CN107070734B - A kind of network control system fault detection method - Google Patents

A kind of network control system fault detection method Download PDF

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CN107070734B
CN107070734B CN201611244648.9A CN201611244648A CN107070734B CN 107070734 B CN107070734 B CN 107070734B CN 201611244648 A CN201611244648 A CN 201611244648A CN 107070734 B CN107070734 B CN 107070734B
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controller
control system
time delay
network control
filter
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CN107070734A (en
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王燕锋
李祖欣
王培良
周哲
钱懿
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Foshan Haixie Technology Co ltd
Weishitong Guangzhou Information Security Technology Co ltd
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Huzhou University
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    • H04L43/00—Arrangements for monitoring or testing data switching networks
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Abstract

A kind of network control system fault detection method, firstly, describing sensor respectively to controller time delay and controller to actuator time delay using two independent Markov chains, network control system is modeled as tool, and there are two the control systems of Markov chain.Fault Detection Filter is constructed on this basis and establishes closed-loop system model using the method for state augmentation.Then, closed-loop system Stochastic stable has been obtained in the form of MATRIX INEQUALITIES and meets H∞The condition of performance gives controller and filter gain matrix and H∞The method for solving of Reduction Level, and obtained transition probability and minimum H∞Relationship between Reduction Level.The fault filter that the mentioned method of case verification obtains is but also good to the robustness of external disturbance not only to Fault-Sensitive, solves the H of the network control system under sensor to controller time delay and controller to actuator time delay transition probability all part unknown condition∞Fault detection problem.

Description

A kind of network control system fault detection method
Technical field
The present invention relates to computer network control field more particularly to a kind of network control system fault detection methods.
Background technique
Network control system (networked control system, NCS) is anti-by sharing the closed loop that network is constituted Control system is presented, has many advantages, such as at low cost, flexible structure, easy to maintain, obtains in complicated industrial control field and widely answer With.However, the introducing of network is inevitably generated the problems such as time delay, data-bag lost, so that the complexity of system is increased, New challenge is brought to the reliability of NCS.The fault detection problem of NCS get the attention and occur it is many research at Fruit.
In NCS, network delay be in many cases it is random, random delay is usually modeled as the Markov of finite state The advantages of chain, this method, is: can describe the dependence between current time time delay and last moment time delay, and can be Data-bag lost is included.Occur following several achievements in the prior art:
1, controller is extended to actuator when sensor to controller (sensor to controller, S-C) The sum of (controller to sensor, C-A) time delay is modeled as Markov chain, and closed loop NCS is modeled as Markov jump line Property system devises H ∞ fault Detection Filter in the situation known to the transition probability whole of time delay.2, control input is made It is an externally input processing, closed loop NCS is modeled as Markov jump linear system, constructs the residual generation of system, event Barrier test problems are converted into H ∞ filtering problem；Also random data packet loss is considered with the presence of the prior art, NCS is modeled as containing There is the Markov jump system of 4 mode, and devises robust failure detector.3, the sum of C-A time delay is extended to when S-C to build Mould is Markov chain, in the case where the transition probability part of Markov chain is unknown, is given existing for fault Detection Filter Adequate condition, and the solution of system function optimization problem is given in the inverse form of Moore-Penrose.It is independent with two Markov chain, which is described, to be described to extend to C-A time delay when S-C respectively, and it is unknown that C-A time delay transition probability all parts are extended in S-C Under conditions of, i.e., carrying out NCS fault detection to control system as shown in Figure 1, there is not been reported.
Summary of the invention
In order to solve prior art problem, provide one kind can be used in extending to C-A time delay transition probability when S-C all the present invention The fault detection method of network control system under conditions of part is unknown.
The technical scheme is that a kind of network control system fault detection method, comprising the following steps:
Step 1:
It utilizesAnd μkSensor in network control system is respectively indicated to the time delay and controller of controller to actuator Time delay, and respectively in finite aggregateWith N={ μmin, μmaxIn value, transfer is general Rate matrix is respectively as follows: ∧=[λij], Π=[πrs], λijAnd πrsIt is defined as follows:
In formula:
ForIt enablesWherein,IfThenWithIt is further represented as Wherein 1≤d≤nM, nMIt is the number for gathering M element；ForIt enables Wherein,WhenThenWithIt is further represented asWherein 1≤g≤nN, nNIt is set N element Number；
Step 2:
To the network control system with time delay:
In formula: xk∈RnIt is system mode vector, yk∈RmIt is system output vector, dk∈RpIt is L2The external disturbance of bounded Signal, fk∈RqIt is L2The fault-signal of bounded, Ap, Bp, Bd, Bf, CpIt is the permanent matrix of appropriate dimension, K is control to be designed Device gain matrix；Fault Detection Filter is constructed in controller end:
In formula:It is filter status vector,It is filter output vector；rk∈RqFor residual error, L be to Filter gain matrix is designed, V is residual error gain matrix；
Step 3:
Definition status evaluated error and residual error error signalrek=rk-fk；Define augmentation vector Obtain closed-loop system equation:
In above formula:
I1=[0 I]T∈R2n×n, I2=[I 0]T∈Rn×2n, I3=[0 I]T∈R(p×q)；
For unknown parameter K and L in processing system, augmentation vector is defined:
Then closed-loop system is written as:
In formula:
WhereinThePiecemeal is unit battle array, remaining is zero gust,ThePiecemeal is unit battle array, Remaining is zero gust；
Step 4:
K and L unknown in step 3 in order to obtain are solved:
Above-mentioned formula meets:
Provide controller gain matrix K and filter gain matrix L and minimum H∞Reduction Level γminDerivation algorithm, Process is as follows:
Step 1: given γ；
Step 2: solvingAndObtain one group of feasible solution Enable k=0；
Step 3: solving non-linear minimisation problem:
WithIt enablesKk=K, Lk=L；
Step 4: whether MATRIX INEQUALITIES solution meets in checking step 4, it is positive real number that satisfaction, which then enables γ=γ-δ, δ, K=k+1 is enabled, third step is gone to；It is unsatisfactory for and is more than given maximum number of iterations, then exit calculating；
Step 5: showing this optimization problem in given the number of iterations without solution if γ is equal to given value；It is given if γ is less than Definite value, then γmin=γ+δ；
Step 5:
Select residual error evaluation functionThreshold valueWherein l0For Initial evaluation moment, L0For evaluation function maximum step-length, pass through comparison JkAnd JthCan be detected out whether faulty generation:
The beneficial effects of the present invention are: firstly, describing sensor respectively to controller using two independent Markov chains When extend to controller to actuator time delay, network control system is modeled as tool, and there are two the control systems of Markov chain.Herein On the basis of construct fault Detection Filter and establish closed-loop system model using the method for state augmentation.Then, with matrix The form of inequality has obtained closed-loop system Stochastic stable and has met H∞Performance condition gives controller and filter gain square Battle array and H∞The method for solving of Reduction Level, and obtained transition probability and minimum H∞Relationship between Reduction Level.It solves Network control system under sensor to controller time delay and controller to actuator time delay transition probability all part unknown condition H∞Fault detection problem.
Detailed description of the invention
Fig. 1: the targeted network control system structure chart of the present invention.
Fig. 2: can be using S-C time delay figure common in network control system of the invention.
Fig. 3: can be using C-A time delay figure common in network control system of the invention.
Fig. 4: the residual signals for the network control system that the present invention is calculated are utilized.
Fig. 5: the residual error evaluation function J for the network control system that the present invention is calculated is utilizedkAnd threshold value JthFigure.
Specific embodiment
A kind of network control system fault detection method, comprising the following steps:
Step 1:
It utilizesAnd μkSensor in network control system is respectively indicated to the time delay and controller of controller to actuator Time delay, and respectively in finite aggregateWith N={ μmin, μmaxIn value, transfer is general Rate matrix is respectively as follows: ∧=[λij], Π=[πrs], λijAnd πrsIt is defined as follows:
In formula:
ForIt enablesWherein,If ThenWithIt is further represented as Wherein 1≤d≤nM, nMIt is the number for gathering M element；ForIt enables Wherein,WhenThenWithIt is further represented asWherein 1≤g≤nN, nNIt is set N element Number；
Step 2:
To the network control system with time delay:
In formula: xk∈RnIt is system mode vector, yk∈RmIt is system output vector, dk∈RpIt is L2The external disturbance of bounded Signal, fk∈RqIt is L2The fault-signal of bounded, Ap, Bp, Bd, Bf, CpIt is the permanent matrix of appropriate dimension, K is control to be designed Device gain matrix；Fault Detection Filter is constructed in controller end:
In formula:It is filter status vector,It is filter output vector；rk∈RqFor residual error, L be to Filter gain matrix is designed, V is residual error gain matrix；
Step 3:
Definition status evaluated error and residual error error signalrek=rk-fk；Define augmentation vector Obtain closed-loop system equation:
In above formula:
I1=[0 I]T∈R2n×n, I2=[I 0]T∈Rn×2n, I3=[0 I]T∈R(p×q)；
For unknown parameter K and L in processing system, augmentation vector is defined:Then Closed-loop system is written as:
In formula:
WhereinThePiecemeal is unit battle array, remaining is zero gust,ThePiecemeal is unit Battle array, remaining is zero gust；
Step 4:
K and L unknown in step 3 in order to obtain are solved:
In above-mentioned formula:
Provide controller gain matrix K and filter gain matrix L and minimum H∞Reduction Level γminDerivation algorithm, Process is as follows:
Step 1: given γ；
Step 2: solvingAndObtain one group of feasible solution:Enable k=0；
Step 3: solving non-linear minimisation problem:
WithIt enablesKk=K, Lk=L；
Step 4: whether MATRIX INEQUALITIES solution meets in checking step 4, it is positive real number that satisfaction, which then enables γ=γ-δ, δ, K=k+1 is enabled, third step is gone to；It is unsatisfactory for and is more than given maximum number of iterations, then exit calculating；
Step 5: showing this optimization problem in given the number of iterations without solution if γ is equal to given value；It is given if γ is less than Definite value, then γmin=γ+δ；
Step 5:
Select residual error evaluation functionThreshold valueWherein l0For Initial evaluation moment, L0For evaluation function maximum step-length, pass through comparison JkAnd JthCan be detected out whether faulty generation:
The main object of the present invention beAnd μkTransition probability part it is unknown under conditions of, design error failure detection filter Wave device simultaneously meets:
1) in ωkWhen=0, system Stochastic stable.
2) under zero initial condition, residual error error signal rekMeet following H∞Performance indicator:
Wherein γ > 0 is H∞Reduction Level.
The lemma that processing array inequality is used in the method for the present invention is introduced first:
1, it is provided in existing technological achievements, when given scalar lambdai>=0 and matrix Pi>=0, i=1,2 ..., N, have it is following at It is vertical:
2, we provide lemma 2 on the basis of lemma 1: for given scalar lambdai>=0, πr>=0 and matrix Pi,r>=0, i =1,2 ..., N1, r=1,2 ..., N2；ThenPerseverance is set up, which can To prove to set up by mathematical induction:
Work as N1=1, N2When=1, there is λ1π1P1,1≤λ1π1P1,1, it is assumed that N1=k1, N2=k2, i.e.,
Work as N1=k1+ 1, N2=k2When+1,
By lemma 1, it is known that:
Therefore,
Work as N1=k1+ 1, N2=k2When+1: I.e. lemma must be demonstrate,proved.
Main Conclusions:
Theorem 1 works as ωkWhen=0, closed-loop system:
It is Stochastic stable, and if only if There are matrix K, L and positive definite matrix Qi,r> 0, Qj,s> 0 makes following MATRIX INEQUALITIES for all i, and j ∈ M, r, s ∈ N is equal It sets up:
The proof of sufficiency of the theorem:
Choose Lyapunov functionSo,
If the formula is set up:
The minimum that wherein α is-Ξ is special Value indicative.For any T >=1, as available from the above equation:
Adequacy must be demonstrate,proved.
Necessity proves:
Assuming that systemIt is Stochastic stable, i.e.,It enables:WhereinAssuming that εk≠ 0, by above formula andOrthotropicity to be known as below the limit be existing:
By εkArbitrariness can further obtain: Known to
Consider formula:
As T → ∞, by above formula andΞ < 0 can be obtained, theorem must be demonstrate,proved.
Inference 1 works as ωkWhen ≠ 0, residual error weight matrix V and scalar γ > 0 are given, if it exists matrix K, L and positive definite matrix Qi,r> 0, Pj,s> 0, Qj,s> 0, so thatPj,sQj,s=I,
In formula:
For all i, j ∈ M, r, s ∈ N is set up, then with the unknown closed-loop system in transition probability part be with Machine is stable, and meets H∞Performance indicator.
It proves, can be obtained by lemma 2:
Therefore:
In formula:
IfIt sets up, then
For above formula, k is added up from 0 to ∞ to be obtained:
It can be obtained by system Stochastic stable and zero initial condition:
ByIt enablesIt can obtain unknown in step 3 for calculating in step 4 K and L formula:
Ginseng in order to illustrate the validity of the method for the present invention, in Fig. 1 in the network control system state equation of controlled device Number are as follows:
Assuming thatAnd μkSensor in network control system is respectively indicated to the time delay and controller of controller to actuator Time delay, and the value in finite aggregate M={ 0,1 } and N={ 0,1 } respectively, in order to obtain transition probability and system performance it Between relationship, consider following four in situation time delay transition probability matrix:
(1)(2)
(3)(4)
Given residual error weight V=[0.1 0.1], acquires minimum H according to inference 1∞Reduction Level γminIt is as shown in the table:
γ under the different transition probability matrixs of table 1minValue
Transition probability matrix A1Π1 A2Π2 A3Π3 A4Π4
γmin 1.0677 1.0536 1.0493 1.0198
From table 1 it follows that the information of known time delay transition probability matrix is more, then H∞Reduction Level γminJust Smaller, i.e. the Disturbance Rejection ability of system is stronger.
Assuming that the original state x of system-1=x-2=[0 0]T, x0=[- 1 1]T, dkFor the random signal for being evenly distributed on [- 0.02 0.02], fault-signal are as follows:The initial mode of network delay And μkRespectively as shown in Figures 2 and 3, for tool There is transition probability matrix A2And Π2NCS, controller gain matrix K is acquired according to step 4 and filter gain L is as follows:
Choose residual error evaluation function:Acquire failure determination threshold value:
Residual signals, residual error evaluation function and threshold curve are respectively such as Shown in Fig. 4 and Fig. 5.It will be seen that when an error occurs, the residual error evaluation function of residual signals has from Fig. 4 and Fig. 5 Significant change.In addition, acquiring J11=0.0019 < Jth=0.0066 < J12=0.0234, it means that the 3rd occurred in failure Time cycle, fault filter just detected failure.
Under conditions of the present invention extends to C-A time delay transition probability in the S-C of NCS part is unknown, the H of NCS is had studied∞ Fault detection problem.New lemma has been obtained to handle unknown time delay transition probability, further in the form of MATRIX INEQUALITIES Adequate condition existing for fault Detection Filter is given, and gives the solution of filter gain matrix using the thought of CCL Method.Case Simulation illustrate obtained fault Detection Filter not only to Fault-Sensitive, but also to external disturbance have robust Property.

Claims (1)

1. a kind of network control system fault detection method, comprising the following steps:
Step 1:
It utilizesAnd μkRespectively indicate sensor in network control system to controller time delay and controller to actuator when Prolong, and respectively in finite aggregateWith N={ μmin, μmaxIn value, transition probability square Battle array is respectively as follows: ∧=[λij], Π=[πrs], λijAnd πrsIt is defined as follows:
πrs=Pr (μk+1=s | μk=r),
In formula:λij>=0, πrs≥0；
ForIt enablesWherein, IfThenWithIt is further represented as Wherein 1≤d≤nM, nMIt is the number for gathering M element；ForIt enablesWherein,WhenThenWithIt is further represented as Wherein 1≤g≤nN, nNIt is set N element Number；
Step 2:
To the network control system with time delay:
In formula (1): xk∈RnIt is system mode vector, yk∈RmIt is system output vector, dk∈RpIt is L2The external disturbance of bounded is believed Number, fk∈RqIt is L2The fault-signal of bounded, Ap, Bp, Bd, Bf, CpIt is the permanent matrix of appropriate dimension, K is controller to be designed Gain matrix；Fault Detection Filter is constructed in controller end:
In formula (2):It is filter status vector,It is filter output vector；rk∈RqFor residual error,
L is filter gain matrix to be designed, and V is residual error gain matrix；
Step 3:
Definition status evaluated error and residual error error signalrek=rk-fk；Define augmentation vectorObtain closed-loop system equation:
In formula (3):
C=[0 CP], I1=[0 I]T∈R2n×n, I2 =[I 0]T∈Rn×2n, I3=[0 I]T∈R(p×q)；
For unknown parameter K and L in processing system, augmentation vector is defined:Then closed loop System is written as:
In formula (4):
WhereinThePiecemeal is unit battle array, remaining is zero gust,ThePiecemeal is unit battle array, remaining It is zero gust；
Step 4:
K and L unknown in step 3 in order to obtain choose Lyapunov functionIt solves:Pj,sQj,s=I (6),
Above-mentioned formula (5) and (6) meet:
Provide controller gain matrix K and filter gain matrix L and minimum H∞Reduction Level γminDerivation algorithm, process It is as follows:
Step 1: given γ；
Step 2: solvingAndObtain one group of feasible solution Enable k=0；
Step 3: solving non-linear minimisation problem:
With
It enablesKk=K, Lk=L；
Step 4: whether MATRIX INEQUALITIES solution meets in checking step 4, it is positive real number that satisfaction, which then enables γ=γ-δ, δ, enables k= K+1 goes to third step；It is unsatisfactory for and is more than given maximum number of iterations, then exit calculating；
Step 5: showing this optimization problem in given the number of iterations without solution if γ is equal to given value；If γ is less than given It is worth, then γmin=γ+δ；
Step 5:
Select residual error evaluation functionThreshold valueWherein l0It is initial Evaluate moment, L0For evaluation function maximum step-length, pass through comparison JkAnd JthCan be detected out whether faulty generation:
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