MODELING AND SENSORLESS CONTROL OF SOLENOIDAL ACTUATORS DISSERTATION ...

157 Pages·2003·2.73 MB·English

MODELING AND SENSORLESS CONTROL
OF
SOLENOIDAL ACTUATORS

DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy in the Graduate
School of The Ohio State University

By
Peter Bejoum Eyabi, M.S.
*****
The Ohio State University
2003

Dissertation Committee:
Prof. Gregory Washington, Adviser Approved by
Prof. Vadim Utkin
Prof. Rama Yedavalli Adviser
Mechanical Engineering Graduate Program

ABSTRACT

Electromagnetic actuators (EMA), which incorporate solenoids, are increasingly
becoming the actuator of choice in industry lately, due to their ruggedness, low cost, and
relative ease of control. Latest applications of solenoid based EMA’s include
Electromagnetic Valve Actuation (EMV) systems. This application presents challenges
that require the improvement of the dynamic characteristics of the EMA. Some of these
problems include, but are not limited to, quiet operation, reduced bounce, less energy
consumption, trajectory shaping with a minimum number of measurements, and high
actuation speeds. These demands, coupled with the nonlinear dynamics of the EMA,
make the use of classical control strategies a less attractive option. A possible attempt to
arrive at intermediate solutions to these problems should include some amount of model
based robust control strategy. This includes the development of an accurate but simple
control based model and a robust digital control strategy.
In this study a basic nonlinear model for a solenoidal EMA will be developed, and
validated, which will include bounce, leakage inductance and temperature effects. The
model is formulated for the linear legion (region before saturation) of the actuator
dynamics, but validation will include operation in the saturation region as well. This
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effectively means that a nonlinear model will be developed that is simple but accurate
enough for control, neglecting hysteresis and magnetic saturation.
Next, an EMV will be designed and built. A nonlinear model for the EMV will be
developed and validated. This model will include secondary nonlinearities like saturation,
hysteresis, mutual inductance and bounce. In this study a variable that is easier and
cheaper to measure, current, will be measured and the information of the position and
velocity variables will be estimated from this measurement. The position estimate will be
used for control. This is called Sensorless Control. The control objective is to reduce
impact noise and seating velocity. The sliding mode methodology will be used here since
it is nonlinear, robust to uncertainties, and easier to design and implement. The estimation
and control algorithms will be validated in simulation and experimentally for the EMA
and EMV, respectively.

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Dedicated to:

“Pater noster, qui est in caeli”

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ACKNOWLEDGMENTS

I am greatly thankful to my advisor, Prof. Gregory Washington who was there for
me when I really needed someone. I also do appreciate his kindness, selflessness and
patience. I just couldn’t have done it without his persistent guidance.
I am also very grateful to the General Motors Powertrain Systems Research Lab
for giving me the opportunity of a lifetime to work with them. My research and
dissertation would not have been possible without the funding from The Powertrain
Systems Research Lab. In particular, I am very grateful to Dr. Hazeem Ezat, Dr. Patrick
Usoro, and Dr. Zongxuan Sun of the Powertrain Systems Lab, for their support, the
confidence and trust they had in me as a student.
I would also like to thank some of my professors who have inspired me and have
greatly contributed to my success in graduate school. This includes Prof. Vadim Utkin, a
great intellectual, who has passed on a lot of knowledge to me and to a lot of other
students I know, to whom we shall forever be grateful. There is my mentor Prof. Ji Wang
of San Jose State University, California, who launched me into the area of controls, and
of course my advisor, Prof Washington, from whom I learnt a lot about “the way things
are supposed to be done”.
I am grateful to Joe West, Gary Gardner, Keith Rogers and Jerry Kingzett of the
Department of Mechanical Engineering, for their technical support.
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VITA

June, 1988…………………B. Eng. (Hons.), Cranfield Institute of Technology, UK

December, 1998…………..MS Mechanical Engineering, San Jose State University,
California

January, 1999-present…….Graduate Research Assistant, The Ohio State University.

FIELDS OF STUDY

Major Field: Mechanical Engineering

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TABLE OF CONTENTS

Page
Abstract………………………………………………………………………………… ii
Dedication……………………………………………………………………………… iv
Acknowledgments……………………………………………………………………… v
Vita……………………………………………………………………………………... vi
List of Tables…………………………………………………………………………... x
List of Figures………………………………………………………………………….. xi
Chapters:
1. Introduction………………………………………………………………………… 1
2. Literature Review…………………………………………………………………... 6
3. Theory of Sliding Mode………………………………………….………………… 14
3.1 Introduction…………..……………………………………………………… 14
3.2 Sliding Mode Estimation Theory………………..…………………………... 15
3.3 Sliding Mode Observers…………………..………………………………… 16
3.4 System Observability………………………..………………………….…… 20
3.5 Theory Of Sliding Mode Control……..……………………………………... 22
4. Thermal Model of EMA…………………………………………………………… 26
4.1 Heat Generation (E )……………..………………………………………... 30
gen
4.2 Energy Loss (E )……………..………………………………………..…… 30
out
4.3 Energy Stored (E )…………………..………………………………………. 33
st
4.4 Computation of Power Losses (i2R )………………………………..….…… 35
o
4.5 Thermal Model Validation……………………………………..……....……. 42
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5. Dynamic Model Of The EMA……………………………………………………... 44
5.1 Model Validation…………………..………………………………………... 54
5.2 Sliding Mode Observer For EMA……………..…………………..………… 55
5.3 Observer Based Sliding Mode Controller…………..……………………….. 59
5.4 Simulation Results………..………………………………………….……… 64
5.5 Experimental Setup………..………………………………………………… 67
5.6 Experimental Results…………………..……………………………….…… 68
6. Electromagnetic Valve Actuator Model…………………………………………... 72
6.1 Mechanical Model…………………..………………………………….…… 75
6.2 Electrical Model……………..………………………………………….…… 78
6.3 Magnetic Model……………..………………………………………….…… 80
6.4 Experimental Calibration Of Electromagnet……………..…………………. 82
6.5 Experimental Equipment…………..………………………………………... 82
6.6 Experimental Procedure……..……………………………………….……… 83
6.7 Dynamic Model Validation………………………………………………….. 84
6.71 Magnetic Subsystem……..…………………………………………... 84
6.72 Electrical Subsystem……..…………………………………………... 87
6.73 Mechanical Subsystem……………………..………………………… 90
6.74 EMV System………..………………………………………………... 93
6.8 Sensorless Observer Design For EMV……………..……………………….. 95
6.81 Nonlinear Observability Theory……………………..………………. 95
6.82 Sensorless Sliding Mode Observer……..……………………………. 98
6.9 Sensorless Controller Design……..………..……………………………….. 100
6.91 Sliding Mode Controller…………..…………………………………. 101
6.10 Simulation Results…………………………………………………………... 105
6.11 Experimental Results………………………………………………………... 111
6.11.1 Equipment………………………………………………………….. 111
6.11.2 Open Loop Control…………………………………………………. 112
6.11.3 Closed Loop Control……………………………………………….. 113
7. Conclusions And Future Work……..……………………………………………… 118
7.1 Electromagnetic Actuator………..………………………………………….. 118
7.2 Electromagnetic Valve Actuator……..……………………………………… 119
References……………………………………………………………………………… 125
Appendix……………………………………………………………………………….. 130
A.1 Derivation Of Leakage Inductance…………………………….………..….. 130
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A.2 Simulation Results…………..……………………………………………... 132
A.3 Design of Electromagnetic Valve Actuators…….………………..……….. 133
A.3.1 Mechanical Design………..……………………………………….. 133
A.3.2 Electrical Design………..…………..……………………………... 134
A.3.3 Magnetic Design…..………..……………………………………... 136
A.4 Glossary of Symbols………………………..…………..………….……….. 141

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