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 PDF

Info

Publication number
CN107132765A
CN107132765A CN201710402532.1A CN201710402532A CN107132765A CN 107132765 A CN107132765 A CN 107132765A CN 201710402532 A CN201710402532 A CN 201710402532A CN 107132765 A CN107132765 A CN 107132765A
Authority
CN
China
Prior art keywords
msub
mrow
mover
angle
attack
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.)
Granted
Application number
CN201710402532.1A
Other languages
Chinese (zh)
Other versions
CN107132765B (en
Inventor
张友安
梁勇
鲍虎
孙玉梅
张彦飞
吴华丽
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.)
Yantai Nanshan University
Naval Aeronautical Engineering Institute of PLA
Original Assignee
Yantai Nanshan University
Naval Aeronautical Engineering Institute of PLA
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 Yantai Nanshan University, Naval Aeronautical Engineering Institute of PLA filed Critical Yantai Nanshan University
Priority to CN201710402532.1A priority Critical patent/CN107132765B/en
Publication of CN107132765A publication Critical patent/CN107132765A/en
Application granted granted Critical
Publication of CN107132765B publication Critical patent/CN107132765B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/107—Simultaneous control of position or course in three dimensions specially adapted for missiles
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/12—Target-seeking control

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Algebra (AREA)
  • Pure & Applied Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Medicines Containing Antibodies Or Antigens For Use As Internal Diagnostic Agents (AREA)
  • Aiming, Guidance, Guns With A Light Source, Armor, Camouflage, And Targets (AREA)

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

A kind of angle-of-attack based on trajectory planning and attack time control method
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
<mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <msub> <mi>cos&amp;theta;</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <msub> <mi>sin&amp;theta;</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>t</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>a</mi> <mi>t</mi> </msub> <mo>/</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
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：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>A</mi> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;angle;</mo> <mi>A</mi> <mi>S</mi> <mi>T</mi> <mo>=</mo> <mi>arccos</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>d</mi> <mrow> <mi>S</mi> <mi>T</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>A</mi> <mi>T</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mi>d</mi> <mrow> <mi>S</mi> <mi>T</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;angle;</mo> <mi>A</mi> <mi>T</mi> <mi>S</mi> <mo>=</mo> <mi>&amp;eta;</mi> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>f</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;xi;</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;angle;</mo> <mi>A</mi> <mi>S</mi> <mi>T</mi> <mo>+</mo> <mo>&amp;angle;</mo> <mi>A</mi> <mi>T</mi> <mi>S</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </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：
<mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>M</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <msub> <mi>cos&amp;theta;</mi> <mi>M</mi> </msub> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>M</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <msub> <mi>sin&amp;theta;</mi> <mi>M</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>M</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>a</mi> <mi>M</mi> </msub> <mo>/</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
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
<mrow> <msub> <mi>a</mi> <mi>M</mi> </msub> <mo>=</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>M</mi> </msub> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>d</mi> </msub> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>M</mi> </msub> <mo>.</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
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
<mrow> <mi>c</mi> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>f</mi> </msub> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>-</mo> <msqrt> <mrow> <mn>1</mn> <mo>+</mo> <msubsup> <mi>k</mi> <mi>L</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mi>x</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow>
The approximate solution is designated as
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>c</mi> <mo>/</mo> <mi>b</mi> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Convolution (3), can withIt is correspondingFor
<mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>=</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
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)],
<mrow> <mi>b</mi> <mo>=</mo> <mn>2</mn> <msub> <mi>t</mi> <mi>f</mi> </msub> <msub> <mi>V</mi> <mi>M</mi> </msub> <msqrt> <mrow> <mn>1</mn> <mo>+</mo> <msubsup> <mi>k</mi> <mi>L</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>k</mi> <mi>L</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <mi>c</mi> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>f</mi> </msub> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>-</mo> <msqrt> <mrow> <mn>1</mn> <mo>+</mo> <msubsup> <mi>k</mi> <mi>L</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mi>x</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>,</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>c</mi> <mo>/</mo> <mi>b</mi> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>=</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
3) is calculated:
<mrow> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>A</mi> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>,</mo> </mrow>
<mrow> <mo>&amp;angle;</mo> <mi>A</mi> <mi>S</mi> <mi>T</mi> <mo>=</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>d</mi> <mrow> <mi>S</mi> <mi>T</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>A</mi> <mi>T</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mi>d</mi> <mrow> <mi>S</mi> <mi>T</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow>
∠ ATS=η-θf,
<mrow> <mover> <mi>&amp;xi;</mi> <mo>^</mo> </mover> <mo>=</mo> <mo>&amp;angle;</mo> <mi>A</mi> <mi>S</mi> <mi>T</mi> <mo>+</mo> <mo>&amp;angle;</mo> <mi>A</mi> <mi>T</mi> <mi>S</mi> <mo>,</mo> </mrow>
<mrow> <msub> <mover> <mi>t</mi> <mo>^</mo> </mover> <mi>f</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mover> <mi>&amp;xi;</mi> <mo>^</mo> </mover> <mo>/</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mover> <mi>&amp;xi;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>A</mi> <mi>T</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;Delta;t</mi> <mi>f</mi> </msub> <mo>=</mo> <mover> <mi>t</mi> <mo>^</mo> </mover> <mo>-</mo> <msub> <mi>t</mi> <mi>f</mi> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mover> <mi>k</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;Delta;x</mi> <mi>a</mi> </msub> <mo>&amp;ap;</mo> <mo>-</mo> <msub> <mi>&amp;Delta;t</mi> <mi>f</mi> </msub> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>/</mo> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mover> <mi>&amp;xi;</mi> <mo>^</mo> </mover> <mo>/</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mover> <mi>&amp;xi;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>k</mi> <mi>L</mi> </msub> <msub> <mover> <mi>k</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msup> <msub> <mi>k</mi> <mi>L</mi> </msub> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mover> <mi>d</mi> <mo>^</mo> </mover> <mrow> <mi>A</mi> <mi>T</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow>
Δya=kLΔxa,
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>&amp;LeftArrow;</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;x</mi> <mi>a</mi> </msub> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>&amp;LeftArrow;</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;y</mi> <mi>a</mi> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>a</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mi>a</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>,</mo> <msub> <mover> <mi>t</mi> <mo>^</mo> </mover> <mrow> <mi>f</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>t</mi> <mo>^</mo> </mover> <mi>f</mi> </msub> <mo>,</mo> </mrow>
4) is by step 3) formula calculate again one time, it is similar to calculate
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>&amp;LeftArrow;</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;x</mi> <mi>a</mi> </msub> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>&amp;LeftArrow;</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;y</mi> <mi>a</mi> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>a</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mi>a</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>a</mi> </msub> <mo>,</mo> <msub> <mover> <mi>t</mi> <mo>^</mo> </mover> <mrow> <mi>f</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>t</mi> <mo>^</mo> </mover> <mi>f</mi> </msub> <mo>,</mo> </mrow>
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)。
CN201710402532.1A 2017-06-01 2017-06-01 Attack angle and attack time control method based on trajectory planning Active CN107132765B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710402532.1A CN107132765B (en) 2017-06-01 2017-06-01 Attack angle and attack time control method based on trajectory planning

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710402532.1A CN107132765B (en) 2017-06-01 2017-06-01 Attack angle and attack time control method based on trajectory planning

Publications (2)

Publication Number Publication Date
CN107132765A true CN107132765A (en) 2017-09-05
CN107132765B CN107132765B (en) 2020-04-28

Family

ID=59733517

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710402532.1A Active CN107132765B (en) 2017-06-01 2017-06-01 Attack angle and attack time control method based on trajectory planning

Country Status (1)

Country Link
CN (1) CN107132765B (en)

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108416098A (en) * 2018-02-02 2018-08-17 北京航空航天大学 A kind of attack time constraint Design of Guidance Law method intercepting maneuvering target
CN108469832A (en) * 2018-02-07 2018-08-31 北京航天时代激光导航技术有限责任公司 A kind of Servo Control method and system under automatic Pilot
CN110414159A (en) * 2019-08-01 2019-11-05 北京航空航天大学 A kind of angle-of-attack constraint method of guidance based on round involute
CN110457647A (en) * 2019-07-29 2019-11-15 上海机电工程研究所 A kind of rotary missile bullet mesh experience time estimation method
CN110703793A (en) * 2019-11-13 2020-01-17 中国人民解放军海军航空大学 Method for attacking maneuvering target by adopting aircraft integral proportion guidance of attitude angle measurement
CN111290418A (en) * 2020-03-02 2020-06-16 中国人民解放军海军航空大学 Small micro-aircraft non-stable loop precise differential guidance method
CN113805605A (en) * 2021-08-30 2021-12-17 湖北航天技术研究院总体设计所 Flight trajectory planning method and system
CN113834385A (en) * 2021-09-08 2021-12-24 中国人民解放军91776部队 Two-dimensional cooperative guidance method for control time of initial track angle freedom
CN113835439A (en) * 2021-09-08 2021-12-24 中国人民解放军91776部队 Two-dimensional cooperative guidance method for control time and angle of initial track angle freedom
CN114326813A (en) * 2021-12-31 2022-04-12 北京航天自动控制研究所 Method and system for predicting remaining flight time of unpowered aircraft
CN115001855A (en) * 2022-07-18 2022-09-02 南京理工大学 Deep reinforcement learning intelligent agent selection attack method based on track approximation
CN116663239A (en) * 2023-04-24 2023-08-29 四川大学 Missile escape area attack distance calculation method based on golden section method
CN118012079A (en) * 2024-04-10 2024-05-10 西安现代控制技术研究所 Multi-angle attack lateral nominal track generation method based on overload capacity

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2999023B2 (en) * 1991-07-31 2000-01-17 三菱重工業株式会社 Flying object control device
CN102706217A (en) * 2012-04-17 2012-10-03 北京理工大学 Method for controlling attack angle and attack time of multiple missiles
CN104035335A (en) * 2014-05-27 2014-09-10 北京航空航天大学 High accuracy longitudinal and cross range analytical prediction method based smooth gliding reentry guidance method
CN104077469A (en) * 2014-05-28 2014-10-01 中国人民解放军海军航空工程学院 Speed prediction based segmentation iteration remaining time estimation method
CN105005311A (en) * 2015-07-29 2015-10-28 中国人民解放军海军航空工程学院 Aircraft pitch channel attack angle synchronous tracking control method

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2999023B2 (en) * 1991-07-31 2000-01-17 三菱重工業株式会社 Flying object control device
CN102706217A (en) * 2012-04-17 2012-10-03 北京理工大学 Method for controlling attack angle and attack time of multiple missiles
CN104035335A (en) * 2014-05-27 2014-09-10 北京航空航天大学 High accuracy longitudinal and cross range analytical prediction method based smooth gliding reentry guidance method
CN104077469A (en) * 2014-05-28 2014-10-01 中国人民解放军海军航空工程学院 Speed prediction based segmentation iteration remaining time estimation method
CN105005311A (en) * 2015-07-29 2015-10-28 中国人民解放军海军航空工程学院 Aircraft pitch channel attack angle synchronous tracking control method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
TSALIK R,SHIMA T: "Inscribed angle guidance", 《JOURNAL OF GUIDANCE，CONTROL AND DYNAMICS》 *
ZHAO Y,SHENG Y Z,LIU X D: "Trajectory reshaping based guidance with impact time and angle constraints", 《CHINESE JOURNAL OF AERONAUTICS》 *
周须峰，孟博: "空空导弹越肩发射的虚拟目标比例导引律", 《飞行力学》 *

Cited By (23)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108416098A (en) * 2018-02-02 2018-08-17 北京航空航天大学 A kind of attack time constraint Design of Guidance Law method intercepting maneuvering target
CN108416098B (en) * 2018-02-02 2021-07-16 北京航空航天大学 Attack time constraint guidance law design method for intercepting maneuvering target
CN108469832A (en) * 2018-02-07 2018-08-31 北京航天时代激光导航技术有限责任公司 A kind of Servo Control method and system under automatic Pilot
CN108469832B (en) * 2018-02-07 2020-06-09 北京航天时代激光导航技术有限责任公司 Turning control method and system under automatic driving
CN110457647A (en) * 2019-07-29 2019-11-15 上海机电工程研究所 A kind of rotary missile bullet mesh experience time estimation method
CN110457647B (en) * 2019-07-29 2020-09-18 上海机电工程研究所 Method for estimating bullet encounter time of rotating missile
CN110414159A (en) * 2019-08-01 2019-11-05 北京航空航天大学 A kind of angle-of-attack constraint method of guidance based on round involute
CN110703793A (en) * 2019-11-13 2020-01-17 中国人民解放军海军航空大学 Method for attacking maneuvering target by adopting aircraft integral proportion guidance of attitude angle measurement
CN110703793B (en) * 2019-11-13 2022-06-24 中国人民解放军海军航空大学 Method for attacking maneuvering target by adopting aircraft integral proportion guidance of attitude angle measurement
CN111290418A (en) * 2020-03-02 2020-06-16 中国人民解放军海军航空大学 Small micro-aircraft non-stable loop precise differential guidance method
CN111290418B (en) * 2020-03-02 2022-05-10 中国人民解放军海军航空大学 Small micro-aircraft non-stable loop precise differential guidance method
CN113805605A (en) * 2021-08-30 2021-12-17 湖北航天技术研究院总体设计所 Flight trajectory planning method and system
CN113805605B (en) * 2021-08-30 2023-08-01 湖北航天技术研究院总体设计所 Flight path planning method and system
CN113834385A (en) * 2021-09-08 2021-12-24 中国人民解放军91776部队 Two-dimensional cooperative guidance method for control time of initial track angle freedom
CN113834385B (en) * 2021-09-08 2023-02-21 中国人民解放军91776部队 Two-dimensional cooperative guidance method for control time of initial track angle freedom
CN113835439A (en) * 2021-09-08 2021-12-24 中国人民解放军91776部队 Two-dimensional cooperative guidance method for control time and angle of initial track angle freedom
CN113835439B (en) * 2021-09-08 2024-03-26 中国人民解放军91776部队 Two-dimensional collaborative guidance method for controlling time and angle freely aiming at initial track angle
CN114326813A (en) * 2021-12-31 2022-04-12 北京航天自动控制研究所 Method and system for predicting remaining flight time of unpowered aircraft
CN114326813B (en) * 2021-12-31 2023-06-20 北京航天自动控制研究所 Method and system for predicting residual flight time of unpowered aircraft
CN115001855A (en) * 2022-07-18 2022-09-02 南京理工大学 Deep reinforcement learning intelligent agent selection attack method based on track approximation
CN116663239A (en) * 2023-04-24 2023-08-29 四川大学 Missile escape area attack distance calculation method based on golden section method
CN116663239B (en) * 2023-04-24 2024-01-05 四川大学 Missile escape area attack distance calculation method based on golden section method
CN118012079A (en) * 2024-04-10 2024-05-10 西安现代控制技术研究所 Multi-angle attack lateral nominal track generation method based on overload capacity

Also Published As

Publication number Publication date
CN107132765B (en) 2020-04-28

Similar Documents

Publication Publication Date Title
CN107132765A (en) A kind of angle-of-attack based on trajectory planning and attack time control method
CN109947123B (en) Unmanned aerial vehicle path tracking and autonomous obstacle avoidance method based on sight guidance law
CN104516356B (en) Dynamic disorder based on RRT evades algorithm
Jung et al. Guidance laws for anti-ship missiles using impact angle and impact time
Prasanna et al. Retro-proportional-navigation: a new guidance law for interception of high speed targets
CN102980449B (en) Method for controlling coordinated operation of multiple missiles
CN107941087A (en) A kind of superb steady gliding reentry guidance method of high lift-drag ratio based on resistance profiles
CN106529073B (en) It is relieved condition analysis method based on the hypersonic target interception bullet for intercepting geometry
CN109358645B (en) Self-adaptive rope hook recovery guidance route and guidance method for small carrier-borne unmanned aerial vehicle
CN112526872B (en) Method for processing guidance and terminal guidance handover and guidance information in constraint with large falling angle
CN112648886B (en) Combined guidance target intercepting method and system
CN106200664A (en) A kind of adapt to attitude control method the most out of control
CN114035616A (en) Method and system for controlling attack of aircraft on moving target
Golan et al. Precursor interceptor guidance using sliding mode approach
CN114217639A (en) Guidance method and system for crossing visual target point based on designated course of unmanned aerial vehicle
Thakar et al. A tangential guidance logic for virtual target based path following
Robb et al. Earliest intercept line guidance: a novel concept for improving mid-course guidance in area air defence
Grzyb et al. The use of special algorithm to control the flight of anti-aircraft missile
Lee et al. Impact time and angle control guidance with rendezvous concept
Wang et al. A three dimensional guidance and control method for suicide UAV and the flight test verification
Shi et al. 3d dubins net-recovery path planning for fixed wing uav
CN113051706B (en) Three-body confrontation defense guidance method adopting virtual point prediction
Dubey et al. Trajectory Planning Using Dubins-Like Paths with Approach Angle and Terminal Time Constraints
Xin et al. Study of Proportional Guidance Trajectory Based on Guiding Principle
Shi et al. Four-Stage Guidance Law for Impact Time and Angle Control based on the Bezier Curve

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
GR01 Patent grant
GR01 Patent grant