Table Of ContentPower Systems
F. Khorrami . P. Krishnamurthy . H. Melkote
Modeling and Adaptive Nonlinear Control of Electric Motors
Springer-Verlag Berlin Heidelberg GmbH
ONLINE LlBRARY
Engineering
http://www.springer.de/engine/
F. Khorrami . P. Krishnamurthy . H. Melkote
Modeling and Adaptive
Nonlinear Control
of Electric Motors
With 184 Figures
Springer
Prof. Farshad Khorrami
Prashanth Krislmamurthy
Dr. Hemant Melkote
ControllRobotics Research Laboratory (CRRL)
Department ofElectrical and Computer Engineering
Polytechnic University
Six Metrotech Center
Brooklyn, NY 11201
USA
E-mail: [email protected]
[email protected]
[email protected]
ISBN 978-3-642-05667-3 ISBN 978-3-662-08788-6 (eBook)
DOI 10.1007/978-3-662-08788-6
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Originally published by Springer-Verlag Berlin Heidelberg New York in 2003
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To my wife, Brenda
Farshad Khorrami
To my parents
Prashanth Krishnamurthy
To my parents
H emant M elkote
Preface
Electromechanical actuators have been utilized in many applications from horne
appliances to sophisticated guidance and control systems. Various electrome
chanical actuators such as electric motors, hydraulic and pneumatic actua
tors, smart materials (e.g., piezoceramics, magnetorestrictive materials, shape
memory alloys, electrorheological fluids, etc.) have been considered. Modeling
and control design for such actuators have been and are being pursued to achieve
a higher level of performance. In this book, we consider modeling and control de
sign of electric motors; namely step motors, brushless DC motors, and induction
motors. These electrical motors are used in many applications; some requiring a
high level of accuracy and performance such as machines used in the electronics
industry for assembly or semiconductor wafer probing and inspection.
It is the intent of this book to focus on recent advances on feedback control
designs for various types of electric motors, with a slight emphasis on stepper
motors. For this purpose, we explore modeling of these devices to the extent
needed to provide a high-performance controller but at the same time amenable
to model-based nonlinear designs. We will also focus on more recent efforts
on nonlinear and adaptive controllers to derive robust and high-performance
feedback controllers, which are essential for applications that require high per
formance and accuracies. It should also be pointed out that once good models
of actuators are developed, controllers should utilize the model as much as pos
sible to achieve high performance and then for robustness purposes, adaptive
robust nonlinear controllers should be added to the controlled system. As will
be shown, in many cases, the adaptive robust nonlinear controller on its own
achieves a reasonably good performance without requiring the exact knowledge
of motor parameters. Therefore, the designer needs to consider that the pro
posed robust adaptive nonlinear controllers need not be augmented with an
inner-Ioop controller that utilizes a tight knowledge of motor parameters. An
other important point is that although we have considered re cent adaptive and
nonlinear control design methodologies, by no means is it implied that if in cer
tain applications, linear or classical designs (such as PID controllers augmented
by notch filters and feedforward terms) perform weIl, one should still pursue the
techniques presented in this book. It is needless to say that many machines and
systems do operate and achieve the required performance via well-designed and
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carefully tuned classical controllers. But eventually, it is hoped that the advo
cated robust and adaptive designs will become standard "universal" controllers
with minimal need for fine tuning of control parameters before and after release
of a product.
A design feature that we pursue in the book is sensorless (output feedback)
control of various motors. In this vein, we consider controllers which utilize var
ious subsets of states as, for instance, the position and velocity, only position,
position and currents, etc. A particular case that we have not covered in this
book is having only current measurements to achieve either position or veloc
ity control. Various approaches including utilization of back emf for position
estimation, zero crossing techniques, open-loop integration of motor dynamics,
etc., have been proposed in the literature and some references to these works
are provided in the appropriate chapters in this book.
Organization of the book
Chap. 1 provides an introduction to various types of motors and the basic prac
tical considerations while employing them in applications. Detailed explanation
of the Sawyer motor (dual-axis linear stepper motor) is deferred to Chap. 2.
Appendix A contains some of the fundamental AC machine concepts.
Chap. 3 develops detailed mathematical models for stepper motors. Vari
ous nonidealities and perturbations that might be encountered in practice are
characterized. Modeling of brushless DC motors and induction motors are post
poned to Chaps. 11 and 12. Furthermore, the Lagrangian approach for deriving
models of various motors is also provided in Chap. 14 where passivity-based
results are given. The Direct-Quadrature (DQ) transformation, a common tool
used to simplify the dynamics of electromechanical systems is introduced. A
more detailed explanation of the DQ transformation and its extensions is con
tained in Appendix B. Although the modeling has been pursued to a reasonable
detail for various motors, it was done with control design in mind; therefore,
yielding mathematical models amenable to control design.
The remaining chapters present control design issues for various motors.
Chap. 4 describes the popular open-loop control techniques of stepping and
micro-stepping utilized for step motors. Thereafter, feedback controllers are
considered. To this extent, state feedback and output feedback (i.e., partial state
measurement) solutions are sought. To make the book somewhat self-contained,
Chaps. 5 and 6 and Appendices D, E, F, and G contain important nonlinear
design tools utilized throughout this book. Chap. 5 introduces the concepts
of relative degree, feedback linearization, system inversion, and zero dynamics.
Furthermore, algorithms for stable system inversion are given in Appendix D.
Application of feedback linearization to stepper motors are given in this chapter
and results for brushless DC and induction motors are postponed to Chaps. 11
and 12. In Chap. 6 and Appendices Fand G, the backstepping technique and its
iii
variants (i.e., tuning functions, robust backstepping, and adaptive backstepping)
and the nonlinear small gain results in conjunction with input-ta-state stability
are presented. For completeness, Lyapunov stability and results are given in
Appendix E. The aforementioned chapters are intended as a quick tutorial for
the reader and proofs are omitted (only constructive proofs are included) and
several worked examples are provided.
The aforementioned robust adaptive nonlinear control design methodologies
are presented in Chap. 7 for various types of stepp er motors under the as
sumption that state variables (i.e., rotor position, rotor velocity, and currents)
are available for feedback. Output feedback solutions are presented in Chaps.
8-10. Chap. 8 includes current level control (the fast electrical dynamics are
neglected) utilizing only position measurements. Chap. 9 presents voltage
level control using position and velo city measurements. Chap. 10 provides a
technique to eliminate velocity measurements. Control of brushless DC motors
whose behavior is similar to that of the stepper motors is briefly explained in
Chap. 11.
Chaps. 12 and 13 are exclusively devoted to modeling and control of induc
ti on motors. Various control design approaches such as Field Oriented Control
(FOC), a nonlinear extension of FOC, input-output decoupling (and dynamic
feedback linearization), and Direct Torque Control (DTC) are given in Chap. 12.
Furthermore, since flux measurements are not normally available in induction
motors, flux observers and output feedback design based on these observers are
given in Chap. 12. The adaptive nonlinear designs for induction motors are
pursued in Chap. 13. These designs include both state and output feedback
solutions.
Another important approach to control design for various motors is the na
tion of passivation. Therefore, energy-based derivation of models of electric
motors and the concept of passivity and some of the theoretical nonlinear re
sults are introduced in Chap. 14. The passivity-based control designs are then
applied to the general Euler-Lagrange systems that include motor dynamics.
Applications to all types of electric motors are then presented in Chap. 14.
Finally, two important issues in motor control designs are tackled in the
last two chapters as generic items on their own and may be incorporated in
other control designs with some effort. These two issues are: torque ripple
minimization (Chap. 15) and friction compensation (Chap. 16). Appendix C
treats field weakening, a method for designing current references to maximize
torque in the presence of current and voltage constraints.
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The first author would like to acknowledge the effort and prior work by former
students on these topics and the two students who are the coauthors of this book.
I also would like to thank several of my colleagues at Brooklyn Poly that I have
interacted with over the years: Profs. J.J. Bongiorno, Jr., P. Sarachik, D. Youla,
iv
B. Friedland (currently at NJIT), L. Shaw, Z.P. Jiang, Z. Pan, V. Kapila, M. Tai,
C. Georgakis, W. Blesser, S. Nourbakhsh, and P. Riseborough. I also would
like to thank Profs. Ü. Özgüner, P.V. Kokotovic, H. Khalil, M.W. Spong,
T.J. Tarn, and Dr. D. Repperger for their support over the years. I would
like to thank Profs. A. Iftar, L. Acar, E. Barbieri, A. Tzes, J. Rastegar, and
Dr. D. Schoenwald for their friendship and intellectual discussions over the years.
Finally, I also would like to thank Profs. B. Paden, D. Dawson, R. Ortega,
M. Bodson, and J. Chiasson for looking over a draft of this book, and for being
the originators of several motor control results treated in this book.
The first author also acknowledges support of the National Science Founda
tion, Army Research Office, and several corporations that have made this work
possible. I would also like to especially thank Drs. G. Anderson and J. Chan
dra of the Army Research Office and Drs. N. Coleman and M. Mattice of the
Picatinny Army Arsenal for their interest and support of our efforts.
Lastly, but not least, I also would like to acknowledge my dear wife, Brenda,
who has been a constant source of inspiration and encouragement to get things
done and putting up with my many late night hours. Without her, many things
would not have been possible. I also would like to thank my sister, Fereshteh,
my brothers, Jamshid and Farshid, and most importantly, my mother, Mahin,
and my late father, Hadi, who have supported and helped me throughout my
life. Their help and support has been and continues to be invaluable.
The second author wishes to express his deep gratitude to his parents, Kr
ishnamurthy and Usha Murthy, and to his brother Ravi Murthy, for all their
support and encouragement through the years. He would also like to thank
Z. Wang and R.S. Chandra for many enlightening discussions.
The third author would like to thank the members of the ControljRobotics
Research Laboratory, namely, S. Jain, I. Zeinoun, J. Lewinsohn, S. Sankara
narayanan, N. Ahmad, Z. Wang, and I. Cherepinsky with whom I had the
opportunity to interact and participate in stimulating discussions.
Farshad Khorrami
Prashanth Krishnamurthy
Hemant Melkote
Brooklyn, NY, April 2003
