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ACTIVE FAULT ANALYSIS OFPARAMETRIC FAULTS INDYNAMIC SYSTEMS
xxxxxxxxxxxxxxxxxxxxxPresented by xxxxxxxxxxxx
Roll xxxxxxRegd. No :- xxxxxxxxx
Branch :- Electrical &ElectronicsEngineering
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CONTENTS1. Importance of fault tolerance
2. Structure of fault tolerant control
system3. Fault Detection and Isolation(FDI)
4. Robust design ofFDI
5. Fault Diagnosis of Nonlinear DynamicSystem
6. System reconfiguration
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1. Importance of fault
tolerance The growing complexity of control system
increases the possibility of component and
system failure. System failure can cause mission abortion,
material damage and human fatality.
The improvement of system reliability can
not been totally dependent upon theimprovement of component reliability,because of the restriction of technologicallevel and cost consideration
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A fault tolerant system is designed with redundancycapacity. When its some components or subsystems fail,it can reconfigure its remaining components andinformation- processing capability to continue operation
properly. Hardware redundancy and Analytical (functional)
redundancy.
Example:Aircraft control system has several channels ofamplifiers. When one of them is failed, the systemcan switch to other channel and continueoperation ( e.g. landing) instead of disaster withhundreds of lives lost.
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Fault tolerance can greatly reduce the systemfault rate and it can use low reliablecomponents to achieve high reliable system.
Single channel system fault rateTriple channel redundant system
More researches need to be done.
Challenges to Control(A collective view), IEEE Trans. AC-32No.4, April 1987.
Aircraft Control SystemA projection to the year 2000, IEEEContr. Syst. Mag, pp11-13, Feb. 1985.
103
h
10 7 h
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2. Structure of fault
tolerant control systems
ActuatorsPlant
DynamicsSensors
ResidualGenerator
DecisionMaking
ReconfigurationAlgorithm
Controller
Output
reference input
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Residual Generation
Observer Approach
Kalman Filter Approach
Parity Space Approach
Decision Making
Fault Detection: Whether there is a fault or not?
Fault Isolation: Where has the fault happened?Fault Estimation: When did the fault happen?
How serious is the fault?
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Approaches to Decision Making
Statistical Hypotheses Test
Fuzzy Logic Inference
Neural Network Classifier
Fault Diagnosis Expert Systems
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3. Fault Detection and
Isolation(1) Observer scheme
System model with faults:
(1)
(2)
Actuator fault
Sensor faultd(t)Unknown Input (Modeling error
and/or disturbances)
( ) ( ) ( ) ( ) ( )x t Ax t Bu t R f t Ed t
1 1
y t Cx t Du t R f t( ) ( ) ( ) ( ) 2 2
f t1( )
f t2 ( )
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Observer equation(3)(4)
Weighted output residual(5)
Consider sensor faults ( )(6)
(7)
(8)(9)
( ) ( ) ( ) ( ) ( ) ( )x t A KC x t B KD u t Ky t ( ) ( ) ( )y t Cx t Du t
r t W y t y t ( ) ( ( ) ( ))
R I, f 02 1
r s H s f s H s d sf d( ) ( ) ( ) ( ) ( ) 2
H s W I sI A Kf c( ) [ ( ) ] 1
H s WC sI A Ed c( ) ( ) 1
A A KCc
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Fault detection rule(Assuming d(t)=0)no fault (10)
with fault (11)
thresholdUnknown Input d(t)will affect the correctness of faultdetection.
It is needed to seek for more robust methods.
Fault isolationWe use mobservers where the ith observer uses
i.e., all sensor outputs but the ith sensor output .
Therefore, the ith observer is free of
|| ( )||r t TD
|| ( )||r t TD
TD
y y y y yi i m1 2 1 1, , , , , ,
yi
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Binary hypotheses test
(14)
(15)According to Generalized Likelihood Ratio Test Theory, Weconstruct the following Decision function of Fault Detection(DFD)
(16)W(k): Covariance matrix ofr(k).
(17), where n(dimension ofr(k)) is the degree of
freedom of distribution
H E r k no fault0 0: [ ( )]
H E r k with fault1 0: [ ( )]
r k N W ( ) ~ ( , )0 ( ) ~ ( )k n2
2
( ) ( ) ( ) ( )k r k W k r k 1
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Innovation test
(20)
White noise: no fault
Zhang, H.G. and H. Y. Zhang, Fault tolerant scheme formultisensor navigation systems, Proc. of 18th Congress of theInternational of Aeronautical Sciences,Beijing, China, Sept. 1992.
r k y k H k x k k ( ) ( ) ( ) ( | ) 1
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(3). Parity space approach Static case
(21)
zero mean Gaussian noise vector,f-sensor fault vector
Ifm>n, we can find a matrix V
VH=0(22)
y Hx f
y Rm
x Rn
p Vy V Vf
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Decision function of Fault Detection(DFD)
(23)
(24)
Fault detection rule:no fault (25)
with fault (26)
p W p1
W E V V VE V [( )( ) ] [ ]
TD TD
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4. Robust design of FDI
It is difficult to distinguish between effects of
fault f(t)and modeling uncertainty d(t).
Eigenstructure assignment:
Design gain matrix Kand weight matrix Wto
makethen residual r(s)is decoupled from uncertainty
(unknown input) d(t)
H s WC sI A KC Ed ( ) [ ( )] 1
0
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5. Fault Diagnosis ofNonlinear Dynamic System
(1)Introduction
Linearized model method may not give
satisfactory result due to mismatch between
linear model and nonlinear behavior.
Analytical solution for FDI of general
nonlinear systems is difficult.Two ways to overcome the difficulties:
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> Restricting the class of nonlinear
systems
>Neuro-Fuzzy approach(2) Bilinear Systems:
)()()(
)()()()()(
2
11
tdEtCxty
tdEtxtuBtAxtxr
iii
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whererespectively the state,
output and unknowndisturbance of thesystem.
Observer:
exists if and only if
0
)(dim
0
0)(
00
2
1
2
1
2
12
2
12
E
EErankx
EC
EEAsIrank
E
EErankErank
E
ECCEErank
)()()(
)()()()()(1
tNytHtx
tytuLtGytFtr
iii
dyx ,,
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Fuzzy Logic Approach forFDI of Nonlinear System
()Takagi-Sugeno fuzzy model
The nonlinear system behavior is
described by
a fuzzy fusion of the outputs of all linear
models which are linearized at different
operating points of the nonlinear system.
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6. System reconfiguratio
(1) Sensor reconfiguration
l Hardware redundancy case:
Switch off faulty sensor(s) and switch on redundantsensor(s)
Analytical redundancy case:
Use observer to estimate the measurement of
faulty sensor(s)
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(2) Actuator reconfiguration
Switch off faulty actuator(s) and switch on
redundant actuator(s)
(3) Control signal reconfiguration
For modeled faults
Bhas changed to because of some faults of
control devices (e.g. surface damage of rudder,
elevator, flap etc).
( ) ( ) ( )x t Ax t Bu t
Bn
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