CN106997208A - A kind of control method of hypersonic aircraft towards under condition of uncertainty - Google Patents

Abstract

The invention discloses a kind of control method of the hypersonic aircraft towards under condition of uncertainty, comprise the following steps：Step S1, according to hypersonic aircraft longitudinal dynamics equation, uses overall-finished housing linearization process to flying speed V and flying height h, obtains its corresponding state equation；Step S2, according to this state equation, designs contragradience sliding mode controller, double power Reaching Laws in selection synovial membrane face are：In formula, k₁＞ 0, k₂The ＞ λ ＞ 0 of ＞ 0, η ＞ 1,1 are parameter；Step S3, test platform is built based on this contragradience sliding mode controller, carries out performance simulation.The inventive method uses double power sliding mode controllers based on Backstepping, and this method, which can be effectively reduced handoff gain and eliminate, buffets problem present in sliding formwork control.

Description

A kind of control method of hypersonic aircraft towards under condition of uncertainty

Technical field

The present invention relates to hypersonic aircraft technical field, and in particular to a kind of high ultrasound towards under condition of uncertainty The flight control method of fast aircraft.

Background technology

Hypersonic aircraft is main to perform aerial mission, near space apart from 20~100km of ground near space region It is the space that the mankind do not develop also very well so far, the great potential in terms of military and civilian is hypersonic to fly Disguise very high and in the field aircraft communication signal of the row device near space region is very strong, hypersonic to fly Row device flies near space and determines that it had both had the advantage of aeronautical technology, there is that spacecraft can not possess again.In army Thing applies upper, and hypersonic aircraft execution speed is very fast, can will trigger quick accurate in the very first time with reaching target Hit the arriving in weapon epoch.It is particularly great in terms of information acquisition, hasty breaching, communication support, long-range strike, early warning Development potentiality.Just because of these huge military values and potential economic value, increasing military power is all competitively Develop hypersonic aircraft.

Due to changeable, complicated flight environment of vehicle and the extraneous strong jamming of the self structure of hypersonic aircraft, it is necessary to Design has good stability, fast response time and the high controller of control accuracy, and this just proposes urgent to advanced control method The demand cut.Expert applies to many advanced control technologies in hypersonic aircraft both at home and abroad at present, and achieves very Good control effect.Wherein several important and successful control method is introduced below.

The main thought of gain preset control method is into multiple linear models by complicated nonlinear Control PROBLEM DECOMPOSITION And the design problem of multiple linear controllers.The method is widely used in Design of Flight Control, and U.S. X-43A flies Row device introduces gain preset method in Control System Design, but the flight time of aircraft is too short, under high maneuver state, The validity of this method can not be proved to.Under High Angle of Attack and strong maneuvering condition, the flight of hypersonic aircraft has by force Non-linear and high coupling, the controller designed just with gain preset method can not much meet the requirement of performance indications.

Control theory of feedback linearization be it is most important in nonlinear control method be also one of most widely used method, it is real Two existing effective ways are：Differential Geometry method and dynamic inversion.They are different from the part of traditional Taylor expansion Linearisation, but nonlinear system is subjected to exact linearization method, wherein the higher order term of Taylor expansion is contained, but because this The method of kind needs to set up on the basis of accurate model, and the error existed to model is very sensitive, so as to reduce whole non- The robustness of linear system.

Sliding mode variable structure control method (SMVSC) is an important method for handling nonlinear system, so-called structure changes sheet Refer to the discontinuous non-linear shear that the feedback controller structure of internal system occurs in matter.When system mode passes through not same district During domain, the structure of feedback control becomes according to a set of switch logic formulated by designer according to system performance index requirement Change so that control system has certain adaptation energy to factors such as inherent Parameters variation and the external environment condition disturbances of controlled device Power, it is ensured that systematic function reaches desired performance indications requirement.But system mode easily causes buffeting in motion switch.For Overcome these defects, many domestic and foreign scholars are proposed some relatively effective methods, such as saturation function method, Reaching Law Method, boundary layer method, High-Order Sliding Mode method etc..

Because hypersonic aircraft is using body coupled structure and flies under conditions of High aititude and big Mach number, Cause its change to gas condition quite sensitive, and hypersonic aircraft also receives structure dynamics in flight course, Dynamic and the influence coupled between them are promoted, its pneumatic and propulsion characteristic is uncertain, or even is difficult to estimate.These because The influence of element so that the model of hypersonic aircraft be it is uncertain, it is changeable, it is unstable, and there are input and output Between close coupling, therefore design the controller with nonlinearity and strong robustness for hypersonic aircraft and become particularly It is important.Meanwhile, there is convergence rate for traditional Reaching Law in sliding mode controller design in the prior art slow and the deficiency such as buffet, The invention provides a kind of new resolving ideas.

The content of the invention

It is an object of the invention to overcome deficiency of the prior art there is provided a kind of towards superb under condition of uncertainty The control method of velocity of sound aircraft, using double power sliding mode controllers based on Backstepping, this method can be effectively reduced and cut Change gain and eliminate and problem is buffeted present in sliding formwork control.

In order to solve the above technical problems, the invention provides a kind of hypersonic aircraft towards under condition of uncertainty Control method, it is characterized in that, comprise the following steps：

Step S1, according to hypersonic aircraft longitudinal dynamics equation, to flying speed V and flying height h using complete State feedback linearization is handled, and obtains its corresponding state equation；

Step S2, according to this state equation, designs contragradience sliding mode controller,

Define sliding-mode surface：

Wherein, c_i＞ 0 is parameter, e_iAnd e₃For system tracking error.

Double power Reaching Laws in selection synovial membrane face are：

In formula, k₁＞ 0, k₂The ＞ λ ＞ 0 of ＞ 0, η ＞ 1,1 are parameter；

Contragradience sliding formwork control ratio is：

Step S3, test platform is built based on this contragradience sliding mode controller, carries out performance simulation.

Further, in step S1, the dynamical equation of hypersonic aircraft longitudinal direction model can be converted into following state Equation form：

WhereinU=[β_c δ_e]^T, V is that flying speed, h are height.

Further, in step s 2, the design process of contragradience sliding mode controller is：Speed different three is decomposed into return Road：Fast loop, slower loop, slow loop；Virtual controlling rule is calculated since the slow loop subsystem farthest from control input, it is first First define the error of subsystems：

WhereinFor the desired command signal of tracking, x_idRestrained for the virtual controlling of subsystem；

First subsystem is that slow loop subsystem tracking error is e₁=x₁-x_d, after both members difference derivationAgain because e₂=x₂-x_2dSubstitute into：

x_2dIt is the virtual controlling rule of slower loop subsystem, design virtual controlling rule x for second subsystem_2dFor：Wherein, k_x1＞ 0 is that virtual controlling restrains design parameter to be asked, and is updated to after formula (11) and obtained：

Second sub- system tracking error e₂=x₂-x_2dAfter both members difference derivationThen again because e₃ =x₃-x_3d, after substitution：

x_3dIt is the virtual controlling rule for returning to subsystems for three subsystems, by formula (13) design virtual controlling rule x_3dFor：Wherein, k_x2＞ 0 is that virtual controlling restrains design parameter to be asked.It is updated to after formula (13) and is obtained

Three subsystems are to return to subsystems tracking error e₃=x₃-x_3dAfter both members difference derivation：

Design control input：

k_x3＞ 0 is controller design parameter, is obtained：

Further, the calculating process of the stability of contragradience sliding mode controller is：

Defining Liapunov function is：

The derivative of the function against time has：

Formula (24) and (25) are substituted into (39) to obtain：

Because coefficient k_xi＞ 0, k₁＞ 0, k₂＞ 0, is obtained：

In summary, system mode can reach diverter surface within the limited time, meet system stable condition.

Further, aircraft altitude is chosen during performance simulation and the initial equilibrium conditionses of flying speed are respectively Nominal parameters under 33528m and 4590.3m/s models, the simulation parameter of double power sliding mode controllers is chosen for：

Control parameter：k_x1=3, k_x2=3, c₁=2, c₂=2, k₁=0.8, k₂=3, η=0.5, λ=1.5.

Further, also this maximum Parameter Perturbation is introduced to dummy vehicle during emulation to verify.

Compared with prior art, the beneficial effect that is reached of the present invention is：Using double power sliding formwork controls based on Backstepping Device processed, the control method, which can be effectively reduced handoff gain and eliminate, buffets problem present in sliding formwork control.Based on contragradience Double power sliding mode controllers of method combine sliding formwork control system is met uncertain problem under matching condition have it is stronger Robustness and Backstepping to the advantage of processing system mismatched uncertainties, ensure that rapidity and the Shandong of control system Rod.

Brief description of the drawings

Fig. 1 is the model framework chart that the longitudinal model feedback linearisation of hypersonic aircraft is obtained；

Fig. 2 is the simulation result using contragradience sliding formwork control ratio of the present invention：Wherein (a) is the tracking response curve pair of speed Than figure, (b) is the tracking response curve comparison figure of height；

Fig. 3 is the comparative result under different parameters perturbation using contragradience sliding formwork control ratio of the present invention：Wherein (a) is flight The tracking response Dependence Results of speed；(b) be flying height tracking response Dependence Results；(c) be flight angular speed tracking Response curve result；(d) it is the tracking response Dependence Results of flying angle；(e) it is the tracking response curve knot of flight angle of rudder reflection Really；(f) be engine regulating valve tracking response Dependence Results.

Embodiment

The invention will be further described below in conjunction with the accompanying drawings.Following examples are only used for clearly illustrating the present invention Technical scheme, and can not be limited the scope of the invention with this.

When hypersonic flight cruising flight, it is assumed that roll angle and sideslip are all zero, then approximate to ignore longitudinal direction and horizontal Lateral coupling, carries out decoupling processing to the longitudinal model of hypersonic aircraft, obtains hypersonic aircraft rigid body and indulge To kinetic model.The control input of aircraft is engine throttle opening degree instruction β_cWith elevator angle δ_e, take aircraft Quantity of state have：Flying speed V, flight path inclination angle γ, angle of attack α, pitch rate q and flying height h, then hypersonic flight Device Longitudinal Dynamic Model is：

Wherein, L, D, T represent aircraft lift, resistance and motor power respectively, and M represents pitching moment, I_yyRepresent vertical To rotary inertia, m is quality, and R represents earth radius, and r represents the earth's core of aircraft away from r=R+h, g is terrestrial gravitation acceleration Constant.

The purpose of hypersonic aircraft control is selection engine's throttling valve opening controlled quentity controlled variable β_cWith lifting angle of rudder reflection δ_e, Ensure that what the flying speed V and flying height h of aircraft be capable of fast accurate traces into designated value V_dAnd h_d.Formula (2)~(3) are right Export flying speed V and flying height h and use overall-finished housing linearization process, i.e., flying speed V and flying height h is carried out Differential process, until control input β_cOr δ_eAppear in differential formula.Thus according to kinetics equation to output flying speed V With flying height h use the expression formula after overall-finished housing linearization process for：

In formula：

b₁₁=(ρ V²s_wcω²/2m)cosα (5)

b₂₁=(ρ V²s_wcω²/2m)sin(α+γ)(7)

In formula：x₀Represent the initial value of quantity of state, D_αRepresent because of resistance, L caused by the angle of attack_αRepresent caused by the angle of attack Lift, T_αThe thrust caused by the angle of attack is represented, ρ represents atmospheric density, S_wAircraft area of reference is represented, c represents Average aerodynamic string It is long, c_eFor elevator coefficient, it in nominal height h is 33528m that other coefficient values, which are, and datum speed v is 4590.3m/s flight shapes Obtained under state.It is that can obtain by above formulah⁽⁴⁾Expression formula contain control input β_cAnd δ_e。

A kind of control method of hypersonic aircraft towards under condition of uncertainty of the present invention, including procedure below：

According to above-mentioned coordinate transform, the dynamical equation (2) of hypersonic aircraft longitudinal direction model can be converted into following shape State equation form：

WhereinU=[β_c δ_e]^T。

Fig. 1 provides the longitudinal model framework chart obtained after the longitudinal model feedback linearisation of hypersonic aircraft, according to The characteristics of state variable, it is broken down into three different loops of speed：Fast loop, slower loop, slow loop, correspond to three respectively Individual subsystem is to return to subsystems, slower loop subsystem, slow loop subsystem.Only consider vertical passage, flying speed V, Height h is slow state.

With reference to《The contragradience sliding formwork control control of hypersonic aircraft track following》, according to the design philosophy of Backstepping, The design that the design i.e. virtual controlling for proceeding by controller from the slow loop subsystem farthest from control input u is restrained, progressively after Move back.The error of subsystems is defined first：

WhereinFor the desired command signal of tracking, x_idRestrained for the virtual controlling of subsystem.

First subsystem is that slow loop subsystem tracking error is e₁=x₁-x_d, control targe is e₁→ 0, both members Obtained respectively after derivationAgain because e₂=x₂-x_2dSubstitute into：

x_2dIt is the virtual controlling rule of slower loop subsystem, design virtual controlling rule x for second subsystem_2dFor：Wherein, k_x1＞ 0 is that virtual controlling restrains design parameter to be asked, and is updated to after formula (11) and obtained：

Second sub- system tracking error e₂=x₂-x_2d, in order that error e₂Minimum, after both members difference derivationThen again because e₃=x₃-x_3d, after substitution：

x_3dIt is the virtual controlling rule for returning to subsystems for three subsystems, by formula (13) design virtual controlling rule x_3dFor：Wherein, k_x2＞ 0 is that virtual controlling restrains design parameter to be asked.It is updated to after formula (13)

Three subsystems are to return to subsystems tracking error e₃=x₃-x_3dAfter both members difference derivation：

Design control input：

k_x3＞ 0 is controller design parameter, is obtained：

What sliding formwork control was solved is matching uncertain problem, and Backstepping solves the problems, such as mismatched uncertainties, so Sliding mode design, final design contragradience sliding formwork control ratio have been carried out after design Backstepping.

Define sliding-mode surface：

Wherein c_i＞ 0, for design parameter to be asked.

There is convergence rate for traditional Reaching Law in sliding formwork control slow and the deficiency such as buffet, in order to realize that finite time is arrived Up to sliding-mode surface, and weaken chattering phenomenon, double power Reaching Laws in selection synovial membrane face are：

In formula, k₁＞ 0, k₂The ＞ λ ＞ 0 of ＞ 0, η ＞ 1,1 are parameter to be asked.

When | S | ＞ 1 represents that system mode away from sliding mode, that is, only has the Section 1 in (19) to play a leading role；When | s | ＜ 1 represents system mode close to sliding formwork state, and only Section 2 plays a major role in formula (19), fully with reference to this two excellent Gesture so that system mode has more preferable motion qualities.

With reference to reachable condition, the sliding moding structure flight control system based on double power Reaching Laws converges to for zero time For：

Wherein t₁,t₂Convergence time to be asked is represented respectively.

Prove：When system mode is away from sliding-mode surface, because 0 ＜ λ ＜ 1, η ＞ 1, so velocity of approach is main by Section 1 Determine, do not consider the influence of Section 2 now, formula (19) can be abbreviated as：

Above formula both sides integration can be obtained：

S^1-η=-(1- η) k₁t+S(0)^1-η (22)

Therefore it is the time required to sliding-mode surface S=0 → S=1 can be obtained：

When system mode moves closer to sliding-mode surface, because 0 ＜ λ ＜ 1, η ＞ 1, velocity of approach is mainly determined by Section 2, Therefore the influence of Section 1 and Parameter Perturbation is not considered, and formula (19) can be abbreviated as：

Formula (32) both sides are integrated：

S^1-λ=-(1- λ) k₂t+1 (25)

Therefore it is the time required to sliding-mode surface S=1 → S=0 can be obtained：

Therefore, convergence time is both sums, i.e.,：

From the above analysis, S=0 is worked as, because when system mode reaches sliding mode, speed is gradually decreased as Zero, with sliding mode realize it is smooth excessively, largely reducing system chatter.As long as suitably increasing k₁It can add with η value Fast velocity of approach of the quantity of state away from Fault slip rate, suitably increases k₂It can accelerate quantity of state close to Fault slip rate with λ Velocity of approach.Theory analysis shows:Double power sliding formworks can effectively eliminate buffeting, and away from and during close to sliding mode All there is velocity of approach quickly, and the Second Order Sliding Mode in High-Order Sliding Mode, with similar convergence property, i.e. S=0.

Derivation is carried out to (18) to obtain：

Formula (12), (14) and (15) is substituted into (27), and (19) and (27) are combined to obtained contragradience sliding formwork control ratio For：

Stability analysis

Defining Liapunov function is：

The derivative of the function against time has：

Formula (24) and (25) are substituted into (39) to obtain：

Because coefficient k_xi＞ 0, k₁＞ 0, k₂＞ 0, is obtained：

In summary, system mode can reach diverter surface within the limited time, meet system stable condition.

The present invention solves the chattering phenomenon of generally existing in sliding formwork control using the control method of double power sliding formworks first, Greatly enhance the accuracy of the control method.

Embodiment

In order to verify the control effect of designed contragradience sliding mode controller, emulation point is carried out to hypersonic aircraft Analysis, gives instruction trace signal, while adjusted design controller parameter, obtains corresponding instruction trace effect, while being checking The robustness of contragradience sliding-mode control, this maximum Parameter Perturbation is introduced to dummy vehicle and is verified, the controlling party is shown Method drastically increases the stability and accuracy of system.

Simulating, verifying is carried out to the hypersonic vehicle having built up from the angle of emulation below, it is imitative in Matlab In true experiment, reference《The contragradience sliding formwork control of hypersonic aircraft track following》Simulating, verifying condition in document, chooses and flies The initial equilibrium conditionses of row device flying height and flying speed are respectively the nominal parameters under 33528m and 4590.3m/s models, The simulation parameter of double power sliding mode controllers is chosen for：

Control parameter：k_x1=3, k_x2=3, c₁=2, c₂=2, k₁=0.8, k₂=3, η=0.5, λ=1.5.

Fig. 2 is the speed and the response curve of height under the conditions of contragradience sliding formwork control ratio, wherein (a) is the tracking of speed Response curve comparison diagram, (b) is the tracking response curve comparison figure of height.It can be seen from Fig. 2 that contragradience sliding-mode control is a kind of Very effective nonlinear control method, speed V and height the h output valve of hypersonic aircraft can preferably trace command Signal, with less overshoot, can realize tenacious tracking, system has preferable tracking performance in 15s.

Maximum Parameter Perturbation amount, the maximum perturbation parameter that Selection Model allows are introduced in the model parameter nominal value of foundation Value is as follows：|Δm|/m₀=0.03, | Δ c_e|/c_e0=0.02, | Δ s_w|/s_w0=0.03, | Δ ρ |/ρ₀=0.03, wherein subscript " 0 " represents the nominal value of relevant parameter.

Response curve with Parameter Perturbation is contrasted with not adding the model response curve of Parameter Perturbation, i.e. Fig. 3 The response curve of each state under Parameter Perturbation, wherein (a) is the tracking response Dependence Results of flying speed；(b) it is flying height Tracking response Dependence Results；(c) be flight angular speed tracking response Dependence Results；(d) it is the tracking response of flying angle Dependence Results；(e) it is the tracking response Dependence Results of flight angle of rudder reflection；(f) be engine regulating valve tracking response curve knot Really.Positive and negative change is gone respectively to each variable parameter in Fig. 3, when to take positive Parameter Perturbation be Parameter Perturbation+100%, negative when taking Parameter Perturbation be -100%.

From figure 3, it can be seen that when Parameter Perturbation reaches maximum, there is less overshoot in speed tracing, and height with Track and angle of attack response occur in that trickle steady-state error, and pitch rate and change in angle of attack are small, and overall control effect is good, instead Step sliding-mode control has good compensating action for Parameter Perturbation and external interference, and whole system has preferable tracing property Energy and stronger robust performance.

Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, without departing from the technical principles of the invention, some improvement and modification can also be made, these improvement and modification Also it should be regarded as protection scope of the present invention.

Claims (6)

1. a kind of control method of hypersonic aircraft towards under condition of uncertainty, it is characterized in that, comprise the following steps：

Step S1, according to hypersonic aircraft longitudinal dynamics equation, total state is used to flying speed V and flying height h Feedback linearization processing, obtains its corresponding state equation；

Step S2, according to this state equation, designs contragradience sliding mode controller,

Define sliding-mode surface：

$S=\underset{i=1}{\overset{2}{\Σ}}{c}_i{e}_i+e_3=c_1{e}_1+c_2{e}_2+e_3$

Wherein, c_i＞ 0 is parameter, e_iAnd e₃For system tracking error.

Double power Reaching Laws in selection synovial membrane face are：

$\stackrel{\·}{S}=-k_1|S{|}^{\mathrm{\η}}\mathrm{sgn}\left(S\right)-k_2|S{|}^{\mathrm{\λ}}\mathrm{sgn}\left(S\right)$

In formula, k₁＞ 0, k₂The ＞ λ ＞ 0 of ＞ 0, η ＞ 1,1 are parameter；

Contragradience sliding formwork control ratio is：

$u=G^T{\left({\mathrm{GG}}^T\right)}^{-1}(-c_1{\stackrel{\·}{e}}_1-c_2{\stackrel{\·}{e}}_2-f+{\stackrel{\·}{x}}_{3d}-k_1|S_V{|}^{\mathrm{\η}}\mathrm{sgn}\left(S\right)-k_2\left|S{|}^{\mathrm{\λ}}\mathrm{sgn}\right(S\left)\right)$

Step S3, test platform is built based on this contragradience sliding mode controller, carries out performance simulation.

2. a kind of control method of hypersonic aircraft towards under condition of uncertainty according to claim 1, it is special Levying is, in step S1, and the dynamical equation of hypersonic aircraft longitudinal direction model can be converted into following state equation form：

${\stackrel{\·}{x}}_1=x_2$

${\stackrel{\·}{x}}_2=x_3$

${\stackrel{\·}{x}}_3=f+Gu$

WhereinU=[β_c δ_e]^T, V It is height for flying speed, h.

3. a kind of control method of hypersonic aircraft towards under condition of uncertainty according to claim 1, it is special Levying is, in step s 2, and the design process of contragradience sliding mode controller is：It is decomposed into three different loops of speed：Fast loop, compared with Slow loop, slow loop；Virtual controlling rule is calculated since the slow loop subsystem farthest from control input, each height is defined first The error of system：

$\left\{\begin{array}{c}{e}_1=x_1-x_d\\ e_i=x_i-x_{id},i=2,3\end{array}\right.---\left(10\right)$

WhereinFor the desired command signal of tracking, x_idRestrained for the virtual controlling of subsystem；

First subsystem is that slow loop subsystem tracking error is e₁=x₁-x_d, after both members difference derivationAgain because e₂=x₂-x_2dSubstitute into：

${\stackrel{\·}{e}}_1=e_2+x_{2d}-{\stackrel{\·}{x}}_d---\left(11\right)$

x_2dIt is the virtual controlling rule of slower loop subsystem, design virtual controlling rule x for second subsystem_2dFor：Wherein, k_x1＞ 0 is that virtual controlling restrains design parameter to be asked, and is updated to after formula (11) and obtained：

${\stackrel{\·}{e}}_1=e_2-k_{x1}{e}_1---\left(12\right)$

Second sub- system tracking error e₂=x₂-x_2dAfter both members difference derivationThen again because e₃=x₃- x_3d, after substitution：

${\stackrel{\·}{e}}_2=e_3+x_{3d}-{\stackrel{\·}{x}}_{2d}---\left(13\right)$

x_3dIt is the virtual controlling rule for returning to subsystems for three subsystems, by formula (13) design virtual controlling rule x_3dFor：Wherein, k_x2＞ 0 is that virtual controlling restrains design parameter to be asked.It is updated to after formula (13) and is obtained

${\stackrel{\·}{e}}_2=-e_1-k_{x2}{e}_2+e_3---\left(14\right)$

Three subsystems are to return to subsystems tracking error e₃=x₃-x_3dAfter both members difference derivation：

${\stackrel{\·}{e}}_3={\stackrel{\·}{x}}_3-{\stackrel{\·}{x}}_{3d}=f+Gu-{\stackrel{\·}{x}}_{3d}---\left(15\right)$

Design control input：

$u=G^T{\left({\mathrm{GG}}^T\right)}^{-1}(-k_{x3}{e}_3-e_2-f+{\stackrel{\·}{x}}_{3d})---\left(16\right)$

k_x3＞ 0 is controller design parameter, is obtained：

${\stackrel{\·}{e}}_3=-k_{x3}{e}_3-e_2.---\left(17\right)$

4. a kind of control method of hypersonic aircraft towards under condition of uncertainty according to claim 1, it is special Levying is, the calculating process of the stability of contragradience sliding mode controller is：

Defining Liapunov function is：

$V_1=\frac{1}{2}{e_1}^2+\frac{1}{2}{e_2}^2+\frac{1}{2}{e_3}^2+\frac{1}{2}{S}^2---\left(29\right)$

The derivative of the function against time has：

$\begin{array}{c}{\stackrel{\·}{V}}_1=e_1{\stackrel{\·}{e}}_1+e_2{\stackrel{\·}{e}}_2+e_3{\stackrel{\·}{e}}_3+S\stackrel{\·}{S}\\ =-k_{x1}{e_1}^2-k_{x2}{e_2}^2-k_{x3}{e_3}^3+S\[c_1(e_2-k_{x1}{e}_1)\\ +c_2(e_3-k_{x2}{e}_2-e_1)+f+Gu-{\stackrel{\·}{x}}_{3d}\]\end{array}---\left(30\right)$

Formula (24) and (25) are substituted into (39) to obtain：

$\begin{array}{c}{\stackrel{\·}{V}}_1=-k_{x1}{e_1}^2-k_{x2}{e_2}^2-k_{x3}{e_3}^2-k_1|S{|}^{\mathrm{\η}}S\mathrm{sgn}\left(S\right)-k_2|S{|}^{\mathrm{\λ}}S\mathrm{sgn}\left(S\right)\\ =-\underset{1}{\overset{3}{\Σ}}{k}_{xi}{e_i}^2-k_1|S{|}^{1+\mathrm{\η}}-k_2|S{|}^{1+\mathrm{\λ}}\end{array}---\left(31\right)$

Because coefficient k_xi＞ 0, k₁＞ 0, k₂＞ 0, is obtained：

${\stackrel{\&CenterDot;}{V}}_1=-\underset{1}{\overset{3}{\&Sigma;}}{k}_{xi}{e_i}^2-k_1|S{|}^{1+\mathrm{\&eta;}}-k_2|S{|}^{1+\mathrm{\&lambda;}}<0---\left(32\right)$

In summary, system mode can reach diverter surface within the limited time, meet system stable condition.

5. a kind of control method of hypersonic aircraft towards under condition of uncertainty according to claim 1, it is special Levying is, the initial equilibrium conditionses that aircraft altitude and flying speed are chosen during performance simulation be respectively 33528m and Nominal parameters under 4590.3m/s models, the simulation parameter of double power sliding mode controllers is chosen for：k_x1=3, k_x2=3, c₁=2, c₂=2, k₁=0.8, k₂=3, η=0.5, λ=1.5.

6. a kind of control method of hypersonic aircraft towards under condition of uncertainty according to claim 1, it is special Levying is, this maximum Parameter Perturbation is also introduced to dummy vehicle during emulation verifies.