Solving Fault Diagnosis Problems: Linear Synthesis Techniques with Julia Code Examples (Studies in Systems, Decision and Control, 482)

✍ Scribed by Andreas Varga

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 462
• Edition: 2
• Category: Library

✦ Synopsis

The goal of this new edition is the same as for the first edition ”to address the fault detection and isolation topics from a computational perspective“, by covering the same important aspects, namely, (1) providing a completely general theoretical treatment of fault and model detection problems for linear time-invariant systems; (2) presenting the best suited numerical approaches to solve the specific computational problems; (3) providing supporting software to solve the analysis and filter synthesis problems. In this second edition, the changes in the theoretical presentation are minor and all known errors and typos have been corrected. The major difference to the first edition is in the underlying computational support, which is now based on software developed in a relatively new language called Julia. The presentation of synthesis procedures and examples is similar to the first edition, but it is now interlaced with Julia codes which can be used to reproduce all computational examples and figures presented in the book. An Appendix has been added to cover some basic issues related to using Julia and the new FaultDetectionTools and DescriptorSystems packages.

✦ Table of Contents

Preface to the Second Edition
Preface to the First Edition
Contents
Acronyms
Synthesis Procedures
Notations and Symbols
General Notations
Fault Diagnosis-Related Notations
Model Detection-Related Notations
List of Figures
List of Tables
Listings
Part I Basics of Fault Diagnosis
1 Introduction
1.1 Linear Synthesis Techniques for Fault Diagnosis
1.2 Outline of the Book
1.3 Notes and References
2 Modelling Systems with Faults
2.1 Types of Faults
2.2 Plant Models with Additive Faults
2.2.1 Models with Parametric Uncertainties
2.2.2 Models with Parametric Faults
2.2.3 Multiple Linear Models
2.3 Physical Fault Models
2.4 Notes and References
3 Fault Diagnosis
3.1 Basic Fault Monitoring Tasks
3.2 Residual Generation
3.3 Fault Detectability
3.4 Fault Isolability
3.5 Fault Detection and Isolation Problems
3.5.1 Exact Fault Detection Problem
3.5.2 Approximate Fault Detection Problem
3.5.3 Exact Fault Detection and Isolation Problem
3.5.4 Approximate Fault Detection and Isolation Problem
3.5.5 Exact Model-Matching Problem
3.5.6 Approximate Model-Matching Problem
3.6 Threshold Selection
3.7 Notes and References
4 Model Detection
4.1 Basic Model Detection Task
4.2 Residual Generation
4.3 Model Detectability
4.4 Model Detection Problems
4.4.1 Exact Model Detection Problem
4.4.2 Approximate Model Detection Problem
4.5 Threshold Selection
4.6 Notes and References
Part II Synthesis of Residual Generators
5 Synthesis of Fault Detection and Isolation Filters
5.1 Nullspace-Based Synthesis
5.2 Solving the Exact Fault Detection Problem
5.3 Solving the Approximate Fault Detection Problem
5.4 Solving the Exact Fault Detection and Isolation Problem
5.5 Solving the Approximate Fault Detection and Isolation Problem
5.6 Solving the Exact Model-Matching Problem
5.7 Solving the Approximate Model-Matching Problem
5.8 Notes and References
6 Synthesis of Model Detection Filters
6.1 Nullspace-Based Synthesis
6.2 Solving the Exact Model Detection Problem
6.3 Solving the Approximate Model Detection Problem
6.4 Notes and References
7 Computational Issues
7.1 Developing Satisfactory Numerical Algorithms
7.2 Modelling Issues
7.2.1 System Representations
7.2.2 Model Conditioning
7.3 Basic Procedural Framework
7.4 Nullspace-Based Reduction
7.5 Least-Order Synthesis
7.6 Coprime Factorization Techniques
7.7 Outer–Inner Factorizations
7.8 Spectral Factorizations
7.9 Linear Rational Equations
7.10 Solution of Least-Distance Problems
7.11 Notes and References
8 Case Studies
8.1 Monitoring Flight Actuator Faults
8.1.1 Nominal Synthesis
8.1.2 Robust Synthesis Using Local Measurements
8.1.3 Local Monitoring of Actuator Faults—Industrial Aspects
8.1.4 Linearized State-Space Models with Additive Actuator Faults
8.2 Monitoring Air Data Sensor Faults
8.2.1 Robust LTI FDI Filter Synthesis
8.2.2 Robust LPV FDI Filter Synthesis
8.2.3 Monitoring Air Data Sensor Faults—Industrial Aspects
8.2.4 Linearized State-Space Models with Additive Sensor Faults
8.3 Notes and References
Part III Background Material
9 System Theoretical Concepts
9.1 Rational Transfer Function Matrices
9.1.1 Transfer Functions
9.1.2 Transfer Function Matrices
9.1.3 Linear Dependence, Normal Rank and Minimal Basis
9.1.4 Poles and Zeros
9.1.5 Additive Decompositions
9.1.6 Fractional Factorizations
9.1.7 Norms
9.1.8 Inner–Outer and Spectral Factorizations
9.1.9 Linear Rational Matrix Equations
9.1.10 Approximate Model-Matching
9.2 Descriptor Systems
9.2.1 Descriptor Realizations of Rational Matrices
9.2.2 Poles, Zeros and Minimal Indices
9.2.3 Operations with Rational Matrices
9.2.4 Minimal Rational Nullspace Bases
9.2.5 Additive Decompositions
9.2.6 Coprime Factorizations
9.2.7 Norms
9.2.8 Inner–Outer and Spectral Factorizations
9.2.9 Linear Rational Equations
9.3 Notes and References
10 Computational Algorithms and Software
10.1 Matrix Decompositions and Condensed Forms
10.1.1 Singular Value Decomposition
10.1.2 QR Factorization
10.1.3 Real Schur Decomposition
10.1.4 Generalized Real Schur Decomposition
10.1.5 Controllability and Observability Staircase Forms
10.1.6 Kronecker-Like Forms
10.2 Solution of Matrix Equations
10.2.1 Linear Matrix Equations
10.2.2 Generalized Algebraic Riccati Equations
10.3 Algorithms for Descriptor Systems
10.3.1 Minimal Realization
10.3.2 Minimal Proper Rational Nullspace Bases
10.3.3 Poles and Zeros Computation
10.3.4 Additive Decompositions
10.3.5 Coprime Factorizations
10.3.6 Inner-Outer Factorization
10.3.7 Linear Rational Matrix Equations
10.4 Special Algorithms
10.4.1 Special Controllability Staircase Form Algorithm
10.4.2 Order Reduction Using Minimum Dynamic Covers of Type I
10.4.3 Order Reduction Using Minimum Dynamic Covers of Type II
10.4.4 Minimal Realization Using Balancing Techniques
10.4.5 Solution of Nehari Problems
10.5 Software Tools
10.5.1 MATLAB Tools
10.5.2 Julia Tools
10.6 Notes and References
Appendix A Introduction to Julia Language and Packages
A.1 Julia Basics
A.2 DescriptorSystems Basics
A.2.1 Building Models
A.2.2 Operations with Rational Transfer Functions
A.2.3 System Analysis
A.2.4 Conversions between Model Representations
A.2.5 Operations with Rational Matrices
A.2.6 Factorizations of Rational Matrices
A.2.7 Solving Approximate Model-Matching Problems
A.3 FaultDetectionTools Basics
A.3.1 Solving Fault Detection Problems
A.3.2 Solving Model Detection Problems
A.4 Notes and References
References
Index