Robust Control Optimization with Metaheuristics

In the automotive industry, a Control Engineer must design a unique control law that is then tested and validated on a single prototype with a level of reliability high enough to to meet a number of complex specifications on various systems. In order to do this, the Engineer uses an experimental iterative process (Trial and Error phase) which relies heavily on his or her experience. This book looks to optimise the methods for synthesising servo controllers ny making them more direct and thus quicker to design. This is achieved by calculating a final controller to directly tackle the high-end system specs.

Table of Contents:
Preface  ix Introduction and Motivations  xi Chapter 1. Metaheuristics for Controller Optimization  1 1.1. Introduction  1 1.2. Evolutionary approaches using differential evolution  2 1.2.1. Standard version 2 1.2.2. Perturbed version 7 1.3. Swarm approaches 8 1.3.1. Particle swarm optimization algorithm 8 1.3.2. Quantum particle swarm algorithm 14 1.3.3. Artificial bee colony optimization algorithm  20 1.3.4. Cuckoo search algorithm 25 1.3.5. Firefly algorithm 31 1.4. Summary  33 Chapter 2. Reformulation of Robust Control Problems for Stochastic Optimization  35 2.1. Introduction  35 2.2. H∞ synthesis  35 2.2.1. Full H∞ synthesis 35 2.2.2. Fixed-structure H∞ synthesis 45 2.2.3. Formulating H∞ synthesis for stochastic optimization 67 2.2.4. Conclusion 105 2.3. μ-Synthesis 105 2.3.1. The problem of performance robustness  105 2.3.2. μ-Synthesis  110 2.4. LPV/LFT synthesis  140 2.4.1. Introduction  140 2.4.2. The LPV/LFT controller synthesis problem  141 2.4.3. Reformulation for stochastic optimization 147 Chapter 3. Optimal Tuning of Structured and Robust H∞ Controllers Against High-level Requirements 171 3.1. Introduction and motivations 171 3.2. Loop-shaping H∞ synthesis  180 3.2.1. Approach principle  180 3.2.2. Generalized gain and phase margins  184 3.2.3. Four-block interpretation of the method  185 3.2.4. Practical implementation 186 3.2.5. Implementation of controllers  190 3.3. A generic method for the declination of requirements 194 3.3.1. General principles 194 3.3.2. Special cases 196 3.3.3. Management of requirement priority level 197 3.4. Optimal tuning of weighting functions 198 3.4.1. Optimization on nominal plant 198 3.4.2. Multiple plant optimization 202 3.4.3. Applicative example – inertial stabilization of line of sight  207 3.5. Optimal tuning of the fixed-structure and fixed-order final controller 238 3.5.1. Introduction  238 3.5.2. Toward eliminating weighting functions  240 3.5.3. Extensions to the approach  259 3.5.4. Link with standard control problems  277 Chapter 4. HinfStoch: A Toolbox for Structured and Robust Controller Computation Based on Stochastic Optimization 279 4.1. Introduction  279 4.2. Structured multiple plant H∞ synthesis 280 4.2.1. Principle  280 4.2.2. Formalism 280 4.3. Structured μ-synthesis 284 4.3.1. Principle  284 4.3.2. Formalism 285 4.4. Structured LPV/LFT synthesis  288 4.4.1. Principle  288 4.4.2. Formalism 289 4.5. Structured and robust synthesis against high-level requirements with HinfStoch_ControllerTuning 292 4.5.1. Principle  292 4.5.2. Formalism 293 4.5.3. Examples 311 Appendices 351 Appendix A. Notions of Coprime Factorizations  353 Appendix B. Examples of LFT Form Used for Uncertain Systems  359 Appendix C. LFT Form Use of an Electromechanical System with Uncertain Flexible Modes  365 Appendix D. FTM (1D) Computation from a Time Signal 383 Appendix E. Choice of Iteration Number for CompLeib Tests  385 Appendix F. PDE versus DE 393 Bibliography 399 Index 407