DTIC ADA439797: Control of Smart Actuators

206 Pages·7.3 MB·English

by  Defense Technical Information Center

PH.D.
THESIS
Control of Smart Actuators
by Xiaobo Tan
Advisor: John S. Baras and P. S. Krishnaprasad
CDCSS PhD 2002-1
(ISR PhD 2002-8)
The Center for Dynamics and Control of Smart Structures (CDCSS) is a joint Harvard University, Boston University, Unriversity of Maryland cen tel;
supported by the Army Research Office under the ODDR&E MURI97 Program Grant No. DAAG55-97-1-0114 (through Harvard University). This
document is a technical report in the CDCSS series originatinga t the University of Maryland.
Web site http://wwwisrund.edui/CDCSS/cdcsshtml
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ABSTRACT
Title of Dissertation: Control of Smart Actuators
Xiaobo Tan, Doctor of Philosophy, 2002
Dissertation directed by: Professor John S. Baras
Professor P. S. Krishnaprasad
Department of Electrical and Computer Engineering
Hysteresis in smart materials hinders wider applicability of such materials in
actuators and sensors. In this dissertation we study modeling, identification and
control of hysteresis in smart actuators. While the approaches are applicable to
control of a wide class of smart actuators, we illustrate the ideas through the
example of controlling a magnetostrictive actuator.
Hysteresis exhibited by magnetostrictive actuators is rate-independent when
the input frequency is low and we can model it by a Preisach operator. It becomes
rate-dependent when the input frequency gets high due to the eddy current effect
and the magnetoelastic dynamics. In this case, we propose a new dynamic hys-
teresis model, consisting of a Preisach operator coupled to an ordinary differential
equation in an unusual way. We establish its well-posedness and study its various
systen-theoretic properties. Existence of periodic solutions under periodic forcing
is proved. Algorithms for simulation of the model are also studied. Parameter
identification methods for both the Preisach operator and the dynamic model are
investigated.
We pursue the problem of hysteresis control along three (lifferent but connected
paths: inverse control, robust control and optimal control.
The idea of inverse control is to construct an inverse operator to cancel out
the hysteretic nonlinearity. Efficient inversion schemes are proposed for both the
Preisach model and the dynamic hysteresis model. We also formulate and study
a novel inversion problem, called the value inversion problem, and apply it to
micro-positioning control.
Inverse compensation is open-loop in nature and therefore susceptible to model
uncertainties and to errors introduced in the inverse schemes. e propose a robust
control framework for smart actuators by combining inverse compensation with
robust control techniques. e present systematic controller design methods which
guarantee robust stability and robust trajectory tracking while taking actuator
saturation into account.
Finally we study optimal control of hysteresis in smart actuators based on a low
dimensional hysteresis model. We characterize the value function as the (unique)
viscosity solution to a Hamilton-Jacobi-Bellman equation of a hybrid form, and
provide a numerical scheme to approximate the solution.
Control of Smart Actuators
by
Xiaobo Tan
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulflillment
of the requirements for the degree of
Doctor of Philosophy
2002
Advisory Committee:
Professor John S. Baras, Chairman / Advisor
Professor P. S. Krishnaprasad, Coadvisor
Professor Reza Ghodssi
Professor Isaak Mayergoyz
Professor Stuart Antman
O Copyrighit by
Xiaobo Tan
2002
DEDICATION
1To ]\oni andAI Dad, andl my wife Youyu
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ACKNOWLEDGEMENTS
It has been my privilege to have both Professor John S. Baras and Professor
P. S. Krishnaprasad as my advisors. I am grateful to them for their thoughtful
guidance and enthusiastic encouragement. They inspired me with their vision and
expertise during the course of my PhD study. Apart from providing technical
directions, they have also offered me with invaluable advices on how to improve
myself as a researcher.
I would like to thank Professor Ramakrishnan Venkataraman, who led me into
the area of hysteresis modeling and control. Venkat also helped me a lot in my
modeling effort through numerous discussions.
I thank Professor Reza Ghodssi, Professor Isaak Mayergoyz and Professor Stu-
art Antman for kindly joining the advisory committee and providing many insight-
fuil suggestions and comments. I also thank Professor Ghodssi for his advice on
my job search.
I would like to thank Professor Andre Tits for taking time to review my work
and offering me useful comments. I also benefited a lot from his robust control
course, which enabled me to successfu lly accomplish the work in Chapter 4.
I gratefully acknowledge the inspiring discussions with Professor Martin Brokate
on the well-posedness of the dynamic hysteresis model during the Hysteresis and
l\icromagnetics M\lo(eling Symposium (HAIAI'01) at the George \V\ashington Uni-
versity.
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I am grateful to my colleagues and friends at Maryland who have offered help
in various ways: Sean Andersson, Fumin Zhang, Dr. George Kantor, Dr. Andrew
Newman, Dr. Amir Handzel, Dr. Eric Justh, Dr. Sameer Joshi, Jia-Shiang Jou,
Chang Zhang, Sudhir Varma, Maben Rabi, Huigang Chen, Zhu Han, Dr. Hongjun
Li, Shah-An Yang, Vijay Bharadwaj and many others. Special thanks are due to
Andrew for creating the thesis template, which makes thesis writing much easier
and more pleasant.
I also want to thank the computing and administrative staff of ISR for their
assistance during my study and life here. Special thanks are due to Althia Kirlew,
Pamela White, Jean Lafonta, Trevor Vaughan and Margaret Jayant.
I am gratefufl for the financial support of my studies and research by the Army
Research Office under the ODDRk-E AIURI97 Program Grant No. DAAG55-97-
1-0114 to the Center for Dynamics and Control of Smart Structures (through
Harvard University), and from the Lockheed Martin Chair endowment funds.
Last, but certainly not the least, I am deeply indebted to my wife, Youyu Feng,
for her constant love, suI)port and encouragement.
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TABLE OF CONTENTS
List of Figures viii
1 Introduction 1
1.1 Contributions of the Dissertation.. ......................... 3
1.1.1 Modeling and control of hysteresis based on the Preisach
o)erator ......... ............................. 4
1.1.2 Optimal control of hysteresis based on the low dimensional
model .......... .............................. 5
1.2 Organization of the Dissertation. .......................... 6
2 Identification and Approximate Inversion of the Preisach Opera-
tor 7
2.1 Introduction to the Preisach Operator ..... ................ 7
2.1.1 The Preisach operator in (), a ) coordinates ........... 8
2.1.2 The Preisach operator in (r, s) coordinates ............. 11
2.1.3 Properties of the Preisach operator ................. 13
2.2 Identification of the Preisach Measure ..................... 14
2.2.1 Review of measure identification methods ............. 14
2.2.2 An identification scheme. ........................ 16
2.2.3 Experimental results .......................... 18
2.3 Inversion of the Preisach Operator ....................... 22
2.3.1 Inversion of the discretized Preisach operator ............ 24
2.3.2 Inversion of the Preisach operator with nonsingular measure 27
2.4 The Value Inversion Problem and Its Application to Micro-Positioning
Control .......... ................................. 31
2.4. 1 The vale inversion I)roblen ..... .................. 31
2.4.2 A state sI)ace reduction scheme. .................... 36
2.4.3 Experiniental results .......................... .41
3 A Dynamic Model for Magnetostrictive Hysteresis 44
3.1 A Dynamic Hysteresis Model ..... ..................... 46
3.2 Well-posedness of the Model ........................... 48
3.2.1 Existence and uniqueness ..... ................... 48
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