CN107132765A - A kind of angle-of-attack based on trajectory planning and attack time control method - Google Patents
A kind of angle-of-attack based on trajectory planning and attack time control method Download PDFInfo
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Abstract
The invention discloses a kind of angle-of-attack based on trajectory planning and attack time control method, it is first assumed that the missile flight track planned is made up of arc section SA and straightway AT, and arc section SA radius is R;Straightway AT passes through target point T (xT,yT) and meet missiles ' terminal angle-of-attack for θfRequirement;Arc section SA originates in guided missile initial position S (x0,y0) and be tangential on point A (x undetermined with straightway ATa,ya), point A (xa,ya) by specified missile attack time tfObtained by iterative algorithm.On the basis of trajectory planning, a kind of Trajectory Tracking Control method based on virtual target is proposed:A kind of compound control scheme for feedovering plus feeding back is proposed in arc section, a kind of angle of sight PD control scheme is proposed in straightway, this method amount of calculation is small, it is easy to engineering construction.
Description
Technical field
The invention belongs to Anti-Ship Missile Attack angle and attack time control technology field, it is related to a kind of based on trajectory planning
Angle-of-attack and attack time control method.
Background technology
In order to solve to control the remaining time of proportional guidance law to estimate problem, Zhang Youan etc. with angle in the case of big angle of lead
People is in document Zhang Youan, Ma Guoxin, Wu Huali.A Biased Proportional Navigation
Guidance Law with Large Impact Angle Constraint and The Time-To-Go
Estimation.Proceedings of the Institution of Mechanical Engineers,Part G-
Journal of Aerospace Engineering, 2014,228 (10):By introducing one from convergent in 1725-1734
Angle α, constructs biasing ratio that a class is constrained with angle-of-attack (Impact Angle), being easy to obtain remaining time estimation and leads
Draw rule, first, under small angle of lead hypothesis, by by the system non-homogeneous differential equation under biasing proportional guidance law effect
Manage as homogeneous differential equation, obtained suitable for angle of lead it is smaller/angle-of-attack it is smaller in the case of remaining time estimation formulas;
When big angle of lead, using the thinking for being suitably segmented in remaining time interval, the phase during remaining time is resolved first
The function that variable is represented as angle α is closed, then using angle α variable quantity as iteration step length, is conservatively determined using method of geometry
Go out the value of the iteration step length, the increment to ensure angle of lead in every section of interval is solved as low-angle finally by segment iteration,
A kind of remaining time algorithm for estimating suitable for big angle of lead/any projected angle of impact constraint is obtained.But the calculating of this method
Process is more complicated.Document Zhao Yao, Sheng Yongzhi, Liu Xiangdong.Trajectory reshaping
based guidance with impact time and angle constraints.Chinese Journal of
Aeronautics,2016,29(4):In 984-994, the method being molded by track realize simultaneously to attack time and attack
The control of angle, but this method still inevitably needs the calculating process by complexity to calculate track to be flown in real time
Length, and the computational methods acquiescently assume that trajectory tilt angle is low-angle, but actual trajectory tilt angle may be wide-angle,
At this moment evaluated error in this way will be than larger.Document Ronny Tsalik, and Tal Shima.Inscribed
Angle Guidance.Journal of guidance,control,and dynamics,2015,38(1):30-40. in,
According to " when guided missile is moved from initial point along arc track to fixed target point, current location and the guided missile initial point of guided missile
Be constant value with the angle of circumference (inscribed angle) that fixed target point is formed " principle, it is proposed that a kind of 3 new rails
Mark shaping guidance concept.This method can produce the angle-of-attack of any direction.Track shaping guidance concept can be regarded as
It is the popularization that 3 classical sights (line-of-sight) are guided with concept.But this method is not accounted for attack time
Control.In order to overcome the shortcoming and deficiency of existing method, the angle of circumference that this method proposes Ronny Tsalik et al. is guided
Method is generalized to can be while be controlled to angle-of-attack and attack time.
The content of the invention
It is an object of the invention to provide a kind of angle-of-attack based on trajectory planning and attack time control method, solve
At present in the case of big angle of lead based on proportional guidance law/the remaining time estimations of the guidance laws such as proportional guidance law is controlled with angle
The problem of calculating process is complicated.
The inventive method is as follows:
The first step, for trajectory planning problem, it is considered to attack from horizon level plane as shown in Figure 1.XIOIYIRepresent ground inertia
System;Guided missile starting point is S (x0,y0);Target point is T (xT,yT);η is azimuth of target;VMIt is missile flight speed (it is assumed that permanent
Value);aMFor guided missile sidestep maneuver acceleration;If guided missile is from starting point S (x0,y0) set out, and initial velocity direction and S on circular arc
(x0,y0) point tangential direction it is consistent, then force the guided missile to be along the nominal sidestep maneuver acceleration that arc track flies strictlyThe center of circle that regulation points to circular arc is its positive direction;tfFor the specified missile attack time;θMNavigated for missile flight
Mark angle;θfFor specified missiles ' terminal angle-of-attack.(the θ in Fig. 1f< 0);ξ is between guided missile starting point velocity attitude and straight line SA
Angle.
According to Fig. 1, feasible tfSpan be:tf,min≤tf≤tf,max, wherein
tf,min=(dST/VM) × (∠ ATS/sin ∠ ATS),
tf,max=(dST/VM)×(sin∠ATS×(π/2)+cos∠ATS)
According to Fig. 1, it can obtain
ξ=∠ AST+ ∠ ATS, ∠ ATS=η-θf, η=arctan [(y0-yT)/(x0-xT)] (1)
Due to θfFor specified (known), in addition, guided missile starting point S (x0,y0) and target point T (xT,yT) it is known, η
It can be obtained by calculating, therefore, ∠ ATS=η-θfIt is known.
According to formula (1), ξ is calculated, only ∠ AST need to be calculated, accordingly determine point A (x undetermineda,ya)。
According to Fig. 1, the radius R that can obtain circular arc SA is R=dSA/ (2sin ξ), wherein, dSARepresent point S (x0,y0) arrive point A
(xa,ya) between air line distance.
According to Fig. 1, the nominal time T that guided missile flies along arc section SA can be obtained1For
T1=(2R/VM) ξ=(dSA/VM)×(ξ/sinξ) (2)
The nominal time T that guided missile flies along straightway AT2For T2=dAT/VM, wherein, dATRepresent straightway AT length.
The time t that guided missile flies along whole piece planned trajectoryfMeet tf=T1+T2。
By to the anti-solution of above formula, obtaining point A (x undetermineda,ya).The Approximating Solutions of its certain precision are obtained first
The basic ideas of solution are:First, arc section SA is approximately replaced with straightway SA, i.e., by tf≈(dSA+dAT)/
VM, reverse goes out A (xa,ya) an approximate solutionThen, with approximate solution obtained aboveAs initial
Value, by the method for iteration, further approaches its Exact Solutions A (xa,ya), finally give the Approximating Solutions for meeting certain required precision
By tf≈(dSA+dAT)/VM, first reverse goes out A (xa,ya) an initial approximate solutionIn formula,
In addition, straight line AT equation is y=yT+kL(x-xT), wherein, kLStraightway AT slope is represented, it is known
, by specified missiles ' terminal angle-of-attack θfIt is determined that, i.e. kL=tan θf, therefore, have
ya=yT+kL(xa-xT), (3)
Assuming that xT> xa, represent point A (x undetermineda,ya) it is in target point T (xT,yT) left side, by tf≈(dSA+dAT)/
VMAnd convolution (3), can approximately it obtain
xa≈-c/b, (4)
Wherein
The approximate solution is designated as
Convolution (3), can withIt is correspondingFor
Then, we have approximately obtained an approximate solutionIt can as following iterative algorithm initial value.
In initial approximation solutionOn the basis of, according to tf=T1+T2, using the method for iteration, can further obtain
More accurate Approximating Solutions
As accurate point A (xa,ya) with approximate pointInstead of when, corresponding accurate tfIt is changed into having errorTherefore, defineWith tfBetween error be
By approximate derivation, it can summarize and obtain approaching A (xa,ya) iterative algorithm it is as follows:
1) gives guided missile starting point S (x0,y0), target point T (xT,yT), missile flight speed VM;Specify the missile attack time
tf(the t specifiedfMeet tf,min≤tf≤tf,max, wherein, tf,min=(dST/VM) × (∠ ATS/sin ∠ ATS), tf,max=
(dST/VM) × (sin ∠ ATS × (pi/2)+cos ∠ ATS)) and missiles ' terminal angle-of-attack θf;The essence of given attack time estimation
Spend ε.
2) calculates kL=tan θf,η=arctan [(y0-yT)/(x0-xT)],
3) is calculated:
∠ ATS=η-θf,
Δya=kLΔxa,
4) is by step 3) formula calculate again one time, it is similar to calculate
5) calculates average
If 6)Then go to step 3), otherwise, go to step 7),
7) iteration terminates.
By iteration, it can finally obtain meeting the Approximating Solutions of certain exact requirements
Second step, for Trajectory Tracking Control problem, imaginary virtual target is with guided missile simultaneously from guided missile starting point S (x0,y0) go out
Hair, the size of their flying speed is identical.Virtual target strictly flies along the track of planning.If guided missile and virtual target
Initial velocity direction it is identical, the side acceleration that they are subject to is also identical, then guided missile also strictly along planning track fly,
Virtual target is all overlapped at any time with the position of guided missile.But this is ideal situation.In practical flight, virtual target with
The initial velocity direction of guided missile is likely to and differed, and guided missile is most likely subject to the interference in the external world in practical flight, flies it
Deviate the track of planning in row track.Accordingly, it would be desirable to force guided missile to fly as far as possible along the track of planning using certain method of guidance
OK.Overlapped for guided missile with virtual target initial position and its speed identical situation, proportional guidance is not applied to.
Therefore, the present invention proposes a kind of new guidance thought:Mark Tracking Control Scheme based on virtual target.Track following
The Trajectory Tracking Control problem of control problem cyclotomy segmental arc and the Trajectory Tracking Control problem of straightway.For the track of arc section
Tracking control problem proposes a kind of compound control scheme for feedovering plus feeding back, and feedforward control amount is the lateral acceleration of virtual target
Degree, feedback control is the ratio control of the difference at the flight track angle of virtual target and guided missile.For the track following control of straightway
Problem processed proposes a kind of PD control scheme at line of sight angle.
1) for the Trajectory Tracking Control problem of arc section, a kind of compound control scheme for feedovering plus feeding back is proposed:
The equation of motion of virtual target is as follows:
The primary condition of virtual target is:Initial position is:(xt(0),yt(0))=(x0,y0)。
The Approximating Solutions obtained according to iterationCalculate∠ AST, ∠ ATS, ξ (0) are as follows:
Therefore, the initial flight flight-path angle of virtual target is
θt(0)=ξ (0)+∠ AST+ η (10)
And
T1=(2R/VM)ξ(0) (11)
The equation of motion of guided missile:
The primary condition of Missile Motion is:(xM(0),yM(0))=(x0,y0), θM(0)=θt(0)+ΔθM(0), wherein,
ΔθM(0) it is the initial flight Track Angle Error for the guided missile assumed.
Turnaround section Guidance Law is
aM=at+kp(θM-θt) (13)
2) for the Trajectory Tracking Control problem of straightway, a kind of visual line angle PD control scheme of bullet is proposed, it is therefore an objective to make
The angle of fall of guided missile as requested strikes target, and the Guidance Law of straightway is
The beneficial effects of the invention are as follows to controlling proportional guidance law based on proportional guidance law/band angle in the case of big angle of lead
Remaining time estimation Deng guidance law calculates simple and efficiency high, it is easy to engineering construction.
Brief description of the drawings
Fig. 1 is planning trajectory schematic diagram provided in an embodiment of the present invention;
Fig. 2 (a) guided missile actual flight path angles and virtual target flight path angular curve;
Fig. 2 (b) guided missiles actual flight path and virtual target flight path (planning flight path) curve;
Fig. 2 (c) guided missiles actual acceleration and virtual target accelerating curve;
The difference curve of Fig. 2 (d) guided missiles actual position coordinate and virtual target position coordinates;
Time control error curve between Fig. 2 (e) guided missiles and virtual target;
Fig. 3 (a) guided missile actual flight path angles and virtual target flight path angular curve;
Fig. 3 (b) guided missiles actual flight path and virtual target flight path (planning flight path) curve;
Fig. 3 (c) guided missiles actual acceleration and virtual target accelerating curve;
The difference curve of Fig. 3 (d) guided missiles actual position coordinate and virtual target position coordinates;
Time control error curve between Fig. 3 (e) guided missiles and virtual target.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Specific implementation step is as follows:
The first step, point A (x are approached with iterative algorithma,ya), step is as follows:
1) gives guided missile starting point S (x0,y0), target point T (xT,yT), missile flight speed VM;Specify the missile attack time
tfWith missiles ' terminal angle-of-attack θf;The precision ε of given attack time estimation.
2) calculates kL=tan θf,η=arctan [(y0-yT)/(x0-xT)],
3) is calculated
∠ ATS=η-θf,
Δya=kLΔxa,
4) is by step 3) formula calculate again one time, it is similar to calculate
5) calculates average
If 6)Then go to step 3), otherwise, go to step 7),
7) iteration terminates.
By iteration, it can finally obtain meeting the Approximating Solutions of certain exact requirements
Second step, planning guided missile track, including arc section and straightway:The guided missile track of the planning is by following virtual mesh
The mark equation of motion is provided:
The primary condition of virtual target is:Initial position is:(xt(0),yt(0))=(x0,y0)。
The Approximating Solutions obtained according to iterationCalculate∠ AST, ∠ ATS, ξ (0) are as follows:
Therefore, the initial flight flight-path angle of virtual target is
θt(0)=ξ (0)+∠ AST+ η
And
T1=(2R/VM)ξ(0)
3rd step, the equation of motion for providing guided missile is as follows:
The primary condition of Missile Motion is:(xM(0),yM(0))=(x0,y0), θM(0)=θt(0)+ΔθM(0), wherein,
ΔθM(0) it is the initial flight Track Angle Error for the guided missile assumed.
4th step, carries out Trajectory Tracking Control:
Turnaround section Guidance Law is:
aM=at+kp(θM-θt)
The Guidance Law of straightway is:
The using effect of the present invention is described further by following emulation experiment:
Without loss of generality, can use guided missile M is origin (0m, 0m), and target T is located at first quartile.Take in iterative algorithm and attack
The precision ε of time Estimate is 0.01s, and simulation step length is taken as 0.001s.It is available when target T is located at other quadrants
The track that mirror on reference axis is planned.Target T is taken to be located at (5000m, 1500m), θf=-30 °, tf=13s,
ΔθM(0)=30 °, the flying speed V of guided missileM=500m/s.Simulation result is as shown in Fig. 2 simulation curve (tf=13s), wherein
Fig. 2 (a) guided missile actual flight path angles and virtual target flight path angular curve;Fig. 2 (b) guided missiles actual flight path and virtual target flight path (rule
Draw flight path) curve;Fig. 2 (c) guided missiles actual acceleration and virtual target accelerating curve;Fig. 2 (d) guided missiles actual position coordinate with
The difference curve of virtual target position coordinates;Time control error curve between Fig. 2 (e) guided missiles and virtual target;Calculated with iteration
Point A (x are approached obtained by method iteration 2 timesa,ya) coordinate be A (4017.6m, 2067.2m), ξ (0) be 57.2 °, plan flight path
Time control error be 0.01s.Fig. 2 (e) represent after virtual target is by target T 0.1145s, guided missile by target T,
That is, the time control error of guided missile is no more than 0.1245s.Guided missile is (actual for 0.2369m relative to the miss distance of target
Miss distance should be much smaller than the value because its value is influenceed by taken simulation step length size, simulation step length here is taken as
0.001s)。
Other conditions are constant, take tf=19s, the time error for planning flight path is still 0.01s.Simulation result is as shown in Figure 3
Simulation curve (tf=19s), wherein Fig. 3 (a) guided missiles actual flight path angle and virtual target flight path angular curve;Fig. 3 (b) guided missiles are actual
Flight path and virtual target flight path (planning flight path) curve;Fig. 3 (c) guided missiles actual acceleration and virtual target accelerating curve;Fig. 3
(d) the difference curve of guided missile actual position coordinate and virtual target position coordinates;Time between Fig. 3 (e) guided missiles and virtual target
Control error curve..Point A (x are approached with obtained by iterative algorithm iteration 3 timesa,ya) coordinate for A (1920.2m,
3278.1m), ξ (0) is 89.6 °.The 0.0032s after virtual target is by target T, guided missile passes through target T, that is to say, that lead
The time control error of bullet is no more than 0.0132s.Guided missile is 0.0476m relative to the miss distance of target.
Approximate iterative algorithm the convergence speed in trajectory planning it can be seen from simulation result is quickly, general to pass through
2-3 iteration, you can be met the requirement that attack time estimated accuracy is 0.01s, what is proposed is tracked based on virtual target
Arc section feedforward plus feedback compound control scheme and straightway bullet line of sight error PD control scheme, preferably realize
Controlled while to attack time with angle-of-attack.When the straightway in trajectory planning is longer, even if initial time guided missile
Heading with planning course bearing there is larger azimuthal error, final guided missile track almost also directly can pass through mesh
Punctuate (directs hit on the target), and the attack time control accuracy of guided missile can reach 0.0132s.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
Any modifications, equivalent substitutions and improvements made within refreshing and principle etc., should be included in the scope of the protection.
Claims (6)
1. a kind of angle-of-attack based on trajectory planning and attack time control method, it is characterised in that enter according to following steps
OK:
Step 1:It is assumed that the missile flight track planned is made up of arc section SA and straightway AT, according to specified missiles ' terminal
Angle-of-attack θfWith specified missile attack time tf, resolved by alternative manner and obtain separation A (xa,ya), arc section SA's
Radius R, and arc section SA flight time;
Step 2:With feedforward plus the compound control scheme of feedback, the arc section Trajectory Tracking Control based on virtual target is realized;
Step 3:With the visual line angle PD control scheme of bullet, straightway Trajectory Tracking Control is realized, makes the attack of guided missile as requested
Angle hit.
2. according to a kind of angle-of-attack based on trajectory planning described in claim 1 and attack time control method, its feature exists
In:In the step 1, if guided missile starting point is S (x0,y0), target point is T (xT,yT), η is azimuth of target, VMFor missile flight
Speed (it is assumed that constant), aMFor guided missile sidestep maneuver acceleration, if guided missile is from starting point S (x0,y0) set out, and initial velocity side
To with S (x on circular arc0,y0) point tangential direction it is consistent, then the nominal lateral machine for forcing guided missile strictly to be flown along arc track
Dynamic acceleration isThe center of circle that regulation points to circular arc is its positive direction, tfFor specified missile attack time, θMFor
Missile flight flight-path angle, θfFor specified missiles ' terminal angle-of-attack, ξ is the folder between guided missile starting point velocity attitude and straight line SA
Angle;
ξ=∠ AST+ ∠ ATS, ∠ ATS=η-θf, η=arctan [(y0-yT)/(x0-xT)] (1)
Circular arc SA radius R is R=dSA/ (2sin ξ), wherein, dSARepresent point S (x0,y0) arrive point A (xa,ya) between straight line away from
From;
The nominal time T that guided missile flies along arc section SA1For
T1=(2R/VM) ξ=(dSA/VM)×(ξ/sinξ) (2)
The nominal time T that guided missile flies along straightway AT2For T2=dAT/VM, wherein, dATRepresent straightway AT length, guided missile edge
The time t of whole piece planned trajectory flightfMeet tf=T1+T2;
By to the anti-solution of above formula, obtaining point A (x undetermineda,ya), the Approximating Solutions of its certain precision are obtained firstFirst
Arc section SA is approximately replaced with straightway SA, i.e., by tf≈(dSA+dAT)/VM, reverse goes out A (xa,ya) an approximate solutionThen, with approximate solution obtained aboveAs initial value, by the method for iteration, it is further approached
Exact Solutions A (xa,ya), finally give the Approximating Solutions for meeting certain required precision
3. according to a kind of angle-of-attack based on trajectory planning described in claim 1 and attack time control method, its feature exists
In:In the step 2, the compound control scheme of feedforward plus feedback is as follows:
The equation of motion of virtual target
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The Approximating Solutions obtained according to iterationCalculate∠ AST, ∠ ATS, ξ (0) are as follows:
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<mi>f</mi>
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<mrow>
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</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
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</mrow>
</mrow>
Therefore, the initial flight flight-path angle of virtual target is
θt(0)=ξ (0)+∠ AST+ η (10)
And
T1=(2R/VM)ξ(0) (11)
The equation of motion of guided missile:
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The primary condition of Missile Motion is:(xM(0),yM(0))=(x0,y0), θM(0)=θt(0)+ΔθM(0), wherein, Δ θM
(0) it is the initial flight Track Angle Error for the guided missile assumed, turnaround section Guidance Law is
aM=at+kp(θM-θt)。 (13)
4. according to a kind of angle-of-attack based on trajectory planning described in claim 1 and attack time control method, its feature exists
In:The Guidance Law of step 3 cathetus section is
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5. according to a kind of angle-of-attack based on trajectory planning described in claim 2 and attack time control method, its feature exists
In:The Approximating SolutionsSolution procedure is as follows:
By tf≈(dSA+dAT)/VM, first reverse goes out A (xa,ya) an initial approximate solutionIn formula,
In addition, straight line AT equation is y=yT+kL(x-xT), wherein, kLStraightway AT slope is represented, it is known, by referring to
Fixed missiles ' terminal angle-of-attack θfIt is determined that, i.e. kL=tan θf, therefore have
ya=yT+kL(xa-xT), (3)
Assuming that xT> xa, represent point A (x undetermineda,ya) it is in target point T (xT,yT) left side, by tf≈(dSA+dAT)/VMAnd
Convolution (3), is approximately obtained
xa≈-c/b, (4)
Wherein
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The approximate solution is designated as
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Convolution (3), can withIt is correspondingFor
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Then an approximate solution has approximately been obtainedIt is used as the initial value of following iterative algorithm;
In initial approximation solutionOn the basis of, according to tf=T1+T2, using the method for iteration, can further obtain more smart
True Approximating Solutions
As accurate point A (xa,ya) with approximate pointInstead of when, corresponding accurate tfIt is changed into having errorDefinitionWith tfBetween error be
By approximate derivation, obtain approaching A (xa,ya) iterative algorithm it is as follows:
1) gives guided missile starting point S (x0,y0), target point T (xT,yT), missile flight speed VM;Specify missile attack time tf, refer to
Fixed tfMeet tf,min≤tf≤tf,max, wherein, tf,min=(dST/VM) × (∠ ATS/sin ∠ ATS), tf,max=(dST/
VM) × (sin ∠ ATS × (pi/2)+cos ∠ ATS)) and missiles ' terminal angle-of-attack θf;The precision ε of given attack time estimation;
2) calculates kL=tan θf,η=arctan [(y0-yT)/(x0-xT)],
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3) is calculated:
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∠ ATS=η-θf,
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5) calculates average
If 6)Then go to step 3), otherwise, go to step 7),
7) iteration terminates;
By iteration, the Approximating Solutions for meeting certain exact requirements are finally given
6. according to a kind of angle-of-attack based on trajectory planning described in claim 2 and attack time control method, its feature exists
In:The tfSpan be:tf,min≤tf≤tf,max, wherein
tf,min=(dST/VM) × (∠ ATS/sin ∠ ATS),
tf,max=(dST/VM)×(sin∠ATS×(π/2)+cos∠ATS)。
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