Nonlinear and Robust Control of PDE Systems

The interest in control of nonlinear partial differential equation (PDE) systems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit 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 systems and illustrates their applications to transport-reaction processes of industrial interest. The controllers use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output tracking and attenuation of the effect of model uncertainty.§Beginning with an introduction to control of PDE systems, the book discusses nonlinear and robust control of hyperbolic and parabolic PDEs with fixed spatial domains, and parabolic PDEs with time-dependent spatial domains. The synthesis of the controllers is performed by using geometric and Lyapunov-based control techniques. The book includes comparisons of the methods followed for controller synthesis with other approaches and discussions of practical implementation issues that can help researchers and engineers understand the development and application of the methods in greater depth. The methods are applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a crystal growth process. The resulting benefits in closed-loop performance and robustness compared to other techniques for control of transport-reaction processes are demonstrated through computer simulations.§The book assumes a basic knowledge about PDE systems and nonlinear control.§Features:§includes new techniques for nonlinear and robust controller design for PDE systems that are not included in other books§provides insight and fundamental understanding into the feedback control of PDE systems§illustrates the application of the controller design methods to numerous transport-reaction processes of industrial interest§offers new research topics and presents significant recent work§Researchers and graduate students in control systems theory and process control, applied mathematicians and process control engineers will find this book a useful resource.