PREFACIO
As of this writing (1966), there are over one hundred books and monographs on the general topic of control and servomechanisms in the English Ianguage alone. Any new author venturing into this field should therefore be prepared to motivate the need for his particular product and to define its specific raison d’être. I believe the time is ripe for a "new look" in control textbooks and offer the following reasons for this assumption:
It is current praxis to distinguish between “classical” and “modern” control, a distinction that not only is arbitrary but also has resulted in an unfortunate and often artificial division between topic areas usually covered in the graduate and undergraduate control programs at our universities.
The vast majority of present texts take the classical view of control. With few exceptions, these texts are direct descendants -first, second, or later generation- of the classic treatises by James, Nichols, and Phillips and Truxal. The outstanding features of the classical approach are:
1. A linear model of the control system is assumed, and the designer then proceeds to describe the system in terms of transfer functions of either the frequency or the Laplace variety, depending upon the type of information he has available.
2. An almost exclusive emphasis is placed upon those specific control systems classified as servomechanisms. In addition, attention is directed in most cases to systems of the single -input -single -output variety,
3. The performance criteria usually specified make it necessary to utilize indirect design techniques of the trial-and-error type.
The classical approach, typically relegated to the undergraduate control programs at our universities, has many outstanding and time-tested advantages. No sophisticated mathematics is required beyond the elements of linear differential equations and complex algebra. The present generation of control engineers is thoroughly indoctrinated with classical design techniques, and-the majority of the control systems now being manufactured are designed by classical methods.
However, classical design methods have numerous shortcomings. Empiricism, trial-and-error design, and a lack of a fundamental theory combine to mike conventional control more an art than a science. For the exacting requirements of the more complex automatic-control problems in modern technology-, classical methods are, in effect, entirely inadequate. This is where “modern control” enters the picture.
The modern theory approaches the control problem in a more fundamental fashion. For example, it defines.the concept of control and establishes test procedures for determining when and under what conditions a system is controllable. Direct synthesis methods are proposed which lead to unique system designs that are optimal in some defined sense. Extensive use is made of the modern computer. Theories are developed for systems with learning and adaptive capabilities.
Modern control theory leans heavily on mathematics that typically are not included on the undergraduate menu, e.8., calculus of variation and matrix algebra. It prefers time-domain system description (state variables) to transfer-function methods since it does not limit itself to linear models. The methods of modern control have been developed in many instances by applied and pure mathematicians, with the result that much of the written presentation is very formal and quite inaccessible to most control engineers. At our universities, modern control theory is reserved for the graduate programs and is presented in courses which are usually completely unintegrated with classical viewpoints. Formalism, isolation from the undergraduate program, and unwillingness to merge the modern concepts with existing conventional methods have prevented a wide dissemination of the modern ideas.
This book undertakes the task of bridging the existing gap between the conventional techniques and modern theory. Its objectives are, specifically:
1. To give a basic presentation of the fundamental control problem
2. To integrate modern concepts with conventional design techniques
3. To strip some of the new theories of some of the mathematical clothing in which they are obscured in order to make them understandable to the senior undergraduate engineering student
4. To bring into focus the importance of the modern computer-analog, digital, and hybrid-in design and on-line operation of control systems
The book aims at an audience consisting of the senior undergraduate and the first-year graduate student and the practicing control engineer. Its contents correspond approximately to six semester credit hours, which could be covered entirely in an undergraduate course sequence, or its first half (through Chap. 7) could be offered on the undergraduate level and the second half on the first-year graduate level.
In order to meet the stated objectives, I have chosen an approach which is very different from the usual one. Examples are used prolifically, but instead of starting with a mathematical model divorced from reality, the origin of the model is discussed and every step of the analysis is clearly motivated from there on. The elements of matrix algebra and variational calculus have been included, but it has been assumed that the student has had at least an elementary background in linear differential equations and transform calculus. However, a summary of Laplace and Fourier transform theorems
has been included as Appendix B.
On occasion, mathematical shortcuts have been taken to preserve simplicity and continuity in the presentation, and for the same purpose, formalism has been avoided.
It has not been possible to cover componentry to any great extent. It is hoped that the examples chosen are sufficiently practical to give the reader a feeling that he always has "one foot on the ground." I have found that the presentation of the material is greatly enhanced by a parallel laboratory course taking the form of a series of simulation experiments. The examples in the text and also the end-of-chapter exercises are put on the analog computer, and the student is given a comparison between analytical results and computer recordings.
It is, of course, impossible to cover in one volume the entire spectrum of topic areas in a field as wide as control. It has been very difficult to decide where to draw the line, but I finally decided that the most natural grouping is the following one:
l . Deterministic control
2. Stochastic control
Stochastic control encompasses topics such as estimation, filtering, adaptive and learning systems, and also biocontrol and has therefore not been included in the present volume.
The methods and philosophy of teaching control courses as reflected in this book were developed in the graduate and undergraduate programs of the Department of Electrical Engineering, University of Florida. I was given the opportunity to write this text during a year as Visiting Professor at the University of Colorado, and I am particularly indebted to Dr. Max Peters, Dean of the College of Engineering, and Dr. Frank Barnes, Chairman of the Department of Electrical Engineering. Dr. John G. Truxal, Dean of the Polytechnic Institute of Brooklyn, reviewed the entire manuscript, and his comments and suggestions have been of considerable assistance in the preparation of the final manuscript. I also wish to express my special gratitude to Mrs. Barbara Salaman, Mrs. Thyra S. Johnston, and my wife, Margaret, for typing the manuscript.
My former and present students at the Universities of Florida and Colorado supplied the incentive for this project. Their enthusiasm has been truly inspirational, and their questioning minds have provided the necessary feedback. In a real sense, this book represents a joint effort in which the collective contributions of all these students constitute an essential ingredient.
Olle I Elgerd ( )