CN105930550B - A kind of air suction type hypersonic missile boosting-Jump probability optimization method - Google Patents
A kind of air suction type hypersonic missile boosting-Jump probability optimization method Download PDFInfo
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Abstract
The present invention relates to a kind of air suction type hypersonic missile boosting-Jump probability optimization methods, it is technically characterized in that the air suction type hypersonic missile trajectory scheme for devising a kind of scramjet engine intermittent cyclical igniting, the air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion comprising side-jet control is established, and trajectory optimisation problem is solved using adaptive pseudo- spectrometry.Optimize obtained boosting-Skipping trajectory and significantly improve the range of guided missile, range is 3.81 times of boosting-cruise trajectory of existing air suction type hypersonic missile；The boosting of design-Skipping trajectory flying height is not fixed, and most of the time flying height is higher, is had stronger penetration ability, is a kind of trajectory mode of great application prospect.
Description
Technical field
The present invention principally falls into missile trajectory optimization field, and in particular to a kind of air suction type hypersonic missile boosting-jump
Jump formula Method of Trajectory Optimization.
Background technique
Traditional air suction type hypersonic missile is after aerial platform transmitting, and included rocket booster is by its boosting to facing
The flying speed of near space height and 4~5Ma, subsequent scramjet engine ignition operation, guided missile fly near space cruise
Row carries out diving attack when guided missile is close to target.Cruise section is the entire flight course time-consuming longest stage, however is being cruised
The overload very little of section guided missile, maneuverability is extremely limited, and flying height and speed are relatively stable, it is likely that are captured by air defence system
And interception, limit its penetration ability.And the air suction type hypersonic missile of the gentle Power compound control mode of direct force is used,
Cruise section overload and maneuverability, which can be improved, can dramatically increase the anti-energy of dashing forward of guided missile by boosting-Jump probability mode
Power and range.
Air suction type hypersonic cruise missile boosting-Jump probability optimization problem, it is different from ballistic missile reentry trajectory,
Air-breathing missile is still the flight course of drive after motors in boost phase penetration, is influenced by scramjet engine working condition,
It is more stringent to the limitation of the angle of attack in trajectory optimisation, and motor power is with the value that angle of attack variation is a time-varying, this
So that optimization process needs more just to be able to satisfy the condition of convergence with points.In addition, compared with reentry vehicle, existing air suction type
The cruise section of hypersonic missile overloads very little, cannot complete the Jump probability of guided missile, bigger motor-driven to have guided missile
Ability is needed using direct force/aerodynamic force complex controll mode, thus necessary in control variable to generate bigger overload
Comprising precise tracking thrust, the complexity of ballistic design is further increased.
Summary of the invention
For the trajectory optimisation problem of air suction type hypersonic missile, the present invention provides a kind of air suction type hypersonic missile
Boosting-Jump probability optimization method, a kind of air suction type hypersonic missile boosting-Jump probability optimization method, the bullet
Road optimization method is used to increase the range and penetration ability of air suction type hypersonic missile, which is characterized in that the trajectory is excellent
Change method designs a kind of air suction type hypersonic missile trajectory of scramjet engine intermittent cyclical igniting, establishes comprising direct
The one air suction type hypersonic missile of the air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion and building of power control
Boosting-Jump probability Optimized model, and the Method of Trajectory Optimization solves trajectory optimisation problem using adaptive pseudo- spectrometry.With
Ballistic missile reentry trajectory is different, and air-breathing missile of the present invention is still the flight course of drive after motors in boost phase penetration, by super
The influence of burning ramjet working condition, it is more stringent to the limitation of the angle of attack in trajectory optimisation, and air suction type of the present invention
The cruise section of hypersonic missile can complete the Jump probability of guided missile, so that guided missile is had bigger maneuverability, using direct
Power/aerodynamic force complex controll mode generates bigger overload, includes precise tracking thrust in control variable, further excellent
Trajectory is changed.
The present invention is achieved by the following technical solutions:
A kind of air suction type hypersonic missile boosting-Jump probability optimization method, the Method of Trajectory Optimization is for increasing
Add the range and penetration ability of air suction type hypersonic missile, the Method of Trajectory Optimization designs a kind of scramjet engine
The air suction type hypersonic missile of air suction type hypersonic missile trajectory, foundation comprising side-jet control of intermittent cyclical igniting is vertical
To the plane overall trajectory equation of motion and air suction type hypersonic missile boosting-Jump probability Optimized model is constructed, and described
Method of Trajectory Optimization solves trajectory optimisation problem using adaptive pseudo- spectrometry.
Further, the air suction type hypersonic missile trajectory of the scramjet engine intermittent cyclical igniting is basic
Flight scenario are as follows: the hypersonic missile is pushed to 25-60 km height by rocket booster, after rocket booster separation,
The hypersonic missile undergoes unpowered hop segments first, when the height of the hypersonic missile be down to 40 kms or less,
When speed is down to 1500m/s, scramjet engine ignition operation, the hypersonic missile is motor-driven near space jump,
Scramjet engine is worked by the way of intermittent cyclical igniting in Skipping trajectory, to reduce the fuel consumption of engine
Amount；After running out of gas, the hypersonic missile enters the unpowered jump flight stage, when leaning on close-target, the high ultrasound
Fast guided missile enters Trajectory-terminal, completes diving attack.
Further, the air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion comprising side-jet control
Specifically: ignore earth rotation and aspherical influence, it is assumed that precise tracking can provide continuously adjustable thrust, obtain the packet
The air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion containing side-jet control are as follows:
In formula, m, v, h, α,θ respectively indicates guided missile quality, speed, terrain clearance, the angle of attack, pitch angle and trajectory tilt angle；
L is range；P is motor power；FNFor the thrust of precise tracking；nyFor normal g-load；Q is dynamic pressure；S is area of reference；g
For acceleration of gravity；R is earth mean radius；IspFor scramjet engine specific impulse；nyNormal g-load, C can be used for guided missilex,Cy
Respectively resistance coefficient and lift coefficient, they are the functions of the angle of attack and Mach number.
Further, the air suction type hypersonic missile boosting-Jump probability Optimized model specifically: become in state
When amount x (t) meets air suction type hypersonic missile boosting-Jump probability constraint condition, seeks optimum control variable u (t), make
Obtain performance indicator J minimalization；
Trajectory is divided into motors in boost phase penetration and and jump by the air suction type hypersonic missile boosting-Jump probability Optimized model
Section optimizes respectively, using motors in boost phase penetration end energy as the performance indicator J of motors in boost phase penetrationMotors in boost phase penetration,Using range as the performance indicator J of hop segmentsHop segments,WhereinFor tf
The scope at moment；
State variable x (t) takes parameter v, θ, h, L, m in the equation of motion, i.e. x=(v, θ, h, L, m)T；Only considering to indulge
In the case where plane motion, control variable is taken as angle of attack and precise tracking thrust FN, i.e. u=(α, FN)T。
Further, the air suction type hypersonic missile boosting-Jump probability constraint condition includes:
(1) normal g-load constrains
In the motors in boost phase penetration and the hop segments, limit of the overload of guided missile by structural strength and airborne equipment ability to bear
System, that is, have
|ny|≤ny max (2)
N in formulay maxFor guided missile maximum permissible load factor；
(2) dynamic pressure constrains
Q in formulamaxFor the limitation of guided missile max-Q；
(3) hot-fluid constrains
Hot-fluid constraint is often referred to the limitation of the hot-fluid at aircraft surface stationary point, that is, has
In formulaFor guided missile maximum heat ductility limit system；
Stationary point heat flow density is calculate by the following formula:
In formula, kQIt is constant related with missile configuration and material, kQ=3.08 × 10-5；RNFor radius of curvature at stationary point,
Take RN=0.02m；ρ is atmospheric density；V is missile velocity；
(4) angle of attack constrains
In order to reduce the perturbation of the separation between two-stage, it is necessary to limit the angle of attack size at booster separation moment:
α(tf1)=0 ° (6)
For the control requirement for meeting guided missile, control amount must be controlled in a certain range, and control amount is unable to acute variation,
On the other hand in hop segments, Scramjet Inlet is also restricted to the angle of attack when working normally, thus to flight course
The guided missile angle of attack have corresponding constraint:
In formula, t01For guided missile emission time in the sky, tf1For motors in boost phase penetration finish time, t02For punching engine point for the first time
Fiery moment, tf2For the moment that runs out of gas, tfFor hop segments finish time；
(5) highly constrained
To reduce flight resistance when enabling guided missile high speed flight, while the firepower of ground environment being avoided to block as far as possible
It cuts, guided missile should be made to be maintained at the flight of near space region, following limitation is made to its flying height:
25km≤h≤60km,tf1≤t≤tf (8)
(6) end conswtraint
Air suction type hypersonic missile enters Trajectory-terminal after hop segments, completes diving attack, to guarantee to dive
Attack has enough kinetic energy, makees following end conswtraint to hop segments trajectory:
H in formulafAnd vfRespectively tfThe height and speed of moment guided missile；
(7) precise tracking thrust constrains
It is limited by precise tracking quantity and specific impulse, the thrust F of precise trackingNHave certain limitations range
FN≤FN max (10)
In formula, FNFor the thrust of precise tracking, FN maxFor precise tracking maximum thrust；
(8) scramjet engine intermittent cyclical ignition condition
For the fuel consumption for reducing scramjet engine, engine is using intermittent cyclical igniting in Skipping trajectory
Mode works, and when experience trough starts to climb, and flying speed is down to speed of ignition lower limit 1500m/s, ultra-combustion ramjet starts
Machine ignition operation；40km is risen to, engine misses, guided missile continues to climb by aircraft kinetic energy, and completes several jump waves
Section, until speed is decreased to speed of ignition lower limit, engine is lighted a fire again；And so on until running out of gas, guided missile enters nothing
Powerhop mission phase；Thus scramjet engine period ignition condition is obtained are as follows:
θ≥0°,h≤40km,v≤1500m/s,t02≤t≤tf2 (11)
Further, it is described trajectory optimisation problem solved using adaptive pseudo- spectrometry specifically includes the following steps:
Step 1: dividing network section as needed, and set and count matching for each section；
Step 2: on each network section, using global Gauss puppet spectrometry by state equation, objective function and constraint
Optimal control problem is converted nonlinear programming problem by conditional discrete；
Step 3: solving nonlinear programming problem using sequential quadratic programming method；
Step 4: judging whether the corresponding quantity of state of each grid section midpoint and control amount meet the pact of the equation of motion
Beam required precision, iteration terminates if meeting the requirements, and step 5 or step 6 are skipped to if being unsatisfactory for；
Step 5: if the magnitude of all elements is suitable in residual vector β, increasing with points, i.e. increase interpolation polynomial
Number；
Step 6: if the magnitude of certain elements is significantly greater than other elements in residual vector β, to corresponding grid regions
Between refined；
Step 7: after all grid sections have all adjusted, return step 2 carries out next iteration.
Further, the hypersonic missile is the cruise body with Waverider structure.
Advantageous effects of the invention:
The present invention devises a kind of Air-breathing hypersonic vehicle trajectory of scramjet engine intermittent cyclical igniting
Scheme, the boosting-Skipping trajectory optimized significantly improve the range of guided missile, and flight time 2306.9s optimizes
Range is 3771.5km, and range is 3.81 times of boosting-cruise trajectory of existing air suction type hypersonic missile, and design helps
Push away-Skipping trajectory flying height is not fixed, and most of the time flying height is higher, has stronger penetration ability, is a kind of
The trajectory mode of great application prospect.
Detailed description of the invention
Fig. 1 is the basic trajectory schematic diagram of boosting of the present invention-jump hypersonic missile；
Fig. 2 is the ballistic curve of the different sparking mode of the present invention；
Fig. 3 is the flying speed change curve of different schemes of the present invention；
Fig. 4 is the vehicle mass change curve of different schemes of the present invention.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is explained in further detail.It should be appreciated that specific embodiment described herein is used only for explaining the present invention, and
It is not used in the restriction present invention.
On the contrary, the present invention covers any substitution done on the essence and scope of the present invention being defined by the claims, repairs
Change, equivalent method and scheme.Further, in order to make the public have a better understanding the present invention, below to of the invention thin
It is detailed to describe some specific detail sections in section description.Part without these details for a person skilled in the art
The present invention can also be understood completely in description.
Embodiment 1
Trajectory optimisation is carried out for the trajectory scheme under different sparking mode, and analyzes the performance superiority and inferiority of different schemes.It is imitative
True condition is as follows:
State variable primary condition: v0=240m/s, θ0=15 °, h0=15km, L0=0km, m0=1780kg；
End conswtraint: vf>=1200m/s, hf>=30km, mf1=671kg, mf=548kg.
Process constraints: ny max=10, qmax=50kpa,FN max=4000N.
In order to investigate influence of the scramjet engine difference sparking mode to trajectory, 4 kinds of different trajectory schemes are compared,
The sparking mode of each scheme scramjet engine is included in table 1.In table 1, scheme 1 uses intermittent cyclical point for what the present invention designed
The trajectory of fiery mode；Scheme 2 uses continuous cycles sparking mode, i.e., one trough guided missile of every experience, which can all light a fire, climbs；Scheme 3
Middle scramjet engine continues working, therefore its ballistic ordinate is limited within the scope of 25~40km；Scheme 4 is flat winged cruise formula
Trajectory, guided missile do not make motor-driven, engine continuous work, level altitude 35km.
Trajectory scheme under the different sparking mode of table 1
Using hp, adaptively pseudo- spectrometry respectively optimizes the above-mentioned trajectory scheme of air suction type hypersonic missile, emulates
As a result as shown in Figure 2 to 4, Fig. 2~Fig. 4 is respectively the flying speed change of the ballistic curve of different sparking mode, different schemes
Change curve；The vehicle mass change curve of different schemes.
In the case of scheme 1 it can be seen from Fig. 2~simulation result shown in Fig. 4, air suction type hypersonic missile passes through
The motors in boost phase penetration of 50s, speed and height increase respectively to 2118.6m/s and 40km, subsequent booster separation, guided missile continue to climb to
Highest 70km, then starting to fall carries out unpowered jump；It experienced the jump of 4 wave bands, missile velocity drops to 1500m/
S, scramjet engine start ignition operation；Scramjet engine is lighted a fire every time can make guided missile 2 wave bands of jump, by 4
After secondary igniting, punching engine runs out of gas, and guided missile enters last unpowered gliding section；Final missile velocity is down to 1200m/
S, flight time 2306.9s, the range optimized are 3771.5km.
For 2 scheme of scheme, before scramjet engine igniting, the trajectory of optimization is identical as scheme 1, hereafter engine
One trough ignition operation of every experience, flight to 40km height tail-off enter unpowered gliding by 4 igniting guided missiles
Section；The ballistic range that final optimization pass obtains is 3033.7km, flight time 1762.8s.
3 scheme of scheme is the Skipping trajectory that scramjet engine continues working, trajectory and scheme 1 before engine ignition
Identical, guided missile jumps motor-driven in 25-40km altitude range after igniting, and the jump post fuel of 2 wave bands is undergone to exhaust, punching press hair
Motivation is closed, and guided missile enters unpowered hop segments.The range that final optimization pass obtains guided missile is 1912.3km, and the flight time is
1089.1s。
In 4 scheme of scheme, it is motor-driven that guided missile does not do jump, motors in boost phase penetration be it is high throw trajectory, then rushed in 35km height super burn
Hydraulic motor ignition operation, guided missile enter flat winged cruise section；After running out of gas, guided missile starts to dive downwards, finally obtains guided missile
Range be 990km, flight time 600s.
It compares this 4 kinds of trajectory schemes and can be seen that scheme 1 and provide best performance trajectory, range is existing air suction type
Flat 3.81 times for flying cruise trajectory of hypersonic missile, and the flying height that this trajectory is not fixed, have stronger prominent
Anti- ability.The main reason for this advantage, is that it is leaner that most of the time of the guided missile in boosting-Skipping trajectory is located at atmosphere
Airspace, flight kinetic energy rejection is smaller；On the other hand, scramjet engine is worked by the way of intermittent cyclical igniting, greatly
The service efficiency for improving fuel greatly, provides farther range for guided missile.
Claims (4)
1. a kind of air suction type hypersonic missile boosting-Jump probability optimization method, which is characterized in that the high ultrasound of the air suction type
Fast guided missile boosting-Jump probability optimization method the following steps are included:
Step 1: designing a kind of air suction type hypersonic missile trajectory of scramjet engine intermittent cyclical igniting, the super burn
The basic flight scenario of the air suction type hypersonic missile trajectory of punching engine intermittent cyclical igniting are as follows: described hypersonic to lead
Bullet is pushed to 25-60 km height by rocket booster, and after rocket booster separation, the hypersonic missile undergoes nothing first
Powerhop section, when the height of the hypersonic missile is down to 40 kms or less, speed is down to 1500m/s, ultra-combustion ramjet
Engine ignition work, the hypersonic missile is in motor-driven, the scramjet engine in Skipping trajectory of near space jump
It is worked by the way of intermittent cyclical igniting, to reduce the fuel consumption of engine；It is described hypersonic to lead after running out of gas
Bullet enters the unpowered jump flight stage, and when leaning on close-target, the hypersonic missile enters Trajectory-terminal, completes to dive and attack
It hits；
Step 2: establishing the air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion comprising side-jet control, specifically
Are as follows: ignore earth rotation and aspherical influence, it is assumed that precise tracking can provide continuously adjustable thrust, obtain described comprising straight
Relay control the air suction type hypersonic missile fore-and-aft plane overall trajectory equation of motion be；
In formula, m, v, h, α,θ respectively indicates guided missile quality, speed, terrain clearance, the angle of attack, pitch angle and trajectory tilt angle；L is
Range；P is motor power；FNFor the thrust of precise tracking；nyNormal g-load can be used for guided missile；Q is dynamic pressure；S is the plane of reference
Product；G is acceleration of gravity；R is earth mean radius；IspFor scramjet engine specific impulse；Cx,CyRespectively resistance coefficient and
Lift coefficient, they are the functions of the angle of attack and Mach number；
Step 3: building air suction type hypersonic missile boosting-Jump probability Optimized model, specifically: in state variable x (t)
When meeting air suction type hypersonic missile boosting-Jump probability constraint condition, seek optimum control variable u (t), so that performance
Index J minimalization；The air suction type hypersonic missile boosting-Jump probability Optimized model by trajectory be divided into motors in boost phase penetration and
It is optimized respectively with hop segments, using motors in boost phase penetration end energy as the performance indicator J of motors in boost phase penetrationMotors in boost phase penetration, JMotors in boost phase penetration=-(v2/2+
gh)|tf1, wherein tf1For motors in boost phase penetration finish time；Using range as the performance indicator J of hop segmentsHop segments,Its
InFor tfThe scope at moment, tfFor hop segments finish time；State variable x (t) takes parameter v, θ in the equation of motion,
H, L, m, i.e. x=(v, θ, h, L, m)T；In the case where only considering fore-and-aft plane movement, control variable is taken as angle of attack and rail control
Motor power FN, i.e. u=(α, FN)T；
Step 4: using trajectory optimisation model described in adaptive pseudo- spectrometry solution procedure 3.
2. a kind of air suction type hypersonic missile boosting-Jump probability optimization method, feature exist according to claim 1
In the air suction type hypersonic missile boosting-Jump probability constraint condition includes:
(1) normal g-load constrains
It is limited in the overload of the motors in boost phase penetration and the hop segments, guided missile by structural strength and airborne equipment ability to bear,
Have
|ny|≤nymax (2)
N in formulaymaxFor guided missile maximum permissible load factor；
(2) dynamic pressure constrains
Q in formulamaxFor the limitation of guided missile max-Q；
(3) hot-fluid constrains
Hot-fluid constraint is often referred to the limitation of the hot-fluid at aircraft surface stationary point, that is, has
In formulaFor guided missile maximum heat ductility limit system；
Stationary point heat flow density is calculate by the following formula:
In formula, kQIt is constant related with missile configuration and material, kQ=3.08 × 10-5；RNFor radius of curvature at stationary point, R is takenN
=0.02m；ρ is atmospheric density；V is missile velocity；
(4) angle of attack constrains
In order to reduce the perturbation of the separation between two-stage, it is necessary to limit the angle of attack size at booster separation moment:
α(tf1)=0 ° (6)
For the control requirement for meeting guided missile, control amount must be controlled in a certain range, and control amount is unable to acute variation, another
For aspect in hop segments, Scramjet Inlet is also restricted to the angle of attack when working normally, and thus leads to flight course
Playing the angle of attack has corresponding constraint:
In formula, t01For guided missile emission time in the sky, tf1For motors in boost phase penetration finish time, t02When lighting a fire for the first time for punching engine
It carves, tf2For the moment that runs out of gas, tfFor hop segments finish time；
(5) highly constrained
To reduce flight resistance when enabling guided missile high speed flight, while the firepower of ground environment being avoided to intercept as far as possible,
Guided missile should be made to be maintained at the flight of near space region, following limitation is made to its flying height:
25km≤h≤60km,tf1≤t≤tf (8)
(6) end conswtraint
Air suction type hypersonic missile enters Trajectory-terminal after hop segments, completes diving attack, to guarantee diving attack
There is enough kinetic energy, following end conswtraint made to hop segments trajectory:
H in formulafAnd vfRespectively tfThe height and speed of moment guided missile；
(7) precise tracking thrust constrains
It is limited by precise tracking quantity and specific impulse, the thrust F of precise trackingNHave certain limitations range
FN≤FNmax (10)
In formula, FNFor the thrust of precise tracking, FNmaxFor precise tracking maximum thrust；
(8) scramjet engine intermittent cyclical ignition condition
For the fuel consumption for reducing scramjet engine, engine is by the way of intermittent cyclical igniting in Skipping trajectory
Work, when experience trough starts to climb, and flying speed is down to speed of ignition lower limit 1500m/s, scramjet engine point
Firer makees；40km is risen to, engine misses, guided missile continues to climb by aircraft kinetic energy, and completes several jump wave bands, directly
It is decreased to speed of ignition lower limit to speed, engine is lighted a fire again；And so on until running out of gas, guided missile enters unpowered jump
Jump mission phase；Thus scramjet engine period ignition condition is obtained are as follows:
θ≥0°,h≤40km,v≤1500m/s,t02≤t≤tf2 (11)。
3. a kind of air suction type hypersonic missile boosting-Jump probability optimization method, feature exist according to claim 1
In, it is described trajectory optimisation problem solved using adaptive pseudo- spectrometry specifically includes the following steps:
Step 1: dividing network section as needed, and set and count matching for each section；
Step 2: on each network section, using global Gauss puppet spectrometry by state equation, objective function and constraint condition
Optimal control problem is converted nonlinear programming problem by discretization；
Step 3: solving nonlinear programming problem using sequential quadratic programming method；
Step 4: judging whether the corresponding quantity of state of each grid section midpoint and control amount meet the constraint essence of the equation of motion
Degree requires, and iteration terminates if meeting the requirements, and step 5 or step 6 are skipped to if being unsatisfactory for；
Step 5: if the magnitude of all elements is suitable in residual vector β, increasing with points, i.e. time of increase interpolation polynomial
Number；
Step 6: if the magnitude of certain elements is significantly greater than other elements in residual vector β, to corresponding grid section into
Row refinement；
Step 7: after all grid sections have all adjusted, return step 2 carries out next iteration.
4. a kind of air suction type hypersonic missile boosting-Jump probability optimization method, feature exist according to claim 1
In the hypersonic missile is the cruise body with Waverider structure.
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| CN103995540A (en) * | 2014-05-22 | 2014-08-20 | 哈尔滨工业大学 | Method for rapidly generating finite time track of hypersonic aircraft |
| CN106227972A (en) * | 2016-08-04 | 2016-12-14 | 北京航空航天大学 | A kind of optimization method of the steady glide trajectories of hypersonic aircraft |
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