Introduction to control engineering modeling, analysis and design

633 Pages·2006·5.107 MB·English

by  Mandal, Ajit K

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Copyright © 2006 New Age International (P) Ltd., Publishers
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Preface
Control engineering is a very important subject to warrant its inclusion as a core course in the
engineering program of studies in universities throughout the world. The subject is
multidisciplinary in nature since it deals with dynamic systems drawn from the disciplines of
electrical, electronics, chemical, mechanical, aerospace and instrumentation engineering. The
common binding thread among all these divergent disciplines is a mathematical model in the
form of differential or difference equations or linguistic models. Once a model is prepared to
describe the dynamics of the system, there is little to distinguish one from the other and the
analysis depends solely on characteristics like linearity or nonlinearity, stationary or time
varying, statistical or deterministic nature of the system. The subject has a strong mathematical
foundation and mathematics being a universal language; it can deal with the subject of
interdisciplinary nature in a unified manner.
Even though the subject has strong mathematical foundation, emphasis throughout the
text is not on mathematical rigour or formal derivation (unless they contribute to understand-
ing the concept), but instead, on the methods of application associated with the analysis and
design of feedback system. The text is written from the engineer’s point of view to explain the
basic concepts involved in feedback control theory. The material in the text has been organized
for gradual and sequential development of control theory starting with a statement of the task
of a control engineer at the very outset.
The book is intended for an introductory undergraduate course in control systems for
engineering students. The numerous problems and examples have been drawn from the disci-
plines of electrical, electronics, chemical, mechanical, and aerospace engineering. This will help
students of one discipline with the opportunity to see beyond their own field of study and thereby
broaden their perceptual horizon. This will enable them to appreciate the applicability of con-
trol system theory to many facets of life like the biological, economic, and ecological control
systems.
This text presents a comprehensive analysis and design of continuous-time control sys-
tems and includes more than introductory material for discrete systems with adequate guide-
lines to extend the results derived in connection with continuous-time systems. The prerequi-
site for the reader is some elementary knowledge of differential equations, vector-matrix analy-
sis and mechanics.
Numerous solved problems are provided throughout the book. Each chapter is followed
by review problems with adequate hints to test the reader’s ability to apply the theory involved.
Transfer function and state variable models of typical components and subsystems have been
derived in the Appendix at the end of the book.
Most of the materials including solved and unsolved problems presented in the book
have been class-tested in senior undergraduates and first year graduate level courses in the
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field of control systems at the Electronics and Telecommunication Engineering Department,
Jadavpur University.
The use of computer-aided design (CAD) tool is universal for practicing engineers and
MATLAB is the most widely used CAD software package in universities through out the world.
MATLAB scripts are provided so that students can learn to use it for calculations and analysis
of control systems. Some representative MATLAB scripts used for solving problems are in-
cluded at the end of each chapter whenever thought relevant. However, the student is encour-
aged to compute simple answers by hand in order to judge that the computer’s output is sound
and not ‘garbage’. Most of the graphical figures were generated using MATLAB and some rep-
resentative scripts for those are also included in the book. We hope that this text will give the
students a broader understanding of control system design and analysis and prepare them for
an advanced course in control engineering.
In writing the book, attempt has been made to make most of the chapters self-contained.
In the introductory chapter, we endeavored to present a glimpse of the typical applications of
control systems that are very commonly used in industrial, domestic and military appliances.
This is followed by an outline of the task that a control-engineering student is supposed to
perform. We have reviewed, in the second chapter, the common mathematical tools used for
analysis and design of linear control systems. This is followed by the procedure for handling the
block diagrams and signal flow graphs containing the transfer functions of various components
constituting the overall system. In chapter 3, the concept of state variable representation along
with the solution of state equations is discussed. The concept of controllability and observabil-
ity are also introduced in this chapter along with the derivation of transfer function from state
variable representation. The specifications for transient state and steady state response of lin-
ear systems have been discussed in chapter 4 along with the Bode technique for frequency
domain response of linear control systems. In chapter 5, the concept of stability has been intro-
duced and Routh-Hurwitz technique along with the Direct method of Lyapunov have been
presented. Frequency domain stability test by Nyquist criteria has been presented in chapter
6. The root locus technique for continuous system has been discussed in chapter 7 and its exten-
sion to discrete cases has been included. The design of compensators has been taken up in
chapter 8. In chapter 9, we present the concept of pole assignment design along with the state
estimation. In chapter 10, we consider the representation of digital control system and its
solution. In chapter 11, we present introductory material for optimal problem and present the
solution of linear regulator problem. Chapter12 introduces the concepts of fuzzy set and fuzzy
logic needed to understand Fuzzy Logic Control Systems presented in chapter 13.
The reader must be familiar with the basic tools available for analyzing systems that
incorporate unwanted nonlinear components or deliberately introduced (relay) to improve sys-
tem performance. Chapter 14 has been included to deal with nonlinear components and their
analysis using MATLAB and SIMULINK through user defined s-functions. Finally, Chapter 15
is concerned with the implementation of digital controllers on finite bit computer, which will
bring out the problems associated with digital controllers. We have used MATLAB and
SIMULINK tools for getting the solution of system dynamics and for rapid verification of con-
troller designs. Some notes for using MATLAB script M-files and function M-files are included
at the end of the book.
The author is deeply indebted to a number of individuals who assisted in the preparation
of the manuscript, although it is difficult to name everyone in this Preface. I would like to thank
Saptarshi for his support and enthusiasm in seeing the text completed, Maya for the many
hours she spent reviewing and editing the text and proof reading. I would like to thank many
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people who have provided valuable support for this book project : Ms Basabi Banerjee for her
effort in writing equations in MSword in the initial draft of the manuscript, Mr. U. Nath for
typing major part of the manuscript and Mr. S. Seal for drawing some figures.
The author would like to express his appreciation to the former graduate students who
have solved many problems used in the book, with special appreciation to Ms Sumitra
Mukhopadhyay, who provided feedback and offered helpful comments when reading a draft
version of the manuscript.
A. K. Mandal