CN107272719A - Hypersonic aircraft attitude motion control method for coordinating based on coordinating factor - Google Patents

Abstract

The invention discloses a kind of hypersonic aircraft attitude motion Robust coordinated control method based on coordinating factor analysis method, belong to aircraft manufacturing technology field.The close coupling problem that this method is moved first against attitude of flight vehicle, resolves into angular movement coupling, inertia coupling by the coupling of attitude mode and is manipulated with rudder face and couple three kinds of forms.Secondly, three kinds of coordinating factors have been separately designed to three of the above coupled mode.Then attitude system is divided into fast loop and slow loop, and separately designs the Robust adaptive controller in two loops.Coordinating factor is finally combined into derivation with robust controller and coordinates torque, torque will be coordinated and be assigned to rudder face, realized and coordinated by control surface deflection.This method effectively raises the control efficiency of rudder face, especially control surface deflection number of times and reduced, and has saved energy.

Description

Coordination factor-based hypersonic aircraft attitude motion coordination control method

Technical Field

The invention discloses a coordination factor-based hypersonic aircraft attitude motion coordination control method, and belongs to the technical field of spacecraft attitude control.

Background

The hypersonic aircraft has important military strategic significance and is a killer mace weapon for 21 century sky battle. At present, the research of hypersonic aircrafts is generally regarded by countries all over the world. However, control of the aircraft is also challenging due to fast and large-span flight. Hypersonic velocity is a hot point of research at present due to the characteristics of strong coupling and strong nonlinearity.

In recent years, a plurality of valuable scientific achievements are obtained in the aspect of attitude motion control of the hypersonic aircraft, and a plurality of students carry out corresponding work aiming at the problem of strong coupling of the attitude motion of the hypersonic aircraft. The learners adopt a neural network self-adaptive technology based on feedback linearization, and provide an online real-time self-adaptive attitude controller. However, feedback linearization relies on the accuracy of the system model, and thus it is difficult to ensure control accuracy when the model is uncertain. The optimal dynamic inverse control method is also proposed by scholars and applied to attitude control, however, when external interference exists in the system, the method is difficult to ensure good control. Subsequently, many scholars have proposed nonlinear control methods. The method comprises the steps that a sliding mode method is used for controlling the aircraft, two sliding mode controllers based on a single ring and an inner ring are designed, and researches show that the sliding mode method has good robustness to parameter uncertainty and external disturbance, but the strong coupling problem is difficult to process. Then, some scholars adopt a layered control idea to process the strong coupling problem of the hypersonic velocity attitude motion based on a nonlinear method, and some scholars adopt a decoupling method to process the strong coupling problem, wherein the method comprises the step of designing an inner-outer loop decoupling controller by adopting a singular value perturbation theory. Although the method realizes the coordination of the attitude motion at a certain degree and lays a foundation for subsequent work, due to the complexity of nonlinear dynamics of the hypersonic aerocraft, the results clearly provide a coordination mechanism to actively link, inhibit or utilize a coupling effect. The main problem of strong coupling of attitude motion of the hypersonic aircraft is the mutual influence among variables, some coupling influences are beneficial to the control of the aircraft, some coupling accumulation is fatal to the control of the aircraft, and long-time coupling accumulation can cause instability of the attitude of the aircraft. Based on the above analysis, it is necessary to research a new control method to deal with the strong coupling problem of the attitude motion of the hypersonic aircraft.

Disclosure of Invention

In order to overcome the defects of the existing coordination control method, the invention provides a coordination factor-based attitude motion coordination control method for a hypersonic aircraft. Firstly, based on a mathematical model of an attitude system, coupling between attitude motions is decomposed into angular motion coupling, inertia coupling and control surface manipulation coupling. And then respectively designing a coordination factor for the coupling modes, combining the coordination factor with a designed robust controller to deduce a coordination moment, and distributing the moment into a control plane deflection instruction to realize coordination. Finally, the validity of the method is verified through simulation, and the method is proved to have a better application prospect.

The invention adopts the following technical scheme for solving the technical problems:

a coordinated factor-based hypersonic aircraft attitude motion coordination control method comprises the following steps:

step 1) performing coupling analysis on an attitude model of the hypersonic aircraft, and decomposing a strong coupling problem among attitude motions into three forms of angular motion coupling, inertial coupling and control surface control coupling; based on the three coupling forms, feeding back the corresponding state variable to the corresponding control surface loop design coordination factor;

step 2) decomposing the attitude system into a slow loop and a fast loop based on a time scale separation principle; designing a slow-loop robust controller and a fast-loop robust controller respectively based on a sliding mode method and a projection mapping method;

and 3) combining the coordination factor with a robust controller to derive a coordination moment, distributing the coordination moment into a control plane instruction by using a control plane distribution matrix, and realizing the coordination of the attitude motion by using the coordinated deflection of the control plane.

The specific process of the step 1) comprises the following steps:

step 1-1), establishing a mathematical model of a hypersonic aircraft attitude system;

whereinDenotes the derivative of Ω, Ω denotes the system slow loop state variable, Ω ═ α, μ]^Tα, μ is the angle of attack, sideslip angle, roll angle, respectively;derivative representing omegaThe number, ω, represents the system fast loop state variable, ω ═ p, q, r]^TP, q, r are roll angle rate, pitch angle rate, yaw rate, respectively; m_cIndicating a fast-loop moment, M_c＝g_fu, wherein g_f∈R^3×3Is a control plane distribution matrix of a fast loop of an attitude system, u ═ 2_e,_a,_r]^TWherein_e,_a,_rThe left elevator auxiliary wing rudder, the right elevator auxiliary wing rudder and the rudder are respectively arranged; f. of_s＝[f_α,f_β,f_μ]^T，f_f＝[f_p,f_q,f_r]^T，

Wherein M and V are the mass and the speed of the aircraft respectively; q is dynamic pressure; s, c and b are respectively a reference area, a reference length and a reference width; c_L,αCoefficient of lift due to angle of attack α, C_Y,βIs the sideslip coefficient caused by sideslip angle β, g is the coefficient of gravity of the earth, C_l,β，C_l,p，C_l.rIs the lift coefficient, C, caused by β, p, r_m,α，C_m,qFor the basic pitching moment coefficient and the pitching moment coefficient caused by q, C_D,αCoefficient of drag, C, due to angle of attack α_n,β,C_n,p,C_n,rr is the yaw moment coefficient, X, caused by β, p, r_cgThe distance from the center of mass to the center of the reference moment,matrix coefficients are assigned to the fast loops. I is_xxIs the product of inertia about the x-axis, I_yyIs the product of inertia about the y-axis, I_zzIn order to be the product of inertia about the z-axis,is I_xxThe derivative of (a) of (b),is I_yyThe derivative of (a) of (b),is I_zzDerivative of f_s，f_f，g_s，g_fAs an attitude system state matrix,/_aero，m_aero，n_aeroRepresenting three-channel moment;

step 1-2) carrying out coupling analysis on the established attitude system model, decomposing the coupling of the attitude into attitude angular motion coupling, inertia coupling and control surface manipulation coupling,

1) attitude angle coupling model:

in the attitude system model established in the step 1-1), the coupling relation of the attitude angles is described as follows:

whereinRespectively expressed as slow loop state variables attack angle, sideslip angle andattitude angle coupling of roll angle;

2) inertial coupling

In the attitude system model established in the step 1-1), the inertial coupling is described as follows:

wherein f is_p，f_q，f_rRepresenting the inertial coupling caused by p, q, r in a fast loop system;

3) control surface steering coupling

In the attitude system model established in the step 1-1), the control surface manipulation coupling is described as follows:

wherein g is_lFor the roll channel steering coupling, g_mFor the pitch channel steering coupling, g_nFor the purpose of the yaw-channel coupling,roll moment coefficients caused by the auxiliary wing rudder and the rudder of the right elevator,the pitch moment coefficient caused by the right elevator auxiliary wing rudder,the coefficient of the pitch moment caused by the rudder,the yaw moment coefficient caused by the right elevating auxiliary wing rudder,yaw moment coefficient caused by rudder;

G_f,a matrix is assigned to the control surface,respectively the lateral force coefficient caused by the left elevator, the lateral force coefficient caused by the right elevator aileron and the lateral force coefficient caused by the rudder,the yaw moment coefficient, the pitch moment coefficient, the roll moment coefficient and the resistance coefficient caused by the left elevator, the drag coefficient caused by the right elevator aileron,for the coefficient of resistance caused by the rudder,a lift coefficient is induced for the left elevator,for the coefficient of lift caused by the rudder,for the yaw moment coefficient caused by the right elevator aileron,for the yaw moment coefficient caused by the rudder,matrix parameters are allocated to the control surfaces of the pitch channels,matrix parameters are allocated to the control surfaces of the yaw channel,distributing matrix parameters for the control surface of the rolling channel;

step 1-3) designing a coordination factor;

for 1) attitude angle coupling in step 1-2),setting 0, expressed as psina-rcos α ═ 0, yields r ═ ptan α, and feeds back r ═ ptan α to the rudder loop, so the coordination factor is designed to be 0Wherein k is₁The more than 0 is the design parameter,is the first component of the rudder coordination factor;

in the step 1-2), the coupling relation of the attack angle and the roll angle is described as p-sigma r < p ≤ pcos alpha + rsin alpha < p + rhor, and the adjustment factor for feeding beta back to the rudder loop is designed as follows:

where | sina | ≠ Δ_α，k₂，k₃A parameter greater than zero is designed for the design,is the second component of the rudder coordination factor;

for the inertial coupling of 2) in the step 1-2), feeding back beta and r to an aileron loop, feeding back beta and q to a rudder loop, and feeding back alpha and p to an elevator loop to increase damping moment and stability moment; the design of the coordination factor is as follows:

wherein λ_e，λ_a，Respectively feeding back the corresponding state variables to the coordination factors, k, of the left elevator rudder, the right elevator aileron rudder and the rudder₄，k₅，k₆，k₇,k₈，k₉A design parameter greater than zero;

for the control surface steering coupling of 3) in the step 1-2), the steering coupling degree of the auxiliary wing rudder and the rudder is defined as:

wherein,

wherein,the three-channel moment coefficient change increment coefficient caused by rudder deflection,is a three-channel moment coefficient change increment coefficient, S, caused by the deflection of the right elevon rudder_cwr,S_cwExpressed as rudder area and vertical fin area; s, L reference area and reference length; y is_cwrThe distance between the center of the rudder surface and the longitudinal axis, chi is the sweepback angle, ξ is a correction factor, and S is satisfied_cwr≤S,S_cw≤S,y_cwrL is more than or equal to L,0 is more than ξ and less than or equal to 1, cos χ is more than 0 and less than or equal to 1, n is the relative execution efficiency of the ailerons, η_k,The ratio of the heel to the tip and the ratio of the stem to the aspect ratio of the exposed wing are respectively;f, slightly comparing the exposed wing with the root; the control surface coordination strategy is designed as_a＝E_rE is more than 0 and less than or equal to 1, and E is the coupling degree of the rudder and the right auxiliary elevator wing rudder.

The specific process of the step 2) comprises the following steps:

step 2-1) introducing uncertain parameter vectors

Representing the system model in the step 1-1) as

Wherein D represents an external disturbance,

θ₁＝C_L,α,θ₂＝C_Y,β,θ₃＝[C_Y,βC_L,α]^T,

wherein C is_L,α，C_Y,β，C_Y,β，C_L,α，C_n,β，C_n,p，C_n,r，C_m,α，C_m,q，C_D,α，C_l,β，C_l,r，C_l,pIs an aircraft aerodynamic parameter.

Step 2-2) projection mapping algorithm

Θ_Ω,Θ_ωRespectively expressed as uncertain parameter vectors theta_Ω,θ_ωIs expressed as:

Θ_Ω＝{θ_Ω∈R⁴|θ_{Ωi min}≤θ_Ωi≤θ_{Ωi max},i＝1,…,4},

Θ_ω＝{θ_ω∈R¹⁷|θ_{ωi min}≤θ_ωi≤θ_{ωi max},i＝1,…,17}

wherein theta is_Ωi，θ_{Ωi min}，θ_{Ωi max}Is the component of the slow loop state variable, the minimum value of the component and the maximum value of the component, theta_ωi，θ_{ωi min}，θ_{ωi max}The component of the fast loop state variable, the minimum value of the component and the maximum value of the component are obtained; order toDenoted by theta_ΩIs determined by the estimated value of (c),representing the estimation error, theta_ωLike theta_ΩAccording to the projection mapping algorithm, the self-adaptation law of uncertain parameters is

WhereinFast and slow loop adaptive functions, 0 as diagonal matrix, tau as adaptive function, and projection operatorIs defined as

Whereinθ_imax，θ_iminFor the estimated value component of the state variable, the maximum value of the state variable component and the minimum value of the state variable component, it is clear that, for the adaptation function tau,

whereinFor adaptive estimation, θ_min，θ_maxIn order to estimate the minimum and maximum values,in order to transpose the estimation error,^-1is the inverse of the parameter-diagonal matrix,is a design parameter;

step 2-3) design of robust controller of attitude angle

Defining a tracking error e₁＝Ω-Ω_cThe sliding mode function is designed as

Wherein K is diag { K ═ d { (K) }₁,K₂,K₃},K_iThe design parameters are expressed more than 0, i is 1,2 and 3, sigma is a sliding mode function, and the first derivative of the sliding mode function is obtained

To obtainIs adaptive toWherein, κ₁＞0,₁∈R^4×4,λ_Ω＝diag{λ₁,λ₂,λ₃,λ₄With } > 0 as controller parameter, g_s，f₁Ψ is a system coefficient matrix Ψ^TIs a transposed matrix of Ψ, e₁In order to be an error, the error is,the slow loop tracks the derivative of the instruction,is an estimate of the state variable of the slow loop,the estimation error is a sliding mode function;

step 2-4) design of attitude angular rate controller

Definition error e₂＝ω-ω_cDerived from the error

Virtual controllerSeen as a perturbation, to obtainWhereinΞ^TThe method is characterized by comprising the following steps of (1) transposing a system matrix of a system fast loop; the attitude angular rate loop control is designed asWhereinIs a fast loop system state matrix g_fThe adverse effect of xi^TFor transposition of the system matrix, θ_ωIs a fast loop state variable, g_fIs a system state matrix, M_cTo control the torque, D is an external disturbance,derivative of the slow-loop controller, κ₂For controlling design parameters, for observingThe output of the device is used for outputting,is a transpose of the matrix of the slow loop state system,defining the observation error by observer estimationIs adaptive to law ofWherein κ₂＞0,₂∈R^17×17＞0,λ_ω∈R^{17 ×17}The parameter > 0 is the parameter of the controller,to estimate the error, the observer is designed as

Wherein,

q₁(e),q₂(e),…,q_n(e) are observer parameters.

The specific process of the step 3) comprises the following steps:

attitude angular rate loop controller M_cAnd control plane allocation matrix g_fThe coordinated moment is denoted as M_c＝g_fTherein, wherein

WhereinMatrix parameters are allocated to the control surfaces of the pitch channels,is inclined toThe aeronautical channel control surface is distributed with matrix parameters,assigning a matrix parameter, λ, to the control surface of the roll channel_e，λ_a，λ_rIs a coordination factor; the control plane command is obtained as g_f ^-1·M_c。

When the coordination strategy adopts the auxiliary wing rudder and the rudder to coordinate and deflect to realize yawing moment and rolling moment, the elevator rudder deflects to realize pitching moment, and the control surface coordination design is as follows:

_coe＝_e,_coa＝E_r,_cor＝_r。

the invention has the following beneficial effects:

1. the controller adds the coordination factor, and the performance is better than that of the controller without the coordination factor. The coordination controller has the advantages of reduced vibration times, small tracking overshoot of the attitude angle, stable tracking and corresponding rapidness.

2. The controller adds a coordination factor and the attitude angular rate becomes stable and fast accordingly.

3. The controller adds the coordination factor, the control efficiency of the control surface is effectively improved, particularly the deflection times of the control surface are reduced, and the energy is saved.

Drawings

FIG. 1 is a schematic diagram of an aircraft attitude motion coordination mechanism.

FIG. 2 is a graph of a comparison of the respective simulations of attitude angle with and without a coordination factor, wherein (a) is a comparison of an angle of attack tracking curve, (b) is a comparison of a sideslip tracking curve, and (c) is a comparison of a roll tracking curve.

Fig. 3 is a simulation comparison graph of the attitude angular rate with and without the coordination factor, wherein (a) is a roll angular rate response comparison graph, and (b) is a pitch angular rate response comparison graph. (c) Is a plot of yaw rate response versus.

FIG. 4 is a plot of control plane deflection with and without the addition of a coordination factor versus (a) aileron deflection versus (b) elevator deflection versus (c) rudder deflection versus.

Detailed Description

The invention is described in further detail below with reference to the accompanying drawings.

In FIG. 1, a fast loop torque command M is derived by designing the fast loop control law_cAnd combines with the designed coordination factor (19) to derive coordination moment, and the coordination moment is finally distributed into a control surface coordination command through a fast loop control surface distribution matrix_e,_a,_rAnd finally realizing the coordinated control among the attitude motions of the hypersonic aircraft through the coordinated deflection of the control surface. Fig. 2, fig. 3 and fig. 4 are simulation verifications, and it can be obtained through simulation diagram analysis and comparison that the addition of the coordination factor can effectively improve the control effect of the controller, and has an obvious effect on the inhibition of coupling.

The hypersonic aircraft attitude system model is as follows:

whereinDenotes the derivative of Ω, Ω denotes the system slow loop state variable, Ω ═ α, μ]^Tα, μ is the angle of attack, sideslip angle, roll angle, respectively;denotes the derivative of ω, ω denotes the system fast loop state variable, ω ═ p, q, r]^TP, q, r are roll angle rate, pitch angle rate, yaw rate, respectively; m_cIndicating a fast-loop moment, M_c＝g_fu, wherein g_f∈R^3×3Is a control plane distribution matrix of a fast loop of an attitude system, u ═ 2_e,_a,_r]^TWherein_e,_a,_rThe left elevator auxiliary wing rudder, the right elevator auxiliary wing rudder and the rudder are respectively arranged; f. of_s＝[f_α,f_β,f_μ]^T，f_f＝[f_p,f_q,f_r]^T，

Wherein M and V are the mass and the speed of the aircraft respectively;is dynamic pressure; s, c and b are respectively a reference area, a reference length and a reference width; c_L,αCoefficient of lift due to angle of attack α, C_Y,βIs the sideslip coefficient caused by sideslip angle β, g is the coefficient of gravity of the earth, C_l,β，C_l,p，C_l.rIs the lift coefficient, C, caused by β, p, r_m,α，C_m,qFor the basic pitching moment coefficient and the pitching moment coefficient caused by q, C_D,αCoefficient of drag, C, due to angle of attack α_n,β,C_n,p,C_n,rr is the yaw moment coefficient, X, caused by β, p, r_cgThe distance from the center of mass to the center of the reference moment,matrix coefficients are assigned to the fast loops. I is_xxIs the product of inertia about the x-axis, I_yyIs the product of inertia about the y-axis, I_zzIn order to be the product of inertia about the z-axis,is I_xxThe derivative of (a) of (b),is I_yyThe derivative of (a) of (b),is I_zzDerivative of f_s，f_f，g_s，g_fAs an attitude system state matrix,/_aero，m_aero，n_aeroRepresenting three channel moments. As can be seen from the attitude system mathematical model, the attitude motion coupling can be decomposed into attitude angle coupling, inertial coupling and control surface manipulation coupling.

The attitude angle coupling can be described as:

whereinAttitude angle couplings, represented as slow loop state variables, angle of attack, sideslip, and roll angle, respectively.

The inertial coupling can be described as:

wherein f is_p，f_q，f_rRepresenting the inertial coupling caused by p, q, r in a fast loop system.

The control surface steering coupling can be described as:

wherein g is_lFor the roll channel steering coupling, g_mFor the pitch channel steering coupling, g_nFor the purpose of the yaw-channel coupling,roll moment coefficients caused by the auxiliary wing rudder and the rudder of the right elevator,the pitch moment coefficient caused by the right elevator auxiliary wing rudder,the coefficient of the pitch moment caused by the rudder,the yaw moment coefficient caused by the right elevating auxiliary wing rudder,rudder induced yaw moment coefficient.

G_f,A matrix is assigned to the control surface,respectively the lateral force coefficient caused by the left elevator, the lateral force coefficient caused by the right elevator aileron and the lateral force coefficient caused by the rudder,the yaw moment coefficient, the pitch moment coefficient, the roll moment coefficient and the resistance coefficient caused by the left elevator, the drag coefficient caused by the right elevator aileron,for the coefficient of resistance caused by the rudder,a lift coefficient is induced for the left elevator,for the coefficient of lift caused by the rudder,for the yaw moment coefficient caused by the right elevator aileron,for the yaw moment coefficient caused by the rudder,assigning matrix parameters, g, to the control surfaces of the pitch channels_q,e，g_q,a，g_q,rMatrix parameters are allocated to the control surfaces of the yaw channel,and distributing matrix parameters to the control surfaces of the rolling channels.

In the formula (7), the rate of change of the side slip angle is made 0, that isCan be set to 0, then

psina-rcosα＝0 (12)

It is possible to derive r ═ pta, which is fed back to the rudder loop, so that the coordination factor is designed as

Wherein k is₁The more than 0 is the design parameter,the first component of the rudder coordination factor.

The coupling relation of the attack angle and the roll angle can be described as p-sigma r < p ≦ pcos alpha + rsin alpha < p + rho r, and if beta is fed back to the rudder loop, the coordination factor is designed as follows:

where | sina | ≠ Δ_α，k₂，k₃A parameter greater than zero is designed for the design,the second component of the rudder coordination factor.

In equation (8), the coordination factor for feeding β, r back to the aileron loop, β, q back to the rudder loop, and α, p back to the elevator loop is designed as:

wherein λ_e，λ_a，λ_r3Respectively feeding back the corresponding state variables to the coordination factors, k, of the left elevator rudder, the right elevator aileron rudder and the rudder₄，k₅，k₆，k₇,k₈，k₉A design parameter greater than zero.

For the rudder surface steering coupling in equation (9), the degree of rudder surface steering coupling to the aileron is defined:

wherein,

wherein,the three-channel moment coefficient change increment coefficient caused by rudder deflection,is a three-channel moment coefficient change increment coefficient, S, caused by the deflection of the right elevon rudder_cwr,S_cwExpressed as rudder area and vertical fin area; s, L reference area and reference length; y is_cwrThe distance between the center of the rudder surface and the longitudinal axis, chi is the sweepback angle, ξ is a correction factor, and S is satisfied_cwr≤S,S_cw≤S,y_cwrL is more than or equal to L,0 is more than ξ and less than or equal to 1, cos χ is more than 0 and less than or equal to 1, n is the relative execution efficiency of the ailerons, η_k,The ratio of the exposed wing to the tip of the foot, the ratio of the stem to the tip of the foot, and the ratio of the exposed wing to the root of the foot,the control surface coordination strategy is designed as

_a＝E_r,0＜E≤1 (18)

And E is the coupling degree of the rudder and the right auxiliary elevator wing rudder. Considering equations (13), (14) and (15), the coordination factor of the attitude motion of the hypersonic aircraft is:

wherein λ_e，λ_r，λ_aThe coordination factors fed back to the left elevator, the rudder and the right auxiliary elevator wing rudder for the corresponding state variables

Introducing uncertain vector vectors, and establishing a posture system model from the following steps:

wherein D represents an external disturbance,

θ₁＝C_L,α,θ₂＝C_Y,β,θ₃＝[C_Y,βC_L,α]^T,

wherein C is_L,α，C_Y,β，C_Y,β，C_L,α，C_n,β，C_n,p，C_n,r，C_m,α，C_m,q，C_D,α，C_l,β，C_l,r，C_l,pIs an aircraft aerodynamic parameter.

Definition of theta_Ω,Θ_ωRespectively expressed as uncertain parameter vectors theta_Ω,θ_ωCan be expressed as:

wherein theta is_Ωi，θ_{Ωi min}，θ_{Ωi max}Is the component of the slow loop state variable, the minimum value of the component and the maximum value of the component, theta_ωi，θ_{ωi min}，θ_{ωi max}The fast loop state variable is a component, a minimum value of the component and a maximum value of the component. Order toDenoted by theta_ΩIs determined by the estimated value of (c),representing the estimation error, theta_ωLike theta_ΩAccording to the projection mapping algorithm, the self-adaptation law of uncertain parameters is

WhereinFast and slow loop adaptive functions, 0 as diagonal matrix, tau as adaptive function, and projection operatorWhereinFor projection operator, define as

Whereinθ_imax，θ_iminThe estimated value component of the state variable, the maximum value of the state variable component, and the minimum value of the state variable component. Obviously, for the adaptation function τ

WhereinFor adaptive estimation, θ_min，θ_maxIn order to estimate the minimum and maximum values,in order to transpose the estimation error,^-1τ is the adaptive function for the design parameter, which is the inverse of the parameter diagonal matrix.

Defining a tracking error e₁＝Ω-Ω_cWherein Ω is_cFor the attitude angle command signal, the sliding mode function is designed as

Wherein K is diag { K ═ d { (K) }₁,K₂,K₃},K_iAnd > 0, i ═ 1,2 and 3, expressed as design parameters, and σ is a sliding mode function. The first derivative of the sliding mode function can be obtained

To obtain

Wherein g is_s，f₁Ψ is a system coefficient matrix Ψ^TIs a transposed matrix of Ψ, K is a design parameter matrix, κ₁> 0 is a controller parameter, e₁In order to be an error, the error is,the slow loop tracks the derivative of the instruction,is an estimated value of a state variable of a slow loop, and the adaptive law of the estimated value is designed as

Wherein₁∈R^4×4,λ_Ω＝diag{λ₁,λ₂,λ₃,λ₄With 0 denotes a design parameter matrix,for estimating the error, as a sliding mode function, Ψ is a slow loop system coefficient matrix. Considering the Lyapunov function

Where σ is a sliding mode function, σ^TIn order to plan a transposition of the meter function,the slow loop estimation error matrix is transposed,for adaptive design of the inverse matrix of the parameter matrix, the derivation of (30) can be obtained

The combination of (28) and (29) can be obtained

Wherein κ₁＞0,₁∈R^4×4,λ_Ω＝diag{λ₁,λ₂,λ₃,λ₄With 0 denotes a design parameter matrix,to estimate the error, σ is a sliding-mode function, σ^TIn order to plan a transposition of the meter function,slow loop estimation error matrix transposition, g_s，f₁Ψ is a system coefficient matrix Ψ^TIs a transposed matrix of Ψ, e₂Is an error, g_sIs a slow loop state system matrix.

Definition error e₂＝ω-ω_c，ω_cFor the attitude angular rate command signal, the error is derived

Wherein xi^TFor transposition of the system matrix, θ_ωIs a fast loop state variable, g_fIs a system state matrix, M_cTo control the torque, D is an external disturbance,the derivative of the slow loop controller. Virtual controllerSeen as a perturbation, can yieldWherein,the attitude angular rate loop control is designed as

WhereinIs a fast loop system state matrix g_fInverse of (a), kappa₂In order to control the design parameters of the device,in order to be the output of the observer,the other parameters are consistent with the above for the transpose of the slow loop state system matrix.Defining the observation error by observer estimationIs adaptive to law of

Wherein κ₂＞0,₂∈R^17×17＞0,λ_ω∈R^17×17The more than 0 is the design parameter,to estimate the error.The observer is designed as

Wherein,

q₁(e),q₂(e),…,q_n(e) are observer parameters.

And (3) proving that: the Lyapunov function is considered to be selected as follows

Wherein e is₂In order to be an error, the error is,for transposing errors, θ_ωIn order to be a fast-loop state variable,in order to estimate the error, the error is estimated,is composed ofThe transpose of (a) is performed,in order to observe the error, the error is observed,in order to transpose the observation error,for the transpose matrix of the adaptive parameter, the derivative of the Lyapunov function for the time t can be obtained

WhereinFor the derivation of the slow loop Lyapunov function over time t,the error is transposed and the phase of the error is reversed,the derivative of the error is a function of,is composed ofThe transpose of (a) is performed,in order to be a fast-loop adaptation function,to be a transpose of the observed error,the derivative of the observer output is obtained by substituting equations (32), (34) and (35) into equation (38)

Let L (e) ═ c > 1, Q (e) ═ ce, then can obtain

Where c is the observer design parameter, and the other parameters are consistent with the foregoing.

The Lyapunov function is uniformly bounded according to the formula (40), so that the designed control law ensures that the controlled system is uniformly bounded.

The robust coordination control of the attitude motion is to combine an attitude angular rate loop controller M after introducing a coordination factor (19)_cAnd control plane allocation matrix g_fThe coordination moment is calculated, the coordination moment is distributed into a control plane instruction, coordination is realized through control plane deflection, and the robust coordination control scheme is shown in fig. 1. In FIG. 1, a fast loop torque command M is derived by designing the fast loop control law_cAnd combines with the designed coordination factor (19) to derive coordination moment, and the coordination moment is finally distributed into a control surface coordination command through a fast loop control surface distribution matrix_e,_a,_rAnd finally realizing the coordinated control among the attitude motions of the hypersonic aircraft through the coordinated deflection of the control surface. The coordinated torque may be expressed as

M_c＝g_f· (41)

Wherein

WhereinMatrix parameters are allocated to the control surfaces of the pitch channels,matrix parameters are allocated to the control surfaces of the yaw channel,assigning a matrix parameter, λ, to the control surface of the roll channel_e，λ_a，λ_rThe coordination factor designed in the foregoing. The control surface command can be obtained

＝g_f ^-1·M_c(43)

When the coordination strategy adopts the auxiliary wing rudder and the rudder to coordinate and deflect to realize yaw moment and roll moment, the elevator rudder deflects to realize pitch moment, and the coordination of the control surface can be designed as

_coe＝_e,_coa＝E_r,_cor＝_r(44)

To prove the effectiveness of the controller, we select a hypersonic aircraft attitude system model described by equation (1), and the basic parameters of the model are as follows: m is 54013lb, M_a8, 13398ft/s, 68898ft, 280000 lb. The design parameters are selected as follows: k is a radical of_i＝1,i＝1…7,K₁＝K₂＝K₃＝4,κ₁＝κ₂The initial condition is set to α for the command signal for the attitude angle, where α is 1 °, β is 5 °, μ is 0 °, and p is q is r is 0 °/s_c＝5°,β_c＝0°,μ_c4 deg. is equal to. The disturbance D is selected from D (t) ([ 0.5sin (1.5t) 0.5cos (2t) 0.5sin (2t)]^TThe simulation results are shown in fig. 2, fig. 3 and fig. 4, when the coordination factor (14) is not added in fig. 2- (a), the overshoot of α is 35%, and after the coordination factor (14) is added, the overshoot is 10%, after the coordination factor (14) is added in fig. 2- (b), the overshoot of β is smaller than that of the uncoordinated factor, after the coordination factor is added in the fast loop (15), the jitter amplitude of the tracking curve of fig. 3- (a) p, the tracking curve of 3- (b) q and the tracking curve of 3- (c) r is obviously reduced, the variation range of the attitude angular rate and the jitter amplitude are smaller than those of the response curve under the action of the uncoordinated controller, and the process of the attitude angular rate approaching balance is smoother and faster due to the coordination controller, in fig. 4, the coordination factor (18) is added to improve the control efficiency of the control of the attitude system and the maneuverability of hypersonic aircraft.

Claims (5)

1. A coordinated factor-based hypersonic aircraft attitude motion coordination control method is characterized by comprising the following steps: the method comprises the following steps:

step 1) performing coupling analysis on an attitude model of the hypersonic aircraft, and decomposing a strong coupling problem among attitude motions into three forms of angular motion coupling, inertial coupling and control surface control coupling; based on the three coupling forms, feeding back the corresponding state variable to the corresponding control surface loop design coordination factor;

step 2) decomposing the attitude system into a slow loop and a fast loop based on a time scale separation principle; designing a slow-loop robust controller and a fast-loop robust controller respectively based on a sliding mode method and a projection mapping method;

and 3) combining the coordination factor with a robust controller to derive a coordination moment, distributing the coordination moment into a control plane instruction by using a control plane distribution matrix, and realizing the coordination of the attitude motion by using the coordinated deflection of the control plane.

2. The coordinated factor-based hypersonic aircraft attitude motion coordination control method according to claim 1, characterized in that the specific process of step 1) comprises the following steps:

step 1-1), establishing a mathematical model of a hypersonic aircraft attitude system;

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mover> <mi>&amp;Omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>f</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mi>&amp;omega;</mi> </mtd> </mtr> <mtr> <mtd> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>f</mi> <mi>f</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>f</mi> </msub> <msub> <mi>M</mi> <mi>c</mi> </msub> </mtd> </mtr> </mtable> </mfenced>

whereinDenotes the derivative of Ω, Ω denotes the system slow loop state variable, Ω ═ α, μ]^Tα, μ pointsRespectively, an attack angle, a sideslip angle and a roll angle;denotes the derivative of ω, ω denotes the system fast loop state variable, ω ═ p, q, r]^TP, q, r are roll angle rate, pitch angle rate, yaw rate, respectively; m_cIndicating a fast-loop moment, M_c＝g_fu, wherein g_f∈R^3×3Is a control plane distribution matrix of a fast loop of an attitude system, u ═ 2_e,_a,_r]^TWherein_e,_a,_rThe left elevator auxiliary wing rudder, the right elevator auxiliary wing rudder and the rudder are respectively arranged; f. of_s＝[f_α,f_β,f_μ]^T，f_f＝[f_p,f_q,f_r]^T，

<mrow> <msub> <mi>f</mi> <mi>&amp;alpha;</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>M</mi> <mi>V</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;beta;</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mo>-</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> <mo>+</mo> <mi>M</mi> <mi>g</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;gamma;</mi> <mi>cos</mi> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>f</mi> <mi>&amp;beta;</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>M</mi> <mi>V</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>Y</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <mi>&amp;beta;</mi> <mo>+</mo> <mi>M</mi> <mi>g</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;gamma;</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>f</mi> <mi>&amp;mu;</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>M</mi> <mi>V</mi> </mrow> </mfrac> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>Y</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <mi>&amp;beta;</mi> <mi>tan</mi> <mi>&amp;gamma;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;mu;</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mi>M</mi> <mi>V</mi> </mrow> </mfrac> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> </mrow>

<mrow> <mo>(</mo> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;gamma;</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;mu;</mi> <mo>+</mo> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;beta;</mi> <mo>)</mo> <mo>-</mo> <mfrac> <mi>g</mi> <mi>V</mi> </mfrac> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;gamma;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;mu;</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;beta;</mi> </mrow>

<mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;beta;</mi> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;alpha;</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;beta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>sin</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mi>&amp;alpha;</mi> <mi>s</mi> <mi>e</mi> <mi>c</mi> <mi>&amp;beta;</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>sin</mi> <mi>&amp;alpha;</mi> <mi>sec</mi> <mi>&amp;beta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <msub> <mi>f</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mi>a</mi> <mi>e</mi> <mi>r</mi> <mi>o</mi> </mrow> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mrow> <mo>)</mo> <mi>q</mi> <mi>r</mi> <mo>-</mo> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mi>p</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>f</mi> <mi>q</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>a</mi> <mi>e</mi> <mi>r</mi> <mi>o</mi> </mrow> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mrow> <mo>)</mo> <mi>p</mi> <mi>r</mi> <mo>-</mo> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <mi>q</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>f</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mrow> <mi>a</mi> <mi>e</mi> <mi>r</mi> <mi>o</mi> </mrow> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mrow> <mo>)</mo> <mi>p</mi> <mi>q</mi> <mo>-</mo> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> <mi>r</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>g</mi> <mi>f</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>g</mi> <mi>l</mi> <mi>p</mi> </msubsup> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msubsup> <mi>g</mi> <mi>m</mi> <mi>q</mi> </msubsup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msubsup> <mi>g</mi> <mi>n</mi> <mi>r</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <msub> <mi>l</mi> <mrow> <mi>a</mi> <mi>e</mi> <mi>r</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>b</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <mi>&amp;beta;</mi> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mi>p</mi> <mi>b</mi> <mo>/</mo> <mn>2</mn> <mi>V</mi> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>.</mo> <mi>r</mi> </mrow> </msub> <mi>r</mi> <mi>b</mi> <mo>/</mo> <mn>2</mn> <mi>V</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow>1

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mrow> <mi>a</mi> <mi>e</mi> <mi>r</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> <mi>q</mi> <mi>c</mi> <mo>/</mo> <mn>2</mn> <mi>V</mi> <mo>)</mo> </mrow> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> <mi>sin</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> </mrow>

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>n</mi> <mrow> <mi>a</mi> <mi>e</mi> <mi>r</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>b</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <mi>&amp;beta;</mi> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mi>p</mi> <mi>b</mi> <mo>/</mo> <mn>2</mn> <mi>V</mi> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mi>r</mi> <mi>b</mi> <mo>/</mo> <mn>2</mn> <mi>V</mi> <mo>)</mo> </mrow> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>Y</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <mi>&amp;beta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>

Wherein M and V are the mass and the speed of the aircraft respectively;is dynamic pressure; s, c and b are respectively a reference area, a reference length and a reference width; c_L,αCoefficient of lift due to angle of attack α, C_Y,βIs the sideslip coefficient caused by sideslip angle β, g is the coefficient of gravity of the earth, C_l,β，C_l,p，C_l.rIs the lift coefficient, C, caused by β, p, r_m,α，C_m,qFor the basic pitching moment coefficient and the pitching moment coefficient caused by q, C_D,αCoefficient of drag, C, due to angle of attack α_n,β,C_n,p,C_n,rr is the yaw moment coefficient, X, caused by β, p, r_cgThe distance from the center of mass to the center of the reference moment,distributing matrix coefficients for the fast loop; i is_xxIs the product of inertia about the x-axis, I_yyIs the product of inertia about the y-axis, I_zzIn order to be the product of inertia about the z-axis,is I_xxThe derivative of (a) of (b),is I_yyThe derivative of (a) of (b),is I_zzDerivative of f_s，f_f，g_s，g_fAs an attitude system state matrix,/_aero，m_aero，n_aeroRepresenting three-channel moment;

step 1-2) carrying out coupling analysis on the established attitude system model, decomposing the coupling of the attitude into attitude angular motion coupling, inertia coupling and control surface manipulation coupling,

1) attitude angle coupling model:

in the attitude system model established in the step 1-1), the coupling relation of the attitude angles is described as follows:

<mrow> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <mi>p</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <mi>r</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <mover> <mi>&amp;beta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>p</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;alpha;</mi> <mo>-</mo> <mi>r</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> </mrow>

<mrow> <mover> <mi>&amp;mu;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>sec</mi> <mi>&amp;beta;</mi> <mrow> <mo>(</mo> <mi>p</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <mi>r</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> </mrow>

whereinRespectively representing the attitude angle coupling of the state variables of the slow loop, such as the attack angle, the sideslip angle and the roll angle;

2) inertial coupling

In the attitude system model established in the step 1-1), the inertial coupling is described as follows:

<mrow> <msub> <mi>f</mi> <mi>p</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>q</mi> <mi>r</mi> <mo>-</mo> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mi>p</mi> </mrow>

<mrow> <msub> <mi>f</mi> <mi>q</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>p</mi> <mi>r</mi> <mo>-</mo> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <mi>q</mi> </mrow>

<mrow> <msub> <mi>f</mi> <mi>r</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>p</mi> <mi>q</mi> <mo>-</mo> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msub> <mi>p</mi> </mrow>

wherein f is_p，f_q，f_rRepresenting the inertial coupling caused by p, q, r in a fast loop system;

3) control surface steering coupling

In the attitude system model established in the step 1-1), the control surface manipulation coupling is described as follows:

<mrow> <msub> <mi>g</mi> <mi>l</mi> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>b</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>g</mi> <mi>m</mi> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>m</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>m</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>g</mi> <mi>n</mi> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>b</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow>

wherein g is_lFor the roll channel steering coupling, g_mFor the pitch channel steering coupling, g_nFor the purpose of the yaw-channel coupling,roll moment coefficients caused by the auxiliary wing rudder and the rudder of the right elevator,the pitch moment coefficient caused by the right elevator auxiliary wing rudder,the coefficient of the pitch moment caused by the rudder,the yaw moment coefficient caused by the right elevating auxiliary wing rudder,yaw moment coefficient caused by rudder;

<mrow> <msub> <mi>G</mi> <mrow> <mi>f</mi> <mo>,</mo> <mi>&amp;delta;</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SbC</mi> <mrow> <mi>l</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> </mrow>

<mrow> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SbC</mi> <mrow> <mi>l</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> </mrow>

<mrow> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SbC</mi> <mrow> <mi>l</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> </mrow>

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>ScC</mi> <mrow> <mi>m</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mi>sin</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>L</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>ScC</mi> <mrow> <mi>m</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mi>sin</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>L</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mrow> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>ScC</mi> <mrow> <mi>m</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>D</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mi>sin</mi> <mi>&amp;alpha;</mi> </mrow>

<mrow> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SbC</mi> <mrow> <mi>n</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>Y</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> </mrow>

<mrow> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SbC</mi> <mrow> <mi>n</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>Y</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> </mrow>

<mrow> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>=</mo> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SbC</mi> <mrow> <mi>n</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>SC</mi> <mrow> <mi>Y</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> </mrow>

G_f,a matrix is assigned to the control surface,respectively a left elevatorThe coefficient of the induced sidestand, the coefficient of the lateral force induced by the right elevator aileron and the coefficient of the lateral force induced by the rudder,the yaw moment coefficient, the pitch moment coefficient, the roll moment coefficient and the resistance coefficient caused by the left elevator, the drag coefficient caused by the right elevator aileron,for the coefficient of resistance caused by the rudder,a lift coefficient is induced for the left elevator,for the coefficient of lift caused by the rudder,for the yaw moment coefficient caused by the right elevator aileron,for the yaw moment coefficient caused by the rudder,assigning matrix parameters, g, to the control surfaces of the pitch channels_q,e，g_q,a，g_q,rMatrix parameters are allocated to the control surfaces of the yaw channel,for the control surface of the rolling channelMatching matrix parameters;

step 1-3) designing a coordination factor;

for 1) attitude angle coupling in step 1-2),setting 0, expressed as psina-rcos α ═ 0, yields r ═ ptan α, and feeds back r ═ ptan α to the rudder loop, so the coordination factor is designed to be 0Wherein k is₁The more than 0 is the design parameter,is the first component of the rudder coordination factor;

in the step 1-2), the coupling relation of the attack angle and the roll angle is described as p-sigma r < p ≤ pcos alpha + rsin alpha < p + rhor, and the adjustment factor for feeding beta back to the rudder loop is designed as follows:

<mrow> <msub> <mi>&amp;lambda;</mi> <msub> <mi>r</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>&amp;beta;</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <mfrac> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>cos</mi> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>sin</mi> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mi>&amp;alpha;</mi> </msub> </mrow> </mfrac> </mrow>

where | sina | ≠ Δ_α，k₂，k₃A parameter greater than zero is designed for the design,is the second component of the rudder coordination factor;

for the inertial coupling of 2) in the step 1-2), feeding back beta and r to an aileron loop, feeding back beta and q to a rudder loop, and feeding back alpha and p to an elevator loop to increase damping moment and stability moment; the design of the coordination factor is as follows:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>&amp;lambda;</mi> <mi>e</mi> </msub> <mo>=</mo> <msub> <mi>k</mi> <mn>4</mn> </msub> <mi>&amp;alpha;</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>5</mn> </msub> <mi>p</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;lambda;</mi> <mi>a</mi> </msub> <mo>=</mo> <msub> <mi>k</mi> <mn>6</mn> </msub> <mi>&amp;beta;</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>7</mn> </msub> <mi>r</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;lambda;</mi> <msub> <mi>r</mi> <mn>3</mn> </msub> </msub> <mo>=</mo> <msub> <mi>k</mi> <mn>8</mn> </msub> <mi>&amp;beta;</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>9</mn> </msub> <mi>q</mi> </mtd> </mtr> </mtable> </mfenced>3

wherein λ_e，λ_a，Are respectively in corresponding statesThe variable is fed back to the coordination factor, k, of the left elevator, the right elevator aileron rudder and the rudder₄，k₅，k₆，k₇,k₈，k₉A design parameter greater than zero;

for the control surface steering coupling of 3) in the step 1-2), the steering coupling degree of the auxiliary wing rudder and the rudder is defined as:

<mrow> <mi>E</mi> <mo>=</mo> <mfrac> <msubsup> <mi>C</mi> <mi>x</mi> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </msubsup> <msubsup> <mi>C</mi> <mi>x</mi> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </msubsup> </mfrac> <mo>&amp;times;</mo> <mn>100</mn> <mi>%</mi> </mrow>

wherein,

<mrow> <msubsup> <mi>C</mi> <mi>x</mi> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </msubsup> <mo>=</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>w</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>w</mi> </mrow> </msub> </mrow> <msup> <mi>S</mi> <mn>2</mn> </msup> </mfrac> <mfrac> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mi>w</mi> <mi>r</mi> </mrow> </msub> <mi>L</mi> </mfrac> <mi>&amp;xi;</mi> <mi>cos</mi> <mi>&amp;chi;</mi> </mrow>

<mrow> <msubsup> <mi>C</mi> <mi>x</mi> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>&amp;lsqb;</mo> <mi>n</mi> <mfrac> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mi>k</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mover> <mi>D</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <msub> <mi>&amp;eta;</mi> <mi>k</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mover> <mi>D</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </mfrac> <mo>&amp;lsqb;</mo> <mover> <mi>D</mi> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mover> <mi>D</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mi>f</mi> <mo>&amp;rsqb;</mo> <mo>&amp;rsqb;</mo> </mrow>

wherein,the three-channel moment coefficient change increment coefficient caused by rudder deflection,is a three-channel moment coefficient change increment coefficient, S, caused by the deflection of the right elevon rudder_cwr,S_cwExpressed as rudder area and vertical fin area; s, L reference area and reference length; y is_cwrThe distance between the center of the rudder surface and the longitudinal axis, chi is the sweepback angle, ξ is a correction factor, and S is satisfied_cwr≤S,S_cw≤S,y_cwrL is more than or equal to L,0 is more than ξ and less than or equal to 1, cos χ is more than 0 and less than or equal to 1, n is the relative execution efficiency of the ailerons, η_k,The ratio of the heel to the tip and the ratio of the stem to the aspect ratio of the exposed wing are respectively;f, slightly comparing the exposed wing with the root; the control surface coordination strategy is designed as_a＝E_rE is more than 0 and less than or equal to 1, and E is the coupling degree of the rudder and the right auxiliary elevator wing rudder.

3. The coordinated control method for the attitude and motion of the hypersonic aircraft based on the coordination factor as claimed in claim 1, wherein the specific process of the step 2) comprises the following steps:

step 2-1) introducing uncertain parameter vectors

Representing the system model in the step 1-1) as

<mrow> <mover> <mi>&amp;Omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>+</mo> <msup> <mi>&amp;Psi;</mi> <mi>T</mi> </msup> <msub> <mi>&amp;theta;</mi> <mi>&amp;Omega;</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mi>&amp;omega;</mi> </mrow>

<mrow> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msup> <mi>&amp;Xi;</mi> <mi>T</mi> </msup> <msub> <mi>&amp;theta;</mi> <mi>&amp;omega;</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>f</mi> </msub> <msub> <mi>M</mi> <mi>c</mi> </msub> <mo>+</mo> <mi>D</mi> </mrow>

Wherein D represents an external disturbance,

<mrow> <msub> <mi>&amp;theta;</mi> <mi>&amp;Omega;</mi> </msub> <mo>=</mo> <msubsup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>&amp;theta;</mi> <mn>1</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>&amp;theta;</mi> <mn>2</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>&amp;theta;</mi> <mn>3</mn> <mi>T</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mrow> <mn>4</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>&amp;omega;</mi> </msub> <mo>=</mo> <msubsup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>&amp;theta;</mi> <mn>4</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>&amp;theta;</mi> <mn>5</mn> <mi>T</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>&amp;theta;</mi> <mn>6</mn> <mi>T</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mrow> <mn>17</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> </mrow>

θ₁＝C_L,α,θ₂＝C_Y,β,θ₃＝[C_Y,βC_L,α]^T,

<mrow> <msub> <mi>&amp;theta;</mi> <mn>4</mn> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mrow> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>Y</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> </mrow>

<mrow> <msub> <mi>&amp;theta;</mi> <mn>5</mn> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mrow> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>&amp;alpha;</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> </mrow>

<mrow> <msub> <mi>&amp;theta;</mi> <mn>6</mn> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mrow> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>&amp;beta;</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mfrac> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> </mrow>

<mrow> <mi>&amp;Psi;</mi> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;Psi;</mi> <mn>1</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>&amp;psi;</mi> <mn>2</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;Psi;</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mrow> <mn>4</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mi>&amp;Xi;</mi> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;Xi;</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>5</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>5</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>6</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;Xi;</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>6</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>6</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>6</mn> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>&amp;Xi;</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mrow> <mn>17</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mrow>

<mrow> <msub> <mi>&amp;Psi;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> </mrow> <mrow> <mi>M</mi> <mi>V</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;beta;</mi> </mrow> </mfrac> <mo>,</mo> <msub> <mi>&amp;Psi;</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>&amp;beta;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;beta;</mi> </mrow> <mrow> <mi>M</mi> <mi>V</mi> </mrow> </mfrac> <mo>,</mo> </mrow>4

<mrow> <msub> <mi>&amp;Psi;</mi> <mn>3</mn> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>&amp;beta;</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;gamma;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;mu;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;beta;</mi> </mrow> <mrow> <mi>M</mi> <mi>V</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mrow> <mo>(</mo> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;gamma;</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;mu;</mi> <mo>+</mo> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>M</mi> <mi>V</mi> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>

<mrow> <msub> <mi>&amp;Xi;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>q</mi> <mi>r</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>p</mi> </mrow> </mtd> <mtd> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>b</mi> <mi>&amp;beta;</mi> </mrow> </mtd> <mtd> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>Sb</mi> <mn>2</mn> </msup> <mi>p</mi> </mrow> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>Sb</mi> <mn>2</mn> </msup> <mi>r</mi> </mrow> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> </mrow>

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;Xi;</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mtable> <mtr> <mtd> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>q</mi> </mrow> </mtd> <mtd> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>c</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mfrac> <mrow> <msup> <mi>qSc</mi> <mn>2</mn> </msup> <mi>q</mi> </mrow> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi> </mi> <mi>sin</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;alpha;</mi> <msup> <mo>&amp;rsqb;</mo> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> </mfenced>

<mrow> <msub> <mi>&amp;Xi;</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>r</mi> </mrow> </mtd> <mtd> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>b</mi> <mi>&amp;beta;</mi> </mrow> </mtd> <mtd> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>Sb</mi> <mn>2</mn> </msup> <mi>p</mi> </mrow> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>Sb</mi> <mn>2</mn> </msup> <mi>r</mi> </mrow> <mrow> <mn>2</mn> <mi>V</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>g</mi> </mrow> </msub> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> <mi>&amp;beta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>

<mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <mi>g</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;gamma;</mi> <mi>cos</mi> <mi> </mi> <mi>u</mi> </mrow> <mrow> <mi>V</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;beta;</mi> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mi>g</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;gamma;</mi> <mi>sin</mi> <mi> </mi> <mi>u</mi> </mrow> <mi>V</mi> </mfrac> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <mrow> <mi>g</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;gamma;</mi> <mi>cos</mi> <mi> </mi> <mi>u</mi> <mi> </mi> <mi>tan</mi> <mi>&amp;beta;</mi> </mrow> <mi>V</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

wherein C is_L,α，C_Y,β，C_Y,β，C_L,α，C_n,β，C_n,p，C_n,r，C_m,α，C_m,q，C_D,α，C_l,β，C_l,r，C_l,pIs an aircraft aerodynamic parameter;

step 2-2) projection mapping algorithm

Θ_Ω,Θ_ωRespectively expressed as uncertain parameter vectors theta_Ω,θ_ωIs expressed as:

Θ_Ω＝{θ_Ω∈R⁴|θ_{Ωi min}≤θ_Ωi≤θ_{Ωi max},i＝1,…,4},

Θ_ω＝{θ_ω∈R¹⁷|θ_ωimin≤θ_ωi≤θ_ωimax,i＝1,…,17}

wherein theta is_Ωi，θ_{Ωi min}，θ_{Ωi max}Is the component of the slow loop state variable, the minimum value of the component and the maximum value of the component, theta_ωi，θ_{ωi min}，θ_{ωi max}The component of the fast loop state variable, the minimum value of the component and the maximum value of the component are obtained; order toDenoted by theta_ΩIs determined by the estimated value of (c),representing the estimation error, theta_ωLike theta_ΩAccording to the projection mapping algorithm, the self-adaptation law of uncertain parameters is

<mrow> <msub> <mover> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>&amp;Omega;</mi> </msub> <mo>=</mo> <msub> <mi>Proj</mi> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> </msub> <mrow> <mo>(</mo> <mi>&amp;Gamma;</mi> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mover> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>&amp;omega;</mi> </msub> <mo>=</mo> <msub> <mi>Proj</mi> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> </msub> <mrow> <mo>(</mo> <mi>&amp;Gamma;</mi> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> </mrow>

Wherein Fast and slow loop adaptive functions, 0 as diagonal matrix, tau as adaptive function, and projection operatorIs defined as

Whereinθ_imax，θ_iminIs the estimated value component of the state variable, the most of the state variable componentsThe large value and the minimum value of the state variable component are, obviously, for the adaptation function tau,

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <msub> <mi>P</mi> <mn>1</mn> </msub> </mtd> <mtd> <mrow> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;Subset;</mo> <mi>&amp;Theta;</mi> <mo>=</mo> <mo>{</mo> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>|</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>&amp;le;</mo> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>&amp;le;</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mrow> <mtable> <mtr> <mtd> <msub> <mi>P</mi> <mn>2</mn> </msub> </mtd> <mtd> <mrow> <msup> <mover> <mi>&amp;theta;</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;Gamma;</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>Proj</mi> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> </msub> <mo>(</mo> <mrow> <mi>&amp;Gamma;</mi> <mi>&amp;tau;</mi> </mrow> <mo>)</mo> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <mn>0</mn> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>&amp;tau;</mi> </mrow> </mtd> </mtr> </mtable> <mo>.</mo> </mrow>

whereinFor adaptive estimation, θ_min，θ_maxIn order to estimate the minimum and maximum values,in order to transpose the estimation error,^-1is the inverse of the parameter diagonal matrix, is the design parameter;

step 2-3) design of robust controller of attitude angle

Defining a tracking error e₁＝Ω-Ω_cThe sliding mode function is designed as

<mrow> <mi>&amp;sigma;</mi> <mo>=</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>K</mi> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>t</mi> </msubsup> <msub> <mi>e</mi> <mn>1</mn> </msub> <mi>d</mi> <mi>t</mi> </mrow>

Wherein K is diag { K ═ d { (K) }₁,K₂,K₃},K_i> 0, i-1, 2,3, denotesDesigning parameters, wherein sigma is a sliding mode function, and solving a first derivative of the sliding mode function to obtain

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&amp;sigma;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>Ke</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>+</mo> <msup> <mi>&amp;Psi;</mi> <mi>T</mi> </msup> <msub> <mi>&amp;theta;</mi> <mi>&amp;Omega;</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mi>&amp;omega;</mi> <mo>-</mo> <msub> <mover> <mi>&amp;Omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>Ke</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>+</mo> <msup> <mi>&amp;Psi;</mi> <mi>T</mi> </msup> <msub> <mi>&amp;theta;</mi> <mi>&amp;Omega;</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>&amp;omega;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mover> <mi>&amp;Omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>Ke</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

To obtain Is adaptive toWherein, κ₁＞0,₁∈R^4×4,λ_Ω＝diag{λ₁,λ₂,λ₃,λ₄With } > 0 as controller parameter, g_s，f₁Ψ is a system coefficient matrix Ψ^TIs a transposed matrix of Ψ, e₁In order to be an error, the error is,the slow loop tracks the derivative of the instruction,is an estimate of the state variable of the slow loop,to estimateError is counted and is a sliding mode function;

step 2-4) design of attitude angular rate controller

Definition error e₂＝ω-ω_cDerived from the error

<mrow> <msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>c</mi> </msub> <mo>=</mo> <msup> <mi>&amp;Xi;</mi> <mi>T</mi> </msup> <msub> <mi>&amp;theta;</mi> <mi>&amp;omega;</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>f</mi> </msub> <msub> <mi>M</mi> <mi>c</mi> </msub> <mo>+</mo> <mi>D</mi> <mo>-</mo> <msub> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>c</mi> </msub> </mrow>

Virtual controllerSeen as a perturbation, to obtainWhereinΞ^TThe method is characterized by comprising the following steps of (1) transposing a system matrix of a system fast loop; the attitude angular rate loop control is designed asWhereinIs a fast loop system state matrix g_fThe adverse effect of xi^TFor transposition of the system matrix, θ_ωIs a fast loop state variable, g_fIs a system state matrix, M_cTo control the torque, D is an external disturbance,derivative of the slow-loop controller, κ₂For controlling design parameters, for observingThe output of the device is used for outputting,is a transpose of the matrix of the slow loop state system,defining the observation error by observer estimation Is adaptive to law ofWherein κ₂＞0,₂∈R^17×17＞0,λ_ω∈R^17×17The parameter > 0 is the parameter of the controller,to estimate the error, the observer is designed as

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>d</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>z</mi> <mo>+</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>z</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mi>L</mi> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mi>z</mi> <mo>-</mo> <mi>L</mi> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msup> <mi>&amp;Xi;</mi> <mi>T</mi> </msup> <msub> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mi>&amp;omega;</mi> </msub> <mo>+</mo> <msub> <mi>g</mi> <mi>f</mi> </msub> <mi>M</mi> <mo>+</mo> <mi>Q</mi> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

Wherein,

q₁(e),q₂(e),...,q_n(e) are observer parameters.

4. The coordinated factor-based hypersonic aircraft attitude and motion coordination control method according to claim 1, characterized in that the specific process of the step 3) comprises the following steps:

attitude angular rate loop controller M_cAnd control plane allocation matrix g_fThe coordinated moment is denoted as M_c＝g_fTherein, wherein

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mrow> <mi>&amp;Gamma;</mi> <mi>f</mi> <mi>&amp;delta;</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow> <mi>f</mi> <mi>&amp;delta;</mi> </mrow> </msub> <mo>+</mo> <mi>&amp;Gamma;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;lambda;</mi> <mi>e</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <mi>&amp;delta;</mi> <mi>e</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <mi>&amp;delta;</mi> <mi>a</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;lambda;</mi> <mi>a</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>q</mi> <mo>,</mo> <mi>&amp;delta;</mi> <mi>r</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </msub> </mtd> <mtd> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>a</mi> </msub> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>g</mi> <mrow> <mi>r</mi> <mo>,</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;lambda;</mi> <mi>r</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>

WhereinAssigning matrix parameters, g, to the control surfaces of the pitch channels_q,e，g_q,a，g_q,rMatrix parameters are allocated to the control surfaces of the yaw channel,assigning a matrix parameter, λ, to the control surface of the roll channel_e，λ_a，λ_rIs a coordination factor; the control plane command is obtained as g_f ^-1·M_c。

5. The coordinated control method for the attitude motion of the hypersonic aerocraft based on the coordination factor as claimed in claim 4, wherein when the coordination strategy adopts the auxiliary wing rudder and the rudder to coordinate and deflect to realize the yaw moment and the roll moment, the elevator rudder deflects to realize the pitch moment, the control plane coordination design is as follows:

_coe＝_e,_coa＝E_r,_cor＝_r。