Set-theoretic Fault-tolerant Control in Multisensor Systems

159 Pages·2013·3.16 MB·English

by  Florin Stoican

Set-theoreticFault-tolerant Control inMultisensorSystems
Set-theoretic
Fault-tolerant Control
in Multisensor Systems
Florin Stoican
Sorin Olaru
Series Editor
Francis Castanié
Firstpublished2013inGreatBritainandtheUnitedStatesbyISTELtdandJohnWiley&Sons,Inc.
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Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1. State of the Art in Fault-tolerant
Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Fault detection and isolation . . . . . . . . . . . . 4
1.2. Control reconfiguration . . . . . . . . . . . . . . . . 6
1.3. Sets in control . . . . . . . . . . . . . . . . . . . . . 9
1.3.1. Set generalities . . . . . . . . . . . . . . . . . . 11
1.3.2. Set operations . . . . . . . . . . . . . . . . . . . 14
1.3.3. Dynamic systems and sets . . . . . . . . . . . 16
1.3.4. Other set-theoretic issues . . . . . . . . . . . . 18
1.4. Existing set-theoretic methods in FTC . . . . . . 22
Chapter 2. Fault Detection and Isolation in
Multisensor Systems . . . . . . . . . . . . . . . . . . . . 27
2.1. Problem statement . . . . . . . . . . . . . . . . . . 28
2.1.1. Multisensor scheme. . . . . . . . . . . . . . . . 29
2.1.2. Fault scenarios . . . . . . . . . . . . . . . . . . . 32
2.2. Fault detection and isolation . . . . . . . . . . . . 35
2.2.1. Partition of the sensor indices . . . . . . . . . 36
2.2.2. Residual sets for FDI . . . . . . . . . . . . . . . 40
vi Set-theoreticFault-tolerantControl
2.3. Recovery mechanism . . . . . . . . . . . . . . . . . 45
2.3.1. Necessary and sufficient conditions . . . . . . 46
2.3.2. Construction of set SR . . . . . . . . . . . . . . 48
j
2.3.3. Inclusion time computation . . . . . . . . . . . 51
Chapter 3. Residual Generation and Reference
Governor Design . . . . . . . . . . . . . . . . . . . . . . . 55
3.1. Residual signals . . . . . . . . . . . . . . . . . . . . 56
3.1.1. Measurement equations residual . . . . . . . 57
3.1.2. Observer-based residual . . . . . . . . . . . . . 58
3.1.3. Receding observation window-based residual 62
3.2. Reference governor synthesis . . . . . . . . . . . . 68
Chapter 4. Reconfiguration of the Control
Mechanism for Fault-tolerant Control . . . . . . . . 73
4.1. Active FTC with fix gain feedback . . . . . . . . . 76
4.1.1. Fix gain feedback synthesis . . . . . . . . . . . 81
4.1.2. Reference governor synthesis . . . . . . . . . . 86
4.2. Active FTC with MPC control . . . . . . . . . . . . 89
4.2.1. A classic MPC design . . . . . . . . . . . . . . . 89
4.2.2. Toward a cooperative view of FTC-MPC . . . 93
4.3. Passive FTC control . . . . . . . . . . . . . . . . . . 96
4.3.1. Quadratic cost function . . . . . . . . . . . . . 98
4.3.2. Penalty function using the gauge function of
the healthy invariant set . . . . . . . . . . . . 99
Chapter 5. Related Problems and Applications . . 103
5.1. Set-theoretic issues . . . . . . . . . . . . . . . . . . 103
5.1.1. Over-approximation methods . . . . . . . . . . 104
5.1.2. Convergence time issues . . . . . . . . . . . . . 105
5.1.3. Cyclic invariance for dwell-time systems. . . 110
5.2. Illustrative examples . . . . . . . . . . . . . . . . . 113
5.2.1. Fault detection and isolation . . . . . . . . . . 114
5.2.2. Recovery mechanism . . . . . . . . . . . . . . . 115
TableofContents vii
5.2.3. Feasible reference generation. . . . . . . . . . 124
5.2.4. Fault-tolerant control results . . . . . . . . . . 126
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Preface
This books presents and expands upon previous results of
the first author’s PhD thesis conducted in SUPELEC, France,
under the supervision of the second author.
Overall, the book presents an insider view on an emerging
research subject: the set-theoretic fault detection and
fault-tolerant control design. Based on the authors’
experience, this book aims to open the field to a larger
audience. It has to be mentioned that the original research
results included in the book are developed from a series of
pioneering results obtained by Dr María Seron and Dr José
De Doná from Newcastle University (Australia) around
5 years ago. We are grateful for having the chance to
collaborate with them in the early days of these
developments and subsequently for the rich discussions and
continuous support that led to a fruitful collaboration. The
current work would not have been possible without using the
results they and their team had uncovered.
We consider the book to be only an introduction into a vast
domain that has the potential to provide novel and
interesting approaches to the well-known and studied theory
of fault-tolerant control. In particular, we believe that the
relationship between set-theoretic methods and fault-tolerant
x Set-theoreticFault-tolerantControl
control reveals new directions and adds a new dimension. By
translating all these fault detection, isolation and control
issues into a set-framework, we can (and have) shed light on
the geometrical interpretation of these types of schemes.
Introduction
In engineering applications, there are strict requirements
on the stability and performance criteria. In this context,
malfunctions in the actuator, sensors or other components of
the system might lead to unsatisfactory performance or even
instability. To address these issues, a fault-tolerant control
(FTC) mechanism needs to be implemented. The main
function of such a scheme will be to steer/maintain the
process to/in a safe state whenever undesirable events
(knownasfaults)occur.Formally,afaultinadynamicsystem
is a deviation of the dynamic processes structure or the
system parameters from the nominal characterization
[BLA 06]. Possible fault sources include permanent causes
(such as wear or damage of the components) or temporary
causes (due to a temporary change in the work conditions).
The cost of design, implementation and maintenance of an
FTC system may be significantly higher than that of a
traditional control system. Therefore, historically, using an
FTC system was justified if safety-critical applications were
dealt with [JIA 10]. Indeed, there are safety-critical systems
in which faults are not merely inconvenient, but can become
catastrophic. The best known (and deadliest) examples are in
the chemical industry and aeronautics. Well-known examples
of malfunctioning in aircraft incidents are discussed in
xii Set-theoreticFault-tolerantControl
[MON 83, MAC 03]. In the chemical/oil industry, the Bhopal
disaster [LAP 02] or the Piper Alpha explosion [RAM 94] are
to be remembered. We may equally mention more recent
disasters such as the BP Deepwater Horizon oil spill
[NOC 10], the nuclear meltdowns at the Chernobyl [STE 03]
and Fukushima plants [POU 06], although these examples
are to be analyzed from several points of view such as
“complexity of interconnected systems,” “external hazard
prevention” and/or “human-machine interaction.”
Certainly, the possibility of failure was exacerbated in
recent decades by continuous increases in complexity of
control schemes: variables, parameters and interconnections.
Furthermore, due to continuous miniaturizations and cost
reductions, the redundancy of components (e.g. sensors)
becomes affordable but subsequently increases the risks
(multiple cheap components may increase precision and
flexibilitybutalsoincreasetheriskoffailure).Notleast,with
the proliferation of computers and the Internet, network
control systems are spreading. With them, concepts such as
“package loss” and “communication delay” become common
issues and can be easily considered to be relevant in the
fault-tolerant perspective of the control design.
Such issues justify a renewed interest in FTC and, as a
result, a great deal of effort was put into developing
closed-loop systems which can tolerate faults, while
maintaining desirable performance and stability properties
[ZHA 08].
The goal of this book is to present a series of advances on
arelativelynewapproachinset-theoreticbasedfaultdetection
and recovery with their implication on FTC design.
Although sets were used in FTC via interval observers for
a decade or so, only recently, a strong characterization of the
sets with respect to the dynamics (namely the positive