CN106843254B - It is a kind of actively to reconstruct fault tolerant control method in real time - Google Patents
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Abstract
A kind of actively to reconstruct fault tolerant control method in real time, this method is based on sliding formwork control, finite-time control technology and Chebyshev neural network, is able to satisfy real-time active tolerant control of flexible aerocraft system when actuator breaks down and is saturated.It introduces and needs the Chebyshev neural network of desired signal only to estimate that the system comprising failure and saturation always disturbs, design nominal control law and compensation control law, it is influenced caused by compensation failure and saturation, weakens the intrinsic buffeting of sliding mode system, improve the precision of posture tracing system.
Description
Technical field
The present invention relates to one kind actively to reconstruct fault tolerant control method in real time, belongs to aircraft manufacturing technology field.
Background technique
With the continuous development of science and technology with the continuous expansion of application field, the structure and task of all kinds of aircraft are increasingly
Complicated and huge, flight environment of vehicle is badly changeable, and reliability has become the major issue in Design of Flight Control.Pass through
The requirement of aircraft minimum safe is realized in the reconstruct of control system or recombination, this for guarantee aircraft smoothly complete task or
It avoids crashing and be of great significance.How to research and develop with the flight control system compared with strong fault tolerance ability to meet high reliability request
With important learning value and application prospect.
Fault Tolerance Control Technology is a kind of significant change for adapting to environment, may be allowed one or more portions in control system
The control system of part failure.The guiding theory of faults-tolerant control is that a control system once breaks down, and system can still be tieed up
It holds its own and operates in safe condition, and meet certain performance indicator under conditions permit.Sliding mode variable structure control is a kind of
Special non-linear discontinuous control method, this control method structure for being system different from other controls is in dynamic process
In, the meeting state current according to system, so that system is run according to the state trajectory of predetermined sliding mode.It is designed joins with model
Number and disturb it is unrelated so that variable-structure control have reaction speed it is fast, it is insensitive to Parameters variation, to disturbance insensitive, physics
Realize the advantages that simple.Chebyshev neural network under certain condition can be with arbitrary accuracy Nonlinear Function Approximation, and has
Stronger self study, adaptive and self organization ability.Chebyshev neural network is combined with Sliding mode variable structure control, to mould
Type uncertainty and non-linear partial estimation compensation can eliminate the buffeting problem of sliding formwork control to a certain extent.Finite time
Control method is a kind of nonlinear control method, is time optimal control method, compared with asymptotically stable system, when limited
Between stable system not only there is faster convergence rate under there are external disturbance and internal uncertain situation, there are also more preferable
Robustness and interference rejection ability.
Summary of the invention
Technology of the invention solves the problems, such as: overcome the deficiencies in the prior art, with the active tolerant control of flexible aircraft
For background, propose that a kind of aircraft based on sliding formwork control technology, finite-time control technology and Chebyshev neural network is real
When actively reconstruct fault tolerant control method.Flexible aircraft real-time fault tolerance control is realized, multiplying property or additivity event occurs in actuator
Under barrier, utmostly meet attitude of flight vehicle tracing control demand.
The technical solution of the invention is as follows:
One kind actively reconstructing fault tolerant control method in real time, and steps are as follows:
(1) flexible aerocraft system model is established；
(2) the flexible aerocraft system model obtained using step (1) establishes flexible aircraft fortune based on quaternary number
It is dynamic to learn error equation and dynamics error equation；
(3) according to the flexible aircraft kinematic error equation and dynamics error equation in step (2), when establishing limited
Between non-singular terminal sliding-mode surface；
(4) according to the finite time non-singular terminal sliding-mode surface established in Chebyshev neural network and step (3), really
Calibration claims control law unWith compensation control law ua, to obtain completely actively reconstructing fault-tolerant controller, and then realize real-time master
Dynamic reconstruct faults-tolerant control.
Compared with the prior art, the invention has the advantages that:
1, control method of the present invention is able to achieve flexible aircraft and actively reconstructs faults-tolerant control in real time.
2, non-odd fast terminal sliding formwork control is applied to flexible attitude of flight vehicle tracing control and led by control method of the present invention
Domain makes system fast and stable and avoid singular problem in finite time
3, control method of the present invention combines neural network with sliding formwork control, and proposition only relies upon expectation letter with basic function
Number Chebyshev neural network carry out the unknown total disturbance of efficiently approximation system.
Detailed description of the invention
Fig. 1 is that the present invention actively reconstructs fault-tolerant controller structural block diagram；
Fig. 2 is that the present invention actively reconstructs faults-tolerant control attitude error and angular speed error；
Fig. 3 is PID control attitude error of the present invention and angular speed error；
Fig. 4 is attitude angle of the present invention and angular speed curve；
Fig. 5 is sliding-mode surface of the present invention and control moment curve；
Fig. 6 is the curve of output of Chebyshev neural network pilot controller of the present invention；
Fig. 7 is flexible mode frequency decay curve of the present invention.
Specific embodiment
A specific embodiment of the invention is further described in detail with reference to the accompanying drawing.As shown in Figure 1, this hair
The bright one kind that proposes actively reconstructs fault tolerant control method in real time, the specific steps are as follows:
(1) consider the factors such as aircraft flexible nature, rotary inertia uncertain, external disturbance, actuator failures and saturation
Influence, establish such as lower flexible aerocraft system model:
Wherein:d∈R3It is external disturbance, δ ∈ R4×3For the coupling moment of rigid body and flexible appendage
Battle array, δTIt is the transposition of δ, η is flexible mode,WithThe respectively first derivative of η and second dervative；J0∈R3×3For known mark
Claim inertia matrix, and is positive definite matrix；Δ J is the uncertain part in inertia matrix, Ω=[Ω1,Ω2,Ω3]TIt is aircraft
Angular velocity component in body coordinate system,It is the first derivative of Ω；× it is oeprator, will × it is used for vector b=[b1,
b2,b3]TIt is available:
L=diag { 2 ζiωni, i=1,2 ..., N } andRespectively damping matrix and
Stiffness matrix, N are rank number of mode, ωni, i=1,2 ..., N are vibration modal frequency matrix, ζi, i=1,2 ..., N is vibration
Damping ratios；
U=[u1,u2,u3]TIt is actively to reconstruct fault-tolerant controller, sat (u)=[sat (u1),sat(u2),sat(u3)]TIt is
The practical dominant vector that actuator generates, sat (ui), i=1,2,3 indicates the non-linear saturated characteristic of actuator and meets sat
(ui)=sign (ui)·min{umi,|ui|, i=1,2,3, sat (ui) it is expressed as sat (ui)=θoi+ui, i=1,2,3,
Middle θoi, i=1,2,3 are as follows:
umi, i=1,2,3 be actuator saturation value, is θ beyond actuator saturation value parto=[θo1,θo2,θo3]T, and it is full
Sufficient ‖ θo‖≤lδθ, lδθIt is positive real number, Gδ=[Gδ1,Gδ2,Gδ3]TIt is additivity failure, i.e., failure influences system with additive way and expires
Sufficient ‖ Gδ‖≤lδf, lδfIt is positive real number；D=diag { δo1,δo2,δo3Be actuator efficiency index value and meet 0 < ετi≤δoi≤1,
I=1,2,3；0<ετi≤ 1, i=1,2,3 indicate the minimum executive capability of actuator, δoi=1, i=1,2,3 indicate i-th of execution
Device is working properly；0<ετi≤δoi≤ 1, i=1,2,3 indicate i-th of actuator partial failure, but the actuator remains to provide
Part executive capability.
(2) the flexible aerocraft system model obtained using step (1) establishes flexible aircraft kinematics based on quaternary number
Error equation and dynamics error equation are as follows:
Flexible aircraft kinematic error equation:
Wherein: (ev,e4)∈R3× R, ev=[e1,e2,e3]TIt is the error quaternary of current flight device posture Yu desired posture
Number vector section, e4It is scalar component, and meetsWithIt is e respectivelyv、e4First derivative；
(qv,q4)∈R3× R, qv=[q1,q2,q3]TIt is the unit quaternion vector section for describing attitude of flight vehicle, q4It is scalar component,
And meetqdv=[qd1,qd2,qd3]TIt is the unit four of description expectation posture
First number vector section, qd4It is scalar component, and meetsΩe=Ω-C Ωd=[Ωe1Ωe2
Ωe3]TThe angular speed error vector being built upon between body coordinate system and target-based coordinate system, Ωd∈R3Be expectation angular speed to
Amount,It is transition matrix, and meets ‖=1 ‖ C,It is the single order of C
Derivative, I3It is 3 × 3 unit matrixs；
Flexible vehicle dynamics error equation are as follows:
Wherein,It is ΩeFirst derivative, ΩdIt is expectation angular speed,It is ΩdFirst derivative；
Flexible vehicle dynamics error equation is rewritten are as follows:
Wherein: F is that model determines part, and R is unknown total disturbance；
(3) according to the flexible aircraft kinematic error equation and dynamics error equation in step (2), when establishing limited
Between non-singular terminal sliding-mode surface:
S=Ωe+K1ev+K2Sc (9)
Wherein S=[S1,S2,S3]T∈R3, Kj=diag { kji} > 0, i=1,2,3, j=1,2, diag (a1,a2,…,an)
Expression diagonal entry is a1,a2,…,anDiagonal matrix；And define Sc=[Sc1,Sc2,Sc3]TIt is as follows:
Whereinr1,r2It is positive odd number, and 0 < r < 1, l1i、l2i, i=1,
2,3 be parameter；εi, i=1,2,3, ι1、ι2For design parameter, sign (a) is sign function, is defined as follows:
Based on finite time non-singular terminal sliding-mode surface, as shown in formula (9), suitable parameter is designed, satisfaction is worked asWhen, control target { e can be achieved in finite timev≡0,e4≡1,Ωe≡0}。
(4) according to the finite time non-singular terminal sliding-mode surface established in Chebyshev neural network and step (3), really
Calibration claims control law unWith compensation control law ua, thus obtain completely actively reconstructing fault-tolerant controller, it is specific as follows:
U=un+ua (11)
un=[un1,un2,un3]T=-ρ S- β sigλ(S)-F (12)
Wherein, ρ=diag (ρ1,ρ2,ρ3),ρi> 0, i=1,2,3, β=diag (β1,β2,β3), βi> 0, i=1,2,3；sigλ(S)=[| S1|λsign(S1),|S2|λsign(S2),|S3|λsign(S3)]T, F is that model determines part, and λ ∈ (0,1) is design
Parameter；
M weight matrix, μ=μ (X)=(1, T1(x1),...,Tn(x1),...,Tn(xm))T, wherein Ti(xj), i=
1 ..., n, j=1 ..., m represent Chebyshev polynomials, and m is the input number of Chebyshev neural network, and n is Qie Bixue
The polynomial order of husband；For robust control item, for compensating the approach error of Chebyshev neural network, definition is such as
Under:
Wherein i=1,2,3, χ1The normal real number that is positive and meet χ1≥εM, εMIt is approach upper error, the scalar that κ is positive；
Tanh () is hyperbolic tangent function.For middle weight matrix M, using following ADAPTIVE CONTROL:
In formulaIt is normal number.Compensate control law uaBy Chebyshev neural network control item M μ
And robust control itemTwo parts composition.Wherein total disturbance of the Chebyshev neural network control item M μ to approximation system,
And robust control itemThen to compensate the approximate error of Chebyshev neural network.Nonlinear feedback-ρ S- β sigλ(S) to
Realize attitude of flight vehicle state variable incoming terminal sliding mode in finite time.
Embodiment:
To verify the reasonability of flexible attitude of flight vehicle Adjusted Option proposed by the present invention and the controller of design to not
Determine, disturbance the problems such as validity, numerical simulation, nominal rotational inertia matrix are carried out to it under present Matlab environment are as follows:
Uncertain part in inertia matrix are as follows:
Δ J=diag [50 30 20] kgm2；
External disturbance d ∈ R3It is the function of time t, is represented by d (t), is specifically taken as:
D (t)=[10*sin (0.1t), 15*sin (0.2t), 20*sin (0.2t)]T；
The quaternary number initial value of attitude of flight vehicle is q=[0.3, -0.2, -0.3,0.8832]TIt is Ω with initial angular velocity
=[0,0,0]T, it is expected that angular speed is the function of time t, it is represented by Ωd(t), it is specifically taken as:
Ωd(t)=0.05 [sin (π t/100), sin (2 π t/100), sin (3 π t/100)]T；
Actuator failures parameter D and GδIt is the function of time t, is respectively as follows:
D=diag (δo1(t),δo2(t),δo3(t))
G=diag (Gδ1(t),Gδ2(t),Gδ3(t))
Flexible appendage parameter:
ωn=(1.0973 1.2761 1.6538 2.2893)；
η=(0.01242 0.01584-0.01749 0.01125)；
ζn=(0.05 0.06 0.08 0.025)；
Specific controller parameter is as follows:
The input of Chebyshev neural network isIt isFirst derivative.
The comparison result of table 1 this patent control method and PID control
Fig. 2 gives attitude quaternion error and attitude angular velocity error in Finite-time convergence characteristic；Fig. 3 gives
PID control attitude error and angular speed error under equal conditions；Fig. 4 is the posture and angular speed variation characteristic of aircraft；Fig. 5 is
Sliding-mode surface and control moment curve；Fig. 6 is the curve of output of Chebyshev neural network pilot controller；Fig. 7 is flexible mode
Frequency decay curve.From simulation result it can be seen that in conjunction with Chebyshev neural network nonsingular fast terminal sliding formwork control
System chatter phenomenon is almost cancelled completely, and angular speed error is strictly controlled at 5 × 10-3.Interior, precision has reached expected and has wanted
It asks.Compared with PID control, the controller performance that the present invention designs is more superior, illustrates that Chebyshev neural network can be effective
Ground approximation system is always interfered, to inhibit to interfere, improves control precision.
Claims (2)
1. a kind of actively reconstruct fault tolerant control method in real time, it is characterised in that steps are as follows:
(1) flexible aerocraft system model is established；Specifically:
Wherein:d∈R3It is external disturbance, δ ∈ R3×3For the coupling matrix of rigid body and flexible appendage,
δTIt is the transposition of δ, η is flexible mode,WithThe respectively first derivative of η and second dervative；J0∈R3×3It is known nominal
Inertia matrix, and be positive definite matrix；Δ J is the uncertain part in inertia matrix, Ω=[Ω1,Ω2,Ω3]TIt is that aircraft exists
Angular velocity component in body coordinate system,It is the first derivative of Ω；× it is oeprator, will × it is used for vector b=[b1,b2,
b3]TIt obtains:
L=diag { 2 ζiωni, i=1,2 ..., N } andRespectively damping matrix and rigidity
Matrix, N are rank number of mode, ωni, i=1,2 ..., N are vibration modal frequency matrix, ζi, i=1,2 ..., N is mode of oscillation
Damping ratio；
U=[u1,u2,u3]TIt is actively to reconstruct fault-tolerant controller, sat (u)=[sat (u1),sat(u2),sat(u3)]TIt is to execute
The practical dominant vector that device generates, sat (ui), i=1,2,3 indicates the non-linear saturated characteristic of actuator and meets sat (ui)=
sign(ui)·min{umi,|ui|, i=1,2,3, sat (ui) it is expressed as sat (ui)=θoi+ui, i=1,2,3, wherein θoiAre as follows:
umi, i=1,2,3 be actuator saturation value, is θ beyond actuator saturation value parto=[θo1,θo2,θo3]T, and meet | |
θo||≤lδθ, lδθIt is positive real number, Gδ=[Gδ1,Gδ2,Gδ3]TIt is additivity failure, i.e., failure influences system and satisfaction with additive way
||Gδ||≤lδf, lδfIt is positive real number；D=diag { δo1,δo2,δo3Be actuator efficiency index value and meet 0 < ετi≤δoi≤1,
I=1,2,3；0<ετi≤ 1, i=1,2,3 indicate the minimum executive capability of actuator, δoi=1, i=1,2,3 indicate i-th of execution
Device is working properly；0<ετi≤δoi≤ 1, i=1,2,3 indicate i-th of actuator partial failure, but the actuator remains to provide
Part executive capability；
(2) the flexible aerocraft system model obtained using step (1), establishes flexible aircraft kinematics based on quaternary number
Error equation and dynamics error equation；
Flexible aircraft kinematic error equation:
Wherein: (ev,e4)∈R3× R, ev=[e1,e2,e3]TIt is the error quaternion arrow of current flight device posture and desired posture
Measure part, e4It is scalar component, and meets WithIt is e respectivelyv、e4First derivative；(qv,q4)
∈R3× R, qv=[q1,q2,q3]TIt is the unit quaternion vector section for describing attitude of flight vehicle, q4It is scalar component, and meetsqdv=[qd1,qd2,qd3]TIt is the unit quaternion arrow of description expectation posture
Measure part, qd4It is scalar component, and meetsΩe=Ω-C Ωd=[Ωe1Ωe2Ωe3]TIt is to build
Found the angular speed error vector between body coordinate system and target-based coordinate system, Ωd∈R3It is expectation angular velocity vector,It is transition matrix, and meets | | C | |=1, It is that the single order of C is led
Number, I3It is 3 × 3 unit matrixs；
Flexible vehicle dynamics error equation are as follows:
Wherein,It is ΩeFirst derivative, ΩdIt is expectation angular speed,It is ΩdFirst derivative；
Flexible vehicle dynamics error equation is rewritten are as follows:
Wherein: F is that model determines part, and R is unknown total disturbance；
(3) according to the flexible aircraft kinematic error equation and dynamics error equation in step (2), it is non-to establish finite time
Unusual terminal sliding mode face；
Finite time non-singular terminal sliding-mode surface S, specifically:
S=Ωe+K1ev+K2Sc；
Wherein ev=[e1,e2,e3]TIt is the error quaternion vector section of current flight device posture Yu desired posture, ΩeIt is to establish
Angular speed error vector between body coordinate system and target-based coordinate system；S=[S1,S2,S3]T∈R3, Kj=diag { kji}>0,
I=1,2,3, j=1,2, diag (a1,a2,…,an) expression diagonal entry be a1,a2,…,anDiagonal matrix；And define Sc
=[Sc1,Sc2,Sc3]TIt is as follows:
Whereinr1,r2It is positive odd number, and 0 < r < 1, l1i、l2i, i=1,2,3
It is parameter；εi, i=1,2,3, ι1、ι2For design parameter, sign (a) is sign function, is defined as follows:
(4) according to the finite time non-singular terminal sliding-mode surface established in Chebyshev neural network and step (3), mark is determined
Claim control law unWith compensation control law ua, to obtain completely actively reconstructing fault-tolerant controller, and then realize actively heavy in real time
Structure faults-tolerant control；
Nominal control law unWith compensation control law ua, specifically:
U=un+ua；
un=[un1,un2,un3]T=-ρ S- β sigλ(S)-F；
Wherein, ρ=diag (ρ1,ρ2,ρ3),ρi> 0, i=1,2,3, β=diag (β1,β2,β3), βi> 0, i=1,2,3；sigλ(S)
=[| S1|λsign(S1),|S2|λsign(S2),|S3|λsign(S3)]T, F is that model determines part, and λ ∈ (0,1) is design ginseng
Number；
M is weight matrix, μ=μ (X)=(1, T1(x1),...,Tn(x1),...,Tn(xm))T, wherein Ti(xj), i=1 ...,
N, j=1 ..., m represent Chebyshev polynomials, and m is the input number of Chebyshev neural network, and n is that Chebyshev is multinomial
The order of formula；For robust control item, for compensating the approach error of Chebyshev neural network, it is defined as follows:
Wherein i=1,2,3, χ1The normal real number that is positive and meet χ1≥εM, εMIt is the approach error upper limit, the scalar that κ is positive；tanh
() is hyperbolic tangent function.
2. one kind according to claim 1 actively reconstructs fault tolerant control method in real time, it is characterised in that: the step (4)
Middle weight matrix M, meets following ADAPTIVE CONTROL:
In formula,It is positive real number.
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