CN107272660B - A kind of random fault detection method of the network control system with packet loss - Google Patents
A kind of random fault detection method of the network control system with packet loss Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/20—Pc systems
- G05B2219/24—Pc safety
- G05B2219/24065—Real time diagnostics
Abstract
The present invention discloses a kind of random fault detection method of network control system with packet loss, consider that there are random packet losss for network control system, quantization error and random the case where breaking down, initially set up the network control system model there are random fault, resettle the model of fault Detection Filter, residual error evaluation mechanism is introduced to detect whether failure occurs, utilize Lyapunov Theory of Stability and linear matrix inequality analysis method, obtain adequate condition existing for augmented system meansquare exponential stability and fault Detection Filter, optimization problem is solved using the tool box Matlab LMI, providing Optimal Fault Detection Filter parameter isThen judge whether failure occurs according to the residual error mechanism established.The present invention considers failure under actual conditions and occurs at random, and the probability of happening of failure meets Bernoulli distribution, is suitable for general fault detection method, reduces conservative.
Description
Technical field
The present invention relates to network control systems, examine more particularly to the random fault of the network control system with packet loss
Survey method.
Background technique
Network control system (Networked Control System, NCS) is by shared communication channel (such as net
Network) closed-loop feedback control system that each element in system is connected to composition, the feedback control with traditional point-to-point connection
System processed is compared, and network control system has many advantages, such as that convenient for installation and maintenance, flexibility is high and is easy to reconstruct.However network
Introducing can bring some new problems, such as the problems such as data quantization, network-induced time delay, data-bag lost, influence system
Performance and stability, or even generate failure.In practical projects, network control system is to performance, safety and reliability
It is required that it is very high, if certain failures cannot exclude in time, it will cause greatly harm and loss, therefore fault detection is in recent years
The hot spot of research.
One step of key of fault detection is exactly to pass through fault Detection Filter as residual error generation mechanism, is obtained quick to failure
The residual signals of sense recycle residual error evaluation mechanism to judge whether failure occurs.In recent years, more and more scholars, which study, exists
The fault detection problem of the network control system of chance phenomenon, for example, in system there are random delay, random packet loss or with
Machine nonlinear disturbance, if not considering that chance phenomenon will generate very big harm to system performance.However most of document is being ground
When studying carefully the fault detection problem of NCS, all assume that fault-signal is certainty, but it is uncertain due to network
Variation characteristic, in actual conditions, failure occurs at random.
Summary of the invention
For above-mentioned problems of the prior art, the present invention provides the random of the network control system with packet loss
Fault detection method.Consider network control system there are random packet loss, quantization error and at random break down in the case where,
Full rank fault Detection Filter is devised, so that network control system is still able to maintain meansquare exponential stability simultaneously in these cases
And meet preset H ∞ performance indicator, it is effectively detected and is out of order.
The technical scheme adopted by the invention is that: a kind of random fault detection side of the network control system with packet loss
Method, comprising the following steps:
1) there are the controlled device mathematical models of the network control system of random fault for foundation:
Wherein: k is discrete time, and k ∈ [0, N-1], N are nature manifolds；For state vector,For reason
The measurement output quantity thought,For finite energy, that is, ωk∈l2The Unknown worm of [0, ∞],For failure to be detected
Signal, A, E1,E2, C, D are the constant matrices with appropriate dimension.αkThe probability that failure occurs in expression system, to meet
The stochastic variable of Bernoulli 0-1 sequence distribution:
Wherein: E { αkIndicate αk=1 probability occurred,It is specific probability numbers, It is αkVariance,
The measurement output of system after quantization are as follows:
Wherein: Δk=diag { Δ1,k,Δ2,k,…,Δm,k, | | Δk||2≤δ2, δ > 0, I are unit matrix.
2) full rank fault Detection Filter is designed:
Wherein:For the state estimation of system,For the input of fault Detection Filter,It is residual
Difference signal, Af,Bf,Cf,DfIt is the parameter for needing determined fault Detection Filter；
The input of fault Detection Filter are as follows:
Wherein: βkIt indicates that the random packet loss situation between controlled device and fault Detection Filter occurs, meets
The stochastic variable of Bernoulli 0-1 sequence distribution:
Wherein: E { βkIndicate βk=1 probability occurred, β is specific probability numbers,f1 2It is βkVariance,
Residual error evaluation mechanism is introduced to detect whether failure occurs, residual error evaluation function J (k) and threshold value J (th) are respectively as follows:
Wherein: L is the maximum time span of evaluation function, and whether system breaks down can be detected by formula (7):
3) adequate condition existing for system meansquare exponential stability and fault Detection Filter are as follows:
Wherein:
Wherein: * represents the transposition of symmetric position matrix,U,X,W,It is the matrix with appropriate dimension
And be it is unknown, ε is known variables, and dependent variable is all known.It is solved using the tool box Matlab LMI, to calibration
γ > 0 is measured, if there is positive definite matrix U, X, W and scalar ε > 0 set up formula (8), then are
System is meansquare exponential stability, and meets H∞Performance indicator can obtain non-optimal fault Detection Filter parameter, it can continue
Carry out step 4)；If above-mentioned known variables do not solve, system is not meansquare exponential stability and cannot obtain non-optimal event
Hinder Fault detection filter parameter, it is not possible to carry out step 4).
4) Optimal Fault Detection Filter parameter is calculated
By solving optimization problem formula (9):
If there is solution, Optimal Fault Detection Filter parameter is obtainedOptimal H∞Performance indicator is γmin,
Obtain Optimal Fault Detection Filter parameter are as follows:
Wherein: G3, V is nonsingular matrix.After obtaining Optimal Fault Detection Filter parameter, according to formula (3) and formula (4)
The residual signals r (k) of available system, then calculating formula (5) and formula (6), finally judge whether failure occurs by formula (7).
If formula (9) cannot obtain Optimal Fault Detection Filter without solution.
Compared with prior art, beneficial effects of the present invention: the present invention consider simultaneously imperfect measurement factor in system,
Packet loss, external disturbance and the failure occurred at random give under the network environment by a series of derivation and there is random event
The design method of fault Detection Filter in the case of barrier only considered really when compared to traditional fault Detection Filter design setting model
The limitation of qualitative failure, this method are more of practical significance, and reduce conservative.
Detailed description of the invention
Attached drawing 1 is the flow chart of the random fault detection method of the network control system with packet loss.
Attached drawing 2 is ω (k) ≠ 0,Residual signals figure when ρ=0.6.
Attached drawing 3 is ω (k) ≠ 0,Residual error evaluation function figure when ρ=0.6.
Attached drawing 4 is ω (k) ≠ 0,Residual error evaluation function figure when ρ=0.6.
Attached drawing 5 is ω (k) ≠ 0,Residual error evaluation function figure when ρ=0.6.
Attached drawing 6 is ω (k) ≠ 0,Residual error evaluation function figure when ρ=0.6.
Attached drawing 7 is ω (k) ≠ 0,Residual error evaluation function figure when ρ=0.6.
Specific embodiment
The following further describes the specific embodiments of the present invention with reference to the drawings.
Referring to attached drawing 1, a kind of random fault detection method of the network control system with packet loss, comprising the following steps:
Step 1: there are the controlled device mathematical models of the network control system of random fault for foundation
It is formula (1) there are the controlled device of the network control system of random fault, it is contemplated that in network control system,
The data of sampling will carry out the quantification treatment of data before carrying out network transmission, and the measurement output of system is formula after quantization
(2)。
Step 2: designing full rank fault Detection Filter
Full rank fault Detection Filter formula (3) is designed, α is selectedkIndicate the probability that failure occurs, αkTo meet Bernoulli
The stochastic variable of 0-1 sequence distribution, works as αkWhen=0, showing system, there is no failures, work as αkWhen=1, show that system determines hair
Raw failure,Bigger, a possibility that breaking down in expression system, is bigger.
Consider under packet drop, the input of fault Detection Filter is formula (4).β in formulakIndicate to occur in controlled device and
Random packet loss situation between fault Detection Filter, βkFor the stochastic variable for meeting the distribution of Bernoulli 0-1 sequence.Work as βk
When=1, shows that no data is lost, work as βkWhen=0, show that data are all lost.
Define residual error error signal:
ek=r (k)-fk (11)
Comprehensively consider formula (1), (3), (4) and (11), pass through the available following augmented system of the method for state augmentation:
Wherein:
Construction residual error evaluation function J (k) and threshold value J (th) are respectively formula (5) and formula (6), and formula (7) can be used to judge event
Whether barrier occurs.Wherein: L is the maximum time span of evaluation function, when the value in residual error evaluation function is greater than threshold value, is occurred
It failure and alarms, otherwise indicates that there is no failures.
Step 3: construction Lyapunov functionUtilize Lyapunov Theory of Stability and linear matrix inequality
Analysis method obtains adequate condition existing for augmented system (12) meansquare exponential stability and fault Detection Filter.Steps are as follows:
Step 3.1: first determining whether the stability of augmented system, obtain the adequate condition of system meansquare exponential stability.
Assuming that inequality (13) is set up, i.e.,
Wherein: * represents the transposition of symmetric position matrix, ψ11=diag { Pl-G-GT,Pl-G-GT,Pl-G-GT,-I ,-I },
ψ22=diag {-Pl,-γ2I }, ψ33=diag {-ε-1I,-εδ-2I },
Wherein:
Φ1=Q+DFE+ETFTDT (15)
Wherein:F=Δkδ-1, E=[00000
δMδN]
Amplify lemma according to cross term, it is known that
Φ1≤Φ2=Q+ ε DDT+ε-1EET (16)
Φ2≤Φ3=Q+ ε DDT+ε-1(δ-1E)Tδ2(δ-1E) (17)
Φ3< 0 and inequality (13) are of equal value, if inequality (13) is set up, Φ1< 0.
Due to Pl> 0, (Pl-G)TPl -1(Pl- G) >=0, therefore Pl-G-GT≥-GTPl -1G, to obtain
Wherein: Ξ11=diag {-GTPl -1G,-GTPl -1G,-GTPl -1G ,-I ,-I }, to (18) premultiplication diag { G-T,G-T,G-T,
I, I, I, I }, the transposition that the right side multiplies it is available
Mending lemma according to Schur can obtain
Υ1+Υ2+ Π < 0 (20)
Wherein:
Work as θkWhen=0,
Wherein:To
By non-zero initial condition andIt is available
Wherein: σ=(- λmax(Γ))-1λmax(Pl) > 0, Asymptotic Stability on available augmented system (12) mean square meaning.
According to Lyapunov Theory of Stability, work as θkWhen=0, scalar γ > 0 is given, there are positive definite matrix Pl> 0, scalar ε
> 0, nonsingular matrix G set up inequality (13).When the adequate condition of step 3.1 is set up, then execute step 3.2；Such as
The adequate condition of fruit step 3.1 is invalid, then augmented system (12) is not meansquare exponential stability, cannot execute step 3.2.
Step 3.2: working as θkWhen ≠ 0,
Wherein:
It is obtained by (20) formula,
Consider that zero initial condition, augmented system (12) exponential mean square stability further have
Meet H∞Performance indicator.
Formula (13) can be write as the form of formula (8), can obtain from formula (8),It represents Ω and W is nonsingular, can look for
To nonsingular matrix G3,G4So that
Enable U=G1,
Define transposed matrix
In the case where without loss of generality, it is assumed that
It is available
To obtain
ZTΨ Z < 0 (32)
Wherein: Z=diag { T, T, T, I, I, T, I, I, I }, formula (8) and formula (32) are of equal value.
It is solved using the tool box Matlab LMI, works as θkWhen ≠ 0, scalar γ > 0 is given, there are positive definite matrix Pl>
0, scalar ε > 0, nonsingular matrix G set up inequality (13).So augmented system (12) meansquare exponential stability, and it is full
Sufficient H∞Performance indicator.When the adequate condition of step 3 is set up, i.e., when formula (8) is set up, then execute step 4；If step 3 is filled
Slitting part is invalid, then augmented system (12) is not meansquare exponential stability and non-optimal fault Detection Filter parameter can not solve
, step 4 cannot be executed.
Step 4: calculating Optimal Fault Detection Filter parameter
For augmented system (12), obtaining Optimal Fault Detection Filter parameter by solution optimization problem formula (9) is
Formula (10), optimal H∞Performance indicator is γmin, according to the residual signals r (k) of formula (3) and formula (4) available system, then
Formula (5) and formula (6) are obtained, finally judges whether failure occurs by formula (7)；If formula (9) cannot obtain optimal failure without solution
Fault detection filter.
Embodiment:
Using a kind of random fault detection method of the network control system with packet loss proposed by the present invention, not outer
I.e. θ in the case where boundary's disturbance and failurekWhen=0, augmented system is meansquare exponential stability.Work as θkWhen ≠ 0, system is just to refer to
Number is stable and meets H∞Performance indicator.Concrete methods of realizing is as follows:
Controlled device is closed network networked control systems, and controlled device mathematical model is formula (1), gives its system parameter
For
C=[0.6 0.8 0], D=0.1
Assuming that quantization resolution ρ=0.6 of system solves different packet loss probability using the tool box MATLAB LMIWith it is random
Probability of malfunctionUnder optimal H∞Performance indicator, as shown in table 1.As can be seen that in network channel probability of malfunction increase (lose
Packet probability reduces), corresponding performance indicator γminAlso it increases with it, i.e. Disturbance Rejection degradation, illustrates that failure occurs general
The probability of rate and packet loss has important influence to system performance.
Minimum γ in the case of 1 different faults of table and drop probabilitiesmin
Assuming that the original state of system is x0=[0 0 0]T, ρ=0.6,With the LMI of MATLAB
It tool box can be in the hope of γ for augmented system (11)min=1.1340, the optimized parameter of corresponding fault Detection Filter is
Cf=[- 0.00713 0.00441 0.00402], Df=-0.00369
Assuming that fault-signal and Unknown worm are respectively
The residual error r (k) and residual error valuation functions J (k) of system are used according to the present invention as shown in attached drawing 2 and attached drawing 3
Residual error evaluation mechanism takes assessment time span L=400, then the calculation formula of threshold value is
By 200 Monte-Carlo Simulations, being averaged J (th)=0.12588 is final threshold value,
0.11973=J (73) < J (th) < J (74)=0.12904
After illustrating that k=70 breaks down, fault-signal can be detected in 5 time steps, moreover it is possible to disturbance
Mutually distinguish.
Different faults probability in the case of ρ=0.6Residual error evaluation function and threshold value such as attached drawing 4, attached drawing 5, attached
Shown in Fig. 6 and attached drawing 7.
When, 0.02093=J (84) < J (th)=0.02142 < J (85)=0.02146
When, 0.07348=J (78) < J (th)=0.07488 < J (79)=0.07593
When, 0.10669=J (76) < J (th)=0.10932 < J (77)=0.11370
When, 0.12740=J (71) < J (th)=0.13410 < J (72)=0.14673
As can be seen that out of order generation, failure in system can be effectively detected in designed fault Detection Filter
The probability of generation is bigger, and duration needed for detecting fault-signal is shorter, illustrates to study the failure occurred at random meaningful.
The above are preferred embodiments of the present invention, is not intended to limit the present invention in any form, all foundations
Technical spirit of the invention any simple modification, equivalent change and modification made to the above embodiment, belong to inventive technique
In the range of scheme.
Claims (1)
1. a kind of random fault detection method of the network control system with packet loss, which is characterized in that the failure in system is
Occur at random, specifically includes the following steps:
1) there are the controlled device mathematical models of the network control system of random fault for foundation:
Wherein: k is discrete time, and k ∈ [0, N-1], N are nature manifolds；For state vector,It is ideal
Output quantity is measured,For the Unknown worm of finite energy, ωk∈l2[0, ∞],For fault-signal to be detected,
A,E1,E2, C, D are the constant matrices with appropriate dimension, αkThe probability that failure occurs in expression system, meets Bernoulli
The distribution of 0-1 sequence:
Wherein: E { αkIndicate αk=1 probability occurred,It is specific probability numbers,f2 2It is αkVariance,
The measurement output of system after quantization are as follows:
Wherein: Δk=diag { Δ1,k,Δ2,k,…,Δm,k, | | Δk||2≤δ2, δ > 0, I are unit matrix；
2) full rank fault Detection Filter is designed:
Wherein:For the state estimation of system,For the input of fault Detection Filter,For residual error letter
Number, Af,Bf,Cf,DfIt is the parameter for needing determined fault Detection Filter；
The input of fault Detection Filter are as follows:
Wherein: βkIt indicates that the random packet loss situation between controlled device and fault Detection Filter occurs, meets Bernoulli
The stochastic variable of 0-1 sequence distribution:
Wherein: E { βkIndicate βk=1 probability occurred,It is specific probability numbers,f1 2It is βkVariance,
Residual error evaluation mechanism is introduced to detect whether failure occurs, residual error evaluation function J (k) and threshold value J (th) are respectively as follows:
Wherein: L is the maximum time span of evaluation function, and whether system breaks down can be judged by formula (7)；
3) adequate condition existing for system meansquare exponential stability and fault Detection Filter are as follows:
Wherein:
Wherein: * represents the transposition of symmetric position matrix,U,X,W,It is that there is the matrix of appropriate dimension and be
Unknown, ε is known variables, and dependent variable is all known；It is solved using the tool box Matlab LMI, gives scalar γ
> 0, if there is positive definite matrixU, X, W and scalar ε > 0 set up formula (8), then system is
Meansquare exponential stability, and meet H∞Performance indicator can obtain non-optimal fault Detection Filter parameter, it can continue
Step 4)；If above-mentioned known variables do not solve, system is not meansquare exponential stability and cannot obtain non-optimal failure inspection
Survey filter parameter, it is not possible to carry out step 4)；
4) Optimal Fault Detection Filter parameter is calculated
By solving optimization problem formula (9):
If there is solution, Optimal Fault Detection Filter parameter is obtainedOptimal H∞Performance indicator is γmin, obtain most
Excellent fault Detection Filter parameter are as follows:
Wherein: G3, V is nonsingular matrix；The residual signals r (k) of system is obtained further according to formula (3) and formula (4), then calculating formula
(5) and formula (6), finally judge whether failure occurs by formula (7)；
If formula (9) cannot obtain Optimal Fault Detection Filter without solution.
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| CN108319147B (en) * | 2018-03-13 | 2020-01-07 | 江南大学 | H-infinity fault-tolerant control method of networked linear parameter change system with short time delay and data packet loss |
| CN108733031B (en) * | 2018-06-05 | 2020-12-04 | 长春工业大学 | Network control system fault estimation method based on intermediate estimator |
| CN108732926A (en) * | 2018-06-05 | 2018-11-02 | 东北石油大学 | Networked system method for estimating state based on insufficient information |
| CN109283916B (en) * | 2018-10-15 | 2021-02-02 | 浙江工业大学 | Data packet loss compensation method for multi-sensor networked control system |
| CN110045716B (en) * | 2019-04-18 | 2020-08-11 | 中广核工程有限公司 | Method and system for detecting and diagnosing early fault of closed-loop control system |
| CN110750754A (en) * | 2019-12-05 | 2020-02-04 | 黑龙江省科学院自动化研究所 | Data processing method based on wireless sensor network in big data environment |
| CN111290274B (en) * | 2020-02-19 | 2022-12-06 | 宿迁学院 | H-infinity control method of network control system with data packet loss |
| CN111505500B (en) * | 2020-04-09 | 2021-01-29 | 江南大学 | Intelligent motor fault detection method based on filtering in industrial field |
| CN113885335B (en) * | 2021-11-08 | 2023-04-28 | 江南大学 | Fault-tolerant control method for networked system with partial decoupling disturbance |
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Effective date of registration: 20200818 Address after: 313000 1-C, building 1, No. 656, Qixing Road, high tech Zone, Wuxing District, Huzhou City, Zhejiang Province Patentee after: Huzhou xinbeilian Network Technology Co.,Ltd. Address before: 518000 Baoan District Xin'an street, Shenzhen, Guangdong, No. 625, No. 625, Nuo platinum Plaza, Patentee before: SHENZHEN SHANGGE INTELLECTUAL PROPERTY SERVICE Co.,Ltd. Effective date of registration: 20200818 Address after: 518000 Baoan District Xin'an street, Shenzhen, Guangdong, No. 625, No. 625, Nuo platinum Plaza, Patentee after: SHENZHEN SHANGGE INTELLECTUAL PROPERTY SERVICE Co.,Ltd. Address before: No. 1800 road 214122 Jiangsu Lihu Binhu District City of Wuxi Province Patentee before: Jiangnan University |
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