CN114781067A - ASV separation trajectory design method based on course differential motion model - Google Patents

ASV separation trajectory design method based on course differential motion model Download PDF

Info

Publication number
CN114781067A
CN114781067A CN202210479166.0A CN202210479166A CN114781067A CN 114781067 A CN114781067 A CN 114781067A CN 202210479166 A CN202210479166 A CN 202210479166A CN 114781067 A CN114781067 A CN 114781067A
Authority
CN
China
Prior art keywords
track
flight
expression
dynamic pressure
formula
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210479166.0A
Other languages
Chinese (zh)
Inventor
刘泓麟
汪锐
徐颖珊
王永圣
安帅斌
梁玉峰
郭昕鹭
董哲
李家鑫
刘凯
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Dalian University of Technology
Original Assignee
Dalian University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Dalian University of Technology filed Critical Dalian University of Technology
Priority to CN202210479166.0A priority Critical patent/CN114781067A/en
Publication of CN114781067A publication Critical patent/CN114781067A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/20—Design reuse, reusability analysis or reusability optimisation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Geometry (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Automation & Control Theory (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention belongs to the technical field of aircraft trajectory design, and relates to an ASV separation trajectory design method based on a flight differential motion model. Aiming at the design problem of a separation track before a backpack two-stage in-orbit aerospace flying aircraft reaches a separation window, the invention firstly considers the characteristics of the separation window required by the aerospace flying aircraft separation, and provides a strategy for climbing the aerospace flying aircraft according to a trajectory in the shape of a parabola by using terminal constraint with separation normal overload of zero. And then, a section design strategy based on a flight path differential dynamics model according to the known track shape is provided for the analysis and research of a parabola separating track strategy, and the feasibility of the designed strategy is verified through a Matlab simulation experiment. The method provided by the invention can greatly improve the operation efficiency of the algorithm while basically ensuring the original precision, provides a new possibility for the design problem of the separation track of the aerospace vehicle, and has a wide application prospect.

Description

ASV separation trajectory design method based on voyage differential motion model
Technical Field
The invention belongs to the technical field of aircraft trajectory design, and relates to an ASV (backpack aerospace vehicle) separation trajectory design method based on a flight differential motion model.
Background
The flight path of the aircraft is also called a mission profile, and the basic principle of designing the flight path of the aircraft is to decompose the mission profile and calculate the flight parameters of each time in each flight segment.
The aerospace craft is a reusable craft which adopts air suction type combined power, has typical characteristics of lift type configuration, horizontal lifting and descending and the like, and can freely fly back and forth in dense atmospheric layers, adjacent spaces and orbital spaces. Compared with the traditional carrying mode, the aerospace vehicle has the advantages that:
(1) the oxygen in the atmospheric layer can be fully utilized, the carrying amount of the oxidant is reduced, and the carrying efficiency is improved;
(2) the winged lift type configuration is adopted, so that the field returning capacity under the emergency condition is improved;
(3) the horizontal take-off and landing at a conventional airport are adopted, and the launching and matching return requirements are simplified;
(4) the transmission mode of flight is formed by completely repeated use, and the transmission cost is greatly reduced.
The aerospace craft breaks through the speed and altitude limits of the traditional craft and the flight mode of the traditional craft, can be used as a world shuttle transport tool and a hypersonic weapon platform, and is a national heavy equipment for core equipment and national safety maintenance of future aerospace integrated operations. Compared with a single-stage rail entering scheme, the two-stage rail entering method has stronger engineering realizability and is the core of the current development. The two-stage orbit-entering aerospace craft adopts a backpack scheme, the combined body takes off horizontally under the boosting of a sub-stage air-breathing engine and climbs to a near space in an accelerating manner, the first stage and the second stage are separated at a high speed, the separated second stage accelerates to enter an orbit to execute a task, and the first stage automatically returns to the field for landing. The configuration of the backpack two-stage orbit-entering aerospace craft is shown in fig. 1, and for the two-stage orbit-entering aerospace craft, before separation occurs, the two-stage orbit-entering aerospace craft must go through the process of separation track ascending, the separation track is the basis for ensuring that the aerospace craft can successfully reach a preset separation window according to design indexes and ensuring that separation tasks are completed, so that the design of the separation track is one of key contents in the research of the two-stage orbit-entering aerospace craft.
The flight profile of the backpack two-stage on-orbit aerospace craft is shown in a flight profile of the aerospace craft shown in fig. 2, the aerospace craft takes off horizontally from a common airport in a turbine mode, keeps the altitude acceleration to cross a sound barrier after accelerating to climb to 10km, the engine is converted into a stamping mode when the speed reaches Ma3.5, then the aerospace craft is separated in two stages after accelerating to climb to Ma6/30km in the stamping mode, one sub-stage returns to a launching airport, and the second sub-stage continuously accelerates to Ma25/200km to enter a track in the rocket power. The separation mechanism of aerospace vehicles can be divided into three main stages, each of which has very different characteristics:
(1) transitioning from a steady cruise state to a ramp-up state;
(2) extend to the track level and prepare for release;
(3) release is done from the track stages to allow translation between the stages, after which pneumatic flight can take place (without interference).
The two-stage separation process of the backpack aerospace vehicle is shown in fig. 3, and the main separation stage and the possible problems of each stage are as follows:
(1) two rail locomotive (OMS) engines are fired simultaneously, with a single maximum thrust of 50kN, during which care needs to be taken to account for the effect of longitudinal torque and exhaust gas on a sub-stage.
(2) The mechanical lift angle of the secondary stage reaches 8 deg., and the high pressure in the gap between the secondary stage and the primary stage causes a large aerodynamic drag, which may cause rotation problems after the secondary stage is released. If the angle of attack is increased, improper rotational control will cause the rear of the second substage to rotate downward, increasing the risk of collision with the first substage.
(3) The two-stage main rocket engine fires with thrust limited to 10% of its normal thrust, which may present the same problems as the first stage.
(4) The mechanical release of the two substages causes aerodynamic interference to both substages, so the main task after release of the two substages is to separate the aircraft at a distance as quickly as possible.
(5) After 3.5-5 s, the thrust of the main rocket engine of the secondary stage is increased to the standard thrust, and if the main rocket engine has a task problem, the aircraft immediately stops the task and executes emergency landing.
At present, in the aspect of separation trajectory research, the trajectory optimization design research of the hypersonic aircraft at the rise section is relatively mature at present, the types of numerical algorithms for trajectory optimization are also various, generally, the method is mainly divided into a direct method and an indirect method, the indirect method has the strategy that the trajectory optimization problem is converted into a Hamiltation boundary value problem to be solved, the precision is relatively high, the theory is clear, in the last 80 th century, Calise and the like perform research on the trajectory optimization problem of the rise section and the guidance law design problem of the hypersonic aircraft, an energy state approximation method and a singular perturbation method are provided, and the solution of the two-point boundary value problem is promoted. Later, Lu considered that the method is not applicable to the climb stage of the hypersonic aircraft before the orbit entering (the parabolic climb trajectory diagram of the aerospace aircraft is shown in FIG. 4), and therefore, the dynamic inverse method is applied to the trajectory optimization problem for the first time. And converting the trajectory optimization problem into a parameter optimization problem by a direct rule, and solving by using a nonlinear programming numerical solution. Michael et al combines the traditional nonlinear programming method with the dynamic inversion method to achieve the goal of implementing optimized trajectory during flight. Dalle et al have given a hypersonic aircraft constant dynamic pressure climbing trajectory design method, but the trajectory that is asked for is not the optimal solution to the situation of time-varying dynamic pressure, and in the hypersonic climbing process, it is difficult to guarantee the invariable constraint of dynamic pressure. Keshmiri establishes a six-degree-of-freedom kinetic equation of the ascending section of the hypersonic aircraft, combines the thought of a direct method, considers the terminal constraint of an estimation optimization problem, and uses a tool kit in MATLAB to carry out track optimization design. The method for simulating the trajectory profile in detail according to the geometry of the trajectory profile by combining a particle dynamics equation is given in the soaring flight to design the trajectory of the automatic landing segment of the carrier, but the design method has defects in the condition that the inclination angle change rate of the trajectory continuous missile path tends to zero; supehua proposes a hypersonic aircraft ascending section trajectory design method based on preset dynamic pressure. It can be seen that, in the aspect of the research on the trajectory of the ascending section of the existing hypersonic aircraft, the algorithm of the trajectory optimization design is relatively mature, most of the optimization design problems are directed at how to reduce the fuel consumption or how to reduce the flight time, and the flight trajectory and the flight parameters are adjusted according to the parameters to be optimized.
Disclosure of Invention
In the separation process of the backpack two-stage in-orbit aerospace craft, the two aerospace craft are influenced by interference force and interference moment generated by the disconnection of the actuating mechanism. The separation safety is also influenced by normal overload of the parallel combination body at the separation time, if the overload vector is the same as the lifting force direction, after the separation occurs, the aircraft suddenly reduces the mass of a sub-stage part, and the aircraft tends to move upwards, the normal overload at the separation time is too large, so that the sub-stage moves upwards, and threatens the two sub-stages, if the overload vector is the same as the gravity, the separated two sub-stages cannot quickly climb upwards, and in combination with the influence of aerodynamic disturbance torque possibly received at the separation time, the two sub-stages easily lose stability and collide with the sub-stage. Aiming at the situations, the invention provides a parabola separating track strategy.
In designing a trajectory for parabolic separation, the following requirements apply:
(1) the flight track of the center of mass of the aerospace vehicle in the air is in a parabolic shape;
(2) the aerospace craft is separated at the top end of the parabola;
(3) designing the normal overload of the aerospace vehicle at the top end of the parabola to be zero;
the trajectory strategy has the following characteristics: 1) at the tail end of the parabolic track, the trajectory inclination angle of the aerospace vehicle is 0, the attack angle is small, the resultant force of the component of the thrust in the vertical direction and the lift force is easily 0, and the purpose that the normal overload is 0 is achieved; 2) the normal overload at the separation moment is designed to be 0, the separated first sub-stage cannot generate an overlarge upward movement trend, and meanwhile, the second sub-stage is easy to generate a head raising moment through control surface control, so that the pneumatic interference area of the first sub-stage is rapidly calculated, and the separation safety is improved; 3) when the aircraft flies along the trajectory of the parabola, the control parameters such as the attack angle, the thrust and the like are stably changed, and the burden on a control system is reduced.
At present, the design and solution of the flight profile under the premise of knowing the track shape are relatively little. The invention provides a track profile design strategy based on flight differentiation, and provides a new possibility for the aerospace vehicle separation track design problem.
The technical scheme of the invention is as follows:
an ASV separation track design method based on a flight differential motion model specifically comprises the following steps:
(1) motion model conversion based on course differential
Firstly, solving a longitudinal motion equation set of the aerospace vehicle, neglecting the effect of earth rotation, assuming the earth as a plane (neglecting the effect of earth radius), and establishing the longitudinal motion equation set of the aerospace vehicle as follows according to the conversion between a track coordinate system and a ground coordinate system:
Figure BDA0003626997420000051
in the formula: v is velocity, theta is track inclination angle, h is aerospace vehicle height, m is vehicle mass, R is vehicle range, T, D and L respectively represent engine thrust, resistance and lift, g represents gravity acceleration, and I represents engine thrust, resistance and liftspDenotes the specific impulse and alpha denotes the angle of attack.
Axial overload nxAnd normal phase overload nyThe kinetic expression of (a):
Figure BDA0003626997420000052
the expression of lift resistance:
Figure BDA0003626997420000053
wherein q is dynamic pressure, S is characteristic area, CD,CLFor the aircraft drag coefficient and lift coefficient, the dynamic pressure expression:
Figure BDA0003626997420000054
where ρ is the atmospheric density.
The method is used for establishing a required aerospace vehicle motion equation system based on range differentiation, and the derivation process is as follows:
the derivative on t is made for the dynamic pressure expression (1.4):
Figure BDA0003626997420000061
substituting the fourth expression in the expressions and the second expression in the expression (1.3) to obtain the derivative of the dynamic pressure to the voyage:
Figure BDA0003626997420000062
equivalently changing the second expression in the expression (1.1), equivalently changing the derivative of the track inclination angle:
Figure BDA0003626997420000063
substituting the fourth equation in equation (1.1) and the first equation in equation (1.3) to obtain the derivative of the ballistic inclination angle with respect to the course:
Figure BDA0003626997420000064
the mass point kinematic equation is changed from the description of (V, theta) under time differentiation into the description of (q, theta);
and (3) carrying out equivalent change on the dynamic pressure expression, and solving the expression of V:
Figure BDA0003626997420000065
and (3) carrying out derivation on the voyage:
Figure BDA0003626997420000066
from the kinetic equation height and derivative of the course:
Figure BDA0003626997420000067
the same applies to the differentiation of the mass with respect to the flight:
Figure BDA0003626997420000071
thus, a motion equation set based on the flight path differential is obtained, namely a motion model based on the flight path differential:
Figure BDA0003626997420000072
and then, equivalently changing a second formula in the formula (1.13) to obtain a track expression of dynamic pressure:
Figure BDA0003626997420000073
and then converting axial direction and normal phase overload:
Figure BDA0003626997420000074
obtain the axial overload and the normal overload in the vertical plane respectively
Figure BDA0003626997420000075
The change of (2):
Figure BDA0003626997420000076
(2) ideal overload solution for parabolic trajectory
The mathematical description of altitude with respect to range is:
h(R)＝hf+a(R-Rf)2 (2.1)
wherein R isfAs a track end course parameter, hfAs a track end height parameter, h0For the climb origin height, a is a parabolic parameter, and the first and second derivatives of height over range are:
Figure BDA0003626997420000081
according to the fourth expression in the expression (1.13), the relationship between the trajectory inclination angle θ and the range in the longitudinal channel can be obtained:
Figure BDA0003626997420000082
let θ derive from the voyage:
Figure BDA0003626997420000083
bringing (2.2) into (2.4) gives:
Figure BDA0003626997420000084
the equation describes the relationship between theta and range on the flight profile of a parabolic climbing orbit.
And also needing overload expression under each abscissa on a track profile, firstly solving the curvature radius of the parabolic track, and solving by using a function curvature radius:
Figure BDA0003626997420000085
substituting formula (2.2) into formula (2.6) yields:
Figure BDA0003626997420000091
wherein R isρThe curvature radius of the parabolic track is obtained by the track parameters and is independent of flight parameters.
The following is to derive an expression for overload of the rational idea phase of each point under the course-dynamic pressure profile, and firstly, the relationship between the time derivative of the track inclination angle and the normal overload is obtained by the second expression (1.15):
Figure BDA0003626997420000092
flying in the skyIn the process, the curvature radius R of each point on the flight pathyThe speed of the point and the change rate of the track inclination angle can be used for solving the following problems:
Figure BDA0003626997420000093
bringing formula (2.8) into formula (2.9) yields the relationship between the track radius of curvature and the normal overload:
Figure BDA0003626997420000094
the combination formula (1.4) converts the formula (2.10) into normal overload nyExpression for dynamic pressure:
Figure BDA0003626997420000095
where ρ is the atmospheric density at that point, let Ry＝RρThe theory-idea phase overload of each point under the course-dynamic pressure profile can be obtained by bringing the formula (2.7) into the formula (2.11), and is recorded as ny,track。
Figure BDA0003626997420000096
(3) Aerospace vehicle parabolic separation track design strategy based on range differential motion model
As shown in fig. 5, after parameters such as an initial abscissa, an initial dynamic pressure, an initial attack angle, and the like are given, calculation of a range change rate of the initial dynamic pressure is performed, an attack angle and a thrust at a next abscissa are estimated, and then, the dynamic pressure, the attack angle, and the thrust after updating of each range are iteratively calculated according to an algorithm, and finally, a specified terminal parameter is reached.
Firstly, parameters such as an initial abscissa, an initial dynamic pressure, an initial attack angle and the like are given.
Then, calculating the derivative of the dynamic pressure to the flight distance in the initial state:
Figure BDA0003626997420000101
entering a loop, estimating alpha (R + delta R) by using a formula:
Figure BDA0003626997420000102
estimate T (R + Δ R), estimated by the axial overload binding kinetics equation:
Figure BDA0003626997420000103
the calculation method for the alpha (R + DeltaR) estimate can be obtained as follows:
Figure BDA0003626997420000104
the T (R + Δ R) estimate is calculated primarily by axial overload, estimated in conjunction with the kinetic equation:
Figure BDA0003626997420000105
after the initial values of α (R + Δ R) and T (R + Δ R) are estimated, an accurate solution is required for each flight, and the value of the angle of attack α (R + Δ R) is calculated accurately by an optimization algorithm. The definitions are given below:
Q(α,T)＝q1(R+ΔR)-q2(R+ΔR) (3.6)
the Q (α, T) function is mainly used for newtonian iterative computation of the angle of attack α (R + Δ R), the physical meaning of which is in the sense of balancing the normal overload by α (R + Δ R). In one aspect, the value of q (R + Δ R) can be calculated using the euler method:
Figure BDA0003626997420000106
on the other hand, q (R + Δ R) can be calculated by formula (1.14) using the data of α (R + Δ R):
q2(R+ΔR)＝f2[α(R+ΔR),R+ΔR] (3.8)
when the condition is satisfied:
Errq＝|q1(R+ΔR)-q2(R+ΔR)|≤ε (3.9)
the iterative calculation on the course can be ended, and the calculation of the next course is carried out.
The invention has the beneficial effects that:
the invention provides a parabolic separation track strategy aiming at the problem that the separation process of a backpack two-stage in-orbit aerospace vehicle is influenced by normal overload, and then provides an ASV separation track design method based on a flight differential motion model. The required flight path differential motion model of the method is obtained by solving a longitudinal motion equation set of the aerospace vehicle, and then the proposed parabolic track strategy is subjected to simulation analysis by using the invented track design method. Simulation results show that the separation track design method can effectively complete track design tasks, and simulated flight profiles can well fit design indexes. The track design method provided by the invention has the characteristics of high precision, high calculation speed, low simulation difficulty and the like. Has wide application prospect.
Drawings
FIG. 1 is a conceptual diagram of a two-stage in-orbit aerospace vehicle structure;
FIG. 2 is a aerospace vehicle flight profile;
FIG. 3 is a schematic diagram of a two-stage separation process for an aerospace vehicle;
FIG. 4 is a diagram of a parabolic climb trajectory for an aerospace vehicle;
FIG. 5 is a trajectory profile simulation design algorithm based on a course differential motion model;
FIG. 6 is a result of a height-course profile simulation;
FIG. 7 is a dynamic pressure-voyage profile simulation result;
FIG. 8 is a speed-course profile simulation result;
FIG. 9 is a simulation result of an angle of attack-course profile;
FIG. 10 is a trace inclination-course profile simulation result;
fig. 11 is a result of a normal overload-voyage profile simulation.
Detailed Description
The following further describes the specific embodiments of the present invention with reference to the drawings and technical solutions.
The invention provides a scheme for designing a track profile based on course differentiation, which can solve the profile parameters of an aerospace vehicle flying along a parabolic track, and specifically comprises the following steps:
(1) motion model conversion based on course differential
Neglecting the earth self-propagation influence, assuming the earth as a plane (neglecting the influence of the earth radius), and establishing a longitudinal motion equation set of the aerospace vehicle according to the conversion between the flight path coordinate system and the ground coordinate system as follows:
Figure BDA0003626997420000121
in the formula: v is velocity, theta is track inclination angle, h is aerospace vehicle height, m is vehicle mass, R is vehicle range, T, D and L respectively represent engine thrust, resistance and lift, g represents gravity acceleration, and I represents engine thrust, resistance and liftspDenotes the specific impulse and alpha denotes the angle of attack.
Axial overload nxAnd normal phase overload nyThe kinetic expression of (c):
Figure BDA0003626997420000122
the method is used for establishing a required aerospace vehicle motion model based on range differentiation, the derivation process is not repeated, and the result is as follows:
Figure BDA0003626997420000131
and then, equivalently changing a second expression in the expression (4.3) to obtain a track expression of dynamic pressure:
Figure BDA0003626997420000132
and then converting axial direction and normal phase overload:
Figure BDA0003626997420000133
obtain the axial overload and the normal overload in the vertical plane respectively
Figure BDA0003626997420000134
The change of (c):
Figure BDA0003626997420000135
(2) ideal overload solution for parabolic trajectory
Mathematical description of altitude in parabolic trajectory with respect to range:
h(R)＝hf+a(R-Rf)2(5.1)
wherein R isfFor track end course parameters, hfAs a track end height parameter, h0For the climb origin height, a is a parabolic parameter, and the first and second derivatives of the height over the course are:
Figure BDA0003626997420000141
according to the fourth expression (5.2) in the expression (4.3), the relation between theta and the range on the flight section of the parabolic climbing track can be deduced:
Figure BDA0003626997420000142
solving the overload expression of each abscissa on the flight path profile, firstly solving the curvature radius expression of each point on the parabolic flight path, and directly giving a result as follows:
Figure BDA0003626997420000143
wherein R isρIs obtained from flight path parameters and is independent of flight parameters.
In the flight process of the aerospace vehicle, the curvature radius R of each point on the flight pathyRelationship to normal overload:
Figure BDA0003626997420000144
convert it into a normal overload nyExpression for dynamic pressure:
Figure BDA0003626997420000145
where ρ is the atmospheric density at that point, let Ry＝RρThe theory idea phase overload of each point under the course-dynamic pressure profile can be obtained by taking the formula (5.4) into the formula (5.6), and is recorded as ny,track。
Figure BDA0003626997420000146
(3) Aerospace vehicle parabolic separation track design strategy based on range differential motion model
As shown in fig. 5, after parameters such as an initial abscissa, an initial dynamic pressure, an initial attack angle, and the like are given, calculation of a range change rate of the initial dynamic pressure is performed, an attack angle and a thrust at a next abscissa are estimated, and then, the dynamic pressure, the attack angle, and the thrust after updating of each range are iteratively calculated according to an algorithm, and finally, a specified terminal parameter is reached.
As shown in fig. 5, the estimation of the angle of attack α (R + Δ R) and the thrust T (R + Δ R) directly affect the speed of iteration, which is also a difficulty in the whole track design process, and q (R + Δ R) can be calculated accordingly, so that the dynamic pressure and angle of attack variation curves can be easily obtained.
Since α (R + Δ R) primarily affects the lift of the aircraft, it is possible to overload n by the aircraft normalyTo estimate the angle of attack, the solution of normal overload with respect to dynamic pressure in the course-based differential motion method is known from the second equation (1.16) and the velocity dynamic pressure expression (1.9):
Figure BDA0003626997420000151
the calculation method for the alpha (R + DeltaR) estimate can be obtained as follows:
Figure BDA0003626997420000152
the T (R + Δ R) estimate is calculated primarily by axial overload, estimated in conjunction with the kinetic equation:
Figure BDA0003626997420000153
after the initial values of α (R + Δ R) and T (R + Δ R) are estimated, an exact solution is needed for each leg, where the value of the angle of attack α (R + Δ R) is calculated exactly by an optimization algorithm. The definitions are given below:
Q(α,T)＝q1(R+ΔR)-q2(R+ΔR) (6.4)
the Q (α, T) function is mainly used for newtonian iterative computation of the angle of attack α (R + Δ R), the physical meaning of which is in the sense of balancing the normal overload by α (R + Δ R). On the one hand, we can calculate the value of q (R + Δ R) by using the euler method:
Figure BDA0003626997420000161
on the other hand, q (R + Δ R) can be calculated by (1.14) using the data of α (R + Δ R):
q2(R+ΔR)＝f2[α(R+ΔR),R+ΔR] (6.6)
when the condition is satisfied:
Errq＝|q1(R+ΔR)-q2(R+ΔR)|≤ε (6.7)
the iterative calculation on the flight can be ended, and the calculation of the next flight is performed.
In order to verify the feasibility of the method proposed by the present invention, a mathematical simulation test was performed using Matlab, and the results are shown in fig. 6 to 11.
Wherein, fig. 6 is a height-range profile simulation result, the height of the starting point of the designed parabolic separation track is 27km, and the height of the tail end of the track is 29.89km, and from the simulation result, after the simulation is performed by the track design method of the present invention, the fitting condition between the track obtained by the simulation and the designed parabolic track is good.
Fig. 7 is a simulation result of dynamic pressure versus flight profile, where the designed dynamic pressure of the separation window is 30Kpa, the initial dynamic pressure is solved by altitude and velocity, and it can be seen in the simulation result graph that the dynamic pressure of the aircraft just reaches 30Kpa at the end of the trajectory, i.e. the vertex of the parabola.
FIG. 8 shows the results of velocity-course profile simulation, with a starting velocity of 1793m/s and an ending velocity of Ma6, converted to 1810.4m/s at a dynamic pressure of 30 KPa. It can be seen that the speed of the aerospace vehicle can follow the designed tip speed at the tip.
Fig. 9 is a simulation result of an angle of attack-course profile, in which the angle of attack is used as an output control in a trajectory design strategy, and the magnitude of the angle of attack is changed to enable the normal overload of actual flight to track the designed overload profile. It can be seen that in this example, the end attack angle value is 0.877 °.
Fig. 10 is a simulation result of the trajectory inclination-course section, according to the nature of the parabolic trajectory, the trajectory inclination in the ideal state varies linearly with the course section, and it can also be seen from the figure that at the end of the trajectory, the trajectory inclination of the aircraft can reach 0 °, coinciding with the designed end trajectory inclination.
Fig. 11 is a simulation result of normal overload-course profile, in which the overload variation solved by dynamic pressure reflects normal overload in an ideal state, and the normal overload is solved by designed ideal track inclination profile and dynamic pressure profile. The normal overload of the lift solution is to solve the lift characteristic of each point through an attack angle section and a trajectory inclination angle section, so that the normal overload is solved and is an actual simulation result. From the comparison of the two, a certain error exists in the middle flight climbing section, the maximum error is 0.00012, and the error can be ignored. Most importantly, the track design method focuses more on parameters at the tail end of the track, and results show that the actual normal overload is 0 at the tail end of the track, so that the design requirement is met.

Claims (1)

1. An ASV separation track design method based on a flight differential motion model is characterized by comprising the following steps:
(1) motion model conversion based on course differential
(1-1) firstly, solving a longitudinal motion equation set of the aerospace vehicle, neglecting the autorotation influence of the earth, assuming the earth as a plane, and establishing the longitudinal motion equation set of the aerospace vehicle as follows according to the conversion between a track coordinate system and a ground coordinate system:
Figure FDA0003626997410000011
in the formula: v is speed, theta is track inclination angle, h is aerospace vehicle height, m is vehicle mass, R is vehicle range, T, D and L respectively represent engine thrust, resistance and lift, g represents gravity acceleration, and IspDenotes the specific impulse, alpha denotes the angle of attack;
axial overload nxAnd normal phase overload nyThe kinetic expression of (a):
Figure FDA0003626997410000012
the expression of lift resistance:
Figure FDA0003626997410000013
wherein q is dynamic pressure, S is characteristic area, CD,CLFor aircraft drag coefficient and lift coefficient, the dynamic pressure expression:
Figure FDA0003626997410000021
wherein ρ is the atmospheric density;
(1-2) establishing an aerospace vehicle motion equation system based on the course differential, wherein the derivation process is as follows:
(1-3) taking the derivative of t for the dynamic pressure expression (1.4):
Figure FDA0003626997410000022
(1-4) substituting the fourth expression in the formula (1.1) and the second expression in the formula (1.3) to obtain the derivative of the dynamic pressure with respect to the flight:
Figure FDA0003626997410000023
(1-5) equivalently changing the second expression in the expression (1.1), and equivalently changing the derivative of the track inclination angle:
Figure FDA0003626997410000024
(1-6) substituting the fourth equation in equation (1.1) and the first equation in equation (1.3) to obtain the derivative of the ballistic inclination angle with respect to the course:
Figure FDA0003626997410000025
the mass point kinematic equation is changed from the description of (V, theta) under time differentiation into the description of (q, theta);
(1-7) carrying out equivalent change on the dynamic pressure expression, and solving the expression of V:
Figure FDA0003626997410000026
(1-8) carrying out derivation on the voyage:
Figure FDA0003626997410000027
(1-9) from the height of the kinetic equation and the derivative of the course:
Figure FDA0003626997410000028
(1-10) obtaining the differential of the quality relative to the flight distance by the same method:
Figure FDA0003626997410000031
(1-11) obtaining a motion equation system based on the flight differential, namely a motion model based on the flight differential:
Figure FDA0003626997410000032
(1-12) then, equivalently changing the second expression in the expression (1.13) to obtain a track expression of dynamic pressure:
Figure FDA0003626997410000033
(1-13) further converting axial and normal phase overloads:
Figure FDA0003626997410000034
(1-14) obtaining the axial overload and the normal overload in the vertical plane respectively
Figure FDA0003626997410000035
The change of (c):
Figure FDA0003626997410000036
(2) ideal overload solution for parabolic trajectory
(2.1) the mathematical description of altitude with respect to range is:
h(R)＝hf+a(R-Rf)2 (2.1)
wherein (R)f,hf) As an end-of-track parameter, h0For the climb origin height, a is a parabolic parameter, and the first and second derivatives of the height over the course are:
Figure FDA0003626997410000041
(2.2) obtaining the relationship between the trajectory inclination angle theta and the range under the longitudinal channel according to the fourth formula in the formula (1.13):
Figure FDA0003626997410000042
(2.3) let θ be derived for the voyage:
Figure FDA0003626997410000043
(2.4) the formula (2.2) is introduced into the formula (2.4) to obtain:
Figure FDA0003626997410000044
equation (2.5) describes the relationship between theta and the range on the flight profile of the parabolic climbing track;
(2.5) also needing overload expression under each abscissa on the track section, firstly solving the curvature radius of the parabolic track, and solving by the curvature radius of a function:
Figure FDA0003626997410000045
(2.6) bringing formulae (2.4) and (2.5) into formula (2.6) gives:
Figure FDA0003626997410000051
wherein R isρThe curvature radius of the parabolic flight path is obtained from flight path parameters and is irrelevant to flight parameters;
Figure FDA0003626997410000052
(2.7) during the flight of the aerospace vehicle, the curvature radius R of each point on the flight pathyThe speed of the point and the change rate of the track inclination angle can be used for solving the following problems:
Figure FDA0003626997410000053
(2.8) bringing formula (2.8) into formula (2.9) to obtain the relationship between the track curvature radius and the normal overload:
Figure FDA0003626997410000054
(2.9) adding nyConversion to kinetic expression:
Figure FDA0003626997410000055
where ρ is the atmospheric density at that point, let Ry＝RρThe theory-idea phase overload of each point under the course-dynamic pressure profile is obtained by bringing the formula (2.7) into the formula (2.11) and is recorded as ny,track；
Figure FDA0003626997410000056
(3) Aerospace vehicle parabolic separation trajectory design strategy based on flight differential dynamics model
After initial abscissa, initial dynamic pressure and initial attack angle parameters are given, calculation of initial dynamic pressure on the flight change rate is carried out, then the attack angle and the thrust at the next abscissa are estimated, the updated dynamic pressure, attack angle and thrust of each flight are iteratively calculated according to an algorithm, and finally the specified terminal parameters are reached; the specific process comprises the following steps:
(3.1) giving parameters such as an initial abscissa, an initial dynamic pressure, an initial attack angle and the like;
(3.2) calculating the derivative of the dynamic pressure to the flight distance in the initial state:
Figure FDA0003626997410000061
(3.3) entering a loop, estimating alpha (R + delta R) by using the formula:
Figure FDA0003626997410000062
(3.4) estimating T (R + DeltaR) by combining the axial overload with the kinetic equation:
Figure FDA0003626997410000063
(3.5) after the iterative initial values of alpha (R + delta R) and T (R + delta R) are estimated, accurate solution under each voyage is needed, and the value of the attack angle alpha (R + delta R) is calculated through an optimization algorithm; the definitions are given below:
Q(α,T)＝q1(R+ΔR)-q2(R+ΔR) (3.4)
the Q (alpha, T) function is mainly used for Newton iterative calculation of an attack angle alpha (R + delta R), and the physical meaning of the Q (alpha, T) function is equal to that of normal overload through the alpha (R + delta R) in balancing;
(3.6) calculating the value of q (R + Delta R) by using an Euler method:
Figure FDA0003626997410000064
(3.7) using the data of α (R + Δ R), q (R + Δ R) is calculated by the formula (1.14):
q2(R+ΔR)＝f2[α(R+ΔR),R+ΔR] (3.6)
(3.8) when the condition is satisfied:
Errq＝|q1(R+ΔR)-q2(R+ΔR)|≤ε (3.7)
namely, the iterative calculation on the voyage is finished, and the calculation of the next voyage is carried out.
CN202210479166.0A 2022-05-05 2022-05-05 ASV separation trajectory design method based on course differential motion model Pending CN114781067A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210479166.0A CN114781067A (en) 2022-05-05 2022-05-05 ASV separation trajectory design method based on course differential motion model

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210479166.0A CN114781067A (en) 2022-05-05 2022-05-05 ASV separation trajectory design method based on course differential motion model

Publications (1)

Publication Number Publication Date
CN114781067A true CN114781067A (en) 2022-07-22

Family

ID=82435011

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210479166.0A Pending CN114781067A (en) 2022-05-05 2022-05-05 ASV separation trajectory design method based on course differential motion model

Country Status (1)

Country Link
CN (1) CN114781067A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115981161A (en) * 2023-02-07 2023-04-18 大连理工大学 Fixed-wing aircraft gliding control gain index optimization method based on direct lift force

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115981161A (en) * 2023-02-07 2023-04-18 大连理工大学 Fixed-wing aircraft gliding control gain index optimization method based on direct lift force

Similar Documents

Publication Publication Date Title
CN106021628B (en) A kind of carrier rocket vertically returns to ballistic design method
Limebeer et al. Faster, higher, and greener: Vehicular optimal control
CN100576124C (en) A kind of longitudinal control method for high altitude lifting of aerospaceplane
CN108928490A (en) A kind of Horizontal Take-off and Landing two-stage enters the aerodynamic arrangement of orbit aerocraft
CN108216679B (en) Solar unmanned aerial vehicle overall parameter determination method and system
CN110510149A (en) A kind of Horizontal Take-off and Landing two-stage, which is entered the orbit, reuses sky and space plane layout
CN109711008A (en) A kind of center of gravity of airplane envelope curve calculation method
CN113895645A (en) Propeller unmanned aerial vehicle autonomous takeoff obstacle crossing capability analysis method
CN112329136A (en) Carrier rocket online flight program reconstruction method based on balanced flight theory
CN114781067A (en) ASV separation trajectory design method based on course differential motion model
Sivan et al. An overview of reusable launch vehicle technology demonstrator
CN113341710B (en) Composite control method and application for agile turning of aircraft
Hu et al. Longitudinal control for balloon-borne launched solar powered UAVs in near-space
CN109614644A (en) A kind of Externally Blown Flap airplane power-boosting effect evaluation method
CN107933958A (en) A kind of re-entry space vehicle longitudinal direction steady state stability design method based on best performance
CN115685764B (en) Task self-adaptive anti-interference tracking control method and system for variable-span aircraft
CN114690793B (en) Sliding mode control-based reusable carrier rocket vertical soft landing guidance method
CN107871057B (en) Two-stage orbit-entering reusable aircraft scale estimation method
Dong et al. Research on guidance and control law design of decelerating transition and vertical landing for a STOVL UAV
CN114162349A (en) Parallelly connected repeatedly usable's two-stage rail aircraft with pneumatic integrated configuration
CN114265420A (en) Guidance control integrated design method suitable for high dynamic and control slow response
CN112325711A (en) Carrier rocket orbit height keeping control method based on balanced flight theory
CN113761670A (en) Balance flight theory and online orbit entering capability evaluation method of carrier rocket
CN113836645B (en) On-line flight program reconstruction and orbit height maintenance control method for carrier rocket
Wang et al. Trajectory optimization for reusable rocket landing

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination