1st Edition

A Practical Guide to Geometric Regulation for Distributed Parameter Systems

ISBN 9781482240139
Published June 18, 2015 by Chapman and Hall/CRC
294 Pages 203 B/W Illustrations

USD $115.00

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Book Description

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.

Table of Contents



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


Formulation of Control System and Interpolation Spaces

Examples with Unbounded Sensing and Control

Examples Linear Regulation


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


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


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



List of Symbols

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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.