Feedback and Control for Everyone

305 Pages·2010·5.034 MB·English

by  Albertos Pérez, P., Mareels, Iven

Pedro Albertos
Iven Mareels
(Authors)
Feedback and Control for Everyone
Pedro Albertos
Iven Mareels
(Authors)
Feedback and Control
for Everyone
With 158 Figures
Authors
Prof. Dr. Pedro Albertos
Department of Systems Engineering and Control
University Politecnica Valencia
POB 22012
46071 Valencia
Spain
Prof. Dr. ir Iven Mareels
Melbourne School of Engineering
The University of Melbourne
Melbourne Vic 3010
Australia
ISBN 978-3-642-03445-9
Library of Congress Control Number: 2009941651
© Springer-Verlag Berlin Heidelberg 2010
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To our friends, teachers and students
Preface
Vertrouwen hebben is goed, in controle zijn is beter!
Confidence is good, but to be in control is better!
La confianza está bien, ¡pero el control es mejor…!
La información suele ser buena, ¡la realimentación es esencial!
Information is important but feedback is essential!
Informatie is belangrijk, maar feedback is essentieel!
Our journey to write a general introduction to control and feedback started with the
realisation that in our chosen field of study the proponents have taken little time to
project the main ideas outside the community of the initiated. We are constantly re-
minded of the fact that there is no general awareness of control engineering, or con-
trol technology, despite its ubiquity when we try to introduce ourselves as control
engineers. Invariably this leads to A what engineer? response. We suspect that most
control engineers do not even try to introduce themselves as such. It certainly is a
poor communication starter.
Colleagues, friends, collaborators often ask rather natural questions like So, what
do you study in control? Is there a non-specialist introduction to the field? Can I read
something to get a feel about this field of systems theory? What questions do you try to
answer? What are the key results? In reply we can point to a wealth of technical litera-
ture, rooted in mathematics, quite acceptable to some engineers or mathematics gradu-
ates, but rather too formidable a hurdle for most. Our apologetic replies, complemented
with the odd reference to the history of the field or some systems philosophy, invari-
ably raises eyebrows, and evokes surprise, disbelief and disapproval.
But how do you write about a theory of everything that is applied everywhere?
Clearly abstraction is the way, but abstraction with precision is for engineers (like we
are) a one way street into mathematics.
The task appears too hard. Certainly we can easily understand why so little has
been done in trying to make control theory and control engineering more widely
accessible. Indeed, excuses are all too easy to find.
(cid:1) Someone else, better qualified, should/will do it.
(cid:1) Our peers will disapprove of our sloppiness, and others may find the material still
too forbidding. It is a laudable quest, but one with more opportunity for failure
than success.
(cid:1) We possibly cannot do this justice, the field is just too big, and still too rapidly
moving, too immature. The whole idea is better postponed.
(cid:1) Doing research is more important, there is so much that still needs to be done,
and can be done, and at least in doing research we are pushing the boundaries of
knowledge.
Yet, with the encouragement of a few friends, and we would like to single out Petar
Kokotovic in particular, and the generous support of our families, we finally ran out
VIII Preface
of excuses and challenged ourselves sufficiently to start writing about control, for
everyone. Not because we are convinced that we can do this well, but rather because
it does matter. Control theory and control engineering is instrumental in the engi-
neered world, and feedback is as fundamental in our natural world as in our techno-
logical world. Feedback and control deserve a larger audience.
How and Where This Book Was Written
Our book project stretches out over 5 years, and progressed like two steps forward,
one backward, two steps forward, one backward. Talking with our common friend,
Karl J. Åström about the way to reach young people (kids, grandsons, children) with
complicated matters, we found a challenging book The Way Life Works (Hoagland
and Dodson 1995) showing it was possible to transmit key concepts with simple lan-
guage. The authors of this book use a lot of illustrations, which we were not able to
do, but the idea was caught and we started to work on it.
Concentrated periods away from our daily duties (research, teaching, management,
the usual stuff, all in the familiar environment) were essential to bringing this book
to life. We spent weeks at a time, locked away from friends and family and colleagues.
In unfamiliar scholarly scenarios, liberated from the internet and mobile telephony,
we could focus on writing, and rewriting, but most importantly criticizing our work:
“Of course there is too much mathematics”. “No, this is far too sloppy”. “You cannot
possibly see the subtle points that we ought to make here”. “How on earth can any-
body understand what we want to say here?”. “Clearly this goes far too deep”. “Sorry
but this is too superficial”. “There is no substance left here”.
Thus, we needed to constantly challenge ourselves that the book is intended for
everyone, as it all too easy to slip back into our familiar territory. In this sense, we
are grateful to a number of high school students and some of our own second year
students who voluntarily read some chapters and provided invaluable feedback. As
a matter of fact, we introduced additional examples and further explanations after
the pre-reading of these young “collaborators”. Thanks to Miguel, as well as Sergio,
Carmen, Tamara, Pablo, Miguel Angel, Felix, Saul, Ismael, Pura, Alvaro, Mercedes and
many others.
In this way, we spent time in Melbourne, Valencia, Prague, Seville, Singapore, San
Diego, Athens and finally Melbourne again to put the capstone down. To our friends
who hosted us, the most unsociable collaborators ever, we owe a great debt of grati-
tude. Thank you.
What to Expect
If you expect to find elegant mathematics, unambiguously stating what control is all
about, and what its great achievements are, do not continue any further. You can lay
the book down right now. We have abandoned any attempt for precision, generality
or completeness. Brevity excludes both precision and generality, and our lack of knowl-
edge makes it impossible to be complete. Despite the fact simplicity wins over preci-
sion, we never try to mislead either, where precision matters and details lack, it will
hopefully be apparent. Our main aim, though, is to provide intuition, and motivation,
Preface IX
and convey some of the beauty of the key ideas as well as the impact of the engineer-
ing achievements. If we perhaps excite a few to go on and read or study the technical
literature, that would be a welcome bonus.
If you expect to find no mathematics at all, sorry we will disappoint you too. We
valiantly did try to eliminate most mathematics, but clearly control and systems theory
is a mathematical field. Its generality demands all the abstraction mathematics can
muster, and to rip it all out, would be to destroy its very heart. The use of mathematics
is really limited, and most of the text does not rely on it at all. In a few places we did
not shy away from the occasional equation, and mathematical expressions, but most
of that can either be skipped or glanced over in a first reading, and normally they are
accompanied with text to explain what the equations say. For those, though, who get
excited as much as ourselves, and are willing to master the ideas behind signals and
systems, or even push its boundaries, some mathematical sophistication and compu-
tational expertise will have to become a part of life. The journey is not without effort,
but the rewards are substantial.
It is our intention that most of the book should be accessible with a basic under-
standing of typical high school calculus. Also, hopefully it is sufficiently self-contained
to allow the reader who wishes to skip the more mathematical bits, to do so and go
on with the narrative without penalty. We will let you be the judge.
Besides ideas, we also want to illustrate through examples some of the technology,
what it is capable of, and where it has been applied and where it is headed. After all
creating technology is what engineers1 do.
How to read this book
Essentially our exposition is a narrative using intuition and simple examples to con-
vey what matters, and what does not in this field.
You can read the different chapters almost in a random way. In each one of them
you will find (we hope) suggestive ideas without the need of much background. Nev-
ertheless, the ideas have been developed in a particular order that we believe will
make it easier to follow the narrative. The first chapter is similar to a summary of the
book, the content of which is worked over in the following chapters. Some of the “re-
viewers” preferred that we first define a concept and then illustrate it through ex-
amples and applications. We decided against this early on in the book, in Chap. 3 to
be precise, and walked through a number of different examples where the presence of
feedback and control is of undisputed importance.
The introductory Chap. 1 develops a feel for the generality of the field, and estab-
lishes some common vocabulary. In some sense, most of the ideas and concepts are
repeated and largely described afterwards. The examples, used here, are revisited from
different angles throughout the remainder of the book. At the end of this chapter, like
at the end of every chapter, there is a section highlighting the main points and pro-
viding hints for further reading and study.
1 The word engineer comes from the Latin ingenerare, a word that can be translated as to create.
X Preface
In Chap. 2, the idea of analogy is developed, both for signals and systems. Analo-
gies are in our opinion at the heart of the abstraction so pervasively used in the study
of signals and systems. The aim is to convince everyone that it is actually possible to
build a meaningful theory of everything, applicable to anything, as long as the limi-
tations are clear. Analogy is certainly not exclusively the domain of systems theory. In
fact, the notion of analogy is rather more common in psychology and the social sci-
ences as a methodology to progressively extend concepts from a simple setting to a
more complicated yet in some sense analogous scenario.
In Chap. 3 we describe some processes where feedback and control are essential.
The engineered examples we have chosen are a manufacturing process for ceramic
tiles, a car wash, a large scale distribution system for irrigation water and a radio
astronomy antenna. We concentrate on what is measured, how this information is
used to decide what to do next, and how decisions are then executed and determine
the future behavior of the process. If sensing, reasoning, computing, deciding and
actuation are done automatically, we are dealing with an automatic control system. If
control is reacting to measurements, feedback is at work. Many human-made control
systems are inspired by nature and feedback is prevalent in all natural processes. In
the human body, all homeostasis is feedback-based. Most psychological and social
processes directly or indirectly use the advantages of feedback.
The two basic ingredients we need to understand feedback are signals and
systems; signals, because feedback must measure before it can take action, and
systems because feedback is used to influence their behavior. Moreover, both in-
gredients are interlaced: whenever we refer to systems we refer to something that
can create or modify a signal. In Chap. 4 signals are presented. What is a signal?
Which properties do they have? How can we represent them? How do we process
them? As usual, we use suggestive examples to communicate the message, but every-
one will be able to identify a large number of signals in their direct environment:
sounds (music, noise, birds chants), sensations (temperature, humidity, light, smell)
and many other physical or physiological quantities (force, speed, displacement,
weight, humor, tiredness, concentration). As quantitative reasoning is at the core of
feedback, the topic is after all approached from an engineering discipline point of
view, the mathematical representation of signals play an important role. Some math-
ematics is used. Nevertheless, the narrative and the reasoning is never based on
mathematical formalism.
Central to systems theory and to feedback is the concept of models. The aim of
Chap. 5 is to present the basic ideas and tools used in dealing with systems and their
models. A model is a convenient representation of a real process of interest, conve-
nient will often mean “it computes”. We mainly consider simple examples to illustrate
the power of modeling. We briefly discuss how to arrive at a model and pay some
attention to structural properties.
Some basic system properties that matter in a feedback context, namely stability,
sensitivity and robustness are presented all too briefly in Chap. 6. These concepts
are the subject of much and rigorous research. In fact there is no end to studying
systems theory. After all it is the theory of everything, so job security will never be an
issue. In particular when dealing with large scale or complex systems the theory is
really in its infancy.
Preface XI
Chapter 7 deals with the central topic of the book. At this point in the book, most
of the ideas about feedback have already been introduced and here, the advantages
and disadvantages of feedback are (re)visited and summarized. It will transpire that
feedback can be used as an advantage to change the behavior of systems in a dramatic
way, despite the fact that it actually imposes constraints on the realm of possibilities.
It is important to emphasize that some form of control or feedback is at work in
any system that performs well. The control subsystem and the possible structures for
interaction with control are the topics in Chap. 8. Here you will read about the many
different ways in which control can interface with a process, and how it alters the
usefulness and capability of control. We will lead you to the conclusion that the best
performance can be achieved when process and control are considered together, in an
integrated way, from the very beginning of design.
Technology is an important driver in the development of feedback, and in turn
feedback is a major driver of technology. The different components that make up the
control subsystem, sensors, communication, filters, actuators, computers and their
software are presented in Chap. 9. This chapter introduces some of the present hard-
ware and software options available to implement control. No doubt, the content of
this chapter will soon belong to the realm of archeology.
Conception, design and testing come next. There are a number of design and vali-
dation methods supported by computational tools available to approach control de-
sign. Some of them are outlined in Chap. 10. The variety of models, goals, constraints
and signals involved in control design make it impossible to enumerate all the op-
tions. There is still much more work to be done in this arena. Control design requires
a lot of creativity and ingenuity, and there is no single recipe for success. Moreover,
despite the fact we indicated that the correct approach for control is to conceive it
from the onset as part of the problem of overall system design, there are actually no
rigorous developments in engineering design along this route (at least as far as we
know).
Obviously, we believe that feedback and control matter a lot, and indeed offer a lot
to society. In Chap. 11, some of these benefits are highlighted. We hope that you will
identify many other benefits. In fact, the purpose of the whole book is to lead you to
realize how much can be obtained by means of an appropriate use of feedback and
control, and how much has been implemented, so that this hidden technology2 will
become clearly exposed. To be balanced, we do also point out some of the risks asso-
ciated with feedback, but when you get this far through the book you will be well-
equipped to decide on such matters for yourself.
Our journey into control concludes in Chap. 12 with a look towards the unpredict-
able future. Some trends are clear. Some immediate evolutionary technology is easily
guessed, but we also present some bolder predictions. The future is open and we will
be excited if some of our readers decide to contribute to expand further on the joy of
feedback3.
2 Directly quoting Karl Astrom, an excellent teacher, researcher and practitioner and a great advo-
cate for control. We always enjoy to be in touch with him.
3 Quoting Petar Kokotovic, a friend, an inspiration and a great leader in control and feedback.