Motion control of underactuated mechanical systems

230 Pages·2018·13.36 MB·English

by  Aguilar-Avelar

Intelligent Systems, Control and Automation:
Science and Engineering
Javier Moreno-Valenzuela
Carlos Aguilar-Avelar
Motion Control of
Underactuated

Mechanical Systems
Intelligent Systems, Control and Automation:
Science and Engineering
Volume 88
Series editor
Professor S.G. Tzafestas, National Technical University of Athens, Greece
Editorial Advisory Board
Professor P. Antsaklis, University of Notre Dame, IN, USA
Professor P. Borne, Ecole Centrale de Lille, France
Professor R. Carelli, Universidad Nacional de San Juan, Argentina
Professor T. Fukuda, Nagoya University, Japan
Professor N.R. Gans, The University of Texas at Dallas, Richardson, TX, USA
Professor F. Harashima, University of Tokyo, Japan
Professor P. Martinet, Ecole Centrale de Nantes, France
Professor S. Monaco, University La Sapienza, Rome, Italy
Professor R.R. Negenborn, Delft University of Technology, The Netherlands
Professor A.M. Pascoal, Institute for Systems and Robotics, Lisbon, Portugal
Professor G. Schmidt, Technical University of Munich, Germany
Professor T.M. Sobh, University of Bridgeport, CT, USA
Professor C. Tzafestas, National Technical University of Athens, Greece
Professor K. Valavanis, University of Denver, Colorado, USA
More information about this series at http://www.springer.com/series/6259
Javier Moreno-Valenzuela Carlos Aguilar-Avelar
(cid:129)
Motion Control
of Underactuated
Mechanical Systems
123
Javier Moreno-Valenzuela Carlos Aguilar-Avelar
Instituto Politécnico Nacional-CITEDI Instituto Politécnico Nacional-CITEDI
Tijuana Tijuana
Mexico Mexico
ISSN 2213-8986 ISSN 2213-8994 (electronic)
Intelligent Systems, Control andAutomation: Science andEngineering
ISBN978-3-319-58318-1 ISBN978-3-319-58319-8 (eBook)
DOI 10.1007/978-3-319-58319-8
LibraryofCongressControlNumber:2017943216
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Preface
The growth in automated manufacturing since the ‘60s has motivated the study
of the control and motion planning of many types of mechanical systems, such as
industrial manipulators. It seems that the term underactuated first appeared when
researchers started to form the question as to how to achieve control in a robot
manipulatorifoneactuatorgoesoff.Withthepassageoftime,thistermhasbecome
more formally defined to describe any system with more degrees offreedom than
actuators.Thisprovidedanew contextforstudyingcertain otherproblemsalready
known from the beginning of the contemporary era, like the control aerospace
systems. Thus, the study of the control of underactuated mechanical systems has
become a prolific field since the late ‘90s. Nowadays, the control of underactuated
systems is studied in many undergraduate and graduate courses and many ofthese
systems have become benchmarks for testing new control methodologies.
Most of the literature in the field has been focused on the regulation problem,
whilethedevelopmentoftrackingcontrolofreferencetrajectories,althoughuseful
in many practical applications, has been a topic rarely studied. It is here that this
bookfindsitsplace,bystudyinganddevelopingnewparadigmsformotioncontrol
of underactuated systems.
A unified perspective on the control of underactuated mechanical systems is
presentedinthisbook.Firstly,itprovidesareliableparameteridentificationmethod
tobeimplementedinareal-timeexperimentalplatform,sinceanaccuratemodelof
asystem allows forperformingmodel-based control implementations,gaintuning,
andnumericalsimulations.Secondly,itgivesavarietyofmotioncontrolalgorithms
fortheFurutapendulumandtheinertiawheelpendulum,whicharetwodegrees-of-
freedom underactuated mechanical systems. This book addresses and solves the
problem of motion control via the trajectory tracking in one joint coordinate while
another joint is regulated.
Modelling and identification play an important role in the results reported.
Specifically, an easy-to-implement parameter identification methodology is
explained by means of the Furuta pendulum and inertia wheel pendulum. Such a
methodology can be easily extended to other systems, allowing researchers and
students to obtain value from this book.
v
vi Preface
This book presents novel ideas on the control of two degrees-of-freedom
underactuated mechanical systems and forms a basis for the development of gen-
eralizations and applications in more complex higher degrees-of-freedom systems
in robotics, marine and aerospace vehicles. The main design philosophies used in
this book embraces techniques like feedback linearization control, energy-based
control, neural networks, adaptive control, and integral dynamic extensions.
Thisbookwaswrittenforstudentsattheundergraduateandgraduatelevelsand
researchers in the areas of nonlinear control and mechatronics, as well as
researchers interested in joining practice and theory.
This book is indebted to the following friends and colleagues who directly or
indirectly influenced its contents. Professor Rafael Kelly for many fruitful discus-
sions on control of robot manipulators, as well as conceptions of Lyapunov func-
tions. Professor Victor Santibáñez for encouraging discussions concerning the
motion control underactuated mechanical systems and control of mechatronic sys-
tems.ProfessorRodolpheSepulchreforhisinspiringlecturesonhowtomakeuseof
controltheoryasaspeciallanguagetoexplainthingsinphysics.ProfessorRicardo
Campaforhiscriticisminthereadingofmanymanuscriptsofthefirstauthor.Weare
also thankful to some graduate students who were advised by the first author. In
particular,SergioPuga-Guzmánforhiscomprehensiveworkinthedevelopmentof
control algorithms based on neural networks, Octavio García-Alarcón for his
enthusiasmintheconstructionoftheFurutapendulumandanearlyprototypeofthe
IWP and Ricardo Rodríguez-Calderón for his work inthe construction andparam-
eter identification ofthe IWP.
We are grateful to CONACyT, Project no. 176587, and Secretaría de
Investigación y Posgrado del Instituto Politécnico Nacional, Mexico, for sup-
porting the research that led to most of the results presented in this book. We are
also grateful to the Instituto Politécnico Nacional-CITEDI for creating an envi-
ronment that allowed us to write this book.
Tijuana, Mexico Javier Moreno-Valenzuela
January 2017 Carlos Aguilar-Avelar
Contents
1 Introduction... .... .... ..... .... .... .... .... .... ..... .... 1
1.1 Background .. .... ..... .... .... .... .... .... ..... .... 1
1.1.1 Underactuated Systems .... .... .... .... ..... .... 1
1.1.2 Nonlinear Dynamics and Control .... .... ..... .... 3
1.1.3 Parameter Identification.... .... .... .... ..... .... 6
1.1.4 Motion Control of Underactuated Systems . ..... .... 7
1.2 Motivations and Objectives.... .... .... .... .... ..... .... 9
1.3 Outline .. .... .... ..... .... .... .... .... .... ..... .... 9
2 Preliminaries .. .... .... ..... .... .... .... .... .... ..... .... 13
2.1 Fundamentals of Nonlinear Systems. .... .... .... ..... .... 13
2.2 Fundamental Properties... .... .... .... .... .... ..... .... 15
2.3 Concepts of Stability .... .... .... .... .... .... ..... .... 15
2.4 Barbalat’s Lemma.. ..... .... .... .... .... .... ..... .... 18
2.5 Boundedness and Ultimate Boundedness . .... .... ..... .... 18
2.6 Feedback Linearization... .... .... .... .... .... ..... .... 19
2.7 Artificial Neural Networks .... .... .... .... .... ..... .... 22
2.7.1 Universal Function Approximation Property ..... .... 24
3 Identification of Underactuated Mechanical Systems ... ..... .... 27
3.1 Introduction .. .... ..... .... .... .... .... .... ..... .... 27
3.2 Identification of the Furuta Pendulum.... .... .... ..... .... 28
3.2.1 Dynamic Model.. .... .... .... .... .... ..... .... 28
3.2.2 Filtered Regression Model.. .... .... .... ..... .... 30
3.2.3 Discretization of the Filtered Regression Model .. .... 32
3.2.4 Experimental Platform. .... .... .... .... ..... .... 33
3.2.5 Motion Control Experiment. .... .... .... ..... .... 34
3.2.6 Joint Velocity Calculation.. .... .... .... ..... .... 35
3.2.7 Least Squares Algorithm... .... .... .... ..... .... 36
3.2.8 Results of the Identification Procedure .... ..... .... 37
vii
viii Contents
3.3 Identification of the Inertia Wheel Pendulum .. .... ..... .... 40
3.3.1 Dynamic Model.. .... .... .... .... .... ..... .... 40
3.3.2 Filtered Regression Model.. .... .... .... ..... .... 42
3.3.3 Discretization of the Filtered Regression Model .. .... 43
3.3.4 Experimental Platform. .... .... .... .... ..... .... 44
3.3.5 Motion Control Experiment. .... .... .... ..... .... 45
3.3.6 Joint Velocity Calculation.. .... .... .... ..... .... 45
3.3.7 Least Squares Algorithm... .... .... .... ..... .... 46
3.3.8 Results of the Identification Procedure .... ..... .... 47
3.4 Concluding Remarks..... .... .... .... .... .... ..... .... 49
4 Composite Control of the Furuta Pendulum.. .... .... ..... .... 51
4.1 Introduction .. .... ..... .... .... .... .... .... ..... .... 51
4.2 Dynamic Model ... ..... .... .... .... .... .... ..... .... 52
4.3 Control Problem Formulation.. .... .... .... .... ..... .... 53
4.4 Design of the Proposed Scheme.... .... .... .... ..... .... 54
4.4.1 Feedback Linearization Part. .... .... .... ..... .... 54
4.4.2 Energy-Based Compensation.... .... .... ..... .... 55
4.4.3 Summary of the Composite Controller .... ..... .... 59
4.5 Analysis of the Closed-Loop Trajectories. .... .... ..... .... 60
4.6 Controller for the Performance Comparison ... .... ..... .... 61
4.6.1 Output Tracking Controller. .... .... .... ..... .... 61
4.7 Experimental Evaluation.. .... .... .... .... .... ..... .... 62
4.7.1 Experimental Results.. .... .... .... .... ..... .... 62
4.7.2 Performance Comparison... .... .... .... ..... .... 65
4.8 Concluding Remarks..... .... .... .... .... .... ..... .... 68
5 Feedback Linearization Control of the Furuta Pendulum .... .... 69
5.1 Introduction .. .... ..... .... .... .... .... .... ..... .... 69
5.2 Dynamic Model and Error Dynamics.... .... .... ..... .... 70
5.3 Control Problem Formulation.. .... .... .... .... ..... .... 72
5.4 Design of the Proposed Scheme.... .... .... .... ..... .... 72
5.5 Analysis of the Closed-Loop Trajectories. .... .... ..... .... 73
5.5.1 Ultimate Bound.. .... .... .... .... .... ..... .... 78
5.5.2 Boundedness of the Error Trajectories. .... ..... .... 79
5.6 Controllers for the Performance Comparison .. .... ..... .... 80
5.6.1 PID Controller... .... .... .... .... .... ..... .... 80
5.6.2 Output Tracking Controller. .... .... .... ..... .... 81
5.7 Experimental Evaluation.. .... .... .... .... .... ..... .... 82
5.7.1 Experimental Results.. .... .... .... .... ..... .... 82
5.7.2 Performance Comparison... .... .... .... ..... .... 85
5.8 Concluding Remarks..... .... .... .... .... .... ..... .... 91
Contents ix
6 Adaptive Neural Network Control of the Furuta Pendulum .. .... 93
6.1 Dynamic Model and Error Dynamics.... .... .... ..... .... 94
6.2 Control Problem Formulation.. .... .... .... .... ..... .... 96
6.3 Design of the Proposed Scheme.... .... .... .... ..... .... 96
6.4 Analysis of the Closed-Loop Trajectories. .... .... ..... .... 99
6.5 Controllers for the Performance Comparison .. .... ..... .... 108
6.5.1 PID Controller... .... .... .... .... .... ..... .... 108
6.5.2 Jung and Kim Controller... .... .... .... ..... .... 109
6.5.3 Chaoui and Sicard Controller ... .... .... ..... .... 109
6.6 Experimental Evaluation.. .... .... .... .... .... ..... .... 110
6.6.1 Experimental Results and Performance Comparison ... 110
6.7 Concluding Remarks..... .... .... .... .... .... ..... .... 118
7 Composite Control of the IWP. .... .... .... .... .... ..... .... 119
7.1 Introduction .. .... ..... .... .... .... .... .... ..... .... 119
7.2 Dynamic Model ... ..... .... .... .... .... .... ..... .... 121
7.3 Control Problem Formulation.. .... .... .... .... ..... .... 122
7.4 Design of the Proposed Scheme.... .... .... .... ..... .... 122
7.4.1 Feedback Linearization Controller.... .... ..... .... 122
7.4.2 Energy-Based Compensation.... .... .... ..... .... 124
7.4.3 Summary of the Composite Controller .... ..... .... 128
7.5 Analysis of the Closed-Loop Trajectories. .... .... ..... .... 128
7.6 Integral Extension.. ..... .... .... .... .... .... ..... .... 130
7.7 Controller for the Performance Comparison ... .... ..... .... 131
7.7.1 LQR Motion Controller.... .... .... .... ..... .... 131
7.8 Experimental Evaluation.. .... .... .... .... .... ..... .... 131
7.8.1 Swing-up ControlþMotion Control .. .... ..... .... 132
7.8.2 Experimental Results.. .... .... .... .... ..... .... 133
7.8.3 Performance Comparison... .... .... .... ..... .... 135
7.9 Concluding Remarks..... .... .... .... .... .... ..... .... 140
8 Feedback Linearization Control of the IWP.. .... .... ..... .... 141
8.1 Dynamic Model and Error Dynamics.... .... .... ..... .... 143
8.2 Control Problem Formulation.. .... .... .... .... ..... .... 145
8.3 Design of the Proposed Scheme.... .... .... .... ..... .... 145
8.4 Analysis of the Closed-Loop Trajectories. .... .... ..... .... 146
8.5 Controllers for the Performance Comparison .. .... ..... .... 150
8.5.1 State Feedback Controller .. .... .... .... ..... .... 150
8.5.2 Particular Feedback Linearization Controller..... .... 151
8.6 Experimental Evaluation.. .... .... .... .... .... ..... .... 154
8.6.1 Experimental Results.. .... .... .... .... ..... .... 155
8.6.2 Performance Comparison... .... .... .... ..... .... 157
8.7 Concluding Remarks..... .... .... .... .... .... ..... .... 158