Hierarchical Sliding Mode Control for Under-actuated Cranes: Design, Analysis and Simulation

210 Pages·2015·5.93 MB·English

by  Dianwei Qian

Dianwei Qian · Jianqiang Yi
Hierarchical
Sliding Mode
Control for Under-
actuated Cranes
Design, Analysis and Simulation
Hierarchical Sliding Mode Control
for Under-actuated Cranes
Dianwei Qian Jianqiang Yi
(cid:129)
Hierarchical Sliding
Mode Control
for Under-actuated Cranes
Design, Analysis and Simulation
123
Dianwei Qian Jianqiang Yi
Schoolof Control andComputer Institute of Automation
Engineering ChineseAcademy of Sciences
NorthChina Electric Power University Beijing
Beijing China
China
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DOI 10.1007/978-3-662-48417-3
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Dedicated to my wife Weiwei Zhao and our
daughter Siqi Qian as well as to my parents
Yubao Qian and Lixiang Bai with love and
gratitude
Dianwei Qian
Dedicated to my wife Li Zhang and our
children with love and gratitude
Jianqiang Yi
Preface
Overheadcranesarewidelyusedinmanyplaces,suchaswarehouses,disastersites,
nuclear plants, shipyards and construction sites. Overhead crane control has been
paid more and more attention in recent years. Concerning the control problem,
numerous theoretical studies and practical implementations have been carried out.
Accordingly,variouscontrolmethodshavebeenpresented.Amongthediversityof
control methods, sliding mode control is recognized as one of the most efficient
design tools.
Many control designs and applications in the fields of sliding mode control for
overhead cranes have been published in various journals and conference proceed-
ings. In spite of these remarkable advances in this field, most of the current
researchesonlyfocusonsomespecialcontrolapplications,ratherthanasystematic
methodology.
The methodology of hierarchical sliding mode control fills the gap between
sliding mode control and its applications in overhead cranes. Hierarchical sliding
mode control presents several control structures for the sliding mode control
applications in overhead cranes. It is a systematic and effective design tool, which
has both theoretical and practical significances.
This book provides readers with a comprehensive overview of sliding mode
controlforoverheadcranesystemswithdetailedproofsofthefundamentalresults.
Capturingthestructurecharacteristicofoverheadcranes,thisispossibletoachieve
novel control structures by the method of sliding mode control. With the under-
standing that the physical structure of overhead crane systems is dismantled, some
appropriatecontrolstructuresareconstructedandhierarchicalslidingmodecontrol
is developed.
The key feature of hierarchical sliding mode control architectures is the hier-
archical sliding surfaces with the guaranteed stability. By explicitly building the
structure specification into the problem formulation, it is possible to construct and
analyze novel sliding surface structures. With hierarchical sliding mode control
architectures,slidingmotioncanbedepictedbyphaseplaneandthisappearstobe
beneficial both for scientific researches and studies.
vii
viii Preface
The book has six chapters. Each chapter concludes with appendices about
simulation programs.
Chapter1startswithabriefintroductionofoverheadcranesystems.Itproceeds
with a brief historical overview of sliding mode control. A review about overhead
crane control is considered next. This chapter proceeds with analysis of some
typicalcontrolproblemsassociated with sliding mode controlfor overheadcranes.
Chapter 2 investigates modeling of overhead crane systems. First, equations of
motionforsingle-pendulum-typeoverheadcranesarepresented.Then,dynamicsof
double-pendulum-type overhead cranes are described. Uncertainties of the two
models are considered next. The chapter proceeds with analysis of oscillations for
pendulum-type motions according to the linearized models of the two types of
overhead cranes.
Chapter 3 introduces several typical design methods of sliding mode control.
The chapter proceeds with applications of these design methods for overhead
cranes. Some simulation results are demonstrated. MATLAB codes about the
simulations are also available in the appendix part.
Chapter 4presents hierarchical sliding modecontrolfor overheadcranes.Three
hierarchical structures are designed for single-pendulum-type overhead cranes and
onehierarchicalstructureisconsideredfordouble-pendulum-typeoverheadcranes.
For each hierarchical structure, it is proved that both the hierarchical sliding sur-
faces and the whole control system are of asymptotically stability in the sense of
Lyapunov. Numerical simulations illustrate the feasibility of these designed hier-
archical structures. MATLAB codes about the simulations are also attached in the
appendix part.
Chapter 5 extends the method of hierarchical sliding mode control to accom-
modate unmatched uncertainties. It starts with compensator design for the unmat-
ched uncertainties of overhead cranes. The compensator and the controller work
togethertorealizetherobustoverheadcranecontrol.Sincethecompensatordesign
needs a strict assumption, this chapter proceeds with the design of intelligent
compensatorbasedonthehierarchicalstructure.Somesimulationsareconductedto
verifytheeffectivenessofthepresentedcontrolscheme.MATLABcodesaboutthe
simulations are also presented.
Chapter 6 summarizes some of the further extensions not captured within this
book, states the open problems, and the challenges for future thinking.
The book can be used for teaching a graduate-level special-topics course in
sliding mode control.
In this book, all the control algorithms and their programs are described sepa-
rately and classified by the chapter name, which can be run successfully in
MATLAB 7.5.0.342 version or in other more advanced versions. If you have
questions about algorithms and simulation programs, please feel free to contact
Dianwei Qian by E-mail: [e-mail].
Beijing Dianwei Qian
Jianqiang Yi
Acknowledgments
Wewouldliketoacknowledgeanumberofresearchscientists,postdoctoralfellows,
andgraduatestudentswhohaveworkedwithusatdifferenttimesandwhosePh.D.
dissertations and technical papers contribute to the chapters in this book. Among
these, we are especially thankful to Professor Dongbin Zhao of the Institute of
Automation, Chinese Academy of Sciences, for his help and support with crane
control applications. We are grateful to Dr. Wei Wang, Dr. Diantong Liu, and
Dr. Yinxing Hao for numerous useful discussions on the design and the analysis
problemsofthemethodsinthisbookduringtheirstayattheInstituteofAutomation,
Chinese Academy of Sciences, in theinitial stagesofthe theory’s development.
Graduate students Jinrong Guo, BinbinYang, and Hong Liu from the School of
Control and Computer Engineering, North China Electric Power University, con-
tributed to the development of the results in this book while working on their
dissertations.
Atlastbutnotleast, wewouldliketothankourfamiliesfortheirunconditional
dedication, love, and support, and to whom—with our humble gratitude—we
dedicate this book.
Beijing Dianwei Qian
Jianqiang Yi
ix
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Crane Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Overhead Cranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Boom Cranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Tower Cranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Review of Sliding Mode Control. . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Variable Structure Control . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Sliding Mode Control. . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 Equivalent-Control-Based Sliding Mode Control . . . . . . . 11
1.2.4 Chattering Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.5 Sliding Mode Control Design for State Space Model . . . . 15
1.2.6 Robustness Against Uncertainties. . . . . . . . . . . . . . . . . . 17
1.2.7 Sliding Order and Sliding Sets . . . . . . . . . . . . . . . . . . . 22
1.3 A Review of Crane Control. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.1 Open-Loop Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.2 Closed-Loop Control . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.4 Challenges of Sliding Mode-Based Crane Control . . . . . . . . . . . 33
1.4.1 Theoretical Challenges. . . . . . . . . . . . . . . . . . . . . . . . . 33
1.4.2 Practical Challenges. . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
A Matlab Codes to Plot Fig. 1.5a. . . . . . . . . . . . . . . . . . . . . . . 35
B Matlab Codes to Plot Fig. 1.5b. . . . . . . . . . . . . . . . . . . . . . . 35
C Matlab Codes to Plot Fig. 1.7 . . . . . . . . . . . . . . . . . . . . . . . 35
D Simulink Model to Plot Figs. 1.8 and 1.9 . . . . . . . . . . . . . . . 36
E Simulink Model to Plot Figs. 1.10 and 1.11. . . . . . . . . . . . . . 37
F Matlab Codes to Plot Fig. 1.12. . . . . . . . . . . . . . . . . . . . . . . 38
G Simulink Model to Plot Figs. 1.13 and 1.14. . . . . . . . . . . . . . 38
H Simulink Model to Plot Figs. 1.15 and 1.16. . . . . . . . . . . . . . 39
I Simulink Model to Plot Figs. 1.17, 1.18, 1.19 and 1.20 . . . . . . 41
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
xi
xii Contents
2 Crane Mathematic Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1 Modeling of Single-Pendulum-Type Cranes. . . . . . . . . . . . . . . . 51
2.1.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1.2 Model with Uncertainties . . . . . . . . . . . . . . . . . . . . . . . 55
2.1.3 Linearized Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.1.4 Modeling of Double-Pendulum-Type Cranes. . . . . . . . . . 57
2.1.5 Model with Uncertainties . . . . . . . . . . . . . . . . . . . . . . . 63
2.1.6 Linearized Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
A Matlab Codes to Plot Fig. 2.2 . . . . . . . . . . . . . . . . . . . . . . . 65
B Matlab Codes to Plot Fig. 2.4 . . . . . . . . . . . . . . . . . . . . . . . 66
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3 Overhead Crane Control by Sliding Mode Methods. . . . . . . . . . . . 67
3.1 Problem Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2 First-Order Sliding Mode Control. . . . . . . . . . . . . . . . . . . . . . . 68
3.2.1 Control Design of Single-Pendulum-Type
Overhead Cranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 Stability Analysis of the Single-Pendulum-Type Crane
Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2.3 Simulations of Nominal Single-Pendulum-Type
Overhead Cranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2.4 Simulations of Uncertain Single-Pendulum-Type
Overhead Cranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2.5 Extensions of Double-Pendulum-Type
Overhead Cranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3 Integral Sliding Mode Control. . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.1 Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.2 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3.3 Simulations of Single-Pendulum-Type Cranes
by ISMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.4 Simulations of Uncertain Single-Pendulum-Type
Cranes by ISMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4 Terminal Sliding Mode Control. . . . . . . . . . . . . . . . . . . . . . . . 86
3.4.1 Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4.2 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4.3 Simulations of Single-Pendulum-Type Cranes by TSM. . . 90
3.4.4 Simulations of Uncertain Single-Pendulum-Type Cranes
by TSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.5 Second-Order Sliding Mode Control. . . . . . . . . . . . . . . . . . . . . 93
3.5.1 Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.5.2 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94