CN103245257A - Guidance law of multi-constraint aircraft based on Bezier curve - Google Patents

Abstract

The invention provides a guidance law of a multi-constraint aircraft based on a Bezier curve, and belongs to the technical field of aircraft dynamics and guidance. According to a specified aircraft motion model and a three-order Bezier curve equation simulative ballistic trajectory, an attack angle and a heeling angle of the aircraft are determined by four controlling points with two middle controlling points described by parameters k1 and k2; a range of the parameters k1 and k2 meeting requirements of miss distance, collision angle and terminal attack angle is acquired through optimization; values of k1 and k2 corresponding to terminal speed maximum and terminal speed minimum are figured out; and according to a given terminal speed, the parameters of k1 and k2 are determined. Based on inverse dynamics, the terminal collision angle, the attack angle and speed constraint are all considered, requirements on the collision angle, the terminal attack angle and terminal collision speed can be met, and accurate attacks on fixed targets are achieved.

Description

Multiple constraint aircraft guidance method based on the Bezier curve

Technical field

The invention belongs to vehicle dynamics and guidance technology field, relate to a kind of aircraft final guidance method, be specifically related to a kind of guidance method that uses when a kind of aircraft is independently attacked fixed ground target.

Background technology

The missile guidance rule is that guidance law is one of fire control system key technology that realizes in the air battle opportunity of combat tracking/interception guiding.The selection of guidance law is most important to the guided missile Europe precision strike target that starts.The factor that classical guidance law is mainly considered is miss distance.Along with the development of technology, no matter anti-warship guided missle or ground-to-ground missile, when guaranteeing miss distance, according to the impingement angle intersection target of expectation, and to keep the attitude of expectation and speed during intersection be that the target of restraining is guided in design.Guidance law mainly contains based on the explicit guidance law of analytical form with based on the guidance law of numerical optimization.

The explicit guidance law of different constraints has been realized in list of references [1]～[10] with different expression-forms.Lu has designed a kind of self-adapting closed loop guidance law based on proportional guidance, can be according to the high-precision hit of the direction (list of references [1]: P.Lu of expectation, D.B.Doman, and J.D.Schierman, " Adaptive Terminal Guidance for Hypervelocity Impact in Specified Direction, " Journal of Guidance Control and Dynamics, Vol.29, No.2,2006, pp.269-278); A.Ratnoo has proposed a kind of guidance rule based on proportional guidance, can be implemented in the plane and hit fixed target (list of references [2]: A.Ratnoo according to all possible impingement angle, and D.Ghose, " Impact Angle Constrained Interception of Stationary Targets; " Journal of Guidance Control and Dynamics, Vol.31, No.6,2008, pp.1816-1821); C.Ryoo has designed a kind of energetic optimum guidance law (list of references [3]: C.Ryoo that satisfies the terminal impingement angle, H.Cho, and M.Tahk, " Optimal Guidance Laws with Impact Angle Constraint; " Journal of Guidance Control and Dynamics, Vol.28, No.4,2005, pp.724-732); Y.Lee has designed a kind of optimal guidance rule (list of references [4]: Y.Lee, C.Ryoo, and E.Kim, " Optimal Guidance with Constraints on Impact Angle and Terminal Acceleration; " AIAA Guidance, Navigation, and Control Conference and Exhibit, 2003, Austin, Texas pp.1-7), can adjust the terminal acceleration when satisfying the requirement of miss distance and terminal impingement angle; R.York has then designed a kind of optimal guidance rule (list of references [5]: R.J.York that can satisfy impingement angle and the requirement of the terminal angle of attack simultaneously, and H.L.Pastrick, " Optimal Terminal Guidance with Constraints at Final Time; " Journal of Spacecraft, Vol.14, No.6,1977, pp.381-383); I.R.Manchester has designed a kind of plane intersection guidance law that the impingement angle constraint is arranged, this guidance law is to have adopted to follow the tracks of a circular arc to the thinking of target, information (the list of references [6]: I.R.Manchester that does not need range-to-go, and A.V.Savkin, " Circular-Navigation-GuidanceLawfor Precision Missile/Target Engagements; " Journal of Guidance Control and Dynamics, Vol.29, No.2,2006, pp.314-320).B.S.Kim has designed a kind of proportional guidance law of biasing, this guidance law is to increase the bias term that becomes for the moment on the basis of traditional proportional guidance, the attitude hit that can realize expecting (list of references [7]: B.S.Kim, J.G.Lee, and H.S.Han, " Biased PNG Law for impact with Angular Constraint; " IEEE Transactions on Aerospace and Electronics Systems, Vol.34, No.1,1998, pp.277-288).R.W.Morgan designed the constraint of a kind of normal acceleration the guidance law (list of references [8]: R.W.Morgan of energetic optimum, H.Tharp, and T.L.Vincent, " Minimum Energy Guidance for Aerodynamically Controlled Missiles; " IEEE Transactions on Automatic Control, Vol.56, No.9,2011, pp.2026-2037).D.Sang has designed a kind of guidance law of considering the restriction of the target seeker angle of visual field, can guarantee target (list of references [9]: D.Sang in target seeker locking visual field all the time by conversion logic, C.Ryoo, and M.Tahk, " A Guidance Law with a Switching Logic for Maintaining Seeker ' s Lock-on for Stationary Targets, " KSAS International Journal, Vol.9, No.2,2008, pp.87-97).A.Naghash has designed the explicit guidance law of a kind of suboptimum based on the inverse dynamics method.The relevant parameter of three rank Bezier curves of trajectory is described by offline optimization, obtain the trajectory of end speed maximum, then this parameter is used for guidance law, but the method is not considered constraint (lists of references [10]: A.Naghash such as impingement angle constraint and the terminal angle of attack, R.Esmaelzadeh, M.Mortazavi, and R.Jamilnia, " Near Optimal Guidance Law for Decent to a Point Using Inverse Problem Approach; " Aerospace Science and Technology, No.12,2008, pp.241-247).

List of references [11]～[13] realize fixed target is accurately collided with desired angle based on the guidance law of online numerical optimization.K.P.Bollino has designed a kind of guidance law based on pseudo-spectral method on-line optimization, constantly revise disturbance and the uncertain deviation of bringing by on-line optimization, the method has higher requirement (list of references [11]: K.P.Bollino to the computing capability of missile-borne computer, I.M.Ross, and D.D.Doman, " Optimal Nonlinear Feedback Guidance for Reentry Vehicles; " AIAA Guidance, Navigation, and Control Conference and Exhibit, 2006, Keystone, Colorado, pp.1-20).H.B.Oza successful Application non-linear mould predictive static planning method is in the guidance of air-to-ground guided missile, the method is when guaranteeing miss distance, can guarantee the constraint of impingement angle, with the minimum target (list of references [12]: H.B.Oza as planning of normal g-load, and R.Padhi, " Impact-Angle-Constrained Suboptimal Model Predictive StaticProgramming Guidance of Air-to-Ground Missiles; " Journal of Guidance Control and Dynamics, Vol.35, No.1,2012, pp.153-164).A.Ratnoo becomes nonlinear programming problem with the guiding problem description of impingement angle constraint in the two dimensional surface, utilize the SDRE technology to carry out finding the solution (list of references [13]: A.Ratnoo then, and D.Ghose, " State-Dependent Riccati-Equation-Based Guidance Law for Impact-Angle-Constrained Trajectories; " Journal of Guidance Control and Dynamics, Vol.32, No.1,2009, pp.320-325).

But all also there is not record can guarantee impingement angle, the terminal angle of attack and the guidance method of regulating terminal impact velocity well simultaneously in the above-mentioned prior art.

Summary of the invention

The objective of the invention is in order to address the above problem, the guidance method of the terminal impingement angle of a kind of consideration based on the inverse dynamics method, the angle of attack and constraint of velocity is proposed, namely based on the multiple constraint aircraft guidance method of Bezier curve, the inventive method can guarantee impingement angle, the terminal angle of attack simultaneously and regulate terminal impact velocity.

The multiple constraint aircraft guidance method based on the Bezier curve that the present invention proposes comprises following step:

The first step, according to concrete aircraft movements model and three rank Bezier curvilinear equations, determine the guiding control instruction, the guiding control instruction adopts the angle of attack of aircraft and angle of heel σ as control variables;

Second goes on foot, calculates by optimizing, and obtains to satisfy the k of miss distance, impingement angle and terminal angle of attack requirement ₁And k ₂Scope;

The 3rd goes on foot, goes on foot in the scope that obtains second, finds the maximum and minimum corresponding k of tip speed of tip speed ₁And k ₂Value according to given tip speed, is determined parameter k ₁And k ₂

The described first step determines that the angle of attack of aircraft and the method for angle of heel σ are:

At first, adopt three rank Bezier curves to come the trajectory of match vertical guide and horizontal plane, concrete formula is as follows:

$\left\{\begin{array}{c}x={(1-\mathrm{\&tau;})}^3{x}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{x}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})x_2+{\mathrm{\&tau;}}^3{x}_f\\ y={(1-\mathrm{\&tau;})}^3{y}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{y}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})y_2+{\mathrm{\&tau;}}^3{y}_f\\ z={(1-\mathrm{\&tau;})}^3{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{z}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})z_2+{\mathrm{\&tau;}}^3{z}_f\end{array}\right.$

Wherein, x, y, z are the arbitrary position coordinateses on the space trajectory of aircraft of match; Parameter τ ∈ [0,1], τ=0 represents starting point, and τ=1 represents terminal point; (x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x _f, y _f, z _f) for controlling four control points of ballistic-shaped, (x ₀, y ₀, z ₀) and (x _f, y _f, z _f) be respectively starting point and the terminal point of trajectory; Four control point (x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂) and (x _f, y _f, z _f) point that is mapped on the XOY plane is respectively (x ₀, y ₀), (x ₁, y ₁), (x ₂, y ₂) and (x _f, y _f), point (x then ₀, y ₀) and (x ₁, y ₁) line and point (x ₂, y ₂) and (x _f, y _f) the intersection point of line be (x _m, y _m); Setting parameter

Parameter

Two control point (x then ₁, y ₁, z ₁) and (x ₂, y ₂, z ₂) use parameter k ₁And k ₂Describe and obtain:

$\left\{\begin{array}{c}{x}_1=x_0+k_1(x_m-x_0)\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00003036851200031.png,HDA00003036851200032.png"\; state="\{\{state\}\}">y</figure-callout>}}_1={\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+\frac{\tan {\mathrm{\&gamma;}}_0}{\cos {\mathrm{\&psi;}}_0}(x_1-x_0)\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00003036851200031.png,HDA00003036851200032.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=z_0-\tan {\mathrm{\&psi;}}_0(x_1-x_0)\end{array}\right.;$ $\left\{\begin{array}{c}{x}_2=x_m+k_2(x_f-x_m)\\ y_2=y_f-\frac{\tan {\mathrm{\&gamma;}}_f}{\cos {\mathrm{\&psi;}}_f}(x_f-x_2)\\ z_2=z_f+\tan {\mathrm{\&psi;}}_f(x_f-x_2)\end{array}\right.;$ k ₁∈[0,1]，k ₂∈[0,1]

Further, determine the instruction a of the normal acceleration under the trajectory coordinate system _YBInstruction a with side acceleration _ZB:

a _yB＝gcosγ+v ²cosγcosψdγ/dx

a _zB＝-v ²cos ²γcosψdψ/dx

Wherein, g is acceleration of gravity, and γ is trajectory tilt angle, and v is the speed of aircraft, and ψ is trajectory deflection angle.

Secondly, determine the normal acceleration a under the trajectory coordinate system _yWith side acceleration a _z:

$\left\{\begin{array}{c}{a}_y=a_{\mathrm{yB}}\left(0\right)\&CenterDot;n_{\&perp;\max }\&CenterDot;g/\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}\\ a_z=a_{\mathrm{zB}}\left(0\right)\&CenterDot;n_{\&perp;\max }\&CenterDot;g/\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}\end{array}\right.\mathrm{if}\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}/g>n_{\&perp;\max }$

$\left\{\begin{array}{c}{a}_y=a_{\mathrm{yB}}\left(0\right)\\ a_z=a_{\mathrm{zB}}\left(0\right)\end{array}\right.\mathrm{if}\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}/g\&le;n_{\&perp;\max }$

Wherein, a _YB(0) is instruction in the corresponding normal acceleration of initial time, a _ZB(0) is instruction in the corresponding side acceleration of initial time, n _{⊥ max}It is the available normal g-load of aircraft.

Then, obtain angle of heel instruction σ _cWith angle of attack instruction α _c: $\left\{\begin{array}{c}{\mathrm{\&sigma;}}_c=\arctan (a_z/a_y)\\ {\mathrm{\&alpha;}}_c={f_L}^{-1}(M_a,{\mathrm{ma}}_y/\left(\mathrm{qS}\cos \mathrm{\&sigma;}\right))\end{array}\right.;$ Wherein, M _aBe Mach number, M _a=v/a, a are local velocity of sound, and m represents the quality of aircraft, dynamic pressure q=ρ v ²2, ρ is atmospheric density, and S is area of reference, f _LBe lift coefficient C _LRepresentative function.

At last, determine the angle of heel σ of aircraft:

Wherein,

Be the constant of setting, the expression angle of heel is to the greatest measure of time differentiate; σ _MinAnd σ _MaxBe the constant of setting, represent minimum of a value and maximum that angle of heel need be set respectively; σ _PrevThe angle of heel of representing the last guidance cycle, t _PrevRepresent the time in last guidance cycle, t represents the current time.

According to the angle of heel σ that obtains, can determine angle of attack instruction α _c, further determine the angle of attack of aircraft:

Wherein,

Be the constant of setting, the expression angle of attack is to the greatest measure of time differentiate; α _MinAnd α _MaxBe the constant of setting, represent minimum of a value and maximum that the angle of attack need be set respectively; α _PrevThe angle of attack of representing the last guidance cycle.

Advantage and the good effect of aircraft guidance method of the present invention are:

(1) can realize precision strike to fixed target;

(2) satisfy the requirement of terminal impingement angle;

(3) satisfy the requirement of terminal Low Angle Of Attack;

(4) satisfy the border requirement of process variables such as the angle of attack, normal g-load.

Description of drawings

Fig. 1 is the whole steps flow chart schematic diagram of aircraft guidance method provided by the invention;

Fig. 2 is the schematic diagram of using the trajectory of Bezier curve estimation in the step 1 of the present invention;

Fig. 3 is trajectory tilt angle, speed, the angle of attack variation curve under the different terminal trajectory tilt angle situations;

Fig. 4 is the vertical guide ballistic curve under the different terminal trajectory tilt angle situations;

Fig. 5 is the k that satisfies miss distance and terminal trajectory tilt angle requirement ₁And k ₂The schematic diagram of span;

Fig. 6 is that tip speed is with k ₁And k ₂The curved surface that changes;

Fig. 7 is that tip speed is with k ₁And k ₂The curve that changes;

Fig. 8 is that tip speed, terminal trajectory tilt angle and miss distance are with k ₂The curve that changes.

The specific embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention is directed to the unpowered glide vehicle final guidance problem that reenters, a kind of multiple constraint aircraft guidance method based on the Bezier curve of proposition, flow process comprises following step as shown in Figure 1:

The first step, according to aircraft movements model and three rank Bezier curve's equation, derive the guiding control instruction.

Step 1.1: set up and reenter the glide vehicle motion model, this model comprises suffered constraints in the equation of motion and the aircraft movements process.

Because hypersonic aircraft is less in the descending branch flying distance, can suppose that the earth is a plane earth, aircraft is counted as motorless particle in descending branch, and the equation of motion of its decline is as follows:

$\stackrel{\&CenterDot;}{v}=(D-\mathrm{mg}\sin \mathrm{\&gamma;})/m$

$\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=(L\cos \mathrm{\&sigma;}-\mathrm{mg}\cos \mathrm{\&gamma;})/\left(\mathrm{mv}\right)$

$\stackrel{\&CenterDot;}{\mathrm{\&psi;}}=L\sin \mathrm{\&sigma;}/(-\mathrm{mv}\cos \mathrm{\&gamma;})$

$\stackrel{\&CenterDot;}{x}=v\cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}$ (1)

$\stackrel{\&CenterDot;}{y}=v\sin \mathrm{\&gamma;}$

$\stackrel{\&CenterDot;}{z}=-v\cos \mathrm{\&gamma;}\sin \mathrm{\&psi;}$

Wherein lift L and resistance D are defined as follows:

L＝qSC _L D＝qSC _D (2)

Wherein, dynamic pressure q=ρ v ²2.M represents the quality of aircraft, and g represents acceleration of gravity, and γ is trajectory tilt angle, and σ is the angle of heel of aircraft, and v is the speed of aircraft, and ψ is trajectory deflection angle, and x, y, z are the position coordinateses of aircraft.The expression derivative of adding some points on the character.Described trajectory refers to the flight path of aircraft.United States standard atmosphere COESA model in 1976 is adopted in the calculating of atmospheric density ρ.S is area of reference, C _LBe lift coefficient, C _DBe resistance coefficient, C _LAnd C _DObtained by given data fitting, can be described as following form:

C _L＝f _L(M _a,α) C _D＝f _D(M _a,α) (3)

Wherein, f _LBe lift coefficient C _LRepresentative function, f _DBe resistance coefficient C _DRepresentative function, α is the angle of attack of aircraft, M _aBe Mach number, M _a=v/a, a are local velocity of sound.

Aircraft suffered constraints in the motion process that descends has: angle of fall constraint, terminal-velocity constraint, control constraint and normal g-load constraint.

(1) owing to the needs that open quick-fried requirement and specific tasks of warhead, terminal trajectory tilt angle need reach the angle of appointment, and then the angle of fall constraints of trajectory tilt angle γ is:

γ _fmin≤γ _f≤γ _fmax (4)

Wherein, γ _FminAnd γ _FmaxBe the constant of an appointment, operated by rotary motion, is selected between 0 degree according to actual needs at-90 degree, establishes t _fThe terminal juncture of expression missile flight, γ _fThe value of the trajectory tilt angle of expression terminal juncture.

(2) for the demand of mission requirements and guidance system, the terminal-velocity of aircraft has also been proposed strict requirement, terminal-velocity is constrained to:

v _fmin≤v _f≤v _fmax (5)

V wherein _FminAnd v _FmaxBe the constant of an appointment, v _FmaxGreater than v _Fmin, generally all be the value greater than 0, specifically selected according to actual needs, it is about 1000m/s that two constants for example can be set.v _fExpression terminal juncture t _fThe time aircraft speed.

(3) adopt angle of attack and angle of heel σ as control variables among the present invention, according to the general requirement of aircraft, need the angle of attack and angle of heel to guarantee in certain scope:

α _min≤α≤α _max σ _min＜σ＜σ _max (6)

Wherein, α _Min, α _Max, σ _Min, σ _MaxIt is given constant.α _MinAnd α _MaxRepresent minimum of a value and maximum that the angle of attack need be set respectively.σ _MinAnd σ _MaxRepresent minimum of a value and maximum that angle of heel need be set respectively.

Owing to consider dynamic process and realizability, the rate of change of the angle of attack and angle of heel also there is corresponding constraint:

$\left|\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}\right|\&le;{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{\max }\left|\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}\right|\&le;{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{\max }---\left(7\right)$

Wherein,

Be given constant, unit is: deg/s, be traditionally arranged to be between 0.1 to 90, and can arrange according to actual needs. The expression angle of heel is to the greatest measure of time differentiate.

The expression angle of attack is to the greatest measure of time differentiate.

(4) the normal g-load n of aircraft in the decline process _⊥Absolute value can not be greater than the available normal g-load n of aircraft _{⊥ max}, this constraint specification is as follows:

|n _⊥|≤n _⊥max (8)

The hot-fluid of aircraft, dynamic pressure also need to meet certain constraint in the decline process, but under study for action, find that hot-fluid and dynamic pressure all can meet the requirements, and are not the principal contradictions of this section, so do not consider separately.

Step 1.2: obtain the multiple constraint steering instruction based on three rank Bezier curves.

Aircraft descending branch trajectory is projected to the Ox of earth axes _dy _dVertical plane and Oy _dz _dHorizontal plane.Trajectory moves according to given Bezier curve law on these two planes.

The Bezier curve P (τ) on n rank is defined as:

$P\left(\mathrm{\&tau;}\right)=\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{B}_i{J}_{n,i}\left(\mathrm{\&tau;}\right)---\left(9\right)$

Wherein, B _iRepresent i control point, the Bernstein basic function

Parameter τ ∈ [0,1], τ=0 represents starting point, and τ=1 represents terminal point.

The r order derivative of multinomial (9) can be write as

$\frac{d^r}{{\mathrm{d\&tau;}}^r}P\left(\mathrm{\&tau;}\right)=\frac{n!}{(n-r)!}\underset{i=0}{\overset{n-r}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;}}^r{B}_i{J}_{n-r,i}---\left(10\right)$

Wherein, Δ ⁰B _i=B _i; Δ ^kB _i=Δ ^K-1B _I+1-Δ ^K-1B _i, k=0 ..., r.Δ ^kB _iI the control point of expression curve P (τ) when the differentiate of k rank.

Adopt three rank Bezier curves to come the trajectory of match vertical guide and horizontal plane in the inventive method, concrete formula is as follows:

$\left\{\begin{array}{c}x={(1-\mathrm{\&tau;})}^3{x}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{x}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})x_2+{\mathrm{\&tau;}}^3{x}_f\\ y={(1-\mathrm{\&tau;})}^3{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00003036851200031.png,HDA00003036851200032.png"\; state="\{\{state\}\}">y</figure-callout>}}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})y_2+{\mathrm{\&tau;}}^3{y}_f\\ z={(1-\mathrm{\&tau;})}^3{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00003036851200031.png,HDA00003036851200032.png"\; state="\{\{state\}\}">z</figure-callout>}}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})z_2+{\mathrm{\&tau;}}^3{z}_f\end{array}\right.---\left(11\right)$

(x, y are to appoint position coordinates, (x on the space trajectory of aircraft of match z) ₀, y ₀, z ₀), (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x _f, y _f, z _f) for controlling four control points of ballistic-shaped, wherein, (x ₀, y ₀, z ₀), (x _f, y _f, z _f) be respectively starting point and the terminal point of trajectory, middle two control point (x ₁, y ₁, z ₁) and (x ₂, y ₂, z ₂) not on trajectory.Middle two control point parameter k ₁And k ₂Describe and obtain.As shown in Figure 2, four control point (x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂) and (x _f, y _f, z _f) point that is mapped on the XOY plane is respectively (x ₀, y ₀), (x ₁, y ₁), (x ₂, y ₂) and (x _f, y _f), point (x then ₀, y ₀) and (x ₁, y ₁) line and point (x ₂, y ₂) and (x _f, y _f) the intersection point of line be (x _m, y _m), according to the plane geometry relation, can access the trajectory tilt angle γ at starting point place ₀Trajectory tilt angle γ with destination county _fHave following relation:

$\tan {\mathrm{\&gamma;}}_0=\frac{y_m-y_0}{x_m-x_0};$ $\tan {\mathrm{\&gamma;}}_f=\frac{y_f-y_m}{x_f-x_m};$

Further, can determine coordinate (x _m, y _m): $\left\{\begin{array}{c}{x}_m=\frac{x_f\tan {\mathrm{\&gamma;}}_f-x_0\tan {\mathrm{\&gamma;}}_0+y_0-y_f}{\tan {\mathrm{\&gamma;}}_f-\tan {\mathrm{\&gamma;}}_0}\\ y_m=-(x_f-x_m)\tan {\mathrm{\&gamma;}}_f+y_f\end{array}\right.$

Setting parameter

Obtain two control point (x then ₁, y ₁, z ₁) and (x ₂, y ₂, z ₂) as shown in the formula:

$\left\{\begin{array}{c}{x}_1=x_0+k_1(x_m-x_0)\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00003036851200031.png,HDA00003036851200032.png"\; state="\{\{state\}\}">y</figure-callout>}}_1={\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+\frac{\tan {\mathrm{\&gamma;}}_0}{\cos {\mathrm{\&psi;}}_0}(x_1-x_0)\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00003036851200031.png,HDA00003036851200032.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=z_0-\tan {\mathrm{\&psi;}}_0(x_1-x_0)\end{array}\right.---\left(12\right)$

$\left\{\begin{array}{c}{x}_2=x_m+k_2(x_f-x_m)\\ y_2=y_f-\frac{\tan {\mathrm{\&gamma;}}_f}{\cos {\mathrm{\&psi;}}_f}(x_f-x_2)\\ z_2=z_f+\tan {\mathrm{\&psi;}}_f(x_f-x_2)\end{array}\right.---\left(13\right)$

Generally speaking, k ₁∈ [0,1], k ₂∈ [0,1]; As long as select suitable k ₁And k ₂, according to formula (12) and (13), just can obtain the coordinate at corresponding middle two control points, so just can control the shape of trajectory.The trajectory of estimating with the Bezier curve as shown in Figure 2.

The equation of motion (1) is write the form of paired x differentiate, and concrete equation is as follows:

dv/dx＝(D-mgsinγ)/(mvcosγcosψ)

dγ/dx＝(Lcosσ-mgcosγ)/(mv ²cosγcosψ)

dψ/dx＝Lsinσ/(-mv ²cos ²γcosψ) (14)

dy/dx＝tanγ/cosψ

dz/dx＝-tanψ

Normal acceleration a under the trajectory coordinate system _yWith side acceleration a _zMay be defined as:

a _y＝Lcosσ/m;a _z＝Lsinσ/m (15)

Can solve the instruction a of normal acceleration according to kinetics equation (14) _YBInstruction a with side acceleration _ZBFor:

a _yB＝gcosγ+v ²cosγcosψdγ/dx (16)

a _zB＝-v ²cos ²γcosψdψ/dx

In order further to find the solution d γ/dx and the d ψ/dx in the formula (16), can be got by kinetics equation,

tanγ＝cosψdy/dx;tanψ＝-dz/dx (17)

Two formula differentiates in top (17) can get

dγ/dx＝(d ²y/dx ²cosψ-dy/dx·dψ/dx·sinψ)cos ²γ (18)

dψ/dx＝-cos ²ψ·d ²z/dx ²

And according to three rank Bezier curve equation (11), can get its to the first derivative of τ and second dervative suc as formula shown in (19) and (20).

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{d\&tau;}=-3{(1-\mathrm{\&tau;})}^2{x}_0+3x_1(3{\mathrm{\&tau;}}^2-4\mathrm{\&tau;}+1)+3x_2(-3{\mathrm{\&tau;}}^2+2\mathrm{\&tau;}))+3{\mathrm{\&tau;}}^2{x}_f\\ \mathrm{dy}/\mathrm{d\&tau;}=-3{(1-\mathrm{\&tau;})}^2{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+3y_1(3{\mathrm{\&tau;}}^2-4\mathrm{\&tau;}+1)+3y_2(-3{\mathrm{\&tau;}}^2+2\mathrm{\&tau;}))+3{\mathrm{\&tau;}}^2{y}_f\\ \mathrm{dz}/\mathrm{d\&tau;}=-3{(1-\mathrm{\&tau;})}^2{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+3z_1(3{\mathrm{\&tau;}}^2-4\mathrm{\&tau;}+1)+3z_2(-3{\mathrm{\&tau;}}^2+2\mathrm{\&tau;}))+3{\mathrm{\&tau;}}^2{z}_f\end{array}\right.---\left(19\right)$

$\left\{\begin{array}{c}{d}^{2}x/d{\mathrm{\&tau;}}^2=6{(1-\mathrm{\&tau;})x}_0+6x_1(3\mathrm{\&tau;}-2)+6x_2(-3\mathrm{\&tau;}+1)+6\mathrm{\&tau;}{x}_f\\ d^{2}y/d{\mathrm{\&tau;}}^2=6(1-\mathrm{\&tau;}){\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+6y_1(3\mathrm{\&tau;}-2)+6y_2(-3\mathrm{\&tau;}+1)+6\mathrm{\&tau;}{y}_f\\ d^{2}z/d{\mathrm{\&tau;}}^2=6(1-\mathrm{\&tau;}){\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA00003036851200021.png,HDA00003036851200031.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+6z_1(3\mathrm{\&tau;}-2)+6z_2(-3\mathrm{\&tau;}+1)+6\mathrm{\&tau;}{z}_f\end{array}\right.---\left(20\right)$

So can obtain first derivative and the second dervative of y and the x of z, respectively suc as formula shown in (21) and (22).

$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{dy}/\mathrm{d\&tau;}}{\mathrm{dx}/\mathrm{d\&tau;}};\frac{\mathrm{dz}}{\mathrm{dx}}=\frac{\mathrm{dz}/\mathrm{d\&tau;}}{\mathrm{dz}/\mathrm{d\&tau;}}---\left(21\right)$

$\frac{d^{2}y}{{\mathrm{dx}}^2}=\frac{\frac{d^{2}y}{{\mathrm{d\&tau;}}^2}-\frac{d^{2}x}{{\mathrm{dt}}^2}\frac{\mathrm{dy}/\mathrm{dt}}{\mathrm{dx}/\mathrm{dt}}}{{\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)}^2};$ $\frac{d^{2}z}{d{x}^2}=\frac{\frac{d^{2}z}{d{\mathrm{\&tau;}}^2}-\frac{d^{2}x}{d{t}^2}\frac{\mathrm{dz}/\mathrm{dt}}{\mathrm{dx}/\mathrm{dt}}}{{\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)}^2}---\left(22\right)$

So the instruction of the normal acceleration of formula (16) is found the solution, but this instruction obtains according to Bezier curve trajectory.In the guidance loop, need to try to achieve normal acceleration a according to current state and given end state in real time _YBWith side acceleration a _ZB, but the actual normal acceleration of using of just at every turn trying to achieve and side acceleration are at the value of initial time, i.e. τ=0 o'clock corresponding value a _YB(0) and a _ZB(0).Each guidance cycle can be upgraded the Bezier curve according to different current states, thereby obtains new guidanceing command.

Because normal g-load is bounded, so consider that the normal acceleration of overload constraint is as follows:

$\left\{\begin{array}{c}{a}_y=a_{\mathrm{yB}}\left(0\right)\&CenterDot;n_{\&perp;\max }\&CenterDot;g/\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}\\ a_z=a_{\mathrm{zB}}\left(0\right)\&CenterDot;n_{\&perp;\max }\&CenterDot;g/\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}\end{array}\right.\mathrm{if}\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}/g>n_{\&perp;\max }---\left(23\right)$

$\left\{\begin{array}{c}{a}_y=a_{\mathrm{yB}}\left(0\right)\\ a_z=a_{\mathrm{zB}}\left(0\right)\end{array}\right.\mathrm{if}\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}/g\&le;n_{\&perp;\max }$

Definition (2) and (3) according to lift and lift coefficient can get

$\begin{array}{c}{\mathrm{\&sigma;}}_c=\arctan (a_z/a_y)\\ {\mathrm{\&alpha;}}_c={f_L}^{-1}(M_a,{\mathrm{ma}}_y/\left(\mathrm{qS}\cos \mathrm{\&sigma;}\right))\end{array}---\left(24\right)$

σ _cThe instruction of expression angle of heel, α _cThe instruction of the expression angle of attack.

But since the size of the angle of attack and angle of heel with and rate of change all need satisfy constraints, the angle of heel σ that use on the historical facts or anecdotes border and angle of attack are definite by formula (25) and (26).

Wherein, σ _PrevThe angle of heel of representing the last guidance cycle, t _PrevThe time of representing the last guidance cycle, α _PrevRepresent the angle of attack in last guidance cycle, t represents the current time.

As long as so choose the parameter k of control Bezier curve shape ₁And k ₂, just can be controlled accordingly according to formula (25) and (26), the control parameter that so only need obtain suitable Bezier curve can obtain steering instruction.

Second goes on foot, calculates by optimizing, and obtains to satisfy the k of miss distance, impingement angle and terminal angle of attack requirement ₁, k ₂Scope;

Formula (25), (26) described guidance law are and parameter k ₁And k ₂Directly related, because k ₁, k ₂Scope be [0,1], so can obtain k by the method cycle calculations of enumerating ₁And k ₂As long as desired scope is k ₁And k ₂Be positioned at this scope, just can satisfy the requirement of miss distance, impingement angle and the terminal angle of attack.

The 3rd the step, according to given tip speed, determine parameter k ₁And k ₂

Terminal position and impingement angle have just been considered during from the choosing of Bezier curve, so as long as aircraft has enough abilities and can realize the described trajectory of this Bezier curve, miss distance and impingement angle all can satisfy so.General by emulation, obtain k ₁And k ₂Scope, embodiment as shown in Figure 5.Under specific primary condition and end condition, can obtain to guarantee the k of miss distance and the constraint of terminal impingement angle ₁And k ₂Scope.Then in this scope, by to k ₁And k ₂Optimization, find the maximum and corresponding k of tip speed minimum of tip speed ₁And k ₂Value.If expectation tip speed maximum only needs to select the maximum corresponding k of tip speed ₁And k ₂Get final product.

From emulation as can be known tip speed to k ₂More responsive, to k ₁Influence little.So fixing k ₁Value, by k ₂Can regulate the size of end speed.As end speed v among Fig. 8 _fWith k ₂Curve map shown in, end speed is with k ₂Monotonic increase.So under nominal condition, realize the end speed expected, adopt the Secant method to revise k in real time according to formula (27) ₂Value, in line interation, can converge to the value of expectation through several times.

$k_2(i+1)=k_2\left(i\right)+\frac{(v_{\mathrm{fdes}}-v_f\left(i\right))(k_2\left(i\right)-k_2(i-1))}{(v_f\left(i\right)-v_f(i-1))}---\left(27\right)$

k ₂(i) k in the i time online iterative process of expression ₂Value, v _FdesThe end speed value of expression expectation, v _f(i) the end speed value of the i time simulation and prediction of expression.

Embodiment:

Among the embodiment, be example with certain hypersonic lifting body aircraft model, 907kg is thought highly of in this flight, and aerodynamic coefficient is relevant with Mach number and the angle of attack.Experiment 1 is the adaptability problem of the guidance rule of checking under the prerequisite of considering normal g-load constraint, the angle of attack and angle of heel constraint, impingement angle constraint and the terminal angle of attack; Experiment 2 is guidance rule problems of further considering the terminal velocity constraint.

Experiment 1: the end speed maximum under the different impingement angle conditions;

Emulation primary condition and terminal condition are as shown in table 1.

The end condition of table 1 emulation primary condition and expectation

The method of guidance that adopts the inventive method to provide, advantage are to guarantee preferably that when guaranteeing accuracy at target terminal impingement angle and terminal angle of attack value are very little.According to the condition that table 1 provides, adopt fmincon order among the matlab2008a, optimize parameter k ₁And k ₂, making the tip speed maximum, the parameter value and the tip speed value that obtain under the terminal trajectory tilt angle condition of difference are as shown in the table.

Simulation result under two kinds of terminal trajectory tilt angle conditions of table 2

Miss distance represents miss distance, is exactly the position deviation of terminal juncture.The trajectory that obtains according to above condition as shown in Figure 3 and Figure 4.Fig. 3 is two kinds of time dependent curve synoptic diagrams of trajectory tilt angle γ, speed v, angle of attack under the terminal trajectory tilt angle.Fig. 4 is two kinds of vertical guide ballistic curve schematic diagrames under the terminal trajectory tilt angle.Among Fig. 3 and Fig. 4, γ _fValue be written as approximately respectively-60deg and-75deg.

Experiment 2: tip speed is regulated and k ₁And k ₂The selection problem;

Under the situation of and selected terminal impingement angle static in target, can be by regulating k ₁And k ₂Value regulate the size of tip speed.At unperturbed emotionally under the condition, at first to find to guarantee that miss distance is 0 and the k that satisfies terminal trajectory tilt angle constraint ₁And k ₂The interval; Try to achieve the value of corresponding given end speed then on the basis in this interval.

Emulation primary condition and terminal condition are as shown in table 3.

The end condition of table 3 emulation primary condition and expectation

By to k ₁And k ₂Carry out combining simulation, obtain to satisfy the k of miss distance constraint and the constraint of terminal trajectory tilt angle ₁And k ₂Scope, as shown in Figure 5.

Further can in above scope, try to achieve suitable k ₁And k ₂To satisfy the tip speed demand.End speed and k ₁And k ₂Relation as shown in Figure 6.

Try to achieve the tip speed minimum point by optimization: (k ₁, k ₂)=(0.80,0.1878), Dui Ying end speed is: 699.9m/s; Tip speed maximum of points: (k ₁, k ₂)=(0.8241,0.5416), Dui Ying end speed is: 1196.2m/s.So, control tip speed between [699.9,1196.2], only need find suitable (k ₁, k ₂) point get final product.As can be seen from Figure 7, work as k ₁When getting different value, corresponding tip speed maximum and minimum of a value change all little, that is to say the main and k of end speed ₂Relevant.

Select k in this example ₁=0.9; By optimizing, can try to achieve corresponding tip speed minimum of a value v _MinK ₂Value k ₂_ v _Min=0.2388, corresponding tip speed minimum of a value v _MinFor: 699.94m/s, respective ends speed maximum v _MaxK ₂Value k ₂_ v _Max=0.6297, corresponding tip speed maximum v _MaxFor: 1195.3m/s.Can find out the minimax tip speed of acquisition and optimize k simultaneously from optimizing the result ₁And k ₂The time result that obtains close; And also can find out k from Fig. 7 ₁In scope shown in Figure 5, select a certain fixing value, only change k ₂Just can obtain to approach maximum and approaching minimum tip speed.Therefore for convenience's sake, in the analysis of back, directly select k ₁=0.9.

If k ₁=0.9, k ₂∈ [k ₂_ v _Min, k ₂_ v _Max], miss distance and terminal trajectory tilt angle all can satisfy well, and as shown in Figure 8, and end speed is with k ₂In this interval monotonic increase, so as long as at the different k of this interval selection ₂Value just can obtain different tip speeds; k ₂Less than k ₂_ v _MinPerhaps greater than k ₂_ v _MaxThe time, because the restriction of control ability can't provide the normal acceleration of the trajectory that meets the expectation, so can't guarantee the requirement of miss distance and terminal impingement angle; And because terminal-velocity v _fAt [k ₂_ v _Min, k ₂_ v _Max] interval is monotonically increasing, so the tip speed that will realize belonging to arbitrarily between [699.94,1195.3] m/s all can find corresponding parameter k by interpolation ₂

That is to say, emotionally under the condition, want control rate v at unperturbed _f∈ [699.94,1195.3] m/s finds suitable k according to Fig. 8 ₂Get final product.In the actual guidance problem, adopt the Secant method can look for suitable k through online iteration several times ₂Thereby, obtain the tip speed of expecting.

Emulation primary condition and terminal condition are as shown in table 3, and to require end speed on this basis be 1100m/s; Select k ₁=0.9, adopt iterative formula (27), ask k ₂, select k ₂Initial value be: 0.5, the iteration stopping condition is | v _Fdes-v _f|＜0.1, can converge to k through 5 iteration ₂=0.428; Simulation result is as shown in table 4.

Table 4 simulation result

Wherein, miss distance represents miss distance, is exactly the position deviation of terminal juncture, Δ v _fExpression physical end speed and the deviation of expecting terminal velocity, Δ γ _fDeviation, the α at expression actual trajectory inclination angle and desired trajectory inclination angle _fThe angle of attack of expression terminal juncture, a _YfThe normal acceleration of expression terminal juncture.

Claims (2)

1. the multiple constraint aircraft guidance method based on the Bezier curve is characterized in that, comprises the steps:

The first step, according to aircraft movements model and three rank Bezier curvilinear equations, determine the guiding control instruction, the guiding control instruction adopts the angle of attack of aircraft and angle of heel σ as control variables, the method for specifically determining is:

At first, adopt three rank Bezier curves to come the trajectory of match vertical guide and horizontal plane, concrete formula is as follows:

$\left\{\begin{array}{c}x={(1-\mathrm{\&tau;})}^3{x}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{x}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})x_2+{\mathrm{\&tau;}}^3{x}_f\\ y={(1-\mathrm{\&tau;})}^3{y}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{y}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})y_2+{\mathrm{\&tau;}}^3{y}_f\\ z={(1-\mathrm{\&tau;})}^3{z}_0+3\mathrm{\&tau;}{(1-\mathrm{\&tau;})}^2{z}_1+3{\mathrm{\&tau;}}^2(1-\mathrm{\&tau;})z_2+{\mathrm{\&tau;}}^3{z}_f\end{array}\right.$

Wherein, x, y, z are the arbitrary position coordinateses on the space trajectory of aircraft of match; Parameter τ ∈ [0,1], τ=0 represents starting point, and τ=1 represents terminal point; (x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x _f, y _f, z _f) for controlling four control points of ballistic-shaped, (x ₀, y ₀, z ₀) and (x _f, y _f, z _f) be respectively starting point and the terminal point of trajectory; Four control point (x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂) and (x _f, y _f, z _f) point that is mapped on the XOY plane is respectively (x ₀, y ₀), (x ₁, y ₁), (x ₂, y ₂) and (x _f, y _f), point (x then ₀, y ₀) and (x ₁, y ₁) line and point (x ₂, y ₂) and (x _f, y _f) the intersection point of line be (x _m, y _m); Setting parameter

Parameter

Two control point (x then ₁, y ₁, z ₁) and (x ₂, y ₂, z ₂) use parameter k ₁And k ₂Describe and obtain:

$\left\{\begin{array}{c}{x}_1=x_0+k_1(x_m-x_0)\\ y_1=y_0+\frac{\tan {\mathrm{\&gamma;}}_0}{\cos {\mathrm{\&psi;}}_0}(x_1-x_0)\\ z_1=z_0-\tan {\mathrm{\&psi;}}_0(x_1-x_0)\end{array}\right.;$ $\left\{\begin{array}{c}{x}_2=x_m+k_2(x_f-x_m)\\ y_2=y_f-\frac{\tan {\mathrm{\&gamma;}}_f}{\cos {\mathrm{\&psi;}}_f}(x_f-x_2)\\ z_2=z_f+\tan {\mathrm{\&psi;}}_f(x_f-x_2)\end{array}\right.;$ k ₁∈[0,1]，k ₂∈[0,1]

Further, determine the instruction a of the normal acceleration under the trajectory coordinate system _YBInstruction a with side acceleration _ZB:

a _yB＝gcosγ+v ²cosγcosψdγ/dx

a _zB＝-v ²cos ²γcosψdψ/dx

Wherein, g is acceleration of gravity, and γ is trajectory tilt angle, and v is the speed of aircraft, and ψ is trajectory deflection angle;

Secondly, determine the normal acceleration a under the trajectory coordinate system _yWith side acceleration a _z:

$\left\{\begin{array}{c}{a}_y=a_{\mathrm{yB}}\left(0\right)\&CenterDot;n_{\&perp;\max }\&CenterDot;g/\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}\\ a_z=a_{\mathrm{zB}}\left(0\right)\&CenterDot;n_{\&perp;\max }\&CenterDot;g/\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}\end{array}\right.\mathrm{if}\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}/g>n_{\&perp;\max }$

$\left\{\begin{array}{c}{a}_y=a_{\mathrm{yB}}\left(0\right)\\ a_z=a_{\mathrm{zB}}\left(0\right)\end{array}\right.\mathrm{if}\sqrt{a_{\mathrm{yB}}{\left(0\right)}^2+a_{\mathrm{zB}}{\left(0\right)}^2}/g\&le;n_{\&perp;\max }$

Wherein, a _YB(0) is instruction in the corresponding normal acceleration of initial time, a _ZB(0) is instruction in the corresponding side acceleration of initial time, n _{⊥ max}It is the available normal g-load of aircraft;

Then, obtain angle of heel instruction σ _cWith angle of attack instruction α _c: $\left\{\begin{array}{c}{\mathrm{\&sigma;}}_c=\arctan (a_z/a_y)\\ {\mathrm{\&alpha;}}_c={f_L}^{-1}(M_a,{\mathrm{ma}}_y/\left(\mathrm{qS}\cos \mathrm{\&sigma;}\right))\end{array}\right.;$ Wherein, M _aBe Mach number, M _a=v/a, a are local velocity of sound, and m represents the quality of aircraft, dynamic pressure q=ρ v ²2, ρ is atmospheric density, and S is area of reference, f _LBe lift coefficient C _LRepresentative function;

At last, determine the angle of heel σ of aircraft:

Wherein,

Be the constant of setting, the expression angle of heel is to the greatest measure of time differentiate; σ _MinAnd σ _MaxBe the constant of setting, represent minimum of a value and maximum that angle of heel need be set respectively; σ _PrevThe angle of heel of representing the last guidance cycle, t _PrevRepresent the time in last guidance cycle, t represents the current time;

According to the angle of heel σ that obtains, can determine angle of attack instruction α _c, further determine the angle of attack of aircraft:

Wherein,

Be the constant of setting, the expression angle of attack is to the greatest measure of time differentiate; α _MinAnd α _MaxBe the constant of setting, represent minimum of a value and maximum that the angle of attack need be set respectively; α _PrevThe angle of attack of representing the last guidance cycle;

Second goes on foot, calculates by optimizing, and obtains to satisfy the k of miss distance, impingement angle and terminal angle of attack requirement ₁And k ₂Scope;

The 3rd goes on foot, goes on foot in the scope that obtains second, finds the maximum and minimum corresponding k of tip speed of tip speed ₁And k ₂Value according to given tip speed, is determined parameter k ₁And k ₂

2. aircraft guidance method according to claim 1 is characterized in that, in described the 3rd step, under nominal condition, realize the end speed expected, at first preset parameter k ₁Value, adopt the Secant method to revise k in real time according to following formula then ₂Value:

$k_2(i+1)=k_2\left(i\right)+\frac{(v_{\mathrm{fdes}}-v_f\left(i\right))(k_2\left(i\right)-k_2(i-1))}{(v_f\left(i\right)-v_f(i-1))}$

k ₂(i) k in the i time online iterative process of expression ₂Value, v _FdesThe end speed value of expression expectation, v _f(i) the end speed value of the i time simulation and prediction of expression;

Through in line interation, determine parameter k ₂, and converge to the end speed of expectation.

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