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2017 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Solving Fault Diagnosis Problems

Linear Synthesis Techniques

verfasst von: Andreas Varga

Verlag: Springer International Publishing

Buchreihe : Studies in Systems, Decision and Control

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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SUCHEN

Über dieses Buch

This book addresses fault detection and isolation topics from a computational perspective. Unlike most existing literature, it bridges the gap between the existing well-developed theoretical results and the realm of reliable computational synthesis procedures.

The model-based approach to fault detection and diagnosis has been the subject of ongoing research for the past few decades. While the theoretical aspects of fault diagnosis on the basis of linear models are well understood, most of the computational methods proposed for the synthesis of fault detection and isolation filters are not satisfactory from a numerical standpoint. Several features make this book unique in the fault detection literature:

Solution of standard synthesis problems in the most general setting, for both continuous- and discrete-time systems, regardless of whether they are proper or not; consequently, the proposed synthesis procedures can solve a specific problem whenever a solution exists

Emphasis on the best numerical algorithms to solve the synthesis problems for linear systems in generalized state-space form (also known as descriptor systems)

Development of general synthesis procedures relying on new computational paradigms, such as factorization-based design based on filter updating techniques and nullspace-based synthesis

Availability of a comprehensive set of free accompanying software tools for descriptor systems, which allows readers to easily implement all synthesis procedures presented in the book and ensures that all results are reproducible

This book is primarily intended for researchers and advanced graduate students in the areas of fault diagnosis and fault-tolerant control. It will also appeal to mathematicians with an interest in control-oriented numerics.

Inhaltsverzeichnis

Frontmatter
11. Correction to: Modelling Systems with Faults
Andreas Varga

Basics of Fault Diagnosis

Frontmatter
Chapter 1. Introduction
Abstract
This introductory chapter presents a short overview of the topics covered in the book and the outlines of the main parts: Part I—Basics of Fault Diagnosis, Part II—Synthesis of Residual Generators and Part III—Background Material.
Andreas Varga
2. Modelling Systems with Faults
Abstract
In this chapter, the main types of faults are first reviewed and linear time-invariant plant models with additive faults are introduced. These models represent the basis of the synthesis approaches of fault detection filters presented in this book. Models with fictive noise inputs can be used to account for the effects of parametric variations. Two approaches are presented to arrive at such models starting from linear parameter-varying models and multiple linear time-invariant models. Physical fault modelling leads naturally to multiple-model representations, which form the basis of the synthesis methods of model detection filters.
Andreas Varga
Chapter 3. Fault Diagnosis
Abstract
In this chapter we describe first the basic fault monitoring tasks, such as fault detection, fault isolation, fault estimation and fault identification. The concepts of fault detectability and fault isolability are then introduced and characterized. Six “canonical” fault detection problems are formulated for the class of linear time-invariant systems with additive faults. The formulation of the exact and approximate synthesis problems are independent of any possible solution method and allow the derivation of general solvability conditions in terms of ranks of certain transfer function matrices. An important aspect to emphasize is that the formulations of approximate problems include, as particular cases, the formulations of exact problems. This chapter is concluded with a discussion of performance requirements for fault diagnosis systems and the selection of thresholds to be used for decision-making.
Andreas Varga
Chapter 4. Model Detection
Abstract
In this chapter, we first formulate the basic model detection task consisting of the identification of that particular model from a collection of linear time-invariant models, which best matches the current plant behaviour. Then, the concept of model detectability is introduced and characterized. Exact and approximate model detection problems are formulated and solvability conditions are derived. These problems target the synthesis of a bank of model detection filters which generate a structured set of residuals allowing the discrimination of models in the case of absence or presence of noise inputs, respectively. The discussion of specific performance requirements for model detection and the selection of thresholds to be used for decision-making conclude the chapter.
Andreas Varga

Synthesis of Residual Generators

Frontmatter
Chapter 5. Synthesis of Fault Detection and Isolation Filters
Abstract
This chapter presents general synthesis procedures of fault detection filters, which solve the fault detection problems formulated in Chap. 3. Two computational paradigms are instrumental in developing generally applicable, numerically reliable and computationally efficient synthesis methods. The first paradigm is the use of factorization-based synthesis methods, which leads to the so-called integrated computational algorithms, with strongly coupled successive computational steps. The second paradigm is the use of the nullspace method as a first synthesis step to reduce all synthesis problems to simpler problems, which allow to easily check the solvability conditions and address least-order synthesis problems. The synthesis procedures are described in terms of input–output models, which allow simpler conceptual presentations. The numerical aspects of equivalent state-space representation based synthesis algorithms are discussed in Chap. 7.
Andreas Varga
Chapter 6. Synthesis of Model Detection Filters
Abstract
This chapter presents general synthesis procedures of residual generators which solve the model detection problems formulated in Chap. 4. Similarly to Chap. 3, the synthesis procedures are described in terms of input–output models. The numerical aspects of equivalent state-space representation based synthesis algorithms are essentially the same as for the synthesis algorithms of fault detection and isolation filters, and the discussion of related computational techniques is covered in Chap. 7.
Andreas Varga
Chapter 7. Computational Issues
Abstract
This chapter discusses the main computational issues underlying the synthesis procedures of fault detection filters presented in Chap. 5. The synthesis procedures of model detection filters, presented in Chap. 6, employ similar computational techniques, and, therefore, are entirely covered in this chapter. While all synthesis procedures have been developed in terms of input–output system representations, the underlying numerical algorithms exclusively rely on state-space representation-based computational methods. The discussion of the computational issues primarily focuses on exploiting all structural features present in the computational steps of the synthesis procedures and developing explicit updating formulas for the state-space representations of partial filter syntheses. All discussed computational procedures rely on the numerical algorithms described in details in Chap. 10, which fulfil standard quality requirements for satisfactory algorithms, such as generality, numerical reliability and computational efficiency.
Andreas Varga
Chapter 8. Case Studies
Abstract
This chapter illustrates the formulation of typical fault monitoring problems in complex technological systems and the application of the linear synthesis techniques, described in this book, to address the challenges of practical applications. Two case studies, both related to flight control applications, are considered. The chosen examples address the monitoring of flight actuator faults and air data sensor faults, in the presence of uncertainties in the aircraft mass.
Andreas Varga

Background Material

Frontmatter
Chapter 9. System Theoretical Concepts
Abstract
Rational transfer function matrices and linear time-invariant descriptor systems are the two main system representations employed in this book. The purpose of this chapter is to provide a concise statement of the main results on rational matrices and descriptor systems to facilitate the understanding of the mathematical terminology used throughout the book. The treatment in depth of most of concepts was not possible in the restricted size of this book. Therefore, at the end of this chapter, we indicate the main references covering the presented results and make suggestions for supplementary readings.
Andreas Varga
Chapter 10. Computational Algorithms and Software

This appendix is primarily intended for numerical experts having interests in control-related numerical techniques. The main algorithms for descriptor systems, which underlie the computational methods used in the synthesis procedures presented in this book, are described in details. The accompanying software tools implement the algorithms presented in this appendix and can be employed to reproduce all computational results presented in this book.

Andreas Varga
Backmatter
Metadaten
Titel
Solving Fault Diagnosis Problems
verfasst von
Andreas Varga
Copyright-Jahr
2017
Electronic ISBN
978-3-319-51559-5
Print ISBN
978-3-319-51558-8
DOI
https://doi.org/10.1007/978-3-319-51559-5

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