1st Edition

A Practical Guide to Geometric Regulation for Distributed Parameter Systems

By Eugenio Aulisa, David Gilliam Copyright 2016
    294 Pages 203 B/W Illustrations
    by Chapman & Hall

    A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wide range of dynamical control systems.

    The first part of the book is devoted to regulation of linear systems, beginning with the mathematical setup, general theory, and solution strategy for regulation problems with bounded input and output operators. The book then considers the more interesting case of unbounded control and sensing. Mathematically, this case is more complicated and general theorems in this area have become available only recently. The authors also provide a collection of interesting linear regulation examples from physics and engineering.

    The second part focuses on regulation for nonlinear systems. It begins with a discussion of theoretical results, characterizing solvability of nonlinear regulator problems with bounded input and output operators. The book progresses to problems for which the geometric theory based on center manifolds does not directly apply. The authors show how the idea of attractive invariance can be used to solve a series of increasingly complex regulation problems. The book concludes with the solutions of challenging nonlinear regulation examples from physics and engineering.

    Acknowledgments

    Preface

    Regulation for Linear Systems

    Regulation: Bounded Input and Output Operators

    Setup and Statement of Problem

    Main Theoretical Result

    The Transfer Function

    SISO Examples with Bounded Control and Sensing

    The MIMO Case

    Linear Regulation with Unbounded Control and Sensing

    Introduction

    Formulation of Control System and Interpolation Spaces

    Examples with Unbounded Sensing and Control

    Examples Linear Regulation

    Introduction

    Harmonic Tracking for a Coupled Wave Equation

    Control of a Damped Rayleigh Beam

    Vibration Regulation of a 2D Plate

    Control of a Linearized Stokes Flow in 2 Dimensions

    Thermal Control of a 2D Fluid Flow

    Thermal Regulation in a 3D Room

    Using Fourier Series for Tracking Periodic Signals

    Zero Dynamics Inverse Design

    Regulation for Nonlinear Systems

    Nonlinear Distributed Parameter Systems

    Introduction

    Nonlinear State Feedback Regulation Problem

    Set-Point Regulation for Nonlinear Systems

    Tracking/Rejection of Piecewise Constant Signals

    Nonlinear Regulation for Time-Dependent Signals

    Fourier Series Methods for Nonlinear Regulation

    Zero Dynamics Design for Nonlinear Systems

    Nonlinear Examples

    Introduction

    Navier-Stokes Flow in a 2D Forked Channel

    Non-Isothermal Navier-Stokes Flow in a 2D Box

    2D Chafee-Infante with Time-Dependent Regulation

    Regulation of 2D Burgers' Using Fourier Series

    Back-Step Navier-Stokes Flow

    Nonlinear Regulation Using Zero Dynamics Design

    Bibliography

    Index

    List of Symbols

    Biography

    Eugenio Aulisa is an associate professor in the Department of Mathematics and Statistics at Texas Tech University, Lubbock, USA. His primary research interests are in computational fluid mechanics, modeling and simulation of multiphase flows, fluid-structure interaction problems, non-linear analysis of fluid flow filtration in porous media, and multigrid solvers with domain decomposition methods. He holds a Ph.D in energetic, nuclear, and environmental control engineering from the University of Bologna, Italy.

    David Gilliam is a professor in the Department of Mathematics and Statistics at Texas Tech University, Lubbock, USA. He also has held visiting and/or affiliate positions at Arizona State University, Tempe, USA; Colorado School of Mines, Golden, USA; University of Texas at Dallas, Richardson, USA; and Washington University in St. Louis, Missouri, USA. His current research interests are in the control of distributed parameter systems governed by partial differential equations. He holds a Ph.D from the University of Utah, Salt Lake City, USA.