Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear Systems: Analytical and Soft Computing Approaches

239 Pages·2014·8.09 MB·English

by  Marcin Witczak (auth.)

Lecture Notes in Electrical Engineering 266
Marcin Witczak
Fault Diagnosis
and Fault-Tolerant
Control Strategies
for Non-Linear
Systems
Analytical and Soft Computing
Approaches
Lecture Notes in Electrical Engineering
Volume 266
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Marcin Witczak
Fault Diagnosis and
Fault-Tolerant Control
Strategies for Non-Linear
Systems
Analytical and Soft Computing Approaches
123
Marcin Witczak
Instituteof ControlandComputation
Engineering
Universityof Zielona Góra
Zielona Góra
Poland
ISSN 1876-1100 ISSN 1876-1119 (electronic)
ISBN 978-3-319-03013-5 ISBN 978-3-319-03014-2 (eBook)
DOI 10.1007/978-3-319-03014-2
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To my beloved and wonderful wife Anna
Preface
A permanent increase in the complexity, efficiency and reliability of modern
industrial systems necessitates a continuous development in control and fault
diagnosis. A moderate combination of these two paradigms is intensively studied
under the name offault-tolerant control. This real world’s development pressure
hastransformedfaultdiagnosisandfault-tolerantcontrol,initiallyperceivedasthe
art of designing a satisfactorily safe system, into the modern science that it is
today.
Indeed,theclassicwayoffaultdiagnosisboilsdowntocontrollingthelimitsof
single variables and then using the resulting knowledge for fault alarm purposes.
Apartfromthesimplicityofsuchanapproach,theobservedincreasingcomplexity
ofmodernsystemsnecessitatesthedevelopmentofnewfaultdiagnosistechniques.
On the other hand, the resulting fault diagnosis system should be suitably inte-
grated with the existing control system in order to prevent the development of
faults into failures, perceived as a complete breakdown of the system being con-
trolled and diagnosed.
Suchadevelopmentcanonlyberealisedbytakingintoaccounttheinformation
hidden in all measurements. One way to tackle such a challenging problem is to
use the so-called model-based approach. Indeed, the application of an adequate
modelofthesystembeingsupervisedisveryprofitablewithrespecttogainingthe
knowledge regarding its behaviour. A further and deeper understanding of the
current system behaviour can be achieved by implementing parameter and state
estimation strategies. The obtained estimates can then be used for supporting
diagnosticdecisionsandincreasingthecontrolquality,whiletheresultingmodels
(along with the knowledge about their uncertainty) can be used for designing
suitable control strategies.
Although the majority of industrial systems are nonlinear in their nature, the
most common approach to settle fault diagnosis and fault-tolerant control prob-
lemsistousewell-knowntoolsforlinearsystems,whicharewidelydescribedand
well documented in many excellent monographs and books. On the other hand,
publications on integrated fault diagnosis and fault-tolerant control for nonlinear
systems are scattered over many papers and a number of book chapters.
Taking into account the above-mentioned conditions, this book presents
selected Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear
Systems in a unified framework. In particular, starting from advanced state
vii
viii Preface
estimationstrategiesuptomodernsoftcomputing,thediscrete-timedescriptionof
thesystemisemployed.Suchachoiceisdictatedbythefactthatthediscrete-time
descriptioniseasierandmorenaturaltoimplementonmoderncomputersthanits
continuous-timecounterpart.Thisisespeciallyimportantforpracticingengineers,
who are hardly ever fluent in complex mathematical descriptions.
The book results from my research in the area of fault diagnosis and fault-
tolerant control for nonlinear systems that has been conducted since 1998. It is
organised as follows. Part I presents original research results regarding state
estimation and neural networks for Robust Fault Diagnosis. Part II is devoted to
the presentation of integrated fault diagnosis and fault-tolerant systems. It starts
with a general fault-tolerant control framework, which is then extended by
introducing robustness with respect to various uncertainties. Finally, it is shown
how to implement the proposed framework for fuzzy systems described by the
well-known Takagi–Sugeno models.
This book is primarily a research monograph which presents, in a unified
framework, some recent results on fault diagnosis and fault-tolerant control of
nonlinear systems. It is intended for researchers, engineers and advanced post-
graduate students in control and electrical engineering, computer science, as well
as mechanical and chemical engineering.
Some of the research results presented in this book were developed with
the kind support of the National Science Centre in Poland under the grant
No. NN514678440 on Predictive fault-tolerant control for nonlinear systems.
Iwouldliketoexpressmysinceregratitudetomyfamilyfortheirsupportand
patience.IamalsogratefultoProf.JózefKorbiczforsuggestingtheproblem,and
forhiscontinuoushelpandsupport.Iwouldliketoexpressmythankstomyfriends
Prof. Vicenç Puig (Universidad Politécnica de Cataluña) and Prof. Christophe
Aubrun (Université de Lorraine) for the long lasting and successful cooperation.
IalsowouldliketoexpressmyspecialthankstoDr.LukaszDziekanforhishelpin
preparing some of the computer programmes, laboratory experiments and
simulations ofChap. 6
Zielona Góra, August 2013 Marcin Witczak
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introductory Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Part I Robust Fault Diagnosis
2 Unknown Input Observers and Filters . . . . . . . . . . . . . . . . . . . . . 19
2.1 Unknown Input Decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Preventing Fault Decoupling. . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 First- and Second-order Extended Unknown Input Observers . . . 25
2.3.1 Convergence Analysis. . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.2 Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Unscented Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 Unscented Transform. . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.2 Principle of the UKF-Based UIF. . . . . . . . . . . . . . . . . . 34
2.5 Determination of an Unknown Input Distribution Matrix . . . . . . 35
2.6 Design of the UIF with Varying Unknown Input
Distribution Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.7 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.7.1 Estimation of E for an Induction Motor. . . . . . . . . . . . . 43
2.7.2 Varying E Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.7.3 Fault Detection and Isolation of a Two-Tank System . . . 47
2.7.4 First- Versus Second-order EUIO . . . . . . . . . . . . . . . . . 53
2.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3 Neural Network-Based Approaches to Fault Diagnosis . . . . . . . . . 57
3.1 Robust Fault Detection with the Multi-Layer Perceptron . . . . . . 58
3.1.1 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.2 Algorithms and Properties of D-OED
for Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.3 Industrial Application . . . . . . . . . . . . . . . . . . . . . . . . . 78
ix
x Contents
3.2 GMDH Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.2.1 Model Uncertainty in the GMDH Neural Network . . . . . 84
3.2.2 Bounded-Error Approach. . . . . . . . . . . . . . . . . . . . . . . 86
3.2.3 Synthesis of the GMDH Neural Network
Via the BEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.2.4 Robust Fault Detection with the GMDH Model . . . . . . . 93
3.2.5 Alternative Robust Fault Detection Procedure:
A Backward Detection Test . . . . . . . . . . . . . . . . . . . . . 95
3.2.6 Industrial Application . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Part II Integrated Fault Diagnosis and Control
4 Integrated Fault Diagnosis and Control: Principles
and Design Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.1 FTC Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.1.1 Fault Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1.2 Stabilisation Problem. . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.1.3 Observer Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.1.4 Integrated Design Procedure. . . . . . . . . . . . . . . . . . . . . 123
4.2 Extension to Non-Linear Systems . . . . . . . . . . . . . . . . . . . . . . 125
4.3 Constrained State Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.3.1 Complete Design Procedure. . . . . . . . . . . . . . . . . . . . . 131
4.4 Application Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.4.1 Description of the Twin-Rotor MIMO System . . . . . . . . 132
4.4.2 Non-Linear Reference Model of Twin-Rotor
MIMO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.4.3 Fault Scenario 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.4.4 Fault Scenario 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.4.5 Fault Scenario 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5 Robust H -Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
1
5.1 Towards Robust Fault-Tolerant Control . . . . . . . . . . . . . . . . . . 143
5.1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.1.2 Fault Estimation Approach. . . . . . . . . . . . . . . . . . . . . . 145
5.1.3 Integrated FTC Design . . . . . . . . . . . . . . . . . . . . . . . . 149
5.1.4 Illustrative Example: Fault Estimation. . . . . . . . . . . . . . 151
5.2 Complete Robust Design of Fault-Tolerant Control. . . . . . . . . . 153
5.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.2.2 Fault Estimation Strategy. . . . . . . . . . . . . . . . . . . . . . . 154