CN110442020A - A kind of novel fault tolerant control method based on whale optimization algorithm - Google Patents
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Abstract
The invention discloses a kind of novel pins to the algorithm based on sliding mode prediction fault tolerant control method of time_varying delay control system actuator failures.It is directed to the faults-tolerant control problem of the uncertain quadrotor system of Discrete-Delay, devises a kind of algorithm based on sliding mode prediction fault tolerant control method based on whale optimization algorithm.Using global sliding mode face as prediction model, to guarantee global robustness, and a kind of power function reference locus with Fault Compensation is devised, while weakening buffeting influences, is directed to uncertain and failure and plays inhibitory effect.During rolling optimization, it is contemplated that searching process needs high-precision fast-response, and using whale optimization algorithm, the algorithm optimizing performance is strong, and parameter setting is few, fast convergence rate, and precision is high.The present invention is used for the robust Fault-Tolerant Control of a kind of uncertain discrete-time system containing Time-varying time-delays.
Description
Technical field
The sliding formwork based on whale optimization algorithm is designed for time_varying delay control system actuator failures the present invention relates to a kind of
It predicts fault tolerant control method, belongs to the robust Fault-Tolerant Control technical field of uncertain discrete control system.
Background technique
With the development of science and technology, society largely becomes one and is driven by various intelligent instruments now
Society.In the case where longtime running external factor influences a series of failure can usually occur for intelligent instrument.In order to enable intelligence
Energy body can be safely operated in case of a fault, flourished for the Fault Tolerance Control Technology of handling failure problem, and
There are some achievements in processing practical problem.It is Active Fault Tolerant and Passive fault-tolerant control both direction that faults-tolerant control, which substantially develops, is being located
Numerous strategies behave excellently are proposed in terms of reason actuator and sensor fault.
Quadrotor drone has come into daily life, and in agricultural, military project is transported, and the tracking etc. that tracks presents
Its indispensable value.In recent years, for UAV Formation Flight, track automation field avoidance, the side such as troubleshooting
Face proposes the considerable control strategy with actual utility, such as sliding formwork control, PREDICTIVE CONTROL, self adaptive control, sliding formwork
Prediction etc..When studying quadrotor discrete system, vulnerable to interference when due to flight, when system modelling, there is also certain mistakes
The design of difference, complexity and control strategy to control system has great influence.In fact, present in flight course
Failure, in system there is time lag more exacerbate the difficulty of control.
The research of discrete control system has become the important composition of control field, examines for the failure with discrete system
It is disconnected with faults-tolerant control to there is greatly exploration to be worth.In discrete system, sliding formwork control can be very good to exist in processing system
The uncertain factors such as Parameter Perturbation, external disturbance, and there is good robustness.Sliding mode variable structure control is substantially
A kind of special nonlinear Control, this control strategy and other control methods are the difference is that system can be in dynamic mistake
Cheng Zhong purposefully constantly changes according to current state, and the sliding mode of system is can to design and the disturbance nothing with system
It closes, this makes SMC have the advantages such as quick response, simple to Parameters variation and the insensitive and physics realization of disturbance.Thus mesh
It is preceding that extensive research and application have been obtained in uncertain discrete-time system control.However in actual control system, time lag is existing
As generally existing.When occurring time lag item in system, simple sliding formwork control is difficult to obtain good control effect, especially when
Between when lagging larger, sliding formwork control is difficult to the requirement for meeting system to rapidity, and is likely to occur unstable phenomenon again.However,
PREDICTIVE CONTROL is on eliminating influence of the time lag to discrete system and good treatment effect.PREDICTIVE CONTROL is in rolling optimization process
In, the solution of control sequence at every moment carries out online, continuous solving optimization problem, this is also containing for rolling optimization
Justice.Also just because of this, rolling optimization can make practical control keep optimal, in turn, the available good place of Time Delay
Reason, reduces its influence to system.So the present invention combines sliding formwork control with the advantage of PREDICTIVE CONTROL, it is directed to time lag
Discrete uncertain system designs algorithm based on sliding mode prediction algorithm, makes full use of Parameter Perturbation and the outside of sliding formwork control processing solution system
Interference, the influence of time lag is avoided using Model Predictive Control, advanced optimizes control effect.
Currently, more and more for the research of algorithm based on sliding mode prediction algorithm, various novel control strategies are constantly proposed, still,
It is seldom furtherd investigate and is analyzed on such issues that handle Time-varying time-delays.
Summary of the invention
Goal of the invention: it is directed to above-mentioned existing processing scheme, proposes a kind of Discrete-Delay being directed to containing faulty item
The control problem of uncertain quadrotor system devises the algorithm based on sliding mode prediction fault tolerant control method based on whale optimization algorithm.Benefit
It uses global sliding mode face as prediction model, to guarantee global robustness, and devises a kind of power letter with Fault Compensation
Number reference locus is directed to uncertain and failure and plays inhibitory effect while weakening buffeting influences.In rolling optimization
In the process, it is contemplated that searching process needs high-precision fast-response, and using whale optimization algorithm, the algorithm optimizing performance is strong, parameter
Setting is few, fast convergence rate, and precision is high.So that with the Time-varying time-delays uncertain discrete-time system in the case of actuator failures
Robust stability is kept, and obtains good effect in rapidity and accuracy.
Technical solution: a kind of algorithm based on sliding mode prediction fault tolerant control method for time_varying delay control system actuator failures, according to
The Design of State algorithm based on sliding mode prediction model of system, the model are global sliding mode switching function, avoid approach procedure unstability, be ensure that complete
The robustness of office；Consider that time lag system is influenced by inner parameter perturbation and external disturbance simultaneously, devise with faulty and
The power function reference locus of uncertainty compensation in turn ensures convergence rate while a greater degree of weakening is buffeted；It is rolling
Whale optimization algorithm is devised in dynamic optimization problem and carries out optimizing, and compared to particle swarm optimization algorithm, which has faster
Convergence rate, more accurate solving precision, less more easy parameter setting.For one kind containing Time-varying time-delays do not know from
The robust Fault-Tolerant Control for the system of dissipating, comprises the following specific steps that:
Step 1) establishes discrete system model:
Step 1.1) Δ A, Δ B, Δ AdThe respectively Parameter Perturbation of system, x (k) ∈ Rn, u (k) ∈ Rp, y (k) ∈ Rq, point
Not Wei system state, input, output.w(k)∈RnFor external disturbance, f (k) is failure function, when τ (k) is uncertain time-varying
It is stagnant, but have its bound [τl, τu].A, B, C, E, AdFor the matrix of appropriate dimension
System (1) is rewritten as formula (2) by step 1.2), wherein d (k)=Δ Ax (k)+Δ Bu (k)+Δ Adx(k-τ(k))
+ v (k)+Ef (k), and d (k) meets | d (k)-d (k-1) |≤d0And dL≤|d(k)|≤dU；
Step 2) algorithm based on sliding mode prediction modelling:
Step 2.1) designs global sliding mode switching function, is located in the original state of system mode track on diverter surface,
Linear sliding mode face approach procedure is eliminated, has ensured the global robustness of system；Wherein y (k) is the reality output of system, and σ can
To be solved by POLE PLACEMENT USING rule, x0For system initial state, y0Output when for original state.S (0)=0, initial time
System mode track is located in diverter surface, eliminates approach procedure.
S (k)=σ y (k)-αkσy0=σ Cx (k)-αkσCx0 (3)
Step 2.2) k+1 moment algorithm based on sliding mode prediction model is (4)；
S (k+1)=σ Cx (k+1)-αk+1σCx0 (4)
Step 2.3) is according to nominal system x (k+1)=Ax (k)+Bu (k)+AdThe available algorithm based on sliding mode prediction mould of x (k- τ (k))
Prediction of the type at (k+P) moment, which exports (5) and its vector, indicates (6)；
SPM(k)=Ω X (k)+Ξ U (k)+Ψ Xd(k)-ΓX0 (6)
Wherein, P is prediction time domain, and M is control time domain, and meets M≤P, and control amount u (k+j) is protected in M-1≤j≤P
It is constant to hold u (k+M-1),
SPM(k)=[s (k+1) ..., s (k+p)]T
X (k)=[x (k+1) ..., x (k+p)]T
X0=[x0..., x0]T
U (k)=[u (k), u (k+1) ..., u (k+M-1)]T
Ω=[(σ CA)T..., (σ CAP)T]T
Γ=[αk, αk+1..., αk+P]T
The design of step 3) reference locus:
In step 3.1) sliding mode predictive control, the selection of reference locus can be constructed according to sliding formwork Reaching Law, thus how
Reduce and avoids the problem that needing to consider carefully when the influence buffeted becomes selection.It is huge in weakening is buffeted in view of power function
Big effect using power function as reference locus, while considering failure and probabilistic influence, embedding in reference locus
Enter AF panel means, make up the reference locus of failure and uncertainty design such as formula (7) to the maximum extent:
WhereinSgn () is expressed as sign function.
The value range of each parameter is as follows, 0 < β <, 1,0 < δ < 1,Penalty function indicates
Are as follows:
Step 3.2) formula (8) is expressed as acquiring by One-step delay estimation technique approximationFeelings that can be unknown in d (k)
It completes under condition to sref(k+1) solution, sref(k+1) vector form meets (9).
Sref(k)=[sref(k+1), sref(k+2) ..., sref(k+P)]T (9)
The design of step 4) feedback compensation:
P step exports the prediction at k moment before step 4.1) prediction model (10) indicates the k moment, when formula (11) is expressed as k
Carve the error between reality output and prediction output；
E (k)=s (k)-s (k | k-P) (11)
Step 4.2) is added to error represented by formula (11) as correction in algorithm based on sliding mode prediction model, available P step
Prediction output and its vector form are respectively (12), (13)；
Wherein,jpAs correction coefficient, with being incremented by for prediction steps, correction coefficient is successively
Successively decrease, j1=1, j1> j2> ... > jp> 0.
The design of step 5) optimality criterion:
Step 5.1) design optimization performance indicator such as formula (14), wherein λiFor non-negative weight coefficient, sampling instant error is indicated
The shared specific gravity in performance indicator；γlThe weight coefficient being positive, for constraining control input；
Optimality criterion is expressed as vector form (15) by step 5.2)；
Wherein,
Step 6) whale optimization algorithm solves control law
Step 6.1) takes optimality criterion J (k) as value function Ψ is adapted to, and initializes whale population, initializes each
ParameterL, ρ.Wherein,WithFor coefficient vector, respectively indicates and swings the factor and convergence factor,With iteration time
Random number of several increases from 2 linear decreases to 0, l between [- 1,1], constant ρ ∈ [0,1] and for be uniformly distributed generation with
Machine number, andWithIt can be calculated by following formula；
Wherein,For the random number between [0,1].
Step 6.2) as parameter (ρ < 0.5), andWhen, whale optimization algorithm takes following iterative formula to calculate most
The figure of merit；
Wherein,For the distance between individual and target prey, current iteration number is t,When being iteration t times most
The position of excellent solution,For the whale individual position vector of t iteration.
Step 6.3) as parameter (ρ < 0.5), andWhen, whale optimization algorithm takes the method search of random search
Optimal solution randomly chooses individual whale positionAnd optimizing is carried out according to formula (18)；
Step 6.4) takes the optimizing mode of bubble-net to carry out optimizing when parameter (ρ > 0.5), whale optimization algorithm,
It is iterated according to following formula；
When the maximum number of iterations is reached, optimizing terminates step 6.5), implements current control amount, and k+1 → k is enabled to return to step
It is rapid 2).
The utility model has the advantages that being directed to the control problem of the uncertain quadrotor system of Discrete-Delay containing faulty item, design
Algorithm based on sliding mode prediction fault tolerant control method based on whale optimization algorithm.It is complete to guarantee using global sliding mode face as prediction model
Office's robustness, and a kind of power function reference locus with Fault Compensation is devised, while weakening buffeting influences, needle
Inhibitory effect is played for uncertain and failure.During rolling optimization, it is contemplated that searching process needs high-precision fast
Response, using whale optimization algorithm, the algorithm optimizing performance is strong, and parameter setting is few, fast convergence rate, and precision is high.So that
Robust stability is kept with the Time-varying time-delays uncertain discrete-time system in the case of actuator failures, and in rapidity and accuracy
It is upper to obtain good effect.Have the advantages that following specific:
1. design global sliding mode switches the algorithm based on sliding mode prediction model as system according to system mode, which has time-varying
Feature avoids approach procedure unstability, ensure that global robustness, can dynamically improve the motion qualities of system；
2. the Time Delay and uncertainty that have in view of Discrete-time Systems with Delay devise a kind of with Fault Compensation
Power function reference locus is directed to uncertain and failure and plays inhibitory effect while weakening buffeting influences；
3. the rolling optimization process using whale algorithm improvement is asked compared to traditional method of derivation and general optimization
Solution speed and convergence precision have very big advantage, and it also has parameter designing few, advantage easy to operate.
The mentioned method of the present invention as it is a kind of for perturbing containing time-varying state time lag, actuator failures, system parameter and
The robust Fault-Tolerant Control method of the discrete system of disturbance has certain practical value, realizes that simply real-time is good, accuracy
Height can effectively improve control system safety and strong operability, save the time, more efficient, can be widely applied to not really
Determine in the actuator failures faults-tolerant control of discrete control system.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is that the experimental provision Qball-X4 tetra- to study four-rotor helicopter control that Quanser company develops revolves
Wing helicopter；
Fig. 3 is Qball-X4 four-rotor helicopter X-axis position curve figure；
Fig. 4 is Qball-X4 four-rotor helicopter Actuator dynamic curve graph；
Fig. 5 is control law curve graph；
Fig. 6 is the control law curve graph of part amplification.
Specific embodiment
Further explanation is done to the present invention with reference to the accompanying drawing.
As shown in Figure 1 in view of there are approach procedures in the linear sliding mode face of general sliding Mode Algorithm design, and approach procedure is easy
There is unstable phenomenon, designs global sliding mode switching function in terms of algorithm based on sliding mode prediction model for this situation, approach procedure is avoided to lose
Surely, it ensure that global robustness.Consideration system there are failure, interference and time lag etc. be many influence system control performances because
Element devises the power function reference locus with faulty and uncertain compensation, and designing power function reference locus is to examine
Consider a greater degree of buffeting problem for weakening sliding formwork and carrying.Whale optimization algorithm is devised in rolling optimization problem to be sought
Excellent, algorithm parameter setting is few, it is convenient to solve, but can fast accurate solve control law, compared to particle swarm optimization algorithm,
The algorithm has faster convergence rate, more accurate solving precision.Discrete system is not known containing Time-varying time-delays for one kind
The robust Fault-Tolerant Control of system, comprises the following specific steps that:
Step 1) establishes discrete system model:
Step 1.1) Δ A, Δ B, Δ AdThe respectively Parameter Perturbation of system, x (k) ∈ Rn, u (k) ∈ Rp, y (k) ∈ Rq, point
Not Wei system state, input, output.w(k)∈RnFor external disturbance, f (k) is failure function, when τ (k) is uncertain time-varying
It is stagnant, but have its bound [τl, τu].A, B, C, E, AdFor the matrix of appropriate dimension
System (1) is rewritten as formula (2) by step 1.2), wherein d (k)=Δ Ax (k)+Δ Bu (k)+Δ Adx(k-τ(k))
+ v (k)+Ef (k), and d (k) meets | d (k)-d (k-1) |≤d0And dL≤|d(k)|≤dU；
Step 2) algorithm based on sliding mode prediction modelling:
Step 2.1) designs global sliding mode switching function, is located in the original state of system mode track on diverter surface,
Linear sliding mode face approach procedure is eliminated, has ensured the global robustness of system；Wherein y (k) is the reality output of system, and σ can
To be solved by POLE PLACEMENT USING rule, x0For system initial state, y0Output when for original state.S (0)=0, initial time
System mode track is located in diverter surface, eliminates approach procedure.
S (k)=σ y (k)-αkσy0=σ Cx (k)-αkσCx0 (3)
Step 2.2) k+1 moment algorithm based on sliding mode prediction model is (4)；
S (k+1)=σ Cx (k+1)-αk+1σCx0 (4)
Step 2.3) is according to nominal system x (k+1)=Ax (k)+Bu (k)+AdThe available algorithm based on sliding mode prediction mould of x (k- τ (k))
Prediction of the type at (k+P) moment, which exports (5) and its vector, indicates (6)；
SPM(k)=Ω X (k)+Ξ U (k)+Ψ Xd(k)-ΓX0 (6)
Wherein, P is prediction time domain, and M is control time domain, and meets M≤P, and control amount u (k+j) is protected in M-1≤j≤P
It is constant to hold u (k+M-1),
SPM(k)=[s (k+1) ..., s (k+p)]T
X (k)=[x (k+1) ..., x (k+p)]T
X0=[x0..., x0]T
U (k)=[u (k), u (k+1) ..., u (k+M-1)]T
Ω=[(σ CA)T..., (σ CAP)T]T
Γ=[αk, αk+1..., αk+P]T
The design of step 3) reference locus:
In step 3.1) sliding mode predictive control, the selection of reference locus can be constructed according to sliding formwork tendency rate, thus how
Reduce and avoids the problem that needing to consider carefully when the influence buffeted becomes selection.It is huge in weakening is buffeted in view of power function
Big effect using power function as reference locus, while considering failure and probabilistic influence, embedding in reference locus
Enter AF panel means, make up the reference locus of failure and uncertainty design such as formula (7) to the maximum extent:
WhereinSgn () is expressed as sign function.
The value range of each parameter is as follows, 0 < β <, 1,0 < δ < 1,Penalty function indicates
Are as follows:
Step 3.2) formula (8) is expressed as acquiring by One-step delay estimation technique approximationFeelings that can be unknown in d (k)
It completes under condition to sref(k+1) solution, sref(k+1) vector form meets (9).
Sref(k)=[sref(k+1), sref(k+2) ..., sref(k+P)]T (9)
The design of step 4) feedback compensation:
P step exports the prediction at k moment before step 4.1) prediction model (10) indicates the k moment, when formula (11) is expressed as k
Carve the error between reality output and prediction output；
E (k)=s (k)-s (k | k-P) (11)
Step 4.2) is added to error represented by formula (11) as correction in algorithm based on sliding mode prediction model, available P step
Prediction output and its vector form are respectively (12), (13)；
Wherein,jpAs correction coefficient, with being incremented by for prediction steps, correction coefficient is successively
Successively decrease, j1=1, j1> j2> ... > jp> 0.
The design of step 5) optimality criterion:
Step 5.1) design optimization performance indicator such as formula (14), wherein λiFor non-negative weight coefficient, sampling instant error is indicated
The shared specific gravity in performance indicator；γlThe weight coefficient being positive, for constraining control input；
Optimality criterion is expressed as vector form (15) by step 5.2)；
Wherein,
Step 6) whale optimization algorithm solves control law
Step 6.1) takes optimality criterion J (k) as value function Ψ is adapted to, and initializes whale population, initializes each
ParameterL, ρ.Wherein,WithFor coefficient vector, respectively indicates and swings the factor and convergence factor,With iteration time
Random number of several increases from 2 linear decreases to 0, l between [- 1,1], constant ρ ∈ [0,1] and for be uniformly distributed generation with
Machine number, andWithIt can be calculated by following formula；
Wherein,For the random number between [0,1].
Step 6.2) as parameter (ρ < 0.5), andWhen, whale optimization algorithm takes following iterative formula to calculate most
The figure of merit；
Wherein,For the distance between individual and target prey, current iteration number is t,When being iteration t times most
The position of excellent solution,For the whale individual position vector of t iteration.
Step 6.3) as parameter (ρ < 0.5), andWhen, whale optimization algorithm takes the method search of random search
Optimal solution randomly chooses individual whale positionAnd optimizing is carried out according to formula (18)；
Step 6.4) takes the optimizing mode of bubble-net to carry out optimizing when parameter (ρ > 0.5), whale optimization algorithm,
It is iterated according to following formula；
When the maximum number of iterations is reached, optimizing terminates step 6.5), implements current control amount, and k+1 → k is enabled to return to step
It is rapid 2).
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, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Illustrate the validity of embodiment with real case emulation below.
Made using the Qball-X4 four-rotor helicopter actuator of flight control system developed by Canadian Quanser company
For application study object.Qball-X4 subject such as Fig. 2.Qball-X4 four-rotor helicopter, there are six dimension variables for system
That is (X, Y, Z, ψ, θ, φ), wherein X, Y, Z are location variable, and ψ is yaw angle, and θ is pitch angle, and φ is roll angle.Present case is imitative
Really select X-axis direction of advance channel signal as research object.
Following hypothesis is made to Q-ball firstly, establishing model for convenience:
(1) collectively regarded as elastically-deformable rigid body will not occur for quadrotor, and Newton-Euler formula can be used；
(2) housing construction is geometrically symmetric, Mass Distribution is uniform, the mass center of body just on the origin of body coordinate system,
And it is overlapped with center of gravity；
(3) in entire flight experiment, since ground is very little in face of the influence of quadrotor, therefore ignore windage, gyro
Effect and air drag torque etc.；
(4) ignore influence of the earth curvature to quadrotor sporting flying, it is assumed that acceleration of gravity remains unchanged, and ground is sat
Mark system is considered as inertial coodinate system；
(5) for quadrotor when doing line movement, the variation of body attitude angle (yaw ψ, pitching θ, rolling φ) is no more than ± 5 °.
Four-rotor helicopter power resources thrust caused by four rotor wing rotations, changes the revolving speed of four rotors, i.e.,
The state of flight of quadrotor is changed, thrust model is as follows:
Wherein FiFor Rotor thrust, K is positive value gain, and ω is actuator bandwidth, uiFor actuator input.
Aircraft in X direction flight when, yaw angle ψ 0, roll angle φ very little can be approximated to be 0, then X-direction position
Dynamic model can simplify are as follows:
Wherein m is body gross mass, and θ is pitch angle,For X-direction acceleration, F is lift.
Actuator dynamic vi:
In X-axis position control model, pitching angle theta is coupled with it, and whole control can be divided into two stages,
One is to enter second stage after waiting pitch angles control to preset value in the pitch angle control stage --- the position control stage.
When position reaches setting position, pitching angle theta is zeroed by pitch angle control channel.In the lesser situation of θ, by linear
Change and obtain the model in the X-direction ideally without external disturbance, Parameter Perturbation and Time-varying time-delays are as follows:
Assuming that pitch angle has been scheduled on 2 ° of ≈ 0.035rad in the X-axis position control stage, consider that external disturbance, parameter are taken the photograph
Dynamic, network delay and actuator failures, introduce the relevant disturbance of Actuator dynamic, perturbation, time lag and failure, each in system (1)
The value of matrix is as follows:
C=[1 0 0],Δ A=0.1A,
Δ B=0.1B, Δ Ad=0.1Ad, x (0)=[1 1 1]T, f (k)=1.5+ [0 0.2sin (2k) of 0.3sin (6k)] x (k), w
(k) element in takes the white Gaussian noise that mean value is zero, and sliding-mode surface coefficient matrix σ is taken as σ=[1 1 1].Whale optimization algorithm
Parameter setting, population scale take 30, and maximum number of iterations takes 50 times, constant b=1,Initial value takes 2, and final value takes 0.Optimize time domain P
The major part of controlled device dynamic effects should be covered, so present case emulation selection takes into account the prediction of rapidity and stability
Time domain P=4, Simulation Control time domain are selected as M=2.Emulation time domain takes k=500, wherein organism parameter value is K=120N, ω
=15rad/s, M=1.4kg.The control input possible time lag of PWM, and vertical direction acceleration dynamic is influenced in turn
And the time lag generated.Due to time lag size be it is uncertain, present case emulation Time-varying time-delays take the random integers between [0,5].
This simulation case the result shows that, algorithm based on sliding mode prediction faults-tolerant control based on whale optimization algorithm designed by the present invention is calculated
Method has very strong robustness in Discrete-time uncertain systems of the processing with time lag and with actuator failures, and at the same time having
Rapidity and convergent accuracy.Compared with the algorithm of general traditional processing Discrete Time-delay uncertain system, quadrotor is straight
Machine body is risen under the action of present case emulation designed control method, by Fig. 3-Fig. 4, can clearly be obtained, position is bent
Line, Actuator dynamic curve, more gently, and convergent speed is obviously improved, and shows that flight course is more smooth, and
More rapidly reach scheduled position.Meanwhile after control law convergence, it is obviously reduced, trembles although still remaining certain buffeting buffeting
The amplitude of vibration has apparent reduction, such as Fig. 6.In general, for the execution containing Parameter Perturbation, external disturbance and Time-varying time-delays
The control method of device failure system, present case emulation is effective.
Claims (1)
1. this method devises the tolerant fail algorithm of uncertain system of the processing with time-varying state time lag, it is characterized in that: it examines
Considering the linear sliding mode face that general sliding Mode Algorithm designs, there are approach procedures, and unstable phenomenon easily occurs in approach procedure, for this
Situation designs global sliding mode switching function in terms of algorithm based on sliding mode prediction model, avoids approach procedure unstability, ensure that global robust
Property.Consideration system is there are failure, many factors for influencing system control performances such as interference and time lag, devises with faulty and not
The power function reference locus of certainty compensation, and design power function reference locus and allow for a greater degree of weakening sliding formwork
Included buffeting problem.Whale optimization algorithm is devised in rolling optimization problem and carries out optimizing, and algorithm parameter setting is few, asks
Solution is convenient, but can fast accurate solve control law, compared to particle swarm optimization algorithm, which has convergence speed faster
Degree, more accurate solving precision.The robust Fault-Tolerant Control of uncertain discrete-time system for one kind containing Time-varying time-delays, including such as
Lower specific steps:
Step 1) establishes discrete system model:
Step 1.1) Δ A, Δ B, Δ AdThe respectively Parameter Perturbation of system, x (k) ∈ Rn, u (k) ∈ Rp, y (k) ∈ Rq, respectively
The state of system inputs, output.w(k)∈RnFor external disturbance, f (k) is failure function, and τ (k) is uncertain Time-varying time-delays,
But there is its bound [τl, τu].A, B, C, E, AdFor the matrix of appropriate dimension
System (1) is rewritten as formula (2) by step 1.2), wherein d (k)=Δ Ax (k)+Δ Bu (k)+Δ Adx(k-τ(k))+v(k)
+ Ef (k), and d (k) meets | d (k)-d (k-1) |≤d0And dL≤|d(k)|≤dU；
Step 2) algorithm based on sliding mode prediction modelling:
Step 2.1) designs global sliding mode switching function, is located in the original state of system mode track on diverter surface, eliminates
Linear sliding mode face approach procedure, has ensured the global robustness of system；Wherein y (k) is the reality output of system, and σ can lead to
Cross the solution of POLE PLACEMENT USING rule, x0For system initial state, y0Output when for original state.S (0)=0, initial time system
State trajectory is located in diverter surface, eliminates approach procedure.
S (k)=σ y (k)-αkσy0=σ Cx (k)-αkσCx0 (3)
Step 2.2) k+1 moment algorithm based on sliding mode prediction model is (4)；
S (k+1)=σ Cx (k+1)-αk+1σCx0 (4)
Step 2.3) is according to nominal system x (k+1)=Ax (k)+Bu (k)+AdThe available algorithm based on sliding mode prediction model of x (k- τ (k)) exists
(k+P) the prediction output (5) at moment and its vector indicate (6)；
SPM(k)=Ω X (k)+Ξ U (k)+Ψ Xd(k)-ΓX0 (6)
Wherein, P is prediction time domain, and M is control time domain, and meets M≤P, and control amount u (k+j) keeps u (k+ in M-1≤j≤P
It is M-1) constant,
SPM(k)=[s (k+1) ..., s (k+p)]T
X (k)=[x (k+1) ..., x (k+p)]T
X0=[x0..., x0]T
U (k)=[u (k), u (k+1) ..., u (k+M-1)]T
Ω=[(σ CA)T..., (σ CAP)T]T
Γ=[αk, αk+1..., αk+P]T
The design of step 3) reference locus:
In step 3.1) sliding mode predictive control, the selection of reference locus can be constructed according to sliding formwork tendency rate, to how to reduce
It avoids the problem that needing to consider carefully when the influence buffeted becomes selection.Weakening the huge work in buffeting in view of power function
With, using power function as reference locus, while consider failure and probabilistic influence, be embedded in reference locus
AF panel means make up the reference locus of failure and uncertainty design such as formula (7) to the maximum extent:
WhereinSgn () is expressed as sign function.Each ginseng
Several value ranges is as follows, 0 < β <, 1,0 < δ < 1,Penalty function indicates are as follows:
Step 3.2) formula (8) is expressed as acquiring by One-step delay estimation technique approximationIt can be in the case where d (k) be unknown
It completes to sref(k+1) solution, sref(k+1) vector form meets (9).
Sref(k)=[sref(k+1), sref(k+2) ..., sref(k+P)]T (9)
The design of step 4) feedback compensation:
P step exports the prediction at k moment before step 4.1) prediction model (10) indicates the k moment, and formula (11) is expressed as k moment reality
Error between border output and prediction output；
E (k)=s (k)-s (k | k-P) (11)
Step 4.2) is added to error represented by formula (11) as correction in algorithm based on sliding mode prediction model, available P step prediction
Output and its vector form are respectively (12), (13)；
Wherein,jpAs correction coefficient, with being incremented by for prediction steps, correction coefficient is successively passed
Subtract, j1=1, j1> j2> ... > jp> 0.
The design of step 5) optimality criterion:
Step 5.1) design optimization performance indicator such as formula (14), wherein λiFor non-negative weight coefficient, indicate sampling instant error in performance
Shared specific gravity in index；γlThe weight coefficient being positive, for constraining control input；
Optimality criterion is expressed as vector form (15) by step 5.2)；
Wherein,
Step 6) whale optimization algorithm solves control law
Step 6.1) takes optimality criterion J (k) as value function Ψ is adapted to, and initializes whale population, initializes parametersL, ρ.Wherein,WithFor coefficient vector, respectively indicates and swings the factor and convergence factor,With the number of iterations
Increase random number from 2 linear decreases to 0, l for [- 1,1] between, constant ρ ∈ [0,1] and be to be uniformly distributed the random of generation
Number, andWithIt can be calculated by following formula；
Wherein,For the random number between [0,1].
Step 6.2) as parameter (ρ < 0.5), andWhen, whale optimization algorithm takes following iterative formula to calculate optimal value；
Wherein,For the distance between individual and target prey, current iteration number is t,Optimal solution when being iteration t times
Position,For the whale individual position vector of t iteration.
Step 6.3) as parameter (ρ < 0.5), andWhen, the method that whale optimization algorithm takes random search is searched optimal
Solution randomly chooses individual whale positionAnd optimizing is carried out according to formula (18)；
Step 6.4) takes the optimizing mode of bubble-net to carry out optimizing when parameter (ρ > 0.5), whale optimization algorithm, according to
Following formula is iterated；
When the maximum number of iterations is reached, optimizing terminates step 6.5), implements current control amount, and enables k+1 → k return step
2)。
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