CN104199286A - Hierarchical dynamic inverse control method for flight vehicle based on sliding mode interference observer - Google Patents

Abstract

The invention discloses a hierarchical dynamic inverse control method for a flight vehicle based on a sliding mode interference observer. The hierarchical dynamic inverse control method comprises the steps of: 1, by considering multi-source interference suffered by the flight vehicle, building a multi-source interference system model based on an flight vehicle longitudinal dynamics model; 2, designing a sliding mode interference observer and estimating multi-source interference based on the multi-source interference system model built in the first step; the third step, constructing a hierarchical dynamic inverse composite controller based on the sliding mode interference observer in the second step, thus enabling speed and height of the flight vehicle to highly follow a reference instruction while compensating multi-source interference. The hierarchical dynamic inverse control method for the flight vehicle based on the sliding mode interference observer has the advantages of strong anti-interference capability, fast tracking speed, high control precision and the like, thus being applicable to tracking and controlling height and speed of the flight vehicle.

Description

A kind of aircraft based on sliding formwork interference observer is passed rank dynamic inversion control method

Technical field

The present invention relates to a kind of aircraft based on sliding formwork interference observer and pass rank dynamic inversion control method, be mainly used in speed and the height tracing control of aerocraft system, belong to aircraft control technology field.

Background technology

At present, some aircraft (as hypersonic aircraft) flight span is large, flight environment of vehicle is complicated, thereby mostly aerocraft system is subject to the impact that multi-source disturbs, wherein multi-source disturb comprise that aerodynamic parameter is uncertain, vehicle mass and moment of inertia is uncertain, not modeling Nonlinear Dynamic, external disturbance and measuring error etc.; So flight control system need to possess certain robustness.

The compound anti-interference controller of the control theory method design of application based on interference observer has interference cancellation capability, when the system that can ensure meets control performance requirement, makes system have certain robustness.At present, for the nonlinear system of aircraft, the mode that mostly adopts dynamic inverse controller to combine with interference observer designs non-linear compound anti-interference controller.But because conventional dynamic inverse controller need to be exported to system (as flying speed and flying height) repetition differentiate, thereby obtain the pseudo-linearized system of input and output, finally design on this basis dynamic inverse controller.This process certainly will be introduced the single order, second order of some interference, three order derivatives even, thereby to a certain degree affects the control effect of compound anti-interference controller.Utilize the response time of aerocraft system state to differ larger feature and pass rank dynamic inverse controller, Applicative time yardstick separation principle, is divided into three subsystems by original system, then to subsystem separate design controller; Thereby avoid the repetition differentiate process to system output, and then can not introduce interference derivative.So based on the control better effects if of passing rank dynamic inverse composite controller of interference observer, and calculated amount is relatively little.

In addition, at interference observer design aspect, most widely used is a kind of derivative BOUNDED DISTURBANCES observer, and the derivative that this type of interference observer requirement is disturbed can not be too large.Because the Interference Estimation error that the derivative disturbing draws is more greatly just larger.In order to address this problem, model description interference observer has been proposed again, although not to disturbing derivative requirement to some extent, need to know the specific descriptions model of interference, this is also not easy to accomplish in practice.And the sliding formwork interference observer that present patent application adopts does not need the derivative of limit interferences, do not need to know again the descriptive model of interference, be more amenable for use with reality.

Summary of the invention

Technology of the present invention is dealt with problems and is: due to some aerocraft system model out of true and be subject to the impact of many interference, so in order to realize high precision control, the invention provides a kind of aircraft based on sliding formwork interference observer and pass rank dynamic inversion control method, it be a kind of there is Interference Cancellation performance pass rank dynamic inverse composite control method, design sliding formwork interference observer is estimated and compensates multi-source to disturb, thereby solve the anti-interference Tracking Control Design problem of aerocraft system, ensureing, under the prerequisite of system robustness, to realize the high precision tracking control of system.

Technical solution of the present invention is that a kind of aircraft based on sliding formwork interference observer is passed rank dynamic inversion control method, and implementation step is as follows:

The first step, consider that the multi-source that aircraft is subject to disturbs and sets up aircraft multi-source EVAC (Evacuation Network Computer Model) model based on aircraft Longitudinal Dynamic Model:

${\stackrel{\·}{x}}_i=f_i\left(x\right)+{\mathrm{\Σ}}_{j=1}^3{g}_{\mathrm{ij}}\left(x\right)u_j+d_i,i=\mathrm{1,2},\·\·\·,5$

Wherein x=[x ₁x ₂x ₃x ₄x ₅] ^tfor the system state of aircraft, x ₁for flying speed V, x ₂for flying height h, x ₃for flight path angle γ, x ₄for angle of attack, x ₅for pitch rate Q; u ₁for accelerator open degree Φ, u ₂for duck rudder kick angle δ _c, u ₃for elevator angle δ _e; f _iand g (x) _ij(x) be all the smooth nonlinear function about x, wherein g _2j(x)=0; d _ifor multi-source disturbs, comprise all kinds of interference that, quality uncertain by aerodynamic parameter and moment of inertia change and modeling does not dynamically cause, d in reality ₂=0; Suppose that multi-source disturbs d _inorm-bounded, || ^d _i||≤σ _i, wherein σ _ifor known normal number, and its span is determined by the actual maximum output of aircraft topworks.

Second step, the multi-source EVAC (Evacuation Network Computer Model) modelling sliding formwork interference observer of setting up based on the first step:

$\left\{\begin{array}{c}{s}_r=x_r-z_r\\ {\stackrel{\·}{z}}_r={\mathrm{\Σ}}_{j=1}^3{g}_{\mathrm{rj}}\left(x\right)u_j-v_r,r=\mathrm{1,3,4,5}\\ {\hat{d}}_r=-(v_r+f_r\left(x\right))\end{array}\right.$

Wherein s _rfor sliding-mode surface; z _rfor middle auxiliary variable; v _r=l _rsgn (s _r) be observer controlled quentity controlled variable; l _rfor interference observer gain; Sgn (s _r) be about s _rsign function, work as s _r>=0 o'clock, sgn (s _r)=1, works as s _rwhen < 0, sgn (s _r)=-1; the d drawing for sliding formwork interference observer _restimated value.

The 3rd step, the sliding formwork interference observer structure based on second step is passed rank dynamic inverse composite controller:

First, aircraft multi-source EVAC (Evacuation Network Computer Model) is decomposed into three subsystems: the subsystem of the subsystem of flying speed subsystem, flying height and flight path angle composition and the angle of attack and pitch rate composition; Then, design respectively three sub-controllers for three subsystems:

1) speed subsystem controller

$\mathrm{\&Phi;}=-g_{11}^{-1}\left(x\right)(f_1\left(x\right)+g_{12}\left(x\right){\mathrm{\&delta;}}_c+g_{13}\left(x\right){\mathrm{\&delta;}}_e-{\stackrel{\&CenterDot;}{V}}_{\mathrm{ref}}+k_1\tilde{V}+{\hat{d}}_1),$

2) height and flight path angle subsystem controller

${\mathrm{\&gamma;}}_{\mathrm{cmd}}=-V_{\mathrm{ref}}^{-1}(k_2\tilde{h}-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}}),$

${\mathrm{\&alpha;}}_{\mathrm{cmd}}={\mathrm{\&alpha;}}^{*}-\widetilde{\mathrm{\&gamma;}},$

${\mathrm{\&delta;}}_c=-g_{32}^{-1}\left(x\right)(f_3\left(x\right)+g_{31}\left(x\right)\mathrm{\&Phi;}+g_{33}\left(x\right){\mathrm{\&delta;}}_e-f_{\mathrm{\&alpha;}}+f_{{\mathrm{\&alpha;}}^{*}}+k_3\widetilde{\mathrm{\&gamma;}}+{\hat{d}}_3-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}})$

3) angle of attack and pitch rate subsystem controller

$Q_{\mathrm{cmd}}={\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}-{\hat{d}}_4-k_4\widetilde{\mathrm{\&alpha;}},$

${\mathrm{\&delta;}}_e=-g_{53}^{-1}\left(x\right)(f_5\left(x\right)+g_{51}\left(x\right)\mathrm{\&Phi;}+g_{52}\left(x\right){\mathrm{\&delta;}}_c-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+{\stackrel{\&CenterDot;}{\hat{d}}}_4+{\hat{d}}_5+k_5\tilde{Q}),$

Wherein y _ref=[V _refh _ref] ^tfor output tracking instruction, V _refand h _refthe trace command of representation speed and height respectively; γ _cmd(t), α _cmdand Q (t) _cmd(t) represent respectively the virtual controlling instruction of flight path angle, the angle of attack and pitch rate; x ^*=[V ^*h ^*γ ^*α ^*q ^*] ^tfor system state finally converges to equilibrium point, V ^*, h ^*, γ ^*, α ^*and Q ^*respectively representation speed, highly, the equilibrium point that finally converges to of flight path angle, the angle of attack and pitch rate, and definition $V^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{V}_{\mathrm{ref}}\left(t\right),h^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{h}_{\mathrm{ref}}\left(t\right),{\mathrm{\&gamma;}}^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{\mathrm{\&gamma;}}_{\mathrm{cmd}}\left(t\right)=0,{\mathrm{\&alpha;}}^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{\mathrm{\&alpha;}}_{\mathrm{cmd}}\left(t\right),$ $Q^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{Q}_{\mathrm{cmd}}\left(t\right)=0;$ $\tilde{x}={\left[\begin{array}{ccccc}\tilde{V}& \tilde{h}& \widetilde{\mathrm{\&gamma;}}& \widetilde{\mathrm{\&alpha;}}& \tilde{Q}\end{array}\right]}^T$ For the tracking error of system state, with be respectively speed, highly, the tracking error of flight path angle, the angle of attack and pitch rate, and definition $\tilde{V}=V-V_{\mathrm{ref}},\tilde{h}=h-h_{\mathrm{ref}},\widetilde{\mathrm{\&gamma;}}=\mathrm{\&gamma;}-{\mathrm{\&gamma;}}_{\mathrm{cmd}},\widetilde{\mathrm{\&alpha;}}={\mathrm{\&alpha;}-\mathrm{\&alpha;}}_{\mathrm{cmd}},\tilde{Q}=Q-Q_{\mathrm{cmd}};$ with be respectively the multi-source interference d that sliding formwork interference observer draws ₁, d ₃, d ₄and d ₅estimated value; k ₁the ride gain that is speed subsystem controller ensures speed tracking error finally converge to zero, k ₂and k ₃the ride gain that is height and flight path angle subsystem controller ensures height tracing error with flight path angle tracking error finally converge to zero, k ₄and k ₅the ride gain that is the angle of attack and pitch rate subsystem controller ensures angle of attack tracking error with pitch rate tracking error finally converge to zero; for dynamic pressure, S is with reference to wing area, for the lift coefficient about angle of attack, T is thrust, T ^*for corresponding to equilibrium point x ^*thrust.

The present invention's advantage is compared with prior art:

(1) with conventional dynamic based on interference observer against compared with composite controller, do not introduce when disturbing derivative the interference of the each passage of system estimated and compensated; And need not ask in real time inverse of a matrix, thereby reduce calculated amount.

(2) with derivative BOUNDED DISTURBANCES observer in the past with have model description interference observer to compare, sliding formwork interference observer does not need limit interferences derivative very little, does not need to know to disturb to specifically describe model yet, only requires the norm-bounded of interference; So be easier to apply in Practical Project.

Brief description of the drawings

Fig. 1 is that a kind of aircraft based on sliding formwork interference observer of the present invention is passed rank dynamic inversion control method FB(flow block);

Fig. 2 is that the aircraft based on sliding formwork interference observer is passed rank dynamic inverse composite controller theory diagram;

Fig. 3 is for passing rank dynamic inverse controller principle block diagram.

Embodiment

As shown in Figure 1, a kind of aircraft based on sliding formwork interference observer of the present invention is passed rank dynamic inversion control method step and is: model hypersonic aircraft multi-source EVAC (Evacuation Network Computer Model) model; Then based on multi-source EVAC (Evacuation Network Computer Model) modelling sliding formwork interference observer, multi-source is disturbed and carries out On-line Estimation; Finally pass rank dynamic inverse composite controllers (theory diagram is shown in Fig. 2) based on sliding formwork interference observer structure.As shown in Figure 2: the rank dynamic inverse composite controller of passing based on sliding formwork interference observer comprises two parts: interior ring is the feedforward compensation device based on sliding formwork interference observer, and outer shroud is for passing rank dynamic inverse feedback controller.Wherein sliding formwork interference observer can disturb by On-line Estimation multi-source, and then offsets multi-source by feedforward compensation device and disturb the impact on system, and feedback controller just can ensure that aircraft completes the tracing task of expection on this basis.Concrete implementation step is as follows:

The first step, set up the multi-source EVAC (Evacuation Network Computer Model) model of hypersonic aircraft:

$\stackrel{\&CenterDot;}{V}=(T\cos \mathrm{\&alpha;}-D)/m-g\sin \mathrm{\&gamma;}+d_1---\left(1\right)$

$\stackrel{\&CenterDot;}{h}=V\sin \mathrm{\&gamma;}+d_2---\left(2\right)$

$\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=-(L+T\sin \mathrm{\&alpha;})/\left(\mathrm{mV}\right)+Q+\left(g\cos \mathrm{\&gamma;}\right)/V+d_3---\left(3\right)$

$\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=(L+T\sin \mathrm{\&alpha;})/\left(\mathrm{mV}\right)-\left(g\cos \mathrm{\&gamma;}\right)/V+d_4---\left(4\right)$

$\stackrel{\&CenterDot;}{Q}=M/I_{\mathrm{yy}}+d_5---\left(5\right)$

Wherein V is flying speed; H is flying height; α is the angle of attack; γ is flight path angle; θ is the angle of pitch, and Q is pitch rate, α=θ-γ; T, L, D and M are respectively the suffered thrust of aircraft, lift, resistance and pitching moment; M is aircraft gross mass; G is acceleration of gravity; I _yyfor aircraft is along the moment of inertia of body axis system y axle, body axis system y axle points to right-hand perpendicular to aircraft symmetrical plane; d _i, i=1,2 ..., 5 is that multi-source disturbs, and comprises that, quality uncertain by aerodynamic parameter and moment of inertia change, modeling is not dynamically and all kinds of interference that cause of external disturbance; In practice, (2) formula is one and resolves process, does not have disturbing factor, so d ₂=0.At this hypothesis composite interference d _inorm-bounded, || d _i||≤σ _i, wherein σ _ifor known normal number, and its span is determined by the actual maximum output of aircraft topworks.Thrust T, lift L, the expression formula of resistance D and pitching moment M is:

T＝T ₁(α)+T ₂(α)Φ，L＝L ₁(α)+L ₂δ _c+L ₃δ _e，

D＝D ₁(α)+D ₂(δ _c)+D ₃(δ _e)，M＝M ₁(α)+M ₂Φ+M ₃δ _c+M ₄δ _e；

$T_1\left(\mathrm{\&alpha;}\right)=C_T^{{\mathrm{\&alpha;}}^3}{\mathrm{\&alpha;}}^3+C_T^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2+C_T^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_T^0,T_2\left(\mathrm{\&alpha;}\right)=C_{T,\mathrm{\&Phi;}}^{{\mathrm{\&alpha;}}^3}{\mathrm{\&alpha;}}^3+C_{T,\mathrm{\&Phi;}}^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2+C_{T,\mathrm{\&Phi;}}^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_{T,\mathrm{\&Phi;}}^0;$

$\stackrel{\&OverBar;}{q}=0.5{\mathrm{\&sigma;V}}^2;L_1\left(\mathrm{\&alpha;}\right)=\stackrel{\&OverBar;}{q}S(C_L^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_L^0),L_2=\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^{{\mathrm{\&delta;}}_c},L_3=\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^{{\mathrm{\&delta;}}_e};$

$D_1\left(\mathrm{\&alpha;}\right)=\stackrel{\&OverBar;}{q}S(C_D^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2+C_D^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_D^0),D_2\left({\mathrm{\&delta;}}_c\right)=\stackrel{\&OverBar;}{q}S(C_D^{{\mathrm{\&delta;}}_c^2}{\mathrm{\&delta;}}_c^2+C_D^{{\mathrm{\&delta;}}_c}{\mathrm{\&delta;}}_c),D_3\left({\mathrm{\&delta;}}_e\right)=\stackrel{\&OverBar;}{q}S(C_D^{{\mathrm{\&delta;}}_e^2}{\mathrm{\&delta;}}_e^2+C_D^{{\mathrm{\&delta;}}_e}{\mathrm{\&delta;}}_e);$

$M_1\left(\mathrm{\&alpha;}\right)=\stackrel{\&OverBar;}{q}S\stackrel{\&OverBar;}{c}(C_M^{{\mathrm{\&alpha;}}^2}{\mathrm{\&alpha;}}^2+C_M^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_M^0)+z_T{T}_1\left(\mathrm{\&alpha;}\right),$ M ₂＝z _TT ₂(α)， $M_3=\stackrel{\&OverBar;}{q}S\stackrel{\&OverBar;}{c}{C}_M^{{\mathrm{\&delta;}}_c},M_4=\stackrel{\&OverBar;}{q}S\stackrel{\&OverBar;}{c}{C}_M^{{\mathrm{\&delta;}}_e}.$ Wherein for dynamic pressure, ρ is atmospheric density, and S is with reference to wing area, for mean chord, z _tfor the coupling coefficient of thrust T and pitching moment M, controlled quentity controlled variable Φ, δ _eand δ _cbe respectively accelerator open degree, elevator angle and duck rudder kick angle.T ₁(α), L ₁(α), D ₁(α) and M ₁(α) be respectively in the expression formula of thrust T, lift L, resistance D and pitching moment M and controlled quentity controlled variable Φ, δ _eand δ _cuncorrelated; T ₂(α), L ₂, L ₃, M ₂, M ₃and M ₄be respectively in the expression formula of thrust T, lift L and pitching moment M and controlled quentity controlled variable Φ, δ _eand δ _crelevant coefficient entry; D ₁(δ _c) and D ₁(δ _e) be controlled quentity controlled variable δ in resistance D expression formula _eand δ _ccontinuous item. with be respectively T ₁(α) in expression formula with α ³, α ², coefficient and constant that α is relevant; with be respectively T ₂(α) in expression formula with α ³, α ², coefficient and constant that α is relevant; with for L ₁(α) coefficient and the constant relevant to α in expression formula; with be respectively resistance coefficient D ₁(α) in expression formula with α ², coefficient and constant that α is relevant; with be respectively M ₁(α) in expression formula with α ², coefficient and constant that α is relevant. with be respectively D ₂(δ _c) and D ₃(δ _e) in expression formula with with relevant coefficient; with be respectively L ₂, L ₃, M ₃and M ₄aerodynamic Coefficient in expression formula.

Control target: design controlled quentity controlled variable u=[Φ δ _cδ _e] ^tmake to export y=[V h] ^ttrack reference instruction y _ref(t)=[V _ref(t) h _ref(t)] ^t, and final system state x=[V h γ α Q] ^tconverge to another equilibrium point x ^*=[V ^*h ^*γ ^*α ^*q ^*] ^t, wherein V _refand h _refthe trace command of representation speed and height respectively, V ^*, h ^*, γ ^*, α ^*and Q ^*respectively representation speed, highly, the equilibrium point that finally converges to of flight path angle, the angle of attack and pitch rate, and definition $V^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{V}_{\mathrm{ref}},h^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{h}_{\mathrm{ref}}\left(t\right),{\mathrm{\&gamma;}}^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{\mathrm{\&gamma;}}_{\mathrm{cmd}}\left(t\right)=0,$

${\mathrm{\&alpha;}}^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{\mathrm{\&alpha;}}_{\mathrm{cmd}}\left(t\right),Q^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{Q}_{\mathrm{cmd}}\left(t\right)=0.$

By multi-source EVAC (Evacuation Network Computer Model) model (1)-(5) of hypersonic aircraft, can be rewritten as general nonlinearity multi-source EVAC (Evacuation Network Computer Model) model:

${\stackrel{\&CenterDot;}{x}}_i=f_i\left(x\right)+{\mathrm{\&Sigma;}}_{j=1}^3{g}_{\mathrm{ij}}\left(x\right)u_j+d_i,i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,5---\left(6\right)$

Wherein state x=[V h γ α Q] ^t, x ₁=V, x ₂=h, x ₃=γ, x ₄=α, x ₅=Q; Control inputs u=[Φ δ _cδ _e] ^t, u ₁=Φ, u ₂=δ _c, u ₃=δ _e; d _ifor multi-source disturbs, comprise, quality uncertain by rudders pneumatic power parameter and moment of inertia change, not modeling dynamically and all kinds of interference that cause of external disturbance, d in reality ₂=0; At this hypothesis composite interference d _inorm-bounded, || d _i||≤σ _i, wherein σ _ifor known normal number, and its span is determined by the actual maximum output of aircraft topworks.F _iand g (x) _ij(x) be all the smooth nonlinear function about x, specifically describe and be:

f ₁(x)＝(T ₁(α)cosα-D ₁(α))/m-gsinγ；f ₂(x)＝Vsinγ；

f ₃(x)＝(L ₁(α)+T ₁(α)sinγ-mgcosγ)/(mV)；f ₅(x)＝M ₁(α)/I _yy；

f ₄(x)＝Q-(L ₁(α)+T ₁(α)sinγ-mgcosγ)/(mV)；

g ₁₁(x)＝(T ₂(α)cosα)/m， $g_{12}\left(x\right)=\stackrel{\&OverBar;}{q}{\mathrm{SC}}_D^{{\mathrm{\&delta;}}_c},g_{13}\left(x\right)=\stackrel{\&OverBar;}{q}{\mathrm{SC}}_D^{{\mathrm{\&delta;}}_e};$

g ₂₁(x)＝0，g ₂₂(x)＝0，g ₂₃(x)＝0

g ₃₁(x)＝(T ₂(α)sinα)/(mV)，g ₃₂(x)＝L ₂/(mV)，g ₃₃(x)＝L ₃/(mV)；

g ₄₁(x)＝-(T ₂(α)sinα)/(mV)，g ₄₂(x)＝-L ₂/(mV)，g ₄₃(x)＝-L ₃/(mV)；

g ₅₁(x)＝M ₂/I _yy，g ₅₂(x)＝M ₃/I _yy，g ₅₃(x)＝M ₄/I _yy。

Note: because control inputs in reality is all limited in very little scope, so in order to simplify controller design, ignored D in the process of model conversation ₂(δ _c) and D ₃(δ _e) in with

Second step, designs sliding formwork interference observer based on multi-source EVAC (Evacuation Network Computer Model) model (6):

$\left\{\begin{array}{c}{s}_r=x_r-z_r\\ {\stackrel{\&CenterDot;}{z}}_r={\mathrm{\&Sigma;}}_{j=1}^3{g}_{\mathrm{rj}}\left(x\right)u_j-v_r\\ {\hat{d}}_r=-(v_r+f_r\left(x\right))\end{array}\right.,r=\mathrm{1,2,3,4,5}---\left(7\right)$

Wherein s _rfor sliding-mode surface; z _rfor middle auxiliary variable; v _r=l _rsgn (s _r) be observer controlled quentity controlled variable; l _rfor interference observer gain; Sgn (s _r) be about s _rsign function, work as s _r>=0 o'clock, sgn (s _r)=1, works as s _rwhen < 0, sgn (s _r)=-1.Design interference observer gain l _r> | ξ _r|, r=1,3,4,5 just can make Interference Estimation error finally converge on zero.

The 3rd step, pass rank dynamic inverse composite controller based on sliding formwork interference observer (7) structure:

First, hypersonic aircraft multi-source EVAC (Evacuation Network Computer Model) model (6) is decomposed into three subsystems: the subsystem (rotatablely moving) of the subsystem (vertical direction particle movement) of flying speed subsystem (horizontal direction particle movement), flying height and flight path angle composition and the angle of attack and pitch rate composition.Pass rank dynamic inverse controller for the ease of design, the virtual controlling instruction of definition flight path angle, the angle of attack and pitch rate is respectively γ _cmd(t), α _cmdand Q (t) _cmd(t).

Then, application working control amount Φ, δ _cand δ _ewith virtual controlling instruction γ _cmd, α _cmdand Q _cmd, to each subsystem separating control, specific design thinking as shown in Figure 3: first controlled quentity controlled variable Φ controls flying speed V tracking velocity reference instruction V _ref; Then virtual controlling instruction γ _cmdcontrol flying height track reference instruction h _ref; Subsequently again by controlled quentity controlled variable δ _cwith virtual controlling instruction α _cmdcontrol flight path angle γ and follow the tracks of virtual controlling instruction γ _cmd, wherein due to angle of attack to the effect of flight path angle γ than controlled quentity controlled variable δ _cmuch bigger, so be mainly applying virtual steering order α _cmdcontrol flight path angle γ, application controls amount δ _cmainly to eliminate controlled quentity controlled variable δ _eon the impact of lift; Finally by controlled quentity controlled variable δ _econtrol pitch rate Q and follow the tracks of virtual controlling instruction Q _cmd, wherein pass through Q _cmdcontrol angle of attack and follow the tracks of virtual controlling instruction α _cmd.

The tracking error of define system state $\tilde{x}={\left[\begin{array}{ccccc}\tilde{V}& \tilde{h}& \widetilde{\mathrm{\&gamma;}}& \widetilde{\mathrm{\&alpha;}}& \tilde{Q}\end{array}\right]}^T.$ Wherein with be respectively speed, highly, the tracking error of flight path angle, the angle of attack and pitch rate, and definition

$\tilde{V}=V-V_{\mathrm{ref}},\tilde{h}=h-h_{\mathrm{ref}},\widetilde{\mathrm{\&gamma;}}=\mathrm{\&gamma;}-{\mathrm{\&gamma;}}_{\mathrm{cmd}},\widetilde{\mathrm{\&alpha;}}={\mathrm{\&alpha;}-\mathrm{\&alpha;}}_{\mathrm{cmd}},\tilde{Q}=Q-Q_{\mathrm{cmd}}.$

1) design rate subsystem controller

To speed tracking error differentiate obtains:

$\stackrel{\&CenterDot;}{V}=(T_1\left(\mathrm{\&alpha;}\right)\cos \mathrm{\&alpha;}-D)/m-g\sin \mathrm{\&gamma;}+d_1-{\stackrel{\&CenterDot;}{V}}_{\mathrm{ref}}+\left(T_2\left(\mathrm{\&alpha;}\right)\mathrm{\&Phi;}\cos \mathrm{\&alpha;}\right)/m---\left(8\right)$

Design controlled quentity controlled variable:

$\mathrm{\&Phi;}={-[\left(T_2\left(\mathrm{\&alpha;}\right)\cos \mathrm{\&alpha;}\right)/m]}^{-1}[(T_1\left(\mathrm{\&alpha;}\right)\cos \mathrm{\&alpha;}-D)/m-g\sin \mathrm{\&gamma;}-{\stackrel{\&CenterDot;}{V}}_{\mathrm{ref}}+k_1\tilde{V}+{\hat{d}}_1]---\left(9\right)$

And substitution (8) formula:

$\stackrel{\&CenterDot;}{\tilde{V}}=-k_1\tilde{V}+e_1---\left(10\right)$

Wherein the d drawing for sliding formwork interference observer ₁estimated value; e ₁for Interference Estimation error, k ₁to need the ride gain of design to ensure system (10) Asymptotic Stability.

2) design height and flight path angle subsystem controller

First, to height tracing error differentiate obtains:

$\stackrel{\&CenterDot;}{\tilde{h}}=\stackrel{\&CenterDot;}{h}-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}}=V\sin \mathrm{\&gamma;}-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}}---\left(11\right)$

Wherein, because the variation range of cruise section flight path angle is [5 °, 5 °]; So sin γ ≈ γ.(11) formula can be rewritten as:

$\stackrel{\&CenterDot;}{\tilde{h}}=\mathrm{V\&gamma;}-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}}=\tilde{V}\mathrm{\&gamma;}+V_{\mathrm{ref}}\mathrm{\&gamma;}-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}}=\tilde{V}\mathrm{\&gamma;}+V_{\mathrm{ref}}(\widetilde{\mathrm{\&gamma;}}+{\mathrm{\&gamma;}}_{\mathrm{cmd}})-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}}---\left(12\right)$

The instruction of design virtual controlling:

${\mathrm{\&gamma;}}_{\mathrm{cmd}}=-V_{\mathrm{ref}}^{-1}(k_2\tilde{h}-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}})---\left(13\right)$

And substitution (12) formula:

$\stackrel{\&CenterDot;}{\tilde{h}}=\tilde{V}\mathrm{\&gamma;}+V_{\mathrm{ref}}\widetilde{\mathrm{\&gamma;}}-k_2\tilde{h}---\left(14\right)$

Wherein k ₂to need the ride gain of design to ensure system (14) Asymptotic Stability.

Then, to flight path angle tracking error differentiate obtains

$\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&gamma;}}}=(\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+T\sin \mathrm{\&alpha;}-\mathrm{mg}\cos \mathrm{\&gamma;}+\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^0+L_3{\mathrm{\&delta;}}_e+L_2{\mathrm{\&delta;}}_c)/\left(\mathrm{mV}\right)+d_3-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}---\left(15\right)$

Wherein for constant K _m> 0 and K _m> 0, meets the coefficient of dependent status, T ^*for corresponding to equilibrium point x ^*thrust.Therefore (15) formula can be rewritten as

$\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&gamma;}}}=(K_{{\mathrm{\&alpha;}}_1}(x,\mathrm{\&Phi;})V^2(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}^{*})+\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^{\mathrm{\&alpha;}}{\mathrm{\&alpha;}}^{*}+T^{*}\sin {\mathrm{\&alpha;}}^{*}-\mathrm{mg}\cos \mathrm{\&gamma;}+\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^0+L_3{\mathrm{\&delta;}}_e+L_2{\mathrm{\&delta;}}_c)/\left(\mathrm{mV}\right)+d_3-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}---\left(16\right)$

The instruction of design virtual controlling:

${\mathrm{\&alpha;}}_{\mathrm{cmd}}={\mathrm{\&alpha;}}^{*}-\widetilde{\mathrm{\&gamma;}}---\left(17\right)$

? substitution (16) formula:

$\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&gamma;}}}=(K_{{\mathrm{\&alpha;}}_1}(x,\mathrm{\&Phi;})V^2(\widetilde{\mathrm{\&alpha;}}-\widetilde{\mathrm{\&gamma;}})+\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^{\mathrm{\&alpha;}}{\mathrm{\&alpha;}}^{*}+T^{*}\sin {\mathrm{\&alpha;}}^{*}-\mathrm{mg}\cos \mathrm{\&gamma;}+\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^0+L_3{\mathrm{\&delta;}}_e+L_2{\mathrm{\&delta;}}_c)/\left(\mathrm{mV}\right)+d_3-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}---\left(18\right)$

Design controlled quentity controlled variable:

${\mathrm{\&delta;}}_c=-{[L_2/\left(\mathrm{mV}\right)]}^{-1}[(\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^{\mathrm{\&alpha;}}{\mathrm{\&alpha;}}^{*}+T^{*}\sin {\mathrm{\&alpha;}}^{*}-\mathrm{mg}\cos \mathrm{\&gamma;}+\stackrel{\&OverBar;}{q}{\mathrm{SC}}_L^0+L_3{\mathrm{\&delta;}}_e)/\left(\mathrm{mV}\right)+k_3\widetilde{\mathrm{\&gamma;}}+{\hat{d}}_3-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}]---\left(19\right)$

Substitution (18) formula:

$\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&gamma;}}}=-[\left(K_{{\mathrm{\&alpha;}}_1}(x,\mathrm{\&Phi;})V\right)/m+k_3]\widetilde{\mathrm{\&gamma;}}+[\left(K_{{\mathrm{\&alpha;}}_1}(x,\mathrm{\&Phi;})V\right)/m]\widetilde{\mathrm{\&alpha;}}+e_3---\left(20\right)$

Wherein the d drawing for sliding formwork interference observer ₃estimated value; e ₃for Interference Estimation error, k ₃to need the ride gain of design to ensure system (20) Asymptotic Stability.

3) the design angle of attack and pitch rate subsystem controller

First, the angle tracking error of attacking against each other differentiate obtains:

$\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&alpha;}}}=\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{\mathrm{cmd}}=\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}+\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=Q-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}+d_4+\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&gamma;}}}=Q-\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&gamma;}}}-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+d_4+\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&gamma;}}}=Q-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+d_4---\left(21\right)$

The instruction of design virtual controlling:

$Q_{\mathrm{cmd}}={\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}-{\hat{d}}_4-k_4\widetilde{\mathrm{\&alpha;}}---\left(22\right)$

Substitution (21) formula:

$\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&alpha;}}}=\tilde{Q}+Q_{\mathrm{cmd}}-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+d_4=\tilde{Q}+{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}-k_4\widetilde{\mathrm{\&alpha;}}-{\hat{d}}_4-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+d_4=\tilde{Q}-k_4\widetilde{\mathrm{\&alpha;}}+e_4---\left(23\right)$

Wherein the d drawing for sliding formwork interference observer ₄estimated value; e ₄for Interference Estimation error, k ₄to need the ride gain of design to ensure system (23) Asymptotic Stability.

Then, to pitch rate tracking error differentiate obtains:

$\stackrel{\&CenterDot;}{\tilde{Q}}=(M_1\left(\mathrm{\&alpha;}\right)+M_2\mathrm{\&Phi;}+M_3{\mathrm{\&delta;}}_3)/I_{\mathrm{yy}}+d_5-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+{\stackrel{\&CenterDot;}{\hat{d}}}_4+k_4(\tilde{Q}-k_4\widetilde{\mathrm{\&alpha;}}+e_4)+(M_4/I_{\mathrm{yy}}){\mathrm{\&delta;}}_e---\left(24\right)$

Design controlled quentity controlled variable:

${\mathrm{\&delta;}}_e=-{[M_4/I_{\mathrm{yy}}]}^{-1}[(M_1\left(\mathrm{\&alpha;}\right)+M_2\mathrm{\&Phi;}+M_3{\mathrm{\&delta;}}_c)/I_{\mathrm{yy}}-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+{\stackrel{\&CenterDot;}{\hat{d}}}_4+{\hat{d}}_5+k_5\tilde{Q}]---\left(25\right)$

Substitution (24) formula:

$\stackrel{\&CenterDot;}{\tilde{Q}}=k_4(\tilde{Q}-k_4\widetilde{\mathrm{\&alpha;}}+e_4)+e_5-k_5\tilde{Q}=(k_4-k_5)\tilde{Q}-k_4^2\widetilde{\mathrm{\&alpha;}}+k_4{e}_4+e_5---\left(26\right)$

Wherein the d drawing for sliding formwork interference observer ₅estimated value; e ₅for Interference Estimation error, k ₅to need the ride gain of design to ensure system (26) Asymptotic Stability.

Design ride gain: k ₁> 0, k ₂> 0, k ₄> 0, k ₅> k ₄can ensure the tracking error of system state $\tilde{x}={\left[\begin{array}{ccccc}\tilde{V}& \tilde{h}& \widetilde{\mathrm{\&gamma;}}& \widetilde{\mathrm{\&alpha;}}& \tilde{Q}\end{array}\right]}^T$ Finally converge on zero.But because the controlled quentity controlled variable of real system all limits within the specific limits, so ride gain can not obtain too greatly in order to avoid cause system out of control.If the concrete controlled quentity controlled variable allowed band of known system just can estimate according to (9) formula, (13) formula, (19) formula, (22) formula and (25) formula the upper limit of ride gain scope.

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

Claims (1)

1. the aircraft based on sliding formwork interference observer is passed a rank dynamic inversion control method, it is characterized in that comprising the following steps:

(1) considering that the multi-source that is subject to of aircraft disturbs also sets up multi-source EVAC (Evacuation Network Computer Model) model based on aircraft Longitudinal Dynamic Model, and wherein multi-source disturbs and comprises, quality uncertain by aerodynamic parameter and moment of inertia changes and modeling does not dynamically cause all kinds of interference;

(2) the multi-source EVAC (Evacuation Network Computer Model) modelling sliding formwork interference observer of setting up based on the first step estimates that multi-source disturbs;

(3) structure of the sliding formwork interference observer based on second step is passed the tracing task that rank dynamic inverse composite controller makes aircraft speed and highly can complete expection when compensation multi-source disturbs;

The aircraft multi-source EVAC (Evacuation Network Computer Model) model of described step (1) is:

${\stackrel{\&CenterDot;}{x}}_i=f_i\left(x\right)+{\mathrm{\&Sigma;}}_{j=1}^3{g}_{\mathrm{ij}}\left(x\right)u_j+d_i,i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,5$

Wherein x=[x ₁x ₂x ₃x ₄x ₅] ^tfor the system state of aircraft, x ₁for flying speed V, x ₂for flying height h, x ₃for flight path angle γ, x ₄for angle of attack, x ₅for pitch rate Q; u ₁for accelerator open degree Φ, u ₂for duck rudder kick angle δ _c, u ₃for elevator angle δ _e; f _iand g (x) _ij(x) be all the smooth nonlinear function about x; d _ifor multi-source disturbs, comprise all kinds of interference that, quality uncertain by aerodynamic parameter and moment of inertia change and modeling does not dynamically cause, d in reality ₂=0; Suppose that multi-source disturbs d _inorm-bounded, || d _i||≤σ _i, wherein σ _ifor known normal number, and its span is determined by the actual maximum output of aircraft topworks;

The sliding formwork interference observer of described step (2) is:

$\left\{\begin{array}{c}{s}_r=x_r-z_r\\ {\stackrel{\&CenterDot;}{z}}_r={\mathrm{\&Sigma;}}_{j=1}^3{g}_{\mathrm{rj}}\left(x\right)u_j-v_r,r=\mathrm{1,3,4,5}\\ {\hat{d}}_r=-(v_r+f_r\left(x\right))\end{array}\right.$

Wherein s _rfor sliding-mode surface, z _rfor middle auxiliary variable, v _r=l _rsgn (s _r) be observer controlled quentity controlled variable, l _rfor interference observer gain, sgn (s _r) be about s _rsign function, work as s _r>=0 o'clock, sgn (s _r)=1, works as s _rwhen < 0, sgn (s _r)=-1, the multi-source drawing for sliding formwork interference observer disturbs d _restimated value;

The rank dynamic inverse composite controller of passing of described step (3) comprises three sub-controllers:

(31) speed subsystem controller

$\mathrm{\&Phi;}=-g_{11}^{-1}\left(x\right)(f_1\left(x\right)+g_{12}\left(x\right){\mathrm{\&delta;}}_c+g_{13}\left(x\right){\mathrm{\&delta;}}_e-{\stackrel{\&CenterDot;}{V}}_{\mathrm{ref}}+k_1\tilde{V}+{\hat{d}}_1),$

(32) height and flight path angle subsystem controller

${\mathrm{\&gamma;}}_{\mathrm{cmd}}=-V_{\mathrm{ref}}^{-1}(k_2\tilde{h}-{\stackrel{\&CenterDot;}{h}}_{\mathrm{ref}}),$

${\mathrm{\&alpha;}}_{\mathrm{cmd}}={\mathrm{\&alpha;}}^{*}-\widetilde{\mathrm{\&gamma;}},$

${\mathrm{\&delta;}}_c=-g_{32}^{-1}\left(x\right)(f_3\left(x\right)+g_{31}\left(x\right)\mathrm{\&Phi;}+g_{33}\left(x\right){\mathrm{\&delta;}}_e-f_{\mathrm{\&alpha;}}+f_{{\mathrm{\&alpha;}}^{*}}+k_3\widetilde{\mathrm{\&gamma;}}+{\hat{d}}_3-{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}),$

(33) angle of attack and pitch rate subsystem controller

$Q_{\mathrm{cmd}}={\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}-{\hat{d}}_4-k_4\widetilde{\mathrm{\&alpha;}},$

${\mathrm{\&delta;}}_e=-g_{53}^{-1}\left(x\right)(f_5\left(x\right)+g_{51}\left(x\right)\mathrm{\&Phi;}+g_{52}\left(x\right){\mathrm{\&delta;}}_c-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&gamma;}}}_{\mathrm{cmd}}+{\stackrel{\&CenterDot;}{\hat{d}}}_4+{\hat{d}}_5+k_5\tilde{Q}),$

Wherein y _ref=[V _refh _ref] ^tfor output tracking instruction, V _refand h _refthe trace command of representation speed and height respectively; γ _cmd(t), α _cmdand Q (t) _cmd(t) represent respectively the virtual controlling instruction of flight path angle, the angle of attack and pitch rate; x ^*=[V ^*h ^*γ ^*α ^*q ^*] ^tfor the equilibrium point of the final convergence of system state, V ^*, h ^*, γ ^*, α ^*and Q ^*respectively representation speed, highly, the equilibrium point that finally converges to of flight path angle, the angle of attack and pitch rate, and definition $V^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{V}_{\mathrm{ref}}\left(t\right),h^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{h}_{\mathrm{ref}}\left(t\right),{\mathrm{\&gamma;}}^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{\mathrm{\&gamma;}}_{\mathrm{cmd}}\left(t\right)=0,{\mathrm{\&alpha;}}^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{\mathrm{\&alpha;}}_{\mathrm{cmd}}\left(t\right),$ $Q^{*}=\underset{t\&RightArrow;\&infin;}{\lim }{Q}_{\mathrm{cmd}}\left(t\right)=0;$ $\tilde{x}={\left[\begin{array}{ccccc}\tilde{V}& \tilde{h}& \widetilde{\mathrm{\&gamma;}}& \widetilde{\mathrm{\&alpha;}}& \tilde{Q}\end{array}\right]}^T$ For the tracking error of system state, with be respectively speed, highly, the tracking error of flight path angle, the angle of attack and pitch rate, and definition $\tilde{V}=V-V_{\mathrm{ref}},\tilde{h}=h-h_{\mathrm{ref}},\widetilde{\mathrm{\&gamma;}}=\mathrm{\&gamma;}-{\mathrm{\&gamma;}}_{\mathrm{cmd}},\widetilde{\mathrm{\&alpha;}}={\mathrm{\&alpha;}-\mathrm{\&alpha;}}_{\mathrm{cmd}},\tilde{Q}=Q-Q_{\mathrm{cmd}};$ with be respectively the multi-source interference d that sliding formwork interference observer draws ₁, d ₃, d ₄and d ₅estimated value; k ₁the ride gain that is speed subsystem controller ensures speed tracking error finally converge to zero, k ₂and k ₃the ride gain that is height and flight path angle subsystem controller ensures height tracing error with flight path angle tracking error finally converge to zero, k ₄and k ₅the ride gain that is the angle of attack and pitch rate subsystem controller ensures angle of attack tracking error with pitch rate tracking error finally converge to zero; for dynamic pressure, S is with reference to wing area, for the lift coefficient about angle of attack, T is thrust, T ^*for corresponding to equilibrium point x ^*thrust.