CN106997208B - A kind of control method towards the hypersonic aircraft under condition of uncertainty - Google Patents
A kind of control method towards the hypersonic aircraft under condition of uncertainty Download PDFInfo
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- G—PHYSICS
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
- G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
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Abstract
The invention discloses a kind of control methods towards the hypersonic aircraft under condition of uncertainty, the following steps are included: step S1, according to hypersonic aircraft longitudinal dynamics equation, overall-finished housing linearization process is used to flying speed V and flying height h, obtains its corresponding state equation；Step S2 designs contragradience sliding mode controller according to this state equation, selects double power Reaching Laws in synovial membrane face are as follows:In formula, k1> 0, k21,1 > λ > 0 of > 0, η > is parameter；Step S3 builds test platform based on this contragradience sliding mode controller, carries out performance simulation.The method of the present invention 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
Technical field
The present invention relates to hypersonic aircraft technical fields, and in particular to a kind of high ultrasound towards under condition of uncertainty
The flight control method of fast aircraft.
Background technique
Hypersonic aircraft mainly executes aerial mission, near space in the near space region apart from 20~100km of ground
The mankind space that develops and uses very well not yet so far, in terms of great potential, it is hypersonic to fly
Concealment of the row device near space region is very high and aircraft communication signal in the field is very strong, hypersonic to fly
Row device, which determines it not only near space flight, has the advantage of aeronautical technology, but also has the advantages of spacecraft can not possess.In army
For thing using upper, it is very fast that hypersonic aircraft executes speed, can first time with reaching target, will cause quickly accurate
Hit the arriving in weapon epoch.Especially information acquisition, hasty breaching, communication support, long-range strike, in terms of it is great
Development potentiality.Just because of these huge military values and potential economic value, more and more military powers are 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 control controller with high accuracy, this just proposes advanced control method urgent
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 by complicated nonlinear Control PROBLEM DECOMPOSITION into multiple linear models
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 strong
Non-linear and high coupling is much unable to satisfy the requirement of performance indicator just with the controller that gain preset method designs.
It is also one of most widely used method that control theory of feedback linearization, which is most important in nonlinear control method, real
Two existing effective ways are as follows: 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
Kind method needs to establish on the basis of accurate model, and very sensitive to error existing for model, to reduce entire 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 is occurred in matter.When system mode passes through not same district
When domain, the structure of feedback control requires the switch logic formulated to become by designer according to a set of according to system performance index
Change, enables control system that there is certain adaptation to factors such as inherent Parameters variation and the external environment disturbances of controlled device
Power guarantees that system performance reaches desired performance indicator requirement.But system mode easily causes to buffet 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..
Since hypersonic aircraft using body coupled structure and flies under conditions of High aititude and big Mach number,
Cause it quite sensitive to the variation of gas condition, and hypersonic aircraft also receives structure dynamics in flight course,
The influence for promoting dynamic and coupling between them, 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 especially
It is important.Meanwhile there are convergence rates slowly and the deficiencies of buffet for Reaching Law traditional in sliding mode controller design in the prior art,
The present invention provides a kind of new resolving ideas.
Summary of the invention
It is an object of the invention to overcome deficiency in the prior art, provide 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
It changes gain and eliminates and buffet problem present in sliding formwork control.
In order to solve the above technical problems, the present invention provides a kind of hypersonic aircrafts towards under condition of uncertainty
Control method, characterized in that the following steps are included:
Step S1, according to hypersonic aircraft longitudinal dynamics equation, to flying speed V and flying height h using complete
State feedback linearization processing, obtains its corresponding state equation；
Step S2 designs contragradience sliding mode controller according to this state equation,
Define sliding-mode surface:
Wherein, ci> 0 is parameter, eiAnd e3For system tracking error.
Select double power Reaching Laws in synovial membrane face are as follows:
In formula, k1> 0, k21,1 > λ > 0 of > 0, η > is parameter；
Contragradience sliding formwork control ratio are as follows:
Step S3 builds test platform 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=[βc
δe]T, V is flying speed, h is height.
Further, in step s 2, the design process of contragradience sliding mode controller are as follows: be decomposed into speed different three and return
Road: fast circuit, slower circuit, slow circuit；Virtual controlling rule is calculated since the slow circuit subsystem farthest from control input, it is first
First define the error of subsystems:
WhereinFor the desired command signal of tracking, xidIt is restrained for the virtual controlling of subsystem；
First subsystem, that is, slow circuit subsystem tracking error is e1=x1-xd, after both members difference derivationAgain because of e2=x2-x2dIt substitutes into:
x2dIt is the virtual controlling rule of slower circuit subsystem for second subsystem, design virtual controlling restrains x2dAre as follows:Wherein, kx1> 0 is that virtual controlling restrains design parameter to be asked, and is obtained after being updated to formula (11):
Second sub- system tracking error e2=x2-x2dBoth members obtain after distinguishing derivationThen again because of e3
=x3-x3d, after substitution:
x3dIt is to return to the virtual controlling rule of subsystems for three subsystems, by formula (13) design virtual controlling rule
x3dAre as follows:Wherein, kx2> 0 is that virtual controlling restrains design parameter to be asked.After being updated to formula (13)
?
Three subsystems return to subsystems tracking error e3=x3-x3dBoth members obtain after distinguishing derivation:
Design control input:
kx3> 0 is controller design parameter, is obtained:
Further, the calculating process of the stability of contragradience sliding mode controller are as follows:
Define Liapunov function are as follows:
The derivative of the function against time has:
Formula (24) and (25) are substituted into (39) to obtain:
Because of coefficient kxi> 0, k1> 0, k2> 0, obtains:
In conclusion system mode can reach diverter surface within the limited time, meet system stable condition.
Further, aircraft altitude is chosen when performance simulation and the initial equilibrium conditions of flying speed are respectively
The simulation parameter of nominal parameters under 33528m and 4590.3m/s model, double power sliding mode controllers is chosen are as follows:
Control parameter: kx1=3, kx2=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 when emulation to verify.
Compared with prior art, the beneficial effects obtained by the present invention are as follows being: using double power sliding formwork controls based on Backstepping
Device processed, which, 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, which combine the uncertain problem that sliding formwork control meets system under matching condition, to be had relatively by force
Robustness and Backstepping to the advantage of processing system mismatched uncertainties, be capable of rapidity and the Shandong of Guarantee control system
Stick.
Detailed description of the invention
Fig. 1 is the model framework chart that hypersonic aircraft longitudinal direction model feedback linearizes；
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) be height tracking response curve comparison figure；
Fig. 3 is the comparison result using contragradience sliding formwork control ratio of the present invention under different parameters perturbation: 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；It (d) is the tracking response Dependence Results of flying angle；It (e) is the tracking response curve knot of flight angle of rudder reflection
Fruit；(f) be engine regulating valve tracking response Dependence Results.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.Following embodiment is only used for clearly illustrating the present invention
Technical solution, and not intended to limit the protection scope of the present invention.
When hypersonic flight cruising flight, it is assumed that roll angle and sideslip are all zero, then approximation ignore it is longitudinal and horizontal
Lateral coupling carries out decoupling processing to hypersonic aircraft longitudinal direction model, and it is vertical to obtain hypersonic aircraft rigid body
To kinetic model.The control input of aircraft is engine throttle opening degree instruction βcWith elevator angle δe, take aircraft
Quantity of state have: flying speed V, track inclination angle γ, angle of attack α, pitch rate q and flying height h, then hypersonic flight
Device Longitudinal Dynamic Model are as follows:
Wherein, L, D, T respectively indicate aircraft lift, resistance and motor power, and M indicates pitching moment, IyyIndicate vertical
To rotary inertia, m is quality, and R indicates that earth radius, r indicate the earth's core of aircraft away from r=R+h, g are terrestrial gravitation acceleration
Constant.
The purpose of hypersonic aircraft control is selection engine's throttling valve opening control amount βcWith lifting angle of rudder reflection δe,
Guarantee that the flying speed V and flying height h of aircraft be capable of fast accurate traces into designated value VdAnd hd.Formula (2)~(3) are right
It exports flying speed V and flying height h and uses overall-finished housing linearization process, i.e., flying speed V and flying height h is carried out
Differential process, until control inputs βcOr δeIt appears in differential formula.Thus according to kinetics equation to output flying speed V
With flying height h using the expression formula after overall-finished housing linearization process are as follows:
In formula:
b11=(ρ V2swcω2/2m)cosα (5)
b21=(ρ V2swcω2/2m)sin(α+γ)(7)
In formula: x0Indicate the initial value of quantity of state, DαIt indicates because of resistance caused by the angle of attack, LαCaused by indicating because of the angle of attack
Lift, TαThrust caused by indicating because of the angle of attack, ρ represent atmospheric density, SwAircraft area of reference is represented, c represents Average aerodynamic string
It is long, ceFor elevator coefficient, it is 33528m that other coefficient values, which are in nominal height h, and datum speed v is 4590.3m/s flight shape
It is obtained under state.It can be obtained by above formulah(4)Expression formula contain control input βcAnd δe。
A kind of control method towards the hypersonic aircraft under condition of uncertainty of the invention, including following procedure:
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=[βc
δe]T。
Fig. 1 provides the longitudinal model framework chart obtained after the linearisation of hypersonic aircraft longitudinal direction model feedback, according to
The characteristics of state variable is broken down into three different circuits of speed: fast circuit, slower circuit, slow circuit respectively correspond three
A subsystem returns to subsystems, slower circuit subsystem, slow circuit subsystem.Only consider vertical passage, flying speed V,
Height h is slow state.
With reference to the contragradience sliding formwork control of hypersonic aircraft track following " control ", according to the design philosophy of Backstepping,
The design that controller is carried out since the slow circuit subsystem farthest from control input u is design that virtual controlling is restrained, gradually after
It moves back.The error of subsystems is defined first:
WhereinFor the desired command signal of tracking, xidIt is restrained for the virtual controlling of subsystem.
First subsystem, that is, slow circuit subsystem tracking error is e1=x1-xd, control target is e1→ 0, both members
Respectively after derivationAgain because of e2=x2-x2dIt substitutes into:
x2dIt is the virtual controlling rule of slower circuit subsystem for second subsystem, design virtual controlling restrains x2dAre as follows:Wherein, kx1> 0 is that virtual controlling restrains design parameter to be asked, and is obtained after being updated to formula (11):
Second sub- system tracking error e2=x2-x2d, in order to make error e2Minimum, both members obtain after distinguishing derivationThen again because of e3=x3-x3d, after substitution:
x3dIt is to return to the virtual controlling rule of subsystems for three subsystems, by formula (13) design virtual controlling rule
x3dAre as follows:Wherein, kx2> 0 is that virtual controlling restrains design parameter to be asked.After being updated to formula (13)
?
Three subsystems return to subsystems tracking error e3=x3-x3dBoth members obtain after distinguishing derivation:
Design control input:
kx3> 0 is controller design parameter, is obtained:
What sliding formwork control 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 ci> 0, for design parameter to be asked.
For Reaching Law traditional in sliding formwork control, there are convergence rates slowly and the deficiencies of buffet, in order to realize that finite time arrives
Up to sliding-mode surface, and weaken chattering phenomenon, select double power Reaching Laws in synovial membrane face are as follows:
In formula, k1> 0, k21,1 > λ > 0 of > 0, η > is parameter to be asked.
When | S | > 1 indicates that system mode far from sliding mode, that is, only has the first item in (19) to play a leading role；When | s |
< 1 indicates system mode close to sliding formwork state, and only Section 2 plays a major role in formula (19), sufficiently combines this two excellent
Gesture, so that system mode has better motion qualities.
In conjunction with reachable condition, the sliding moding structure flight control system based on double power Reaching Laws converges to for zero time
Are as follows:
Wherein t1,t2Respectively indicate convergence time to be asked.
It proves: when system mode is far from sliding-mode surface, because of 0 < λ < 1, η > 1, so velocity of approach is mainly by first item
It determines, does not consider the influence of Section 2 at this time, formula (19) can write a Chinese character in simplified form are as follows:
Above formula both sides integral can be obtained:
S1-η=-(1- η) k1t+S(0)1-η (22)
Therefore the time required to sliding-mode surface S=0 → S=1 can be obtained are as follows:
When system mode moves closer to sliding-mode surface, because of 0 < λ < 1, η > 1, velocity of approach is mainly determined by Section 2,
Therefore the influence of first item and Parameter Perturbation is not considered, and formula (19) can write a Chinese character in simplified form are as follows:
Formula (32) both sides are integrated:
S1-λ=-(1- λ) k2t+1 (25)
Therefore the time required to sliding-mode surface S=1 → S=0 can be obtained are as follows:
Therefore, convergence time is sum of the two, it may be assumed that
From the above analysis, work as S=0, because speed is gradually decreased as when system mode reaches sliding mode
Zero, with sliding mode realize it is smooth excessively, largely reduced system chatter.As long as suitably increasing k1It can add with the value of η
Fast velocity of approach of the quantity of state far from Fault slip rate, suitably increase k2It can accelerate quantity of state close to Fault slip rate with λ
Velocity of approach.Theoretical analysis shows that: double power sliding formworks can effectively eliminate buffeting, and when far from and close to sliding mode
All there is cracking velocity of approach, with the Second Order Sliding Mode in High-Order Sliding Mode, there is similar convergence property, i.e. S=0.
Derivation is carried out to (18) to obtain:
Formula (12), (14) and (15) are substituted into (27), and (19) and (27) are combined to obtained contragradience sliding formwork control ratio
Are as follows:
Stability analysis
Define Liapunov function are as follows:
The derivative of the function against time has:
Formula (24) and (25) are substituted into (39) to obtain:
Because of coefficient kxi> 0, k1> 0, k2> 0, obtains:
In conclusion system mode can reach diverter surface within the limited time, meet system stable condition.
The present invention solves chattering phenomenon 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 verifying
The robustness of contragradience sliding-mode control introduces this maximum Parameter Perturbation to dummy vehicle and verifies, shows the controlling party
Method greatly improves 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 test, referring to simulating, verifying condition in " the contragradience sliding formwork control of hypersonic aircraft track following " document, chooses and fly
The initial equilibrium conditions of row device flying height and flying speed are respectively the nominal parameters under 33528m and 4590.3m/s model,
The simulation parameter of double power sliding mode controllers is chosen are as follows:
Control parameter: kx1=3, kx2=3, c1=2, c2=2, k1=0.8, k2=3, η=0.5, λ=1.5.
Fig. 2 is the response curve of the speed and height under the conditions of contragradience sliding formwork control ratio, wherein (a) is the tracking of speed
Response curve comparison diagram, (b) be height tracking response curve comparison figure.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 commands
Signal has lesser overshoot, and tenacious tracking may be implemented in 15s, and system has preferable tracking performance.
Maximum Parameter Perturbation amount, the maximum perturbation parameter that Selection Model allows are introduced in the model parameter nominal value of foundation
It is worth as follows: | Δ m |/m0=0.03, | Δ ce|/ce0=0.02, | Δ sw|/sw0=0.03, | Δ ρ |/ρ0=0.03, wherein subscript
The nominal value of " 0 " expression relevant parameter.
Response curve with Parameter Perturbation is compared with the model response curve that Parameter Perturbation is not added, i.e. Fig. 3
The response curve of each state under Parameter Perturbation, wherein (a) is the tracking response Dependence Results of flying speed；It (b) is flying height
Tracking response Dependence Results；(c) be flight angular speed tracking response Dependence Results；It (d) is the tracking response of flying angle
Dependence Results；It (e) is the tracking response Dependence Results of flight angle of rudder reflection；(f) be engine regulating valve tracking response curve knot
Fruit.Positive and negative variation 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 lesser overshoot in speed tracing, and height with
There is subtle steady-state error in track and angle of attack response, and pitch rate and change in angle of attack are small, and whole 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
It can be with stronger robust performance.
The above is only a 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, several improvements and modifications, these improvements and modifications can also be made
Also it should be regarded as protection scope of the present invention.
Claims (6)
1. a kind of control method towards the hypersonic aircraft under condition of uncertainty, characterized in that the following steps are included:
Step S1 uses total state to flying speed V and flying height h according to hypersonic aircraft longitudinal dynamics equation
Feedback linearization processing, obtains its corresponding state equation；
Step S2 designs contragradience sliding mode controller according to this state equation,
Define sliding-mode surface:
Wherein, ci> 0 is parameter, eiAnd e3For system tracking error,
Select double power Reaching Laws of sliding-mode surface are as follows:
In formula, k1> 0, k21,1 > λ > 0 of > 0, η > is parameter；
Contragradience sliding formwork control ratio are as follows:
In formula,x3dIt is to return to the virtual controlling rule of subsystems for three subsystems；
Step S3 builds test platform based on this contragradience sliding mode controller, carries out performance simulation.
2. a kind of control method towards the hypersonic aircraft under condition of uncertainty according to claim 1, special
Sign is, in step S1, the dynamical equation of hypersonic aircraft longitudinal direction model is converted into following state equation form:
WhereinU=[βc δe]T, V
It is height for flying speed, h.
3. a kind of control method towards the hypersonic aircraft under condition of uncertainty according to claim 1, special
Sign is, in step s 2, the design process of contragradience sliding mode controller are as follows: be decomposed into three different circuits of speed: fast circuit, compared with
Slow circuit, slow circuit；Virtual controlling rule is calculated since the slow circuit subsystem farthest from control input, defines each height first
The error of system:
WhereinFor the desired command signal of tracking, xidIt is restrained for the virtual controlling of subsystem；
First subsystem, that is, slow circuit subsystem tracking error is e1=x1-xd, after both members difference derivationAgain because of e2=x2-x2dIt substitutes into:
x2dIt is the virtual controlling rule of slower circuit subsystem for second subsystem, design virtual controlling restrains x2dAre as follows:Wherein, kx1> 0 is that virtual controlling restrains design parameter to be asked, and is obtained after being updated to formula (11):
Second sub- system tracking error e2=x2-x2dBoth members obtain after distinguishing derivationThen again because of e3=x3-
x3d, after substitution:
x3dIt is to return to the virtual controlling rule of subsystems for three subsystems, x is restrained by formula (13) design virtual controlling3dAre as follows:Wherein, kx2> 0 is that virtual controlling restrains design parameter to be asked, and is obtained after being updated to formula (13)
Three subsystems return to subsystems tracking error e3=x3-x3dBoth members obtain after distinguishing derivation:
Design control input:
kx3> 0 is controller design parameter, is obtained:
4. a kind of control method towards the hypersonic aircraft under condition of uncertainty according to claim 1, special
Sign is the calculating process of the stability of contragradience sliding mode controller are as follows:
Define Liapunov function are as follows:
The derivative of the function against time has:
Formula (24) and (25) are substituted into (39) to obtain:
Because of coefficient kxi> 0, k1> 0, k2> 0, obtains:
In conclusion system mode can reach diverter surface within the limited time, meet system stable condition.
5. a kind of control method towards the hypersonic aircraft under condition of uncertainty according to claim 1, special
Sign is, when performance simulation choose aircraft altitude and flying speed initial equilibrium conditions be respectively 33528m and
The simulation parameter of nominal parameters under 4590.3m/s model, double power sliding mode controllers is chosen are as follows: kx1=3, kx2=3, c1=2,
c2=2, k1=0.8, k2=3, η=0.5, λ=1.5.
6. a kind of control method towards the hypersonic aircraft under condition of uncertainty according to claim 1, special
Sign is, when emulation also introduces this maximum Parameter Perturbation to dummy vehicle and verifies.
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