[eBook Code] Metaheuristic Optimization for the Design of Automatic Control Laws (eBook Code, 1st)

PREFACE ix

CHAPTER 1. INTRODUCTION AND MOTIVATIONS 1

1.1. Introduction: automatic control and optimization 1

1.2. Motivations to use metaheuristic algorithms 3

1.3. Organization of the book 5

CHAPTER 2. SYMBOLIC REGRESSION 7

2.1. Identification problematic and brief state of the art 7

2.2. Problem statement and modeling 10

2.2.1. Problem statement 10

2.2.2. Problem modeling 10

2.3. Ant colony optimization 13

2.3.1. Ant colony social behavior 13

2.3.2. Ant colony optimization 14

2.3.3. Ant colony for the identification of nonlinear functions with unknown structure 16

2.4. Numerical results 18

2.4.1. Parameter settings 18

2.4.2. Experimental results 19

2.5. Discussion 22

2.5.1. Considering real variables 22

2.5.2. Local minima 22

2.5.3. Identification of nonlinear dynamical systems 23

2.6. A note on genetic algorithms for symbolic regression 23

2.7. Conclusions 25

CHAPTER 3. PID DESIGN USING PARTICLE SWARM OPTIMIZATION 27

3.1. Introduction 27

3.2. Controller tuning: a hard optimization problem 29

3.2.1. Problem framework 29

3.2.2. Expressions of time domain specifications 30

3.2.3. Expressions of frequency domain specifications 32

3.2.4. Analysis of the optimization problem 35

3.3. Particle swarm optimization implementation 35

3.4. PID tuning optimization 37

3.4.1. Case study: magnetic levitation 37

3.4.2. Time response optimization 39

3.4.3. Time response optimization with penalization on the control input 41

3.4.4. Time response optimization with penalization on the control input and constraint on module margin 42

3.5. PID multiobjective optimization 43

3.6. Conclusions 48

CHAPTER 4. TUNING AND OPTIMIZATION OF H∞ CONTROL LAWS  51

4.1. Introduction 51

4.2. H∞ synthesis 54

4.2.1. Full-order H∞ synthesis 54

4.2.2. Tuning the filters as an optimization problem 57

4.2.3. Reduced-order H∞ synthesis 58

4.3. Application to the control of a pendulum in the cart 60

4.3.1. Case study 60

4.3.2. H∞ synthesis schemes 64

4.3.3. Optimization of the parameters of the filters 66

4.3.4. Reduced-order H∞ synthesis: one DOF case 70

4.3.5. Reduced-order H∞ synthesis: three DOF case 71

4.3.6. Conclusions 76

4.4. Static output feedback design 77

4.5. Industrial examples 82

4.5.1. Mold level control in continuous casting 83

4.5.2. Linear parameter varying control of a missile 83

4.5.3. Internal combustion engine air path control 86

4.5.4. Inertial line-of-sight stabilization 86

4.6. Conclusions 87

CHAPTER 5. PREDICTIVE CONTROL OF HYBRID SYSTEMS 89

5.1. Problematic 89

5.2. Predictive control of power systems 92

5.2.1. Open-loop control and unit commitment 92

5.2.2. Closed-loop control 94

5.3. Optimization procedure 96

5.3.1. Classical optimization methods for unit commitment 96

5.3.2. General synopsis of the optimization procedure 97

5.3.3. Ant colony optimization for the unit commitment 98

5.3.4. Computation of real variables 100

5.3.5. Feasibility criterion 101

5.3.6. Knowledge-based genetic algorithm 102

5.4. Simulation results 107

5.4.1. Real-time updating of produced powers 107

5.4.2. Case study 107

5.5. Conclusions and discussions 108

CONCLUSION 111

BIBLIOGRAPHY 115

INDEX 127