CN103425135A - Near space vehicle robust control method with input saturation - Google Patents

Abstract

The invention discloses a near space vehicle robust control method with input saturation. According to the control method, controllers are designed for a slow loop and a fast loop in a near space vehicle attitude motion system respectively; for a slow loop system, compound disturbance in a self-adaptive processing system is adopted to design the controller based on a dynamic sliding mode method, and further the problem of buffeting of the controller is solved; for a fast loop system, considering that order of magnitude of external disturbance is far higher that that of uncertain items of the system, the compound disturbance is processed by the aid of a nonlinear disturbance observer technique, the controller is designed based on a normal sliding mode method of a double-power reaching law, meanwhile a compensator is constructed by the aid of radial basis function neural networks to perform saturation compensation on the designed controller, and further the problem of limitation to saturation of a control plane of a near space vehicle is solved.

Description

A kind of have a saturated Near Space Flying Vehicles robust control method of input

Technical field

The invention belongs to the flight control technology field, specifically, is a kind of saturated Near Space Flying Vehicles robust control method of input that has.

Background technology

Near Space Flying Vehicles (Near Space Vehicle, NSV) refer to the aircraft operated near space (being often referred to apart from the spatial domain of ground 20-100 km) scope, the spatial domain be positioned under near space is the conventional lighter-than-air vehicles running space, and the spatial domain be located thereon is the spacecraft running space.In view of unique geographic position and the potential value near space zone, the research of NSV has obtained the extensive concern of countries in the world.Because the NSV flight range extensively and easily is subject to the violent outer impact of disturbing, so necessary, it is designed to the flight controller with strong robustness.Simultaneously, the impossible unlimited increase in NSV control surface deflection angle, there is saturated limited problem in rudder face.If ignore the input saturation nonlinearity in the controller design process, may cause the hydraulic performance decline of control system, even cause the unstable of system.

For nonlinear system, it is a kind of effective control method that sliding formwork is controlled (Sliding Mode Control, SMC), and it changes system state by applying discontinuous control signal, forces system to be slided along predetermined sliding mode.But in the system control procedure, controlled quentity controlled variable need on purpose constantly change in the transition mode according to the system current state, causes the system actual path to pass through back and forth in the sliding mode both sides, thereby produces the system chatter problem.Dynamic sliding mode is controlled (Dynamic Sliding Mode Control, DSMC) by designing new switching function, this switching function is relevant with single order or the higher derivative of system control inputs amount, district in single order by discontinuous term being transferred to controlled quentity controlled variable or higher derivative, through integration, obtain essential continuous sliding formwork control law in time, effectively reduce system chatter.

Consider radial base neural net (Radial Basis Function Neural Networks, RBFNNs) can approach the arbitrary continuation function with arbitrary accuracy, so adopt RBFNNs to construct a kind of compensator for the input saturation problem, utilize RBFNNs to estimate that actuator exceeds the part of saturated restriction, in design of control law, it is offset, thereby it is saturated that actuator can be exited.

Summary of the invention

The purpose of this invention is to provide a kind of aircraft that can make and have systematic uncertainty, external disturbance is inputted saturated Near Space Flying Vehicles robust control method with having of the attitude angle signal of inputting tracking appointment under saturated combined influence.

For solving the problems of the technologies described above, the present invention is a kind of has the saturated Near Space Flying Vehicles robust control method of input, according to singular perturbation principle and markers separation principle, the stance loop of aircraft is divided into to He Kuai loop, slow loop, the closed-loop control system of the method based on being comprised of slow loop control system, fast loop control system and aircraft realizes, it is characterized in that, comprise the following steps:

(1) respectively slow loop control system and fast loop control system are transformed into to the affine nonlinear system equation form;

(2) design respectively the controller in He Kuai loop, slow loop according to the affine nonlinear system equation in ,Kuai loop, slow loop; Wherein, for slow loop controller, adopt Dynamic sliding mode to design, adopt adaptive method to be processed the composite interference in slow circuit system simultaneously; For fast loop controller, adopt common sliding formwork to design, utilize Nonlinear Disturbance Observer to be approached the composite interference in fast loop, construct a kind of compensator based on radial base neural net designed controller is carried out to saturation compensation simultaneously;

(3) utilize the slow loop controller and the fast loop controller that obtain in step (2) to carry out robust control to aircraft.

Preferred version further, the present invention has the saturated Near Space Flying Vehicles robust control method of input, and the affine nonlinear equation of slow, the fast loop system of described step (1) is:

The affine nonlinear system equation in A, slow loop is:

In formula, Ω=[α, β, μ] ^TFor current attitude angle signal, α, β and μ mean respectively the angle of attack, yaw angle and roll angle, Expression is to the Ω differentiate; f _s(Ω)=[f _S1, f _S2, f _S3] ^T, ω _cControl law for slow loop controller;

$f_{s1}=\frac{1}{\mathrm{MV}\cos \mathrm{\β}}(-\stackrel{\‾}{q}{\mathrm{SC}}_{L,\mathrm{\α}}+\mathrm{Mg}\cos \mathrm{\γ}\cos \mathrm{\μ}-T_x\sin \mathrm{\α}),T_x=T\cos \left({\mathrm{\δ}}_y\right)\cos \left({\mathrm{\δ}}_z\right),$

$f_{s2}=\frac{1}{\mathrm{MV}}(\stackrel{\‾}{q}{\mathrm{SC}}_{Y,\mathrm{\β}}\mathrm{\β}+\mathrm{Mg}\cos \mathrm{\γ}\sin \mathrm{\μ}-T_x\sin \mathrm{\β}\cos \mathrm{\α}),$

$\begin{array}{c}{f}_{s3}=\frac{1}{\mathrm{MV}}\stackrel{\‾}{q}{\mathrm{SC}}_{Y,\mathrm{\β}}\mathrm{\β}\tan \mathrm{\γ}\cos \mathrm{\μ}+\frac{1}{\mathrm{MV}}\stackrel{\‾}{q}{\mathrm{SC}}_{L,\mathrm{\α}}(\tan \mathrm{\γ}\sin \mathrm{\μ}+\tan \mathrm{\β})-\frac{g}{V}\cos \mathrm{\γ}\cos \mathrm{\μ}\tan \mathrm{\β}\\ +\frac{T_x}{\mathrm{MV}}[\sin \mathrm{\α}(\tan \mathrm{\γ}\sin \mathrm{\μ}+\tan \mathrm{\β})-\cos \mathrm{\α}\tan \mathrm{\γ}\cos \mathrm{\μ}\sin \mathrm{\β}]\end{array};$

M means vehicle mass; V means aircraft flight speed;

Mean dynamic pressure; S means the wing area of reference; γ means pitch angle; T means motor power; G means acceleration of gravity; δ _yMean the deflection angle of thrust vectoring rudder face along side direction; δ _zMean thrust vectoring rudder face deflection angle longitudinally; C _{L, α}The lift coefficient that expression is caused by angle of attack α; C _{Y, β}The lateral force coefficient that expression is caused by yaw angle β;

$g_s\left(\mathrm{\Ω}\right)=\left[\begin{array}{ccc}-\tan \mathrm{\β}& 1& -\sin \mathrm{\α}\tan \mathrm{\β}\\ \sin \mathrm{\α}& 0& -\cos \mathrm{\α}\\ \cos \mathrm{\α}\sec \mathrm{\β}& 0& \sin \mathrm{\α}\sec \mathrm{\β}\end{array}\right];$

D _sMean slow loop composite interference, while setting up system equation, without providing expression, in the slow loop controller design, only need its derivative value, by adaptive approach, obtain D _sThe estimated value in the derivative upper bound;

The affine nonlinear system equation in B, fast loop is:

In formula, ω=[p, q, r] ^TFor current attitude angle rate signal, p, q and r mean respectively roll angle speed, pitch rate and yawrate, Expression is to ω differentiate, f _f(ω)=[f _F1, f _F2, f _F3] ^T,

$f_{f1}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_z+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_z+n_{\mathrm{aero}}{I}_{\mathrm{xz}}{I}_y$

$+(I_{\mathrm{xy}}^2{I}_z-I_y{I}_z^2+I_y^2{I}_z-I_{\mathrm{xz}}^2{I}_y)\mathrm{qr}+(I_y{I}_z{I}_{\mathrm{xz}}-I_{\mathrm{xz}}{I}_y^2+I_x{I}_y{I}_{\mathrm{xz}})\mathrm{pq},$

$+(I_y{I}_z{I}_{\mathrm{xy}}+I_x{I}_z{I}_{\mathrm{xy}}-I_z^2{I}_{\mathrm{xy}})\mathrm{pr}-I_{\mathrm{xy}}{I}_{\mathrm{xz}}{I}_y(q^2-p^2)-I_{\mathrm{xz}}{I}_{\mathrm{xy}}{I}_z(p^2-r^2))$

$f_{f2}=\frac{1}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}(-l_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_y{I}_z+m_{\mathrm{aero}}(I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2)$

$-I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}{n}_{\mathrm{aero}}-I_{\mathrm{xy}}(I_y{I}_z{I}_{\mathrm{xz}}+I_x{I}_y{I}_{\mathrm{xz}}-I_y^2{I}_{\mathrm{xz}})\mathrm{pq},$

$-(I_{\mathrm{xy}}+I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{qr}+(I_y{I}_{\mathrm{xy}}^2{I}_{\mathrm{xz}}+I_{\mathrm{xz}}-I_{\mathrm{xy}}^2{I}_z)(p^2-r^2)$

$+(I_z-I_x-I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{pr})$

$f_{f3}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_{\mathrm{xy}}+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}+(I_x{I}_y-I_{\mathrm{xy}}^2)n_{\mathrm{aero}}$

$+(I_y{I}_{\mathrm{xz}}^2+I_x^2{I}_y-I_x{I}_{\mathrm{xy}}^2-I_x{I}_y^2-I_y{I}_{\mathrm{xy}}^2)\mathrm{pq},$

$+(I_y^2{I}_{\mathrm{xz}}-I_y{I}_z{I}_{\mathrm{xz}}+I_{\mathrm{xy}}^2{I}_{\mathrm{xz}}-I_x{I}_y{I}_{\mathrm{xz}}+I_{\mathrm{xz}}{I}_{\mathrm{xy}}^2)\mathrm{qr}+I_{\mathrm{xy}}{I}_{\mathrm{xz}}^2(p^2-r^2)$

$+(I_z{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_x{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_y{I}_{\mathrm{xy}}{I}_{\mathrm{xz}})\mathrm{pr}+(I_x{I}_y{I}_{\mathrm{xy}}-I_{\mathrm{xy}}^3)(p^2-q^2))$

$l_{\mathrm{aero}}=\stackrel{\‾}{q}\mathrm{Sb}(C_{l,\mathrm{\β}}\mathrm{\β}+C_{l,p}\frac{\mathrm{pb}}{2V}+C_{l,r}\frac{\mathrm{rb}}{2V}),m_{\mathrm{aero}}=\stackrel{\‾}{q}\mathrm{Sc}(C_{m,\mathrm{\α}}+C_{m,q}\frac{\mathrm{qc}}{2V}),$

$n_{\mathrm{aero}}=\stackrel{\‾}{q}\mathrm{Sb}(C_{n,\mathrm{\β}}\mathrm{\β}+C_{n,p}\frac{\mathrm{pb}}{2V}+C_{n,r}\frac{\mathrm{rb}}{2V});$

I _x, I _yAnd I _zMean respectively the moment of inertia around x, y and z axes; I _Xy, I _XzAnd I _YzMean the product of inertia; B means span length; C means mean aerodynamic chord; C _{L, β}The rolling moment coefficient that expression is caused by yaw angle β; C _l,pThe rolling moment increment coefficient that expression is caused by roll angle speed p; C _l,rThe rolling moment increment coefficient that expression is caused by yawrate r; C _{M, α}The pitching moment coefficient that expression is caused by angle of attack α; C _m,qThe pitching moment increment coefficient that expression is caused by pitch rate q; C _{N, β}The yawing moment coefficient that expression is caused by yaw angle β; C _n,pThe yawing increment coefficient that expression is caused by roll angle speed p; C _n,rThe yawing increment coefficient that expression is caused by yawrate r;

g _f(ω)=g _f1g _fδ(ω)，

$g_{f1}=\left[\begin{array}{ccc}\frac{I_y{I}_z}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_z{I}_{\mathrm{xy}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_y{I}_{\mathrm{xz}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}\\ -\frac{I_{\mathrm{xy}}{I}_y{I}_z}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}& \frac{I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}& -\frac{I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}\\ \frac{I_y{I}_{\mathrm{xy}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_{\mathrm{xy}}{I}_{\mathrm{xz}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_x{I}_y-I_{\mathrm{xy}}^2}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}\end{array}\right],$

$g_{\mathrm{f\δ}}\left(\mathrm{\ω}\right)=\left[\begin{array}{ccccc}\stackrel{\‾}{q}{\mathrm{bSC}}_{l,{\mathrm{\δ}}_a}& \stackrel{\‾}{q}{\mathrm{bSC}}_{l,{\mathrm{\δ}}_e}& \stackrel{\‾}{q}{\mathrm{bSC}}_{l,{\mathrm{\δ}}_r}& 0& 0\\ \stackrel{\‾}{q}{\mathrm{ScC}}_{m,{\mathrm{\δ}}_a}& \stackrel{\‾}{q}{\mathrm{ScC}}_{m,{\mathrm{\δ}}_e}& \stackrel{\‾}{q}{\mathrm{ScC}}_{m,{\mathrm{\δ}}_r}& 0& \frac{{\mathrm{\πTX}}_T}{180}\\ \stackrel{\‾}{q}{\mathrm{SbC}}_{n,{\mathrm{\δ}}_a}& \stackrel{\‾}{q}{\mathrm{SbC}}_{n,{\mathrm{\δ}}_e}& \stackrel{\‾}{q}{\mathrm{SbC}}_{n,{\mathrm{\δ}}_r}& -\frac{{\mathrm{\πTX}}_T}{180}& 0\end{array}\right];$

Expression is by aileron rudder δ _aThe rolling moment increment coefficient caused;

Expression is by elevating rudder δ _eThe rolling moment increment coefficient caused;

Expression is by yaw rudder δ _rThe rolling moment increment coefficient caused;

Expression is by aileron rudder δ _aThe pitching moment increment coefficient caused;

Expression is by elevating rudder δ _eThe pitching moment increment coefficient caused;

Expression is by yaw rudder δ _rThe pitching moment increment coefficient caused;

Expression is by aileron rudder δ _aThe yawing increment coefficient caused;

Expression is by elevating rudder δ _eThe yawing increment coefficient caused; Expression is by yaw rudder δ _rThe yawing increment coefficient caused; X _TMean the distance of engine jet pipe apart from barycenter;

D _fFor fast loop composite interference, this composite interference utilizes Nonlinear Disturbance Observer to be approached estimation, v=[v ₁, v ₂, v ₃, v ₄, v ₅] ^TFor the control law of fast loop controller is the actuator input vector, δ (v)=[δ _a, δ _e, δ _r, δ _y, δ _z] ^TFor being subject to the output vector of actuator saturation properties influence, specifically meet following relation:

${\mathrm{\&delta;}}_a=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1>{\mathrm{\&delta;}}_{\mathrm{aM}}\\ v_1,& -{\mathrm{\&delta;}}_{\mathrm{aM}}\&le;v_1\&le;{\mathrm{\&delta;}}_{\mathrm{aM}}\\ -{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1<-{\mathrm{\&delta;}}_{\mathrm{aM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_e=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2>{\mathrm{\&delta;}}_{\mathrm{eM}}\\ v_2,& -{\mathrm{\&delta;}}_{\mathrm{eM}}\&le;v_2\&le;{\mathrm{\&delta;}}_{\mathrm{eM}}\\ -{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2<-{\mathrm{\&delta;}}_{\mathrm{eM}}\end{array}\right.,$

${\mathrm{\&delta;}}_r=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3>{\mathrm{\&delta;}}_{\mathrm{rM}}\\ v_3,& -{\mathrm{\&delta;}}_{\mathrm{rM}}\&le;v_3\&le;{\mathrm{\&delta;}}_{\mathrm{rM}}\\ -{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3<-{\mathrm{\&delta;}}_{\mathrm{rM}}\end{array}\right.,$

${\mathrm{\&delta;}}_y=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4>{\mathrm{\&delta;}}_{\mathrm{yM}}\\ v_4,& -{\mathrm{\&delta;}}_{\mathrm{yM}}\&le;v_4\&le;{\mathrm{\&delta;}}_{\mathrm{yM}}\\ -{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4<-{\mathrm{\&delta;}}_{\mathrm{yM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_z=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5>{\mathrm{\&delta;}}_{\mathrm{zM}}\\ v_5,& -{\mathrm{\&delta;}}_{\mathrm{zM}}\&le;v_5\&le;{\mathrm{\&delta;}}_{\mathrm{zM}}\\ -{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5<-{\mathrm{\&delta;}}_{\mathrm{zM}}\end{array}\right.,$

In formula, v ₁, v ₂, v ₃, v ₄And v ₅Be the element of vector v, δ _a, δ _e, δ _r, δ _yAnd δ _zMean that respectively aileron rudder kick angle, elevator angle, control surface steering angle, push vector helm are along side direction and deflection angle longitudinally; δ _AM, δ _EM, δ _RM, δ _YMAnd δ _ZMBe respectively aileron rudder corner, elevating rudder corner, yaw rudder corner, push vector helm along lateral deflection angle and the push vector helm saturated limited value of deflection angle longitudinally.

Preferred version further, the present invention has the saturated Near Space Flying Vehicles robust control method of input, and the controller model in slow, the fast loop in described step (2) is as follows:

A, utilize Dynamic sliding mode to design slow loop controller, adopt adaptive method to be processed composite interference in slow circuit system simultaneously, finally obtain the controller model in following slow loop:

${\mathrm{\&omega;}}_c=g_s{\left(\mathrm{\&Omega;}\right)}^{-1}{\&Integral;}_0^t({\mathrm{\&psi;}}_1+{\mathrm{\&psi;}}_2)\mathrm{dt}$

In formula, g _s(Ω) ^-1Expression is to matrix g _s(Ω) invert; ${\mathrm{\&psi;}}_1=-{\stackrel{\&CenterDot;}{f}}_s\left(\mathrm{\&Omega;}\right)+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}}_c-(A_{s1}+A_{s2}){\stackrel{\&CenterDot;}{e}}_s-A_{s2}{A}_{s1}{e}_s,$ E _s=Ω-Ω _cFor slow Trace-on-Diagram error, Ω _cMean predefined reference instruction signal, Expression is to f _s(Ω) differentiate,

Expression is to e _sDifferentiate,

Expression is to Ω _cAsk second derivative; ${\mathrm{\&psi;}}_2=-B_{s1}{\mathrm{\&sigma;}}_{s2}-B_{s2}\mathrm{sgm}\left({\mathrm{\&sigma;}}_{s2}\right)-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)\right\}{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}},$ ${\mathrm{\&sigma;}}_{s2}={\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{s1}+A_{s2}{\mathrm{\&sigma;}}_{s1},$

For β _DsThe estimated value vector, β _DsFor slow loop composite interference D _sThe upper dividing value of first order derivative,

A _S1, A _S2Parameter matrix for slow loop dynamic sliding-mode surface, specifically meet following relation: A _S1=diag{a _S1,1, a _S1,2, a _S1,30, A _S2=diag{a _S2,1, a _S2,2, a _S2,30; B _S1, B _S2Parameter matrix for slow loop sliding formwork Reaching Law, specifically meet following relation: B _S1=diag{b _S1,1, b _S1,2, b _S1,30, B _S2=diag{b _S2,1, b _S2,2, b _S2,30; B _S3Parameter matrix for slow loop composite interference derivative adaptive law, specifically meet following relation: B _S3=diag{b _S3,1, b _S3,2, b _S3,30;

With

Value is provided by the High-Order Sliding Mode differentiator;

B, adopt common sliding formwork to design fast loop controller, be specially:

B1, design Nonlinear Disturbance Observer are approached the composite interference in fast loop

${\hat{D}}_f=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}\left|{\widehat{\mathrm{\&beta;}}}_f\right|+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\widehat{\mathrm{\&beta;}}}_f$

In formula,

Estimated value for composite interference in fast loop; K is parameter matrix and the K=diag{k in composite interference estimated value ginseng expression formula ₁, k ₂, k ₃0; σ=η-ω, $\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)+\mathrm{\&delta;}\left(v\right)-K{\mathrm{\&sigma;}}_f;$

For β _fEstimated value, β _fFor the upper dividing value of fast loop composite interference,

Γ _βFor the parameter matrix in the adaptive law of the composite interference upper bound, fast loop and

For Γ _βTransposed matrix;

For fast loop sliding-mode surface, e _f=ω-ω _cFor fast loop tracking error, A _fFor the parameter matrix of fast loop sliding-mode surface, concrete satisfied: A _f=diag{a _{F, 1}, a _{F, 2}, a _{F, 3}0;

B2, utilize radial base neural net to estimate that actuator exceeds the part of saturated restriction

$v_{\mathrm{\&xi;}}={\hat{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)$

In formula, v _ξFor actuator exceeds the estimated value of saturated restricted part; For the weights of radial base neural net, ${\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}={\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{s}_{\mathrm{\&xi;}}\left(z\right){\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)-\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{\hat{W}}_{\mathrm{\&xi;}},$ γ and Γ _ξBe respectively real number and parameter matrix in the neural network weight adaptive law, and γ 0,

For Γ _ξTransposed matrix, Expression is to column vector σ _fCarry out transposition; s _ξ(z)=[s _{ξ 1}, s _{ξ 2}..., s _{ξ l}] ^TFor the radial basis vector, l is the total nodes of network, z=[ω _c, e _f] ^TFor network input vector, s _ξ(z) in, element adopts the gaussian basis functional form,

c _kFor the center vector of k node of network, b _kFor the sound stage width parameter of k node of network, k=1,2 ..., l;

B3, according to the estimated value of composite interference in the fast loop obtained in b1 Exceed the estimated value v of saturated restricted part with the actuator obtained in b2 _ξ, adopt common slip-form can obtain following controller model:

v=v ₀-v _ξ+v _r

In formula, v ₀Control item when not considering actuator saturation, its concrete form is

$\begin{array}{c}{v}_0=g_f{\left(\mathrm{\&omega;}\right)}^T{\left(g_f\left(\mathrm{\&omega;}\right)g_f{\left(\mathrm{\&omega;}\right)}^T\right)}^{-1}(-f_f\left(\mathrm{\&omega;}\right)+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c-A_f{e}_f-{\hat{D}}_f\\ -B_{f1}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_1}-B_{f2}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_2})\end{array};$ G _f(ω) ^TExpression is to g _f(ω) carry out transposition; B _F1, B _F2For the parameter matrix in the sliding formwork Reaching Law of fast loop, and meet following relation: B _F1=diag{b _F1,1, b _F1,2, b _F1,30, B _F2=diag{b _F2,1, b _F2,2, b _F2,30, c ₁, c ₂For meeting the real number of following relation: c ₁1,0<c ₂<1,

Expression is to ω _cDifferentiate; v _r=-K _rSgn (g _f(ω) ^Tσ _f) be the robust control item, K _rFor the parameter matrix of robust control item, specifically meet following relation: K _r=diag{k _{R, 1}, k _{R, 2}, k _{R, 3}, k _{R, 4}, k _{R, 5}0.

Preferred version further, the present invention has the saturated Near Space Flying Vehicles robust control method of input, and the slow loop controller obtained in described step (3) and fast loop controller carry out robust control to aircraft, are specially:

3-1, attitude angle current demand signal Ω is deducted to predetermined attitude angle command signal Ω _cCan obtain attitude of flight vehicle angular error signal e _s, by this error signal e _sBe sent to slow loop controller, based on Dynamic sliding mode, control and can obtain attitude angle speed command signal ω _c

3-2, attitude angle speed current demand signal ω is deducted to attitude angle speed command signal ω _cCan obtain attitude of flight vehicle angular speed error signal e _f, by error signal e _fBe sent to fast loop controller, can obtain the actuator input signal v in fast loop based on radial base neural net compensation and sliding formwork control, v is sent to the output vector δ (v) that actuator can be subject to the actuator saturation properties influence, actuator output vector δ (v) is sent to the aircraft command receiver, thereby can realizes the predetermined attitude angle Ω of aircraft _cTracking control.

The present invention compared with prior art, has following significant advantage: the present invention, according to the affected difference of composite interference in He Kuai loop, slow loop, adopts diverse ways to design the controller model in He Kuai loop, slow loop; In slow loop, adopt adaptive method to obtain the first order derivative Estimation of Upper-Bound value of composite interference, and adopt Dynamic sliding mode to carry out CONTROLLER DESIGN, in fast loop, adopt Nonlinear Disturbance Observer to be approached composite interference, construct a kind of compensator by radial base neural net simultaneously and solve the saturated limited problem of rudder face, common sliding-mode method based on two power Reaching Laws is carried out the controller design, and these two controllers combine and make aircraft in the situation that have systematic uncertainty, unknown external disturbance and input the saturated limited good control performance that has.

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail;

The accompanying drawing explanation

Fig. 1 is the control program structural drawing that the present invention has the saturated Near Space Flying Vehicles robust control method of input.

Embodiment

As shown in Figure 1, the present invention is a kind of has the saturated Near Space Flying Vehicles robust control method of input, according to singular perturbation principle and markers separation principle, the stance loop of aircraft is divided into to He Kuai loop, slow loop, the closed-loop control system of the method based on being comprised of slow loop control system, fast loop control system and aircraft realizes, it is characterized in that, comprise the following steps:

(1) respectively slow loop control system and fast loop control system are transformed into to the affine nonlinear system equation form, as follows:

The affine nonlinear system equation in A, slow loop is:

In formula, Ω=[α, β, μ] ^TFor current attitude angle signal, α, β and μ mean respectively the angle of attack, yaw angle and roll angle,

Expression is to the Ω differentiate; f _s(Ω)=[f _S1, f _S2, f _S3] ^T, ω _cControl law for slow loop controller;

$f_{s1}=\frac{1}{\mathrm{MV}\cos \mathrm{\&beta;}}(-\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{L,\mathrm{\&alpha;}}+\mathrm{Mg}\cos \mathrm{\&gamma;}\cos \mathrm{\&mu;}-T_x\sin \mathrm{\&alpha;}),T_x=T\cos \left({\mathrm{\&delta;}}_y\right)\cos \left({\mathrm{\&delta;}}_z\right),$

$f_{s2}=\frac{1}{\mathrm{MV}}(\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{Y,\mathrm{\&beta;}}\mathrm{\&beta;}+\mathrm{Mg}\cos \mathrm{\&gamma;}\sin \mathrm{\&mu;}-T_x\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}),$

$\begin{array}{c}{f}_{s3}=\frac{1}{\mathrm{MV}}\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{Y,\mathrm{\&beta;}}\mathrm{\&beta;}\tan \mathrm{\&gamma;}\cos \mathrm{\&mu;}+\frac{1}{\mathrm{MV}}\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{L,\mathrm{\&alpha;}}(\tan \mathrm{\&gamma;}\sin \mathrm{\&mu;}+\tan \mathrm{\&beta;})-\frac{g}{V}\cos \mathrm{\&gamma;}\cos \mathrm{\&mu;}\tan \mathrm{\&beta;}\\ +\frac{T_x}{\mathrm{MV}}[\sin \mathrm{\&alpha;}(\tan \mathrm{\&gamma;}\sin \mathrm{\&mu;}+\tan \mathrm{\&beta;})-\cos \mathrm{\&alpha;}\tan \mathrm{\&gamma;}\cos \mathrm{\&mu;}\sin \mathrm{\&beta;}]\end{array};$

M means vehicle mass; V means aircraft flight speed;

Mean dynamic pressure; S means the wing area of reference; γ means pitch angle; T means motor power; G means acceleration of gravity; δ _yMean the deflection angle of thrust vectoring rudder face along side direction; δ _zMean thrust vectoring rudder face deflection angle longitudinally; C _{L, α}The lift coefficient that expression is caused by angle of attack α; C _{Y, β}The lateral force coefficient that expression is caused by yaw angle β;

$g_s\left(\mathrm{\&Omega;}\right)=\left[\begin{array}{ccc}-\tan \mathrm{\&beta;}& 1& -\sin \mathrm{\&alpha;}\tan \mathrm{\&beta;}\\ \sin \mathrm{\&alpha;}& 0& -\cos \mathrm{\&alpha;}\\ \cos \mathrm{\&alpha;}\sec \mathrm{\&beta;}& 0& \sin \mathrm{\&alpha;}\sec \mathrm{\&beta;}\end{array}\right];$

D _sMean slow loop composite interference, while setting up system equation, without providing expression, in the slow loop controller design, only need its derivative value, by adaptive approach, obtain D _sThe estimated value in the derivative upper bound;

The affine nonlinear system equation in B, fast loop is:

In formula, ω=[p, q, r] ^TFor current attitude angle rate signal, p, q and r mean respectively roll angle speed, pitch rate and yawrate,

Expression is to ω differentiate, f _f(ω)=[f _F1, f _F2, f _F3] ^T,

$f_{f1}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_z+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_z+n_{\mathrm{aero}}{I}_{\mathrm{xz}}{I}_y$

$+(I_{\mathrm{xy}}^2{I}_z-I_y{I}_z^2+I_y^2{I}_z-I_{\mathrm{xz}}^2{I}_y)\mathrm{qr}+(I_y{I}_z{I}_{\mathrm{xz}}-I_{\mathrm{xz}}{I}_y^2+I_x{I}_y{I}_{\mathrm{xz}})\mathrm{pq},$

$+(I_y{I}_z{I}_{\mathrm{xy}}+I_x{I}_z{I}_{\mathrm{xy}}-I_z^2{I}_{\mathrm{xy}})\mathrm{pr}-I_{\mathrm{xy}}{I}_{\mathrm{xz}}{I}_y(q^2-p^2)-I_{\mathrm{xz}}{I}_{\mathrm{xy}}{I}_z(p^2-r^2))$

$f_{f2}=\frac{1}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}(-l_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_y{I}_z+m_{\mathrm{aero}}(I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2)$

$-I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}{n}_{\mathrm{aero}}-I_{\mathrm{xy}}(I_y{I}_z{I}_{\mathrm{xz}}+I_x{I}_y{I}_{\mathrm{xz}}-I_y^2{I}_{\mathrm{xz}})\mathrm{pq},$

$-(I_{\mathrm{xy}}+I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{qr}+(I_y{I}_{\mathrm{xy}}^2{I}_{\mathrm{xz}}+I_{\mathrm{xz}}-I_{\mathrm{xy}}^2{I}_z)(p^2-r^2)$

$+(I_z-I_x-I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{pr})$

$f_{f3}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_{\mathrm{xy}}+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}+(I_x{I}_y-I_{\mathrm{xy}}^2)n_{\mathrm{aero}}$

$+(I_y{I}_{\mathrm{xz}}^2+I_x^2{I}_y-I_x{I}_{\mathrm{xy}}^2-I_x{I}_y^2-I_y{I}_{\mathrm{xy}}^2)\mathrm{pq},$

$+(I_y^2{I}_{\mathrm{xz}}-I_y{I}_z{I}_{\mathrm{xz}}+I_{\mathrm{xy}}^2{I}_{\mathrm{xz}}-I_x{I}_y{I}_{\mathrm{xz}}+I_{\mathrm{xz}}{I}_{\mathrm{xy}}^2)\mathrm{qr}+I_{\mathrm{xy}}{I}_{\mathrm{xz}}^2(p^2-r^2)$

$+(I_z{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_x{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_y{I}_{\mathrm{xy}}{I}_{\mathrm{xz}})\mathrm{pr}+(I_x{I}_y{I}_{\mathrm{xy}}-I_{\mathrm{xy}}^3)(p^2-q^2))$

$l_{\mathrm{aero}}=\stackrel{\&OverBar;}{q}\mathrm{Sb}(C_{l,\mathrm{\&beta;}}\mathrm{\&beta;}+C_{l,p}\frac{\mathrm{pb}}{2V}+C_{l,r}\frac{\mathrm{rb}}{2V}),m_{\mathrm{aero}}=\stackrel{\&OverBar;}{q}\mathrm{Sc}(C_{m,\mathrm{\&alpha;}}+C_{m,q}\frac{\mathrm{qc}}{2V}),$

$n_{\mathrm{aero}}=\stackrel{\&OverBar;}{q}\mathrm{Sb}(C_{n,\mathrm{\&beta;}}\mathrm{\&beta;}+C_{n,p}\frac{\mathrm{pb}}{2V}+C_{n,r}\frac{\mathrm{rb}}{2V});$

I _x, I _yAnd I _zMean respectively the moment of inertia around x, y and z axes; I _Xy, I _XzAnd I _YzMean the product of inertia; B means span length; C means mean aerodynamic chord; C _{L, β}The rolling moment coefficient that expression is caused by yaw angle β; C _l,pThe rolling moment increment coefficient that expression is caused by roll angle speed p; C _l,rThe rolling moment increment coefficient that expression is caused by yawrate r; C _{M, α}The pitching moment coefficient that expression is caused by angle of attack α; C _m,qThe pitching moment increment coefficient that expression is caused by pitch rate q; C _{N, β}The yawing moment coefficient that expression is caused by yaw angle β; C _n,pThe yawing increment coefficient that expression is caused by roll angle speed p; C _n,rThe yawing increment coefficient that expression is caused by yawrate r;

g _f(ω)=g _f1g _fδ(ω)，

$g_{f1}=\left[\begin{array}{ccc}\frac{I_y{I}_z}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_z{I}_{\mathrm{xy}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_y{I}_{\mathrm{xz}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}\\ -\frac{I_{\mathrm{xy}}{I}_y{I}_z}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}& \frac{I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}& -\frac{I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}\\ \frac{I_y{I}_{\mathrm{xy}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_{\mathrm{xy}}{I}_{\mathrm{xz}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_x{I}_y-I_{\mathrm{xy}}^2}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}\end{array}\right],$

$g_{\mathrm{f\&delta;}}\left(\mathrm{\&omega;}\right)=\left[\begin{array}{ccccc}\stackrel{\&OverBar;}{q}{\mathrm{bSC}}_{l,{\mathrm{\&delta;}}_a}& \stackrel{\&OverBar;}{q}{\mathrm{bSC}}_{l,{\mathrm{\&delta;}}_e}& \stackrel{\&OverBar;}{q}{\mathrm{bSC}}_{l,{\mathrm{\&delta;}}_r}& 0& 0\\ \stackrel{\&OverBar;}{q}{\mathrm{ScC}}_{m,{\mathrm{\&delta;}}_a}& \stackrel{\&OverBar;}{q}{\mathrm{ScC}}_{m,{\mathrm{\&delta;}}_e}& \stackrel{\&OverBar;}{q}{\mathrm{ScC}}_{m,{\mathrm{\&delta;}}_r}& 0& \frac{{\mathrm{\&pi;TX}}_T}{180}\\ \stackrel{\&OverBar;}{q}{\mathrm{SbC}}_{n,{\mathrm{\&delta;}}_a}& \stackrel{\&OverBar;}{q}{\mathrm{SbC}}_{n,{\mathrm{\&delta;}}_e}& \stackrel{\&OverBar;}{q}{\mathrm{SbC}}_{n,{\mathrm{\&delta;}}_r}& -\frac{{\mathrm{\&pi;TX}}_T}{180}& 0\end{array}\right];$

Expression is by aileron rudder δ _aThe rolling moment increment coefficient caused;

Expression is by elevating rudder δ _eThe rolling moment increment coefficient caused; Expression is by yaw rudder δ _rThe rolling moment increment coefficient caused;

Expression is by aileron rudder δ _aThe pitching moment increment coefficient caused; Expression is by elevating rudder δ _eThe pitching moment increment coefficient caused;

Expression is by yaw rudder δ _rThe pitching moment increment coefficient caused; Expression is by aileron rudder δ _aThe yawing increment coefficient caused;

Expression is by elevating rudder δ _eThe yawing increment coefficient caused;

Expression is by yaw rudder δ _rThe yawing increment coefficient caused; X _TMean the distance of engine jet pipe apart from barycenter;

D _fFor fast loop composite interference, this composite interference utilizes Nonlinear Disturbance Observer to be approached estimation, v=[v ₁, v ₂, v ₃, v ₄, v ₅] ^TFor the control law of fast loop controller is the actuator input vector, δ (v)=[δ _a, δ _e, δ _r, δ _y, δ _z] ^TFor being subject to the output vector of actuator saturation properties influence, specifically meet following relation:

${\mathrm{\&delta;}}_a=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1>{\mathrm{\&delta;}}_{\mathrm{aM}}\\ v_1,& -{\mathrm{\&delta;}}_{\mathrm{aM}}\&le;v_1\&le;{\mathrm{\&delta;}}_{\mathrm{aM}}\\ -{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1<-{\mathrm{\&delta;}}_{\mathrm{aM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_e=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2>{\mathrm{\&delta;}}_{\mathrm{eM}}\\ v_2,& -{\mathrm{\&delta;}}_{\mathrm{eM}}\&le;v_2\&le;{\mathrm{\&delta;}}_{\mathrm{eM}}\\ -{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2<-{\mathrm{\&delta;}}_{\mathrm{eM}}\end{array}\right.,$

${\mathrm{\&delta;}}_r=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3>{\mathrm{\&delta;}}_{\mathrm{rM}}\\ v_3,& -{\mathrm{\&delta;}}_{\mathrm{rM}}\&le;v_3\&le;{\mathrm{\&delta;}}_{\mathrm{rM}}\\ -{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3<-{\mathrm{\&delta;}}_{\mathrm{rM}}\end{array}\right.,$

${\mathrm{\&delta;}}_y=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4>{\mathrm{\&delta;}}_{\mathrm{yM}}\\ v_4,& -{\mathrm{\&delta;}}_{\mathrm{yM}}\&le;v_4\&le;{\mathrm{\&delta;}}_{\mathrm{yM}}\\ -{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4<-{\mathrm{\&delta;}}_{\mathrm{yM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_z=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5>{\mathrm{\&delta;}}_{\mathrm{zM}}\\ v_5,& -{\mathrm{\&delta;}}_{\mathrm{zM}}\&le;v_5\&le;{\mathrm{\&delta;}}_{\mathrm{zM}}\\ -{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5<-{\mathrm{\&delta;}}_{\mathrm{zM}}\end{array}\right.,$

In formula, v ₁, v ₂, v ₃, v ₄And v ₅Be the element of vector v, δ _a, δ _e, δ _r, δ _yAnd δ _zMean that respectively aileron rudder kick angle, elevator angle, control surface steering angle, push vector helm are along side direction and deflection angle longitudinally; δ _AM, δ _EM, δ _RM, δ _YMAnd δ _ZMBe respectively aileron rudder corner, elevating rudder corner, yaw rudder corner, push vector helm along lateral deflection angle and the push vector helm saturated limited value of deflection angle longitudinally.

(2) design respectively the controller in He Kuai loop, slow loop according to the affine nonlinear system equation in ,Kuai loop, slow loop; Wherein, for slow loop controller, adopt Dynamic sliding mode to design, adopt adaptive method to be processed the composite interference in slow circuit system simultaneously; For fast loop controller, adopt common sliding formwork to design, utilize Nonlinear Disturbance Observer to be approached the composite interference in fast loop, construct a kind of compensator based on radial base neural net designed controller is carried out to saturation compensation, be specially simultaneously:

A, utilize Dynamic sliding mode to design slow loop controller, adopt adaptive method to be processed composite interference in slow circuit system simultaneously, finally obtain the controller model in following slow loop:

${\mathrm{\&omega;}}_c=g_s{\left(\mathrm{\&Omega;}\right)}^{-1}{\&Integral;}_0^t({\mathrm{\&psi;}}_1+{\mathrm{\&psi;}}_2)\mathrm{dt}$

In formula, g _s(Ω) ^-1Expression is to matrix g _s(Ω) invert; ${\mathrm{\&psi;}}_1=-{\stackrel{\&CenterDot;}{f}}_s\left(\mathrm{\&Omega;}\right)+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}}_c-(A_{s1}+A_{s2}){\stackrel{\&CenterDot;}{e}}_s-A_{s2}{A}_{s1}{e}_s,$ E _s=Ω-Ω _cFor slow Trace-on-Diagram error, Ω _cMean predefined reference instruction signal,

Expression is to f _s(Ω) differentiate,

Expression is to e _sDifferentiate,

Expression is to Ω _cAsk second derivative; ${\mathrm{\&psi;}}_2=-B_{s1}{\mathrm{\&sigma;}}_{s2}-B_{s2}\mathrm{sgm}\left({\mathrm{\&sigma;}}_{s2}\right)-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)\right\}{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}},$ ${\mathrm{\&sigma;}}_{s2}={\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{s1}+A_{s2}{\mathrm{\&sigma;}}_{s1},$

For β _DsThe estimated value vector, β _DsFor slow loop composite interference D _sThe upper dividing value of first order derivative,

A _S1, A _S2For the parameter matrix of slow loop dynamic sliding-mode surface, this parameter matrix is to be greater than 0 diagonal matrix, and each element on diagonal line all is greater than 0, specifically meets following relation: A _S1=diag{a _S1,1, a _S1,2, a _S1,30, A _S2=diag{a _S2,1, a _S2,2, a _S2,30; B _S1, B _S2Parameter matrix for slow loop sliding formwork Reaching Law, specifically meet following relation: B _S1=diag{b _S1,1, b _S1,2, b _S1,30, B _S2=diag{b _S2,1, b _S2,2, b _S2,30; B _S3Parameter matrix for slow loop composite interference derivative adaptive law, specifically meet following relation: B _S3=diag{b _S3,1, b _S3,2, b _S3,30;

With

Value is provided by the High-Order Sliding Mode differentiator;

B, adopt common sliding formwork to design fast loop controller, be specially:

B1, design Nonlinear Disturbance Observer are approached the composite interference in fast loop

${\hat{D}}_f=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}\left|{\widehat{\mathrm{\&beta;}}}_f\right|+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\widehat{\mathrm{\&beta;}}}_f$

In formula, Estimated value for composite interference in fast loop; K is parameter matrix and the K=diag{k in composite interference estimated value expression formula ₁, k ₂, k ₃0; σ=η-ω, $\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)+\mathrm{\&delta;}\left(v\right)-K{\mathrm{\&sigma;}}_f;$

For β _fEstimated value, β _fFor the upper dividing value of fast loop composite interference,

Γ _βFor the parameter matrix in the adaptive law of the composite interference upper bound, fast loop and

For Γ _βTransposed matrix;

For fast loop sliding-mode surface, e _f=ω-ω _cFor fast loop tracking error, A _fFor the parameter matrix of fast loop sliding-mode surface, concrete satisfied: A _f=diag{a _{F, 1}, a _{F, 2}, a _{F, 3}0;

B2, utilize radial base neural net to estimate that actuator exceeds the part of saturated restriction

$v_{\mathrm{\&xi;}}={\hat{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)$

In formula, v _ξFor actuator exceeds the estimated value of saturated restricted part;

For the weights of radial base neural net, ${\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}={\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{s}_{\mathrm{\&xi;}}\left(z\right){\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)-\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{\hat{W}}_{\mathrm{\&xi;}},$ γ and Γ _ξBe respectively real number and parameter matrix in the neural network weight adaptive law, and γ 0,

For Γ _ξTransposed matrix,

Expression is to column vector σ _fCarry out transposition; s _ξ(z)=[s _{ξ 1}, s _{ξ 2}..., s _{ξ l}] ^TFor the radial basis vector, l is the total nodes of network, z=[ω _c, e _f] ^TFor network input vector, s _ξ(z) in, element adopts the gaussian basis functional form,

c _kFor the center vector of k node of network, b _kFor the sound stage width parameter of k node of network, k=1,2 ..., l;

B3, according to the estimated value of composite interference in the fast loop obtained in b1

Exceed the estimated value v of saturated restricted part with the actuator obtained in b2 _ξ, adopt common slip-form can obtain following controller model:

v=v ₀-v _ξ+v _r

In formula, v ₀Control item when not considering actuator saturation, its concrete form is

$\begin{array}{c}{v}_0=g_f{\left(\mathrm{\&omega;}\right)}^T{\left(g_f\left(\mathrm{\&omega;}\right)g_f{\left(\mathrm{\&omega;}\right)}^T\right)}^{-1}(-f_f\left(\mathrm{\&omega;}\right)+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c-A_f{e}_f-{\hat{D}}_f\\ -B_{f1}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_1}-B_{f2}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_2})\end{array};$ G _f(ω) ^TExpression is to g _f(ω) carry out transposition; B _F1, B _F2For the parameter matrix in the sliding formwork Reaching Law of fast loop, and meet following relation: B _F1=diag{b _F1,1, b _F1,2, b _F1,30, B _F2=diag{b _F2,1, b _F2,2, b _F2,30, c ₁, c ₂For meeting the real number of following relation: c ₁1,0<c ₂<1,

Expression is to ω _cDifferentiate; v _r=-K _rSgn (g _f(ω) ^Tσ _f) be the robust control item, K _rFor the parameter matrix of robust control item, specifically meet following relation: K _r=diag{k _{R, 1}, k _{R, 2}, k _{R, 3}, k _{R, 4}, k _{R, 5}0;

(3) utilize the slow loop controller and the fast loop controller that obtain in step (2) to carry out robust control to aircraft, be specially:

3-1, attitude angle current demand signal Ω is deducted to predetermined attitude angle command signal Ω _cCan obtain attitude of flight vehicle angular error signal e _s, by this error signal e _sBe sent to slow loop controller, based on Dynamic sliding mode, control and can obtain attitude angle speed command signal ω _c

3-2, attitude angle speed current demand signal ω is deducted to attitude angle speed command signal ω _cCan obtain attitude of flight vehicle angular speed error signal e _f, by error signal e _fBe sent to fast loop controller, based on radial base neural net compensation and sliding formwork control, can obtain the actuator input signal v in fast loop, v is sent to the output vector that actuator can be subject to the actuator saturation properties influence

By the actuator output vector

Be sent to the aircraft command receiver, thereby can realize the predetermined attitude angle Ω of aircraft _cTracking control.

Succinct in order to narrate in the specific embodiment of the invention, be defined as follows relevant mark:

Mark: to a certain vector, || mean its each element is done to signed magnitude arithmetic(al); || ^cExpression is first done signed magnitude arithmetic(al) to its each element and is done the computing of power side again; Sgn () means its each element is done to the sign function computing; || || mean Euclid norm (if matrix means the F-norm);

Expression is done integral operation to its each element; Diag () means to form pair of horns battle array, diag{sgn () by each element of vector } mean first its each element to be done the sign function computing and then formed the pair of horns battle array.For example

χ=[χ ₁, χ ₂..., χ _n] ^T,

Expression is to each element differentiate of χ,

|χ|＝[|χ ₁|，|χ ₂|，...，|χ _n|] ^T，

|χ| ^c＝[|χ ₁| ^c，|χ ₂| ^c，...，|χ _n| ^c] ^T，

sgn(χ)＝[sgn(χ ₁)，sgn(χ ₂)，...，sgn(χ _n)] ^T，

$\stackrel{\&CenterDot;}{\mathrm{\&chi;}}={[{\stackrel{\&CenterDot;}{\mathrm{\&chi;}}}_1,{\stackrel{\&CenterDot;}{\mathrm{\&chi;}}}_2,...,{\stackrel{\&CenterDot;}{\mathrm{\&chi;}}}_n]}^T,$

$\left|\mathrm{\&chi;}\right||=\sqrt{{\mathrm{\&chi;}}_1^2+{\mathrm{\&chi;}}_2^2+\&CenterDot;\&CenterDot;\&CenterDot;+{\mathrm{\&chi;}}_n^2}\left(\right|\left|W\right||=\sqrt{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ij}}^2},W\&Element;R^{n\&times;m}),$

${\&Integral;}_0^t\mathrm{\&chi;dt}={[{\&Integral;}_0^t{\mathrm{\&chi;}}_1\mathrm{dt},{\&Integral;}_0^t{\mathrm{\&chi;}}_2\mathrm{dt},...,{\&Integral;}_0^t{\mathrm{\&chi;}}_n\mathrm{dt}]}^T,$

Dynamic sliding mode is controlled

For making design process there is good legibility, at first briefly introduce Dynamic sliding mode and control relevant knowledge.Without loss of generality, consider as next class MIMO nonlinear affine system:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=f\left(x\right)+g\left(x\right)u\\ y=h\left(x\right)\end{array}\right.---\left(1\right)$

Wherein, x ∈ R ⁿFor the system state vector, y ∈ R ^mFor the system output vector, u ∈ R ^mFor system control inputs vector, f (x) ∈ R ⁿ, g (x) ∈ R ^{N * m}And h (x) ∈ R ^mIn each component smooth function that is relevant x.If sliding-mode surface σ=[σ ₁(x), σ ₂(x) ..., σ _m(x)] ^T∈ R ^mSmoothly switch functional vector for system (1).Before analyzing Dynamic sliding mode control, need as given a definition and supposing:

Definition 1: smooth scalar function σ _i(x) to the gradient of state vector x

For

${\&dtri;\mathrm{\&sigma;}}_i\left(x\right)=\frac{{\&PartialD;\mathrm{\&sigma;}}_i\left(x\right)}{\&PartialD;x}=[\frac{{\&PartialD;\mathrm{\&sigma;}}_i\left(x\right)}{{\&PartialD;x}_1},\frac{{\&PartialD;\mathrm{\&sigma;}}_i\left(x\right)}{{\&PartialD;x}_2},...,\frac{{\&PartialD;\mathrm{\&sigma;}}_i\left(x\right)}{{\&PartialD;x}_n}]---\left(2\right)$

Definition 2: smooth scalar function σ _i(x) to the Lie derivative L of smooth vector field f (x) _fσ _i(x) be

$L_f{\mathrm{\&sigma;}}_i\left(x\right)={\&dtri;\mathrm{\&sigma;}}_i\left(x\right)f\left(x\right)---\left(3\right)$

Multiple Lie derivative is by following recurrence relation definition

$L_f^0{\mathrm{\&sigma;}}_i\left(x\right)={\mathrm{\&sigma;}}_i\left(x\right),k_f^{k_i}{\mathrm{\&sigma;}}_i\left(x\right)=L_f{L}_f^{k_i-1}{\mathrm{\&sigma;}}_i\left(x\right)=\&dtri;\left(L_f^{k_i-1}{\mathrm{\&sigma;}}_i\left(x\right)\right)f\left(x\right),k_i=\mathrm{1,2,3},...---\left(4\right)$

Definition 3: if smooth scalar function σ _i(x) Lie derivative of smooth vector field f (x) met to following two formulas:

$L_f^{k_i}{\mathrm{\&sigma;}}_i\left(x\right)=0,k_i=\mathrm{0,1},...,r_i-1---\left(5\right)$

$L_f^{r_i}{\mathrm{\&sigma;}}_i\left(x\right)\&NotEqual;0---\left(6\right)$

Claim σ _i(x) to the relative rank of f (x), be r _i.Simultaneously, claim σ=[σ ₁(x), σ ₂(x) ..., σ _m(x)] ^TRelative rank to f (x) are r, wherein r=max{r ₁, r ₂..., r _m.

Suppose 1: to MIMO nonlinear system (1), after system enters σ=0 sliding-mode surface, mode of motion can guarantee that x converges to initial point.

Suppose 2: to MIMO nonlinear system (1), sliding-mode surface σ has relative rank vector [r to input u ₁, r ₂..., r _m], to all x in domain, have following equation to set up:

$\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_{g_j}{L}_f^{k_i}{\mathrm{\&sigma;}}_i\left(x\right)=0,k_i=\mathrm{0,1},...,r_i-1---\left(7\right)$

$\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_{g_j}{L}_f^{r_i-1}{\mathrm{\&sigma;}}_i\left(x\right)\&NotEqual;0---\left(8\right)$

Wherein, g _jFor the j column vector of matrix g (x), i=1,2 ..., m.

Suppose 3: to MIMO nonlinear system (1), following matrix is all reversible to all x in domain.

To sliding-mode surface, each component differentiate can be taken off equation:

${\mathrm{\&sigma;}}_i^{\left(k_i\right)}=L_f^{k_i}{\mathrm{\&sigma;}}_i\left(x\right),k_i=\mathrm{0,1},...,r_i-1---\left(10\right)$

${\mathrm{\&sigma;}}_i^{\left(r_i\right)}=L_f^{r_i}{\mathrm{\&sigma;}}_i\left(x\right)+\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_{g_j}{L}_f^{r_i-1}{\mathrm{\&sigma;}}_i\left(x\right)u_j---\left(11\right)$

$\begin{array}{c}{\mathrm{\&sigma;}}_i^{(r_i+1)}=L_f^{r_i+1}{\mathrm{\&sigma;}}_i\left(x\right)+\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_{g_j}{L}_f^{r_i}{\mathrm{\&sigma;}}_i\left(x\right)u_j+\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_f{L}_{g_j}{L}_f^{r_i-1}{\mathrm{\&sigma;}}_i\left(x\right)u_j\\ +\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_{g_l}\left(\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_{g_j}{L}_f^{r_i-1}{\mathrm{\&sigma;}}_i\left(x\right)u_j\right)u_l+\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{L}_{g_j}{L}_f^{r_i-1}{\mathrm{\&sigma;}}_i\left(x\right){\stackrel{\&CenterDot;}{u}}_j\end{array}---\left(12\right)$

Wherein, i=1,2 ..., m.

Get new sliding-mode surface:

${\mathrm{\&theta;}}_i={\mathrm{\&sigma;}}_i^{\left(r_i\right)}+c_{i,1}{\mathrm{\&sigma;}}_i^{(r_i-1)}+c_{i,2}{\mathrm{\&sigma;}}_i^{(r_i-2)}+\&CenterDot;\&CenterDot;\&CenterDot;+c_{i,r_i-1}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_i+c_{i,r_i}{\mathrm{\&sigma;}}_i+c_{i,r_i+1}---\left(13\right)$

Wherein, parameter c to be designed _i,j(i=1,2 ..., m, j=1,2 ..., r _i+ 1) should make polynomial expression (13) Hurwitz stable.

To formula (13), differentiate can obtain:

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i={\mathrm{\&sigma;}}_i^{(r_i+1)}+c_{i,1}{\mathrm{\&sigma;}}_i^{\left(r_i\right)}+c_{i,2}{\mathrm{\&sigma;}}_i^{(r_i-1)}+\&CenterDot;\&CenterDot;\&CenterDot;+c_{i,r_i-1}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&sigma;}}}_i+c_{i,r_i}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_i\\ ={\mathrm{\&sigma;}}_i^{(r_i+1)}+\underset{j=1}{\overset{r_i}{\mathrm{\&Sigma;}}}{c}_{i,j}{\mathrm{\&sigma;}}_i^{(r_i+1-j)}\end{array}---\left(14\right)$

Can obtain following vector relations formula according to formula (12), (14):

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=A(x,u)+B\left(x\right)\stackrel{\&CenterDot;}{u}+C(x,u)\\ A(x,u)=A_1\left(x\right)+A_2\left(x\right)u+A_3\left(x\right)u+A_4\left(x\right)u\end{array}\right.---\left(15\right)$

Wherein, $\stackrel{\&CenterDot;}{\mathrm{\&theta;}}={[{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1,{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2,...,{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_m]}^T,$

$A_1\left(x\right)={[L_f^{r_1+1}{\mathrm{\&sigma;}}_1\left(x\right),L_f^{r_2+1}{\mathrm{\&sigma;}}_2\left(x\right),...,L_f^{r_m+1}{\mathrm{\&sigma;}}_m\left(x\right)]}^T\&Element;R^m---\left(16\right)$

$C(x,u)={[\underset{j=1}{\overset{r_1}{\mathrm{\&Sigma;}}}{c}_{1,j}{\mathrm{\&sigma;}}_1^{(r_1+1-j)},\underset{j=1}{\overset{r_2}{\mathrm{\&Sigma;}}}{c}_{2,j}{\mathrm{\&sigma;}}_2^{(r_2+1-j)},...,\underset{j=1}{\overset{r_m}{\mathrm{\&Sigma;}}}{c}_{m,j}{\mathrm{\&sigma;}}_m^{(r_m+1-j)}]}^T\&Element;R^m---\left(21\right)$

For guaranteeing the establishment of sliding formwork arrival condition, sliding formwork Reaching Law Φ _θDesirable suitable form, as exponential approach is restrained:

${\mathrm{\&Phi;}}_{\mathrm{\&theta;}}=-{\stackrel{\&OverBar;}{C}}_1\mathrm{\&theta;}-{\stackrel{\&OverBar;}{C}}_2\mathrm{sgn}\left(\mathrm{\&theta;}\right)---\left(22\right)$

Wherein,

For the parameter matrix in the sliding formwork Reaching Law, and meet following relation:

${\stackrel{\&OverBar;}{C}}_1=\mathrm{diag}\{{\stackrel{\&OverBar;}{c}}_{\mathrm{1,1}},{\stackrel{\&OverBar;}{c}}_{\mathrm{1,2}},...,{\stackrel{\&OverBar;}{c}}_{1,m}\}>0,$ ${\stackrel{\&OverBar;}{C}}_2=\mathrm{diag}\{{\stackrel{\&OverBar;}{c}}_{\mathrm{2,1}},{\stackrel{\&OverBar;}{c}}_{\mathrm{2,2}},...,{\stackrel{\&OverBar;}{c}}_{2,m}\}>0.$

Can obtain the Dynamic sliding mode controller by formula (15), (22) is:

$\stackrel{\&CenterDot;}{u}=B^{-1}\left(x\right)({\mathrm{\&Phi;}}_{\mathrm{\&theta;}}-A(x,u)-C(x,u))---\left(23\right)$

To formula (23) integration, can obtain:

$u\left(t\right)=u\left(0\right)+{\&Integral;}_0^t\left(B^{-1}\left(x\right)({\mathrm{\&Phi;}}_{\mathrm{\&theta;}}-A(x,u)-C(x,u))\right)\mathrm{dt}---\left(24\right)$

Visible, Dynamic sliding mode is controlled and is passed through Reaching Law Φ _θIn discontinuous term put in integration, obtain the stepless control item on whole time domain, thereby effectively reduce the buffeting of controller.

1, NSV slow loop controller design

Before being carried out to the controller design, the NSV attitude system needs following hypothesis:

Suppose 4: to NSV attitude motion system, composite interference D in slow loop _s=[D _{S, 1}, D _{S, 2}, D _{S, 3}] ^TAnd first order derivative

Bounded, | D _s,i|≤β _s,i, β _s,i0, β _s=[β _{S, 1}, β _{S, 2}, β _{S, 3}] ^T,

β _{Ds, i}0, β _Ds=[β _{Ds, 1}, β _{Ds, 2}, β _{Ds, 3}] ^TComposite interference D in fast loop _f=[D _{F, 1}, D _{F, 2}, D _{F, 3}] ^TBounded, | D _f,i|≤β _f,i, β _f,i0, β _f=[β _{F, 1}, β _{F, 2}, β _{F, 3}] ^T, i=1,2,3.

Suppose 5: to NSV attitude motion system, expectation attitude angle vector Ω _cKnown continuous and its second derivative existence.

Suppose 6: to NSV attitude motion system, ride gain matrix g _s(Ω) and g _f(ω) generalized inverse exists.

In the slow circuit system of NSV, the uncertainty of a taking into account system, the composite interference in slow loop only is comprised of the indeterminate of system, based on Dynamic sliding mode, controls the corresponding controller of design.

Theorem 1: for the slow circuit system of NSV, the sliding-mode surface of design formula (25), (26), employing formula (27) exponential approach restrains to guarantee the establishment of sliding formwork arrival condition, composite interference D _sThe adaptive law of first order derivative Estimation of Upper-Bound value is taken as formula (28), and slow loop dynamic sliding mode controller design is formula (29), and slow Trace-on-Diagram error asymptotic convergence is in initial point.

${\mathrm{\&sigma;}}_{s1}=e_s+{\&Integral;}_0^t{A}_{s1}{e}_s\mathrm{dt}---\left(25\right)$

${\mathrm{\&sigma;}}_{s2}={\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{s1}+A_{s2}{\mathrm{\&sigma;}}_{s1}---\left(26\right)$

${\mathrm{\&Phi;}}_{{\mathrm{\&sigma;}}_{s2}}=-B_{s1}{\mathrm{\&sigma;}}_{s2}-B_{s2}\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)---\left(27\right)$

${\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_{\mathrm{ds}}=B_{s3}\left|{\mathrm{\&sigma;}}_{s2}\right|---\left(28\right)$

$\left\{\begin{array}{c}{\mathrm{\&omega;}}_c=g_s{\left(\mathrm{\&Omega;}\right)}^{-1}{\&Integral;}_0^t({\mathrm{\&psi;}}_1+{\mathrm{\&psi;}}_2)\mathrm{dt}\\ {\mathrm{\&psi;}}_1=-{\stackrel{\&CenterDot;}{f}}_s\left(\mathrm{\&Omega;}\right)+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}}_c-(A_{s1}+A_{s2}){\stackrel{\&CenterDot;}{e}}_s-A_{s2}{A}_{s1}{e}_s\\ {\mathrm{\&psi;}}_2=-B_{s1}{\mathrm{\&sigma;}}_{s2}-B_{s2}\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)\right\}{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\end{array}\right.---\left(29\right)$

Wherein, e _s=Ω-Ω _cFor slow Trace-on-Diagram error; g _s(Ω) ^-1Expression is to matrix g _s(Ω) invert; A _S1, A _S2Parameter matrix for slow loop dynamic sliding-mode surface, specifically meet following relation: A _S1=diag{a _S1,1, a _S1,2, a _S1,30, A _S2=diag{a _S2,1, a _S2,2, a _S2,30; B _S1, B _S2Parameter matrix for slow loop sliding formwork Reaching Law, specifically meet following relation: B _S1=diag{b _S1,1, b _S1,2, b _S1,30, B _S2=diag{b _S2,1, b _S2,2, b _S2,30; B _S3Parameter matrix for slow loop composite interference derivative adaptive law, specifically meet following relation: B _S3=diag{b _S3,1, b _S3,2, b _S3,30; For β _DsThe estimated value vector, β _DsFor slow loop composite interference D _sThe upper dividing value of first order derivative.

Proof: select the Lyapunov function to be

$V_s=\frac{1}{2}{\mathrm{\&sigma;}}_{s2}^T{\mathrm{\&sigma;}}_{s2}+\frac{1}{2}{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}^T{B}_{s3}^{-1}{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}---\left(30\right)$

Wherein, ${\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}={\mathrm{\&beta;}}_{\mathrm{ds}}-{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}},$ And have ${\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&beta;}}}}_{\mathrm{ds}}={\stackrel{\&CenterDot;}{\mathrm{\&beta;}}}_{\mathrm{ds}}-{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_{\mathrm{ds}}=-{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_{\mathrm{ds}}.$

Consider formula (25), (29), to formula (26), differentiate can obtain

${\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{s2}={\stackrel{\&CenterDot;}{f}}_s\left(\mathrm{\&Omega;}\right)+{\mathrm{\&psi;}}_1+{\mathrm{\&psi;}}_2+{\stackrel{\&CenterDot;}{D}}_s-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}}_c+A_{s1}{\stackrel{\&CenterDot;}{e}}_s+A_{s2}{\stackrel{\&CenterDot;}{e}}_s+A_{s2}{A}_{s1}{e}_s$

$\left(31\right)$

$={\stackrel{\&CenterDot;}{D}}_s-B_{s1}{\mathrm{\&sigma;}}_{s2}-B_{s2}\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)\right\}{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}$

According to formula (28), (31), to formula (30), differentiate can obtain

${\stackrel{\&CenterDot;}{V}}_s={\mathrm{\&sigma;}}_{s2}^T{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{s2}-{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}^T{B}_{s3}^{-1}{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_{\mathrm{ds}}$

$={\mathrm{\&sigma;}}_{s2}^T({\stackrel{\&CenterDot;}{D}}_s-B_{s1}{\mathrm{\&sigma;}}_{s2}-B_{s2}\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)-\mathrm{diag}\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)\left\}{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\right)-{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}^T\left|{\mathrm{\&sigma;}}_{s2}\right|$

$\&le;-{{\mathrm{\&sigma;}}_{s2}}^T{B}_{s1}{\mathrm{\&sigma;}}_{s2}-{{\mathrm{\&sigma;}}_{s2}}^T{B}_{s2}\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)+{\left|{\mathrm{\&sigma;}}_{s2}\right|}^T{\mathrm{\&beta;}}_{\mathrm{ds}}-{\left|{\mathrm{\&sigma;}}_{s2}\right|}^T{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}-{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}^T\left|{\mathrm{\&sigma;}}_{s2}\right|$

$\left(32\right)$

$=-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{s1,i}{\mathrm{\&sigma;}}_{s2,i}^2-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{s2,i}\left|{\mathrm{\&sigma;}}_{s2,i}\right|$

Wherein, σ _S2=[σ _S2,1, σ _S2,2, σ _S2,3] ^T.

Visible, if σ _S2≠ 0, So sliding-mode surface σ _S2Meet the arrival condition, σ _S2Asymptotic convergence is in initial point.Work as σ _S2After converging on initial point, from formula (25) and (26), sliding-mode surface σ _S1Converge on initial point, final tracking error e _sConverge on initial point, i.e. card.

Annotate 1: the ω in formula (29) _cFor the control vector in the slow loop of NSV, be also the expectation input vector in the fast loop of NSV simultaneously.

Annotating needed differential term in the 2:NSV slow loop controller is obtained by High-Order Sliding Mode differentiator (Higher-Order Sliding Mode Differentiator, HOSMD).N rank HOSMD is shown below

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{z}}_0={\mathrm{\&zeta;}}_0=-{\mathrm{\&lambda;}}_0{|z_0-\stackrel{\&OverBar;}{f}\left(t\right)|}^{n/(n+1)}\mathrm{sgn}(z_0-\stackrel{\&OverBar;}{f}\left(t\right))+z_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\stackrel{\&CenterDot;}{z}}_i={\mathrm{\&zeta;}}_i=-{\mathrm{\&lambda;}}_i{|z_i-{\mathrm{\&zeta;}}_{i-1}|}^{(n-i)/(n-i+1)}\mathrm{sgn}(z_i-{\mathrm{\&zeta;}}_{i-1})+z_{i+1}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\stackrel{\&CenterDot;}{z}}_{n-1}={\mathrm{\&zeta;}}_{n-1}=-{\mathrm{\&lambda;}}_{n-1}{|z_{n-1}-{\mathrm{\&zeta;}}_{n-2}|}^{(1/2)}\mathrm{sgn}(z_{n-1}-{\mathrm{\&zeta;}}_{n-2})+z_n\\ {\stackrel{\&CenterDot;}{z}}_n=-{\mathrm{\&lambda;}}_n\mathrm{sgn}(z_n-{\mathrm{\&zeta;}}_{n-1})\end{array}\right.---\left(33\right)$

Wherein, z _iAnd ζ _iFor the internal state of system (33), λ ₀, λ ₁..., λ _nFor differentiator parameter to be designed.The purpose of HOSMD is to make ζ _iWith arbitrary accuracy, approach

I+1 rank differential estimated value.

Annotate 3: in order to obtain the derivative of reference instruction signal, can allow it by following second order instruction references model

$G\left(s\right)=\frac{{\mathrm{\&omega;}}_n^2}{s^2+2{\mathrm{\&xi;}}_n{\mathrm{\&omega;}}_{n}s+{\mathrm{\&omega;}}_n^2}---\left(34\right)$

Wherein, ω _nAnd ξ _nBe parameter to be designed, concrete meaning refers to respectively free-running frequency and damping ratio, and s is the variable in the corresponding complex field of Laplace transform.

2, the fast loop of NSV controller design

Due to the slow loop of NSV composite interference D _sOnly be subject to the impact of model uncertainty, thus its upper bound of adaptive method On-line Estimation adopted in slow loop, thus designed controller.But in fast loop, composite interference D _fAlso be subject to the impact of external disturbance, and the order of magnitude of external disturbance is much larger than the order of magnitude of model indeterminate.If the composite interference in fast loop still adopts adaptive method to process, because the designed Interference Cancellation item gone out can not accurately be offset the composite interference suffered with bucking-out system, make the system motion track repeatedly pass through equilibrium point, cause the control system hydraulic performance decline, therefore adopt Nonlinear Disturbance Observer to be approached composite interference in fast loop, thereby design corresponding Interference Cancellation item.But, if the controller design of fast loop still adopts the Dynamic sliding mode method, the derivative that in control item, will contain interference observer output, the stability proof of closed-loop system and the boundedness proof of evaluated error derivative are different from conventional method, make the whole design proposal complexity of controlling, so the controller design of fast loop adopts common sliding formwork to control, utilize two power Reaching Laws to reduce controller and buffet.

In fast loop, because there is saturated limited situation in rudder face, consider that RBFNNs can approach the arbitrary continuation function with arbitrary accuracy, adopts RBFNNs to carry out saturation compensation to controller here.Concrete, utilize RBFNNs to estimate that actuator exceeds the part of saturated restriction, in design of control law, it is offset, thereby it is saturated that actuator is exited.

According to the saturation function characteristic, know

δ(v)=sat(v)=v+ξ(v) (35)

Wherein, ξ (v) part saturated for actuator exceeds.

Utilize RBFNNs to be approached ξ (v), specific as follows:

$\mathrm{\&xi;}\left(v\right)=W_{\mathrm{\&xi;}}^{*T}{s}_{\mathrm{\&xi;}}\left(z\right)+{\mathrm{\&epsiv;}}_{\mathrm{\&xi;}}---\left(36\right)$

Wherein,

For optimum weight matrix and satisfied

L is the total nodes of network; Z=[ω _c, e _f] ^TFor the network input vector; ε _ξ=[ε _{ξ, 1}, ε _{ξ, 2}, ε _{ξ, 3}, ε _{ξ, 4}, ε _{ξ, 5}] ^TFor its approximation accuracy, by adjusting RBFNNs nodes and weights, ε _ξCan be arbitrarily small, suppose here | ε _{ξ, i}|≤ε _{M ξ, i}, ε _{M ξ, i}0; s _ξ(z)=[s _{ξ 1}, s _{ξ 2}..., s _{ξ l}] ^TFor radial basis vector, wherein s _{ξ k}For the gaussian basis function:

$s_{\mathrm{\&xi;k}}=\exp (-\frac{{\left|\right|z-c_k\left|\right|}^2}{2b_k^2})---\left(37\right)$

Wherein, c _kFor the center vector of k node of network, b _kFor the sound stage width parameter of k node of network, k=1,2 ..., l.

Design control law

v=v ₀-v _ξ+v _r (38)

Wherein, v ₀Control item when not considering actuator saturation,

For the actual output of RBFNNs, v _rFor the robust item.

Formula (36), (38) substitution formula (35) can be obtained

$\mathrm{\&delta;}\left(v\right)=v_0-v_{\mathrm{\&xi;}}+v_r+W_{\mathrm{\&xi;}}^{*T}{s}_{\mathrm{\&xi;}}\left(z\right)+{\mathrm{\&epsiv;}}_{\mathrm{\&xi;}}$

$=v_0-{\hat{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)+W_{\mathrm{\&xi;}}^{*T}{s}_{\mathrm{\&xi;}}\left(z\right)+v_r+{\mathrm{\&epsiv;}}_{\mathrm{\&xi;}}---\left(39\right)$

$=v_0+{\tilde{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)+v_r+{\mathrm{\&epsiv;}}_{\mathrm{\&xi;}}$

Wherein, ${\tilde{W}}_{\mathrm{\&xi;}}=W_{\mathrm{\&zeta;}}^{*}-{\tilde{W}}_{\mathrm{\&xi;}}.$

For realizing that effectively the approaching of unknown composite interference in fast loop introduced to following auxiliary variable

σ=η-ω (40)

$\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)-{\mathrm{K\&sigma;}}_f---\left(41\right)$

Wherein, K is parameter matrix and the K=diag{k in the composite interference estimated value ginseng expression formula of fast loop ₁, k ₂, k ₃0,

For β _f=[β _{F, 1}, β _{F, 2}, β _{F, 3}] ^TEstimated value, σ=[σ ₁, σ ₂, σ ₃] ^TFor auxiliary variable, σ _f=[σ _F1, σ _F2, σ _F3] ^TFor the designed sliding-mode surface in fast loop, hereinafter provide expression.

Fast loop composite interference D _fThe observability estimate value as follows:

${\hat{D}}_f=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}\left|{\widehat{\mathrm{\&beta;}}}_f\right|+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\widehat{\mathrm{\&beta;}}}_f---\left(42\right)$

Consider formula (41), to formula (40), differentiate can obtain

$\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f-{\mathrm{K\&sigma;}}_f-D_f---\left(43\right)$

Define fast loop composite interference D _fApproximate error be

${\tilde{D}}_f=D_f-{\hat{D}}_f---\left(44\right)$

Formula (42), (43) substitution formula (44) can be obtained

${\tilde{D}}_f=\mathrm{K\&sigma;}+\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+D_f-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}\left|{\widehat{\mathrm{\&beta;}}}_f\right|-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\widehat{\mathrm{\&beta;}}}_f$

$=-\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}-{\mathrm{K\&sigma;}}_f-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}\left|{\widehat{\mathrm{\&beta;}}}_f\right|-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\widehat{\mathrm{\&beta;}}}_f---\left(45\right)$

Theorem 2: for the fast loop of NSV system, the sliding-mode surface of design formula (46), the two power Reaching Laws of employing formula (47) are set up to guarantee sliding formwork arrival condition, interference observer is by formula (42) design, and parameter update law is taken as formula (48), utilize RBFNNs to compensate the saturation nonlinearity of actuator, wherein the weight matrix adaptive law is suc as formula shown in (49), a fast loop controller design accepted way of doing sth (50), fast loop tracking error asymptotic convergence is in initial point, and the interference observer approximate error also finally converges on initial point.

${\mathrm{\&sigma;}}_f=e_f+{\&Integral;}_0^t{A}_f{e}_f\mathrm{dt}---\left(46\right)$

${\mathrm{\&Phi;}}_{{\mathrm{\&sigma;}}_f}=-B_{f1}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_1}-B_{f2}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_2}---\left(47\right)$

${\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_f={\mathrm{\&Gamma;}}_{\mathrm{\&beta;}}\left(\right|\mathrm{\&sigma;}|+|{\mathrm{\&sigma;}}_f\left|\right)---\left(48\right)$

${\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}={\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{s}_{\mathrm{\&xi;}}\left(z\right){\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)-\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{\hat{W}}_{\mathrm{\&xi;}}---\left(49\right)$

$\left\{\begin{array}{c}v=v_0-v_{\mathrm{\&xi;}}+v_r\\ v_0=g_f{\left(\mathrm{\&omega;}\right)}^T{\left(g_f\left(\mathrm{\&omega;}\right)g_f{\left(\mathrm{\&omega;}\right)}^T\right)}^{-1}(-f_f\left(\mathrm{\&omega;}\right)+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c-A_f{e}_f-{\hat{D}}_f-B_{f1}\mathrm{diag}\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_1}\\ -B_{f2}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_2})\\ v_{\mathrm{\&xi;}}={\hat{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)\\ v_r=-K_r\mathrm{sgn}\left(g_f{\left(\mathrm{\&omega;}\right)}^T{\mathrm{\&sigma;}}_f\right)\end{array}\right.---\left(50\right)$

Wherein, e _f=ω-ω _cFor fast loop tracking error; g _f(ω) ^TExpression is to g _f(ω) carry out transposition; A _fFor the parameter matrix of fast loop sliding-mode surface, and meet following relation: A _f=diag{a _{F, 1}, a _{F, 2}, a _{F, 3}0; B _F1, B _F2For the parameter matrix in the sliding formwork Reaching Law of fast loop, and meet following relation: B _F1=diag{b _F1,1, b _F1,2, b _F1,30, B _F2=diag{b _F2,1, b _F2,2, b _F2,30, c ₁, c ₂For meeting the real number of following relation: c ₁1,0<c ₂<1; Γ _βFor the parameter matrix in the adaptive law of the composite interference upper bound, fast loop and satisfied

For Γ _βTransposed matrix; γ and Γ _ξBe respectively real number and parameter matrix in the network weight adaptive law, and meet γ 0,

For Γ _ξTransposed matrix; K _rFor the parameter matrix of robust control item, specifically meet following relation: K _r=diag{k _{R, 1}, k _{R, 2}, k _{R, 3}, k _{R, 4}, k _{R, 5}0.

Proof: select the Lyapunov function to be

$V_f=\frac{1}{2}{\mathrm{\&sigma;}}_f^T{\mathrm{\&sigma;}}_f+\frac{1}{2}{\mathrm{\&sigma;}}^T\mathrm{\&sigma;}+\frac{1}{2}{\widetilde{\mathrm{\&beta;}}}_f^T{\mathrm{\&Gamma;}}_{\mathrm{\&beta;}}^{-1}{\widetilde{\mathrm{\&beta;}}}_f+\frac{1}{2}\mathrm{tr}\left({\tilde{W}}_{\mathrm{\&xi;}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}^{-1}{\tilde{W}}_{\mathrm{\&xi;}}\right)---\left(51\right)$

Wherein, ${\widetilde{\mathrm{\&beta;}}}_f={\mathrm{\&beta;}}_f-{\widehat{\mathrm{\&beta;}}}_f,$ And have $\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&beta;}}}={\stackrel{\&CenterDot;}{\mathrm{\&beta;}}}_f-{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_f=-{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_f,$ ${\tilde{W}}_{\mathrm{\&xi;}}=W_{\mathrm{\&xi;}}^{*}-{\hat{W}}_{\mathrm{\&xi;}},$ And have ${\stackrel{\&CenterDot;}{\tilde{W}}}_{\mathrm{\&xi;}}={\stackrel{\&CenterDot;}{W}}_{\mathrm{\&xi;}}^{*}-{\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}=-{\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}.$

To formula (46), differentiate can obtain

${\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_f=f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+D_f-{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c+A_f{e}_f---\left(52\right)$

According to formula (39), (44), (50) and (52), can obtain

${\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_f=f_f\left(\mathrm{\&omega;}\right)+D_f-{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c+A_f{e}_f+g_f\left(\mathrm{\&omega;}\right)(v_0+{\tilde{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)+v_r+{\mathrm{\&epsiv;}}_{\mathrm{\&xi;}})$

$={\tilde{D}}_f-B_{f1}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_1}-B_{f2}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c2})---\left(53\right)$

$+g_f\left(\mathrm{\&omega;}\right){\tilde{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)-g_f\left(\mathrm{\&omega;}\right)K_r\mathrm{sgn}\left(g_f{\left(\mathrm{\&omega;}\right)}^T{\mathrm{\&sigma;}}_f\right)+g_f\left(\mathrm{\&omega;}\right){\mathrm{\&epsiv;}}_{\mathrm{\&xi;}}$

Consider formula (43), (53), to formula (51), differentiate can obtain

${\stackrel{\&CenterDot;}{V}}_f={\mathrm{\&sigma;}}_f^T{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_f+{\mathrm{\&sigma;}}^T\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}-{\widetilde{\mathrm{\&beta;}}}_f^T{\mathrm{\&Gamma;}}_{\mathrm{\&beta;}}^{-1}{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_f-\mathrm{tr}\left({\tilde{W}}_{\mathrm{\&xi;}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}^{-1}{\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}\right)$

$={\mathrm{\&sigma;}}_f^T{\tilde{D}}_f-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f1,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_1}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f2,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_2}$

$\left(54\right)$

$+{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right){\tilde{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)-{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)K_r\mathrm{sgn}\left(g_f{\left(\mathrm{\&omega;}\right)}^T{\mathrm{\&sigma;}}_f\right)+{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right){\mathrm{\&epsiv;}}_{\mathrm{\&xi;}}$

$-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_i{\mathrm{\&sigma;}}_i^2-{\left|\mathrm{\&sigma;}\right|}^T{\widehat{\mathrm{\&beta;}}}_f-{\mathrm{\&sigma;}}^T{\mathrm{K\&sigma;}}_f-{\mathrm{\&sigma;}}^T{D}_f-{\widetilde{\mathrm{\&beta;}}}_f^T{\mathrm{\&Gamma;}}_{\mathrm{\&beta;}}^{-1}{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_f-\mathrm{tr}\left({\tilde{W}}_{\mathrm{\&xi;}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}^{-1}{\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}\right)$

Consider that formula (45) can obtain

${\mathrm{\&sigma;}}_f^T{\tilde{D}}_f={\mathrm{\&sigma;}}_f^T\mathrm{K\&sigma;}+{\mathrm{\&sigma;}}_f^T\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+{\mathrm{\&sigma;}}_f^T{D}_f-{\left|{\mathrm{\&sigma;}}_f\right|}^T\left|{\widehat{\mathrm{\&beta;}}}_f\right|-{\left|{\mathrm{\&sigma;}}_f\right|}^T{\widehat{\mathrm{\&beta;}}}_f$

$\&le;{\mathrm{\&sigma;}}_f^T\mathrm{K\&sigma;}+{\left|{\mathrm{\&sigma;}}_f\right|}^T\left|{\widehat{\mathrm{\&beta;}}}_f\right|+{\left|{\mathrm{\&sigma;}}_f\right|}^T{\mathrm{\&beta;}}_f-{\left|{\mathrm{\&sigma;}}_f\right|}^T\left|{\widehat{\mathrm{\&beta;}}}_f\right|-{\left|{\mathrm{\&sigma;}}_f\right|}^T{\widehat{\mathrm{\&beta;}}}_f---\left(55\right)$

$={\mathrm{\&sigma;}}_f^T\mathrm{K\&sigma;}+{\left|{\mathrm{\&sigma;}}_f\right|}^T{\widetilde{\mathrm{\&beta;}}}_f$

Formula (55) substitution formula (54) can be obtained

${\stackrel{\&CenterDot;}{V}}_f\&le;-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f1,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_1}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f2,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_2}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_i{\mathrm{\&sigma;}}_i^2$

$-{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)K_r\mathrm{sgn}\left(g_f{\left(\mathrm{\&omega;}\right)}^T{\mathrm{\&sigma;}}_f\right)+{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right){\mathrm{\&epsiv;}}_{\mathrm{\&xi;}}+{\left|{\mathrm{\&sigma;}}_f\right|}^T{\widetilde{\mathrm{\&beta;}}}_f-{\left|\mathrm{\&sigma;}\right|}^T{\widehat{\mathrm{\&beta;}}}_f$

$+{\left|\mathrm{\&sigma;}\right|}^T{\mathrm{\&beta;}}_f+{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right){\tilde{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)-{\widetilde{\mathrm{\&beta;}}}_f^T{\mathrm{\&Gamma;}}_{\mathrm{\&beta;}}^{-1}{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_f-\mathrm{tr}\left({\tilde{W}}_{\mathrm{\&xi;}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}^{-1}{\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}\right)$

$\&le;-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f1,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_1}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f2,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_2}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_i{\mathrm{\&sigma;}}_i^2$

$-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}(k_{r,i}-{\mathrm{\&epsiv;}}_{\mathrm{M\&xi;},i})\left|{\mathrm{\&sigma;}}_f^T{g}_{f,i}\right|+{\left|{\mathrm{\&sigma;}}_f\right|}^T{\widetilde{\mathrm{\&beta;}}}_f+{\left|\mathrm{\&sigma;}\right|}^T{\widetilde{\mathrm{\&beta;}}}_f$

$-{\widetilde{\mathrm{\&beta;}}}_f^T{\mathrm{\&Gamma;}}_{\mathrm{\&beta;}}^{-1}{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_f-\mathrm{tr}({\tilde{W}}_{\mathrm{\&xi;}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}^{-1}{\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}-{\tilde{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right){\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right))---\left(56\right)$

Wherein, g _f,iRepresenting matrix g _f(ω) i column vector.

Parameter update law formula (48), (49) substitution formula (56) can be obtained

${\stackrel{\&CenterDot;}{V}}_f\&le;-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f1,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_1}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f2,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_2}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_i{\mathrm{\&sigma;}}_i^2$

$\left(57\right)$

$-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}(k_{r,i}-{\mathrm{\&epsiv;}}_{\mathrm{M\&xi;},i})\left|{\mathrm{\&sigma;}}_f^T{g}_{f,i}\right|+\mathrm{tr}\left(\mathrm{\&gamma;}\right|\left|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\right|\left|{\tilde{W}}_{\mathrm{\&xi;}}^T{\hat{W}}_{\mathrm{\&xi;}}\right)$

Note as lower inequality:

$\mathrm{tr}\left({\tilde{W}}_{\mathrm{\&xi;}}^T(W_{\mathrm{\&xi;}}^{*}-{\tilde{W}}_{\mathrm{\&xi;}})\right)\&le;\left|\right|{\tilde{W}}_{\mathrm{\&xi;}}\left|\right|\left|\right|W_{\mathrm{\&xi;}}^{*}\left|\right|-{\left|\right|{\tilde{W}}_{\mathrm{\&xi;}}\left|\right|}^2---\left(58\right)$

So have:

$\mathrm{tr}\left(\mathrm{\&gamma;}\right|\left|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\right|\left|{\tilde{W}}_{\mathrm{\&xi;}}^T{\hat{W}}_{\mathrm{\&xi;}}\right)=\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|\mathrm{tr}\left({\tilde{W}}_{\mathrm{\&xi;}}^T(W_{\mathrm{\&xi;}}^{*}-{\tilde{W}}_{\mathrm{\&xi;}})\right)$

$\&le;\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|\left(\right|\left|{\tilde{W}}_{\mathrm{\&xi;}}\right||W_M-{\left|\right|{\tilde{W}}_{\mathrm{\&xi;}}\left|\right|}^2)---\left(59\right)$

$=\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|(-{\left(\right|\left|{\tilde{W}}_{\mathrm{\&xi;}}\right||-\frac{1}{2}{W}_M)}^2+\frac{1}{4}{W}_M^2)$

Formula (59) substitution formula (57) can be obtained

${\stackrel{\&CenterDot;}{V}}_f\&le;-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f1,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_1}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f2,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_2}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_i{\mathrm{\&sigma;}}_i^2$

$-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}(k_{r,i}-{\mathrm{\&epsiv;}}_{\mathrm{M\&xi;},i})\left|{\mathrm{\&sigma;}}_f^T{g}_{f,i}\right|+\frac{1}{4}{W}_M^2\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|$

$-\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|{\left(\right|\left|{\tilde{W}}_{\mathrm{\&xi;}}\right||-\frac{1}{2}{W}_M)}^2---\left(60\right)$

$\&le;-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f1,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_1}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{f2,i}{\left|{\mathrm{\&sigma;}}_{f,i}\right|}^{1+c_2}-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_i{\mathrm{\&sigma;}}_i^2$

$-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}(k_{r,i}-{\mathrm{\&epsiv;}}_{\mathrm{M\&xi;},i}-\frac{1}{4}{W}_M^2\mathrm{\&gamma;}|)\left|{\mathrm{\&sigma;}}_f^T{g}_{f,i}\right|-\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|{\left(\right|\left|{\tilde{W}}_{\mathrm{\&xi;}}\right||-\frac{1}{2}{W}_M)}^2$

If

So σ is arranged _f, the σ asymptotic convergence is in initial point, according to the known tracking error e of formula (46) _fConverge on initial point, according to the known interference observer approximate error of formula (45) Converge on initial point, i.e. card.

Annotate 4: for two power Reaching Laws, when system state away from sliding mode (| σ _f,i| 1) time, in formula (47), first plays a leading role, and now two power Reaching Law speed is higher than general Reaching Law; When system state approach sliding mode (| σ _f,i|<1) time, (47) second of formulas play a leading role, and now two power Reaching Law speed is lower than general Reaching Law, and two combinations have realized and the smooth transition of sliding mode, have weakened the buffeting of controller.

The present invention has carried out respectively the controller design to the He Kuai loop, slow loop in Near Space Flying Vehicles attitude motion system.For slow circuit system, adopt the composite interference in the adaptive method disposal system, carry out the controller design based on the Dynamic sliding mode method, and then solve the buffeting problem of controller; For fast loop system, consider that the order of magnitude of external disturbance is far longer than the order of magnitude of system indeterminate, utilize the Nonlinear Disturbance Observer technology to be processed composite interference, common sliding-mode method based on two power Reaching Laws is carried out the controller design, utilize radial base neural net to construct a kind of compensator simultaneously designed controller is carried out to saturation compensation, and then solve the saturated limited problem of vehicle rudder.

Claims (4)

1. one kind has the saturated Near Space Flying Vehicles robust control method of input, according to singular perturbation principle and markers separation principle, the stance loop of aircraft is decomposed into to He Kuai loop, slow loop, the closed-loop control system of the method based on being comprised of slow loop control system, fast loop control system and aircraft realizes, it is characterized in that, comprise the following steps:

(1) respectively slow loop control system and fast loop control system are transformed into to the affine nonlinear system equation form;

(2) design respectively the controller in He Kuai loop, slow loop according to the affine nonlinear system equation in ,Kuai loop, slow loop; Wherein, for slow loop controller, adopt Dynamic sliding mode to design, utilize adaptive method to be processed the composite interference in slow circuit system simultaneously; For fast loop controller, adopt common sliding formwork to design, utilize Nonlinear Disturbance Observer to be approached the composite interference in fast loop, construct a kind of compensator based on radial base neural net designed controller is carried out to saturation compensation simultaneously;

(3) utilize the slow loop controller and the fast loop controller that obtain in step (2) to carry out robust control to aircraft.

2. according to claim 1 have a saturated Near Space Flying Vehicles robust control method of input, it is characterized in that, the affine nonlinear equation of slow, the fast loop system of described step (1) is:

The affine nonlinear system equation in A, slow loop is:

In formula, Ω=[α, β, μ] ^TFor current attitude angle signal, α, β and μ mean respectively the angle of attack, yaw angle and roll angle,

Expression is to the Ω differentiate; f _s(Ω)=[f _S1, f _S2, f _S3] ^T, ω _cControl law for slow loop controller; D _sMean slow loop composite interference;

$f_{s1}=\frac{1}{\mathrm{MV}\cos \mathrm{\&beta;}}(-\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{L,\mathrm{\&alpha;}}+\mathrm{Mg}\cos \mathrm{\&gamma;}\cos \mathrm{\&mu;}-T_x\sin \mathrm{\&alpha;}),T_x=T\cos \left({\mathrm{\&delta;}}_y\right)\cos \left({\mathrm{\&delta;}}_z\right),$

$f_{s2}=\frac{1}{\mathrm{MV}}(\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{Y,\mathrm{\&beta;}}\mathrm{\&beta;}+\mathrm{Mg}\cos \mathrm{\&gamma;}\sin \mathrm{\&mu;}-T_x\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}),$

$\begin{array}{c}{f}_{s3}=\frac{1}{\mathrm{MV}}\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{Y,\mathrm{\&beta;}}\mathrm{\&beta;}\tan \mathrm{\&gamma;}\cos \mathrm{\&mu;}+\frac{1}{\mathrm{MV}}\stackrel{\&OverBar;}{q}{\mathrm{SC}}_{L,\mathrm{\&alpha;}}(\tan \mathrm{\&gamma;}\sin \mathrm{\&mu;}+\tan \mathrm{\&beta;})-\frac{g}{V}\cos \mathrm{\&gamma;}\cos \mathrm{\&mu;}\tan \mathrm{\&beta;}\\ +\frac{T_x}{\mathrm{MV}}[\sin \mathrm{\&alpha;}(\tan \mathrm{\&gamma;}\sin \mathrm{\&mu;}+\tan \mathrm{\&beta;})-\cos \mathrm{\&alpha;}\tan \mathrm{\&gamma;}\cos \mathrm{\&mu;}\sin \mathrm{\&beta;}]\end{array};$

M means vehicle mass; V means aircraft flight speed;

Mean dynamic pressure; S means the wing area of reference; γ means pitch angle; T means motor power; G means acceleration of gravity; δ _yMean the deflection angle of thrust vectoring rudder face along side direction; δ _zMean thrust vectoring rudder face deflection angle longitudinally; C _{L, α}The lift coefficient that expression is caused by angle of attack α; C _{Y, β}The lateral force coefficient that expression is caused by yaw angle β;

$g_s\left(\mathrm{\&Omega;}\right)=\left[\begin{array}{ccc}-\tan \mathrm{\&beta;}& 1& -\sin \mathrm{\&alpha;}\tan \mathrm{\&beta;}\\ \sin \mathrm{\&alpha;}& 0& -\cos \mathrm{\&alpha;}\\ \cos \mathrm{\&alpha;}\sec \mathrm{\&beta;}& 0& \sin \mathrm{\&alpha;}\sec \mathrm{\&beta;}\end{array}\right];$

The affine nonlinear system equation in B, fast loop is:

In formula, ω=[p, q, r] ^TFor current attitude angle rate signal, p, q and r mean respectively roll angle speed, pitch rate and yawrate,

Expression is to ω differentiate, f _f(ω)=[f _F1, f _F2, f _F3] ^T,

$f_{f1}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_z+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_z+n_{\mathrm{aero}}{I}_{\mathrm{xz}}{I}_y$

$+(I_{\mathrm{xy}}^2{I}_z-I_y{I}_z^2+I_y^2{I}_z-I_{\mathrm{xz}}^2{I}_y)\mathrm{qr}+(I_y{I}_z{I}_{\mathrm{xz}}-I_{\mathrm{xz}}{I}_y^2+I_x{I}_y{I}_{\mathrm{xz}})\mathrm{pq},$

$+(I_y{I}_z{I}_{\mathrm{xy}}+I_x{I}_z{I}_{\mathrm{xy}}-I_z^2{I}_{\mathrm{xy}})\mathrm{pr}-I_{\mathrm{xy}}{I}_{\mathrm{xz}}{I}_y(q^2-p^2)-I_{\mathrm{xz}}{I}_{\mathrm{xy}}{I}_z(p^2-r^2))$

$f_{f2}=\frac{1}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}(-l_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_y{I}_z+m_{\mathrm{aero}}(I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2)$

$-I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}{n}_{\mathrm{aero}}-I_{\mathrm{xy}}(I_y{I}_z{I}_{\mathrm{xz}}+I_x{I}_y{I}_{\mathrm{xz}}-I_y^2{I}_{\mathrm{xz}})\mathrm{pq},$

$-(I_{\mathrm{xy}}+I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{qr}+(I_y{I}_{\mathrm{xy}}^2{I}_{\mathrm{xz}}+I_{\mathrm{xz}}-I_{\mathrm{xy}}^2{I}_z)(p^2-r^2)$

$+(I_z-I_x-I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{pr})$

$f_{f3}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_{\mathrm{xy}}+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}+(I_x{I}_y-I_{\mathrm{xy}}^2)n_{\mathrm{aero}}$

$+(I_y{I}_{\mathrm{xz}}^2+I_x^2{I}_y-I_x{I}_{\mathrm{xy}}^2-I_x{I}_y^2-I_y{I}_{\mathrm{xy}}^2)\mathrm{pq},$

$+(I_y^2{I}_{\mathrm{xz}}-I_y{I}_z{I}_{\mathrm{xz}}+I_{\mathrm{xy}}^2{I}_{\mathrm{xz}}-I_x{I}_y{I}_{\mathrm{xz}}+I_{\mathrm{xz}}{I}_{\mathrm{xy}}^2)\mathrm{qr}+I_{\mathrm{xy}}{I}_{\mathrm{xz}}^2(p^2-r^2)$

$+(I_z{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_x{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_y{I}_{\mathrm{xy}}{I}_{\mathrm{xz}})\mathrm{pr}+(I_x{I}_y{I}_{\mathrm{xy}}-I_{\mathrm{xy}}^3)(p^2-q^2))$

$l_{\mathrm{aero}}=\stackrel{\&OverBar;}{q}\mathrm{Sb}(C_{l,\mathrm{\&beta;}}\mathrm{\&beta;}+C_{l,p}\frac{\mathrm{pb}}{2V}+C_{l,r}\frac{\mathrm{rb}}{2V}),m_{\mathrm{aero}}=\stackrel{\&OverBar;}{q}\mathrm{Sc}(C_{m,\mathrm{\&alpha;}}+C_{m,q}\frac{\mathrm{qc}}{2V}),$

$n_{\mathrm{aero}}=\stackrel{\&OverBar;}{q}\mathrm{Sb}(C_{n,\mathrm{\&beta;}}\mathrm{\&beta;}+C_{n,p}\frac{\mathrm{pb}}{2V}+C_{n,r}\frac{\mathrm{rb}}{2V});$

I _x, I _yAnd I _zMean respectively the moment of inertia around x, y and z axes; I _Xy, I _XzAnd I _YzMean the product of inertia; B means span length; C means mean aerodynamic chord; C _{L, β}The rolling moment coefficient that expression is caused by yaw angle β, C _l,pThe rolling moment increment coefficient that expression is caused by roll angle speed p; C _l,rThe rolling moment increment coefficient that expression is caused by yawrate r; C _{M, α}The pitching moment coefficient that expression is caused by angle of attack α; C _m,qThe pitching moment increment coefficient that expression is caused by pitch rate q; C _{N, β}The yawing moment coefficient that expression is caused by yaw angle β; C _n,pThe yawing increment coefficient that expression is caused by roll angle speed p; C _n,rThe yawing increment coefficient that expression is caused by yawrate r;

g _f(ω)=g _f1g _fδ(ω)，

$g_{f1}=\left[\begin{array}{ccc}\frac{I_y{I}_z}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_z{I}_{\mathrm{xy}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_y{I}_{\mathrm{xz}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}\\ -\frac{I_{\mathrm{xy}}{I}_y{I}_z}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}& \frac{I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}& -\frac{I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}\\ \frac{I_y{I}_{\mathrm{xy}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_{\mathrm{xy}}{I}_{\mathrm{xz}}}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}& \frac{I_x{I}_y-I_{\mathrm{xy}}^2}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}\end{array}\right],$

$g_{\mathrm{f\&delta;}}\left(\mathrm{\&omega;}\right)=\left[\begin{array}{ccccc}\stackrel{\&OverBar;}{q}{\mathrm{bSC}}_{l,{\mathrm{\&delta;}}_a}& \stackrel{\&OverBar;}{q}{\mathrm{bSC}}_{l,{\mathrm{\&delta;}}_e}& \stackrel{\&OverBar;}{q}{\mathrm{bSC}}_{l,{\mathrm{\&delta;}}_r}& 0& 0\\ \stackrel{\&OverBar;}{q}{\mathrm{ScC}}_{m,{\mathrm{\&delta;}}_a}& \stackrel{\&OverBar;}{q}{\mathrm{ScC}}_{m,{\mathrm{\&delta;}}_e}& \stackrel{\&OverBar;}{q}{\mathrm{ScC}}_{m,{\mathrm{\&delta;}}_r}& 0& \frac{{\mathrm{\&pi;TX}}_T}{180}\\ \stackrel{\&OverBar;}{q}{\mathrm{SbC}}_{n,{\mathrm{\&delta;}}_a}& \stackrel{\&OverBar;}{q}{\mathrm{SbC}}_{n,{\mathrm{\&delta;}}_e}& \stackrel{\&OverBar;}{q}{\mathrm{SbC}}_{n,{\mathrm{\&delta;}}_r}& -\frac{{\mathrm{\&pi;TX}}_T}{180}& 0\end{array}\right];$

Expression is by aileron rudder δ _aThe rolling moment increment coefficient caused;

Expression is by elevating rudder δ _eThe rolling moment increment coefficient caused;

Expression is by yaw rudder δ _rThe rolling moment increment coefficient caused;

Expression is by aileron rudder δ _aThe pitching moment increment coefficient caused;

Expression is by elevating rudder δ _eThe pitching moment increment coefficient caused;

Expression is by yaw rudder δ _rThe pitching moment increment coefficient caused;

Expression is by aileron rudder δ _aThe yawing increment coefficient caused;

Expression is by elevating rudder δ _eThe yawing increment coefficient caused;

Expression is by yaw rudder δ _rThe yawing increment coefficient caused; X _TMean the distance of engine jet pipe apart from barycenter;

D _fFor fast loop composite interference, this composite interference utilizes Nonlinear Disturbance Observer to be approached estimation, v=[v ₁, v ₂, v ₃, v ₄, v ₅] ^TFor the control law of fast loop controller is the actuator input vector, δ (v)=[δ _a, δ _e, δ _r, δ _y, δ _z] ^TFor being subject to the output vector of actuator saturation properties influence, specifically meet following relation:

${\mathrm{\&delta;}}_a=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1>{\mathrm{\&delta;}}_{\mathrm{aM}}\\ v_1,& -{\mathrm{\&delta;}}_{\mathrm{aM}}\&le;v_1\&le;{\mathrm{\&delta;}}_{\mathrm{aM}}\\ -{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1<-{\mathrm{\&delta;}}_{\mathrm{aM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_e=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2>{\mathrm{\&delta;}}_{\mathrm{eM}}\\ v_2,& -{\mathrm{\&delta;}}_{\mathrm{eM}}\&le;v_2\&le;{\mathrm{\&delta;}}_{\mathrm{eM}}\\ -{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2<-{\mathrm{\&delta;}}_{\mathrm{eM}}\end{array}\right.,$

${\mathrm{\&delta;}}_r=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3>{\mathrm{\&delta;}}_{\mathrm{rM}}\\ v_3,& -{\mathrm{\&delta;}}_{\mathrm{rM}}\&le;v_3\&le;{\mathrm{\&delta;}}_{\mathrm{rM}}\\ -{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3<-{\mathrm{\&delta;}}_{\mathrm{rM}}\end{array}\right.,$

${\mathrm{\&delta;}}_y=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4>{\mathrm{\&delta;}}_{\mathrm{yM}}\\ v_4,& -{\mathrm{\&delta;}}_{\mathrm{yM}}\&le;v_4\&le;{\mathrm{\&delta;}}_{\mathrm{yM}}\\ -{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4<-{\mathrm{\&delta;}}_{\mathrm{yM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_z=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5>{\mathrm{\&delta;}}_{\mathrm{zM}}\\ v_5,& -{\mathrm{\&delta;}}_{\mathrm{zM}}\&le;v_5\&le;{\mathrm{\&delta;}}_{\mathrm{zM}}\\ -{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5<-{\mathrm{\&delta;}}_{\mathrm{zM}}\end{array}\right.,$

In formula, v ₁, v ₂, v ₃, v ₄And v ₅Be the element of vector v, δ _a, δ _e, δ _r, δ _yAnd δ _zMean that respectively aileron rudder kick angle, elevator angle, control surface steering angle, push vector helm are along side direction and deflection angle longitudinally; δ _AM, δ _EM, δ _RM, δ _YMAnd δ _ZMBe respectively aileron rudder corner, elevating rudder corner, yaw rudder corner, push vector helm along lateral deflection angle and the push vector helm saturated limited value of deflection angle longitudinally.

3. according to claim 2 have a saturated Near Space Flying Vehicles robust control method of input, it is characterized in that, the controller model in slow, the fast loop in described step (2) is as follows:

A, utilize Dynamic sliding mode to design slow loop controller, adopt adaptive method to be processed composite interference in slow circuit system simultaneously, finally obtain the controller model in following slow loop:

${\mathrm{\&omega;}}_c=g_s{\left(\mathrm{\&Omega;}\right)}^{-1}{\&Integral;}_0^t({\mathrm{\&psi;}}_1+{\mathrm{\&psi;}}_2)\mathrm{dt}$

In formula, g _s(Ω) ^-1Expression is to matrix g _s(Ω) invert; ${\mathrm{\&psi;}}_1=-{\stackrel{\&CenterDot;}{f}}_s\left(\mathrm{\&Omega;}\right)+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}}_c-(A_{s1}+A_{s2}){\stackrel{\&CenterDot;}{e}}_s-A_{s2}{A}_{s1}{e}_s,$ E _s=Ω-Ω _cFor slow Trace-on-Diagram error, Ω _cMean predefined reference instruction signal,

Expression is to f _s(Ω) differentiate,

Expression is to e _sDifferentiate,

Expression is to Ω _cAsk second derivative; ${\mathrm{\&psi;}}_2=-B_{s1}{\mathrm{\&sigma;}}_{s2}-B_{s2}\mathrm{sgm}\left({\mathrm{\&sigma;}}_{s2}\right)-\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_{s2}\right)\right\}{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}},$ ${\mathrm{\&sigma;}}_{s2}={\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{s1}+A_{s2}{\mathrm{\&sigma;}}_{s1},$

For β _DsThe estimated value vector, β _DsFor slow loop composite interference D _sThe upper dividing value of first order derivative,

A _S1, A _S2Parameter matrix for slow loop dynamic sliding-mode surface, specifically meet following relation: A _S1=diag{a _S1,1, a _S1,2, a _S1,30, A _S2=diag{a _S2,1, a _S2,2, a _S2,30; B _S1, B _S2Parameter matrix for slow loop sliding formwork Reaching Law, specifically meet following relation: B _S1=diag{b _S1,1, b _S1,2, b _S1,30, B _S2=diag{b _S2,1, b _S2,2, b _S2,30; B _S3Parameter matrix for slow loop composite interference derivative adaptive law, specifically meet following relation: B _S3=diag{b _S3,1, b _S3,2, b _S3,30;

With Value is provided by the High-Order Sliding Mode differentiator;

B, adopt common sliding formwork to design fast loop controller, be specially:

B1, design Nonlinear Disturbance Observer are approached the composite interference in fast loop

${\hat{D}}_f=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}\left|{\widehat{\mathrm{\&beta;}}}_f\right|+\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\widehat{\mathrm{\&beta;}}}_f$

In formula,

Estimated value for composite interference in fast loop; K is parameter matrix and the K=diag{k in composite interference estimated value expression formula ₁, k ₂, k ₃0; σ=η-ω,

Expression is to the η differentiate; $\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=-\mathrm{K\&sigma;}-\mathrm{diag}\left\{\mathrm{sgn}\left(\mathrm{\&sigma;}\right)\right\}{\widehat{\mathrm{\&beta;}}}_f+f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)+\mathrm{\&delta;}\left(v\right)-K{\mathrm{\&sigma;}}_f;$

For β _fEstimated value, β _fFor the upper dividing value of fast loop composite interference,

Γ _βFor the parameter matrix in the adaptive law of the composite interference upper bound, fast loop and

For Γ _βTransposed matrix;

For fast loop sliding-mode surface, e _f=ω-ω _cFor fast loop tracking error, A _fFor the parameter matrix of fast loop sliding-mode surface, concrete satisfied: A _f=diag{a _{F, 1}, a _{F, 2}, a _{F, 3}0;

B2, utilize radial base neural net to estimate that actuator exceeds the part of saturated restriction

$v_{\mathrm{\&xi;}}={\hat{W}}_{\mathrm{\&xi;}}^T{s}_{\mathrm{\&xi;}}\left(z\right)$

In formula, v _ξFor actuator exceeds the estimated value of saturated restricted part;

For the weights of radial base neural net, ${\stackrel{\&CenterDot;}{\hat{W}}}_{\mathrm{\&xi;}}={\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{s}_{\mathrm{\&xi;}}\left(z\right){\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)-\mathrm{\&gamma;}\left|\right|{\mathrm{\&sigma;}}_f^T{g}_f\left(\mathrm{\&omega;}\right)\left|\right|{\mathrm{\&Gamma;}}_{\mathrm{\&xi;}}{\hat{W}}_{\mathrm{\&xi;}},$ γ and Γ _ξBe respectively real number and parameter matrix in the neural network weight adaptive law, and γ 0,

For Γ _ξTransposed matrix, Expression is to column vector σ _fCarry out transposition; s _ξ(z)=[s _{ξ 1}, s _{ξ 2}..., s _{ξ l}] ^TFor the radial basis vector, l is the total nodes of network, z=[ω _c, e _f] ^TFor network input vector, s _ξ(z) in, element adopts the gaussian basis functional form,

c _kFor the center vector of k node of network, b _kFor the sound stage width parameter of k node of network, k=1,2 ..., l;

B3, according to the estimated value of composite interference in the fast loop obtained in b1

Exceed the estimated value v of saturated restricted part with the actuator obtained in b2 _ξ, adopt common slip-form can obtain following controller model:

v=v ₀-v _ξ+v _r

In formula, v ₀Control item when not considering actuator saturation, its concrete form is

$\begin{array}{c}{v}_0=g_f{\left(\mathrm{\&omega;}\right)}^T{\left(g_f\left(\mathrm{\&omega;}\right)g_f{\left(\mathrm{\&omega;}\right)}^T\right)}^{-1}(-f_f\left(\mathrm{\&omega;}\right)+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c-A_f{e}_f-{\hat{D}}_f\\ -B_{f1}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_1}-B_{f2}\mathrm{diag}\left\{\mathrm{sgn}\left({\mathrm{\&sigma;}}_f\right)\right\}{\left|{\mathrm{\&sigma;}}_f\right|}^{c_2})\end{array};$ G _f(ω) ^TExpression is to g _f(ω) carry out transposition; B _F1, B _F2For the parameter matrix in the sliding formwork Reaching Law of fast loop, and meet following relation: B _F1=diag{b _F1,1, b _F1,2, b _F1,30, B _F2=diag{b _F2,1, b _F2,2, b _F2,30, c ₁, c ₂For meeting the real number of following relation: c ₁1,0<c ₂<1,

Expression is to ω _cDifferentiate; v _r=-K _rSgn (g _f(ω) ^Tσ _f) be the robust control item, K _rFor the parameter matrix of robust control item, specifically meet following relation: K _r=diag{k _{R, 1}, k _{R, 2}, k _{R, 3}, k _{R, 4}, k _{R, 5}0.

4. according to claim 3 have a saturated Near Space Flying Vehicles robust control method of input, it is characterized in that, the slow loop controller obtained in described step (3) and fast loop controller carry out robust control to aircraft, are specially:

3-1, attitude angle current demand signal Ω is deducted to predetermined attitude angle command signal Ω _cCan obtain attitude of flight vehicle angular error signal e _s, by this error signal e _sBe sent to slow loop controller, based on Dynamic sliding mode, control and can obtain attitude angle speed command signal ω _c

3-2, attitude angle speed current demand signal ω is deducted to attitude angle speed command signal ω _cCan obtain attitude of flight vehicle angular speed error signal e _f, by error signal e _fBe sent to fast loop controller, can obtain the actuator input signal v in fast loop based on radial base neural net compensation and sliding formwork control, v is sent to the output vector δ (v) that actuator can be subject to the actuator saturation properties influence, actuator output vector δ (v) is sent to the aircraft command receiver, thereby can realizes the predetermined attitude angle Ω of aircraft _cTracking control.