Solving Fault Diagnosis Problems (eBook)

Preface 7
Contents 11
Acronyms 15
Synthesis Procedures 16
Notations and Symbols 17
List of Figures 22
List of Tables 23
Listings 24
Part I Basics of Fault Diagnosis 26
1 Introduction 27
1.1 Linear Synthesis Techniques for Fault Diagnosis 27
1.2 Outline of the Book 29
1.3 Notes and References 30
2 Modelling Systems with Faults 31
2.1 Types of Faults 32
2.2 Plant Models with Additive Faults 33
2.2.1 Models with Parametric Uncertainties 36
2.2.2 Models with Parametric Faults 40
2.2.3 Multiple Linear Models 43
2.3 Physical Fault Models 46
2.4 Notes and References 48
3 Fault Diagnosis 50
3.1 Basic Fault Monitoring Tasks 50
3.2 Residual Generation 53
3.3 Fault Detectability 54
3.4 Fault Isolability 61
3.5 Fault Detection and Isolation Problems 66
3.5.1 Exact Fault Detection Problem 67
3.5.2 Approximate Fault Detection Problem 68
3.5.3 Exact Fault Detection and Isolation Problem 69
3.5.4 Approximate Fault Detection and Isolation Problem 70
3.5.5 Exact Model-Matching Problem 72
3.5.6 Approximate Model-Matching Problem 74
3.6 Threshold Selection 74
3.7 Notes and References 78
4 Model Detection 80
4.1 Basic Model Detection Task 80
4.2 Residual Generation 82
4.3 Model Detectability 83
4.4 Model Detection Problems 86
4.4.1 Exact Model Detection Problem 86
4.4.2 Approximate Model Detection Problem 87
4.5 Threshold Selection 87
4.6 Notes and References 89
Part II Synthesis of Residual Generators 91
5 Synthesis of Fault Detection and Isolation Filters 93
5.1 Nullspace-Based Synthesis 94
5.2 Solving the Exact Fault Detection Problem 98
5.3 Solving the Approximate Fault Detection Problem 104
5.4 Solving the Exact Fault Detection and Isolation Problem 115
5.5 Solving the Approximate Fault Detection and Isolation Problem 123
5.6 Solving the Exact Model-Matching Problem 129
5.7 Solving the Approximate Model-Matching Problem 135
5.8 Notes and References 144
6 Synthesis of Model Detection Filters 148
6.1 Nullspace-Based Synthesis 148
6.2 Solving the Exact Model Detection Problem 150
6.3 Solving the Approximate Model Detection Problem 157
6.4 Notes and References 166
7 Computational Issues 168
7.1 Developing Satisfactory Numerical Algorithms 169
7.2 Modelling Issues 171
7.2.1 System Representations 172
7.2.2 Model Conditioning 175
7.3 Basic Procedural Framework 180
7.4 Nullspace-Based Reduction 183
7.5 Least-order Synthesis 192
7.6 Coprime Factorization Techniques 200
7.7 Outer--Inner Factorizations 203
7.8 Spectral Factorizations 208
7.9 Linear Rational Equations 210
7.10 Solution of Least Distance Problems 212
7.11 Notes and References 218
8 Case Studies 221
8.1 Monitoring Flight Actuator Faults 222
8.1.1 Nominal Synthesis 223
8.1.2 Robust Synthesis Using Local Measurements 232
8.1.3 Local Monitoring of Actuator Faults---Industrial Aspects 236
8.1.4 Linearized State-Space Models with Additive Actuator Faults 241
8.2 Monitoring Air Data Sensor Faults 246
8.2.1 Robust LTI FDI Filter Synthesis 247
8.2.2 Robust LPV FDI Filter Synthesis 256
8.2.3 Monitoring Air Data Sensor Faults---Industrial Aspects 262
8.2.4 Linearized State-Space Models with Additive Sensor Faults 263
8.3 Notes and References 265
Part III Background Material 267
9 System Theoretical Concepts 268
9.1 Rational Transfer Function Matrices 268
9.1.1 Transfer Functions 269
9.1.2 Transfer Function Matrices 270
9.1.3 Linear Dependence, Normal Rank, Minimal Basis 271
9.1.4 Poles and Zeros 274
9.1.5 Additive Decompositions 277
9.1.6 Fractional Factorizations 278
9.1.7 Norms 281
9.1.8 Inner--Outer and Spectral Factorizations 282
9.1.9 Linear Rational Matrix Equations 284
9.1.10 Approximate Model-Matching 285
9.2 Descriptor Systems 288
9.2.1 Descriptor Realizations of Rational Matrices 289
9.2.2 Poles, Zeros and Minimal Indices 290
9.2.3 Operations with Rational Matrices 296
9.2.4 Minimal Rational Nullspace Bases 299
9.2.5 Additive Decompositions 302
9.2.6 Coprime Factorizations 302
9.2.7 Norms 306
9.2.8 Inner--Outer and Spectral Factorizations 308
9.2.9 Linear Rational Equations 311
9.3 Notes and References 316
10 Computational Algorithms and Software 317
10.1 Matrix Decompositions and Condensed Forms 317
10.1.1 Singular Value Decomposition 318
10.1.2 QR Decomposition 320
10.1.3 Real Schur Decomposition 323
10.1.4 Generalized Real Schur Decomposition 325
10.1.5 Controllability and Observability Staircase Forms 329
10.1.6 Kronecker-Like Forms 333
10.2 Solution of Matrix Equations 339
10.2.1 Linear Matrix Equations 339
10.2.2 Generalized Algebraic Riccati Equations 341
10.3 Algorithms for Descriptor Systems 343
10.3.1 Minimal Realization 343
10.3.2 Minimal Proper Rational Nullspace Bases 347
10.3.3 Poles and Zeros Computation 355
10.3.4 Additive Decompositions 355
10.3.5 Coprime Factorizations 357
10.3.6 Inner--Outer Factorization 364
10.3.7 Linear Rational Matrix Equations 369
10.4 Special Algorithms 375
10.4.1 Special Controllability Staircase Form Algorithm 375
10.4.2 Order Reduction Using Minimum Dynamic Covers of Type I 378
10.4.3 Order Reduction Using Minimum Dynamic Covers of Type II 384
10.4.4 Minimal Realization Using Balancing Techniques 389
10.4.5 Solution of Nehari Problems 390
10.5 Numerical Software 392
10.6 Notes and References 395
References 398
Index 406