CN109506517A - A kind of midcourse guidance Method of Trajectory Optimization of belt restraining - Google Patents
A kind of midcourse guidance Method of Trajectory Optimization of belt restraining Download PDFInfo
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- CN109506517A CN109506517A CN201811394403.3A CN201811394403A CN109506517A CN 109506517 A CN109506517 A CN 109506517A CN 201811394403 A CN201811394403 A CN 201811394403A CN 109506517 A CN109506517 A CN 109506517A
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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Abstract
The invention discloses a kind of midcourse guidance Method of Trajectory Optimization of belt restraining, the Method of Trajectory Optimization is handed over to the next shift speed for reducing terminal guidance in interceptor, method includes the following steps: optimizing trajectory according to the midcourse guidance of set belt restraining, the interceptor fore-and-aft plane overall trajectory equation of motion including trajectory constraint and end conswtraint is established, and constructs interceptor trajectory optimisation model；Using hp, adaptively pseudo- spectrometry carries out solving optimization to trajectory.The present invention can reduce terminal guidance in interceptor and hand over to the next shift speed, provide good terminal guidance state of flight, improve intersection accuracy, be a kind of trajectory mode of great prospect.
Description
Technical field
The invention belongs to missile trajectory optimization field more particularly to a kind of midcourse guidance Method of Trajectory Optimization of belt restraining.
Background technique
Traditional interceptor is when facing high-speed target, by guided missile time constant, steering engine reaction time and Guidance and control system
The limitation of the performances such as response speed of uniting, in the case where relative velocity is excessive, will lead to middle terminal guidance and hands over to the next shift unsuccessfully；Even if handing over to the next shift into
Function, guidance precision certainly will reduce, to influence interception model.
Feature big for high-speed target flight span and that feature is obvious, can be to the flight bullet in interceptor midcourse guidance stage
Road optimizes, and by designing track of climbing, using gravity to, which reduces interceptor, flies to the speed in area of handing over to the next shift, to reduce bullet mesh
Relative velocity, and while carrying out trajectory optimisation, it can also realize to the optimal of the important indicators such as flight time and energy
Change.At the same time, it is most important to final interception effect to enter the original state in terminal guidance stage for interceptor, by midcourse guidance
The trajectory in stage optimizes, and can further constrain the SOT state of termination, and interceptor is made to enter the terminal guidance stage with optimum posture.
Summary of the invention
Faced when intercepting high-speed target by excessive relative velocity cause middle terminal guidance hand over to the next shift failure aiming at the problem that, this hair
Bright to provide a kind of midcourse guidance Method of Trajectory Optimization of belt restraining, the present invention can reduce terminal guidance in interceptor and hand over to the next shift speed, mention
For good terminal guidance state of flight, intersection accuracy is improved.
The invention is realized in this way a kind of midcourse guidance Method of Trajectory Optimization of belt restraining, the Method of Trajectory Optimization is used
It hands over to the next shift speed in reducing terminal guidance in interceptor, method includes the following steps:
Optimize trajectory according to the midcourse guidance of set belt restraining, establishes the interceptor including trajectory constraint and end conswtraint
The fore-and-aft plane overall trajectory equation of motion, and construct interceptor trajectory optimisation model；
Using hp, adaptively pseudo- spectrometry carries out solving optimization to trajectory.
Preferably, the midcourse guidance optimization trajectory setting of the belt restraining are as follows: after the interceptor completes cruise section, according to height
Fast target information is flown in the midcourse guidance stage according to optimization trajectory, using descent trajectory of climbing, using gravity reduce in end
Speed of handing over to the next shift is guided, flight attitude is adjusted, to provide good flying condition for terminal guidance, improves intersection accuracy.
Preferably, ignore earth rotation and aspherical influence, the interceptor fore-and-aft plane overall trajectory equation of motion tool
Body are as follows:
In formula (1),Respectively indicate guided missile quality, speed, terrain clearance, the angle of attack, pitch angle and trajectory
Inclination 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
For area of reference；G is acceleration of gravity；R is earth mean radius；IspFor scramjet engine specific impulse；Cx,CyRespectively hinder
Force coefficient and lift coefficient are the functions of the angle of attack and Mach number；
The constraint of its trajectory are as follows:
(1) normal g-load constrains
Interceptor is limited in flight course by structural strength and airborne equipment ability to bear,
Its normal g-load constraint representation are as follows:
|ny|≤nymax (2)
In formula (1), nymaxFor guided missile maximum permissible load factor；
(2) dynamic pressure constrains
In formula (2), ρ is atmospheric density, and v is interceptor speed, qmaxFor 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, usesIndicate interceptor hot-fluid, restriction table
It is shown as:
In formula (4),For guided missile maximum heat ductility limit system；
Stationary point heat flow density is calculate by the following formula:
In formula (5), kQIt is constant related with missile configuration and material, kQ=3.08 × 10-5；RNFor curvature at stationary point half
Diameter takes RN=0.02m；ρ is atmospheric density；V is missile velocity；
(4) angle of attack constrains
For the control requirement for meeting interceptor, control amount must be controlled in a certain range, and control amount cannot acutely become
Change, therefore the angle of attack as control amount needs to meet certain constraint condition.On the other hand have in the guided missile angle of attack of flight course
Corresponding constraint:
In formula (6), α1And α2Indicate angle of attack maximum value, t0Indicate that interceptor starts the initial time of trajectory optimisation, t1To block
Cut bullet fly to optimization trajectory peak at the time of, tfIndicate that terminal guidance is handed over to the next shift the moment in trajectory optimisation end；
(5) highly constrained
Optimization trajectory is divided into climb section and descending branch, therefore is handed over to the next shift according to terminal guidance in target position information and end to height
The requirement of degree, interceptor can be indicated in optimization the highly constrained of trajectory are as follows:
In formula (7), h1min h1maxInterceptor is respectively indicated in the height minima and maximum value for section of climbing, h2min h2max
Interceptor is respectively indicated in the height minima and maximum value of descending branch, t0Indicate interceptor start trajectory optimisation it is initial when
It carves, t1At the time of flight for interceptor to optimization trajectory peak, tfIndicate that terminal guidance is handed over to the next shift the moment in trajectory optimisation end；
Its end conswtraint are as follows:
In order to which terminal guidance is handed over to the next shift speed in reducing, adjustment interceptor enters the state of flight of terminal guidance, needs to interceptor
Speed v, height h and trajectory tilt angle θ constrained.Further, since interceptor height and high speed mesh after trajectory optimisation
Absolute altitude degree is different, and corresponding state especially height is different with the constraint representation of trajectory tilt angle, specifically: when interceptor height is high
When target, end conswtraint is indicated are as follows:
In formula (8), vf, vfminAnd vfmaxRespectively indicate interceptor terminal velocity, terminal velocity minimum value and maximum value, hf1,
hfmin1And hfmax1Respectively indicate interceptor terminal height, terminal height minima and maximum value, θf1, θfmin1And θfmax1Table respectively
Show interceptor terminal trajectory tilt angle, terminal trajectory tilt angle minimum value and maximum value；
When interceptor height is lower than target, end conswtraint is indicated are as follows:
In formula (9), vf, vfminAnd vfmaxRespectively indicate interceptor terminal velocity, terminal velocity minimum value and maximum value, hf2,
hfmin2And hfmax2Respectively indicate interceptor terminal height, terminal height minima and maximum value, θf2, θfmin2And θfmax2Table respectively
Show interceptor terminal trajectory tilt angle, terminal trajectory tilt angle minimum value and maximum value.
Preferably, the interceptor trajectory optimisation model specifically:
When state variable x (t) meets trajectory constraint condition, seek optimum control variable u (t), so that performance indicator J takes
Minimum；
The performance indicator of the trajectory optimized should be Jt0And tfRespectively indicate trajectory optimisation beginning and end
At the time of, the physical meaning of this performance indicator J is the flight time；
State variable x (t) takes the parameter in the equation of motion, i.e. x=[v, θ, h, L]T, only considering fore-and-aft plane movement
In the case of, control variable is taken as angle of attack i.e. u=α.
Preferably, it is described using hp adaptively pseudo- spectrometry solving optimization is carried out to trajectory the following steps are included:
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.
Compared with the prior art the shortcomings that and deficiency, the invention has the following advantages: the present invention can reduce interception
Terminal guidance is handed over to the next shift speed in bullet, provides good terminal guidance state of flight, is improved intersection accuracy, is a kind of trajectory of great prospect
Mode.
Detailed description of the invention
Fig. 1 is that the midcourse guidance of belt restraining of the present invention optimizes the basic trajectory schematic diagram of trajectory；
Fig. 2 is present invention optimization Ballistic Simulation of Underwater curve；
Fig. 3 is the height change curve of present invention optimization trajectory；
Fig. 4 is the speed change curves of present invention optimization trajectory；
Fig. 5 is the trajectory tilt angle change curve of present invention optimization trajectory；
Fig. 6 is the angle of attack variation curve of present invention optimization trajectory.
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 further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
The present invention provides the midcourse guidance Method of Trajectory Optimization of belt restraining, and the Method of Trajectory Optimization is for reducing interceptor
Middle terminal guidance is handed over to the next shift speed, method includes the following steps:
S1, trajectory is optimized according to the midcourse guidance of set belt restraining, establishing includes that trajectory constraint and end conswtraint are blocked
It cuts and plays the fore-and-aft plane overall trajectory equation of motion, and construct interceptor trajectory optimisation model.
In step sl, the midcourse guidance of the belt restraining optimizes trajectory, as shown in Figure 1, setting are as follows: the interceptor is completed
After cruise section, according to high-speed target information, fly in the midcourse guidance stage according to optimization trajectory, using descent trajectory of climbing,
Using gravity reduce in terminal guidance hand over to the next shift speed, adjust flight attitude, to provide good flying condition for terminal guidance, raising is blocked
Cut precision.
In step sl, ignore earth rotation and aspherical influence, the interceptor fore-and-aft plane overall trajectory movement side
Journey specifically:
In formula (1),Respectively indicate guided missile quality, speed, terrain clearance, the angle of attack, pitch angle and trajectory
Inclination 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
For area of reference；G is acceleration of gravity；R is earth mean radius；IspFor scramjet engine specific impulse；Cx,CyRespectively hinder
Force coefficient and lift coefficient are the functions of the angle of attack and Mach number；
The constraint of its trajectory are as follows:
(1) normal g-load constrains
Interceptor is limited in flight course by structural strength and airborne equipment ability to bear, normal g-load constraint
It indicates are as follows:
|ny|≤nymax (2)
In formula (1), nymaxFor guided missile maximum permissible load factor；
(2) dynamic pressure constrains
In formula (2), ρ is atmospheric density, and v is interceptor speed, qmaxFor 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, usesIndicate interceptor hot-fluid, restriction table
It is shown as:
In formula (4),For guided missile maximum heat ductility limit system；
Stationary point heat flow density is calculate by the following formula:
In formula (5), kQIt is constant related with missile configuration and material, kQ=3.08 × 10-5；RNFor curvature at stationary point half
Diameter takes RN=0.02m；ρ is atmospheric density；V is missile velocity；
(4) angle of attack constrains
For the control requirement for meeting interceptor, control amount must be controlled in a certain range, and control amount cannot acutely become
Change, therefore the angle of attack as control amount needs to meet certain constraint condition.On the other hand have in the guided missile angle of attack of flight course
Corresponding constraint:
In formula (6), α1And α2Indicate angle of attack maximum value, t0Indicate that interceptor starts the initial time of trajectory optimisation, t1To block
Cut bullet fly to optimization trajectory peak at the time of, tfIndicate that terminal guidance is handed over to the next shift the moment in trajectory optimisation end；
(5) highly constrained
Optimization trajectory is divided into climb section and descending branch, therefore is handed over to the next shift according to terminal guidance in target position information and end to height
The requirement of degree, interceptor can be indicated in optimization the highly constrained of trajectory are as follows:
In formula (7), h1min h1maxInterceptor is respectively indicated in the height minima and maximum value for section of climbing, h2min h2max
Interceptor is respectively indicated in the height minima and maximum value of descending branch, t0Indicate interceptor start trajectory optimisation it is initial when
It carves, t1At the time of flight for interceptor to optimization trajectory peak, tfIndicate that terminal guidance is handed over to the next shift the moment in trajectory optimisation end；
Its end conswtraint are as follows:
In order to which terminal guidance is handed over to the next shift speed in reducing, adjustment interceptor enters the state of flight of terminal guidance, needs to interceptor
Speed v, height h and trajectory tilt angle θ constrained.Further, since interceptor height and high speed mesh after trajectory optimisation
Absolute altitude degree is different, and corresponding state especially height is different with the constraint representation of trajectory tilt angle, specifically: when interceptor height is high
When target, end conswtraint is indicated are as follows:
In formula (8), vf, vfminAnd vfmaxRespectively indicate interceptor terminal velocity, terminal velocity minimum value and maximum value, hf1,
hfmin1And hfmax1Respectively indicate interceptor terminal height, terminal height minima and maximum value, θf1, θfmin1And θfmax1Table respectively
Show interceptor terminal trajectory tilt angle, terminal trajectory tilt angle minimum value and maximum value；
When interceptor height is lower than target, end conswtraint is indicated are as follows:
In formula (9), vf, vfminAnd vfmaxRespectively indicate interceptor terminal velocity, terminal velocity minimum value and maximum value, hf2,
hfmin2And hfmax2Respectively indicate interceptor terminal height, terminal height minima and maximum value, θf2, θfmin2And θfmax2Table respectively
Show interceptor terminal trajectory tilt angle, terminal trajectory tilt angle minimum value and maximum value.
In step sl, the interceptor trajectory optimisation model specifically: meet trajectory constraint item in state variable x (t)
When part, seek optimum control variable u (t), so that performance indicator J minimalization；
The interceptor midcourse guidance perfecting by stage trajectory the purpose is to reduce terminal velocity, that is, in terminal guidance hand over to the next shift speed
Degree considers that targeted cache characteristic, the performance indicator of the trajectory optimized should bet0And tfIt is excellent to respectively indicate trajectory
At the time of changing beginning and end, the physical meaning of this performance indicator J is the flight time.
State variable x (t) takes the parameter in the equation of motion, i.e. x=[v, θ, h, L]T；Only considering fore-and-aft plane movement
In the case of, control variable is taken as angle of attack i.e. u=α.
S2, using hp, adaptively pseudo- spectrometry carries out solving optimization to trajectory.
In step s 2, it is described using hp adaptively pseudo- spectrometry solving optimization is carried out to trajectory the following steps are included:
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.
In practical application of the invention, trajectory optimisation is carried out for the trajectory scheme under different sparking mode, and analyze
The performance superiority and inferiority of different schemes.Simulated conditions are as follows: state variable primary condition: v0=1800m/s, θ0=0 °, h0=25km,
L0=0km, m0=400kg；Trajectory constraint is as shown in table 1:
The constraint of 1 trajectory of table
Its height is higher than object height at the end of considering interceptor trajectory optimisation, then end conswtraint, which is arranged, is
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 Fig. 2~Fig. 6.
The trajectory of optimization takes the trajectory side first climbed and declined afterwards it can be seen from Fig. 2~simulation result shown in fig. 6
Case, maximum height of climbing are 42km, and flight maximum speed reaches 3000m/s, by optimizing trajectory, at the end of final midcourse guidance
Interceptor height is 26km, and speed 1082.43m/s, trajectory tilt angle is -30 degree, all meets end conswtraint；Meanwhile the angle of attack,
The major parameters such as trajectory tilt angle, speed and height also all meet trajectory constraint.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (5)
1. a kind of midcourse guidance Method of Trajectory Optimization of belt restraining, the Method of Trajectory Optimization is handed over for reducing terminal guidance in interceptor
Class's speed, which is characterized in that method includes the following steps:
Optimize trajectory according to the midcourse guidance of set belt restraining, establishing includes that trajectory constraint and the interceptor of end conswtraint are longitudinal
The plane overall trajectory equation of motion, and construct interceptor trajectory optimisation model；
Using hp, adaptively pseudo- spectrometry carries out solving optimization to trajectory.
2. the midcourse guidance Method of Trajectory Optimization of belt restraining as described in claim 1, which is characterized in that the middle system of the belt restraining
Lead optimization trajectory setting are as follows: after the interceptor completes cruise section, according to high-speed target information, in the midcourse guidance stage according to optimization
Trajectory flies, using descent trajectory of climbing, using gravity reduce in terminal guidance hand over to the next shift speed, adjust flight attitude, with for
Terminal guidance provides good flying condition, improves intersection accuracy.
3. the midcourse guidance Method of Trajectory Optimization of belt restraining as described in claim 1, which is characterized in that ignore earth rotation and non-
Spherical influence, the interceptor fore-and-aft plane overall trajectory equation of motion specifically:
In formula (1), m, v, h, α,θ respectively indicates guided missile quality, speed, terrain clearance, the angle of attack, pitch angle and trajectory tilt angle；L
For 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 reference
Area；G is acceleration of gravity；R is earth mean radius；IspFor scramjet engine specific impulse；Cx,CyRespectively resistance coefficient
And lift coefficient, it is the function of the angle of attack and Mach number；
Wherein, trajectory, which constrains, includes:
(1) normal g-load constrains
Its constraint representation are as follows:
|ny|≤nymax (2)
In formula (2), nymaxFor guided missile maximum permissible load factor；
(2) dynamic pressure constrains
Its constraint representation are as follows:
In formula (3), ρ is atmospheric density, and v is interceptor speed, qmaxFor the limitation of guided missile max-Q；
(3) hot-fluid constrains
WithIndicate interceptor hot-fluid, constraint representation are as follows:
Formula (4), inFor guided missile maximum heat ductility limit system；
Stationary point heat flow density is calculate by the following formula:
In formula (5), 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
Its constraint representation are as follows:
In formula (6), α1And α2Indicate angle of attack maximum value, t0Indicate that interceptor starts the initial time of trajectory optimisation, t1For interceptor
At the time of at flight to optimization trajectory peak, tfIndicate that terminal guidance is handed over to the next shift the moment in trajectory optimisation end；
(5) highly constrained
Its constraint representation are as follows:
In formula (7), h1min h1maxInterceptor is respectively indicated in the height minima and maximum value for section of climbing, h2min h2maxTable respectively
Show interceptor in the height minima and maximum value of descending branch, t0Indicate that interceptor starts the initial time of trajectory optimisation, t1To block
Cut bullet fly to optimization trajectory peak at the time of, tfIndicate that terminal guidance is handed over to the next shift the moment in trajectory optimisation end；
When interceptor height is higher than target, the end conswtraint is indicated are as follows:
In formula (8), vf, vfminAnd vfmaxRespectively indicate interceptor terminal velocity, terminal velocity minimum value and maximum value, hf1, hfmin1
And hfmax1Respectively indicate interceptor terminal height, terminal height minima and maximum value, θf1, θfmin1And θfmax1It respectively indicates and blocks
It cuts and plays terminal trajectory tilt angle, terminal trajectory tilt angle minimum value and maximum value.
When interceptor height is lower than target, the end conswtraint is indicated are as follows:
In formula (9), vf, vfminAnd vfmaxRespectively indicate interceptor terminal velocity, terminal velocity minimum value and maximum value, hf2, hfmin2
And hfmax2Respectively indicate interceptor terminal height, terminal height minima and maximum value, θf2, θfmin2And θfmax2It respectively indicates and blocks
It cuts and plays terminal trajectory tilt angle, terminal trajectory tilt angle minimum value and maximum value.
4. the midcourse guidance Method of Trajectory Optimization of belt restraining as described in claim 1, which is characterized in that the interceptor trajectory is excellent
Change model specifically:
When state variable x (t) meets trajectory constraint condition, seek optimum control variable u (t) so that performance indicator J take it is minimum
Value；
The performance indicator of the trajectory optimized should bet0And tfRespectively indicate trajectory optimisation beginning and end when
It carves, the physical meaning of this performance indicator J is the flight time；
State variable x (t) takes the parameter in the equation of motion, i.e. x=[v, θ, h, L]T, the case where only considering fore-and-aft plane movement
Under, control variable is taken as angle of attack i.e. u=α.
5. the midcourse guidance Method of Trajectory Optimization of belt restraining as described in claim 1, which is characterized in that described adaptive using hp
Pseudo- spectrometry to trajectory carry out solving optimization the following steps are included:
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.
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