9783540003182

Modern technological systems rely on sophisticated control functions to meet increased performance requirements. For such systems, Fault Tolerant Control Systems (FTCS) need to be developed. Active FTCS are dependent on a Fault Detection and Identification (FDI) process to monitor system performance and to detect and isolate faults in the systems. The main objective of this book is to study and to validate some important issues in real-time Active FTCS by means of theoretical analysis and simulation. Several models are presented to achieve this objective, taking into consideration practical aspects of the system to be controlled, performance deterioration in FDI algorithms, and limitations in reconfigurable control laws.

Dedication

v

Preface

vii

Table of Contents

xiii

List of Tables

xvii

List of Figures

xix

Nomenclature

xxi

Introduction

1

(10)

Fault Tolerant Control System (FTCS)

1

(3)

Definition of FTCS

1

(1)

Classification of FTCS

2

(2)

Background and Motivations

4

(2)

Advances in Fault Tolerant Control Systems

6

(3)

Scope of the Book

9

(2)

Active Fault Tolerant Control in Prospective

11

(11)

Introduction

11

(1)

Faults in Dynamic Systems

11

(2)

Fault Detection and Identification (FDI)

13

(5)

Approaches to FDI

13

(3)

Diagnostic procedure of FDI

16

(1)

Performance measures in FDI

17

(1)

Control System Reconfiguration

18

(2)

Applications of FTCS

20

(2)

Stochastic Stability

22

(8)

Introduction

22

(1)

Definitions of Stochastic Stability

23

(3)

Conditions for Stochastic Stability

26

(4)

FTCS with Markovian Parameters (FTCSMP)

30

(15)

Mathematical Models

31

(4)

Dynamical system models

31

(2)

Failure and FDI processes

33

(2)

Calculation of Transition Rates

35

(2)

The Uniqueness of FTCSMP Model

37

(1)

Errors in detection and identification

37

(1)

Detection delays and false alarms

37

(1)

Stochastic Stability of FTCSMP

38

(7)

Supermartingales

39

(1)

Stochastic Lyapunov functions

39

(1)

The weak infinitesimal operator

40

(1)

Dynkin's formula

41

(2)

Conditions for stochastic stability

43

(2)

Stochastic Stability of FTCSMP

45

(38)

Introduction

45

(1)

Stochastic Stability of FTCSMP in the Presence of Noise

46

(21)

Dynamical model of FTCSMP in the presence of noise

47

(2)

Sufficient conditions for stochastic stability

49

(4)

Necessary conditions for stochastic stability

53

(3)

A necessary and sufficient condition for exponential stability

56

(5)

A numerical example

61

(6)

Stability of FTCSMP with Multiple Failure Processes

67

(15)

Dynamical model of FTCSMP with multiple failures

68

(2)

Transition probabilities for failure and FDI processes

70

(1)

Stochastic stability

70

(2)

A necessary and sufficient condition for exponential stability

72

(4)

Remarks and special cases

76

(3)

A numerical example

79

(3)

Chapter Summary

82

(1)

Performance and Stability of FTCSMP Under Imperfect FDI

83

(20)

Introduction

83

(1)

Effects of Detection Delays on the Stability of FTCSMP

84

(8)

Dynamical model of FTCSMP with detection delays

85

(1)

Interpretation of detection delays in FDI process

85

(1)

Exponentially distributed detection delays

86

(1)

γ distributed detection delays

86

(2)

A necessary and sufficient condition for stochastic stability

88

(1)

A numerical example

89

(3)

Effects of Detection Errors on the Stability of FTCSMP

92

(9)

A new FTCSMP model

93

(1)

The role of FDI in fault tolerant control law design

94

(3)

A necessary and sufficient condition for stochastic stability

97

(1)

A numerical example

97

(4)

Chapter Summary

101

(2)

FTCSMP with Actuator Saturation and Parameter Uncertainties

103

(45)

Introduction

103

(1)

Stability of FTCSMP Driven by Actuators with Saturation

104

(20)

Dynamical model of FTCSMP with actuator saturation limit

105

(1)

Actuators with saturation limits

105

(1)

Exponential stability of FTCSSA

106

(3)

A sufficient condition for exponential stability of FTCSSA

109

(4)

Remarks and special cases

113

(6)

A numerical example

119

(5)

Stabilization of FTCSMP with Parameter Uncertainties

124

(22)

Dynamical model of FTCSMP with parameter uncertinities

126

(2)

The model of parameter uncertainties

128

(1)

Stabilization of uncertain FTCSMP

129

(9)

Special cases

138

(3)

A numerical example

141

(5)

Chapter Summary

146

(2)

Synthesis of Fault Tolerant Control Laws

148

(36)

Introduction

148

(2)

Design Approaches to Fault Tolerant Control Laws

150

(19)

The problem statement

150

(3)

A control law on finite time horizon

153

(5)

Control laws on infinite time horizons

158

(5)

A numerical example

163

(6)

A Fault Tolerant Control Law in Noisy Environment

169

(12)

The problem statement

169

(1)

A control law on finite time horizon

170

(3)

A control law on infinite time horizon

173

(7)

A numerical example

180

(1)

Chapter Summary

181

(3)

Epilogue

184

(4)

Summary

184

(4)

Bibliography

188

(19)

Index

207

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Active Fault Tolerant Control Systems

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