Metaheuristic Optimization for the Design of Automatic Control Laws

The classic approach in Automatic Control relies on the use of simplified models of the systems and reformulations of the specifications. In this framework, the control law can be computed using deterministic algorithms. However, this approach fails when the system is too complex for its model to be sufficiently simplified, when the designer has many constraints to take into account, or when the goal is not only to design a control but also to optimize it. This book presents a new trend in Automatic Control with the use of metaheuristic algorithms. These kinds of algorithm can optimize any criterion and constraint, and therefore do not need such simplifications and reformulations. The first chapter outlines the author’s main motivations for the approach which he proposes, and presents the advantages which it offers. In Chapter 2, he deals with the problem of system identification. The third and fourth chapters are the core of the book where the design and optimization of control law, using the metaheuristic method (particle swarm optimization), is given. The proposed approach is presented along with real-life experiments, proving the efficiency of the methodology. Finally, in Chapter 5, the author proposes solving the problem of predictive control of hybrid systems. Contents 1. Introduction and Motivations. 2. Symbolic Regression. 3. PID Design Using Particle Swarm Optimization. 4. Tuning and Optimization of H-infinity Control Laws. 5. Predictive Control of Hybrid Systems. About the Authors Guillaume Sandou is Professor in the Automatic Department of Supélec, in Gif Sur Yvette, France. He has had 12 books, 8 journal papers and 1 patent published, and has written papers for 32 international conferences.His main research interests include modeling, optimization and control of industrial systems; optimization and metaheuristics for Automatic Control; and constrained control.

Table of Contents:
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

About the Author :
Guillaume SANDOU is Associate Professor, SUPELEC Systems Sciences (E3S), Control Department, Gif sur Yvette, France.