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Analysis and Control of Nonlinear Systems

Part of the Mathematical Engineering Book Series

DOI: 10.1007/978-3-642-00839-9

ISBN: 978-3-642-00838-2

Publisher: Springer Berlin Heidelberg - Springer Journals

May 5, 2009

1 - 10 of 14 Chapters

LitStream

Chapter 1Introduction

Lévine, Jean

Pages: 1 –10

[This book is made of two parts, Theory and Applications. In the first Part, two major problems of automatic control are addressed: trajectory generation, or motion planning, and tracking of these trajectories. In order to make this book as self-contained as possible we have included a survey of...
LitStream

Introduction to Differential Geometry

Lévine, Jean

Pages: 13 –41

[This Chapter aims at introducing the reader to the basic concepts of differential geometry such as diffeomorphism, tangent and cotangent space, vector field, differential form. Special emphasis is put on the integrability of a family of vector fields, or distribution1, according to its role in...
LitStream

Introduction to Dynamical Systems

Lévine, Jean

Pages: 43 –86

[This chapter is devoted to the study of the dynamical behaviors of nonlinear uncontrolled systems: stability, instability of flows around an equilibrium or a periodic orbit and comparison to their tangent linear approximation. We consider the set of (uncontrolled) differential equation, or...
LitStream

Controlled Systems, Controllability

Lévine, Jean

Pages: 87 –105

[Controllability is one of the so-called structural properties of systems depending on inputs. It has initially been studied in the framework of linear systems to describe the possibility of generating arbitrary motions. For nonlinear systems, several extensions are possible. They are outlined in...
LitStream

Jets of Infinite Order, Lie-Bäcklund’s Equivalence

Lévine, Jean

Pages: 107 –130

[A cart of mass M rolls along the axis OX of the overhead crane. Its position is denoted by x. It is actuated by a motor that produces a horizontal force of intensity F. Moreover, the cart carries a winch of radius ρ around which is winding a cable hoisting the load attached at its end. The...
LitStream

Differentially Flat Systems

Lévine, Jean

Pages: 131 –179

[Denition 6.1. We say that the system (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Flatness and Motion Planning

Lévine, Jean

Pages: 181 –191

[Let us consider the nonlinear system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Flatness and Tracking

Lévine, Jean

Pages: 193 –199

[For the solution of the motion planning problem, all we required was the knowledge of a dynamical model and the time, in other words, anticipative data: the reference trajectory was computed from the present time to some future time according to what we know about the system’s evolution. This...
LitStream

DC Motor Starting Phase

Lévine, Jean

Pages: 203 –209

[This chapter is aimed at showing that, even for DC motor control, a quite standard application of control, described by a single input linear system, the so-called flatness-based approach may dramatically improve its performance in a transient phase.]
LitStream

Displacements of a Linear Motor With Oscillating Masses

Lévine, Jean

Pages: 211 –224

[The aim of this chapter is to show, on a barely undamped oscillating system, roughly approximated by a simple single-input linear model, the importance of feedforward design to simultaneously achieve, with the same smooth controller (no switch), high precision positioning, fast displacements,...

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