CN110456642A - Elastic Vehicles robust finite-time control method based on Singular Perturbation Analysis - Google Patents
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Abstract
The Elastic Vehicles robust finite-time control method based on Singular Perturbation Analysis that the present invention relates to a kind of, for the slow subsystem of characterization rigid body, angle of rudder reflection controller is designed using dynamic surface control, utilize neural network estimating system uncertain information, learning evaluation information is introduced into neural network weight more new law by construction firstorder filter and auxiliary signal and realizes learning error finite time convergence control, while difference scores rank is added to guarantee tracking error finite time convergence control in control law；Elastic mode inhibition is carried out for the fast subsystem design sliding mode control algorithm of characterization system resilience mode.Speed tracing is realized for speed subsystem design PID controller.
Description
Technical field
The present invention relates to a kind of flying vehicles control methods, fly more particularly to a kind of elasticity based on Singular Perturbation Analysis
Device robust finite-time control method, belongs to flight control method.
Background technique
Contemporary aircraft is due to largely using light composite material and being designed as slender bodies, lifting body, high aspect ratio etc.
Distinctive appearance, Elastic mode influence more to protrude compared to conventional aircraft, and ignoring Elastic mode design Flight Control Law can
It can lead to aircraft performance decline even flight unstability.
Elastic mode is mostly considered as self-stabilization and directly carries out controller to rigid body by existing aircraft elastomer control research
Design is unable to satisfy the high-precision demand of control；Elastic mode is considered as a kind of disturbance by some scholars, is realized by compensation policy
Elastic part control, however this roadmap lacks the in-depth analysis and research for elastodynamics.Some scholars are adopted
Elastomer control problem is handled with the intelligence learnings method such as neural network, but intelligence learning is mostly adjusted only in accordance with tracking error, accidentally
Poor convergence time is difficult to ensure.
《Novel auxiliary error compensation design for the adaptive neural
control of a constrained flexible air-breathing hypersonic vehicle》(Xiangwei
Bu,Xiaoyan Wu,Zhen Ma,Rui Zhang,Jiaqi Huang,《Neurocomputing》,2016,171:313-
324.) Elastic mode influence for a kind of Elastic Vehicles is considered as systematic uncertainty and proposes a neural network by a text estimates
Meter method provides neural network weight adaptive law according to tracking error.However, simply being considered for elastodynamics
Lack for uncertainty and analyse in depth, it cannot be guaranteed that calming to Elastic mode, and adjusts neural network only in accordance with tracking error
It cannot be guaranteed pace of learning, boundedness only can guarantee for tracking error and learning error, it is difficult to obtain satisfied tracking performance.
Summary of the invention
Technical problems to be solved
To solve the problems, such as that the aerocraft system elastomer under non-linear unknown situation controls, the invention proposes a kind of bases
In the Elastic Vehicles robust finite-time control method of Singular Perturbation Analysis.This method considers that elastomer and rigid body markers are special
Sign is different, and system dynamics is decomposed into slow subsystem and fast subsystem by singular perturbation algorithm.For characterization rigidity
The slow subsystem of body designs angle of rudder reflection controller using dynamic surface control, using neural network estimating system uncertain information,
Learning evaluation information is introduced into neural network weight more new law by construction firstorder filter and auxiliary signal and realizes that study misses
Poor finite time convergence control, while difference scores rank is added to guarantee tracking error finite time convergence control in control law；For
The fast subsystem design sliding mode control algorithm for characterizing system resilience mode carries out Elastic mode inhibition.It is set for speed subsystem
It counts PID controller and realizes speed tracing.
Technical solution
A kind of Elastic Vehicles robust finite-time control method based on Singular Perturbation Analysis, it is characterised in that step is such as
Under:
Step 1: consider Elastic Vehicles vertical passage kinetic model:
The kinematics model is by seven quantity of statesU=[δ is inputted with two controlse,
Φ]TComposition；Wherein, V indicates speed, and h indicates height, and γ indicates that flight path angle, α indicate that the angle of attack, q indicate rate of pitch, η
WithIndicate Elastic mode, δeIndicate that angle of rudder reflection, Φ indicate throttle valve opening；m,IyyTurn of quality, pitch axis is respectively indicated with g
Acceleration caused by dynamic inertia and gravity；ζ, ω and N respectively indicate damping ratio, frequency of natural vibration and the broad sense of Elastic mode
Power；
The expression formula of power and torque and each coefficient are as follows:
Wherein,Indicate dynamic pressure,Indicate mean aerodynamic chord, zTIndicate that moment of thrust brachium, S indicate pneumatic area of reference,WithIt is
Aerodynamic parameter, Nα、N0For the related coefficient for characterizing elastodynamics；
Step 2: definition height tracing error is eh=h-hd, design flight-path angle instruction γdAre as follows:
Wherein, hdIndicate elevation references instruction,Indicate the first differential of elevation references instruction, kh> 0 and ki> 0 is design
Parameter；
According to time-scale separation, regard speed as slow dynamics, the first differential of design flight-path angle instruction are as follows:
Wherein,Indicate the second-order differential of elevation references instruction；
Step 3: taking x1=γ, x2=θ, x3=q, wherein θ=α+γ indicates pitch angle；Posture subsystem (3)-(6) are written as
Following form:
Wherein,
Definitionρ σ=η, ρ B2=β1；Posture subsystem (9) is written as following form:
ρ=0 is set, and posture subsystem (10) is written as following slow subsystem form:
Wherein, ' s ' indicates slow subsystem, δesIndicate the control input of slow subsystem；
Formula (14) are substituted into formula (10), slow subsystem (11)-(14) are written as following form:
Slow subsystem (15) can further be written as following Strict-feedback form:
Wherein, fi, i=1,3 be the unknown smoothed non-linearity function obtained by formula (15), gi, i=1,3 obtains by formula (15)
Known nonlinear function；
Step 4: defining ψ1=σ-σs,Formula (6) is written as following form:
Wherein, δef=δe-δesIndicate the control input of fast subsystem；
Formula (14) are substituted into formula (17), fast subsystem (17) is written as following form:
Formula (18) is further written as following matrix form:
Wherein, ψ=[ψ1,ψ2]T,
Step 5: step 1: defining track angle tracking error are as follows:
e1=x1s-γd (20)
Design pitch angle virtual controlling amount are as follows:
Wherein,Indicate the estimated value of neural network optimal weights vector, θ1Indicate Base Function vector, k1>0、
kf1>0、0<η1<1；
Design firstorder filter are as follows:
Wherein,It indicatesBy the signal obtained after filter expressed by formula (22),For the letter obtained after filtering
NumberDifferential signal, α2>0；
DefinitionIt is as follows to design firstorder filter:
X in formulaf1、θf1For x1s、θ1By the signal obtained after filter shown in formula (23),If
Count companion matrix P1, auxiliary vector Q1、W1It is as follows:
In formula, l1> 0, neural network weightIt is obtained by following adaptive law:
Wherein, γ1> 0, Γ1Be positive permanent several diagonal matrix；
Step 2: pitching angle tracking error is defined are as follows:
Design pitch rate virtual controlling amount are as follows:
Wherein, k2>0、kf2>0、0<η2<1；
Design firstorder filter are as follows:
Wherein,It indicatesBy the signal obtained after filter expressed by formula (28),For the letter obtained after filtering
NumberDifferential signal, α3> 0 is design parameter；
Step 3: pitch rate tracking error is defined are as follows:
Design slow subsystem angle of rudder reflection are as follows:
Wherein,Indicate the estimated value of neural network optimal weights vector, θ3Indicate Base Function vector, k3>
0、kf3>0、0<η3<1；
It enablesIt is as follows to design firstorder filter:
X in formulaf3、θf3For x3s、θ3By the signal obtained after filter shown in formula (31),If
Count companion matrix P3, auxiliary vector Q3、W3It is as follows:
In formula, l3> 0, neural network weightIt is obtained by following adaptive law:
Wherein, γ3> 0, Γ3Be positive permanent several diagonal matrix；
Step 6: defining sliding formwork switching function are as follows:
C=G ψ (34)
Wherein, G ∈ R2×2For the matrix of design；
Design fast subsystem angle of rudder reflection are as follows:
δef=(GQf)+[-G(Pfψ)-Kf sign(c)] (35)
Wherein, mole Roger Penrose of '+' representing matrix is inverse, KfFor the positive definite matrix of design；
Step 7: defining speed tracing error are as follows:
Wherein, VdFor speed reference instruction；
Design throttle valve opening Φ are as follows:
Wherein, kpV>0、kiV> 0 and kdV> 0 is design parameter；
Step 8: according to the angle of rudder reflection δ of obtained slow subsystemesWith the angle of rudder reflection δ of fast subsystemef, obtain posture
The angle of rudder reflection δ of subsysteme=δes+δef, in conjunction with the throttle valve opening Φ of speed subsystem, return to vehicle dynamics model
(1)-(6) carry out tracing control to height and speed.
Beneficial effect
A kind of Elastic Vehicles robust finite-time control method based on Singular Perturbation Analysis proposed by the present invention, and it is existing
There is technology to compare to have the beneficial effect that
(1) hard and soft mode is decoupled based on markers feature, gives the fast subsystem and table of characterization Elastic mode
Levy the slow subsystem of rigid body.Elasticity is realized to fast subsystem and slow subsystem design controller respectively on this basis
Mode is calm to be tracked with system.
(2) present invention introduces difference scores rank design controllers to guarantee tracking error finite time convergence control, and passes through
It constructs extension filter and auxiliary signal and learning evaluation information introducing neural network weight more new law is realized that parameter learning is limited
Time Convergence.
Detailed description of the invention
The present invention is based on the flow charts of the Elastic Vehicles robust finite-time control method of Singular Perturbation Analysis by Fig. 1
Specific embodiment
Now in conjunction with embodiment, attached drawing, the invention will be further described:
Referring to Fig.1, the present invention is based on the Elastic Vehicles robust finite-time controls of Singular Perturbation Analysis to be applied to one kind
Elastic hypersonic aircraft kinetic model, is realized by following steps:
(a) consider elastic hypersonic aircraft vertical passage kinetic model:
The kinematics model is by seven quantity of statesU=[δ is inputted with two controlse,
Φ]TComposition；Wherein, V indicates speed, and h indicates height, and γ indicates that flight path angle, α indicate that the angle of attack, q indicate rate of pitch, η
WithIndicate Elastic mode, δeIndicate that angle of rudder reflection, Φ indicate throttle valve opening；m,IyyTurn of quality, pitch axis is respectively indicated with g
Acceleration caused by dynamic inertia and gravity；ζ, ω and N respectively indicate damping ratio, frequency of natural vibration and the broad sense of Elastic mode
Power.
The expression formula of power and torque and each coefficient are as follows:
Wherein,Indicate dynamic pressure, ρ0Indicate atmospheric density,Indicate mean aerodynamic chord, zTIndicate moment of thrust brachium, S table
Show pneumatic area of reference.
(b) defining height tracing error is eh=h-hd, design flight-path angle instruction γdAre as follows:
Wherein, hdIndicate elevation references instruction,Indicate the first differential of elevation references instruction, kh=0.5, ki=0.1.
According to time-scale separation, regard speed as slow dynamics, the first differential of design flight-path angle instruction are as follows:
Wherein,Indicate the second-order differential of elevation references instruction.
(c) x is taken1=γ, x2=θ, x3=q, wherein θ=α+γ indicates pitch angle.Posture subsystem (3)-(6) be written as with
Lower form:
Wherein,
Definitionρ σ=η, ρ B2=β1.Posture subsystem (9) is written as following form:
ρ=0 is set, and posture subsystem (10) is written as following slow subsystem form:
Wherein, ' s ' indicates slow subsystem, δesIndicate the control input of slow subsystem.
Formula (14) are substituted into formula (10), slow subsystem (11)-(14) are written as following form:
Slow subsystem (15) can further be written as following Strict-feedback form:
Wherein,
(d) ψ is defined1=σ-σs,Formula (6) is written as following form:
Wherein, δef=δe-δesIndicate the control input of fast subsystem.
Formula (14) are substituted into formula (17), fast subsystem (17) is written as following form:
Formula (18) is further written as following matrix form:
Wherein, ψ=[ψ1,ψ2]T,
(e) step 1: track angle tracking error is defined are as follows:
e1=x1s-γd (20)
Design pitch angle virtual controlling amount are as follows:
Wherein,Indicate the estimated value of neural network optimal weights vector, θ1Indicate Base Function vector, k1=
2, kf1=1, η1=0.5.
Design firstorder filter are as follows:
Wherein,It indicatesBy the signal obtained after filter expressed by formula (22),For the letter obtained after filtering
NumberDifferential signal, α2=0.05.
DefinitionIt is as follows to design firstorder filter:
X in formulaf1、θf1For x1s、θ1By the signal obtained after filter shown in formula (23),
Design assistant matrix P1, auxiliary vector Q1、W1It is as follows:
In formula, l1=0.1 is provided by designer, neural network weightIt is obtained by following adaptive law:
Wherein, γ1=1, Γ1The diagonal matrix for being 0.5 for diagonal element.
Step 2: pitching angle tracking error is defined are as follows:
Design pitch rate virtual controlling amount are as follows:
Wherein, k2=2, kf2=1.5, η2=0.5.
Design firstorder filter are as follows:
Wherein,It indicatesBy the signal obtained after filter expressed by formula (28),For the letter obtained after filtering
NumberDifferential signal, α3=0.05.
Step 3: pitch rate tracking error is defined are as follows:
Design slow subsystem angle of rudder reflection are as follows:
Wherein,Indicate the estimated value of neural network optimal weights vector, θ3Indicate Base Function vector, k3=
10, kf3=5, η3=0.5.
It enablesIt is as follows to design firstorder filter:
X in formulaf3、θf3For x3s、θ3By the signal obtained after filter shown in formula (31),
Design assistant matrix P3, auxiliary vector Q3、W3It is as follows:
In formula, l3=0.1, neural network weightIt is obtained by following adaptive law:
Wherein, γ3=3, Γ3The diagonal matrix for being 0.5 for diagonal element.
(g) sliding formwork switching function is defined are as follows:
C=G ψ (34)
Wherein,
Design fast subsystem angle of rudder reflection are as follows:
Wherein, mole Roger Penrose of '+' representing matrix is inverse,
(h) speed tracing error is defined are as follows:
Wherein, VdFor speed reference instruction.
Design throttle valve opening Φ are as follows:
Wherein, kpV=5, kiV=0.001, kdV=0.001.
(i) according to the control of obtained slow subsystem input δesControl with fast subsystem inputs δef, obtain posture
The angle of rudder reflection δ of subsysteme=δes+δef, in conjunction with the throttle valve opening Φ of speed subsystem, return to hypersonic aircraft power
Model (1)-(6) are learned, tracing control is carried out to height and speed.
Claims (1)
1. a kind of Elastic Vehicles robust finite-time control method based on Singular Perturbation Analysis, it is characterised in that step is such as
Under:
Step 1: consider Elastic Vehicles vertical passage kinetic model:
The kinematics model is by seven quantity of statesU=[δ is inputted with two controlse,Φ]TGroup
At；Wherein, V indicate speed, h indicate height, γ indicate flight path angle, α indicate the angle of attack, q indicate rate of pitch, η andTable
Show Elastic mode, δeIndicate that angle of rudder reflection, Φ indicate throttle valve opening；m,IyyThe rotary inertia of quality, pitch axis is respectively indicated with g
With acceleration caused by gravity；ζ, ω and N respectively indicate damping ratio, frequency of natural vibration and the generalized force of Elastic mode；
The expression formula of power and torque and each coefficient are as follows:
T=A1+B1η,
D=A2+B2η,
L=A3+B3η,
Myy=A4+B4η,
Wherein,Indicate dynamic pressure,Indicate mean aerodynamic chord, zTIndicate that moment of thrust brachium, S indicate pneumatic area of reference,WithIt is
Aerodynamic parameter, Nα、N0For the related coefficient for characterizing elastodynamics；
Step 2: definition height tracing error is eh=h-hd, design flight-path angle instruction γdAre as follows:
Wherein, hdIndicate elevation references instruction,Indicate the first differential of elevation references instruction, kh> 0 and ki> 0 is design parameter；
According to time-scale separation, regard speed as slow dynamics, the first differential of design flight-path angle instruction are as follows:
Wherein,Indicate the second-order differential of elevation references instruction；
Step 3: taking x1=γ, x2=θ, x3=q, wherein θ=α+γ indicates pitch angle；Posture subsystem (3)-(6) are written as following
Form:
Wherein,
Definitionρ σ=η, ρ B2=β1；Posture subsystem (9) is written as following form:
ρ=0 is set, and posture subsystem (10) is written as following slow subsystem form:
Wherein, ' s ' indicates slow subsystem, δesIndicate the control input of slow subsystem；
Formula (14) are substituted into formula (10), slow subsystem (11)-(14) are written as following form:
Slow subsystem (15) can further be written as following Strict-feedback form:
Wherein, fi, i=1,3 be the unknown smoothed non-linearity function obtained by formula (15), gi, i=1,3 obtains by formula (15)
Know nonlinear function；
Step 4: defining ψ1=σ-σs,Formula (6) is written as following form:
Wherein, δef=δe-δesIndicate the control input of fast subsystem；
Formula (14) are substituted into formula (17), fast subsystem (17) is written as following form:
Formula (18) is further written as following matrix form:
Wherein, ψ=[ψ1,ψ2]T,
Step 5: step 1: defining track angle tracking error are as follows:
e1=x1s-γd (20)
Design pitch angle virtual controlling amount are as follows:
Wherein,Indicate the estimated value of neural network optimal weights vector, θ1Indicate Base Function vector, k1>0、kf1>
0、0<η1<1；
Design firstorder filter are as follows:
Wherein,It indicatesBy the signal obtained after filter expressed by formula (22),For the signal obtained after filtering
Differential signal, α2>0；
DefinitionIt is as follows to design firstorder filter:
X in formulaf1、θf1For x1s、θ1By the signal obtained after filter shown in formula (23),Design assistant
Matrix P1, auxiliary vector Q1、W1It is as follows:
In formula, l1> 0, neural network weightIt is obtained by following adaptive law:
Wherein, γ1> 0, Γ1Be positive permanent several diagonal matrix；
Step 2: pitching angle tracking error is defined are as follows:
Design pitch rate virtual controlling amount are as follows:
Wherein, k2>0、kf2>0、0<η2<1；
Design firstorder filter are as follows:
Wherein,It indicatesBy the signal obtained after filter expressed by formula (28),For the signal obtained after filtering
Differential signal, α3> 0 is design parameter；
Step 3: pitch rate tracking error is defined are as follows:
Design slow subsystem angle of rudder reflection are as follows:
Wherein,Indicate the estimated value of neural network optimal weights vector, θ3Indicate Base Function vector, k3>0、kf3>
0、0<η3<1；
It enablesIt is as follows to design firstorder filter:
X in formulaf3、θf3For x3s、θ3By the signal obtained after filter shown in formula (31),It designs auxiliary
Help matrix P3, auxiliary vector Q3、W3It is as follows:
In formula, l3> 0, neural network weightIt is obtained by following adaptive law:
Wherein, γ3> 0, Γ3Be positive permanent several diagonal matrix；
Step 6: defining sliding formwork switching function are as follows:
C=G ψ (34)
Wherein, G ∈ R2×2For the matrix of design；
Design fast subsystem angle of rudder reflection are as follows:
δef=(GQf)+[-G(Pfψ)-Kfsign(c)] (35)
Wherein, mole Roger Penrose of '+' representing matrix is inverse, KfFor the positive definite matrix of design；
Step 7: defining speed tracing error are as follows:
Wherein, VdFor speed reference instruction；
Design throttle valve opening Φ are as follows:
Wherein, kpV>0、kiV> 0 and kdV> 0 is design parameter；
Step 8: according to the angle of rudder reflection δ of obtained slow subsystemesWith the angle of rudder reflection δ of fast subsystemef, obtain posture subsystem
Angle of rudder reflection δe=δes+δef, in conjunction with the throttle valve opening Φ of speed subsystem, vehicle dynamics model (1)-(6) are returned to,
Tracing control is carried out to height and speed.
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| CN111309040A (en) * | 2020-03-02 | 2020-06-19 | 中国人民解放军海军航空大学 | Aircraft longitudinal pitch angle control method adopting simplified fractional order differential |
| CN113110540A (en) * | 2021-04-14 | 2021-07-13 | 西北工业大学 | Elastomer aircraft global finite time control method based on time scale decomposition |
| CN114779636A (en) * | 2022-04-17 | 2022-07-22 | 西北工业大学 | Aircraft robust adaptive control method considering pneumatic servo elasticity |
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| CN107390531A (en) * | 2017-09-05 | 2017-11-24 | 西北工业大学 | The hypersonic aircraft control method of parameter learning finite time convergence control |
| CN108333939A (en) * | 2018-02-07 | 2018-07-27 | 中国航空工业集团公司西安飞机设计研究所 | A kind of time-scale separation aircraft elastomer intelligent control method based on neural network |
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| CN107368091A (en) * | 2017-08-02 | 2017-11-21 | 华南理工大学 | A kind of stabilized flight control method of more rotor unmanned aircrafts based on finite time neurodynamics |
| CN107390531A (en) * | 2017-09-05 | 2017-11-24 | 西北工业大学 | The hypersonic aircraft control method of parameter learning finite time convergence control |
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| CN111309040A (en) * | 2020-03-02 | 2020-06-19 | 中国人民解放军海军航空大学 | Aircraft longitudinal pitch angle control method adopting simplified fractional order differential |
| CN111309040B (en) * | 2020-03-02 | 2023-07-04 | 中国人民解放军海军航空大学 | Aircraft longitudinal pitch angle control method adopting simplified fractional order differentiation |
| CN113110540A (en) * | 2021-04-14 | 2021-07-13 | 西北工业大学 | Elastomer aircraft global finite time control method based on time scale decomposition |
| CN113110540B (en) * | 2021-04-14 | 2023-01-13 | 西北工业大学 | Elastomer aircraft global finite time control method based on time scale decomposition |
| CN114779636A (en) * | 2022-04-17 | 2022-07-22 | 西北工业大学 | Aircraft robust adaptive control method considering pneumatic servo elasticity |
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Application publication date: 20191115 |