CN105182985A - Hypersonic flight vehicle dive segment full amount integration guidance control method - Google Patents

Abstract

The invention provides a hypersonic flight vehicle dive segment full amount integration guidance control method. A technical scheme is characterized in that firstly, a sensor measures states of a hypersonic flight vehicle relative to a ground system, wherein the states comprise a speed, a speed inclination angle, a track yaw angle, a rolling angular speed, a yaw angular speed, a pitching angular speed, a pitch angle, a yaw angle, a rolling angle and the like; then the above obtained quantities of states, positional information of an object relative to the ground system and a control parameter are substituted into a formula so as to calculate a rudder deflection angle vector, wherein the positional information is measured in advance; finally, the rudder deflection angle vector is used to control the hypersonic flight vehicle. In the invention, based on an aircraft full amount coupling integration guidance control model, an adaptive-block dynamic surface inversion method is used to realize integrated guidance control, and a problem of repeated design can be effectively avoided so that time and economic cost of a guidance control system design are reduced.

Description

Hypersonic aircraft dive section full dose integration guidance control method

Technical field

The invention belongs to aircraft guidance control field, be particularly with the coupling integrated Guidance and control method of hypersonic aircraft dive section full dose of angle of fall constraint.

Background technology

Hypersonic aircraft adopts high lift-drag ratio profile, can realize remote autonomous navigation.Due to its high flight Mach number, there is many excellent abilities, mainly comprise quick-reaction capability (QRC), extremely strong penetration ability, efficient lethality, high maneuver fight capability etc., be subject to the great attention of each major country of the world, be militarily with a wide range of applications and prospect.At dive section, hypersonic aircraft has the features such as the large and overload of Mach number variation range is large, and violent change can occur flight state, center of mass motion and all present the features such as fast time variant, non-linear, strong coupling and uncertainty around center of mass motion.Traditional aircraft guidance control system carries out separate design based on singular perturbation theory to guidance subsystem and control subsystem, then they combined, and the performance of difference access control subsystem and guidance subsystem.And hypersonic aircraft integration guidance control design case, refer to and the guidance subsystem of hypersonic aircraft and control subsystem are integrally designed, directly produce angle of rudder reflection instruction by the relative movement information of hypersonic aircraft and target.In the design process, owing to having taken into full account that intercoupling between guidance subsystem and control subsystem affects, so the overall performance of guidance control system can be promoted, reduced its design cost, and the reliability of hypersonic aircraft total system can have been improved.

In the existing open source literature that can find, at dive section, the guidance control system of hypersonic aircraft is all separately design, and then they is coordinated together.The method that guidance subsystem often adopts has the methods such as the guidance of optimal Guidance, sliding formwork, Motorized dive Closed Loop Guidance, and the method that control subsystem often adopts has the methods such as the control of dynamic inversion control, sliding formwork, PREDICTIVE CONTROL, back stepping control, adaptive control and Active Disturbance Rejection Control.The research of the full dose integration guidance control problem of the domestic and international hypersonic aircraft dive section to the constraint of the band angle of fall at present yet there are no open source literature.

Summary of the invention

The present invention is directed to the hypersonic aircraft dive section Guidance and control problem with angle of fall constraint, propose a kind of Guidance and control method of hypersonic aircraft dive section, the method is the integration guidance control method based on the inverting of adaptive block dynamic surface.

The basic ideas of the method are: first, set up the hypersonic aircraft of band angle of fall constraint relative to the center of mass motion equation of target based on the angle of sight, and set up hypersonic aircraft around center of mass motion equation; Then, opposing connection center of mass motion equation carries out differomorphism, sets up the coupling integrated Guidance and control model of aircraft full dose with center of mass motion equation with around barycenter kinetics equation simultaneous; Finally, adaptive block dynamic surface inversion method is utilized to realize integrated Guidance and control based on this Integrated Model.

Technical scheme of the present invention is, a kind of hypersonic aircraft dive section full dose integration guidance control method, if hypersonic aircraft flight is at dive section, utilizes following process to control at any time:

First measure by sensor the state that hypersonic aircraft relative to ground is, comprise speed v, speed inclination angle theta, flight path crab angle σ, angular velocity in roll ω _x, yaw rate ω _y, rate of pitch ω _z, the angle of pitch crab angle ψ, roll angle γ and hypersonic aircraft are relative to position component x, y and z in the system of ground of ground system initial point; Then the positional information by quantity of state obtained above, the target that records in advance relative to ground being and controling parameters are updated to formula (1) and calculate angle of rudder reflection vector $\stackrel{\→}{u}={\left[\begin{array}{ccc}{\mathrm{\δ}}_z& {\mathrm{\δ}}_y& {\mathrm{\δ}}_x\end{array}\right]}^T,$ Wherein, δ _z, δ _yand δ _xbe respectively the pitching angle of rudder reflection of hypersonic aircraft, driftage angle of rudder reflection and rolling angle of rudder reflection; Finally utilize angle of rudder reflection vector hypersonic aircraft is controlled.

$\{\begin{array}{c}{\stackrel{\→}{s}}_0={\left[\begin{array}{cc}{x}_{01}+k_F\frac{v}{r}{x}_F& x_{02}\end{array}\right]}^T\\ {\stackrel{\→}{x}}_{1v}=g_0^{-1}\left(t\right)\·\{-\frac{v}{r}{k}_0{\stackrel{\→}{s}}_0-\frac{e_0}{r}sat({\stackrel{\→}{s}}_0,{\stackrel{\→}{d}}_0)-\[\begin{array}{c}{k}_F-\frac{v}{r}{x}_{01}+k_F\frac{\stackrel{\·}{v}r-\stackrel{\·}{r}v}{r^2}{x}_F\\ 0\end{array}\]-{\stackrel{\→}{f}}_0\left({\stackrel{\→}{x}}_0\right)\}\\ {\mathrm{\τ}}_1{\stackrel{\·}{\stackrel{\→}{x}}}_{1d}^{*}+{\stackrel{\→}{x}}_{1d}^{*}={\stackrel{\→}{x}}_{1v},{\stackrel{\→}{x}}_{1d}^{*}\left(0\right)={\stackrel{\→}{x}}_{1v}\left(0\right)\\ {\stackrel{\·}{\stackrel{\→}{x}}}_{1d}={\left[\begin{array}{cc}{\stackrel{\·}{\stackrel{\→}{x}}}_{1d}^{*}& 0\end{array}\right]}^T\\ {\stackrel{\→}{x}}_{1d}={\left[\begin{array}{cc}{\stackrel{\→}{x}}_{1d}^{*}& 0\end{array}\right]}^T\\ {\stackrel{\→}{s}}_1={\stackrel{\→}{x}}_1-{\stackrel{\→}{x}}_{1d}\\ {\stackrel{\·}{\hat{e}}}_1={\mathrm{\υ}}_1({\stackrel{\→}{s}}_1^T{\stackrel{\→}{s}}_1-{\mathrm{\μ}}_1{\hat{e}}_1),{\hat{e}}_1\left(0\right)=0\\ {\stackrel{\→}{x}}_{2v}=-g_1^{-1}\left({\stackrel{\→}{x}}_1\right)\[{\stackrel{\→}{f}}_1\left({\stackrel{\→}{x}}_1\right)+{\hat{e}}_1{\stackrel{\→}{s}}_1+k_1{\stackrel{\→}{s}}_1-{\stackrel{\·}{\stackrel{\→}{x}}}_{1d}\]\\ {\mathrm{\τ}}_2{\stackrel{\·}{\stackrel{\→}{x}}}_{2d}+{\stackrel{\→}{x}}_{2d}={\stackrel{\→}{x}}_{2v},{\stackrel{\→}{x}}_{2d}\left(0\right)={\stackrel{\→}{x}}_{2v}\left(0\right)\\ {\stackrel{\→}{s}}_2={\stackrel{\→}{x}}_2-{\stackrel{\→}{x}}_{2d}\\ {\stackrel{\·}{\hat{e}}}_2={\mathrm{\υ}}_2({\stackrel{\→}{s}}_2^T{\stackrel{\→}{s}}_2-{\mathrm{\μ}}_2{\hat{e}}_2),{\hat{e}}_1\left(0\right)=0\\ \stackrel{\→}{u}=-g_2^{-1}\left(t\right)\[{\stackrel{\→}{f}}_2({\stackrel{\→}{x}}_1,{\stackrel{\→}{x}}_2)+{\hat{e}}_2{\stackrel{\→}{s}}_2+k_2{\stackrel{\→}{s}}_2-{\stackrel{\·}{\stackrel{\→}{x}}}_{2d}\]\end{array}---\left(1\right)$

Wherein, x ₀₁for hypersonic aircraft is relative to the sight line inclination angle λ of target _drate of change k _ffor sight line inclination angle λ _derror term coefficient, its size determines dynamic surface the weight of decline angle error item, determines its size according to actual conditions; V and for hypersonic aircraft is relative to the velocity magnitude on ground and rate of change thereof; R and be respectively hypersonic aircraft relative to the distance of target and rate of change thereof; x _ffor sight line inclination angle λ _dthe local speed tilt angle gamma in moment is landed with hypersonic aircraft _dFnamely (also the angle of fall, given according to aerial mission) and; x ₀₂for hypersonic aircraft is relative to the sight line drift angle λ of target _trate of change

Wherein, g ₀t () is defined as follows shown in formula, subscript "-1 " representing matrix inverse:

$g_0\left(t\right)=\frac{Q\·S\·C_L^{\mathrm{\α}}}{m\·r}\left[\begin{array}{cc}{S}_{H_{2,2}}& S_{H_{2,3}}\\ -\frac{S_{H_{3,2}}}{{\mathrm{cos\λ}}_D}& -\frac{S_{H_{3,3}}}{{\mathrm{cos\λ}}_D}\end{array}\right]$

In above formula, t is for hypersonic aircraft is with the duration of dive section starting point for flying zero point; The dynamic pressure of Q suffered by hypersonic aircraft; S is the area of reference of hypersonic aircraft; for the lift coefficient of hypersonic aircraft is for the partial derivative of its angle of attack; M is the quality of hypersonic aircraft; SH _i,ji, j=1,2,3 are respectively the transition matrix S that half speed is tied to sight line system _hin element, i represents capable, and j represents row.

Wherein, k ₀=diag (k ₀₁, k ₀₂) be the gain matrix of positive definite, determine according to actual conditions; e ₀for positive controling parameters, determine according to actual conditions; Sat () is saturation function; for boundary layer thickness, determine according to actual conditions;

Wherein, be defined as follows shown in formula:

${\stackrel{\→}{f}}_0\left({\stackrel{\→}{x}}_0\right)=\left[\begin{array}{c}\frac{-2\stackrel{\·}{r}{\stackrel{\·}{\mathrm{\λ}}}_D}{r}-{\stackrel{\·}{\mathrm{\λ}}}_T^2{\mathrm{sin\λ}}_D{\mathrm{cos\λ}}_D+\frac{1}{r}(S_{H_{2,1}}{a}_V+S_{H_{2,2}}{g}_{Hy}+S_{H_{2,3}}{g}_{Hz})\\ \frac{-2\stackrel{\·}{r}{\stackrel{\·}{\mathrm{\λ}}}_T}{r}+2{\stackrel{\·}{\mathrm{\λ}}}_D{\stackrel{\·}{\mathrm{\λ}}}_T{\mathrm{tan\λ}}_D-\frac{1}{{\mathrm{rcos\λ}}_D}(S_{H_{3,1}}{a}_V+S_{H_{3,2}}{g}_{Hy}+S_{H_{3,3}}{g}_{Hz})\end{array}\right]$

In above formula, a _vfor hypersonic aircraft acceleration half speed system x-axis to component, its expression is as follows:

$a_V=g_{Hx}-\frac{D}{m}$

In above formula, D is the resistance that hypersonic aircraft is subject to; g _hx, g _hyand g _hzfor the component of acceleration of gravity in half speed system, its expression is as follows:

$\left\{\begin{array}{c}{g}_{Hx}=-\frac{\mathrm{\μ}}{R^3}(x\cos \mathrm{\θ}\cos \mathrm{\σ}+(y+R_e)\sin \mathrm{\θ}-z\cos \mathrm{\θ}\sin \mathrm{\σ})\\ g_{Hy}=-\frac{\mathrm{\μ}}{R^3}(-x\sin \mathrm{\θ}\cos \mathrm{\σ}+(y+R_e)\cos \mathrm{\θ}+z\sin \mathrm{\θ}\sin \mathrm{\σ})\\ g_{Hz}=-\frac{\mathrm{\μ}}{R^3}(x\sin \mathrm{\σ}+z\cos \mathrm{\σ})\end{array}\right.$

In above formula, μ is Gravitational coefficient of the Earth; R is the distance of hypersonic aircraft relative to the earth's core; R _efor earth radius; θ and σ is respectively speed inclination angle and the flight path crab angle of hypersonic aircraft; X, y and z are respectively the position component in ground system of hypersonic aircraft relative to ground system initial point.

Wherein, with be respectively first virtual controlling filtering output and rate of change; τ ₁=diag (τ ₁₁, τ ₁₂) be the time constant filter matrix of positive definite, determine according to actual conditions; with for filtering output and the rate of change thereof of expansion;

Wherein,

${\stackrel{\→}{x}}_1={\left[\begin{array}{ccc}{\mathrm{\αcos\γ}}_V& {\mathrm{\αsin\γ}}_V& \mathrm{\β}\end{array}\right]}^T$

In above formula, α, γ _vthe angle of attack of hypersonic aircraft, angle of heel and yaw angle is respectively with β.

Wherein, for unknown constant e ₁estimated value; υ ₁with μ ₁be respectively the constant being greater than zero, determine according to actual conditions; k ₁=diag (k ₁₁, k ₁₂, k ₁₃) be the gain matrix of positive definite, determine according to actual conditions;

Wherein, in each element be shown below, subscript "-1 " representing matrix inverse:

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{1,1}=-cos\mathrm{\α}({\mathrm{tan\βcos\γ}}_V+{\mathrm{\αsec\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{1,2}=sin\mathrm{\α}({\mathrm{tan\βcos\γ}}_V+{\mathrm{\αsec\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{1,3}={\mathrm{cos\γ}}_V$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{2,1}=cos\mathrm{\α}({\mathrm{\αsec\βcos\γ}}_V-{\mathrm{tan\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{2,2}=-sin\mathrm{\α}({\mathrm{\αsec\βcos\γ}}_V-{\mathrm{tan\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{2,3}={\mathrm{sin\γ}}_V$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{3,1}=sin\mathrm{\α}$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{3,2}=cos\mathrm{\α}$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{3,3}=0$

Wherein, be defined as follows shown in formula:

${\stackrel{\→}{f}}_1\left({\stackrel{\→}{x}}_1\right)=\left[\begin{array}{c}{\mathrm{cos\γ}}_V{\stackrel{\→}{f}}_{1_{1,1}}^{\′}-{\mathrm{\αsin\γ}}_V{\stackrel{\→}{f}}_{1_{2,1}}^{\′}\\ {\mathrm{sin\γ}}_V{\stackrel{\→}{f}}_{1_{1,1}}^{\′}+{\mathrm{\αcos\γ}}_V{\stackrel{\→}{f}}_{1_{2,1}}^{\′}\\ {\stackrel{\→}{f}}_{1_{3,1}}^{\′}\end{array}\right]$

In above formula,

${\stackrel{\→}{f}}_{1_{1,1}}^{\′}=\frac{-\sec \mathrm{\β}}{mv}({\mathrm{mg}}_{Hz}{\mathrm{sin\γ}}_V+{\mathrm{mg}}_{Hy}{\mathrm{cos\γ}}_V+Q\·S\·C_{La})$

${\stackrel{\→}{f}}_{1_{2,1}}^{\′}=\frac{1}{mv}\[{\mathrm{tan\βcos\γ}}_V{\mathrm{mg}}_{Hy}+(tan\mathrm{\θ}+{\mathrm{tan\βsin\γ}}_V){\mathrm{mg}}_{Hz}+({\mathrm{tan\θsin\γ}}_V+tan\mathrm{\β})Q\·S\·C_{La}\]$

${\stackrel{\→}{f}}_{1_{3,1}}^{\′}=\frac{1}{mv}({\mathrm{mg}}_{Hz}{\mathrm{cos\γ}}_V-{\mathrm{mg}}_{Hy}{\mathrm{sin\γ}}_V)$

In above formula, C _lafor the lift coefficient that the body of hypersonic aircraft produces.

Wherein, with be respectively second virtual controlling filtering output and rate of change; τ ₂=diag (τ ₂₁, τ ₂₂, τ ₂₃) be the time constant filter matrix of positive definite, determine according to actual conditions;

Wherein,

${\stackrel{\→}{x}}_2={\left[\begin{array}{ccc}{\mathrm{\ω}}_x& {\mathrm{\ω}}_y& {\mathrm{\ω}}_z\end{array}\right]}^T$

In above formula, ω _x, ω _yand ω _zbe respectively the angular velocity in roll of hypersonic aircraft, yaw rate and rate of pitch.

Wherein, for unknown constant e ₂estimated value; υ ₂with μ ₂be respectively the constant being greater than zero, determine according to actual conditions; k ₂=diag (k ₂₁, k ₂₂, k ₂₃) be the gain matrix of positive definite, determine according to actual conditions;

Wherein, g ₂t () is defined as follows shown in formula, subscript "-1 " representing matrix inverse:

$g_2\left(t\right)=Q\·S\·l\·\left[\begin{array}{ccc}\frac{C_{M_x}^{{\mathrm{\δ}}_z}}{I_x}& \frac{C_{M_x}^{{\mathrm{\δ}}_y}}{I_x}& \frac{C_{M_x}^{{\mathrm{\δ}}_x}}{I_x}\\ \frac{C_{M_y}^{{\mathrm{\δ}}_z}}{I_y}& \frac{C_{M_y}^{{\mathrm{\δ}}_y}}{I_y}& \frac{C_{M_y}^{{\mathrm{\δ}}_x}}{I_y}\\ \frac{C_{M_z}^{{\mathrm{\δ}}_z}}{I_z}& \frac{C_{M_z}^{{\mathrm{\δ}}_y}}{I_z}& \frac{C_{M_z}^{{\mathrm{\δ}}_x}}{I_z}\end{array}\right]$

In above formula, l is the reference length of hypersonic aircraft; I _x, I _yand I _zbe respectively the moment of inertia of hypersonic aircraft relative body axis system three axle; be respectively the pitching rudder bias term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; be respectively the driftage rudder bias term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; be respectively the rolling rudder bias term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient.

Wherein, be defined as follows shown in formula:

${\stackrel{\→}{f}}_2({\stackrel{\→}{x}}_1,{\stackrel{\→}{x}}_2)=\left[\begin{array}{c}\frac{(I_y-I_z){\mathrm{\ω}}_y{\mathrm{\ω}}_z}{I_x}\\ \frac{(I_z-I_x){\mathrm{\ω}}_x{\mathrm{\ω}}_z}{I_y}\\ \frac{(I_x-I_y){\mathrm{\ω}}_x{\mathrm{\ω}}_y}{I_z}\end{array}\right]+Q\·S\·l\·\left[\begin{array}{c}\frac{C_{M_{x}0}+C_{M_x}^{Ma}Ma+C_{M_x}^{H}H+C_{M_x}^{\mathrm{\α}}\mathrm{\α}+C_{M_x}^{\mathrm{\β}}\mathrm{\β}}{I_x}\\ \frac{C_{M_{y}0}+C_{M_y}^{Ma}Ma+C_{M_y}^{H}H+C_{M_y}^{\mathrm{\α}}\mathrm{\α}+C_{M_y}^{\mathrm{\β}}\mathrm{\β}}{I_y}\\ \frac{(C_{M_{z}0}+C_{M_z}^{Ma}Ma+C_{M_z}^{H}H+C_{M_z}^{\mathrm{\α}}\mathrm{\α}+C_{M_z}^{\mathrm{\β}}\mathrm{\β}}{I_z}\end{array}\right]$

In above formula, with be respectively the constant term in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; Ma is the Mach number of hypersonic aircraft; H is the height on hypersonic aircraft distance ground; with be respectively the Mach number term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; with be respectively the height term coefficient in rolling moment coefficient, yawing moment coefficient and pitching moment coefficient; with be respectively the angle of attack term coefficient in rolling moment coefficient, yawing moment coefficient and pitching moment coefficient; with be respectively the yaw angle term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient.

The variable related on the right of equal sign in formula (1), except the variable needing in above-mentioned explanation to determine according to actual conditions, other variable all can utilize existing sensor measurement device to obtain or calculate.

Compared with existing Guidance and control method, the present invention has the following advantages:

1) the present invention is in the process of derivation hypersonic aircraft integration guidance Controlling model, by quantity of state ${\stackrel{\→}{x}}_1^{\′}={\left[\begin{array}{ccc}\mathrm{\α}& \mathrm{\β}& {\mathrm{\γ}}_V\end{array}\right]}^T$ Be transformed to through differomorphism ${\stackrel{\→}{x}}_1={\left[\begin{array}{ccc}{\mathrm{\αcos\γ}}_V& {\mathrm{\αsin\γ}}_V& \mathrm{\β}\end{array}\right]}^T,$ The dive section BTT (Bank-to-Turn, banked turn) so just making integration guidance Controlling model be applicable to hypersonic aircraft completely controls;

2) the integration guidance control method that the present invention proposes has taken into full account hypersonic aircraft center of mass motion and the coupling between center of mass motion, significantly improves the guidance control system overall performance of hypersonic aircraft;

3) the present invention design based on adaptive block dynamic surface backstepping control law due to integration guidance Controlling model in uncertainty estimate, so there is stronger robustness, and it is owing to employing low-pass first order filter to calculate with avoid the calculating expansion issues caused by the method for inversion itself;

4) in traditional hypersonic aircraft guidance subsystem and control subsystem design process, in order to the overall performance reaching expectation needs to carry out amendment design repeatedly to subsystems, and guidance subsystem and control subsystem are used as an entirety by the integration guidance control method designed by the present invention, therefore design problem repeatedly be can effectively avoid, thus time and the financial cost of guidance control system design reduced.

Accompanying drawing illustrates:

Fig. 1 is the principle schematic of integration guidance control method provided by the invention;

Fig. 2 is the height of hypersonic aircraft in emulation experiment, speed and local speed change of pitch angle curve;

Fig. 3 is the angle of attack of hypersonic aircraft in emulation experiment, yaw angle and angle of heel change curve;

Fig. 4 is the roll angle speed of hypersonic aircraft in emulation experiment, yawrate and pitch rate change curve;

Fig. 5 is the pitching angle of rudder reflection of hypersonic aircraft in emulation experiment, go off course angle of rudder reflection and rolling angle of rudder reflection change curve;

Fig. 6 is the change curve that the mistake of hypersonic aircraft in emulation experiment is loaded in component in body system;

Fig. 7 is the change curve of position component in the system of ground of hypersonic aircraft in emulation experiment.

Embodiment:

Below in conjunction with specific embodiment, the present invention is described further.

Fig. 1 is the principle schematic of integration guidance control method provided by the invention.As shown in the figure, first measure by sensor the state that hypersonic aircraft relative to ground is; Then, the positional information by quantity of state obtained above, the target that records in advance relative to ground being and controling parameters are updated in integration guidance control method formula (1) derived and go to calculate angle of rudder reflection vector finally, angle of rudder reflection vector is utilized hypersonic aircraft is controlled.

The hypersonic aircraft Integrated Model set up based on following formula of integration guidance control method provided by the invention, the dynamics that this model embodiment hypersonic aircraft is followed at dive section and Kinematics Law:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_F=x_{01}\\ {\stackrel{\·}{\stackrel{\→}{x}}}_0={\stackrel{\→}{f}}_0\left({\stackrel{\→}{x}}_0\right)+g_0\left(t\right){\stackrel{\→}{x}}_1^{*}+{\stackrel{\→}{\mathrm{\Δ}}}_{x_0}\\ {\stackrel{\·}{\stackrel{\→}{x}}}_1={\stackrel{\→}{f}}_1\left({\stackrel{\→}{x}}_1\right)+g_1\left({\stackrel{\→}{x}}_1\right){\stackrel{\→}{x}}_2+{\stackrel{\→}{\mathrm{\Δ}}}_{x_1}\\ {\stackrel{\·}{\stackrel{\→}{x}}}_2={\stackrel{\→}{f}}_2({\stackrel{\→}{x}}_1,{\stackrel{\→}{x}}_2)+g_2\left(t\right)\stackrel{\→}{u}+{\stackrel{\→}{\mathrm{\Δ}}}_{x_2}\\ \stackrel{\→}{y}={\left[\begin{array}{cc}{x}_F& {\stackrel{\→}{x}}_0\end{array}\right]}^T\end{array}\right.---\left(2\right)$

Wherein, ${\stackrel{\→}{x}}_1^{*}={\left[\begin{array}{cc}{\mathrm{\αcos\γ}}_V& {\mathrm{\αsin\γ}}_V\end{array}\right]}^T;$ with be respectively uncertain unknown limited function vector; the output of integrated model.

Wherein, represent the hypersonic aircraft of band angle of fall constraint and the Equation of Relative Motion with Small of target, provided by following formula:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_F=x_{01}\\ \stackrel{\·}{\stackrel{\→}{x}}={\stackrel{\→}{f}}_0\left({\stackrel{\→}{x}}_0\right)+g_0\left(t\right){\stackrel{\→}{x}}_1^{*}+{\stackrel{\→}{\mathrm{\Δ}}}_{x_0}\end{array}\right.$

Wherein, represent hypersonic aircraft around center of mass motion equation, provided by following formula:

${\stackrel{\·}{\stackrel{\→}{x}}}_1={\stackrel{\→}{f}}_1\left({\stackrel{\→}{x}}_1\right)+g_1\left({\stackrel{\→}{x}}_1\right){\stackrel{\→}{x}}_2+{\stackrel{\→}{\mathrm{\Δ}}}_{x_1}$

Wherein, represent hypersonic aircraft around barycenter kinetics equation, provided by following formula:

${\stackrel{\·}{\stackrel{\→}{x}}}_2={\stackrel{\→}{f}}_2({\stackrel{\→}{x}}_1,{\stackrel{\→}{x}}_2)+g_2\left(t\right)\stackrel{\→}{u}+{\stackrel{\→}{\mathrm{\Δ}}}_{x_2}$

Integrated Model (2) for the hypersonic aircraft obtained of deriving derives integration guidance control method, shown in (1).In actual applications, the motion state of hypersonic aircraft and controling parameters are substituted in formula (1), calculates the angle of rudder reflection of hypersonic aircraft.

Utilize the present invention to carry out emulation experiment, simulated conditions comprises following 1) to 4) bar:

1) emulate starting condition (namely hypersonic aircraft is in dive section starting point) to be set to: ground system initial point longitude and latitude is respectively φ ₀=0 °, λ ₀=0 °, the initial coordinate of hypersonic aircraft in earth axes is x=0m, y=30000m, z=0m, and speed inclination angle is θ=0 °, and flight path crab angle is σ=0 °, and speed is v=1800m/s, and the angle of pitch is crab angle is ψ=0 °, and roll angle is γ=0 °, and angular velocity in roll, yaw rate and rate of pitch are respectively ω _x=ω _y=ω _z=0 °; Target is arranged on ground, and longitude and latitude is φ _t=1 °, λ _t=1 °;

2) process constraints is set to: angle of attack ∈ [0 °, 20 °], maximum angle of attack variation rate maximum angle of heel rate of change pitching angle of rudder reflection δ _z∈ [-30 °, 10 °], driftage angle of rudder reflection δ _y∈ [-20 °, 20 °], rolling angle of rudder reflection δ _x∈ [-20 °, 20 °], overload level is n≤30g;

3) end conswtraint condition is for landing moment local speed tilt angle gamma _dF∈ [-90 ,-60] °.

4) controller parameter is chosen for:

Table 1 controller parameter table

Parameter	Value	Parameter	Value	Parameter	Value
						k F	0.8	k 11	10	k 21	10
k 01	0.1	k 12	20	k 22	20
						k 02	0.08	k 13	10	k 23	50
e 0	0.5	τ 11	0.05	τ 21	0.02
						d 0	0.05	τ 12	0.05	τ 22	0.02
		υ 1	50	τ 23	0.02
								μ 1	0.1	υ 2	50
				μ 2	0.1

Fig. 2 is the height of hypersonic aircraft in emulation experiment, speed and local speed change of pitch angle curve.Horizontal ordinate is the time, and time point 0 represents that hypersonic aircraft is when dive section starting point, and ordinate is respectively the height (upper figure) of hypersonic aircraft, speed (middle figure) and local speed inclination angle (figure below).From height change curve, when hypersonic aircraft arrives target, height is close to zero; From speed change curves, hypersonic aircraft arrives target hourly velocity and is about 1400.5m/s; From local speed change of pitch angle curve, during hypersonic aircraft arrival target, local speed inclination angle is about-69.3 °, meets local speed tilt angle gamma _dFthe constraint condition of ∈ [-90 ,-60] °.

Fig. 3 is the angle of attack of hypersonic aircraft in emulation experiment, yaw angle and angle of heel change curve.Horizontal ordinate is the time, and time point 0 represents that hypersonic aircraft is when dive section starting point, and ordinate is respectively the angle of attack (upper figure) of hypersonic aircraft, yaw angle (middle figure) and angle of heel (figure below).From angle of attack variation curve, ° scope that the angle of attack remains on [1.1,10.9], meets constraint α ∈ [0 °, 20 °]; From yaw angle change curve, its maximum amplitude is about about 0.6 °, remains at change in less scope, meets the requirement that BTT controls; Changed from angle of heel, angle of heel starts greatly the upset of BTT-180 ° about about 51s.

Fig. 4 is the roll angle speed of hypersonic aircraft in emulation experiment, yawrate and pitch rate change curve.Horizontal ordinate is the time, and time point 0 represents that hypersonic aircraft is when dive section starting point, and ordinate is respectively angular velocity in roll (upper figure), yaw rate (middle figure) and rate of pitch (figure below).From angular velocity in roll change curve and yaw rate change curve, hypersonic aircraft is when canting overturns, angular velocity in roll can have greatly changed to produce required angle of heel, yaw rate also can have greatly changed, to eliminate the yaw angle caused by cross coupling simultaneously; From rate of pitch change curve, rate of pitch occurred to change by a relatively large margin to produce the required angle of attack in the initial moment of diving.

Fig. 5 is the pitching angle of rudder reflection of hypersonic aircraft in emulation experiment, go off course angle of rudder reflection and rolling angle of rudder reflection change curve.Horizontal ordinate is the time, and time point 0 represents that hypersonic aircraft is when dive section starting point, and ordinate is respectively pitching angle of rudder reflection (upper figure), driftage angle of rudder reflection (middle figure) and rolling angle of rudder reflection (figure below).From pitching angle of rudder reflection change curve, pitching angle of rudder reflection occurs to change by a relatively large margin to produce required rate of pitch at dive section initial time, and it is inclined to maintain less rudder at residual non-uniformity; From driftage angle of rudder reflection and rolling angle of rudder reflection change curve, when canting overturns, driftage angle of rudder reflection and rolling angle of rudder reflection can have greatly changed to produce corresponding yaw rate and angular velocity in roll, and in all the other flight time they all to maintain less rudder inclined.

Fig. 6 is the change curve that the mistake of hypersonic aircraft in emulation experiment is loaded in component in body system.Horizontal ordinate is the time, time point 0 represents that hypersonic aircraft is when dive section starting point, and ordinate is respectively the overload of hypersonic aircraft suffered by body system x-axis (upper figure), y-axis (middle figure) and z-axis (figure below) direction.From the overload change curve in three directions, the overload suffered by hypersonic aircraft meets overload constraint condition n≤30g.

Fig. 7 is the change curve of position component in the system of ground of hypersonic aircraft in emulation experiment.Horizontal ordinate is the time, time point 0 represents that hypersonic aircraft is when dive section starting point, and ordinate is respectively the position component in ground system x-axis (upper figure), y-axis (middle figure) and z-axis (figure below) direction of hypersonic aircraft relative to ground system initial point.From the change curve of hypersonic aircraft relative to the location components of ground system initial point, hypersonic aircraft is in whole flight course, and trajectory change is level and smooth, and offset landings is about 3.9m, reaches the accuracy requirement of Guidance and control.

The above is only the preferred embodiment of the present invention, and protection scope of the present invention is also not only confined to above-described embodiment, and the technical scheme under all genus thinking of the present invention all belongs to protection scope of the present invention.It is noted that the those of ordinary skill for field of the present invention, improvements and modifications without departing from the principles of the present invention, these improvements and modifications also should be considered as protection scope of the present invention.

The content be not described in detail in instructions of the present invention belongs to the known prior art of professional and technical personnel in the field.

Claims (1)

1. a hypersonic aircraft dive section full dose integration guidance control method, is characterized in that, comprise the steps:

If hypersonic aircraft flight, at dive section, utilizes following process to control at any time:

First measure by sensor the state that hypersonic aircraft relative to ground is, comprise speed v, speed inclination angle theta, flight path crab angle σ, angular velocity in roll ω _x, yaw rate ω _y, rate of pitch ω _z, the angle of pitch crab angle ψ, roll angle γ and hypersonic aircraft are relative to position component x, y and z in the system of ground of ground system initial point; Then formula (1) is utilized to calculate angle of rudder reflection vector $\stackrel{\→}{u}={\left[\begin{array}{ccc}{\mathrm{\δ}}_z& {\mathrm{\δ}}_y& {\mathrm{\δ}}_x\end{array}\right]}^T,$ Wherein, δ _z, δ _yand δ _xbe respectively the pitching angle of rudder reflection of hypersonic aircraft, driftage angle of rudder reflection and rolling angle of rudder reflection; Finally utilize angle of rudder reflection vector hypersonic aircraft is controlled;

Wherein, formula one is as follows:

$\left\{\begin{array}{c}{\stackrel{\→}{s}}_0={\left[\begin{array}{cc}{x}_{01}+k_F\frac{v}{r}{x}_F& x_{02}\end{array}\right]}^T\\ {\stackrel{\→}{x}}_{1v}=g_0^{-1}\left(t\right)\·\{-\frac{v}{r}{k}_0{\stackrel{\→}{s}}_0-\frac{e_0}{r}sat({\stackrel{\→}{s}}_0,{\stackrel{\→}{d}}_0)-\[\begin{array}{c}{k}_F-\frac{v}{r}{x}_{01}+k_F\frac{\stackrel{\·}{v}r-\stackrel{\·}{r}v}{r^2}{x}_F\\ 0\end{array}\]-{\stackrel{\→}{f}}_0\left({\stackrel{\→}{x}}_0\right)\}\\ {\mathrm{\τ}}_1{\stackrel{\·}{\stackrel{\→}{x}}}_{1d}^{*}+{\stackrel{\→}{x}}_{1d}^{*}={\stackrel{\→}{x}}_{1v},{\stackrel{\→}{x}}_{1d}^{*}\left(0\right)={\stackrel{\→}{x}}_{1v}\left(0\right)\\ {\stackrel{\·}{\stackrel{\→}{x}}}_{1d}={\left[\begin{array}{cc}{\stackrel{\·}{\stackrel{\→}{x}}}_{1d}^{*}& 0\end{array}\right]}^T\\ {\stackrel{\→}{x}}_{1d}={\left[\begin{array}{cc}{\stackrel{\→}{x}}_{1d}^{*}& 0\end{array}\right]}^T\\ {\stackrel{\→}{s}}_1={\stackrel{\→}{x}}_1-{\stackrel{\→}{x}}_{1d}\\ {\stackrel{\·}{\hat{e}}}_1={\mathrm{\υ}}_1({\stackrel{\→}{s}}_1^T{\stackrel{\→}{s}}_1-{\mathrm{\μ}}_1{\hat{e}}_1),{\hat{e}}_1\left(0\right)=0\\ {\stackrel{\→}{x}}_{2v}=-g_1^{-1}\left({\stackrel{\→}{x}}_1\right)\[{\stackrel{\→}{f}}_1\left({\stackrel{\→}{x}}_1\right)+{\hat{e}}_1{\stackrel{\→}{s}}_1+k_1{\stackrel{\→}{s}}_1-{\stackrel{\·}{\stackrel{\→}{x}}}_{1d}\]\\ {\mathrm{\τ}}_2{\stackrel{\·}{\stackrel{\→}{x}}}_{2d}+{\stackrel{\→}{x}}_{2d}={\stackrel{\→}{x}}_{2v},{\stackrel{\→}{x}}_{2d}\left(0\right)={\stackrel{\→}{x}}_{2v}\left(0\right)\\ {\stackrel{\→}{s}}_2={\stackrel{\→}{x}}_2-{\stackrel{\→}{x}}_{2d}\\ {\stackrel{\·}{\hat{e}}}_2={\mathrm{\υ}}_2({\stackrel{\→}{s}}_2^T{\stackrel{\→}{s}}_2-{\mathrm{\μ}}_2{\hat{e}}_2),{\hat{e}}_1\left(0\right)=0\\ \stackrel{\→}{u}=-g_2^{-1}\left(t\right)\[{\stackrel{\→}{f}}_2({\stackrel{\→}{x}}_1,{\stackrel{\→}{x}}_2)+{\hat{e}}_2{\stackrel{\→}{s}}_2+k_2{\stackrel{\→}{s}}_2-{\stackrel{\·}{\stackrel{\→}{x}}}_{2d}\]\end{array}\right.$ (formula one)

Wherein, x ₀₁for hypersonic aircraft is relative to the sight line inclination angle λ of target _drate of change k _ffor sight line inclination angle λ _derror term coefficient, its size determines dynamic surface the weight of decline angle error item, determines its size according to actual conditions; V and for hypersonic aircraft is relative to the velocity magnitude on ground and rate of change thereof; R and be respectively hypersonic aircraft relative to the distance of target and rate of change thereof; x _ffor sight line inclination angle λ _dthe local speed tilt angle gamma in moment is landed with hypersonic aircraft _dFand; x ₀₂for hypersonic aircraft is relative to the sight line drift angle λ of target _trate of change

Wherein, g ₀t () is defined as follows shown in formula, subscript "-1 " representing matrix inverse:

$g_0\left(t\right)=\frac{Q\·S\·C_L^{\mathrm{\α}}}{m\·r}\left[\begin{array}{cc}{S}_{H_{2,2}}& S_{H_{2,3}}\\ -\frac{S_{H_{3,2}}}{{\mathrm{cos\λ}}_D}& -\frac{S_{H_{3,3}}}{{\mathrm{cos\λ}}_D}\end{array}\right]$

In above formula, t is for hypersonic aircraft is with the duration of dive section starting point for flying zero point; The dynamic pressure of Q suffered by hypersonic aircraft; S is the area of reference of hypersonic aircraft; for the lift coefficient of hypersonic aircraft is for the partial derivative of its angle of attack; M is the quality of hypersonic aircraft; be respectively the transition matrix S that half speed is tied to sight line system _hin element, i represents capable, and j represents row;

Wherein, k ₀=diag (k ₀₁, k ₀₂) be the gain matrix of positive definite, determine according to actual conditions; e ₀for positive controling parameters, determine according to actual conditions; Sat () is saturation function; for boundary layer thickness, determine according to actual conditions;

Wherein, be defined as follows shown in formula:

${\stackrel{\→}{f}}_0\left({\stackrel{\→}{x}}_0\right)=\left[\begin{array}{c}\frac{-2\stackrel{\·}{r}{\stackrel{\·}{\mathrm{\λ}}}_D}{r}-{\stackrel{\·}{\mathrm{\λ}}}_T^2{\mathrm{sin\λ}}_D{\mathrm{cos\λ}}_D+\frac{1}{r}(S_{H_{2,1}}{a}_V+S_{H_{2,2}}{g}_{Hy}+S_{H_{2,3}}{g}_{Hz})\\ \frac{-2\stackrel{\·}{r}{\stackrel{\·}{\mathrm{\λ}}}_T}{r}+2{\stackrel{\·}{\mathrm{\λ}}}_D{\stackrel{\·}{\mathrm{\λ}}}_T{\mathrm{tan\λ}}_D-\frac{1}{{\mathrm{rcos\λ}}_D}(S_{H_{3,1}}{a}_V+S_{H_{3,2}}{g}_{Hy}+S_{H_{3,3}}{g}_{Hz})\end{array}\right]$

In above formula, a _vfor hypersonic aircraft acceleration half speed system x-axis to component, its expression is as follows:

$a_V=g_{Hx}-\frac{D}{m}$

In above formula, D is the resistance that hypersonic aircraft is subject to; g _hx, g _hyand g _hzfor the component of acceleration of gravity in half speed system, its expression is as follows:

$\left\{\begin{array}{c}{g}_{Hx}=-\frac{\mathrm{\μ}}{R^3}(x\cos \mathrm{\θ}\cos \mathrm{\σ}+(y+R_e)\sin \mathrm{\θ}-z\cos \mathrm{\θ}\sin \mathrm{\σ})\\ g_{Hy}=-\frac{\mathrm{\μ}}{R^3}(-x\sin \mathrm{\θ}\cos \mathrm{\σ}+(y+R_e)\cos \mathrm{\θ}+z\sin \mathrm{\θ}\sin \mathrm{\σ})\\ g_{Hz}=-\frac{\mathrm{\μ}}{R^3}(x\sin \mathrm{\σ}+z\cos \mathrm{\σ})\end{array}\right.$

In above formula, μ is Gravitational coefficient of the Earth; R is the distance of hypersonic aircraft relative to the earth's core; R _efor earth radius; θ and σ is respectively speed inclination angle and the flight path crab angle of hypersonic aircraft; X, y and z are respectively the position component in ground system of hypersonic aircraft relative to ground system initial point;

Wherein, with be respectively first virtual controlling filtering output and rate of change; τ ₁=diag (τ ₁₁, τ ₁₂) be the time constant filter matrix of positive definite, determine according to actual conditions; with for filtering output and the rate of change thereof of expansion;

Wherein,

${\stackrel{\→}{x}}_1={\left[\begin{array}{ccc}{\mathrm{\αcos\γ}}_V& {\mathrm{\αsin\γ}}_V& \mathrm{\β}\end{array}\right]}^T$

In above formula, α, γ _vthe angle of attack of hypersonic aircraft, angle of heel and yaw angle is respectively with β;

Wherein, for unknown constant e ₁estimated value; υ ₁with μ ₁be respectively the constant being greater than zero, determine according to actual conditions; k ₁=diag (k ₁₁, k ₁₂, k ₁₃) be the gain matrix of positive definite, determine according to actual conditions;

Wherein, in each element be shown below:

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{1,1}=-cos\mathrm{\α}({\mathrm{tan\βcos\γ}}_V+{\mathrm{\αsec\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{1,2}=sin\mathrm{\α}({\mathrm{tan\βcos\γ}}_V+{\mathrm{\αsec\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{1,3}={\mathrm{cos\γ}}_V$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{2,1}=cos\mathrm{\α}({\mathrm{\αsec\βcos\γ}}_V-{\mathrm{tan\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{2,2}=-sin\mathrm{\α}({\mathrm{\αsec\βcos\γ}}_V-{\mathrm{tan\βsin\γ}}_V)$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{2,3}={\mathrm{sin\γ}}_V$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{3,1}=sin\mathrm{\α}$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{3,2}=cos\mathrm{\α}$

$g_1{\left({\stackrel{\→}{x}}_1\right)}_{3,3}=0$

Wherein, be defined as follows shown in formula:

${\stackrel{\→}{f}}_1\left({\stackrel{\→}{x}}_1\right)=\left[\begin{array}{c}{\mathrm{cos\γ}}_V{\stackrel{\→}{f}}_{1_{1,1}}^{\′}-{\mathrm{\αsin\γ}}_V{\stackrel{\→}{f}}_{1_{2,1}}^{\′}\\ {\mathrm{sin\γ}}_V{\stackrel{\→}{f}}_{1_{1,1}}^{\′}-{\mathrm{\αcos\γ}}_V{\stackrel{\→}{f}}_{1_{2,1}}^{\′}\\ {\stackrel{\→}{f}}_{1_{3,1}}^{\′}\end{array}\right]$

In above formula,

${\stackrel{\→}{f}}_{1_{1,1}}^{\′}=\frac{-\sec \mathrm{\β}}{mv}({\mathrm{mg}}_{Hz}{\mathrm{sin\γ}}_V+{\mathrm{mg}}_{Hy}{\mathrm{cos\γ}}_V+Q\·S\·C_{La})$

${\stackrel{\→}{f}}_{1_{2,1}}^{\′}=\frac{1}{mv}\[{\mathrm{tan\βcos\γ}}_V{\mathrm{mg}}_{Hy}+(tan\mathrm{\θ}+{\mathrm{tan\βsin\γ}}_V){\mathrm{mg}}_{Hz}+({\mathrm{tan\θsin\γ}}_V+tan\mathrm{\β})Q\·S\·C_{La}\]$

${\stackrel{\→}{f}}_{1_{3,1}}^{\′}=\frac{1}{mv}({\mathrm{mg}}_{Hz}{\mathrm{cos\γ}}_V-{\mathrm{mg}}_{Hy}{\mathrm{sin\γ}}_V)$

In above formula, C _lafor the lift coefficient that the body of hypersonic aircraft produces;

Wherein, with be respectively second virtual controlling filtering output and rate of change; τ ₂=diag (τ ₂₁, τ ₂₂, τ ₂₃) be the time constant filter matrix of positive definite, determine according to actual conditions;

Wherein,

${\stackrel{\→}{x}}_2={\left[\begin{array}{ccc}{\mathrm{\ω}}_x& {\mathrm{\ω}}_y& {\mathrm{\ω}}_z\end{array}\right]}^T$

In above formula, ω _x, ω _yand ω _zbe respectively the angular velocity in roll of hypersonic aircraft, yaw rate and rate of pitch;

Wherein, for unknown constant e ₂estimated value; υ ₂with μ ₂be respectively the constant being greater than zero, determine according to actual conditions; k ₂=diag (k ₂₁, k ₂₂, k ₂₃) be the gain matrix of positive definite, determine according to actual conditions;

Wherein, g ₂t () is defined as follows shown in formula:

$g_2\left(t\right)=Q\·S\·l\·\left[\begin{array}{ccc}\frac{C_{M_x}^{{\mathrm{\δ}}_z}}{I_x}& \frac{C_{M_x}^{{\mathrm{\δ}}_y}}{I_x}& \frac{C_{M_x}^{{\mathrm{\δ}}_x}}{I_x}\\ \frac{C_{M_y}^{{\mathrm{\δ}}_z}}{I_y}& \frac{C_{M_y}^{{\mathrm{\δ}}_y}}{I_y}& \frac{C_{M_y}^{{\mathrm{\δ}}_x}}{I_y}\\ \frac{C_{M_z}^{{\mathrm{\δ}}_z}}{I_z}& \frac{C_{M_z}^{{\mathrm{\δ}}_y}}{I_z}& \frac{C_{M_z}^{{\mathrm{\δ}}_x}}{I_z}\end{array}\right]$

In above formula, l is the reference length of hypersonic aircraft; I _x, I _yand I _zbe respectively the moment of inertia of hypersonic aircraft relative body axis system three axle; with be respectively the pitching rudder bias term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; with be respectively the driftage rudder bias term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; with be respectively the rolling rudder bias term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient;

Wherein, be defined as follows shown in formula:

${\stackrel{\→}{f}}_2({\stackrel{\→}{x}}_1,{\stackrel{\→}{x}}_2)=\left[\begin{array}{c}\frac{(I_y-I_z){\mathrm{\ω}}_y{\mathrm{\ω}}_z}{I_x}\\ \frac{(I_z-I_x){\mathrm{\ω}}_x{\mathrm{\ω}}_z}{I_y}\\ \frac{(I_x-I_y){\mathrm{\ω}}_x{\mathrm{\ω}}_y}{I_z}\end{array}\right]+Q\·S\·l\·\left[\begin{array}{c}\frac{C_{M_{x}0}+C_{M_x}^{Ma}Ma+C_{M_x}^{H}H+C_{M_x}^{\mathrm{\α}}\mathrm{\α}+C_{M_x}^{\mathrm{\β}}\mathrm{\β}}{I_x}\\ \frac{C_{M_{y}0}+C_{M_y}^{Ma}Ma+C_{M_y}^{H}H+C_{M_y}^{\mathrm{\α}}\mathrm{\α}+C_{M_y}^{\mathrm{\β}}\mathrm{\β}}{I_y}\\ \frac{(C_{M_{z}0}+C_{M_z}^{Ma}Ma+C_{M_z}^{H}H+C_{M_z}^{\mathrm{\α}}\mathrm{\α}+C_{M_z}^{\mathrm{\β}}\mathrm{\β}}{I_z}\end{array}\right]$

In above formula, with be respectively the constant term in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; Ma is the Mach number of hypersonic aircraft; H is the height on hypersonic aircraft distance ground; with be respectively the Mach number term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient; with be respectively the height term coefficient in rolling moment coefficient, yawing moment coefficient and pitching moment coefficient; with be respectively the angle of attack term coefficient in rolling moment coefficient, yawing moment coefficient and pitching moment coefficient; with be respectively the yaw angle term coefficient in the rolling moment coefficient of hypersonic aircraft, yawing moment coefficient and pitching moment coefficient.