Magdi S. Mahmoud

Yuanqing Xia

ANALYSIS AND SYNTHESIS OF FAULT-TOLERANT CONTROL SYSTEMS

ANALYSIS ANDSYNTHESIS OFFAULT-TOLERANTCONTROL SYSTEMS

ANALYSIS ANDSYNTHESIS OFFAULT-TOLERANTCONTROL SYSTEMS

Magdi S. MahmoudKing Fahd University of Petroleum and Minerals, Saudi Arabia

Yuanqing XiaBeijing Institute of Technology, China

This edition first published 2014C© 2014 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Mahmoud, Magdi S.Analysis and synthesis of fault-tolerant control systems / Magdi S. Mahmoud, Yuanqing Xia.

pages cmIncludes bibliographical references and index.ISBN 978-1-118-54133-3 (cloth)

1. Automatic control. 2. Fault tolerance (Engineering) 3. Control theory. I. Xia, Yuanqing. II. Title.III. Title: Analysis and synthesis of FTCS.

TJ213.M268428 2013629.8–dc23

2013023504

A catalogue record for this book is available from the British Library.

ISBN: 978-1-118-54133-3

Typeset in 10/12pt Times by Aptara Inc., New Delhi, India

1 2014

To my loving wife, SalwaTo the ‘M’ family:

Medhat, Monda, Mohamed,Menna, Malak, Mostafa

and Mohamed

MSM

To my honest and diligentwife, Wang Fangyu

To my lovely daughter,Xia Jingshu

YX

Contents

Preface xv

Acknowledgments xvii

1 Introduction 11.1 Overview 11.2 Basic Concepts of Faults 21.3 Classification of Fault Detection Methods 3

1.3.1 Hardware redundancy based fault detection 31.3.2 Plausibility test 31.3.3 Signal-based fault diagnosis 41.3.4 Model-based fault detection 5

1.4 Types of Fault-Tolerant Control System 81.5 Objectives and Structure of AFTCS 81.6 Classification of Reconfigurable Control Methods 10

1.6.1 Classification based on control algorithms 101.6.2 Classification based on field of application 11

1.7 Outline of the Book 111.7.1 Methodology 111.7.2 Chapter organization 12

1.8 Notes 13References 13

2 Fault Diagnosis and Detection 172.1 Introduction 172.2 Related Work 17

2.2.1 Model-based schemes 172.2.2 Model-free schemes 182.2.3 Probabilistic schemes 19

2.3 Integrated Approach 192.3.1 Improved multi-sensor data fusion 192.3.2 Unscented transformation 212.3.3 Unscented Kalman filter 22

viii Contents

2.3.4 Parameter estimation 232.3.5 Multi-sensor integration architectures 24

2.4 Robust Unscented Kalman Filter 262.4.1 Introduction 262.4.2 Problem formulation 282.4.3 Residual generation 292.4.4 Residual evaluation 29

2.5 Quadruple Tank System 302.5.1 Model of the QTS 312.5.2 Fault scenarios in QTS 322.5.3 Implementation structure of UKF 332.5.4 UKF with centralized multi-sensor data fusion 352.5.5 UKF with decentralized multi-sensor data fusion 352.5.6 Drift detection 35

2.6 Industrial Utility Boiler 382.6.1 Steam flow dynamics 382.6.2 Drum pressure dynamics 402.6.3 Drum level dynamics 402.6.4 Steam temperature 412.6.5 Fault model for the utility boiler 422.6.6 Fault scenarios in the utility boiler 432.6.7 UKF with centralized multi-sensor data fusion 432.6.8 UKF with decentralized multi-sensor data fusion 432.6.9 Drift detection 452.6.10 Remarks 45

2.7 Notes 46References 46

3 Robust Fault Detection 493.1 Distributed Fault Diagnosis 49

3.1.1 Introduction 493.1.2 System model 503.1.3 Distributed FDI architecture 553.1.4 Distributed fault detection method 553.1.5 Adaptive thresholds 573.1.6 Distributed fault isolation method 623.1.7 Adaptive thresholds for DFDI 643.1.8 Fault detectability condition 673.1.9 Fault isolability analysis 693.1.10 Stability and learning capability 71

3.2 Robust Fault Detection Filters 743.2.1 Reference model 743.2.2 Design of adaptive threshold 763.2.3 Iterative update of noise mean and covariance 773.2.4 Unscented transformation (UT) 793.2.5 Car-like mobile robot application 82

Contents ix

3.3 Simultaneous Fault Detection and Control 903.3.1 Introduction 933.3.2 System model 933.3.3 Problem formulation 953.3.4 Simultaneous fault detection and control problem 963.3.5 Two-tank system simulation 106

3.4 Data-Driven Fault Detection Design 1083.4.1 Introduction 1093.4.2 Problem formulation 1113.4.3 Selection of weighting matrix 1123.4.4 Design of FDF for time-delay system 1133.4.5 LMI design approach 1143.4.6 Four-tank system simulation 119

3.5 Robust Adaptive Fault Estimation 1223.5.1 Introduction 1243.5.2 Problem statement 1253.5.3 Adaptive observer 127

3.6 Notes 131References 131

4 Fault-Tolerant Control Systems 1354.1 Model Prediction-Based Design Approach 135

4.1.1 Introduction 1354.1.2 System description 1364.1.3 Discrete-time UKF 1384.1.4 Unscented Transformation (UT) 1414.1.5 Controller reconfiguration 1434.1.6 Model predictive control 1444.1.7 Interconnected CSTR units 1494.1.8 Four-tank system 1514.1.9 Simulation results 1524.1.10 Drift detection in the interconnected CSTRs 1524.1.11 Information fusion from UKF 1524.1.12 Drift detection in the four-tank system 156

4.2 Observer-Based Active Structures 1604.2.1 Problem statement 1604.2.2 A separation principle 1624.2.3 FDI residuals 1644.2.4 Control of integrity 1644.2.5 Overall stability 1654.2.6 Design outline 1654.2.7 Design of an active FTC scheme 1664.2.8 Extraction of FDI–FTC pairs 1664.2.9 Simulation 169

4.3 Notes 172References 172

x Contents

5 Fault-Tolerant Nonlinear Control Systems 1755.1 Comparison of Fault Detection Schemes 1755.2 Fault Detection in Nonlinear Systems 1765.3 Nonlinear Observer-Based Residual Generation Schemes 176

5.3.1 General considerations 1765.3.2 Extended Luenberger observer 1775.3.3 Nonlinear identity observer approach 1775.3.4 Unknown input observer approach 1785.3.5 The disturbance decoupling nonlinear observer approach 1785.3.6 Adaptive nonlinear observer approach 1785.3.7 High-gain observer approach 1785.3.8 Sliding-mode observer approach 1785.3.9 Geometric approach 1795.3.10 Game-theoretic approach 1795.3.11 Observers for Lipschitz nonlinear systems 1795.3.12 Lyapunov-reconstruction-based passive scheme 1805.3.13 Time-varying results 1855.3.14 Optimization-based active scheme 1875.3.15 Learning-based active scheme 1905.3.16 Adaptive backstepping-based active scheme 1915.3.17 Switched control-based active scheme 1935.3.18 Predictive control-based active scheme 195

5.4 Integrated Control Reconfiguration Scheme 1975.4.1 Introduction 1975.4.2 Basic features 1985.4.3 Nonlinear model of a pendulum on a cart 1995.4.4 NGA adaptive filter design 2015.4.5 Simulation results 2075.4.6 Performance evaluation 2095.4.7 Comparative studies 211

5.5 Notes 215References 215

6 Robust Fault Estimation 2196.1 Introduction 2196.2 System Description 2206.3 Multiconstrained Fault Estimation 221

6.3.1 Observer design 2216.3.2 Existence conditions 2266.3.3 Improved results 2286.3.4 Simulation results 232

6.4 Adaptive Fault Estimation 2356.4.1 Introduction 2366.4.2 Problem statement 2386.4.3 Robust adaptive estimation 2396.4.4 Internal stability analysis 240

Contents xi

6.4.5 Robust performance index 2416.4.6 Simulation 242

6.5 Adaptive Tracking Control Scheme 2446.5.1 Attitude dynamics 2446.5.2 Fault detection scheme 2486.5.3 Fault-tolerant tracking scheme 250

6.6 Notes 254References 254

7 Fault Detection of Networked Control Systems 2577.1 Introduction 2577.2 Problem Formulation 2587.3 Modified Residual Generator Scheme 259

7.3.1 Modified residual generator and dynamic analysis 2597.3.2 Residual evaluation 2617.3.3 Co-design of residual generator and evaluation 264

7.4 Quantized Fault-Tolerant Control 2677.4.1 Introduction 2677.4.2 Problem statement 2687.4.3 Quantized control design 2717.4.4 Simulation 276

7.5 Sliding-Mode Observer 2787.5.1 Introduction 2787.5.2 Dynamic model 2807.5.3 Limited state measurements 2867.5.4 Simulation results: full state measurements 2907.5.5 Simulation results: partial state measurements 293

7.6 Control of Linear Switched Systems 2947.6.1 Introduction 2957.6.2 Problem formulation 2957.6.3 Stability of a closed-loop system 2967.6.4 Simulation 300

7.7 Notes 303References 303

8 Industrial Fault-Tolerant Architectures 3078.1 Introduction 3078.2 System Architecture 3088.3 Architecture of a Fault-Tolerant Node 309

8.3.1 Basic architecture 3098.3.2 Architecture with improved reliability 3108.3.3 Symmetric node architecture 3108.3.4 Results 311

8.4 Recovery Points 3128.5 Networks 3148.6 System Fault Injection and Monitoring 315

xii Contents

8.6.1 Monitoring systems 3158.6.2 Design methodology 316

8.7 Notes 318References 319

9 Fault Estimation for Stochastic Systems 3219.1 Introduction 3219.2 Actuator Fault Diagnosis Design 3229.3 Fault-Tolerant Controller Design 3249.4 Extension to an Unknown Input Case 3259.5 Aircraft Application 326

9.5.1 Transforming the system into standard form 3279.5.2 Simulation results 329

9.6 Router Fault Accommodation in Real Time 3309.6.1 Canonical controller and achievable behavior 3339.6.2 Router modeling and desired behavior 3349.6.3 Description of fault behavior 3369.6.4 A least restrictive controller 338

9.7 Fault Detection for Markov Jump Systems 3389.7.1 Introduction 3399.7.2 Problem formulation 3409.7.3 H∞ bounded real lemmas 3439.7.4 H∞ FD filter design 3459.7.5 Simulation 347

9.8 Notes 352References 353

10 Applications 35510.1 Detection of Abrupt Changes in an Electrocardiogram 355

10.1.1 Introduction 35510.1.2 Modeling ECG signals with an AR model 35610.1.3 Linear models with additive abrupt changes 35810.1.4 Off-line detection of abrupt changes in ECG 36110.1.5 Online detection of abrupt changes in ECG 363

10.2 Detection of Abrupt Changes in the Frequency Domain 36510.2.1 Introduction 36510.2.2 Problem formulation 36610.2.3 Frequency domain ML ratio estimation 36810.2.4 Likelihood of the hypothesis of no abrupt change 37210.2.5 Effect of an abrupt change 37410.2.6 Simulation results 382

10.3 Electromechanical Positioning System 38310.3.1 Introduction 38310.3.2 Problem formulation 38510.3.3 Test bed 386

Contents xiii

10.4 Application to Fermentation Processes 38710.4.1 Nonlinear faulty dynamic system 38810.4.2 Residual characteristics 38910.4.3 The parameter filter 39910.4.4 Fault filter 40010.4.5 Fault isolation and identification 40110.4.6 Isolation speed 40110.4.7 Parameter partition 40210.4.8 Adaptive intervals 40210.4.9 Simulation studies 405

10.5 Flexible-Joint Robots 41510.5.1 Problem formulation 41510.5.2 Fault detection scheme 41710.5.3 Adaptive fault accommodation control 42010.5.4 Control with prescribed performance bounds 42210.5.5 Simulation results 425

10.6 Notes 429References 430

A Supplementary Information 435A.1 Notation 435

A.1.1 Kronecker products 436A.1.2 Some definitions 437A.1.3 Matrix lemmas 438

A.2 Results from Probability Theory 440A.2.1 Results-A 440A.2.2 Results-B 441A.2.3 Results-C 441A.2.4 Minimum mean square estimate 442

A.3 Stability Notions 444A.3.1 Practical stabilizability 444A.3.2 Razumikhin stability 445

A.4 Basic Inequalities 447A.4.1 Schur complements 447A.4.2 Bounding inequalities 449

A.5 Linear Matrix Inequalities 453A.5.1 Basics 453A.5.2 Some standard problems 454A.5.3 The S-procedure 455

A.6 Some Formulas on Matrix Inverses 456A.6.1 Inverse of block matrices 456A.6.2 Matrix inversion lemma 457References 458

Index 459