initial and terminal lateral lift-drag ratios are set in step 2), the initial and terminal lateral lift-drag ratios share four combinations, namely, an initial positive combination and a terminal positive combination, an initial positive combination and a terminal negative combination, an initial negative combination and a terminal negative combination, and an initial negative combination and a terminal positive combination, and each iteration selects one combination, and the total includes 4 iterations. As shown in FIG. 1, in this embodiment, let i init Each of 1,2,3, and 4 represents a different combination, and i is initially set to init And =1. And according to the set initial terminal symbol, combining the established size boundary of the lateral flight corridor to establish a complete lateral feasible section boundary. Considering the roll reversal, the complete lateral feasible section boundary should consist of both positive and negative sections.
In order to make the transition from the lateral upper boundary to the lower boundary natural, corresponding transition section boundaries are respectively designed according to the difference of initial and terminal lateral lift-drag ratio signs. With positive initial side lift-drag ratio L z0 Negative terminal lateral lift-drag ratio L zf For example, the complete lateral feasible profile boundary can be represented by the piecewise function of equation (2-1);
in the formula (2-1), L zup And L zdn Respectively representing the upper and lower boundaries of the lateral corridor, e brk1 And e brk2 All represent transition points on the lateral boundary, e represents normalized energy, e 0 And e f Respectively representing normalized initial and terminal energies, a zi ,b zi ,c zi (i =1, 2) respectively represent the quadratic coefficients of transition piece junctions, L zmax Represents the lateral lift-drag ratio L z The absolute value of the maximum value of (a). Therefore, the corrected lateral feasible boundary is not limited to the restriction on the size of the lateral lift-drag ratio any more, and the value range of the roll reversal point is also limited. For the same reason, L is changed respectively z0 And L zf The modified lateral feasible boundary can be found in the other three cases.
According to the established lateral corridor boundary, an initial lateral lift-drag ratio profile with general significance can be generated through profile interpolation, and a function expression of the reference lateral profile generated in the step 2) of the embodiment is shown as a formula (2-2);
L z (e)＝ω z L zup (e)+(1-ω z )L zdn (e) (2-2)
in the formula (2-2), L z (e) Lateral lift-to-drag ratio profile, ω, representing normalized energy z ∈[0,1]Representing the weight coefficient, e representing the normalized energy, L zup (e) Upper boundary, L, of lateral corridor representing normalized energy zdn (e) Representing the lower boundary of the lateral corridor of normalized energy.
In this embodiment, the detailed step of step 3) solving the longitudinal flight corridor and generating the reference longitudinal profile according to the reference lateral profile includes:
3.1 Solving maximum and minimum feasible longitudinal drag acceleration boundaries from the reference lateral profile;
3.2 On the basis of obtaining the maximum and minimum feasible longitudinal resistance acceleration boundaries, an initial longitudinal profile D (e) can be obtained by interpolation by using the resistance acceleration range determined by the formula (3-1) and used as a reference longitudinal profile;
D(e)＝ω D D fbmax +(1-ω D )D fbmin (3-1)
in the formula (3-1), ω is D Weight coefficient representing longitudinal drag acceleration profile, D fbmax And D fbmin Representing the maximum and minimum feasible longitudinal drag acceleration boundaries, respectively.
In the embodiment, the function expression for solving the maximum and minimum feasible longitudinal resistance acceleration boundaries in the step 3.1) is shown as the formula (3-2);
in the formula (3-2), D fbmax And D fbmin Representing maximum and minimum feasible longitudinal drag acceleration boundaries, respectively, V representing aircraft speed, h representing aircraft current altitude, g representing gravitational acceleration, r representing the distance from the geocenter to the aircraft centroid, L D Representing lift-to-drag ratio, υ representing roll angle, L representing lift acceleration, e being normalized energy, L z (e) Represents the lateral lift-drag ratio profile of the normalized energy. According to the previous analysis, the main factors influencing the formula (3-2) are the change intervals of the attack angle and the height. The process constraint is required to be met in the height calculation process, so that the resistance acceleration solved at the moment naturally meets the process constraint requirement. Therefore, in combination with the formula (2-1), the formula (2-2) and the formula (3-2), any one of the lateral section weight coefficients ω is given z A corresponding family of feasible three-dimensional profiles can be generated.
Step 3) according to the obtained initial lateral profile, establishing a coupling relation between the longitudinal resistance acceleration and the lateral profile as shown in a formula (3-3);
in the formula (3-3), D fb Representing longitudinal drag acceleration, L representing lift acceleration, upsilon representing roll angle, D representing drag acceleration, V representing aircraft speed, g representing gravitational acceleration, r representing the distance from the earth's center to the aircraft's center of mass, L representing gravitational acceleration, and D denotes the lift-to-drag ratio, L z (e) Express normalizationLateral lift-to-drag ratio profile of energy. Meanwhile, the magnitude of the resistance acceleration also satisfies the definition formula (1-2). Therefore, the formula (3-3) only has one free variable attack angle, and the variation range of the resistance acceleration can be obtained by traversing all feasible attack angles. The maximum and minimum resistance accelerations obtained by the expression (3-3) are respectively shown in the expression (3-2).
Obviously, the maximum resistant acceleration D feamax The formula (3-4) must be satisfied;
D feamax ≤D max (3-4)
in the formula (3-4), D max To represent
D q (E)、D n (E) The minimum value of the three is shown as formula (1-4). Let omega D And (3) representing the weight coefficient of the longitudinal resistance acceleration profile, and interpolating the resistance acceleration range determined by the formula (3-3) to obtain an initial longitudinal profile D (e) as shown in the formula (3-2).
In this embodiment, the functional expression for solving the reference trajectory according to the obtained three-dimensional profile in step 4) is shown in formulas (4-1) to (4-3);
in the expressions (4-1) to (4-3), σ represents the velocity azimuth, E represents energy, φ represents the geocentric latitude, r represents the geocentric distance, D represents the resistive acceleration, V represents the aircraft velocity, L z Denotes the lateral lift-to-drag ratio, ω e Representing the rotational angular velocity of the earth and lambda represents longitude. In order to quickly obtain the designed three-dimensional profile, namely the reference trajectory corresponding to the longitudinal and lateral sub-profiles, energy-based energy is introducedSolving a lateral reduced order equation of motion of the quantity, wherein the equation is shown in formulas (4-1) to (4-3); since only the lateral ballistic state corresponding to the three-dimensional section needs to be solved quickly, the height can be linearly assumed, and equations (4-1) - (4-3) are solved through quick integration. Substituting the designed three-dimensional section into an equation system, and integrating to obtain the terminal energy E after giving an initial value f Corresponding lateral motion state. It should be noted that the linear height used in solving the lateral reduced order equation of motion is not a true reference height value, but is merely a hypothetical value that is made to facilitate fast calculations. The actual reference height can be obtained only after the reference control quantity is calculated according to the three-dimensional profile.
In the process of solving the reference control quantity corresponding to the three-dimensional profile, a second derivative related to energy is further solved for the standard resistance acceleration profile, as shown in a formula (4-4);
L D cosυ＝a(D″-b) (4-4)
in the formula (4-4), L D Expressing lift-drag ratio, upsilon is an inclination angle, D' is a second derivative of resistance acceleration to energy, and the calculation formula of parameters a and b is shown as formula (4-5);
in the formula (4-5), h s Representing generalized altitude, V is aircraft speed, D is drag acceleration, C D ,C′ D ,C″ D The drag coefficient and its first and second derivatives with respect to energy, respectively, h represents the current altitude of the aircraft, g represents the gravitational acceleration, and r represents the distance of the geocenter from the aircraft's center of mass. Therefore, the planned total lift-drag ratio can be obtained by combining the standard lateral profile as shown in the formula (4-6);
in the formula (4-6), a and b are parameters obtained by the formula (4-5), D 'represents the second derivative of the resistance acceleration to the energy, and L' represents z Is the lateral lift-drag ratio.Also, the first and second derivatives of the resistance coefficient need not be taken into account when determining the reference value. The reference attack angle alpha can be obtained by inverse interpolation by using the resistance coefficient table about the attack angle, the Mach number and the like given by the aircraft r 。
For computational convenience, the aerodynamic coefficients of an aircraft are typically fitted directly to a binary functional form with respect to angle of attack and mach number. Note the book
Representing the fitted aerodynamic coefficient function, then the reference angle of attack alpha r As shown in formula (4-7);
in the formula (4-7), ma represents Mach number, and α represents angle of attack.
At the same time, for a reference inclination angle v r It can be directly obtained by the following formula (4-8):
in the formula (4-8), L z For the lateral lift-drag ratio, a and b are parameters obtained by the formula (4-5), and D' represents the second derivative of the resistance acceleration to the energy. When the reference attack angle alpha is obtained by solving according to the formula (4-7) r The actual reference height and velocity can then be determined inversely using the definition of resistive acceleration. Defined by the resistive acceleration, the resistance coefficient can be solved inversely. Since the height and the speed are energy-dependent, the reference height h can be determined simultaneously in combination with the energy definition r And velocity V r 。
Solving to obtain a reference attack angle alpha r The actual reference height and velocity can then be determined inversely using the definition of resistive acceleration. The resistance coefficient can be reversely solved by the definition of the resistance acceleration as shown in the formula (4-9);
in the formula (4-9), m represents the mass of the aircraft, D r Representing the reference drag acceleration, ρ representing the atmospheric density, V representing the aircraft velocity, and S representing the aircraft reference area.
In order to verify the feasibility and the accuracy of generating the trajectory based on the three-dimensional profile, a guidance law needs to be designed to perform simulation verification on the reference trajectory. On one hand, the resistance acceleration implies the motion information such as longitudinal height, speed and the like, and is directly related to the total voyage; on the other hand, the course angle movement amount obtained by dividing the three-dimensional sectional area into a lateral reduced order motion equation set well expresses the lateral movement characteristic of the trajectory. Therefore, two control law tracking resistive acceleration profiles and a resolved heading angle profile are designed. Referring to a drag acceleration profile tracking scheme of a space shuttle, a second-order PD controller is designed to track drag acceleration, and the functional expression of the second-order PD controller is shown as a formula (4-10);
(D″-D″ r )+2ξω(D′-D′ r )+ω 2 (D-D r )＝0 (4-10)
in the formula (4-10), D 'and D' r Representing the second derivative of actual and reference resistive accelerations to energy, and representing the second derivative of reference resistive acceleration to energy, D ' and D ', respectively ' r Representing the first derivatives of actual and reference resistive accelerations with respect to energy, D and D, respectively r Representing actual and reference resistive accelerations, ξ, ω, respectively, the damping coefficient and the frequency.
Combining with kinetic equation to obtain required longitudinal lift-drag ratio L D cos upsilon is represented by the formula (4-11);
L D cosυ＝a[D″ r -2ξω(D′-D′ r )-ω 2 (D-D r )-b] (4-11)
in the formula (4-11), a and b are parameters obtained by the formula (4-5), D ″ r Representing the second derivative of the reference drag acceleration to energy, D 'and D' r Representing the first derivatives of actual and reference resistive accelerations with respect to energy, D and D, respectively r Representing actual and reference resistive accelerations, ξ, ω, respectivelyDamping coefficient and frequency, respectively.
For the course angle, the first derivative of the course angle with respect to energy is known from the kinetic equation to contain the controlled quantity. Therefore, only one first-order PD controller is designed as shown in the formula (4-12);
(σ′-σ′ r )+k σ (σ-σ r )＝0 (4-12)
in formula (4-12), σ 'and σ' r Representing the first derivatives of the actual and reference course angles with respect to energy, σ and σ, respectively r Representing actual and reference course angles, k, respectively σ To adjust the coefficients. Substituting the formula (4-1) to obtain the lateral lift-drag ratio L z As shown in formulas (4-13);
in formula (4-13), σ 'and σ' r Representing the first derivatives of the actual and reference course angles with respect to energy, σ and σ, respectively r Respectively representing actual and reference course angles, k σ For the adjustment coefficient, r represents the geocentric distance, phi represents the geocentric latitude, sigma is the heading angle, D is the resistive acceleration, and V is the aircraft speed.
Referring to FIG. 2, in step 4) of this embodiment, let ω be d And (4) gradually changing from 0 to 1, obtaining a corresponding longitudinal resistance acceleration profile, combining the lateral profile in the step 2), continuously solving a corresponding ballistic drop point, and storing and recording.
Referring to fig. 2, in step 4) of this embodiment, let ω be z And gradually changing from 0 to 1, obtaining a corresponding longitudinal lateral section, then continuously solving a corresponding ballistic drop point, and storing records.
Referring to fig. 2, in step 6) of this embodiment, let i be according to the initial terminal numbering rule init Increment from 1 to 4 and then go to 2) continue to iteratively solve for the corresponding ballistic drop point.
At the moment, the reference motion state and the control quantity based on the three-dimensional profile are completely solved, and a method for performing simulation verification on the trajectory of the planned three-dimensional profile is provided, namely, a reference bullet based on the three-dimensional profile is obtainedAnd (4) carrying out the following steps. The coverage area is actually the set of all flight trajectory landing points. Therefore, solving the coverage area calculation problem of the aircraft which meets all the setting processes, controls and terminal constraints based on the current state is converted into solving all the sets of the trajectory drop points which meet the requirements of the flight mission. The corresponding lateral and longitudinal profiles under different combinations of the initial and terminal are different in feasible boundary, so that the calculated drop point distribution of the three-dimensional profile trajectory has respective emphasis. Therefore, in order to obtain a coverage area based on a three-dimensional profile, it is necessary to rapidly solve the change of the weight coefficient ω from 0 to 1 for different combinations in turn z All feasible three-dimensional profile ballistic drop points are generated. Since the analytic solution of the set of all the drop points is too complex, the present embodiment solves all the feasible ballistic drop points under the four combinations by numerical integration to generate a three-dimensional profile coverage area.
In order to test the feasibility and the effectiveness of the drop point of the trajectory generated based on the three-dimensional profile, a reference profile datum in the lateral corridor is selected at will, and a simulation experiment is carried out by tracking all the trajectories of the longitudinal resistance acceleration profiles corresponding to the reference profile datum. The calculation example sets the longitude and latitude (0 degree ) of the glide starting point, the initial direction is the east direction, the initial height is 50.73km, the initial speed is 6380m/s, the shift height is required to be 30km, and the shift speed is 2500m/s.
Fig. 6, 7, and 8 are the tracking and planning comparison results of the resistance acceleration profile, the course angle curve, and the ground track curve, respectively, for the purpose of performing feasibility verification on the proposed three-dimensional profile trajectory.
Fig. 9, 10, 11 are the initial positive and negative terminal lateral profile, the drag acceleration profile, and the ground track planning results, respectively, which aim to give the trajectory and the drop point in the case of the initial positive and negative terminal.
Fig. 12, fig. 13, and fig. 14 are respectively a trajectory outer falling point boundary of the initial negative terminal positive and the initial negative terminal negative, and a coverage area boundary obtained by combining all cases, and meanwhile, a coverage area boundary and a longitudinally preferential falling point set boundary of the conventional two-dimensional method are also given in the coverage area boundary of fig. 14, and fig. 15 is a reference cross section for obtaining a coverage area of the conventional two-dimensional method. It can be seen clearly from the comparison that the coverage of the glider maneuvering target obtained by the three-dimensional profile method after the attack angle profile constraint is removed is effectively released compared with the traditional method. Compared with a longitudinal priority strategy, the accuracy of a lateral priority strategy in solving a three-dimensional section coverage area is further highlighted.
In summary, in the three-dimensional section coverage area calculation method based on lateral priority in the embodiment, reference attack angles and inclination angles do not need to be optimally designed in advance, all feasible trajectory drop points are obtained through sequential traversal simulation by establishing a lateral flight corridor and using a method for solving a longitudinal feasible section by using a coupling relation, and therefore the coverage area based on the three-dimensional section is finally obtained. Because the constraint conditions such as heat flux density, dynamic pressure, overload and the like are taken into consideration in the corridor establishing process, the obtained trajectory does not exceed the set constraint value, and the feasibility of the trajectory is verified through a tracking algorithm. The longitudinal and lateral movement coupling is comprehensively considered in the design process, the maneuvering capability of the hypersonic aerocraft is fully exerted, and theoretically, the maneuvering coverage area of the glider of the hypersonic aerocraft is effectively enlarged compared with that of a traditional two-dimensional method. According to the three-dimensional section coverage area calculation method based on lateral priority, the strategy of lateral section priority design is adopted, the longitudinal and lateral task requirements of the aircraft are comprehensively considered, the maneuvering capacity boundary of the gliding aircraft is approached through combination of multiple groups of sections, so that the required target coverage area of the gliding terminal is obtained, and effective technical support is provided for the trajectory planning and guidance method of the gliding aircraft.
In addition, the present embodiment further provides a three-dimensional cross-sectional coverage area calculation system based on lateral priority, which includes a computer device programmed to execute the steps of the three-dimensional cross-sectional coverage area calculation method based on lateral priority of the present embodiment, or a storage medium of the computer device having a computer program stored thereon programmed to execute the three-dimensional cross-sectional coverage area calculation method based on lateral priority of the present embodiment. In addition, the present embodiment also provides a computer readable storage medium, which stores a computer program programmed to execute the foregoing three-dimensional cross-sectional coverage area calculation method based on lateral precedence according to the present embodiment.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to those skilled in the art without departing from the principles of the present invention should also be considered as within the scope of the present invention.
Claims (10)
1. A three-dimensional section coverage area calculation method based on lateral priority is characterized by comprising the following implementation steps:
1) Comprehensively considering five constraint conditions of heat flux density, dynamic pressure, overload, attack angle and roll angle, and determining the size boundary of a lateral flight corridor with the lateral lift-drag ratio and energy as references;
2) Setting initial and terminal lateral lift-drag ratio symbols, converting the size boundary of a lateral flight corridor into a complete lateral feasible profile boundary and generating a reference lateral profile;
3) Solving a longitudinal flight corridor according to the reference lateral profile and generating a reference longitudinal profile;
4) A three-dimensional section is formed according to the reference lateral section and the reference longitudinal section; solving a reference trajectory according to the obtained three-dimensional profile, designing a tracking controller to verify the feasibility of the reference trajectory and storing a trajectory drop point;
5) Judging whether the iteration times are smaller than a preset threshold value, and if the iteration times are smaller than the preset threshold value, skipping to execute the step 2) to perform the next iteration; otherwise, skipping to execute the step 6);
6) And obtaining a three-dimensional section coverage area formed by a ballistic drop point set.
2. The three-dimensional cross-sectional coverage area calculation method based on lateral priority as claimed in claim 1, wherein the detailed steps of step 1) comprise: under the condition of comprehensively considering five constraint conditions of heat flux density, dynamic pressure, overload, attack angle and inclination angle according to formula(1-9) determining the lift-to-drag ratio L for the range of aircraft altitudes D The combined vertical type (1-12) and the combined vertical type (1-13) solve the variation range of the lateral lift-drag ratio corresponding to the current attack angle, and then traverse all the attack angles to determine the size boundary of the lateral flight corridor;
in the formulae (1-9), (1-12) and (1-13), h feamin Denotes the minimum safety height, h feamax Denotes the maximum feasible height, h min Representing the current minimum feasible altitude of the aircraft, h max Represents the current maximum feasible altitude of the aircraft, [ h ] f ,h 0 ]A value interval of a given height; l represents lift acceleration, upsilon represents a roll angle, E represents the energy of the aircraft at the current moment, mu represents an earth gravity constant, and r represents the distance from the earth center to the mass center of the aircraft; l is z Denotes the lateral lift-to-drag ratio, L D The lift-to-drag ratio is shown.
3. The method for calculating a three-dimensional profile coverage area based on lateral precedence according to claim 1, wherein when signs of initial and terminal lateral lift-drag ratios are set in step 2), the initial and terminal lateral lift-drag ratios share four combinations of initial positive and terminal positive, initial positive and terminal negative, initial negative and terminal negative, and initial negative and terminal positive, and each iteration selects one combination, which includes a total of 4 iterations.
4. The method for calculating the coverage area of the three-dimensional profile based on the lateral priority as claimed in claim 1, wherein the functional expression of the reference lateral profile generated in step 2) is as shown in formula (2-2);
L z (e)＝ω z L zup (e)+(1-ω z )L zdn (e) (2-2)
in the formula (2-2), L z (e) Lateral lift-drag ratio profile, ω, representing normalized energy z ∈[0,1]Representing the weight coefficient, e the normalized energy, L zup (e) Upper boundary, L, of lateral corridor representing normalized energy zdn (e) Representing the lower boundary of the lateral corridor of normalized energy.
5. The method of claim 1 wherein the step 3) of solving longitudinal flight corridors from the reference lateral profile and generating a reference longitudinal profile comprises the detailed steps of:
3.1 Solving maximum and minimum feasible longitudinal drag acceleration boundaries from the reference lateral profile;
3.2 On the basis of obtaining the maximum and minimum feasible longitudinal resistance acceleration boundaries, an initial longitudinal profile D (e) can be obtained by interpolation by using the resistance acceleration range determined by the formula (3-1) and used as a reference longitudinal profile;
D(e)＝ω D D fbmax +(1-ω D )D fbmin (3-1)
in the formula (3-1), ω is D Weight coefficient representing longitudinal drag acceleration profile, D fbmax And D fbmin Representing the maximum and minimum feasible longitudinal drag acceleration boundaries, respectively.
6. The method for calculating the coverage area of the three-dimensional profile based on the lateral priority as claimed in claim 5, wherein the functional expression for solving the maximum and minimum feasible longitudinal resistance acceleration boundaries in the step 3.1) is shown as the formula (3-2);
in the formula (3-2), D fbmax And D fbmin Representing maximum and minimum feasible longitudinal drag acceleration boundaries, respectively, V representing aircraft speed, h representing aircraft current altitude, g representing gravitational acceleration, r representing the distance from the geocenter to the aircraft centroid, L D Representing lift-to-drag ratio, υ representing roll angle, L representing lift acceleration, e being normalized energy, L z (e) Represents the lateral lift-to-drag ratio profile of the normalized energy.
7. The method for calculating the coverage area of the three-dimensional profile based on the lateral priority as claimed in claim 1, wherein the functional expressions for solving the reference trajectory according to the obtained three-dimensional profile in the step 4) are shown in formulas (4-1) to (4-3);
in the expressions (4-1) to (4-3), σ represents the velocity azimuth, E represents the energy, φ represents the geocentric latitude, r represents the geocentric distance, D represents the resistive acceleration, V represents the aircraft velocity, L represents the aircraft velocity, and z denotes the lateral lift-drag ratio, ω e Represents the rotational angular velocity of the earth, and λ represents longitude.
8. A three-dimensional profile coverage area calculation system based on lateral precedence, comprising a computer device, characterized in that: the computer device is programmed to perform the steps of the method for calculating a three-dimensional profile coverage area based on lateral precedence according to any one of claims 1 to 7.
9. A three-dimensional profile coverage area calculation system based on lateral precedence, comprising a computer device, characterized in that: the storage medium of the computer device has stored thereon a computer program programmed to execute the method for calculating a three-dimensional profile coverage area based on lateral precedence according to any of claims 1 to 7.
10. A computer-readable medium, characterized in that: the computer readable storage medium has stored thereon a computer program programmed to execute the method for calculating a three-dimensional cross-sectional coverage area based on lateral precedence according to any of claims 1 to 7.
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| CN107941087A (en) * | 2017-10-18 | 2018-04-20 | 北京航空航天大学 | A kind of superb steady gliding reentry guidance method of high lift-drag ratio based on resistance profiles |
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| CN106643341A (en) * | 2017-02-24 | 2017-05-10 | 北京临近空间飞行器系统工程研究所 | Mechanical-thermal control coupling design method based on quasi-equilibriumgliding principle |
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