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Preface
Striking developments have taken place since 1980 in feedback control theory. The subject has become
both more rigorous and more applicable. The rigor is not for its own sake, but rather that even
in an engineering discipline rigor can lead to clarity and to methodical solutions to problems. The
applicability is a consequence both of new problem formulations and new mathematical solutions
to these problems. Moreover, computers and software have changed the way engineering design is
done. These developments suggest a fresh presentation of the subject, one that exploits these new
developments while emphasizing their connection with classical control.
Control systems are designed so that certain designated signals, such as tracking errors and
actuator inputs, do not exceed pre-specified levels. Hindering the achievement of this goal are
uncertainty about the plant to be controlled (the mathematical models that we use in representing
real physical systems are idealizations) and errors in measuring signals (sensors can measure signals
only to a certain accuracy). Despite the seemingly obvious requirement of bringing plant uncertainty
explicitly into control problems, it was only in the early 1980s that control researchers re-established
the link to the classical work of Bode and others by formulating a tractable mathematical notion
of uncertainty in an input-output framework and developing rigorous mathematical techniques to
cope with it. This book formulates a precise problem, called the robust performance problem, with
the goal of achieving specified signal levels in the face of plant uncertainty.
The book is addressed to students in engineering who have had an undergraduate course in
signals and systems, including an introduction to frequency-domain methods of analyzing feedback
control systems, namely, Bode plots and the Nyquist criterion. A prior course on state-space theory
would be advantageous for some optional sections, but is not necessary. To keep the development
elementary, the systems are single-input/single-output and linear, operating in continuous time.
Chapters 1 to 7 are intended as the core for a one-semester senior course; they would need
supplementing with additional examples. These chapters constitute a basic treatment of feedback
design, containing a detailed formulation of the control design problem, the fundamental issue
of performance/stability robustness tradeoff, and the graphical design technique of loopshaping,
suitable for benign plants (stable, minimum phase). Chapters 8 to 12 are more advanced and
are intended for a first graduate course. Chapter 8 is a bridge to the latter half of the book,
extending the loopshaping technique and connecting it with notions of optimality. Chapters 9 to
12 treat controller design via optimization. The approach in these latter chapters is mathematical
rather than graphical, using elementary tools involving interpolation by analytic functions. This
mathematical approach is most useful for multivariable systems, where graphical techniques usually
break down. Nevertheless, we believe the setting of single-input/single-output systems is where this
new approach should be learned.
There are many people to whom we are grateful for their help in this book: Dale Enns for
sharing his expertise in loopshaping; Raymond Kwong and Boyd Pearson for class testing the book;
iii
and Munther Dahleh, Ciprian Foias, and Karen Rudie for reading earlier drafts. Numerous Caltech
students also struggled with various versions of this material: Gary Balas, Carolyn Beck, Bobby
Bodenheimer, and Roy Smith had particularly helpful suggestions. Finally, we would like to thank
the AFOSR, ARO, NSERC, NSF, and ONR for partial financial support during the writing of this
book. |
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