CN108363299A - A kind of optimal terminal guidance method of exosphere interception - Google Patents
A kind of optimal terminal guidance method of exosphere interception Download PDFInfo
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- 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
- G05B13/042—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 in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The invention discloses a kind of exospheres to intercept optimal terminal guidance method, specifically includes：Step 1: establishing engagement model；Step 2: establishing energetic optimum control problem；Step 3: gravitation difference model linearization is handled；Step 4: solving optimal control problem；Step 5: determining residual non-uniformity.For the present invention compared to traditional proportional guidance Proportional Navigation (PN), the present invention considers gravitational influence, and propellant expenditure is reduced；The present invention is compared to Predictor-corrector guidance rule Predictive Guidance (PG), and propellant expenditure of the present invention is suitable with its, but the Guidance Law due to having obtained analytical form, and calculation amount of the invention greatly reduces.
Description
Technical field
The invention belongs to aeronautical and space technology, weapon fields, are related to a kind of exosphere interception terminal guidance method.
Background technology
Since the speed of intercontinental ballistic missile (ICBM) is up to 7~8km/s, altitude of the apogee is up to 2000km, so mesh
Preceding only roadbed midcourse defense system (GMD) can intercept ICBM.Roadbed interceptor (Ground-Based Intercept
), Missile the weapon of GMD, main after transmitting there are three mission phases：Motors in boost phase penetration (boost phase) is slided
Row section (coast phase) and terminal guidance section (terminal guidance phase).
Proportional guidance law is most widely used guidance law, because it is simple, effectively, and it is easy to implement.Augmentation ratio
Guidance law adds an item for coping with target maneuver to proportional guidance law, for coping with target maneuver.Trajectory forming guidance
Rule is to adapt to the needs of some special tasks, it is contemplated that the Guidance Law of ballistic-shaped constraint.Explicit Guidance is restrained due to it
Simply, effectively, have become the Typical Representative of trajectory forming Guidance Law.
Invention content
The purpose of the present invention is to solve the above problems, propose a kind of guidance side being suitable for strategic anti-missile interception latter end
Method, by adjusting a weight coefficient in energetic optimum target function, it can take into account consideration and be constrained with and without terminal velocity
Two kinds of situations.
A kind of optimal terminal guidance method of exosphere interception, including following steps：
Step 1: establishing engagement model
If E is the earth's core, static relative to inertial space, E-xyz is Earth central inertial system, and M represents blocker, and T represents target,
C represents blocker and the point of impingement of target.
In Earth central inertial system, the position vector of blocker M and target T are denoted as XM=[xM,yM,zM T] and XT=[xT,yT,
zT]T.Wherein, the transposition of the subscript T representation vectors and outside bracket.The velocity vector of blocker M and target T are denoted asWithThe thrust acceleration of blocker isAnd target
No control is slided.Blocker and target are acted on by terrestrial gravitation, their gravitational acceleration is respectively gMAnd gT, it is directed to the earth's core
E。
Blocker and target have the following equation of motion
Wherein, gMAnd gTCalculation formula it is as follows
Wherein, μ is Gravitational coefficient of the Earth, the Euclid norm of symbol " | | | | " representation vector.
Step 2: establishing energetic optimum control problem
In order to take into account two kinds of situations with and without constraint of velocity, such as next index letter based on energetic optimum is chosen
Number
Wherein, k is a weight coefficient.VTMfIt is VTMTerminal value, VTM=VT-VMIt is speed of the target relative to blocker
Spend vector.It is VTMfDesired value.tfIt is terminal juncture, also known as flight time, tgo=tf- t is residual non-uniformity.If
Do not consider that terminal velocity constrains, k=0 can be enabled.If it is desired that obtaining VTMFinally converge toK=∞ can be enabled.Weighting coefficient
It is used for so that aMFinally gradually converge to 0.And index n is bigger, aMIt is convergent faster.
The Equation of Relative Motion with Small of target-blocker is as follows
Wherein, XTM=XT-XMIt is position vector of the target relative to blocker.Remember XTMfFor XTMIn the value of terminal juncture.It is aobvious
So, in order to ensure to hit target, there is terminal condition XTMf=0.gTMIt is the difference of acceleration of gravity suffered by target and blocker, under
Formula calculates
Step 3: gravitation difference model linearization is handled
By observing l-G simulation test, have been found that blocker can just be hit target under no control state, gTMApproximation with
Linearly changes, and g is carved with when hitting targetTMf=0.Therefore, here using if Linear Model with Side is come approximate relatively heavy
Power model
Wherein, gTM0It is gTMThe value carved at the beginning, and be known.
Step 4: solving optimal control problem
By the linearization process of step 3, can be led with the optimal control problem established in Analytical Solution step 2
The normal acceleration of bullet is as follows,
Wherein
Wherein, VTM0It is VTMThe value carved at the beginning；XTM0It is XTMThe value carved at the beginning；
Step 5: determining residual non-uniformity
Wherein
RTM0It is the distance of guided missile and target,It is the component of guided missile and target relative velocity along direction of visual lines,It is
The component of guided missile and target relative attraction acceleration along direction of visual lines.
The advantage of the invention is that：
(1) compared to traditional proportional guidance Proportional Navigation (PN), the present invention considers the earth's core and draws
The influence of power, propellant expenditure are reduced；
(2) compared to Predictor-corrector guidance rule Predictive Guidance (PG), propellant expenditure of the present invention is suitable with its,
But due to the Guidance Law for having obtained analytical form, calculation amount of the invention greatly reduces.
Description of the drawings
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the Space Interception schematic diagram under terrestrial gravitation field action；
Fig. 3 is movement schematic diagram of the target relative to blocker；
Fig. 4 is the belligerent schematic diagram of exoatmosphere two dimension；
Fig. 5 is the corresponding geometric locus of suboptimum guidance law and its floor projection curve (the case where endless constraint of velocity)；
Fig. 6 is the curve (the case where endless constraint of velocity) that the projection of acceleration in y-direction changes over time；
Fig. 7 is the curve (the case where endless constraint of velocity) that the projection of acceleration in a z-direction changes over time；
Fig. 8 is the curve (the case where endless constraint of velocity) that laterally diverted speed increment changes over time；
Fig. 9 is the curve (the case where endless constraint of velocity) for playing mesh relative gravity acceleration and changing over time；
Figure 10 is the curve (the case where endless constraint of velocity) for playing mesh relative position and changing over time；
Figure 11 is the corresponding geometric locus of suboptimum guidance law and its floor projection curve (having the case where terminal velocity constraint)；
Figure 12 is the curve (having the case where terminal velocity constraint) that the projection of acceleration in y-direction changes over time；
Figure 13 is the curve (having the case where terminal velocity constraint) that the projection of acceleration in a z-direction changes over time；
Figure 14 is the curve (having the case where terminal velocity constraint) that laterally diverted speed increment changes over time；
Figure 15 is the curve (having the case where terminal velocity constraint) for playing mesh relative gravity acceleration and changing over time；
Figure 16 is the curve (having the case where terminal velocity constraint) for playing mesh relative position and changing over time.
Specific implementation mode
Below in conjunction with drawings and examples, the present invention is described in further detail.
The present invention obtains a kind of gravitational target-seeking guidance law of three-dimensional of consideration using optimal control theory, is suitable for war
The slightly Guidance Law of anti-missile interception latter end, by adjusting a weight coefficient in energetic optimum target function, it can take into account consideration
With and without two kinds of situations of terminal velocity constraint.In derivation, since Gravity Models has strong nonlinearity, former optimal control
Problem processed can not be solved.For this purpose, using a linear model come the approximate non-linear Gravity Models of original.It, will due to this simplification
The guidance law obtained is known as suboptimum guidance law.In Exoatmospheric intercept task, restrained compared to conventional lead, suboptimum guidance law
The fuel of consumption is few, and it is small to guide the corresponding assumed (specified) load of resolving.
The optimal terminal guidance method of a kind of exosphere interception, as shown in Figure 1, it is as follows：
Step 1: establishing engagement model
As shown in Fig. 2, studying here the Exoatmospheric intercept target the problem of.Assuming that the earth's core E is quiet relative to inertial space
Only, with E it is then the former heart, establishes inertial reference system GEI:E-xyz.
In figure, M represents blocker, and T represents target, and C represents blocker and the point of impingement of target.In reference system GEI, block
The position vector for cutting device M and target T is denoted as XM=[xM,yM,zM]TAnd XT=[xT,yT,zT]T, xMIndicate that blocker position vector exists
The component in the directions reference axis x, yMIndicate blocker position vector in the component in the directions reference axis y, zMIndicate blocker position vector
Component in the directions reference axis z, xTIndicate target location vector in the component in the directions reference axis x, yTIndicate that target location vector exists
The component in the directions reference axis y, zTComponent of the expression target location vector in the directions reference axis z.Wherein, the subscript and outside bracket
The transposition of T representation vectors.The velocity vector of blocker M and target T are denoted asWith Indicate blocker velocity vector the directions reference axis x component,Indicate blocker velocity vector in the directions reference axis y
Component,Indicate blocker velocity vector the directions reference axis z component,Indicate target velocity vector in the directions reference axis x
Component,Indicate target velocity vector the directions reference axis y component,Indicate target velocity vector in the directions reference axis z
Component.The thrust acceleration of blocker isTarget is slided without control,Indicate that blocker thrust accelerates
The vectorial component in the directions reference axis x of degree,Indicate blocker thrust acceleration vector the directions reference axis y component,Table
Show blocker thrust acceleration vector the directions reference axis z component.Blocker and target are acted on by terrestrial gravitation, they
Gravitational acceleration gMAnd gTIt is directed to the earth's core E.
Blocker and target have the following equation of motion
Wherein, gMAnd gTCalculation formula it is as follows
Wherein, μ is Gravitational coefficient of the Earth, the Euclid norm of symbol " | | | | " representation vector.
Step 2: establishing energetic optimum control problem
In order to take into account two kinds of situations with and without constraint of velocity, devise such as next index based on energetic optimum
Function
Here, k is a weight coefficient.N, which is one, can adjust a taking human as the positive integer of selectionMConvergent speed
Degree.VTMfIt is VTMTerminal value, VTM=VT-VMIt is velocity vector of the target relative to blocker.It is VTMfDesired value.tf
It is terminal juncture, also known as flight time.tgo=tf- t is residual non-uniformity.First item is to constrain end on the right of formula (6)
Hold velocity vector.If not considering that terminal velocity constrains, k=0 can be enabled.If it is desired that obtaining VTMFinally converge toK can be enabled
=∞.Section 2 is to minimize motor-driven consumed energy on the right of formula (6).Wherein, weighting coefficientBe used for so that
aMFinally gradually converge to 0.And index n is bigger, aMIt is convergent faster.The Equation of Relative Motion with Small of target-blocker is as follows
Wherein, XTM=XT-XMIt is position vector of the target relative to blocker.Remember XTMfFor XTMIn the value of terminal juncture.It is aobvious
So, in order to ensure to hit target, there is terminal condition XTMf=0.gTMIt is the difference of acceleration of gravity suffered by target and blocker, under
Formula calculates
Step 3: gravitation difference model linearization is handled
Due to gTMIt is a nonlinear function, optimal control problem above can not Analytical Solution.But, imitative by observing
True experiment, has been found that blocker can just be hit target under no control state, gTMApproximation changes linearly over time, and
G is carved with when hitting targetTMf=0.Therefore, here using if Linear Model with Side is come approximate relative gravity model.
Wherein, gTM0It is gTMThe value carved at the beginning, and be known.
Step 4: solving optimal control problem
Since step 3 squadron gravitational acceleration has done simplification, obtained solution is not the optimal solution of former problem.Therefore,
Thus obtained Guidance Law is known as suboptimum guidance law.The Hamiltonian function for simplifying optimal control problem is as follows
Co-state equation is
Governing equation is
Remember that the right first item of target function is
Then transversality condition is
Wherein：λ2fIndicate λ2In t=tfThe value at moment
It can be obtained by formula (12), (13) and (16)
λ1=C1 (17)
Wherein, C1It is constant vector undetermined.Formula (18), which is substituted into formula (14), to be obtained
Formula (10) and (19) are updated to formula (8), then integral can obtain
Wherein, VTM0It is VTMThe value carved at the beginning；XTM0It is XTMThe value carved at the beginning
Formula (20) is substituted into formula (7), then integral can obtain
Work as t=tfWhen, due to XTMf=0, then it can be obtained by formula (21)
In addition, working as t=tfWhen, it can be obtained by formula (20)
Simultaneous formula (22), (23) can obtain
Wherein
Consider in two kinds of situation now：1) do not consider that terminal velocity constrains；2) consider terminal velocity constraint.
Situation one：Do not consider that terminal velocity constrains
Formula (24) (25) is substituted into formula (19), and enables t=0 that can obtain the optimal acceleration of initial time.Due to not examining
Consider terminal velocity constraint, enables k=0, then have
In practical applications, guidance system is using currently practical state as the original state of above-mentioned optimal control problem, so
Afterwards guidanceing command for current time is generated using above formula.
Situation two：Consider terminal velocity constraint
In order to consider that terminal velocity constrains, k is enabled to tend to be infinitely great.Consider first following two it is relevant with command acceleration
The limit
Formula (29) and (30) are substituted into formula (19), and enable t=0 that can obtain the value that optimal acceleration is carved at the beginning, such as
Under
Equally, as long as using the current state of aircraft as the original state of above-mentioned optimal control problem, so that it may to utilize
Above formula generates command acceleration in real time.
Step 5: determining residual non-uniformity
It is moved now from blocker angle object observing, as shown in Figure 3.In figure, coordinate system M-x1y1 are to be connected in block
A coordinate system on device is cut, this coordinate system relative inertness space is without rotation.T is the target location at current time, δVIt is VTMWith
The angle of sight, δgIt is gTMWith the angle of sight.The curve that P points are crossed in figure is the i.e. a when blocker is in without control stateM=
0, track of the target relative to blocker.VectorIt is Zero effort miss vector.As shown in figure 4, in Exoatmospheric intercept process
In, blocker realizes crossrange maneuvering using precise tracking, and to eliminate miss distance, blocker appearance is adjusted using attitude control engine
State so that elastomer axis tracks sight, to meet the needs of target seeker object observing.Since the directions precise tracking thrust F are hung down
Directly in blocker axis, and elastomer axis is approximate with sight overlaps, therefore aMApproximately perpendicular to sight.Actually intercepting process
In, sight is rotating, but amplitude very little, as shown in Figure 4.(figure Chinese and English indicates that part please be changed to Chinese, if it can, will
It is added to specification here, does not occur Chinese character explanation in attached drawing preferably) it is therefore assumed here that sight does not rotate.Due to aMIt hangs down
Directly in sight, aMIt will not be to being had an impact along the movement of initial direction of visual lines.It is thus possible to analyze the phase along initial direction of visual lines
To movement, to determine flight time tf。
NoteIt is VTMAlong the component of direction of visual lines,It is VTMPerpendicular to the component of direction of visual lines.NoteIt is gTMEdge regards
The component in line direction,It is gTMPerpendicular to the component of direction of visual lines.It is XTMUnit vector, i.e.,
It enablesWithNote that during belligerent, since interceptor gradually subtracts at a distance from target
It is small, so
Estimation flight time t nowf.As it is assumed that sight does not rotate, can be obtained according to formula (10)
Formula (32) integral can be obtained
Work as t=tfWhen, RTMf=0, then have
There are two roots for above-mentioned quadratic equation, as follows
Wherein
Only consider interceptor can succeed interception target the case where, i.e., Δ >=0 the case where.For the ease of analyzing and deriving,
Craftsmenship both the above root is deformed below.Referring initially to tf1
Similar has
Now determine which root is flight time tf.IfDue to RTM0＞ 0, thenTherefore,
According to formula (37), haveBeing substituted into formula (38) (39) can obtain：0 ＜ tf2＜ tf1.Due to tf2Closest to first
Begin the moment 0, then tf2At the time of being exactly that interceptor is hit target.IfThen haveIt can further obtain：tf1
0 ＜ t of ＜f2.Due to tf＞ 0, then still have tf=tf2.In a word
In formula (40) generation, is arrived in formula (28) and formula (31), and is unfolded, can be obtained
It noticesWithThen have
Using formula (a × b) × c=(ac) b- (bc) a, can obtain
Wherein, sight rotational angular velocity ωLOSIt is calculated by following formula
Formula (40) is updated to formula (31), and is unfolded, can be obtained
According to formula (43) and (45), aMThe expression formula of line of sight rate form is can be written as, as follows in two kinds of situation
Situation one：Do not consider that terminal velocity constrains
Formula (43) is updated in formula (28), can be obtained
Situation two：Consider terminal velocity constraint
Formula (43) and (45) are updated in formula (31), can be obtained
In practical applications, guidance system is using currently practical state as the original state of above-mentioned optimal control problem, so
Formula (46) or (47) is utilized to generate guidanceing command for current time afterwards.Due toThen have
IfIt can enable
Simulating, verifying carried out to Guidance Law the endless constraint of velocity the case where below, and by suboptimum guidance law (SOG),
The simulation result of proportional guidance law (PN), augmentation proportional guidance law (APN) and Predictor-corrector guidance rule (PG) is compared.SOG, PN and
APN can be by Unified Expression in the form of following
For PN, N1=3+n, N2=0.
For APN, N1=3+n, N2=(3+n)/2.
For SOG,
Here, n >=0.The instruction of PG can be expressed as
Wherein, N1=3+n.ZEM is zero control miss azimuth.In each guidance period, missile-borne computer assumes aM=0, profit
Formula (1) (2) (3) (4) is carried out in line integral with numerical method.Work as XTM·VTMWhen=0, emulation terminates, and enables in emulation
Flight time is tgo, and enable the X of end timeTMFor ZEM.Then, missile-borne computer is accelerated using formula (50) computations
Degree.In this example, n=0.
In powered phase, KKV feedings are flown to predicted set-forward position (Predicted Interception Point) by boost motor
Dragging track.Here the case where considering no PIP errors first, i.e. KKV is uncontrolled to hit target.
In the terminal guidance stage, the initial position of KKV
XM0=[786280.91, -1300973.39,7286277.30]T(m)
Initial velocity
VM0=[2837.72,5409.49,1553.36]T(m/s)
The initial position of target
XT0=[981407.04, -861312.60,7722585.39]T(m)
Initial velocity
VT0=[1725.21, -6831.13, -976.11]T(m/s)
It is as follows to define Incremental Velocity for Lateral Divert (LDS)
Since sidestep maneuver acceleration is directly proportional to mass-flow rate of propellant, this variable can be used for more different guidance laws
Propellant expenditure size.
Simulation result is as shown in table 1, Fig. 5 to Figure 10.Table 1 compares the corresponding lateral divert of different guidance laws
The calculating time used with emulation speed.As can be seen from the table, PG consumption energy is minimum, but assumed (specified) load is far longer than
Other guidance laws.The energy expenditure of APN is about the half of PN.The energy expenditure of SOG is almost suitable with PG, but assumed (specified) load
Much smaller than PG.
1 simulation result of table compares
| Guidance Law | ΔV(m/s) | Simulation time (s) |
| SOG | 1.032 | 0.0844 |
| PN | 91.51 | 0.0813 |
| APN | 46.95 | 0.0744 |
| PG | 0 | 12.7356 |
The corresponding geometric locus of suboptimum guidance law and its floor projection curve of Fig. 5 displayings, wherein C points are the points of impingement.It says
It is bright：Because the corresponding track of other methods track corresponding with SOG is very close, human eye can not be differentiated, so only drawing here
SOG corresponding geometric locuses.It is in the plane being made of current gaze and the earth's core to define plane EMT.DefinitionIt is along XTMSide
To unit vector.DefinitionIt it is one in EMT planes, and perpendicular to the unit vector of current gaze.In XMOn throwing
Shadow is positive value.DefinitionIt is perpendicular to the unit vector of EMT planes, by formulaIt determines.Fig. 6 illustrates these four
The corresponding acceleration edge of guidance lawThe component curve in direction, is denoted asFig. 7 illustrates the corresponding acceleration of these four guidance laws
Spend edgeThe component curve in direction, is denoted asIt can be seen from the figure that command acceleration acts predominantly in EMT planes, and
The command acceleration of SOG and PG is very small, and almost 0.Therefore, in fig. 8, the corresponding crossrange maneuvering demands of SOG and PG are several
It is 0.In addition, the crossrange maneuvering demand of APN is about the half of PN.As it can be seen that SOG is integrated with the advantages of APN and PG：Simply,
Reliably, calculation amount is small, and required motor-driven energy expenditure is small.Fig. 9, Figure 10 are to be based on the corresponding g of SOG engagement simulations respectivelyTMWith
XTMCurve is previously with regard to g with verificationTMAnd XTMLinear hypothesis.
During deriving suboptimum guidance law in front, it is assumed that relative gravity changes linearly over time, and sight is approximate
It does not rotate.In order to verify the two in wide range it is assumed that amplifying initial missile-target distance to about 4000km.In the terminal guidance stage
Initial time considers there is the case where predicted set-forward position error of about 50km here.
At this point, the initial position of KKV is
XM0=[192442.95, -2085138.26,6726394.99]T(m),
Initial velocity is
VM0=[3418.94,5190.08,3269.23]T(m/s),
The initial position of target is
XT0=[569875.90,1928987.06,7526018.77]T(m),
Initial velocity is
VT0=[2262.74, -6806.83,834.46]T(m/s)。
At this point, in the initial time in terminal guidance stage, the course drift ideal course as outlined about 1.5deg of KKV.Here, ideal boat
To referring to meeting the directional velocity for hitting target requirement under no control state.In addition, enabling the figure parameters n of four kinds of guidance laws be here
1.Simulation result is as shown in table 2, Figure 11 to Figure 16.
In Figure 11, M indicates that the initial position of blocker, T indicate that the initial position of target, C indicate that blocker has target
The point of impingement.
In Figure 12,Indicate projection of the blocker normal acceleration in the directions reference axis y.
In Figure 13,Indicate projection of the blocker normal acceleration in the directions reference axis z.
In Figure 14, Δ V indicates sidestep maneuver velocity variable
In Figure 15, gTMIndicate blocker and target relative gravity acceleration
In Figure 16, XTMIndicate blocker and target Relative position vector
2 simulation result of table compares
| Guidance Law | ΔV(m/s) | Simulation time (s) |
| SOG | 230.93 | 0.1636 |
| PN | 399.67 | 0.1628 |
| APN | 292.87 | 0.1730 |
| PG | 232.60 | 42.7442 |
Claims (1)
1. a kind of exosphere intercepts optimal terminal guidance method, which is characterized in that include the following steps：
Step 1: establishing engagement model；
Establish the relative position relation of blocker, target and the earth in inertial space, the equation of motion of blocker and target is：
Wherein, XMIndicate the position vector of blocker M, XM=[xM,yM,zM]T, xMIndicate blocker position vector in the reference axis side x
To component, yMIndicate blocker position vector in the component in the directions reference axis y, zMIndicate blocker position vector in reference axis z
The component in direction, XTIndicate the position vector of target T, XT=[xT,yT,zT]T, xTIndicate target location vector in the reference axis side x
To component, yTIndicate target location vector in the component in the directions reference axis y, zTIndicate target location vector in the directions reference axis z
Component；VMIndicate the velocity vector of blocker M, Indicate blocker velocity vector in reference axis
The component in the directions x,Indicate blocker velocity vector the directions reference axis y component,Indicate that blocker velocity vector exists
The component in the directions reference axis z, VTIndicate the velocity vector of target T, Indicate that target velocity vector exists
The component in the directions reference axis x,Indicate target velocity vector the directions reference axis y component,Indicate that target velocity vector exists
The component in the directions reference axis z, aMIndicate the thrust acceleration of blocker, Indicate blocker thrust
Vector acceleration the directions reference axis x component,Indicate blocker thrust acceleration vector the directions reference axis y component,Indicate blocker thrust acceleration vector in the component in the directions reference axis z, gMAnd gTDrawing for blocker and target is indicated respectively
Power acceleration；
gMAnd gTCalculation formula it is as follows
Wherein, μ is Gravitational coefficient of the Earth, the Euclid norm of symbol " | | | | " representation vector；
Step 2: establishing energetic optimum control problem；
Establish the target function based on energetic optimum：
Wherein, k indicates weight coefficient, and n is positive integer, VTMfIt is VTMTerminal value, VTM=VT-VMIt is target relative to blocker
Velocity vector；It is VTMfDesired value；tfIt is terminal juncture, also known as flight time；tgo=tf- t is residual non-uniformity；
The Equation of Relative Motion with Small of target-blocker is as follows
Wherein, XTM=XT-XMIt is position vector of the target relative to blocker, remembers XTMfFor XTMIn the value of terminal juncture, then XTMf
=0；gTMIt is the difference of acceleration of gravity suffered by target and blocker：
Step 3: gravitation difference model linearization is handled；
Using such as Linear Model with Side come approximate relative gravity model：
Wherein, gTM0It is gTMThe value carved at the beginning；
Step 4: solving optimal control problem；
The optimal control problem established in Analytical Solution step 2, the normal acceleration for obtaining guided missile are as follows
Wherein
VTM0It is VTMThe value carved at the beginning；XTM0It is XTMThe value carved at the beginning；
Step 5: determining residual non-uniformity；
Residual non-uniformity is：
Wherein
RTM0It is the distance of guided missile and target,It is the component of guided missile and target relative velocity along direction of visual lines,It is guided missile
With target relative attraction acceleration along the component of direction of visual lines.
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| CN112033235A (en) * | 2020-09-04 | 2020-12-04 | 清华大学 | Air combat three-body confrontation optimal prediction guidance method adopting golden section search |
| CN114357807A (en) * | 2022-03-11 | 2022-04-15 | 北京航空航天大学 | Optimal guidance method and device for atmospheric interception |
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