CN104503471A - Terminal guidance method for maneuvering aircraft multi-terminal constraint backstepping sliding mode - Google Patents

Abstract

Provided is a terminal guidance method for maneuvering aircraft multi-terminal constraint backstepping sliding mode. The method comprises three main steps: step 1, analyzing terminal constraint of a terminal guidance problem and number; step 2, determining a sliding mode variable structure control order, designing a sliding variable quantity; step 3, and designing limited time backstepping, to obtain the guidance law of the whole system. The design basis of the method is the backstepping design of reaching in limited time, and the design of the terminal guidance law is a problem of reaching in a limited time. The backstepping design in variable structure control is a regression design method combining selection of a Lyapunov function and the design of a controller. Beginning from a minimum order differential equation of the system, the method designs in a stabilization manner layer by layer, and finally global stabilization is realized, so as to provide the control law of the whole system.

Description

A kind of maneuvering-vehicle multiple terminals constraint inverting Sliding Mode Guidance method

Technical field

The invention belongs to aeronautical and space technology, weapon field, relate to a kind of maneuvering-vehicle multiple terminals constraint inverting Sliding Mode Guidance method.Specifically, for maneuvering-vehicle terminal guidance problem, the Guidance Law that this method for designing obtains, can make aircraft while arrival or hit, meet each end conswtraint, as the constraint of terminal trajectory tilt angle, normal g-load constraint etc.

Background technology

Some maneuvering-vehicle is when attacking fixed target, and except needs are considered to reduce except miss distance, some special warhead is expected with certain angle hit, thus obtains better damage effectiveness.As some reenters Maneuvering Missile at its terminal guidance section, need the velocity reversal of flight substantially perpendicular to the ground, terminal guidance system worked well can be made like this.In addition, bullet is obtain maximum Penetration Depth, needs final with certain impingement angle hit.Antitank missile is then wished with the weakness at hit tank top, the large angle of fall armoring.Some anti-warship guided missle needs steep dive to attack, or attack from the side strengthen to the prominent anti-power of naval vessels with injure power etc.Therefore, the control of terminal point has become an important performance of precision strike weapon.

In article " Terminal Guidance for Impact Attitude Angle Constrained Flight Trajectories ", first M.Kim and Kelly Grider provided a kind of Terminal Guidance Laws with angle of fall constraint type in 1973, through development for many years, both at home and abroad to the Design of Guidance Law about being with angle restriction, had the research of many comparative maturities, part achievement has started application in practice.When designing the Guidance Law of band angle restriction, conventional design philosophy is based on proportional guidance law and additional bias item, based on the theory of optimal control, or based on variable-structure control.Many documents, when solving band angle restriction Terminal Guidance Laws, rely on the linearization to the equation of motion, draw the Guidance Law of analytical form.When the end conswtraint needing to consider is more, the result of Guidance Law is comparatively complicated.And seldom have and consider the constraint of terminal normal g-load, may there is larger normal acceleration in the simulation result display aircraft flight end of certain methods, easily occur obvious miss distance under environment and the probabilistic situation of correlation parameter.

Summary of the invention

One, goal of the invention: for the terminal guidance problem of maneuvering-vehicle, the present invention uses backstepping Based Inverse Design Method, there is provided a kind of maneuvering-vehicle multiple terminals to retrain inverting Sliding Mode Guidance Law method for designing, it provides a kind of method for designing with multiple end conswtraint end guidance law.Guidance Law can meet multiple end conswtraint, as the constraint of terminal trajectory tilt angle, normal g-load constraint.

Two, technical scheme:

Design basis of the present invention is " back-stepping design that finite time arrives ".Wherein, maneuvering-vehicle terminal guidance section---to hit from terminal guidance, although the flight time is unknown, limited.Therefore, the design of Terminal Guidance Laws is the problem of " finite time arrival "." backstepping back-stepping design " in variable-structure control is that Lyapunov function chosen a kind of Fertilizer Test of Regression Design method combined with the design of controller, it is by from system lowest-order subdifferential equation, successively Stabilization finally reaches Stabilization, thus provides the control law of whole system.

A kind of maneuvering-vehicle multiple terminals of the present invention constraint inverting Sliding Mode Guidance method, the method concrete steps are as follows:

Step one: end conswtraint and the number of analyzing terminal guidance problem.

For general terminal guidance problem, first require aircraft hit, at least there is an end conswtraint relevant to displacement.Next, the aircraft of different task demand needs when arrival or hit, requires predetermined trajectory tilt angle or hit impingement angle, the end conswtraint that just existence one is relevant to angle.Finally, in some cases, also likely need to consider that other retrain, in order to make aircraft keep better stability and robustness under environment and the probabilistic situation of correlation parameter, adding the constraint of terminal normal g-load has certain necessity.

Step 2: determine Sliding mode variable structure control exponent number, design slip variable.

After analyzing the end conswtraint that terminal guidance problem will consider, just according to end conswtraint number determination Sliding mode variable structure control exponent number, and then problem can be converted into the design of slip variable.Suitable variable is found in the design of this slipping plane, make variable and certain order derivative thereof level off to 0 with meet each end conswtraint and combine.

Step 3: finite time back-stepping design, obtains the Guidance Law of whole system.

After devising suitable slip variable, the backstepping back-stepping design using finite time to arrive, provides the final Guidance Law of whole system.This Guidance Law accurately can arrive target by directing aircraft, meets each end conswtraint simultaneously.

Three, advantage and effect:

1, method for designing of the present invention, does not need linearization, compares the result that classic method obtains more succinct.

2, the derivation in the present invention adopts by rank hierarchical design, and process is understandable, meets each end conswtraint by rank.

3, the Terminal Guidance Laws that the inventive method obtains still can have fine robustness under there is multiple disturbance situation.

Accompanying drawing explanation

Fig. 1 is design flow diagram of the present invention;

Fig. 2 is the quantity of state variation diagram of simple example numerical simulation; Reflection different time of arrival 2s, 4s and 6s, the change curve of quantity of state---displacement x and speed v;

Fig. 3 is the bullet-order relation schematic diagram of actual citing mathematical model;

Fig. 4 is the ballistic curve comparison diagram that terminal trajectory tilt angle is constrained to-90 ° ,-80 ° ,-70 ° and-60 ° emulation;

Fig. 5 is the trajectory tilt angle change curve comparison diagram that terminal trajectory tilt angle is constrained to-90 ° ,-80 ° ,-70 ° and-60 ° emulation;

Fig. 6 is the normal g-load change curve comparison diagram that terminal trajectory tilt angle is constrained to-90 ° ,-80 ° ,-70 ° and-60 ° emulation;

Fig. 7 is the slip variable of terminal trajectory tilt angle when being constrained to-90 ° and one, second derivative variation diagram.

In figure, symbol description is as follows:

M is aircraft barycenter, and T is the position of target, x _bfor body axle, H is height, and x is longitudinal range, and LOS is sight line, and λ is the angle of sight, and V is the speed of aircraft, and γ is trajectory tilt angle, and α is the angle of attack, and θ is the angle of pitch, a _mfor normal acceleration; γ _fbe the constraint of terminal trajectory tilt angle, s is slip variable, and s ', s " are respectively slip variable one, second derivative.

Embodiment

Below in conjunction with accompanying drawing and instantiation, the present invention is described further.

Background knowledge illustrates:

First, before the method for designing introducing multiple terminals constraint terminal guidance problem Guidance Law, the concept of back-stepping design is briefly described, and corresponding mathematical description is done to Based Inverse Design Method used by the present invention.

Backstepping back-stepping design in variable-structure control is that Lyapunov function chosen a kind of Fertilizer Test of Regression Design method combined with the design of controller.Its basic thought is that the nonlinear system of complexity is resolved into the subsystem being no more than system order, by the subsystem from the minimum order of system, successively Stabilization " room for manoeuvre " " inverting ", finally reach Stabilization, thus provide the control law of whole system.

For a high order system, its n-1 order derivative is known, and has

f ⁿ(x)＝A(x)+B(x)·u

Design High-Order Sliding Mode variable-structure control u, makes f (x) and n-1 order derivative thereof

f,f′,...,f ^n-1→0

Realize in finite time.Following Backstepping Based Inverse Design Method can be used, consider 2 the most frequently used rank systems at this, have

f″(x)＝A(x)+B(x)·u

Slipping plane is made to be

s ₁＝f(x)

Can set candidate Lyapunov function as

$V_1=\frac{1}{2}{s_1}^2$

Above formula differentiate obtains

${\stackrel{\·}{V}}_1=s_1\·{\stackrel{\·}{s}}_1$

For ensureing slipping plane s ₁within the limited time, level off to zero, it is suitable to select make negative definite.NathanHarl is utilized to provide one in article " Reentry Terminal Guidance Through Sliding Mode Control " at this system of selection, as follows

${\stackrel{\·}{s}}_1=-n\·\frac{s_1}{t_r-t}$

Wherein n be greater than 1 positive constant coefficient, t _rfor the moment of convergence zero, select like this slipping plane s can be ensured ₁at t _rmoment convergence zero, can by t when using Guidance Law _r-t residual non-uniformity T _goreplace.

Because system Relative order is 2, then establish slipping plane s ₂for

$s_2={\stackrel{\·}{s}}_1+n\·\frac{s_1}{t_r-t}$

Consider candidate Lyapunov function

$V_2=\frac{1}{2}{s_2}^2$

Differentiate obtains

${\stackrel{\·}{V}}_2=s_1\·{\stackrel{\·}{s}}_2$

At this, Reaching Law can be made to be

${\stackrel{\·}{s}}_2=-\mathrm{\η}\·\mathrm{sign}\left(s_2\right)$

In above formula, η is positive number, and its size affects speed of convergence.To s ₂differentiate obtains

${\stackrel{\·}{s}}_2={\stackrel{\·\·}{s}}_1+n\frac{{\stackrel{\·}{s}}_1}{t_r-t}+n\frac{s_1}{{(t_r-t)}^2}=A\left(x\right)+B\left(x\right)\·u+n\frac{f^{\′\left(x\right)}}{t_r-t}+n\frac{f\left(x\right)}{{(t_r-t)}^2}$

Wherein there is control item, simultaneous two formula, can control u expression formula be

$u=-\frac{1}{B\left(x\right)}[\mathrm{\η}\·\mathrm{sign}(f^{\′}\left(x\right)+n\·\frac{f\left(x\right)}{t_r-t})+A\left(x\right)+n\frac{f^{\′}\left(x\right)}{t_r-t}+n\frac{f\left(x\right)}{{(t_r-t)}^2}]$

For weakening the flutter that sign function may cause, the most frequently used method is sign function sign (s) replaced with saturation function sat (s) in desirable sliding mode.For the system of higher order, the like.

Simple example:

At this, describe the Based Inverse Design Method that the finite time used by the present invention arrives.For further illustrating design procedure, at the simple control system example of this measure one.Consider simple two―step element: the particle of a certain unit mass in coordinate axis, distance initial point distance is x, and speed is v, asks corresponding control u, makes particle get back to initial point.The state equation of this two―step element is

$\left\{\begin{array}{c}\stackrel{\·}{x}=v\\ \stackrel{\·}{v}=u\end{array}\right.$

Consider that control needs to make displacement x → 0, simultaneously speed v → 0, system could be stablized.Therefore, there are two end conswtraints, are respectively displacement x _f=0, and speed v _f=0.System has two end conswtraints, and corresponding systematic education is 2.The key of design finds suitable slipping plane, according to by rank design philosophy, needs to make slip variable and 1 order derivative asymptotic convergence thereof in 0.

Design procedure is as follows, first First order design, selects slipping plane

s ₁＝x

Selection Lyapunov function is

$V_1=\frac{1}{2}{s_1}^2$

For making Lyapunov function positive definite, its derivative negative definite, according to the background knowledge introduced above, can make

${\stackrel{\·}{s}}_1=-n\·\frac{s_1}{T_{\mathrm{go}}}$

Wherein n > 0, then select slipping plane

$s_2={\stackrel{\·}{s}}_1+n\·\frac{s_1}{T_{\mathrm{go}}}$

Getting Lyapunov function is

$V_2=\frac{1}{2}{s_2}^2$

For making upper Lyapunov function positive definite, its derivative negative definite, due to s ₂there is control item in derivative, therefore can make

${\stackrel{\·}{s}}_2=-k\·\mathrm{sgn}\left(s_2\right)$

Wherein k is positive number, and

${\stackrel{\·}{s}}_2={\stackrel{\·\·}{s}}_1+n\·\frac{{\stackrel{\·}{s}}_1}{T_{\mathrm{go}}}+n\·\frac{s_1}{T_{\mathrm{go}}}=u+n\·\frac{v}{T_{\mathrm{go}}}+n\·\frac{x}{T_{\mathrm{go}}}$

Two formula simultaneous, can control be

$u=-\frac{n}{T_{\mathrm{go}}}v-\frac{n}{{T_{\mathrm{go}}}^2}x-k\·\mathrm{sgn}(v+\frac{n}{T_{\mathrm{go}}}x)$

Make initial position x ₀=2, initial velocity v ₀=1, be designed with and limit be respectively 2s, 4s and 6s the time of arrival of time of arrival.As shown in Figure 2, Numerical Simulation Results, uses this Based Inverse Design Method to simulation result, and controlled quentity controlled variable can arrive steady state (SS) in corresponding finite time.

Method for designing is set forth:

After describing the Based Inverse Design Method that finite time arrives, provide its application on Design of Terminal Guidance Law below.As shown in Figure 1, give FB(flow block) of the present invention, in conjunction with FB(flow block), these technical method concrete steps are as follows:

Step 1: end conswtraint and the number of analyzing terminal guidance problem.

For general terminal guidance problem, first require aircraft hit, at least there is an end conswtraint relevant to displacement.Secondly, the aircraft of different task demand needs when arrival or hit, requires certain trajectory tilt angle or hit impingement angle.If space shuttle is at landing phase, velocity reversal is approximate consistent with runway; Some is motor-driven reenters bullet, and terminal guidance section requires that final abhiseca at a certain angle strikes target.The end conswtraint that so just existence one is relevant to angle.Finally, in order to make aircraft keep better stability and robustness under environment and the probabilistic situation of correlation parameter, adding the constraint of terminal normal g-load has certain necessity.

Step 2: determine Sliding mode variable structure control exponent number, design slip variable.

After analyzing the end conswtraint that terminal guidance problem will consider, just can according to end conswtraint number determination Sliding mode variable structure control exponent number, end conswtraint number is n, then exponent number is also n.Problem is converted into the suitable slip variable of design, makes to occur control item in its n order derivative; Require slip variable and n-1 order derivative thereof level off to 0 with meet each end conswtraint and combine; Need simultaneously design sliding mode control law, make slip variable and n-1 order derivative thereof all asymptotic convergence in 0.

Step 3: finite time back-stepping design, obtains the Guidance Law of whole system.

After devising suitable slip variable, the backstepping back-stepping design using finite time to arrive, provides the final Guidance Law of whole system." finite time " is the residual non-uniformity of flight, by estimating in real time, can not need for exact value.

Practical application is illustrated:

For better showing this method for designing, with the instantiation reentering Maneuvering Missile, above-mentioned method for designing is described further below.

Maneuverable reentry vehicle model selected by example is the Maneuvering Missile of Pan Xing-2 guided missile of the U.S..When bullet arrives overhead, target area 45 km height, start trajectory pull-up.Consider thermal protection, bullet is at the maximum angles-of-attack of the approximate maintenance of this section.There is one section of approximate flat section of flying after trajectory pull-up, under inertial guidance system controls, carry out deceleration control.Finally carry out drop-down Guidance control, Map and image database inclination angle meets related constraint, hit simultaneously.The drop-down lead segment of bullet is a terminal guidance problem being typically with multiple terminals constraint, as follows to this mathematical modeling.

In order to simplify problem, with fixed target and aircraft barycenter for benchmark, aircraft movements is decomposed into pitch plane and turning plane.Exploratory flight device moves in the determined pitch plane of barycenter M, target T and the earth's core, all regards aircraft and target as particle, and bullet-order relation schematic diagram as shown in Figure 3.In figure, T is the position of target, x _bfor body axle, H is height, and x is longitudinal range, LOS is sight line, λ is the angle of sight, and V is the speed of aircraft, and γ is trajectory tilt angle, rotate counterclockwise as just with velocity reversal around horizontal direction, α is the angle of attack, and rotate counterclockwise as just with body direction of principal axis around velocity reversal, θ is the angle of pitch, rotate counterclockwise as just with body direction of principal axis around horizontal direction, a _mfor normal acceleration.Kinematical equation is

$\left\{\begin{array}{c}\stackrel{\·}{x}=V\·\cos \left(\mathrm{\γ}\right)\\ \stackrel{\·}{h}=V\·\sin \left(\mathrm{\γ}\right)\\ \stackrel{\·}{V}=-\frac{D}{m}-g\·\sin \left(\mathrm{\γ}\right)\\ \stackrel{\·}{\mathrm{\γ}}=\frac{L}{\mathrm{mV}}-\frac{g\·\cos \left(\mathrm{\γ}\right)}{V}\end{array}\right.$

Wherein L is lift, and D is resistance, and m is quality, and g is acceleration of gravity.

For improving the fighting efficiency of bullet, General Requirements maneuvering-vehicle can with certain angle of fall or trajectory tilt angle hit, and namely terminal trajectory tilt angle is required to meet constraint γ (end)=γ _f, wherein γ _ffor the terminal trajectory tilt angle of demand.In addition, terminal normal g-load is easier there is more obvious miss distance under environment and correlation parameter uncertainty, and another needs the end conswtraint considered to be normal acceleration, i.e. a _m(end)=0.Bullet is generally axisymmetric, and terminal normal acceleration is zero, and the angle of attack can be made less, and due to θ ≈ α+γ, such bullet (i.e. body axle) can be similar to consistent with velocity reversal.

The design of Terminal Guidance Laws is divided into pitch plane and turning plane, and the optimal guidance law of turning plane is proportional guidance law, does not need bamboo product.Guidance Law in this design pitch plane.

According to above-mentioned method for designing, there is following corresponding design procedure.

Step 1: end conswtraint and the number of analyzing terminal guidance problem.

Need the end conswtraint considered to have trajectory tilt angle and normal acceleration constraint, and aircraft finally need hit, adds that range retrains, and has three constraints.

Step 2: determine Sliding mode variable structure control exponent number, design slip variable.

Due to by three end conswtraints, the design of Terminal Guidance Laws is three rank sliding formwork control problems, and key is choosing of slipping plane f (x).First constraint is range, and f → 0 can ensure aircraft hit; And the single order of displacement is led as speed, consider that the longitudinal velocity of aircraft is directly related with trajectory tilt angle, therefore design second and be constrained to longitudinal velocity, f ' → 0 can ensure that terminal trajectory tilt angle meets constraint requirements; The second order of displacement is led as acceleration, and the single order that the second order of range leads i.e. trajectory tilt angle is led as normal acceleration, and " → 0 can ensure that terminal normal acceleration meets constraint requirements to f; In addition, in vertical direction, hit trends towards zero by residual non-uniformity and ensures.Had above analysis, structure slipping plane is as follows

$s=\frac{T-x}{V}-\cos \left({\mathrm{\γ}}_F\right)\·T_{\mathrm{go}}$

In above formula, T is target location, and x is current flight device lengthwise position, and V is speed, γ _ffor the final trajectory tilt angle that end conswtraint requires, T _gofor residual non-uniformity, s → 0 can make final miss distance be zero, meets range requirement, thus hit.Suppose speed term constant (changing less in reality), can obtain above formula differentiate

$\stackrel{\·}{s}=-\cos \left(\mathrm{\γ}\right)+\cos \left({\mathrm{\γ}}_F\right)$

γ → γ can be made _f, thus make final trajectory tilt angle meet constraint.Continue can obtain above formula differentiate

$\stackrel{\·\·}{s}=\sin \left(\mathrm{\γ}\right)\·\frac{a_m}{V}$

Wherein a _mfor normal acceleration.Because when the large angle of fall reenters, sin (γ) is non-vanishing, therefore can ensure that final normal acceleration is zero, thus indirectly make the final angle of attack very little.Flight control system first-order lag link can be represented there is following relation between command acceleration and actual acceleration at this

${\stackrel{\·}{a}}_m=\frac{1}{T_{\mathrm{\α}}}(a_{\mathrm{cmd}}-a_m)$

Wherein T _αfor flight control system time constant, a _cmdfor command acceleration.It is right to continue differentiate can obtain

$\stackrel{\·\·\·}{s}=\frac{\cos \left(\mathrm{\γ}\right)}{V^2}\·{a_m}^2+\frac{\sin \left(\mathrm{\γ}\right)}{T_{\mathrm{\α}}V}\·(a_{\mathrm{cmd}}-a_m)$

Control item command acceleration u (a has been there is in above formula _cmd).

Step 3: finite time back-stepping design, obtains the Guidance Law of whole system.

Therefore according to the Backstepping Based Inverse Design Method of above-mentioned finite time, the control u (a of Guidance Law can be tried to achieve _cmd) be

$u\left(a_{\mathrm{cmd}}\right)=\frac{T_{\mathrm{\α}}V}{\sin \left(\mathrm{\γ}\right)}(\stackrel{\·\·\·}{s}-\frac{\cos \left(\mathrm{\γ}\right)}{V^2}\·{a_m}^2)+a_m$

Wherein

$\left\{\begin{array}{c}\stackrel{\·\·\·}{s}=-\mathrm{\η}\·\mathrm{sign}\left(s_3\right)-n\frac{\stackrel{\·\·}{s}\·{T_{\mathrm{go}}}^2+2[\stackrel{\·}{s}\·T_{\mathrm{go}}+s]}{{T_{\mathrm{go}}}^3}\\ -n[\frac{\stackrel{\·}{s}\·T_{\mathrm{go}}+\stackrel{\·}{s}}{{T_{\mathrm{go}}}^2}+n\frac{\stackrel{\·}{s}\·T_{\mathrm{go}}+2s}{{T_{\mathrm{go}}}^3}]\\ s_3=\stackrel{\·\·}{s}+n\frac{\stackrel{\·}{s\·}{T}_{\mathrm{go}}+s}{{T_{\mathrm{go}}}^2}+\frac{n}{T_{\mathrm{go}}}(\stackrel{\·}{s}+n\frac{s}{T_{\mathrm{go}}})\\ \stackrel{\·\·}{s}=\sin \left(\mathrm{\γ}\right)\·\frac{a_m}{V}\\ \stackrel{\·}{s}=-\cos \left(\mathrm{\γ}\right)+\cos \left({\mathrm{\γ}}_F\right)\\ s=\frac{T-x}{V}-\cos \left({\mathrm{\γ}}_F\right)\·T_{\mathrm{go}}\end{array}\right.$

Command acceleration u (a is drawn according to above-mentioned Guidance Law _cmd) after, corresponding instruction angle of attack can be tried to achieve _cmd.

Reentering Maneuvering Missile and reenter latter end---drop-down lead segment initial point kinematic parameter is: speed V ₀=800m/s, trajectory tilt angle γ ₀=-10 °, height h ₀=10km.End conswtraint is: target location T=7km, terminal normal g-load constraint a _m(end)=0.Retraining the maximum angle of attack is in addition α _max=25 °, maximum yaw angle is β _max=15 °.Consider that terminal trajectory tilt angle is constrained to-90 ° ,-80 ° ,-70 ° and-60 ° of four kinds of situations respectively, figure below 4-7 provides Numerical Simulation Results.Fig. 4 is range altitude curve, and under the constraint of different terminals trajectory tilt angle, the Terminal Guidance Laws using the inventive method to derive can guide bullet with the angle pinpointing of demand.Fig. 5 is corresponding trajectory tilt angle curve, and simulation result display trajectory tilt angle finally can meet constraint requirements.Fig. 6 is corresponding normal g-load curve, and the final normal g-load of display context of methods is very little, and simulation result terminal normal g-load is ideally less than 0.02g, and g is acceleration of gravity.Fig. 7 provides under this method terminal inclination angle is constrained to-90 ° of situations, slip variable and one, second derivative situation of change in time, show its can asymptotic convergence to zero, thus corresponding end conswtraint can be met.

The Numerical Simulation Results of Fig. 4-7 shows, the Guidance Law using the inventive method to obtain, can make aircraft while hit, meet each end conswtraint.

Claims (1)

1. a maneuvering-vehicle multiple terminals constraint inverting Sliding Mode Guidance method, is characterized in that: the method concrete steps are as follows:

Step one: end conswtraint and the number of analyzing terminal guidance problem;

For general terminal guidance problem, first require aircraft hit, at least there is an end conswtraint relevant to displacement; Next, the aircraft of different task demand needs when arrival or hit, requires predetermined trajectory tilt angle or hit impingement angle, the end conswtraint that just existence one is relevant to angle; Finally, in some cases, also likely need to consider that other retrain, in order to make aircraft keep better stability and robustness under environment and the probabilistic situation of correlation parameter, adding the constraint of terminal normal g-load has its necessity;

Step 2: determine Sliding mode variable structure control exponent number, design slip variable;

After analyzing the end conswtraint that terminal guidance problem will consider, just according to end conswtraint number determination Sliding mode variable structure control exponent number, and then problem is converted into the design of slip variable; Suitable variable is found in the design of this slipping plane, make variable and certain order derivative thereof level off to 0 with meet each end conswtraint and combine;

Step 3: finite time back-stepping design, obtains the Guidance Law of whole system;

After devising suitable slip variable, use the backstepping back-stepping design that finite time arrives, provide the final Guidance Law of whole system, this Guidance Law accurately can arrive target by directing aircraft, meets each end conswtraint simultaneously.