CN106096091A - A kind of airplane motion analogy method - Google Patents

Abstract

The invention discloses a kind of airplane motion analogy method, comprise the steps of S1, the original state parameter of input aircraft；S2, inputs aircraft current state parameter；S3, calculates the derivative of earth's axis system kinematic parameter；S4, using the original state parameter in described step S1 as initial value for integral；Using the derivative in described step S3 as integration rate, it is integrated, solves current four element values of aircraft, fly axis system current angular velocity, aircraft current location, aircraft earth's axis system present speed, aircraft relative to the current angle of attack of earth's axis system speed, aircraft relative to the current yaw angle of earth's axis system speed；S5, calculates aircraft true empty-running speed, the actual angle of attack and actual yaw angle；S6, delivers to aerodynamics evaluation module, the aerodynamic force suffered by accurate simulated aircraft and aerodynamic moment by described aircraft true empty-running speed, the actual angle of attack, actual yaw angle.It is an advantage of the current invention that: to realize the atmospheric perturbation fine analog to aircraft flight Parameters variation process, make airplane motion response the most true to nature.

Description

A kind of airplane motion analogy method

Technical field

The present invention relates to airplane design technical field, be specifically related to a kind of airplane motion analogy method.

Background technology

In field of airplane design and flight simulation field, it usually needs the assessment atmospheric perturbation impact on airplane motion, especially It is the atmospheric perturbation that turbulent flow and wind shear etc. are frequently encountered by practical flight, carries out atmospheric perturbation in flight simulation environment Journey simulation is requisite function in Project R&D and pilot training.Such as, aircraft enters experience wind shear of nearly stage, needs Fine analog aircraft angle of attack and the progressive formation of yaw angle, so that airplane aerodynamic and the truest aircraft of motion are suitable.At present, greatly Gas disturbance is generally directly injected in airplane motion equation with the form of terrestrial coordinate system three axle wind speed component, directly changes and flies Machine ground velocity increment, have ignored ground velocity continually varying dynamic process in Live Flying, reduces people's fidelity at loop test, Have impact on control law and the credibility of flight quality assessment result.

Summary of the invention

It is an object of the invention to provide a kind of airplane motion analogy method, to solve or at least to alleviate in background technology to be deposited The problem at least one place.

The technical solution used in the present invention is: provides a kind of airplane motion analogy method, comprises the steps of

S1, the original state parameter of input aircraft, described original state parameter comprises the initial Eulerian angles of aircraft, aircraft body Axle system initial angular velocity, aircraft initial position, aircraft earth's axis system initial velocity, aircraft are relative to the initial angle of attack of earth's axis system speed With aircraft relative to the initial side-slip angle of earth's axis system speed；

S2, inputs aircraft current state parameter, and described aircraft current state parameter comprises the body axle of bonding force suffered by aircraft It it is the body axle system three axle component of three axle components and bonding force square；Aircraft gross mass, the moment of inertia of each axle of axis system that is diversion and used Property long-pending；The wind speed of current aircraft local environment three axle components in earth's axis system；

S3, calculates the derivative of earth's axis system kinematic parameter, calculates current four element values of aircraft correction,

$norm=\sqrt{(q_1^2+q_2^2+q_3^2+q_4^2)}$

q₁=q₁/norm

q₂=q₂/norm

q₃=q₃/norm

q₄=q₄/norm

In formula, norm is the modulus value of current four elements, q₁、q₂、q₃And q₄For revised four element currencys；

Current direction cosine matrix is calculated according to revised four element currencys；Calculate according to described direction cosine matrix The aircraft earth's axis system present speed three axle components in earth's axis system, described component is also the derivative of aircraft current location；Calculating flies The derivative of machine earth's axis system present speed；Aircraft is relative to the derivative of the earth's axis system current angle of attack of speed；Aircraft is relative to earth's axis system speed Spend the derivative of current yaw angle；Calculating the derivative flying axis system current angular velocity, described current angular velocity comprises current rolling Angular velocity, rate of pitch and yaw rate；Calculate the derivative of four elements；

Initial for aircraft in described step S1 Eulerian angles are converted to four element initial values by S4, and in addition to initial Eulerian angles Other original state parameters are together as initial value for integral；By the derivative of four elements in described step S3, fly axis system roll angle The derivative of speed, the derivative of rate of pitch, the derivative of yaw rate, the derivative of aircraft current location, aircraft earth's axis system work as The derivative of front speed, aircraft currently break away relative to earth's axis system speed relative to derivative and the aircraft of the earth's axis system current angle of attack of speed The derivative at angle, as integration rate, is integrated, and solves current four element values of aircraft, flies axis system current angular velocity, aircraft Current location, aircraft earth's axis system present speed, aircraft relative to the current angle of attack of earth's axis system speed, aircraft relative to earth's axis system speed The current yaw angle of degree；

S5, calculates aircraft airspeed at three axle components of earth's axis system, according to described aircraft airspeed at three axle components of earth's axis system Calculate the aircraft airspeed three axle components in body axle system, calculate aircrafts according to described aircraft airspeed at three axle components of body axle system actual Air speed, the actual angle of attack and actual yaw angle；

S6, delivers to aerodynamics evaluation module by described aircraft true empty-running speed, the actual angle of attack, actual yaw angle, accurately simulates Aerodynamic force suffered by aircraft and aerodynamic moment.

Preferably, in described step S4, initial for aircraft Eulerian angles being converted to four element initial values, concrete conversion method is,

q₁₀=cos (θ₀/2)cos(φ₀/2)cos(ψ₀/2)+sin(θ₀/2)sin(φ₀/2)sin(ψ₀/2)

q₂₀=cos (θ₀/2)sin(φ₀/2)cos(ψ₀/2)-sin(θ₀/2)cos(φ₀/2)sin(ψ₀/2)

q₃₀=sin (θ₀/2)cos(φ₀/2)cos(ψ₀/2)+cos(θ₀/2)sin(φ₀/2)sin(ψ₀/2)

q₄₀=cos (θ₀/2)cos(φ₀/2)sin(ψ₀/2)-sin(θ₀/2)sin(φ₀/2)cos(ψ₀/2)

In formula, q₁₀、q₂₀、q₃₀And q₄₀It is four element initial values, φ₀For roll angle, θ₀For the angle of pitch, ψ₀For course angle.

Preferably, in described step S3,

The specific algorithm of current direction cosine matrix is,

$MDC=\left[\begin{array}{ccc}Ax& Ay& Az\\ Bx& By& Bz\\ Dx& Dy& Dz\end{array}\right],$

$Ax=q_1^2+q_2^2-q_3^2-q_4^2$

Ay=2 (q₂q₃-q₁q₄)

Az=2 (q₂q₄+q₁q₃)

Bx=2 (q₂q₃+q₁q₄)

$By=q_1^2-q_2^2+q_3^2-q_4^2$

Bz=2 (q₃q₄-q₁q₂)

Dx=2 (q₂q₄-q₁q₃)

Dy=2 (q₃q₄+q₁q₂)

$Dz=q_1^2-q_2^2-q_3^2+q_4^2$

In formula, q₁、q₂、q₃And q₄For revised four element currencys；

The aircraft earth's axis system present speed three axle component specific algorithms in earth's axis system are,

$\left[\begin{array}{c}{V}_{xg}\\ V_{yg}\\ V_{zg}\end{array}\right]=\left[\begin{array}{ccc}Ax& Ay& Az\\ Bx& By& Bz\\ Dx& Dy& Dz\end{array}\right]\left[\begin{array}{ccc}cos\mathrm{\α}cos\mathrm{\β}& -cos\mathrm{\α}sin\mathrm{\β}& -sin\mathrm{\α}\\ \sin \mathrm{\β}& cos\mathrm{\β}& 0\\ sin\mathrm{\α}\cos \mathrm{\β}& -\sin \mathrm{\α}sin\mathrm{\β}& \cos \mathrm{\α}\end{array}\right]\left[\begin{array}{c}V\\ 0\\ 0\end{array}\right]$

In formula, V_xg、V_ygAnd V_zgFor the aircraft earth's axis system speed three axle components in earth's axis system, V is that aircraft earth's axis system is current Speed, α is the aircraft current angle of attack relative to earth's axis system speed, and β is the aircraft current yaw angle relative to earth's axis system speed；

The derivative of aircraft earth's axis system present speed specifically,

$\begin{array}{c}\stackrel{\·}{V}=({\mathrm{cos\αcos\βF}}_{xt}+{\mathrm{sin\βF}}_{yt}+{\mathrm{sin\αcos\βF}}_{zt})/m\\ +g(cos\mathrm{\α}cos\mathrm{\β}Dx+sin\mathrm{\α}cos\mathrm{\β}Dz+\sin \mathrm{\β}Dy)\end{array};$

Aircraft relative to the earth's axis system current angle of attack of speed derivative specifically,

$\begin{array}{c}\stackrel{\·}{\mathrm{\α}}=q-(p\cos \mathrm{\α}+r\sin \mathrm{\α})\sin \mathrm{\β}/\cos \mathrm{\β}\\ +(-{\mathrm{sin\αF}}_{xt}+{\mathrm{cos\αF}}_{zt})/m/V\\ +g(Dz\cos \mathrm{\α}-Dx\sin \mathrm{\α})/\cos \mathrm{\β}/V\end{array};$

Aircraft relative to the earth's axis system current yaw angle of speed derivative specifically,

$\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=p\sin \mathrm{\α}-r\cos \mathrm{\α}\\ +(-\cos \mathrm{\α}\sin {\mathrm{\βF}}_{xt}+{\mathrm{cos\βF}}_{yt}-{\mathrm{sin\αsin\βF}}_{zt})/m/V\\ +g(-\cos \mathrm{\α}\sin \mathrm{\β}Dx-\sin \mathrm{\α}\sin \mathrm{\β}Dz+\cos \mathrm{\β}Dy)/V\end{array};$

P for flying the current angular velocity in roll of axis system, q is rate of pitch, r is yaw rate, and g is aircraft present bit The gravity acceleration value put, F_xt、F_yt、F_ztBody axle system three axle component for aircraft currently suffered bonding force；

Fly the derivative of axis system current angular velocity specifically,

B₁=L+ (I_y-I_z)qr+I_zxpq

B₂=M+ (I_z-I_x)rp-I_zx(p²-r²)

B₃=N+ (I_x-I_y)pq-I_zxqr

$\stackrel{\·}{p}=(B_1{I}_z+B_3{I}_{zx})/(I_x{I}_z-I_{zx}{I}_{zx})$

$\stackrel{\·}{q}=B_2/I_y$

$\stackrel{\·}{r}=(B_1{I}_{zx}+B_3{I}_x)/(I_x{I}_z-I_{zx}{I}_{zx})$

For fly the current angular velocity in roll of axis system derivative,For the derivative of rate of pitch,For yaw rate Derivative, B₁、B₂、B₃For intermediate variable, the body axle system three axle component of L, M, N respectively aircraft currently suffered bonding force square, I_x、 I_y、I_z、I_zxThe moment of inertia of axis system x-axis, y-axis and z-axis of being respectively diversion, I_zxInertia for be diversion axis system z-axis and y-axis Long-pending；

The derivative of four elements is,

$\begin{array}{c}{\stackrel{\·}{q}}_1=-0.5({\mathrm{pq}}_2+{\mathrm{qq}}_3+{\mathrm{rq}}_4)\\ {\stackrel{\·}{q}}_2=0.5({\mathrm{pq}}_1+{\mathrm{rq}}_3-{\mathrm{qq}}_4)\\ {\stackrel{\·}{q}}_3=0.5({\mathrm{qq}}_1-{\mathrm{rq}}_2+{\mathrm{pq}}_4)\\ {\stackrel{\·}{q}}_4=0.5({\mathrm{rq}}_1+{\mathrm{qq}}_2-{\mathrm{pq}}_3)\end{array}.$

Preferably, in described step S5, aircraft airspeed at three axle component specific algorithms of earth's axis system is,

$\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]=\left[\begin{array}{c}{V}_{xg}-W_{xg}\\ V_{yg}-W_{yg}\\ V_{zg}-W_{zg}\end{array}\right]$

In formula, V_x、V_y、V_zIt is respectively the aircraft airspeed three axle components in earth's axis system, V_xg、V_yg、V_zgIt is respectively aircraft ground The speed three axle components in earth's axis system, W_xg、W_yg、W_zgThe respectively wind speed of aircraft local environment three axle components in earth's axis system；

Aircraft airspeed at three axle components of body axle system is,

$\left[\begin{array}{c}{V}_{xt}\\ V_{yt}\\ V_{zt}\end{array}\right]=\left[\begin{array}{ccc}Ax& Bx& Dx\\ Ay& By& Dy\\ Az& Bz& Dz\end{array}\right]\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]$

In formula, V_xt、V_yt、V_ztIt is respectively the aircraft airspeed three axle components in body axle system；

The specific algorithm of aircraft airspeed, the elevation angle and yaw angle is,

$V_V=\sqrt{V_{xt}^2+V_{yt}^2+V_{zt}^2}$

α_V=arctan (V_zt/V_xt)

β_V=arcsin (V_yt/V_V)

In formula, V_VFor aircraft airspeed, α_VFor aircraft angle of attack, β_VFor aircraft yaw angle.

The beneficial effects of the present invention is:

The method of the present invention can realize atmospheric perturbation to flight parameters such as aircraft angle of attack, yaw angle, true air speed and ground velocity The fine analog of change procedure, makes airplane motion response the most true to nature.

Use this algorithm improvement full digital trigger technique platform, engineering simulator, comprehensive " iron bird " testing stand and flight training mould Intend the airplane motion algorithm in the flight simulation such as device, it is possible to increase Design of Flight Control, test and the accuracy trained and Effectiveness, increases people's credibility in loop test assessment result.

Accompanying drawing explanation

Fig. 1 is the flow chart of the airplane motion analogy method of one embodiment of the invention.

Detailed description of the invention

Clearer for the purpose making the present invention implement, technical scheme and advantage, below in conjunction with in the embodiment of the present invention Accompanying drawing, the technical scheme in the embodiment of the present invention is further described in more detail.In the accompanying drawings, the most identical or class As label represent same or similar element or there is the element of same or like function.Described embodiment is the present invention A part of embodiment rather than whole embodiments.The embodiment described below with reference to accompanying drawing is exemplary, it is intended to use In explaining the present invention, and it is not considered as limiting the invention.Based on the embodiment in the present invention, ordinary skill people The every other embodiment that member is obtained under not making creative work premise, broadly falls into the scope of protection of the invention.Under Face combines accompanying drawing and is described in detail embodiments of the invention.

In describing the invention, it is to be understood that term " " center ", " longitudinally ", " laterally ", "front", "rear", The orientation of the instruction such as "left", "right", " vertically ", " level ", " top ", " end " " interior ", " outward " or position relationship are for based on accompanying drawing institute The orientation shown or position relationship, be for only for ease of and describe the present invention and simplify description rather than instruction or the dress of hint indication Put or element must have specific orientation, with specific azimuth configuration and operation, therefore it is not intended that protect the present invention The restriction of scope.

The effect of this innovatory algorithm for convenience of description, establishes a set of airplane motion simulated program.Emulation was set at 0 second Starting, introduce the earth's axis system north orientation step wind when 0.2 second, when 0.4 second, step terminates, and introduces the earth's axis system east orientation step wind when 0.6 second, When 0.8 second, step terminates, and when 1 second, emulation terminates.Wherein, step monsoon intensity is 5m/s.

As it is shown in figure 1, the airplane motion analogy method in the present embodiment, comprise the steps of

S1, the original state parameter of input aircraft, described original state parameter comprises the initial Eulerian angles of aircraft, aircraft body Axle system initial angular velocity, aircraft initial position, aircraft earth's axis system initial velocity, aircraft are relative to the initial angle of attack of earth's axis system speed With aircraft relative to the initial side-slip angle of earth's axis system speed；The initial Eulerian angles of described aircraft comprise aircraft pitch angle, aircraft rolling Angle and vector angle；The described axis system initial angular velocity that flies comprises and flies the initial angular velocity in roll of axis system, flies axis It is initial pitch angle speed, flies the initial yaw rate of axis system；Described aircraft initial position comprises aircraft initial north orientation position Put, aircraft initial east orientation position, the initial sky of aircraft is to position.

In the present embodiment,

Aircraft pitch angle θ₀=2deg；

Aircraft roll angle φ₀=0deg；

Vector angle ψ₀=45deg；

Fly axis system initial angular velocity in roll p₀=0deg/s；

Fly axis system initial pitch angle speed q₀=0deg/s；

Fly initial yaw rate r of axis system₀=0deg/s；

Aircraft initial north orientation position x₀=0m；

Aircraft initial east orientation position y₀=0m；

The initial sky of aircraft is to position z₀=500m；

Aircraft earth's axis system initial velocity V₀=120m/s；

Aircraft is relative to the initial angle of attack α of earth's axis system speed₀=2deg；

Aircraft is relative to the initial side-slip angle beta of earth's axis system speed₀=0deg.

S2, inputs aircraft current state parameter, and described aircraft current state parameter comprises the body axle of bonding force suffered by aircraft It it is the body axle system three axle component of three axle components and bonding force square；Aircraft gross mass, the moment of inertia of each axle of axis system that is diversion and used Property long-pending；The wind speed of current aircraft local environment three axle components in earth's axis system.

In the present embodiment, input aircraft current state, be all set to fixed value

The body axle system three axle component of bonding force suffered by aircraft (without gravity) is respectively

Fxt=34.224191441307575；Fyt=0；Fzt=0.024677670778336；

The body axle system three axle component of bonding force square suffered by aircraft

L=0；M=0；N=0；

Aircraft Quality performance data

MassT=100kg；Ix=100000；Iy=100000；Iy=100000；Izx=-10；

The wind speed of aircraft local environment three axle components in earth's axis system

Earth's axis system north orientation step wind 5m/s when 0.2 second, when 0.4 second, step terminates；

Earth's axis system east orientation step wind 5m/s when 0.6 second, when 0.8 second, step terminates.

S3, calculates the derivative of earth's axis system kinematic parameter, calculates current four element values of aircraft correction,

$norm=\sqrt{(q_1^2+q_2^2+q_3^2+q_4^2)}$

q₁=q₁/norm

q₂=q₂/norm

q₃=q₃/norm

q₄=q₄/norm

In formula, norm is the modulus value of current four elements, q₁、q₂、q₃And q₄For revised four element currencys；

Current direction cosine matrix is calculated according to revised four element currencys；Calculate according to described direction cosine matrix The aircraft earth's axis system present speed three axle components in earth's axis system, described component is also the derivative of aircraft current location；Calculating flies The derivative of machine earth's axis system present speed；Aircraft is relative to the derivative of the earth's axis system current angle of attack of speed；Aircraft is relative to earth's axis system speed Spend the derivative of current yaw angle；Calculating the derivative flying axis system current angular velocity, described current angular velocity comprises current rolling Angular velocity, rate of pitch and yaw rate；Calculate the derivative of four elements；

Initial for aircraft in described step S1 Eulerian angles are converted to four element initial values by S4, and in addition to initial Eulerian angles Other original state parameters are together as initial value for integral；By the derivative of four elements in described step S3, fly axis system roll angle The derivative of speed, the derivative of rate of pitch, the derivative of yaw rate, the derivative of aircraft current location, aircraft earth's axis system work as The derivative of front speed, aircraft currently break away relative to earth's axis system speed relative to derivative and the aircraft of the earth's axis system current angle of attack of speed The derivative at angle, as integration rate, is integrated, and solves current four element values of aircraft, flies axis system current angular velocity, aircraft Current location, aircraft earth's axis system present speed, aircraft relative to the current angle of attack of earth's axis system speed, aircraft relative to earth's axis system speed The current yaw angle of degree；

S5, calculates aircraft airspeed at three axle components of earth's axis system, according to described aircraft airspeed at three axle components of earth's axis system Calculate the aircraft airspeed three axle components in body axle system, calculate aircrafts according to described aircraft airspeed at three axle components of body axle system actual Air speed, the actual angle of attack and actual yaw angle；

S6, delivers to aerodynamics evaluation module by described aircraft true empty-running speed, the actual angle of attack, actual yaw angle, accurately simulates Aerodynamic force suffered by aircraft and aerodynamic moment.

In the present embodiment, initial for aircraft Eulerian angles are converted to four element initial value, the specifically sides of conversion by described step S4 Method is,

q₁₀=cos (θ₀/2)cos(φ₀/2)cos(ψ₀/2)+sin(θ₀/2)sin(φ₀/2)sin(ψ₀/2)

q₂₀=cos (θ₀/2)sin(φ₀/2)cos(ψ₀/2)-sin(θ₀/2)cos(φ₀/2)sin(ψ₀/2)

q₃₀=sin (θ₀/2)cos(φ₀/2)cos(ψ₀/2)+cos(θ₀/2)sin(φ₀/2)sin(ψ₀/2)

q₄₀=cos (θ₀/2)cos(φ₀/2)sin(ψ₀/2)-sin(θ₀/2)sin(φ₀/2)cos(ψ₀/2)

In formula, q₁₀、q₂₀、q₃₀And q₄₀It is four element initial values, φ₀For roll angle, θ₀For the angle of pitch, ψ₀For course angle.

In the present embodiment, in described step S3,

The specific algorithm of current direction cosine matrix is,

$MDC=\left[\begin{array}{ccc}Ax& Ay& Az\\ Bx& By& Bz\\ Dx& Dy& Dz\end{array}\right],$

$Ax=q_1^2+q_2^2-q_3^2-q_4^2$

Ay=2 (q₂q₃-q₁q₄)

Az=2 (q₂q₄+q₁q₃)

Bx=2 (q₂q₃+q₁q₄)

$By=q_1^2-q_2^2+q_3^2-q_4^2$

Bz=2 (q₃q₄-q₁q₂)

Dx=2 (q₂q₄-q₁q₃)

Dy=2 (q₃q₄+q₁q₂)

$Dz=q_1^2-q_2^2-q_3^2+q_4^2$

In formula, q₁、q₂、q₃And q₄For revised four element currencys；

The aircraft earth's axis system present speed three axle component specific algorithms in earth's axis system are,

$\left[\begin{array}{c}{V}_{xg}\\ V_{yg}\\ V_{zg}\end{array}\right]=\left[\begin{array}{ccc}Ax& Ay& Az\\ Bx& By& Bz\\ Dx& Dy& Dz\end{array}\right]\left[\begin{array}{ccc}cos\mathrm{\α}cos\mathrm{\β}& -cos\mathrm{\α}sin\mathrm{\β}& -sin\mathrm{\α}\\ \sin \mathrm{\β}& cos\mathrm{\β}& 0\\ sin\mathrm{\α}\cos \mathrm{\β}& -\sin \mathrm{\α}sin\mathrm{\β}& \cos \mathrm{\α}\end{array}\right]\left[\begin{array}{c}V\\ 0\\ 0\end{array}\right]$

In formula, V_xg、V_ygAnd V_zgFor the aircraft earth's axis system speed three axle components in earth's axis system, V is that aircraft earth's axis system is current Speed, α is the aircraft current angle of attack relative to earth's axis system speed, and β is the aircraft current yaw angle relative to earth's axis system speed；

The derivative of aircraft earth's axis system present speed specifically,

$\begin{array}{c}\stackrel{\·}{V}=({\mathrm{cos\αcos\βF}}_{xt}+{\mathrm{sin\βF}}_{yt}+{\mathrm{sin\αcos\βF}}_{zt})/m\\ +g(cos\mathrm{\α}cos\mathrm{\β}Dx+sin\mathrm{\α}cos\mathrm{\β}Dz+\sin \mathrm{\β}Dy)\end{array};$

Aircraft relative to the earth's axis system current angle of attack of speed derivative specifically,

$\begin{array}{c}\stackrel{\·}{\mathrm{\α}}=q-(p\cos \mathrm{\α}+r\sin \mathrm{\α})\sin \mathrm{\β}/\cos \mathrm{\β}\\ +(-{\mathrm{sin\αF}}_{xt}+{\mathrm{cos\αF}}_{zt})/m/V\\ +g(Dz\cos \mathrm{\α}-Dx\sin \mathrm{\α})/\cos \mathrm{\β}/V\end{array};$

Aircraft relative to the earth's axis system current yaw angle of speed derivative specifically,

$\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=p\sin \mathrm{\α}-r\cos \mathrm{\α}\\ +(-\cos \mathrm{\α}\sin {\mathrm{\βF}}_{xt}+{\mathrm{cos\βF}}_{yt}-{\mathrm{sin\αsin\βF}}_{zt})/m/V\\ +g(-\cos \mathrm{\α}\sin \mathrm{\β}Dx-\sin \mathrm{\α}\sin \mathrm{\β}Dz+\cos \mathrm{\β}Dy)/V\end{array};$

P for flying the current angular velocity in roll of axis system, q is rate of pitch, r is yaw rate, and g is aircraft present bit The gravity acceleration value put, F_xt、F_yt、F_ztBody axle system three axle component for aircraft currently suffered bonding force；

Fly the derivative of axis system current angular velocity specifically,

B₁=L+ (I_y-I_z)qr+I_zxpq

B₂=M+ (I_z-I_x)rp-I_zx(p²-r²)

B₃=N+ (I_x-I_y)pq-I_zxqr

$\stackrel{\·}{p}=(B_1{I}_z+B_3{I}_{zx})/(I_x{I}_z-I_{zx}{I}_{zx})$

$\stackrel{\·}{q}=B_2/I_y$

$\stackrel{\·}{r}=(B_1{I}_{zx}+B_3{I}_x)/(I_x{I}_z-I_{zx}{I}_{zx})$

For fly the current angular velocity in roll of axis system derivative,For the derivative of rate of pitch,For yaw rate Derivative, B₁、B₂、B₃For intermediate variable, the body axle system three axle component of L, M, N respectively aircraft currently suffered bonding force square, I_x、 I_y、I_z、I_zxThe moment of inertia of axis system x-axis, y-axis and z-axis of being respectively diversion, I_zxInertia for be diversion axis system z-axis and y-axis Long-pending；

The derivative of four elements is,

$\begin{array}{c}{\stackrel{\·}{q}}_1=-0.5({\mathrm{pq}}_2+{\mathrm{qq}}_3+{\mathrm{rq}}_4)\\ {\stackrel{\·}{q}}_2=0.5({\mathrm{pq}}_1+{\mathrm{rq}}_3-{\mathrm{qq}}_4)\\ {\stackrel{\·}{q}}_3=0.5({\mathrm{qq}}_1-{\mathrm{rq}}_2+{\mathrm{pq}}_4)\\ {\stackrel{\·}{q}}_4=0.5({\mathrm{rq}}_1+{\mathrm{qq}}_2-{\mathrm{pq}}_3)\end{array}.$

In the present embodiment, in described step S5, aircraft airspeed at three axle component specific algorithms of earth's axis system is,

$\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]=\left[\begin{array}{c}{V}_{xg}-W_{xg}\\ V_{yg}-W_{yg}\\ V_{zg}-W_{zg}\end{array}\right]$

In formula, V_x、V_y、V_zIt is respectively the aircraft airspeed three axle components in earth's axis system, V_xg、V_yg、V_zgIt is respectively aircraft ground The speed three axle components in earth's axis system, W_xg、W_yg、W_zgThe respectively wind speed of aircraft local environment three axle components in earth's axis system；

Aircraft airspeed at three axle components of body axle system is,

$\left[\begin{array}{c}{V}_{xt}\\ V_{yt}\\ V_{zt}\end{array}\right]=\left[\begin{array}{ccc}Ax& Bx& Dx\\ Ay& By& Dy\\ Az& Bz& Dz\end{array}\right]\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]$

In formula, V_xt、V_yt、V_ztIt is respectively the aircraft airspeed three axle components in body axle system；

The specific algorithm of aircraft airspeed, the elevation angle and yaw angle is,

$V_V=\sqrt{V_{xt}^2+V_{yt}^2+V_{zt}^2}$

α_V=arctan (V_zt/V_xt)

β_V=arcsin (V_yt/V_V)

In formula, V_VFor aircraft airspeed, α_VFor aircraft angle of attack, β_VFor aircraft yaw angle.

Last it is noted that above example is only in order to illustrate technical scheme, it is not intended to limit.To the greatest extent The present invention has been described in detail by pipe with reference to previous embodiment, it will be understood by those within the art that: it is still Technical scheme described in foregoing embodiments can be modified, or wherein portion of techniques feature is carried out equivalent replace Change；And these amendments or replacement, do not make the essence of appropriate technical solution depart from the essence of various embodiments of the present invention technical scheme God and scope.

Claims (4)

1. an airplane motion analogy method, it is characterised in that comprise the steps of

S1, the original state parameter of input aircraft, described original state parameter comprises the initial Eulerian angles of aircraft, flies axis system Initial angular velocity, aircraft initial position, aircraft earth's axis system initial velocity, aircraft are relative to the initial angle of attack of earth's axis system speed and fly Machine is relative to the initial side-slip angle of earth's axis system speed；

S2, inputs aircraft current state parameter, and described aircraft current state parameter comprises the body axle system three of bonding force suffered by aircraft The body axle system three axle component of axle component and bonding force square；Aircraft gross mass, the moment of inertia of each axle of axis system that is diversion and the product of inertia； The wind speed of current aircraft local environment three axle components in earth's axis system；

S3, calculates the derivative of earth's axis system kinematic parameter, calculates current four element values of aircraft correction,

$norm=\sqrt{(q_1^2+q_2^2+q_3^2+q_4^2)}$

q₁=q₁/norm

q₂=q₂/norm

q₃=q₃/norm

q₄=q₄/norm

In formula, norm is the modulus value of current four elements, q₁、q₂、q₃And q₄For revised four element currencys；

Current direction cosine matrix is calculated according to revised four element currencys；Aircraft is calculated according to described direction cosine matrix The earth's axis system present speed three axle components in earth's axis system, described component is also the derivative of aircraft current location；Calculate aircraft ground The derivative of axle system present speed；Aircraft is relative to the derivative of the earth's axis system current angle of attack of speed；Aircraft is worked as relative to earth's axis system speed The derivative of front yaw angle；Calculating the derivative flying axis system current angular velocity, described current angular velocity comprises current roll angle speed Degree, rate of pitch and yaw rate；Calculate the derivative of four elements；

Initial for aircraft in described step S1 Eulerian angles are converted to four element initial values by S4, with other in addition to initial Eulerian angles Original state parameter is together as initial value for integral；By the derivative of four elements in described step S3, fly axis system angular velocity in roll Derivative, the derivative of rate of pitch, the derivative of yaw rate, the derivative of aircraft current location, aircraft earth's axis system the fastest The derivative of degree, aircraft relative to the derivative of the earth's axis system current angle of attack of speed and aircraft relative to the earth's axis system current yaw angle of speed Derivative, as integration rate, is integrated, and solves current four element values of aircraft, to fly axis system current angular velocity, aircraft current Position, aircraft earth's axis system present speed, aircraft relative to the current angle of attack of earth's axis system speed, aircraft relative to earth's axis system speed Current yaw angle；

S5, calculates the aircraft airspeed three axle components in earth's axis system, calculates at three axle components of earth's axis system according to described aircraft airspeed Aircraft airspeed at three axle components of body axle system, calculates aircraft reality according to described aircraft airspeed at three axle components of body axle system empty The angle of attack fast, actual and actual yaw angle；

S6, delivers to aerodynamics evaluation module, accurate simulated aircraft by described aircraft true empty-running speed, the actual angle of attack, actual yaw angle Suffered aerodynamic force and aerodynamic moment.

2. airplane motion analogy method as claimed in claim 1, it is characterised in that: by initial for aircraft Euler in described step S4 Angle is converted to four element initial values, and concrete conversion method is,

q₁₀=cos (θ₀/2)cos(φ₀/2)cos(ψ₀/2)+sin(θ₀/2)sin(φ₀/2)sin(ψ₀/2)

q₂₀=cos (θ₀/2)sin(φ₀/2)cos(ψ₀/2)-sin(θ₀/2)cos(φ₀/2)sin(ψ₀/2)

q₃₀=sin (θ₀/2)cos(φ₀/2)cos(ψ₀/2)+cos(θ₀/2)sin(φ₀/2)sin(ψ₀/2)

q₄₀=cos (θ₀/2)cos(φ₀/2)sin(ψ₀/2)-sin(θ₀/2)sin(φ₀/2)cos(ψ₀/2)

In formula, q₁₀、q₂₀、q₃₀And q₄₀It is four element initial values, φ₀For roll angle, θ₀For the angle of pitch, ψ₀For course angle.

3. airplane motion analogy method as claimed in claim 1, it is characterised in that: in described step S3,

The specific algorithm of current direction cosine matrix is,

$MDC=\left[\begin{array}{ccc}Ax& Ay& Az\\ Bx& By& Bz\\ Dx& Dy& Dz\end{array}\right],$

$Ax=q_1^2+q_2^2-q_3^2-q_4^2$

Ay=2 (q₂q₃-q₁q₄)

Az=2 (q₂q₄+q₁q₃)

Bx=2 (q₂q₃+q₁q₄)

$By=q_1^2-q_2^2+q_3^2-q_4^2$

Bz=2 (q₃q₄-q₁q₂)

Dx=2 (q₂q₄-q₁q₃)

Dy=2 (q₃q₄+q₁q₂)

$Dz=q_1^2-q_2^2-q_3^2+q_4^2$

In formula, q₁、q₂、q₃And q₄For revised four element currencys；

The aircraft earth's axis system present speed three axle component specific algorithms in earth's axis system are,

$\left[\begin{array}{c}{V}_{xg}\\ V_{yg}\\ V_{zg}\end{array}\right]=\left[\begin{array}{ccc}Ax& Ay& Az\\ Bx& By& Bz\\ Dx& Dy& Dz\end{array}\right]\left[\begin{array}{ccc}\cos \mathrm{\α}\cos \mathrm{\β}& -\cos \mathrm{\α}\sin \mathrm{\β}& -\sin \mathrm{\α}\\ \sin \mathrm{\β}& \cos \mathrm{\β}& 0\\ \sin \mathrm{\α}\cos \mathrm{\β}& -\sin \mathrm{\α}\sin \mathrm{\β}& \cos \mathrm{\α}\end{array}\right]\left[\begin{array}{c}V\\ 0\\ 0\end{array}\right]$

In formula, V_xg、V_ygAnd V_zgFor the aircraft earth's axis system speed three axle components in earth's axis system, V is that aircraft earth's axis system is the fastest Degree, α is the aircraft current angle of attack relative to earth's axis system speed, and β is the aircraft current yaw angle relative to earth's axis system speed；

The derivative of aircraft earth's axis system present speed specifically,

$\begin{array}{c}\stackrel{\·}{V}=({\mathrm{cos\αcos\βF}}_{xt}+{\mathrm{sin\βF}}_{yt}+{\mathrm{sin\αcos\βF}}_{zt})/m\\ +g(\cos \mathrm{\α}\cos \mathrm{\β}Dx+\sin \mathrm{\α}\cos \mathrm{\β}Dz+\sin \mathrm{\β}Dy)\end{array};$

Aircraft relative to the earth's axis system current angle of attack of speed derivative specifically,

$\begin{array}{c}\stackrel{\·}{\mathrm{\α}}=q-(p\cos \mathrm{\α}+r\sin \mathrm{\α})\sin \mathrm{\β}/\cos \mathrm{\β}\\ +(-{\mathrm{sin\αF}}_{xt}+{\mathrm{cos\αF}}_{zt})/m/V\\ +g(Dz\cos \mathrm{\α}-Dx\sin \mathrm{\α})/\cos \mathrm{\β}/V\end{array};$

Aircraft relative to the earth's axis system current yaw angle of speed derivative specifically,

$\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=p\sin \mathrm{\α}-r\cos \mathrm{\α}\\ +(-{\mathrm{cos\αsin\βF}}_{xt}+{\mathrm{cos\βF}}_{yt}-{\mathrm{sin\αsin\βF}}_{zt})/m/V\\ +g(-\cos \mathrm{\α}\sin \mathrm{\β}Dx-\sin \mathrm{\α}\sin \mathrm{\β}Dz+\cos \mathrm{\β}Dy)/V\end{array};$

P for flying the current angular velocity in roll of axis system, q is rate of pitch, r is yaw rate, and g is aircraft current location Gravity acceleration value, F_xt、F_yt、F_ztBody axle system three axle component for aircraft currently suffered bonding force；

Fly the derivative of axis system current angular velocity specifically,

B₁=L+ (I_y-I_z)qr+I_zxpq

B₂=M+ (I_z-I_x)rp-I_zx(p²-r²)

B₃=N+ (I_x-I_y)pq-I_zxqr

$\stackrel{\·}{p}=(B_1{I}_z+B_3{I}_{zx})/(I_x{I}_z-I_{zx}{I}_{zx})$

$\stackrel{\·}{q}=B_2/I_y$

$\stackrel{\·}{r}=(B_1{I}_{zx}+B_3{I}_x)/(I_x{I}_z-I_{zx}{I}_{zx})$

For fly the current angular velocity in roll of axis system derivative,For the derivative of rate of pitch,Leading for yaw rate Number, B₁、B₂、B₃For intermediate variable, the body axle system three axle component of L, M, N respectively aircraft currently suffered bonding force square, I_x、I_y、I_z、 I_zxThe moment of inertia of axis system x-axis, y-axis and z-axis of being respectively diversion, I_zxThe product of inertia for be diversion axis system z-axis and y-axis；

The derivative of four elements is,

$\begin{array}{c}{\stackrel{\·}{q}}_1=-0.5({\mathrm{pq}}_2+{\mathrm{qq}}_3+{\mathrm{rq}}_4)\\ {\stackrel{\·}{q}}_2=0.5({\mathrm{pq}}_1+{\mathrm{rq}}_3-{\mathrm{qq}}_4)\\ {\stackrel{\·}{q}}_3=0.5({\mathrm{qq}}_1-{\mathrm{rq}}_2+{\mathrm{pq}}_4)\\ {\stackrel{\·}{q}}_4=0.5({\mathrm{rq}}_1+{\mathrm{qq}}_2-{\mathrm{pq}}_3)\end{array}.$

4. airplane motion analogy method as claimed in claim 1, it is characterised in that: in described step S5, aircraft airspeed is in the earth's axis Three axle component specific algorithms of system are,

$\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]=\left[\begin{array}{c}{V}_{xg}-W_{xg}\\ V_{yg}-W_{yg}\\ V_{zg}-W_{zg}\end{array}\right]$

In formula, V_x、V_y、V_zIt is respectively the aircraft airspeed three axle components in earth's axis system, V_xg、V_yg、V_zgIt is respectively aircraft ground velocity to exist Three axle components in earth's axis system, W_xg、W_yg、W_zgThe respectively wind speed of aircraft local environment three axle components in earth's axis system；

Aircraft airspeed at three axle components of body axle system is,

$\left[\begin{array}{c}{V}_{xt}\\ V_{yt}\\ V_{zt}\end{array}\right]=\left[\begin{array}{ccc}Ax& Bx& Dx\\ Ay& By& Dy\\ Az& Bz& Dz\end{array}\right]\left[\begin{array}{c}{V}_x\\ V_y\\ V_z\end{array}\right]$

In formula, V_xt、V_yt、V_ztIt is respectively the aircraft airspeed three axle components in body axle system；

The specific algorithm of aircraft airspeed, the elevation angle and yaw angle is,

$V_V=\sqrt{V_{xt}^2+V_{yt}^2+V_{zt}^2}$

α_V=arctan (V_zt/V_xt)

β_V=arcsin (V_yt/V_V)

In formula, V_VFor aircraft airspeed, α_VFor aircraft angle of attack, β_VFor aircraft yaw angle.