Model-based tracking control of nonlinear systems

317 Pages·2012·6.301 MB·English

by  Elzbieta Jarzebowska

M CRC S : M M M
ERIES ODERN ECHANICS AND ATHEMATICS
Mechanical Engineering o
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Model-Based Control of Nonlinear Systems presents model-based l Elżbieta Jarzębowska
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control techniques for nonlinear, constrained systems. It covers constructive
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control design methods with an emphasis on modeling constrained
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systems, generating dynamic control models, and designing tracking e Model-Based Tracking
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control algorithms for the models.

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The book’s interdisciplinary approach illustrates how system modeling and r Control of Nonlinear Systems
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control theory are essential to control design projects. Organized according c
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to the steps in a control design project, the text first discusses kinematic and
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dynamic modeling methods, including programmed constraints, Lagrange’s n
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equations, Boltzmann−Hamel equations, and generalized programmed

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motion equations. The next chapter describes basic control concepts and
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the use of nonlinear control theory. After exploring stabilization strategies n
for nonlinear systems, the author presents existing model-based tracking t
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control algorithms and path-following strategies for nonlinear systems. o
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The final chapter develops a new model reference tracking strategy for
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programmed motion. f

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Throughout the text, two examples of mechanical systems are used to
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illustrate the theory and simulation results. The first example is a unicycle n
model (nonholonomic system) and the second is a two-link planar l
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manipulator model (holonomic system). With a focus on constructive
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modeling and control methods, this book provides the tools and techniques a
to support the control design process. r

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Features y
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• Addresses dynamic modeling and control design methods for
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nonlinear mechanical systems
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• Covers kinematics and dynamic model formulation
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• Describes the design of control algorithms
• Presents a new tracking control strategy architecture
• Includes problems and references in each chapter J
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K11043 s
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K11043_Cover.indd 1 4/16/12 1:48 PM

Model-Based Tracking
Control of Nonlinear Systems
CRC S : M M M
ERIES ODERN ECHANICS AND ATHEMATICS
Series Editors: David Gao and Martin Ostoja-Starzewski
PUBLISHED TITLES
BEYOND PERTURBATION: INTRODUCTION TO THE HOMOTOPY ANALYSIS METHOD
by Shijun Liao
ClassiCal and Generalized Models of elastiC rods
by Dorin Ie¸san
ConfiGurational forCes: therMoMeChaniCs, PhysiCs, MatheMatiCs, and nuMeriCs
by Gérard A. Maugin
CONTINUUM MECHANICS AND PLASTICITY
by Han-Chin Wu
HYBRID AND INCOMPATIBLE FINITE ELEMENT METHODS
by Theodore H.H. Pian and Chang-Chun Wu
INTRODUCTION TO ASYMPTOTIC METHODS
by Jan Awrejcewicz and Vadim A. Krysko
MECHANICS OF ELASTIC COMPOSITES
by Nicolaie Dan Cristescu, Eduard-Marius Craciun, and Eugen Soós
M -B t C n s
odel ased raCkinG ontrol of onlinear ysteMs
by Elz·bieta Jarz˛ebowska
M a M t
odelinG and nalytiCal ethods in riBoloGy
by Ilya I. Kudish and Michael J. Covitch
MICROSTRUCTURAL RANDOMNESS AND SCalinG IN MECHANICS OF MATERIALS
by Martin Ostoja-Starzewski
CRC S : M M M
ERIES ODERN ECHANICS AND ATHEMATICS
Model-Based Tracking
Control of Nonlinear Systems
Elżbieta Jarzębowska
Warsaw University of Technology
Warsaw, Poland
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
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Version Date: 20120504
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To my Parents, who equipped me with passion and courage for life, and to
the memory of Prof. Roman Gutowski, who introduced me to mechanics.

Contents
Preface......................................................................................................................xi
The Author...........................................................................................................xiii
1. Introduction......................................................................................................1
1.1. Scope.and.Outline..................................................................................3
1.2. Mechanics.and.Nonlinear.Control......................................................6
1.3. Role.of.Modeling.in.a.Control.Design.Process................................20
References........................................................................................................21
2. Dynamics Modeling of Constrained Systems.........................................25
2.1. Introduction—Art.of.Modeling.........................................................25
2.1.1. Selection.of.Coordinates........................................................26
2.1.2. Generalized.Velocities.and.Quasi-Velocities......................29
2.2. Constrained.Systems...........................................................................31
2.2.1. Holonomic.Constraints..........................................................32
2.2.2. Nonholonomic.Constraints...................................................33
2.2.3. Programmed.Constraints......................................................35
2.3. Equations.of.Motion.for.Systems.with.
First Order Constraints.....................................................................37
2.3.1. D’Alembert.Principle..............................................................38
2.3.2. Lagrange’s.Equations.for.Holonomic.Systems...................45
2.3.3. Lagrange’s.Equations.for.First.Order.Nonholonomic.
Systems.....................................................................................50
2.3.4. Maggi’s.Equations...................................................................52
2.3.5. Nielsen’s.Equations.................................................................55
2.3.6. Equations.of.Motion.in.Quasi-Coordinates........................58
2.4. Equations.of.Motion.for.Systems.with.High.Order.
Constraints...........................................................................................67
2.4.1. An.Extended.Concept.of.Constraints—Programmed.
Constraints...............................................................................67
2.4.2. Generalized.Programmed.Motion.Equations.
Specified.in.Generalized.Coordinates.................................76
2.4.3. Generalized.Programmed.Motion.Equations.
Specified.in.Quasi-Coordinates............................................88
Problems...........................................................................................................94
References........................................................................................................94
vii
viii Contents
3. Introduction to Nonlinear Control Theory..............................................99
3.1. Stability.Properties.of.Nonlinear.Systems.......................................99
3.1.1. State-Space.Representation.of.Nonlinear.Systems.............99
3.1.2. Stability.Theorems.of.the.Lyapunov.Direct.Method.......101
3.1.3. Special.Formulations.of.Stability.Theorems.....................103
3.2. Classification.of.Control.Problems..................................................111
3.2.1. Stabilization...........................................................................112
3.2.2. Trajectory.and.Motion.Tracking.........................................115
3.2.3. Path.Following......................................................................117
3.3. Control.Properties.of.Nonlinear.Systems.......................................118
3.3.1. Classification.of.Constrained.Control.Systems................118
3.3.2. Accessibility.and.Controllability........................................122
3.3.3. Stabilizability.........................................................................131
3.3.4. Differential.Flatness.............................................................135
3.4. Kinematic.Control.Models................................................................136
3.5. Dynamic.Control.Models.................................................................144
3.6. Feedback.Linearization.of.Nonlinear.Systems..............................147
3.7. Model-Based.Control.Design.Methods...........................................152
3.8. Flatness-Based.Control.Design.Methods.......................................155
3.8.1. Basic.Notions.of.Equivalence.and.Flatness.......................155
3.8.2. Flatness.in.Control.Applications........................................159
3.8.3. Flatness-Based.Control.Design—Examples......................161
3.8.4. Concluding.Remarks—Verifying.Flatness........................167
3.9. Other.Control.Design.Techniques.for.Nonlinear.Systems..........167
3.9.1. Backstepping.........................................................................169
3.9.2. Sliding.Mode.Control...........................................................173
Problems.........................................................................................................175
References......................................................................................................176
4. Stabilization Strategies for Nonlinear Systems....................................183
Problems.........................................................................................................189
References......................................................................................................189
5. Model-Based Tracking Control of Nonlinear Systems........................191
5.1. A.Unified.Control-Oriented.Model.for.Constrained.Systems....191
5.2. Tracking.Control.of.Holonomic.Systems........................................196
5.3. Tracking.Control.of.First.Order.Nonholonomic.Systems............200
5.4. Tracking.Control.of.Underactuated.Systems.................................206
5.5. Tracking.Control.Algorithms.Specified.in.
Quasi-Coordinates............................................................................212
Problems.........................................................................................................222
References......................................................................................................222