CN104238357A - Fault-tolerant sliding-mode control method for near-space vehicle - Google Patents

Abstract

The invention discloses a fault-tolerant sliding-mode control method for a near-space vehicle. According to the fault-tolerant sliding-mode control method for the near-space vehicle, for the situation that the order of the magnitude of external disturbance in a quick loop and slow loop system is greatly larger than the order of the magnitude of uncertain times of the system, the nonlinear disturbance observer technology is used for processing hybrid disturbance, and unknown hybrid disturbance is estimated by a disturbance observer through known system information; in order to solve the problem that saturation of the control surface of the near-space vehicle is limited, the upper bound of the deflection angle output of a steering engine is applied to design of a control law, it is guaranteed that the input is within a certain range, auxiliary variables are designed, the deflection angle output of the steering engine is automatically adjusted through the self-adaption law, and therefore the situation that when the upper bound of the deflection angle is too large, the output is too large is avoided; a compensator is established through a radial basis function neural network and is used for fault-tolerant compensation when the steering engine breaks down, and therefore the problem that the steering engine of the near-space vehicle breaks down is solved. By the adoption of the fault-tolerant sliding-mode control method for the near-space vehicle, under the conditions of system uncertainties, unknown external disturbance, limited input saturation and a fault of the steering engine, the near-space vehicle has good control performance.

Description

A kind of fault-tolerant sliding-mode control of Near Space Flying Vehicles

Technical field

The present invention relates to technical field of flight control, particularly relate to a kind of fault-tolerant sliding-mode control of Near Space Flying Vehicles.

Background technology

Near Space Flying Vehicles (near-space vehicle, NSV) aircraft operated near space (being often referred to the spatial domain apart from ground 20-100 km) scope is referred to, the spatial domain be positioned under near space is conventional lighter-than-air vehicles running space, and the spatial domain be located thereon is spacecraft running space.Near Space Flying Vehicles has the advantages such as mobility strong, flight envelope is large, viability is strong, and the flight control difficulty studying this type of aircraft is larger.

First, in order to design the control system with high precision and strong robust stabilizing ability, need to take into full account that when Near Space Flying Vehicles Controller gain variations system architecture uncertainty and external disturbance are on the impact of system; Secondly, the increase that NSV control surface deflection angle can not be unlimited, namely there is saturated limitation problem in rudder face, if ignore input saturation nonlinearity in Controller gain variations process, may cause the hydraulic performance decline of control system, even cause the instability of system; In addition, NSV may run into steering wheel failure problems when performing aerial mission, compensates steering wheel fault, task may be caused to complete, even cause NSV to crash if do not consider.

The interference observer technology of explicit physical meaning, relatively simple in Project Realization, be usually used in the interference approached in uncertain system.Nonlinear Disturbance Observer utilizes system Given information to estimate unknown external disturbance, during the control law of design system, can utilize the output of interference observer, thus offsets the impact that external interference produces system.

Consider radial base neural net (Radial Basis Function Neural Networks, RBFNNs) arbitrary continuation function can be approached with arbitrary accuracy, so adopt RBFNNs to construct a kind of compensator to steering wheel fault, RBFNNs is utilized to estimate Actuators Failures part, in design of control law, it is offset, thus stability and safety flight under actuator is applauded.

For nonlinear system, it is a kind of effective control method that sliding formwork controls (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 system control process, controlled quentity controlled variable needs on purpose constantly to change in transition mode according to system current state, system actual path is caused to pass through back and forth in sliding mode both sides, thus its control method has good adaptability and strong robustness to systematic parameter perturbation and external disturbance, and other nonlinear control methods have the features such as operand is little, engineering adaptability is strong relatively, very high theoretical research is had to be worth, and Successful utilization is in control fields such as Industry Control, robot, boats and ships, control effects is good.

The fault-tolerant sliding-mode control of existing Near Space Flying Vehicles generally adopts T-S fuzzy model to approach into the dynamic attitude mode of spacecraft more, consider seldom for external disturbance and actuator saturation phenomenon, mostly external disturbance and actuator saturation phenomenon are used as fault tolerance information to process, it can not reflect its dynamic perfromance completely, needed to carry out fault diagnosis before fault-tolerant, carry out fault-tolerant according to diagnostic message to fault, these class methods require higher to fault diagnosis, if can not to be out of order information by Precise Diagnosis, then can not get good fault-tolerant effect, even can not ensure that aircraft stabilized flight causes crashing into spacecraft.The advantage of this patent method is to utilize interference observer and neural network to process external disturbance and fault respectively simultaneously, for actuator input saturation problem, patent uses the saturated upper bound of actuator to carry out design control law, and utilize the auxiliary variable of design to carry out adjusting actuator output size, guarantee to there will not be actuator to export excessive problem.In addition the controller designed by this patent does not need the concrete failure diagnosis information directly obtained about topworks, but processes by introducing neural network, thus makes controller have stronger fault-tolerant ability to actuator failure; On the other hand, as can be seen from the expression formula of control law, the impact that the controlled quentity controlled variable of trying to achieve all in saturation range, and can eliminate external disturbance, it is saturated to input and actuator failures is brought to system.

Summary of the invention

Technical matters to be solved by this invention is the defect for background technology, there is provided one that aircraft can be made to have systematic uncertainty, external disturbance, follows the tracks of the fault-tolerant sliding-mode control of the Near Space Flying Vehicles of the attitude angle signal of specifying under inputting the combined influence of saturated and steering wheel fault.

The present invention is for solving the problems of the technologies described above by the following technical solutions:

A fault-tolerant sliding-mode control for Near Space Flying Vehicles, comprises the following steps:

Step 1), according to singular perturbation principle and time-scale separation principle, the stance loop of aircraft is decomposed into slow loop and fast loop;

Step 2), respectively the control system in the control system in slow loop and fast loop is transformed into corresponding affine nonlinear system equation form;

Step 3), the controller in slow loop and fast loop is generated respectively according to the affine nonlinear system equation in slow loop, fast loop;

Step 4), utilize step 3) in generate slow loop controller and fast loop control unit robust control is carried out to aircraft.

As the further prioritization scheme of fault-tolerant sliding-mode control of a kind of Near Space Flying Vehicles of the present invention, step 2) in affine nonlinear equation corresponding to the control system in described slow loop be:

$\stackrel{\·}{\mathrm{\Ω}}=f_s\left(\mathrm{\Ω}\right)+g_s\left(\mathrm{\Ω}\right){\mathrm{\ω}}_c+D_s$

In formula, Ω=[α, β, μ] ^tfor current pose angle signal, α, β and μ represent the angle of attack, yaw angle and roll angle respectively, represent Ω differentiate; f _s(Ω)=[f _s1, f _s2, f _s3] ^t, ω _cfor the control law of slow loop controller; D _srepresent slow loop composite interference;

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

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

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

M represents vehicle mass; V represents vehicle flight speeds; represent dynamic pressure; S represents wing area of reference; γ represents pitch angle; T represents motor power; G represents acceleration of gravity; δ _yrepresent thrust vectoring rudder face deflection angle laterally; δ _zrepresent thrust vectoring rudder face deflection angle longitudinally; C _{l, α}represent the lift coefficient caused by angle of attack α; C _{y, β}represent the lateral force coefficient caused by yaw angle β;

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

As the further prioritization scheme of fault-tolerant sliding-mode control of a kind of Near Space Flying Vehicles of the present invention, step 2) in affine nonlinear equation corresponding to the control system in described fast loop be:

$\stackrel{\·}{\mathrm{\ω}}=f_f\left(\mathrm{\ω}\right)+g_f\left(\mathrm{\ω}\right)\mathrm{\δ}\left(v\right)+D_f$

In formula, ω=[p, q, r] ^tfor current pose angle rate signal, p, q and r represent roll angle speed, pitch rate and yawrate respectively, represent ω differentiate, f _f(ω)=[f _f1, f _f2, f _f3] ^t,

$\begin{array}{c}{f}_{f1}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_z+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_z+n_{\mathrm{aero}}{I}_{\mathrm{xz}}{I}_y\\ +(I_{\mathrm{xy}}^2{I}_z-I_y{I}_z^2+I_y^2{I}_z-I_{\mathrm{xz}}^2{I}_y)\mathrm{qr}+(I_y{I}_z{I}_{\mathrm{xz}}-I_{\mathrm{xz}}{I}_y^2+I_x{I}_y{I}_{\mathrm{xz}})\mathrm{pq}\\ +(I_y{I}_z{I}_{\mathrm{xy}}+I_x{I}_z{I}_{\mathrm{xy}}-I_z^2{I}_{\mathrm{xy}})\mathrm{pr}-I_{\mathrm{xy}}{I}_{\mathrm{xz}}{I}_y(q^2-p^2)-I_{\mathrm{xz}}{I}_{\mathrm{xy}}{I}_z(p^2-r^2))\end{array},$

$\begin{array}{c}{f}_{f2}=\frac{1}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}(-l_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_y{I}_z+m_{\mathrm{aero}}(I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2)\\ -I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}{n}_{\mathrm{aero}}-I_{\mathrm{xy}}(I_y{I}_z{I}_{\mathrm{xz}}+I_x{I}_y{I}_{\mathrm{xz}}-I_y^2{I}_{\mathrm{xz}})\mathrm{pq}\\ -(I_{\mathrm{xy}}+I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{qr}+(I_y{I}_{\mathrm{xy}}^2{I}_{\mathrm{xz}}+I_{\mathrm{xz}}-I_{\mathrm{xy}}^2{I}_z)(p^2-r^2)\\ +(I_z-I_x-I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{pr})\end{array},$

$\begin{array}{c}{f}_{f3}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_{\mathrm{xy}}+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}+(I_x{I}_y-I_{\mathrm{xy}}^2)n_{\mathrm{aero}}\\ +(I_y{I}_{\mathrm{xz}}^2+I_x^2{I}_y-I_x{I}_{\mathrm{xy}}^2-I_x{I}_y^2-I_y{I}_{\mathrm{xy}}^2)\mathrm{pq}\\ +\left(I_y^2{I}_{\mathrm{xz}}-I_y{I}_z{I}_{\mathrm{xz}}+I_{\mathrm{xy}}^2{I}_{\mathrm{xz}}-I_x{I}_y{I}_{\mathrm{xz}}+I_{\mathrm{xz}}{I}_{\mathrm{xy}}^2\right)\mathrm{qr}+I_{\mathrm{xy}}{I}_{\mathrm{xz}}^2(p^2-r^2)\\ +(I_z{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_x{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_y{I}_{\mathrm{xy}}{I}_{\mathrm{xz}})\mathrm{pr}+(I_x{I}_y{I}_{\mathrm{xy}}-I_{\mathrm{xy}}^3)(p^2-q^2))\end{array}y,$

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

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

I _x, I _yand I _zrepresent the moment of inertia around x, y and z axes respectively; I _xy, I _xzand I _yzrepresent the product of inertia; B represents spanwise length; C represents mean aerodynamic chord; C _{l, β}represent the rolling moment coefficient caused by yaw angle β, C _l,prepresent the rolling moment increment coefficient caused by roll angle speed p; C _l,rrepresent the rolling moment increment coefficient caused by yawrate r; C _{m, α}represent the pitching moment coefficient caused by angle of attack α; C _m,qrepresent the pitching moment increment coefficient caused by pitch rate q; C _{n, β}represent the yawing moment coefficient caused by yaw angle β; C _n,prepresent the yawing increment coefficient caused by roll angle speed p; C _n,rrepresent the yawing increment coefficient caused by yawrate r;

g _f(ω)＝g _f1g _fδ(ω)，

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

$g_{\mathrm{f\δ}}\left(\mathrm{\ω}\right)=\left[\begin{array}{ccccc}\stackrel{\‾}{q}\mathrm{bS}{C}_{l,{\mathrm{\δ}}_a}& \stackrel{\‾}{q}\mathrm{bS}{C}_{l,{\mathrm{\δ}}_e}& \stackrel{\‾}{q}\mathrm{bS}{C}_{l,{\mathrm{\δ}}_r}& 0& 0\\ \stackrel{\‾}{q}\mathrm{Sc}{C}_{m,{\mathrm{\δ}}_a}& \stackrel{\‾}{q}\mathrm{Sc}{C}_{m,{\mathrm{\δ}}_e}& \stackrel{\‾}{q}\mathrm{Sc}{C}_{m,{\mathrm{\δ}}_r}& 0& \frac{\mathrm{\πT}{X}_T}{180}\\ \stackrel{\‾}{q}\mathrm{Sb}{C}_{n,{\mathrm{\δ}}_a}& \stackrel{\‾}{q}\mathrm{Sb}{C}_{n,{\mathrm{\δ}}_e}& \stackrel{\‾}{q}\mathrm{Sb}{C}_{n,{\mathrm{\δ}}_r}& -\frac{\mathrm{\πT}{X}_T}{180}& 0\end{array}\right];$

represent by aileron rudder δ _athe rolling moment increment coefficient caused; represent by elevating rudder δ _ethe rolling moment increment coefficient caused; represent by yaw rudder δ _rthe rolling moment increment coefficient caused; represent by aileron rudder δ _athe pitching moment increment coefficient caused; represent by elevating rudder δ _ethe pitching moment increment coefficient caused; represent by yaw rudder δ _rthe pitching moment increment coefficient caused; represent by aileron rudder δ _athe yawing increment coefficient caused; represent by elevating rudder δ _ethe yawing increment coefficient caused; represent by yaw rudder δ _rthe yawing increment coefficient caused; X _trepresent the distance of engine jet pipe distance barycenter;

D _ffor fast loop composite interference, this composite interference utilizes Nonlinear Disturbance Observer to carry out approximation timates, v=[v ₁, v ₂, v ₃, v ₄, v ₅] ^tfor control law and the actuator input vector of fast loop control unit, δ (v)=[δ _a, δ _e, δ _r, δ _y, δ _z] ^tfor the output vector by actuator saturation properties influence, specifically meet following relation:

${\mathrm{\&delta;}}_a=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1>{\mathrm{\&delta;}}_{\mathrm{aM}}\\ v_1,& -{\mathrm{\&delta;}}_{\mathrm{aM}}\&le;v_1\&le;{\mathrm{\&delta;}}_{\mathrm{aM}}\\ -{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1<-{\mathrm{\&delta;}}_{\mathrm{aM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_e=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2>{\mathrm{\&delta;}}_{\mathrm{eM}}\\ v_2,& -{\mathrm{\&delta;}}_{\mathrm{eM}}\&le;v_2\&le;{\mathrm{\&delta;}}_{\mathrm{eM}}\\ -{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2<-{\mathrm{\&delta;}}_{\mathrm{eM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_r=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3>{\mathrm{\&delta;}}_{\mathrm{rM}}\\ v_3,& -{\mathrm{\&delta;}}_{\mathrm{rM}}\&le;v_3\&le;{\mathrm{\&delta;}}_{\mathrm{rM}}\\ -{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3<-{\mathrm{\&delta;}}_{\mathrm{rM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_y=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4>{\mathrm{\&delta;}}_{\mathrm{yM}}\\ v_4,& -{\mathrm{\&delta;}}_{\mathrm{yM}}\&le;v_4\&le;{\mathrm{\&delta;}}_{\mathrm{yM}}\\ -{\mathrm{\&delta;}}_{\mathrm{yM}},& v_4<-{\mathrm{\&delta;}}_{\mathrm{yM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_z=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5>{\mathrm{\&delta;}}_{\mathrm{zM}}\\ v_5,& -{\mathrm{\&delta;}}_{\mathrm{zM}}\&le;v_5\&le;{\mathrm{\&delta;}}_{\mathrm{zM}}\\ -{\mathrm{\&delta;}}_{\mathrm{zM}},& v_5<-{\mathrm{\&delta;}}_{\mathrm{zM}}\end{array}\right.,$

V ₁, v ₂, v ₃, v ₄and v ₅be the element of vector v, δ _a, δ _e, δ _r, δ _yand δ _zrepresent respectively aileron rudder kick angle, elevator angle, control surface steering angle, push vector helm laterally with the deflection angle of longitudinal direction; δ _aM, δ _eM, δ _rM, δ _yMand δ _zMbe respectively the saturated limited value of aileron rudder corner, elevating rudder corner, yaw rudder corner, push vector helm laterally deflection angle and push vector helm longitudinally deflection angle.

As the further prioritization scheme of fault-tolerant sliding-mode control of a kind of Near Space Flying Vehicles of the present invention, step 3) described in generate the concrete steps of slow loop controller as follows:

Step 3.1.1), utilize Nonlinear Disturbance Observer to approach the composite interference in slow loop:

$\left\{\begin{array}{c}{\hat{D}}_s=z+Q\left(\mathrm{\&Omega;}\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(\mathrm{\&Omega;}\right)z-L\left(\mathrm{\&Omega;}\right)(Q\left(\mathrm{\&Omega;}\right)+f_s\left(\mathrm{\&Omega;}\right)+g_s\left(\mathrm{\&Omega;}\right){\mathrm{\&omega;}}_c)\end{array}\right.$

In formula, for the estimated value of composite interference in slow loop; Z is the state variable of Nonlinear Disturbance Observer, and L (Ω) and Q (Ω) they are intermediate variable, and for the diagonal matrix that diagonal element is greater than zero, Q (Ω)=[q ₁(Ω), q ₂(Ω) ..., q _n(Ω)] ^t∈ R ⁿfor nonlinear function vector, n is the dimension of external disturbance;

Step 3.1.2), according to step 3.1.1) in the estimated value of composite interference in the slow loop that obtains common slip-form is adopted to obtain the controller in slow loop:

${\mathrm{\&omega;}}_c=-g_s{\left(\mathrm{\&Omega;}\right)}^{-1}(f_s\left(\mathrm{\&Omega;}\right)-{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_c+{\hat{D}}_s+K_s{e}_s+{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\mathrm{sgn}\left(e_s\right))$

In formula, g _s(Ω) ^-1represent matrix g _s(Ω) invert; e _s=Ω-Ω _cfor slow Trace-on-Diagram error, Ω _crepresent the reference instruction signal preset, β _dsfor slow loop composite interference evaluated error upper dividing value, k _sfor the parameter matrix of slow loop sliding-mode surface, specifically meet following relation: K _s=diag{k _s1, k _s2, k _s3> 0.

As the further prioritization scheme of fault-tolerant sliding-mode control of a kind of Near Space Flying Vehicles of the present invention, step 3) described in generate the concrete steps of fast loop control unit as follows:

Step 3.2.1), utilize radial base neural net to estimate actuator failures part:

$P_m(\mathrm{\&omega;},v)={\hat{W}}^{T}h\left(\mathrm{\&omega;}\right)+\mathrm{\&epsiv;}$

In formula, P _mfor the estimated value of actuator failures part; for the weights of radial base neural net, for i-th vectorial adaptive law, k _wand Γ _wbe respectively the real number in neural network weight adaptive law and parameter matrix, and k _w> 0, for Γ _wtransposed matrix, for fast loop sliding-mode surface, s ^trepresent and transposition is carried out to column vector s; H (ω)=[h ₁, h ₂..., h _l] ^tfor radial basis vector, l is the total nodes of network, ω=[p, q, r] ^tfor network input vector, in h (ω), element adopts Gaussian bases form, namely c _kfor the center vector of a network kth node, b _kfor the sound stage width parameter of a network kth node, k=1,2 ..., l;

Step 3.2.2), utilize Nonlinear Disturbance Observer to approach the composite interference in fast loop:

$\left\{\begin{array}{c}{\hat{D}}_f=z+Q\left(e_f\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(e_f\right)(f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}{\hat{W}}^{T}h\left(x\right)+{\hat{D}}_f-{\mathrm{\&omega;}}_c)\end{array}\right.$

In formula, for the estimated value of composite interference in fast loop; Z is the state variable of interference observer, L (e _f) and Q (e _f) be intermediate variable, and q (e _f)=[q ₁(e _f), q ₂(e _f) ..., q _n(e _f)] ^t∈ R ⁿfor nonlinear function vector, ω _crepresent the reference instruction signal preset, for the adaptive weight of radial base neural net;

Step 3.2.3), according to step 3.2.1) in the estimated value P of actuator failures part that obtains _m, and step 3.2.2) in the estimated value of composite interference in the fast loop that obtains generate the controller in fast loop:

Wherein, U _m=diag{u _1M, u _2M..., u _mM∈ R ^{m × m}, u _iMbe the saturation limit amplitude of i-th actuator, i=1,2 ..., m; Λ _s=diag{|s ₁|, | s ₂| ..., | s _n|, ε _u> 0 is positive parameter, and there is following form:

${\stackrel{\&OverBar;}{v}}_i=\frac{\left|s_i\right|\mathrm{sat}\left(s_i\right)}{\left|\right|s\left|\right|+{\mathrm{\&gamma;}}_i(\frac{e^{\mathrm{\&kappa;}{\mathrm{\&chi;}}_i}+e^{-\mathrm{\&kappa;}{\mathrm{\&chi;}}_i}}{2}-1)+{\mathrm{\&epsiv;}}_v}$

S _ifor i-th element of s, γ _i> 0, κ > 0, ε _v> 0, sat (s _i) be saturation function between [-1,1], its form is as follows:

$\mathrm{sat}\left(s_i\right)=\left\{\begin{array}{cc}1,& s_i\&GreaterEqual;{\mathrm{\&xi;}}_i\\ s_i/{\mathrm{\&xi;}}_i,& \left|s_i\right|\&le;{\mathrm{\&xi;}}_i\\ -1,& s_i\&le;-{\mathrm{\&xi;}}_i\end{array}\right.$

Wherein ξ _i> 0 is the boundary layer parameters of saturation function, χ=[χ ₁, χ ₂..., χ _n] ^tfor auxiliary variable, its adaptive law is:

Wherein K _f=K _f ^t> 0, ${\mathrm{\&Lambda;}}_{\mathrm{\&Xi;}}=\mathrm{diag}\{0.5{\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_1},0.5{\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_2},...,0.5{\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_n}\},$ $\mathrm{\&Xi;}=\mathrm{diag}\{0.5e^{{\mathrm{\&kappa;\&chi;}}_1},0.5e^{{\mathrm{\&kappa;\&chi;}}_2},...,0.5e^{{\mathrm{\&kappa;\&chi;}}_n}\},$ V _rDfor compensation term, its concrete form is:

$v_{\mathrm{rD}}=\left\{\begin{array}{cc}\frac{(\widehat{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0|\left|e_f\right||+\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0^2)s}{{\left|\right|s\left|\right|}^2},& \left|\right|s\left|\right|>\mathrm{\&sigma;}\\ 0,& \left|\right|s\left|\right|\&le;\mathrm{\&sigma;}\end{array}\right.$

Wherein σ > 0, $\mathrm{\&zeta;}=0.5{\mathrm{\&zeta;}}_0^2,$ $\left|\right|{\stackrel{\&CenterDot;}{D}}_f\left|\right|\&le;{\mathrm{\&zeta;}}_0\left|\right|\mathrm{\&omega;}\left|\right|,$ for the estimated value of ζ.

As the further prioritization scheme of fault-tolerant sliding-mode control of a kind of Near Space Flying Vehicles of the present invention, step 4) described in utilize slow loop controller and fast loop control unit to carry out robust control to aircraft concrete steps as follows:

Step 4.1), attitude angle current demand signal Ω is deducted predetermined attitude angle command signal Ω _cobtain attitude of flight vehicle angular error signal e _s, by this error signal e _sbe sent to slow loop controller, obtain attitude angular rate command signal ω based on dynamic sliding mode control _c;

Step 4.2), attitude angular rate current demand signal ω is deducted attitude angular rate command signal ω _cobtain attitude of flight vehicle angular speed error signal e _f, by error signal e _fbe sent to fast loop control unit, compensate based on radial base neural net and actuator input signal v that the output of interference observer obtains in fast loop, v is sent to the output vector δ (v) that actuator obtains being subject to actuator saturation properties influence;

Step 4.3), actuator output vector δ (v) is sent to aircraft command receiver, realizes the predetermined attitude angle Ω of aircraft _ctracing control.

The present invention adopts above technical scheme compared with prior art, has following technique effect:

The present invention, according to affected difference in slow loop and fast loop, adopts diverse ways to design the controller model in slow loop and fast loop:

Mainly affect by composite interference in slow loop, without confined conditions such as input-bound and steering wheel faults, adopt the sliding-mode control based on interference observer;

Need in fast loop to consider multiple confined condition, in invention, adopt Nonlinear Disturbance Observer to approach composite interference.

For the saturated limited problem of vehicle rudder, steering wheel deflection angle is exported the upper bound and is used for design control law, guarantee to export within the specific limits, and Design assistant variable, automatically steering wheel deflection angle is regulated to export by adaptive law, in order to avoid when the deflection angle upper bound is excessive, export excessive phenomenon; Utilize radial base neural net to construct a kind of compensator to break down in situation to steering wheel and carry out fault-tolerant compensation simultaneously, and then solve aircraft steering engine failure problems.

Common sliding-mode method based on Reaching Law carries out Controller gain variations, and these two controllers combine and make aircraft when having systematic uncertainty, unknown external disturbance, have good control performance when inputting saturated limited and steering wheel fault.

Accompanying drawing explanation

Fig. 1 is the principle schematic of the fault-tolerant sliding-mode control of a kind of Near Space Flying Vehicles of the present invention.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

As shown in Figure 1, the invention discloses a kind of fault-tolerant sliding-mode control of Near Space Flying Vehicles, according to singular perturbation principle and time-scale separation principle, the stance loop of aircraft is divided into slow loop and fast loop, the method realizes based on the closed-loop control system be made up of slow loop control system, fast loop control system and aircraft, it is characterized in that, comprise the following steps:

(1) respectively slow loop control system and fast loop control system are transformed into 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 pose angle signal, α, β and μ represent the angle of attack, yaw angle and roll angle respectively, represent Ω differentiate; f _s(Ω)=[f _s1, f _s2, f _s3] ^t, ω _cfor the control law of 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 represents vehicle mass; V represents vehicle flight speeds; represent dynamic pressure; S represents wing area of reference; γ represents pitch angle; T represents motor power; G represents acceleration of gravity; δ _yrepresent thrust vectoring rudder face deflection angle laterally; δ _zrepresent thrust vectoring rudder face deflection angle longitudinally; C _{l, α}represent the lift coefficient caused by angle of attack α; C _{y, β}represent the lateral force coefficient 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 _srepresent slow loop composite interference, without the need to providing expression when setting up system equation, in slow loop controller design, only needing its derivative value, obtain D by adaptive approach _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 pose angle rate signal, p, q and r represent roll angle speed, pitch rate and yawrate respectively, represent ω differentiate, f _f(ω)=[f _f1, f _f2, f _f3] ^t,

$\begin{array}{c}{f}_{f1}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_z+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_z+n_{\mathrm{aero}}{I}_{\mathrm{xz}}{I}_y\\ +(I_{\mathrm{xy}}^2{I}_z-I_y{I}_z^2+I_y^2{I}_z-I_{\mathrm{xz}}^2{I}_y)\mathrm{qr}+(I_y{I}_z{I}_{\mathrm{xz}}-I_{\mathrm{xz}}{I}_y^2+I_x{I}_y{I}_{\mathrm{xz}})\mathrm{pq}\\ +(I_y{I}_z{I}_{\mathrm{xy}}+I_x{I}_z{I}_{\mathrm{xy}}-I_z^2{I}_{\mathrm{xy}})\mathrm{pr}-I_{\mathrm{xy}}{I}_{\mathrm{xz}}{I}_y(q^2-p^2)-I_{\mathrm{xz}}{I}_{\mathrm{xy}}{I}_z(p^2-r^2))\end{array},$

$\begin{array}{c}{f}_{f2}=\frac{1}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}(-l_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_y{I}_z+m_{\mathrm{aero}}(I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2)\\ -I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}{n}_{\mathrm{aero}}-I_{\mathrm{xy}}(I_y{I}_z{I}_{\mathrm{xz}}+I_x{I}_y{I}_{\mathrm{xz}}-I_y^2{I}_{\mathrm{xz}})\mathrm{pq}\\ -(I_{\mathrm{xy}}+I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{qr}+(I_y{I}_{\mathrm{xy}}^2{I}_{\mathrm{xz}}+I_{\mathrm{xz}}-I_{\mathrm{xy}}^2{I}_z)(p^2-r^2)\\ +(I_z-I_x-I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{pr})\end{array},$

$\begin{array}{c}{f}_{f3}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_{\mathrm{xy}}+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}+(I_x{I}_y-I_{\mathrm{xy}}^2)n_{\mathrm{aero}}\\ +(I_y{I}_{\mathrm{xz}}^2+I_x^2{I}_y-I_x{I}_{\mathrm{xy}}^2-I_x{I}_y^2-I_y{I}_{\mathrm{xy}}^2)\mathrm{pq}\\ +(I_y^2{I}_{\mathrm{xz}}-I_y{I}_z{I}_{\mathrm{xz}}+I_{\mathrm{xy}}^2{I}_{\mathrm{xz}}-I_x{I}_y{I}_{\mathrm{xz}}+I_{\mathrm{xz}}{I}_{\mathrm{xy}}^2)\mathrm{qr}+I_{\mathrm{xy}}{I}_{\mathrm{xz}}^2(p^2-r^2)\\ +(I_z{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_x{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_y{I}_{\mathrm{xy}}{I}_{\mathrm{xz}})\mathrm{pr}+(I_x{I}_y{I}_{\mathrm{xy}}-I_{\mathrm{xy}}^3)(p^2-q^2))\end{array},$

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

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

I _x, I _yand I _zrepresent the moment of inertia around x, y and z axes respectively; I _xy, I _xzand I _yzrepresent the product of inertia; B represents spanwise length; C represents mean aerodynamic chord; C _{l, β}represent the rolling moment coefficient caused by yaw angle β; C _l,prepresent the rolling moment increment coefficient caused by roll angle speed p; C _l,rrepresent the rolling moment increment coefficient caused by yawrate r; C _{m, α}represent the pitching moment coefficient caused by angle of attack α; C _m,qrepresent the pitching moment increment coefficient caused by pitch rate q; C _{n, β}represent the yawing moment coefficient caused by yaw angle β; C _n,prepresent the yawing increment coefficient caused by roll angle speed p; C _n,rrepresent the yawing increment coefficient caused by yawrate r;

g _f(ω)＝g _f1g _fδ(ω)，

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

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

represent by aileron rudder δ _athe rolling moment increment coefficient caused; represent by elevating rudder δ _ethe rolling moment increment coefficient caused; represent by yaw rudder δ _rthe rolling moment increment coefficient caused; represent by aileron rudder δ _athe pitching moment increment coefficient caused; represent by elevating rudder δ _ethe pitching moment increment coefficient caused; represent by yaw rudder δ _rthe pitching moment increment coefficient caused; represent by aileron rudder δ _athe yawing increment coefficient caused; represent by elevating rudder δ _ethe yawing increment coefficient caused; represent by yaw rudder δ _rthe yawing increment coefficient caused; X _trepresent the distance of engine jet pipe distance barycenter;

D _ffor fast loop composite interference, this composite interference utilizes Nonlinear Disturbance Observer to carry out approximation timates, v=[v ₁, v ₂, v ₃, v ₄, v ₅] ^tfor control law and the actuator input vector of fast loop control unit, δ (v)=[δ _a, δ _e, δ _r, δ _y, δ _z] ^tfor the output vector by 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 _zrepresent respectively aileron rudder kick angle, elevator angle, control surface steering angle, push vector helm laterally with the deflection angle of longitudinal direction; δ _aM, δ _eM, δ _rM, δ _yMand δ _zMbe respectively the saturated limited value of aileron rudder corner, elevating rudder corner, yaw rudder corner, push vector helm laterally deflection angle and push vector helm longitudinally deflection angle.

(2) controller in slow loop and fast loop is designed respectively according to the affine nonlinear system equation in slow loop, fast loop; Wherein, slow loop controller is adopted to general sliding formwork to design, utilize interference observer to process the composite interference in slow circuit system simultaneously; For fast loop control unit, Nonlinear Disturbance Observer is utilized to approach the composite interference in fast loop, steering wheel is deflected the upper bound and auxiliary variable is used for Controller gain variations, guarantee that steering wheel exports in controlled range, construct when a kind of compensator breaks down to steering wheel based on radial base neural net simultaneously and carry out fault-tolerant compensation, be specially:

A, utilize sliding formwork thought to design slow loop controller, adopt interference observer to process composite interference in slow circuit system simultaneously, be specially:

A1, design Nonlinear Disturbance Observer approach the composite interference in slow loop:

$\left\{\begin{array}{c}{\hat{D}}_s=z+Q\left(\mathrm{\&Omega;}\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(\mathrm{\&Omega;}\right)z-L\left(\mathrm{\&Omega;}\right)(Q\left(\mathrm{\&Omega;}\right)+f_s\left(\mathrm{\&Omega;}\right)+g_s\left(\mathrm{\&Omega;}\right){\mathrm{\&omega;}}_c)\end{array}\right.$

In formula, for the estimated value of composite interference in slow loop; Z is the state variable of interference observer, and L (Ω) and Q (Ω) they are intermediate variable, and for the diagonal matrix that diagonal element is greater than zero, Q (Ω)=[q ₁(Ω), q ₂(Ω) ..., q _n(Ω)] ^t∈ R ⁿfor nonlinear function vector, n is the dimension of external disturbance.

A2, estimated value according to composite interference in the slow loop obtained in a1 adopt common slip-form can obtain following controller model: ${\mathrm{\&omega;}}_c=-g_s{\left(\mathrm{\&Omega;}\right)}^{-1}(f_s\left(\mathrm{\&Omega;}\right)-{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_c+{\hat{D}}_s+K_s{e}_s+{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\mathrm{sgn}\left(e_s\right))$

In formula, g _s(Ω) ^-1represent matrix g _s(Ω) invert; e _s=Ω-Ω _cfor slow Trace-on-Diagram error, Ω _crepresent the reference instruction signal preset, β _dsfor slow loop composite interference evaluated error upper dividing value, k _sfor the parameter matrix of slow loop sliding-mode surface, specifically meet following relation: K _s=diag{k _s1, k _s2, k _s3> 0.

B, design return to the wrong sliding mode controller of the appearance of a street, and specific design process is:

B1, radial base neural net is utilized to estimate actuator failures part

$P_m(\mathrm{\&omega;},v)={\hat{W}}^{T}h\left(\mathrm{\&omega;}\right)+\mathrm{\&epsiv;}$

In formula, P _mfor the estimated value of actuator failures part; for the weights of radial base neural net, k _wand Γ _wbe respectively the real number in neural network weight adaptive law and parameter matrix, and k _w> 0, for Γ _wtransposed matrix, for fast loop sliding-mode surface, s ^trepresent and transposition is carried out to column vector s; H (ω)=[h ₁, h ₂..., h _l] ^tfor radial basis vector, l is the total nodes of network, ω=[p, q, r] ^tfor network input vector, in h (ω), element adopts Gaussian bases form, namely c _kfor the center vector of a network kth node, b _kfor the sound stage width parameter of a network kth node, k=1,2 ..., l;

B2, design Nonlinear Disturbance Observer approach the composite interference in fast loop

$\left\{\begin{array}{c}{\hat{D}}_f=z+Q\left(e_f\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(e_f\right)(f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}{\hat{W}}^{T}h\left(\mathrm{\&omega;}\right)+{\hat{D}}_f-{\mathrm{\&omega;}}_c)\end{array}\right.$

In formula, for the estimated value of composite interference in fast loop; Z is the state variable of interference observer, L (e _f) and Q (e _f) be intermediate variable, and for the diagonal matrix that diagonal element is greater than zero, Q (e _f)=[q ₁(e _f), q ₂(e _f) ..., q _n(e _f)] ^t∈ R ⁿfor nonlinear function vector, n is the dimension of external disturbance, ω _crepresent reference instruction signal, for the adaptive weight of radial base neural net.

B3, estimated value P according to the actuator failures part obtained in b1 _m, and the estimated value of composite interference in the fast loop obtained in b2 fault-tolerant sliding mode controller is as following form:

Wherein, U _m=diag{u _1M, u _2M..., u _mM∈ R ^{m × m}, u _iMbe the saturation limit amplitude of i-th actuator, i=1,2 ..., m; Λ _s=diag{|s ₁|, | s ₂| ..., | s _n|, ε _u> 0 is positive parameter, $\stackrel{\&OverBar;}{v}=[{\stackrel{\&OverBar;}{v}}_1,{\stackrel{\&OverBar;}{v}}_2,...,{\stackrel{\&OverBar;}{v}}_n]{\&Element;R}^n,$ And there is following form:

${\stackrel{\&OverBar;}{v}}_i=\frac{\left|s_i\right|\mathrm{sat}\left(s_i\right)}{\left|\right|s\left|\right|+{\mathrm{\&gamma;}}_i(\frac{e^{\mathrm{\&kappa;}{\mathrm{\&chi;}}_i}+e^{-{\mathrm{\&kappa;\&chi;}}_i}}{2}-1)+{\mathrm{\&epsiv;}}_v}$

S _ifor i-th element of s, γ _i> 0, κ > 0 and ε _v> 0, sat (s _i) be saturation function between [-1,1], its form is as follows:

$\mathrm{sat}\left(s_i\right)=\left\{\begin{array}{cc}1,& s_i\&GreaterEqual;{\mathrm{\&xi;}}_i\\ s_i/{\mathrm{\&xi;}}_i,& \left|s_i\right|\&le;{\mathrm{\&xi;}}_i\\ -1,& s_i\&le;-{\mathrm{\&xi;}}_i\end{array}\right.$

Wherein ξ _i> 0 is the boundary layer parameters of saturation function, χ=[χ ₁, χ ₂..., χ _n] ^tfor auxiliary variable, its adaptive law is designed to:

Wherein K _f=K _f ^t> 0, ${\mathrm{\&Lambda;}}_{\mathrm{\&Xi;}}=\mathrm{diag}\{{0.5\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_1},0.5{\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_2},...,0.5{\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_n}\},$ $\mathrm{\&Xi;}=\mathrm{diag}\{{0.5e}^{{\mathrm{\&kappa;\&chi;}}_1},0.5e^{{\mathrm{\&kappa;\&chi;}}_2},...,0.5e^{{\mathrm{\&kappa;\&chi;}}_n}\},$ V _rDfor compensation term, its concrete form is:

$v_{\mathrm{rD}}=\left\{\begin{array}{cc}\frac{(\widehat{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0|\left|e_f\right||+\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0^2)s}{{\left|\right|s\left|\right|}^2},& \left|\right|s\left|\right|>\mathrm{\&sigma;}\\ 0,& \left|\right|s\left|\right|\&le;\mathrm{\&sigma;}\end{array}\right.$

Wherein σ > 0, $\mathrm{\&zeta;}=0.5{\mathrm{\&zeta;}}_0^2,$ $\left|\right|{\stackrel{\&CenterDot;}{D}}_f\left|\right|\&le;{\mathrm{\&zeta;}}_0\left|\right|\mathrm{\&omega;}\left|\right|,$ for the estimated value of ζ.

(3) utilize the slow loop controller that obtains in step (2) and fast loop control unit to carry out robust control to aircraft, be specially: 3-1, attitude angle current demand signal Ω is deducted predetermined attitude angle command signal Ω _cattitude of flight vehicle angular error signal e can be obtained _s, by this error signal e _sbe sent to slow loop controller, attitude angular rate command signal ω can be obtained based on dynamic sliding mode control _c;

3-2, attitude angular rate current demand signal ω is deducted attitude angular rate command signal ω _cattitude of flight vehicle angular speed error signal e can be obtained _f, by error signal e _fbe sent to fast loop control unit, the actuator input signal v that can obtain in fast loop is controlled based on radial base neural net compensation and sliding formwork, v being sent to actuator can by the output vector δ (v) of actuator saturation properties influence, then actuator output vector δ (v) is sent to aircraft command receiver, thus can realizes the predetermined attitude angle Ω of aircraft _ctracing control.

Succinct in order to describe in the specific embodiment of the invention, be defined as follows associated token:

Mark: to a certain vector, || represent and signed magnitude arithmetic(al) is done to its each element; || ^crepresent that first doing signed magnitude arithmetic(al) to its each element does the computing of power side again; Sgn () expression does sign function computing to its each element; || || represent Euclid norm (if matrix, then representing F-norm); represent and integral operation is done to its each element; Diag () represents by each element of vector formation pair of horns battle array, diag{sgn () } represent and first sign function computing done to its each element and then form pair of horns battle array.Such as χ=[χ ₁, χ ₂..., χ _n] ^t, represent each element differentiate of χ, then

|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，

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

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

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

Controller specific design process

1, NSV slow loop controller design

Following hypothesis is needed before Controller gain variations is carried out to NSV attitude system:

Suppose 1: 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 ${\stackrel{\&CenterDot;}{D}}_s={[{\stackrel{\&CenterDot;}{D}}_{s,1},{\stackrel{\&CenterDot;}{D}}_{s,2},{\stackrel{\&CenterDot;}{D}}_{s,3}]}^T$ Bounded, namely || D _s||≤β, β > 0, $\left|\right|\stackrel{\&CenterDot;}{D_s}\left|\right|\&le;{\mathrm{\&beta;}}_d,$ β _d＞0。

Suppose 2: to NSV attitude motion system, expect attitude angle vector Ω _cknown continuously and its first order derivative exist.

Suppose 3: to NSV attitude motion system, state can be surveyed and ride gain matrix g _s(Ω) generalized inverse exists.

In the slow circuit system of NSV, only consider the composite interference of system, the output based on interference observer designs corresponding controller.

Because system exists uncertain and external interference, for reducing external interference to the impact of system, improving Systematical control precision, introducing interference observer being approached the interference of system.Interference observer is designed to following form:

$\left\{\begin{array}{c}{\hat{D}}_s=z+Q\left(\mathrm{\&Omega;}\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(\mathrm{\&Omega;}\right)z-L\left(\mathrm{\&Omega;}\right)(Q\left(\mathrm{\&Omega;}\right)+f_s\left(\mathrm{\&Omega;}\right)+g_s\left(\mathrm{\&Omega;}\right){\mathrm{\&omega;}}_c)\end{array}\right.---\left(1\right)$

In formula, for the estimated value of composite interference in slow loop; Z is the state variable of interference observer, and L (Ω) and Q (Ω) they are intermediate variable, and q (Ω)=[q ₁(Ω), q ₂(Ω) ..., q _n(Ω)] ^t∈ R ⁿfor nonlinear function vector.For simplified design, L (Ω) is diagonal matrix form, i.e. L (Ω)=diag{L ₁(Ω), L ₂(Ω) ..., L _n(Ω) }, L _i(Ω) > 0 or L=diag{L ₁, L ₂..., L _n, L _i> 0, i=1,2,3.

Interference observer is exported differentiate can obtain:

$\begin{array}{c}{\stackrel{\&CenterDot;}{\hat{D}}}_s=\stackrel{\&CenterDot;}{z}+\stackrel{\&CenterDot;}{Q}\left(\mathrm{\&Omega;}\right)\\ =-L\left(\mathrm{\&Omega;}\right)z-L\left(\mathrm{\&Omega;}\right)(Q\left(\mathrm{\&Omega;}\right)+f_s\left(\mathrm{\&Omega;}\right)+g_s\left(\mathrm{\&Omega;}\right){\mathrm{\&omega;}}_c)+\frac{\&PartialD;Q\left(\mathrm{\&Omega;}\right)}{\&PartialD;\mathrm{\&Omega;}}\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}\\ =-L\left(\mathrm{\&Omega;}\right)z-L\left(\mathrm{\&Omega;}\right)Q\left(\mathrm{\&Omega;}\right)+L\left(\mathrm{\&Omega;}\right)D_s\\ =L\left(\mathrm{\&Omega;}\right)(D_s-z-Q\left(\mathrm{\&Omega;}\right))\\ =L\left(\mathrm{\&Omega;}\right){\tilde{D}}_s\end{array}---\left(2\right)$

Wherein ${\tilde{D}}_s=D_s-{\hat{D}}_s.$

For the stability of Analysis interference observer error, Lyapunov equation is elected as:

$V_d=\frac{1}{2}{{\tilde{D}}_s}^T{\tilde{D}}_s---\left(3\right)$

To V _ddifferentiate can obtain

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_d={{\tilde{D}}_s}^T{\stackrel{\&CenterDot;}{\tilde{D}}}_s\\ ={{\tilde{D}}_s}^T{\stackrel{\&CenterDot;}{D}}_s-{{\tilde{D}}_s}^T{\stackrel{\&CenterDot;}{\hat{D}}}_s\\ ={{\tilde{D}}_s}^T{\stackrel{\&CenterDot;}{D}}_s-{{\tilde{D}}_s}^{T}L\left(\mathrm{\&Omega;}\right){\tilde{D}}_s\\ \&le;\frac{1}{2}{{\tilde{D}}_s}^T{\tilde{D}}_s+\frac{1}{2}{{\stackrel{\&CenterDot;}{D}}_s}^T{\stackrel{\&CenterDot;}{D}}_s-{{\tilde{D}}_s}^{T}L\left(\mathrm{\&Omega;}\right){\tilde{D}}_s\\ \&le;-{{\tilde{D}}_s}^T(L\left(\mathrm{\&Omega;}\right)-\frac{1}{2}I){\tilde{D}}_s+\frac{1}{2}{{\mathrm{\&beta;}}_d}^2\\ \&le;-{\mathrm{\&kappa;}}_d{V}_d+M_d\end{array}---\left(4\right)$

Wherein ${\mathrm{\&kappa;}}_d=\min \left\{2{\mathrm{\&lambda;}}_{\min }(L\left(\mathrm{\&Omega;}\right)-\frac{1}{2}{I}_3)\right\},M_d=\frac{1}{2}{{\mathrm{\&beta;}}_d}^2.$

Right both sides integration can obtain:

$0\&le;V_d\&le;\frac{M_d}{{\mathrm{\&kappa;}}_d}+(V_d\left(0\right)-\frac{M_d}{{\mathrm{\&kappa;}}_d})e^{-{\mathrm{\&kappa;}}_{d}t}---\left(5\right)$

From formula (5), error signal is finally uniformly bounded, and namely Interference Estimation error exists upper bound β _d, namely

Theorem 1: for the slow circuit system of NSV, the sliding-mode surface of design formula (6), composite interference evaluated error the adaptive law of Estimation of Upper-Bound value is taken as formula (7), and interference observer is designed to formula (1), and slow loop sliding mode controller design is formula (8), then slow Trace-on-Diagram error asymptotic convergence is in initial point.

${\mathrm{\&sigma;}}_s=e_s+{\&Integral;}_0^t{A}_s{e}_s\mathrm{dt}---\left(5\right)$

${\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}={\mathrm{\&gamma;}}_s\left|\right|{\mathrm{\&sigma;}}_s\left|\right|---\left(7\right)$

${\mathrm{\&omega;}}_c=-g_s{\left(\mathrm{\&Omega;}\right)}^{-1}(f_s\left(\mathrm{\&Omega;}\right)-{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_c+{\hat{D}}_s+A_s{e}_s+{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\mathrm{sgn}\left({\mathrm{\&sigma;}}_s\right)+K_s{\mathrm{\&sigma;}}_s)---\left(8\right)$

Wherein, e _s=Ω-Ω _cfor slow Trace-on-Diagram error; g _s(Ω) ^-1represent matrix g _s(Ω) invert; A _sfor the parameter matrix of slow loop sliding-mode surface, specifically meet following relation: A _s=diag{a _{s, 1}, a _{s, 2}, a _{s, 3}> 0, K _s> 0, γ _s> 0, for β _dsestimated value vector, β _dsfor the upper dividing value of slow loop composite interference evaluated error

Prove: selection Lyapunov function is:

$V_s=\frac{1}{2}{\mathrm{\&sigma;}}_s^T{\mathrm{\&sigma;}}_s+\frac{1}{2{\mathrm{\&gamma;}}_d}{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}^2---\left(9\right)$

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 (8), can obtain formula (6) differentiate:

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_s=f_s\left(\mathrm{\&Omega;}\right)+g_s\left(\mathrm{\&Omega;}\right){\mathrm{\&omega;}}_c+D_s-{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_c+A_s{e}_s\\ =f_s\left(\mathrm{\&Omega;}\right)-(f_s\left(\mathrm{\&Omega;}\right)-{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_c+{\hat{D}}_s+A_s{e}_s+{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\mathrm{sgn}\left(e_s\right)+K_s{\mathrm{\&sigma;}}_s)+D_s-{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_c+A_s{e}_s\\ =-K_s{\mathrm{\&sigma;}}_s+{\tilde{D}}_s-{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\mathrm{sgn}\left({\mathrm{\&sigma;}}_s\right)\end{array}---\left(10\right)$

According to formula (7), (10), can obtain formula (9) differentiate:

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_s={\mathrm{\&sigma;}}_s^T{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_s-\frac{1}{{\mathrm{\&gamma;}}_d}{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}{\stackrel{\&CenterDot;}{\widehat{\mathrm{\&beta;}}}}_{\mathrm{ds}}\\ ={\mathrm{\&sigma;}}_s^T(-K_s{\mathrm{\&sigma;}}_s+{\tilde{D}}_s-{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}\mathrm{sgn}\left({\mathrm{\&sigma;}}_s\right))-{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}\left|\right|{\mathrm{\&sigma;}}_s\left|\right|\\ \&le;-K_s{\mathrm{\&sigma;}}_s^T{\mathrm{\&sigma;}}_s+\left|\right|{\mathrm{\&sigma;}}_s\left|\right|{\mathrm{\&beta;}}_{\mathrm{ds}}-{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\underset{i=1}{\overset{n=3}{\mathrm{\&Sigma;}}}\left|{\mathrm{\&sigma;}}_{s,i}\right|-{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}}\left|\right|{\mathrm{\&sigma;}}_s\left|\right|\\ =-K_s{\mathrm{\&sigma;}}_s^T{\mathrm{\&sigma;}}_s+\left|\right|{\mathrm{\&sigma;}}_s\left|\right|({\mathrm{\&beta;}}_{\mathrm{ds}}-{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}-{\widetilde{\mathrm{\&beta;}}}_{\mathrm{ds}})\\ =-K_s{\mathrm{\&sigma;}}_s^T{\mathrm{\&sigma;}}_s\end{array}---\left(11\right)$

Visible, if σ _s≠ 0, then so sliding-mode surface σ _smeet reaching condition, σ _sasymptotic convergence in initial point, final tracking error e _sconverge on initial point, namely demonstrate,prove.

Note 1: the ω in formula (8) _cfor the control vector in the slow loop of NSV, it is also the expectation input vector in the fast loop of NSV simultaneously.

Note 2: in order to obtain the derivative of reference instruction signal, can allow it by following second order instruction references model:

$G\left(s\right)=\frac{{\mathrm{\&omega;}}_n^2}{s^2+2{\mathrm{\&xi;}}_n{\mathrm{\&omega;}}_{n}s+{\mathrm{\&omega;}}_n^2}---\left(12\right)$

Wherein, ω _nand ξ _nbe parameter to be designed, concrete meaning refers to free-running frequency and damping ratio respectively.

2, NSV fast loop Controller gain variations

Because the slow loop of NSV is only subject to composite interference D _simpact, therefore in slow loop, have employed the controller based on Nonlinear Disturbance Observer.In fast loop, the order of magnitude for the interference of speed circuit system peripheral is far longer than the order of magnitude of system indeterminate, adopts Nonlinear Disturbance Observer technical finesse composite interference with sample; For the saturated limited problem of vehicle rudder, steering wheel deflection angle is exported the upper bound and is used for design control law, guarantee to export within the specific limits, and Design assistant variable, automatically steering wheel deflection angle is regulated to export by adaptive law, in order to avoid when the deflection angle upper bound is excessive, export excessive phenomenon; Consider that RBFNNs can approach arbitrary continuation function with arbitrary accuracy, adopt RBFNNs to break down in situation to steering wheel here and carry out fault-tolerant compensation.Particularly, utilize RBFNNs to estimate the part that actuator failures lost efficacy, in design of control law, it is offset, thus make aircraft stabilized flight.

The affine nonlinear system equation in fast loop is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&omega;}=f_f\left(\mathrm{\&omega;}\right)}+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+D_f\\ y={\mathrm{\&omega;}}_c\end{array}\right.---\left(13\right)$

In formula, ω=[p, q, r] ^tfor current pose angle rate signal, p, q and r represent roll angle speed, pitch rate and yawrate respectively, representing ω differentiate, when considering steering wheel breakdown loss usefulness, in the affine nonlinear system equation in fast loop, adding performance factors M=diag{m ₁, m ₂, m ₃, m _ithe remaining control rate coefficient of i-th actuator, wherein 0 < m _i≤ 1, work as m _iwhen=1, represent that i-th actuator does not break down, i=1,2,3.The affine nonlinear system equation in fast loop is rewritten as:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&omega;}}=f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{M\&delta;}\left(v\right)+D_f\\ y={\mathrm{\&omega;}}_c\end{array}\right.---\left(14\right)$

For ease of designing fault-tolerant sliding formwork control law, formula (14) is converted to:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&omega;}}=f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}\left(e_s\right)P_m(\mathrm{\&omega;},v)+D_f\\ y=\mathrm{\&omega;}\end{array}\right.---\left(15\right)$

Wherein P _m(ω, v)=L (e _s) g _f(ω) (M-I ₃) δ (v), I ₃for three-dimensional unit matrix, L (e _s) be the diagonal matrix in interference observer, L (e _s)=diag{L ₁(e _s), L ₂(e _s) ..., L _n(e _s), L _i(e _s) > 0 or L=diag{L ₁, L ₂..., L _n, L _i> 0, i=1,2,3.

The fast circuit system of NSV (15) control objectives is, in composite interference, when actuator saturation and steering wheel fault, designs fault-tolerant sliding mode controller and guarantees that closed-loop system (15) can tenacious tracking reference signal ω _c.

For convenience of design control law, tracking error is defined as:

e _f＝ω-ω _c＝[ω ₁-ω _c,1,ω ₂-ω _c,2,ω ₃-ω _c,3] ^T (16)

Sliding-mode surface elects following form as:

$s={\mathrm{Ce}}_f+{\&Integral;}_0^{t}P{e}_f\mathrm{dt}---\left(17\right)$

Wherein C=diag{c ₁, c ₂, c ₃, c _i> 0, P=diag{p ₁, p ₂, p ₃, p _i> 0.

Following hypothesis is needed before Controller gain variations is carried out to the fast circuit system of NSV:

Suppose 4: for the fast circuit system of NSV, composite interference D _f=[D _{f, 1}, D _{f, 2}, D _{f, 3}] ^t, there is a certain constant ζ in derivative bounded ₀make set up, wherein ζ ₀> 0 is unknown, i=1,2,3.

Suppose 5: to the fast circuit system of NSV, expect attitude angular velocity vector ω _ccontinuous and its first order derivative exists, and there is unknown constant Δ ₀> 0 and Δ ₁> 0 makes || ω _c||≤Δ ₀with set up.

Suppose 6: to the fast circuit system of NSV, state can be surveyed and ride gain matrix g _f(ω) generalized inverse exists.

Consider that radial base neural net can approach arbitrary continuation function with arbitrary accuracy, therefore can by P _m(ω, v) is expressed as following form

P _m(ω,v)＝W ^*Th(ω)+ε (18)

Wherein, W ^*∈ R ^{l × 3}for network best initial weights matrix and meet l is total nodes of network; H (ω) ∈ R ^lit is the radial basis function vector formed by Gaussian function; ε=[ε ₁, ε ₂, ε ₃] ^tfor the minimum approximation error of network, ε can be made arbitrarily small by adjustment number of network node and weights, might as well suppose here the unknown, i=1,2,3,

Design following Nonlinear Disturbance Observer to the composite interference D in the fast circuit system of NSV (15) _festimate:

$\left\{\begin{array}{c}{\hat{D}}_f=z+Q\left(e_f\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(e_f\right)(f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}{\hat{W}}^{T}h\left(\mathrm{\&omega;}\right)+{\hat{D}}_f-{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c)\end{array}\right.---\left(19\right)$

In formula, for the estimated value of composite interference in fast loop; Z is the state variable of interference observer, L (e _f) and Q (e _f) be intermediate variable, and q (e _f)=[q ₁(e _f), q ₂(e _f) ..., q _n(e _f)] ^t∈ R ⁿfor nonlinear function vector, ω _crepresent reference instruction signal, for the adaptive weight of radial base neural net.

Interference observer is exported differentiate can obtain:

$\begin{array}{c}{\stackrel{\stackrel{\&CenterDot;}{^}}{D}}_s=\stackrel{\&CenterDot;}{z}+\frac{\&PartialD;Q\left(e_f\right)}{{\&PartialD;e}_f}{\stackrel{\&CenterDot;}{e}}_f\\ =-L(f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}{\hat{W}}^{T}g\left(\mathrm{\&omega;}\right)+{\hat{D}}_f-{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c)+L(\stackrel{\&CenterDot;}{\mathrm{\&omega;}}-{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c)\\ =-L(f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}{\hat{W}}^{T}h\left(\mathrm{\&omega;}\right)+{\hat{D}}_f-{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c)\\ +L(f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}(W^{*T}h\left(\mathrm{\&omega;}\right)+\mathrm{\&epsiv;})+{\hat{D}}_f-{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c)\\ =L{\tilde{D}}_f+{\tilde{W}}^{T}h\left(\mathrm{\&omega;}\right)+\mathrm{\&epsiv;}\end{array}---\left(20\right)$

Wherein ${\tilde{D}}_f=D_f-{\hat{D}}_f,\tilde{W}=W^{*}-\hat{W}.$

For the stability of Analysis interference observer error, Lyapunov equation is elected as:

$V_{\mathrm{df}}=\frac{1}{2}{{\tilde{D}}_f}^T{\tilde{D}}_f---\left(21\right)$

To V _dfdifferentiate can obtain:

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_{\mathrm{df}}={{\tilde{D}}_f}^T{\stackrel{\stackrel{\&CenterDot;}{~}}{D}}_f\\ ={{\tilde{D}}_f}^T{\stackrel{\&CenterDot;}{D}}_f-{{\tilde{D}}_f}^{T}L{\tilde{D}}_f-{{\tilde{D}}_f}^T{\tilde{W}}^{T}h\left(\mathrm{\&omega;}\right)-{{\tilde{D}}_f}^T\mathrm{\&epsiv;}\\ \&le;-{{\tilde{D}}_f}^{T}L{\tilde{D}}_f+0.5{{\tilde{D}}_f}^T{\tilde{D}}_f+0.5{{\stackrel{\&CenterDot;}{D}}_f}^T{\stackrel{\&CenterDot;}{D}}_f+\mathrm{\&tau;}\left|\right|{\tilde{D}}_f\left|\right|\left|\right|\tilde{W}\left|\right|+0.5{{\tilde{D}}_f}^T{\tilde{D}}_f+0.5{\mathrm{\&epsiv;}}^T\mathrm{\&epsiv;}\\ \&le;-{{\tilde{D}}_f}^{T}L{\tilde{D}}_f+{{\tilde{D}}_f}^T{\tilde{D}}_f+0.5{\left|\right|{\stackrel{\&CenterDot;}{D}}_f\left|\right|}^2+0.5{\mathrm{\&tau;}}^2{\left|\right|{\tilde{D}}_f\left|\right|}^2+0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}\\ \&le;-{{\tilde{D}}_f}^{T}L{\tilde{D}}_f+{{\tilde{D}}_f}^T{\tilde{D}}_f+0.5{\left|\right|{\stackrel{\&CenterDot;}{D}}_f\left|\right|}^2+0.5{\mathrm{\&tau;}}^2{{\tilde{D}}_f}^T{\tilde{D}}_f+0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}\\ \&le;-{{\tilde{D}}_f}^T(L-(1+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f+0.5{\left|\right|{\stackrel{\&CenterDot;}{D}}_f\left|\right|}^2+0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}\end{array}---\left(22\right)$

Wherein || h (ω) ||≤τ, I ₃for three-dimensional unit matrix.

Consider hypothesis 4, can obtain:

$V_{\mathrm{df}}\&le;-{{\tilde{D}}_f}^T(L-(1+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f+\mathrm{\&zeta;}{\left|\right|\mathrm{\&omega;}\left|\right|}^2+0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}---\left(23\right)$

Wherein $\mathrm{\&zeta;}=0.5{\mathrm{\&zeta;}}_0^2.$

According to hypothesis 5, obtain:

||ω||＝||e _f+ω _c||≤||e _f||+||ω _c||≤||e _f||+Δ ₀ (24)

Formula (24) is brought into (23) to obtain:

$\begin{array}{c}{V}_{\mathrm{df}}\&le;-{{\tilde{D}}_f}^T(L-(1+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f+\mathrm{\&zeta;}{\left(\right|\left|e_f\right||+{\mathrm{\&Delta;}}_0)}^2+0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}\\ \&le;-{{\tilde{D}}_f}^T(L-(1+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f+\mathrm{\&zeta;}{\left|\right|e_f\left|\right|}^2+2\mathrm{\&zeta;}{\mathrm{\&Delta;}}_0\\ +{{\mathrm{\&Delta;}}_0}^2+0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}\end{array}---\left(25\right)$

Below by the fault-tolerant sliding mode controller based on the fast circuit system of interference observer, neural network and sliding mode technology design NSV.

Consideration formula (16), obtains sliding-mode surface differentiate:

$\begin{array}{c}\stackrel{\&CenterDot;}{s}=C{\stackrel{\&CenterDot;}{e}}_f+{\mathrm{Pe}}_f\\ {\mathrm{Cf}}_f+{\mathrm{Cg}}_f\mathrm{\&delta;}\left(v\right)+{\mathrm{CL}}^{-1}{W}^{*T}h\left(\mathrm{\&omega;}\right)+{\mathrm{CL}}^{-1}\mathrm{\&epsiv;}+{\mathrm{CD}}_f-C{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_c+{\mathrm{Pe}}_f\end{array}---\left(26\right)$

In order to solve actuator saturation problem, design of control law is as follows:

Wherein, U _m=diag{u _1M, u _2M..., u _mM∈ R ^{m × m}, u _iMbe the saturation limit amplitude of i-th actuator, i=1,2 ..., m; Λ _s=diag{|s ₁|, | s ₂| ..., | s _n|, for positive parameter, $\stackrel{\&OverBar;}{v}=[{\stackrel{\&OverBar;}{v}}_1,{\stackrel{\&OverBar;}{v}}_2,...,{\stackrel{\&OverBar;}{v}}_n]\&Element;R^n,$ And there is following form:

${\stackrel{\&OverBar;}{v}}_i=\frac{\left|s_i\right|\mathrm{sat}\left(s_i\right)}{\left|\right|s\left|\right|+{\mathrm{\&gamma;}}_i(\frac{e^{{\mathrm{\&kappa;\&chi;}}_i}+e^{-\mathrm{\&kappa;}{\mathrm{\&chi;}}_i}}{2}-1)+{\mathrm{\&epsiv;}}_v}---\left(28\right)$

S _ifor i-th element of s, γ _i> 0, κ > 0 and ε _v> 0 is positive parameter, sat (s _i) be saturation function between [-1,1], its form is as follows:

$\mathrm{sat}\left(s_i\right)=\left\{\begin{array}{cc}1,& s_i\&GreaterEqual;{\mathrm{\&xi;}}_i\\ s_i/{\mathrm{\&xi;}}_i,& \left|s_i\right|\&le;{\mathrm{\&xi;}}_i\\ -1,& s_i\&le;-{\mathrm{\&xi;}}_i\end{array}\right.---\left(29\right)$

Wherein ξ _i> 0 is the boundary layer parameters of the saturation function of design, χ=[χ ₁, χ ₂..., χ _n] ^tfor the auxiliary variable of design, its adaptive law is designed to:

Wherein,

K _f＝K _f ^T＞0, ${\mathrm{\&Lambda;}}_{\mathrm{\&Xi;}}=\mathrm{diag}\{{0.5\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_1},{0.5\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_2},...,0.5{\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_n}\},\mathrm{\&Xi;}=\mathrm{diag}\{0.5e^{{\mathrm{\&kappa;\&chi;}}_1},{0.5e}^{{\mathrm{\&kappa;\&chi;}}_2},...,0.5e^{{\mathrm{\&kappa;\&chi;}}_n}\},$ V _rDfor compensation term, its concrete form is:

$v_{\mathrm{rD}}=\left\{\begin{array}{cc}\frac{(\widehat{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0|\left|e_f\right||+\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0^2)s}{{\left|\right|s\left|\right|}^2},& \left|\right|s\left|\right|>\mathrm{\&sigma;}\\ 0,& \left|\right|s\left|\right|\&le;\mathrm{\&sigma;}\end{array}\right.---\left(31\right)$

Wherein σ > 0 is positive parameter, for the estimated value of ζ.

According to Λ _Ξcan draw with the definition of Ξ:

$\stackrel{\&CenterDot;}{\mathrm{\&Xi;}}={\mathrm{\&Lambda;}}_{\mathrm{\&Xi;}}\stackrel{\&CenterDot;}{\mathrm{\&chi;}}---\left(32\right)$

According to formula (27), can obtain:

By formula (28)-(29), known:

$\left|{\stackrel{\&OverBar;}{v}}_i\right|=\frac{\left|s_i\right|}{\left|\right|s\left|\right|+{\mathrm{\&gamma;}}_i(\frac{e^{{\mathrm{\&kappa;\&chi;}}_i}+e^{-\mathrm{\&kappa;}{\mathrm{\&chi;}}_i}}{2}-1)+{\mathrm{\&epsiv;}}_v}---\left(34\right)$

Because $\left|s_i\right|\&le;\left|\right|s\left|\right|,\frac{e^{{\mathrm{\&kappa;\&chi;}}_i}+e^{-{\mathrm{\&kappa;\&chi;}}_i}}{2}\&GreaterEqual;1,$ γ _i> 0, κ > 0 and ε _v> 0, thus obtain

$\left|{\stackrel{\&OverBar;}{v}}_i\right|<1\mathrm{and}\left|\right|\stackrel{\&OverBar;}{v}\left|\right|<1---\left(35\right)$

(35) are brought into (33), obtain:

||v||≤||U _M|| (36)

From formula (36), the output of designed control law exports at actuator within the scope in the upper bound.

The stability of lower surface analysis closed-loop system, Lyapunov equation is elected as:

$V=\frac{1}{2}{s}^{T}s+\frac{1}{2}{{\tilde{D}}_f}^T{\tilde{D}}_f+\frac{1}{2}{\widetilde{\mathrm{\&epsiv;}}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}^{-1}\widetilde{\mathrm{\&epsiv;}}+\frac{1}{2\mathrm{\&rho;}}{\widetilde{\mathrm{\&zeta;}}}^2+\frac{1}{2}\mathrm{tr}\left({\tilde{W}}^T{\mathrm{\&Gamma;}}_W^{-1}\tilde{W}\right)+\frac{1}{2}{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}---\left(37\right)$

Wherein, ${\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}={\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}^T>0,$ ${\mathrm{\&Gamma;}}_W={\mathrm{\&Gamma;}}_W^T>0$ Be design parameter with ρ > 0, $\widetilde{\mathrm{\&epsiv;}}=\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}-\widehat{\mathrm{\&epsiv;}},$ for estimated value, and to have $\stackrel{\stackrel{\&CenterDot;}{~}}{\mathrm{\&epsiv;}}=-\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&epsiv;}},\widetilde{\mathrm{\&zeta;}}=\mathrm{\&zeta;}-\widehat{\mathrm{\&zeta;}},$ for the estimated value of ζ, and have

Consideration formula (25)-(29), can obtain formula (37) differentiate:

By formula (30), (32) are brought formula (38) into and are obtained:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;-s^T\mathrm{Ks}-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}+s^T{\mathrm{CL}}^{-1}{\tilde{W}}^{T}h\left(\mathrm{\&omega;}\right)+s^T{\mathrm{CL}}^{-1}\widetilde{\mathrm{\&epsiv;}}+s^{T}C{\tilde{D}}_f\\ -{{\tilde{D}}_f}^T(L-(1+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f+\widetilde{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widetilde{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0\left|\right|e_f\left|\right|+\widetilde{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0^2\\ +0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}-{\widetilde{\mathrm{\&epsiv;}}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&epsiv;}}-\frac{1}{\mathrm{\&rho;}}\widetilde{\mathrm{\&zeta;}}\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&zeta;}}-\mathrm{tr}\left({\hat{W}}^T{\mathrm{\&Gamma;}}_W^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{W}\right)\\ \&le;{-s}^T\mathrm{Ks}-{{\tilde{D}}_f}^T(L-(1+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}+s^{T}C{L}^{-1}{\tilde{W}}^{T}h\left(\mathrm{\&omega;}\right)\\ +s^T{\mathrm{CL}}^{-1}\widetilde{\mathrm{\&epsiv;}}+0.5s^T\left({\mathrm{CC}}^T\right)s+0.5{{\tilde{D}}_f}^T{\tilde{D}}_f+\widetilde{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widetilde{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0\left|\right|e_f\left|\right|\\ +\widetilde{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0^2+0.5{\left|\right|\widetilde{W\left|\right|}}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}-{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&epsiv;}}-\frac{1}{\mathrm{\&rho;}}\widetilde{\mathrm{\&zeta;}}\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&zeta;}}-\mathrm{tr}\left({\tilde{W}}^T{\mathrm{\&Gamma;}}_W^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{W}\right)\\ \&le;{-s}^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(L-(1.5+{0.5\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}\\ +s^T{\mathrm{CL}}^{-1}{\tilde{W}}^{T}h\left(\mathrm{\&omega;}\right)+s^T{\mathrm{CL}}^{-1}\widetilde{\mathrm{\&epsiv;}}+\widetilde{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widetilde{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0\left|\right|e_f\left|\right|+\widetilde{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0^2\\ +0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}-{\widetilde{\mathrm{\&epsiv;}}}^T{\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&epsiv;}}-\frac{1}{\mathrm{\&rho;}}\widetilde{\mathrm{\&zeta;}}\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&zeta;}}-\mathrm{tr}\left({\stackrel{\&CenterDot;}{W}}^T{\mathrm{\&Gamma;}}_W^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{W}\right)\end{array}---\left(39\right)$

Design following parameter update law:

$\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&epsiv;}}={\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}({\left({\mathrm{CL}}^{-1}\right)}^{T}s-k_{\mathrm{\&epsiv;}}\widehat{\mathrm{\&epsiv;}})---\left(40\right)$

$\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&zeta;}}=\mathrm{\&rho;}({\left|\right|e_f\left|\right|}^2+2{\mathrm{\&Delta;}}_0|\left|e_f\right||+{\mathrm{\&Delta;}}_0^2-k_{\mathrm{\&zeta;}}\widehat{\mathrm{\&zeta;}})---\left(41\right)$

${\stackrel{\stackrel{\&CenterDot;}{^}}{w}}_i={\mathrm{\&Gamma;}}_W(s^T{\left(C_1{L}^{-1}\right)}_{i}h\left(\mathrm{\&omega;}\right)-k_W{\hat{w}}_i)---\left(42\right)$

Wherein, k _ε> 0, k _ζ> 0 and k _w> 0 is design parameter.

Bring formula (40) into (39) can obtain:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;-s^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(L-(1.5+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}\\ +s^T{\mathrm{CL}}^{-1}{\tilde{W}}^{T}h\left(\mathrm{\&omega;}\right)+\widetilde{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widetilde{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0\left|\right|e_f\left|\right|+\widetilde{\mathrm{\&xi;}}{\mathrm{\&Delta;}}_0^2+0.5{\left|\right|\tilde{w}\left|\right|}^2\\ +0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}+k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widehat{\mathrm{\&epsiv;}}-\frac{1}{\mathrm{\&rho;}}\widetilde{\mathrm{\&zeta;}}\stackrel{\stackrel{\&CenterDot;}{^}}{\mathrm{\&zeta;}}-\mathrm{tr}\left({\tilde{W}}^T{\mathrm{\&Gamma;}}_W^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{W}\right)\end{array}---\left(43\right)$

Bring formula (41) into (43) can obtain:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;{-s}^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(l-(1.5+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}\\ +s^T{\mathrm{CL}}^{-1}{\tilde{W}}^{T}h\left(\mathrm{\&omega;}\right)+0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}+k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widehat{\mathrm{\&epsiv;}}\\ +k_{\mathrm{\&zeta;}}\widetilde{\mathrm{\&zeta;}}\widehat{\mathrm{\&zeta;}}-\mathrm{tr}\left({\tilde{W}}^T{\mathrm{\&Gamma;}}_W^{-1}\stackrel{\stackrel{\&CenterDot;}{^}}{W}\right)\end{array}---\left(44\right)$

Consideration formula (42), can obtain

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;{-s}^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(L-(1.5+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}\\ +0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}+k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widehat{\mathrm{\&epsiv;}}+k_{\mathrm{\&zeta;}}\widetilde{\mathrm{\&zeta;}}\widehat{\mathrm{\&zeta;}}+k_W\mathrm{tr}\left({\tilde{W}}^T\hat{W}\right)\\ \&le;{-s}^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(L-(1.5+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}\\ +0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}+k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\mathrm{\&epsiv;}-k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widetilde{\mathrm{\&epsiv;}}+k_{\mathrm{\&zeta;}}\widetilde{\mathrm{\&zeta;}}\mathrm{\&zeta;}-k_{\mathrm{\&zeta;}}{\widetilde{\mathrm{\&zeta;}}}^2+k_W\mathrm{tr}\left({\tilde{W}}^T\hat{W}\right)\\ \&le;{-s}^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(L-(1.5+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}\\ +0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}+0.5k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widetilde{\mathrm{\&epsiv;}}+0.5k_{\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}}^T\mathrm{\&epsiv;}-k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widetilde{\mathrm{\&epsiv;}}+0.5k_{\mathrm{\&zeta;}}{\widetilde{\mathrm{\&zeta;}}}^2\\ +0.5k_{\mathrm{\&zeta;}}{\mathrm{\&zeta;}}^2-k_{\mathrm{\&zeta;}}{\widetilde{\mathrm{\&zeta;}}}^2+k_W\mathrm{tr}\left({\tilde{W}}^T\hat{W}\right)\\ \&le;{-s}^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(L-(1.5+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}\\ +0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5(k_{\mathrm{\&epsiv;}}+1){\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}-0.5k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widetilde{\mathrm{\&epsiv;}}-0.5k_{\mathrm{\&zeta;}}{\mathrm{\&zeta;}}^2+k_W\mathrm{tr}\left({\tilde{W}}^T\hat{W}\right)\end{array}---\left(45\right)$

Consider as lower inequality:

$\mathrm{tr}\left({\tilde{W}}^T\hat{W}\right)=\mathrm{tr}\left({\tilde{W}}^T(W^{*}-\tilde{W})\right)\&le;{\left|\right|\tilde{W}\left|\right|\left|\right|W^{*}\left|\right|-\left|\right|\tilde{W}\left|\right|}^2\&le;-0.5{\left|\right|\tilde{W}\left|\right|}^2+0.5{\stackrel{\&OverBar;}{W}}^2---\left(46\right)$

Formula (46) is substituted into formula (45) can obtain:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;-s^T(K-0.5{\mathrm{CC}}^T)s-{{\tilde{D}}_f}^T(L-(1.5+0.5{\mathrm{\&tau;}}^2)I_3){\tilde{D}}_f-0.5k_{\mathrm{\&epsiv;}}{\widetilde{\mathrm{\&epsiv;}}}^T\widetilde{\mathrm{\&epsiv;}}-0.5k_{\mathrm{\&zeta;}}{\widetilde{\mathrm{\&zeta;}}}^2\\ -{\mathrm{\&Xi;}}^T\mathrm{\&Xi;}-(0.5k_W-0.5){\left|\right|\tilde{W}\left|\right|}^2+0.5(k_{\mathrm{\&epsiv;}}+1)+0.5k_{\mathrm{\&zeta;}}{\mathrm{\&zeta;}}^2+0.5k_W{\left|\right|W\left|\right|}^2\\ \&le;-{\mathrm{\&kappa;}}_{f}V+M_f\end{array}---\left(47\right)$

Wherein,

$\begin{array}{c}{\mathrm{\&kappa;}}_f=\min \{2{\mathrm{\&lambda;}}_{\min }(K-{\mathrm{CC}}^T),{\mathrm{\&lambda;}}_{\min }(2L-(3+{\mathrm{\&tau;}}^2)I_3),k_{\mathrm{\&epsiv;}}/{\mathrm{\&lambda;}}_{\max }\left({\mathrm{\&Gamma;}}_{\mathrm{\&epsiv;}}^{-1}\right),k_{\mathrm{\&zeta;}}\mathrm{\&rho;},(k_W-1)/{\mathrm{\&lambda;}}_{\max }\left({\mathrm{\&Gamma;}}_W^{-1}\right),2\}>0,\\ M_f=0.5(k_{\mathrm{\&epsiv;}}+1){\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}^T\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}+0.5k_{\mathrm{\&zeta;}}{\mathrm{\&zeta;}}^2+0.5k_W{\left|\right|\stackrel{\&OverBar;}{W}\left|\right|}^2>0.\end{array}$

Can obtain formula (47) both sides integration:

$0\&le;V\&le;\frac{M_f}{{\mathrm{\&kappa;}}_f}+(V\left(0\right)-\frac{M_f}{{\mathrm{\&kappa;}}_f})e^{-{\mathrm{\&kappa;}}_{f}t}---\left(48\right)$

Following theorem can be obtained according to above-mentioned analytic process:

Theorem 2: there is actuator failure and input the fast circuit system of saturated limited NSV for satisfied hypothesis 4-6, Nonlinear Disturbance Observer is by formula (19) design, parameter update law is taken as formula (30), formula (40)-Shi (42), a sliding-mode surface design accepted way of doing sth (17) form, saturated faults-tolerant control rule is by formula (27) and formula (28) design, then all signals of closed-loop system are all ultimately uniform boundary.

Prove: the Lyapunov function shown in selecting type (37).From above-mentioned analytic process formula (38)-Shi (48), all signals of closed-loop system are all bounded.

Card is finished.

Note 3: the controller designed by the present invention does not need the concrete failure diagnosis information directly obtained about topworks, but process by introducing neural network, thus make controller have stronger fault-tolerant ability to actuator failure; On the other hand, as can be seen from the expression formula of control law, the controlled quentity controlled variable of trying to achieve all in saturation range, and then eliminates the saturated impact brought to system of input.

Claims (6)

1. a fault-tolerant sliding-mode control for Near Space Flying Vehicles, is characterized in that, comprise the following steps:

Step 1), according to singular perturbation principle and time-scale separation principle, the stance loop of aircraft is decomposed into slow loop and fast loop;

Step 2), respectively the control system in the control system in slow loop and fast loop is transformed into corresponding affine nonlinear system equation form;

Step 3), the controller in slow loop and fast loop is generated respectively according to the affine nonlinear system equation in slow loop, fast loop;

Step 4), utilize step 3) in generate slow loop controller and fast loop control unit robust control is carried out to aircraft.

2. the fault-tolerant sliding-mode control of Near Space Flying Vehicles according to claim 1, is characterized in that, step 2) in affine nonlinear equation corresponding to the control system in described slow loop be:

$\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}=f_s\left(\mathrm{\&Omega;}\right)+g_s\left(\mathrm{\&Omega;}\right){\mathrm{\&omega;}}_c+D_s$

In formula, Ω=[α, β, μ] ^tfor current pose angle signal, α, β and μ represent the angle of attack, yaw angle and roll angle respectively, represent Ω differentiate; f _s(Ω)=[f _s1, f _s2, f _s3] ^t, ω _cfor the control law of slow loop controller; D _srepresent 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 represents vehicle mass; V represents vehicle flight speeds; represent dynamic pressure; S represents wing area of reference; γ represents pitch angle; T represents motor power; G represents acceleration of gravity; δ _yrepresent thrust vectoring rudder face deflection angle laterally; δ _zrepresent thrust vectoring rudder face deflection angle longitudinally; C _{l, α}represent the lift coefficient caused by angle of attack α; C _{y, β}represent the lateral force coefficient caused by yaw angle β;

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

3. the fault-tolerant sliding-mode control of Near Space Flying Vehicles according to claim 2, is characterized in that, step 2) in affine nonlinear equation corresponding to the control system in described fast loop be:

$\stackrel{\&CenterDot;}{\mathrm{\&omega;}}=f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+D_f$

In formula, ω=[p, q, r] ^tfor current pose angle rate signal, p, q and r represent roll angle speed, pitch rate and yawrate respectively, represent ω differentiate, f _f(ω)=[f _f1, f _f2, f _f3] ^t,

$\begin{array}{c}{f}_{f1}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_z+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_z+n_{\mathrm{aero}}{I}_{\mathrm{xz}}{I}_y\\ +(I_{\mathrm{xy}}^2{I}_z-I_y{I}_z^2+I_y^2{I}_z-I_{\mathrm{xz}}^2{I}_y)\mathrm{qr}+(I_y{I}_z{I}_{\mathrm{xz}}-I_{\mathrm{xz}}{I}_y^2+I_x{I}_y{I}_{\mathrm{xz}})\mathrm{pq}\\ +(I_y{I}_z{I}_{\mathrm{xy}}+I_x{I}_z{I}_{\mathrm{xy}}-I_z^2{I}_{\mathrm{xy}})\mathrm{pr}-I_{\mathrm{xy}}{I}_{\mathrm{xz}}{I}_y(q^2-p^2)-I_{\mathrm{xz}}{I}_{\mathrm{xy}}{I}_z(p^2-r^2))\end{array},$

$\begin{array}{c}{f}_{f2}=\frac{1}{I_x{I}_y^2{I}_z-I_z{I}_y{I}_{\mathrm{xy}}^2-I_y^2{I}_{\mathrm{xz}}^2}(-l_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_y{I}_z+m_{\mathrm{aero}}(I_x{I}_y{I}_z-2I_z{I}_{\mathrm{xy}}^2-I_y{I}_{\mathrm{xz}}^2))\\ -I_{\mathrm{xy}}{I}_y{I}_{\mathrm{xz}}{n}_{\mathrm{aero}}-I_{\mathrm{xy}}(I_y{I}_z{I}_{\mathrm{xz}}+I_x{I}_y{I}_{\mathrm{xz}}-I_y^2{I}_{\mathrm{xz}})\mathrm{pq}\\ -(I_{\mathrm{xy}}+I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{qr}+(I_y{I}_{\mathrm{xy}}^2{I}_{\mathrm{xz}}+I_{\mathrm{xz}}-I_{\mathrm{xy}}^2{I}_z)(p^2-r^2)\\ +(I_z-I_x-I_{\mathrm{xy}}(I_{\mathrm{xy}}{I}_z^2-I_x{I}_z{I}_{\mathrm{xy}}-I_y{I}_z{I}_{\mathrm{xy}}))\mathrm{pr})\end{array},$

$\begin{array}{c}{f}_{f3}=\frac{1}{I_x{I}_y{I}_z-I_{\mathrm{xy}}^2{I}_z-I_{\mathrm{xz}}^2{I}_y}(l_{\mathrm{aero}}{I}_y{I}_{\mathrm{xy}}+m_{\mathrm{aero}}{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}(I_x{I}_y-I_{\mathrm{xy}}^2)n_{\mathrm{aero}}\\ +(I_y{I}_{\mathrm{xz}}^2+I_x^2{I}_y-I_x{I}_{\mathrm{xy}}^2-I_x{I}_y^2-I_y{I}_{\mathrm{xy}}^2)\mathrm{pq}\\ +(I_y^2{I}_{\mathrm{xz}}-I_y{I}_z{I}_{\mathrm{xz}}+I_{\mathrm{xy}}^2{I}_{\mathrm{xz}}-I_x{I}_y{I}_{\mathrm{xz}}+I_{\mathrm{xz}}{I}_{\mathrm{xy}}^2)\mathrm{qr}+I_{\mathrm{xy}}{I}_{\mathrm{xz}}^2(p^2-r^2)\\ +(I_z{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_x{I}_{\mathrm{xy}}{I}_{\mathrm{xz}}-I_y{I}_{\mathrm{xy}}{I}_{\mathrm{xz}})\mathrm{pr}+(I_x{I}_y{I}_{\mathrm{xy}}-I_{\mathrm{xy}}^3)(p^2-q^2))\end{array},$

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

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

I _x, I _yand I _zrepresent the moment of inertia around x, y and z axes respectively; I _xy, I _xzand I _yzrepresent the product of inertia; B represents spanwise length; C represents mean aerodynamic chord; C _{l, β}represent the rolling moment coefficient caused by yaw angle β, C _l,prepresent the rolling moment increment coefficient caused by roll angle speed p; C _l,rrepresent the rolling moment increment coefficient caused by yawrate r; C _{m, α}represent the pitching moment coefficient caused by angle of attack α; C _m,qrepresent the pitching moment increment coefficient caused by pitch rate q; C _{n, β}represent the yawing moment coefficient caused by yaw angle β; C _n,prepresent the yawing increment coefficient caused by roll angle speed p; C _n,rrepresent the yawing increment coefficient caused by yawrate r;

g _f(ω)＝g _f1g _fδ(ω)，

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

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

represent by aileron rudder δ _athe rolling moment increment coefficient caused; represent by elevating rudder δ _ethe rolling moment increment coefficient caused; represent by yaw rudder δ _rthe rolling moment increment coefficient caused; represent by aileron rudder δ _athe pitching moment increment coefficient caused; represent by elevating rudder δ _ethe pitching moment increment coefficient caused; represent by yaw rudder δ _rthe pitching moment increment coefficient caused; represent by aileron rudder δ _athe yawing increment coefficient caused; represent by elevating rudder δ _ethe yawing increment coefficient caused; represent by yaw rudder δ _rthe yawing increment coefficient caused; X _trepresent the distance of engine jet pipe distance barycenter;

D _ffor fast loop composite interference, this composite interference utilizes Nonlinear Disturbance Observer to carry out approximation timates, v=[v ₁, v ₂, v ₃, v ₄, v ₅] ^tfor control law and the actuator input vector of fast loop control unit, δ (v)=[δ _a, δ _e, δ _r, δ _y, δ _z] ^tfor the output vector by actuator saturation properties influence, specifically meet following relation:

${\mathrm{\&delta;}}_a=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1>{\mathrm{\&delta;}}_{\mathrm{aM}}\\ v_1,& -{\mathrm{\&delta;}}_{\mathrm{aM}}\&le;v_1\&le;{\mathrm{\&delta;}}_{\mathrm{aM}}\\ -{\mathrm{\&delta;}}_{\mathrm{aM}},& v_1<-{\mathrm{\&delta;}}_{\mathrm{aM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_e=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2>{\mathrm{\&delta;}}_{\mathrm{eM}}\\ v_2,& -{\mathrm{\&delta;}}_{\mathrm{eM}}\&le;v_2\&le;{\mathrm{\&delta;}}_{\mathrm{eM}}\\ -{\mathrm{\&delta;}}_{\mathrm{eM}},& v_2<-{\mathrm{\&delta;}}_{\mathrm{eM}}\end{array}\right.,$ ${\mathrm{\&delta;}}_r=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3>{\mathrm{\&delta;}}_{\mathrm{rM}}\\ v_3,& -{\mathrm{\&delta;}}_{\mathrm{rM}}\&le;v_3\&le;{\mathrm{\&delta;}}_{\mathrm{rM}}\\ -{\mathrm{\&delta;}}_{\mathrm{rM}},& v_3<-{\mathrm{\&delta;}}_{\mathrm{rM}}\end{array}\right.,$

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

V ₁, v ₂, v ₃, v ₄and v ₅be the element of vector v, δ _a, δ _e, δ _r, δ _yand δ _zrepresent respectively aileron rudder kick angle, elevator angle, control surface steering angle, push vector helm laterally with the deflection angle of longitudinal direction; δ _aM, δ _eM, δ _rM, δ _yMand δ _zMbe respectively the saturated limited value of aileron rudder corner, elevating rudder corner, yaw rudder corner, push vector helm laterally deflection angle and push vector helm longitudinally deflection angle.

4. the fault-tolerant sliding-mode control of Near Space Flying Vehicles according to claim 3, is characterized in that, step 3) described in generate the concrete steps of slow loop controller as follows:

Step 3.1.1), utilize Nonlinear Disturbance Observer to approach the composite interference in slow loop:

$\left\{\begin{array}{c}{\hat{D}}_s=z+Q\left(\mathrm{\&Omega;}\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(\mathrm{\&Omega;}\right)z-L\left(\mathrm{\&Omega;}\right)(Q\left(\mathrm{\&Omega;}\right)+f_s\left(\mathrm{\&Omega;}\right)+g_s\left(\mathrm{\&Omega;}\right){\mathrm{\&omega;}}_c)\end{array}\right.$

In formula, for the estimated value of composite interference in slow loop; Z is the state variable of Nonlinear Disturbance Observer, and L (Ω) and Q (Ω) they are intermediate variable, and for the diagonal matrix that diagonal element is greater than zero, Q (Ω)=[q ₁(Ω), q ₂(Ω) ..., q _n(Ω)] ^t∈ R ⁿfor nonlinear function vector, n is the dimension of external disturbance;

Step 3.1.2), according to step 3.1.1) in the estimated value of composite interference in the slow loop that obtains common slip-form is adopted to obtain the controller in slow loop:

${\mathrm{\&omega;}}_c=-g_s{\left(\mathrm{\&Omega;}\right)}^{-1}(f_s\left(\mathrm{\&Omega;}\right)-{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_c+{\hat{D}}_s+K_s{e}_s+{\widehat{\mathrm{\&beta;}}}_{\mathrm{ds}}\mathrm{sgn}\left(e_s\right))$

In formula, g _s(Ω) ^-1represent matrix g _s(Ω) invert; e _s=Ω-Ω _cfor slow Trace-on-Diagram error, Ω _crepresent the reference instruction signal preset, β _dsfor slow loop composite interference evaluated error upper dividing value, k _sfor the parameter matrix of slow loop sliding-mode surface, specifically meet following relation: K _s=diag{k _s1, k _s2, k _s3> 0.

5. the fault-tolerant sliding-mode control of Near Space Flying Vehicles according to claim 4, is characterized in that, step 3) described in generate the concrete steps of fast loop control unit as follows:

Step 3.2.1), utilize radial base neural net to estimate actuator failures part:

$P_m(\mathrm{\&omega;},v)={\hat{W}}^{T}h\left(\mathrm{\&omega;}\right)+\mathrm{\&epsiv;}$

In formula, P _mfor the estimated value of actuator failures part; for the weights of radial base neural net, for i-th vectorial adaptive law, k _wand Γ _wbe respectively the real number in neural network weight adaptive law and parameter matrix, and k _w> 0, for Γ _wtransposed matrix, for fast loop sliding-mode surface, s ^trepresent and transposition is carried out to column vector s; H (ω)=[h ₁, h ₂..., h _l] ^tfor radial basis vector, l is the total nodes of network, ω=[p, q, r] ^tfor network input vector, in h (ω), element adopts Gaussian bases form, namely c _kfor the center vector of a network kth node, b _kfor the sound stage width parameter of a network kth node, k=1,2 ..., l;

Step 3.2.2), utilize Nonlinear Disturbance Observer to approach the composite interference in fast loop:

$\left\{\begin{array}{c}{\hat{D}}_f=z+Q\left(e_f\right)\\ \stackrel{\&CenterDot;}{z}=-L\left(e_f\right)(f_f\left(\mathrm{\&omega;}\right)+g_f\left(\mathrm{\&omega;}\right)\mathrm{\&delta;}\left(v\right)+L^{-1}{\hat{W}}^{T}h\left(x\right)+{\hat{D}}_f-{\mathrm{\&omega;}}_c)\end{array}\right.$

In formula, for the estimated value of composite interference in fast loop; Z is the state variable of interference observer, L (e _f) and Q (e _f) be intermediate variable, and q (e _f)=[q ₁(e _f), q ₂(e _f) ..., q _n(e _f)] ^t∈ R ⁿfor nonlinear function vector, ω _crepresent the reference instruction signal preset, for the adaptive weight of radial base neural net;

Step 3.2.3), according to step 3.2.1) in the estimated value P of actuator failures part that obtains _m, and step 3.2.2) in the estimated value of composite interference in the fast loop that obtains generate the controller in fast loop:

Wherein, U _m=diag{u _1M, u _2M..., u _mM∈ R ^{m × m}, u _iMbe the saturation limit amplitude of i-th actuator, i=1,2 ..., m;

Λ _s=diag{|s ₁|, | s ₂| ..., | s _n|, ε _u> 0 is positive parameter, $\stackrel{\&OverBar;}{v}=[{\stackrel{\&OverBar;}{v}}_1,{\stackrel{\&OverBar;}{v}}_2,...,{\stackrel{\&OverBar;}{v}}_n]\&Element;R^n,$ And there is following form:

${\stackrel{\&OverBar;}{v}}_i=\frac{\left|s_i\right|\mathrm{sat}\left(s_i\right)}{\left|\right|s\left|\right|+{\mathrm{\&gamma;}}_i(\frac{e^{{\mathrm{\&kappa;\&chi;}}_i}+e^{-{\mathrm{\&kappa;\&chi;}}_i}}{2}-1)+{\mathrm{\&epsiv;}}_v}$

S _ifor i-th element of s, γ _i> 0, κ > 0, ε _v> 0, sat (s _i) be saturation function between [-1,1], its form is as follows:

$\mathrm{sat}\left(s_i\right)=\left\{\begin{array}{cc}1,& s_i\&GreaterEqual;{\mathrm{\&xi;}}_i\\ s_i/{\mathrm{\&xi;}}_i,& \left|s_i\right|\&le;{\mathrm{\&xi;}}_i\\ -1,& s_i\&le;-{\mathrm{\&xi;}}_i\end{array}\right.$

Wherein ξ _i> 0 is the boundary layer parameters of saturation function, χ=[χ ₁, χ ₂..., χ _n] ^tfor auxiliary variable, its adaptive law is:

Wherein K _f=K _f ^t> 0, ${\mathrm{\&Lambda;}}_{\mathrm{\&Xi;}}=\mathrm{diag}\{0.5{\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_1},{0.5\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_2},...,{0.5\mathrm{\&kappa;e}}^{{\mathrm{\&kappa;\&chi;}}_n}\},$ $\mathrm{\&Xi;}=\mathrm{diag}\{{0.5e}^{{\mathrm{\&kappa;\&chi;}}_1},{0.5e}^{{\mathrm{\&kappa;\&chi;}}_2},...,{0.5e}^{{\mathrm{\&kappa;\&chi;}}_n}\},$ V _rDfor compensation term, its concrete form is:

$v_{\mathrm{rD}}=\left\{\begin{array}{cc}\frac{(\widehat{\mathrm{\&zeta;}}{\left|\right|e_f\left|\right|}^2+2\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0|\left|e_f\right||+\widehat{\mathrm{\&zeta;}}{\mathrm{\&Delta;}}_0^2)s}{{\left|\right|s\left|\right|}^2},& \left|\right|s\left|\right|>\mathrm{\&sigma;}\\ 0,& \left|\right|s\left|\right|\&le;\mathrm{\&sigma;}\end{array}\right.$

Wherein σ > 0, $\mathrm{\&zeta;}=0.5{\mathrm{\&zeta;}}_0^2,$ $\left|\right|{\stackrel{\&CenterDot;}{D}}_f\left|\right|\&le;{\mathrm{\&zeta;}}_0\left|\right|\mathrm{\&omega;}\left|\right|,$ for the estimated value of ζ.

6. the fault-tolerant sliding-mode control of Near Space Flying Vehicles according to claim 5, is characterized in that, step 4) described in utilize slow loop controller and fast loop control unit to carry out robust control to aircraft concrete steps as follows:

Step 4.1), attitude angle current demand signal Ω is deducted predetermined attitude angle command signal Ω _cobtain attitude of flight vehicle angular error signal e _s, by this error signal e _sbe sent to slow loop controller, obtain attitude angular rate command signal ω based on dynamic sliding mode control _c;

Step 4.2), attitude angular rate current demand signal ω is deducted attitude angular rate command signal ω _cobtain attitude of flight vehicle angular speed error signal e _f, by error signal e _fbe sent to fast loop control unit, compensate based on radial base neural net and actuator input signal v that the output of interference observer obtains in fast loop, v is sent to the output vector δ (v) that actuator obtains being subject to actuator saturation properties influence;

Step 4.3), actuator output vector δ (v) is sent to aircraft command receiver, realizes the predetermined attitude angle Ω of aircraft _ctracing control.