Nonlinear and Robust Control of PDE Systems

The book presents state-of-the-art methods for the synthesis of nonlinear and robust feedback controllers for transport-reaction processes. The book will be an essential resource for chemical engineers, control engineers, and mechanical engineers.

"The concrete aspect of this book is its strength, and it may inspire theoreticians in the control of PDEs so that they realize design methods in the finite-dimensional case have interesting extensions in their area; it may encourage practitioners, giving them confidence in dealing with PDEs. The development is illustrated with applications from the chemical industry throughout the book (reactor, chemical vapor deposition, crystal growth)." Zentralblatt Math

"This book deals with nonlinear and robust feedback controllers for hyperbolic and parabolic PDEs with fixed spatial domains and parabolic PDEs with time-dependent spatial domains. It includes applications to transport-reaction processes of industrial interest and also discusses practical implementation issues." Monatshefte für Mathematik

Résumé
The interest in control of nonlinear partial differential equation (PDE) sys­ tems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations. Drawing from recent advances in dynamics of PDE systems and nonlinear control theory, control of nonlinear PDEs has evolved into a very active research area of systems and control. This book­ the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys­ tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded. We use geometric and Lyapunov-based control techniques to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output track­ ing, and attenuation of the effect of model uncertainty. The controllers are successfully applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a Czochralski crystal growth process. The book includes comparisons of the proposed nonlinear and robust control methods with other approaches and discussions of practical implementation issues.

Contenu
1 Introduction.- 1.1 Motivation.- 1.2 Examples of Transport-Reaction Processes.- 1.3 Background on Control of PDE Systems.- 1.4 Objectives and Organization of the Book.- 2 Feedback Control of Hyperbolic PDE Systems.- 2.1 Introduction.- 2.2 First-Order Hyperbolic PDE Systems.- 2.3 Characteristic Index.- 2.4 State Feedback Control.- 2.5 Closed-Loop Stability.- 2.6 Output Feedback Control.- 2.7 Application to a Nonisothermal Plug-Flow Reactor.- 2.8 Conclusions.- 3 Robust Control of Hyperbolic PDE Systems.- 3.1 Introduction.- 3.2 Preliminaries.- 3.3 Uncertainty Decoupling.- 3.4 Robust Control: Uncertain Variables.- 3.5 Two-Time-Scale Hyperbolic PDE Systems.- 3.6 Robustness with Respect to Unmodeled Dynamics.- 3.7 Application to a Fixed-Bed Reactor.- 3.8 Conclusions.- 4 Feedback Control of Parabolic PDE Systems.- 4.1 Introduction.- 4.2 Preliminaries.- 4.3 Examples of Processes Modeled by Nonlinear Parabolic PDEs.- 4.4 Galerkin's Method.- 4.5 Accuracy of ODE System Obtained From Galerkin's Method.- 4.6 Construction of ODE Systems of Desired Accuracy via AIMs.- 4.7 Nonlinear Output Feedback Control.- 4.8 Applications.- 4.9 Conclusions.- 5 Robust Control of Parabolic PDE Systems.- 5.1 Introduction.- 5.2 Preliminaries.- 5.3 Robust State Feedback Control of Parabolic PDE Systems.- 5.4 Robust Output Feedback Controller Synthesis.- 5.5 Application to a Catalytic Rod with Uncertainty.- 5.6 Conclusions.- 6 Nonlinear and Robust Control of Parabolic PDE Systems with Time-Dependent Spatial Domains.- 6.1 Introduction.- 6.2 Preliminaries.- 6.3 Nonlinear Model Reduction.- 6.4 Nonlinear Output Feedback Control.- 6.5 Application to a Catalytic Rod with Moving Boundary.- 6.6 Robust Control of Parabolic PDEs with Time-Dependent Spatial Domains.- 6.7 Application to a Catalytic Rod withMoving Boundary and Uncertainty.- 6.8 Conclusions.- 7 Case Studies.- 7.1 Nonlinear Control of Rapid Thermal Chemical Vapor Deposition.- 7.2 Nonlinear Control of Czochralski Crystal Growth.- 7.3 Conclusions.- Appendix A: Proofs of Chapter 2.- Appendix B: Proofs of Chapter 3.- Appendix C: Proofs of Chapter 4.- Appendix D: Proofs of Chapter 5.- Appendix E: Proofs of Chapter 6.- Appendix F: Karhunen-Loève Expansion.- References.