`
`EIectn'ca! and
`
`Computer Engineering
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`M. E. Van Valkenburg, Series Editor Electrical Engineering
`Michael R. Lightner. Series Editor Computer Engineering
`
`INTRODUCTION TO
`P. R. Bélanger, E. L. Adler, and N. C. Rumin
`CIRCUITS WITH ELECTRONICS: AN INTEGRATED APPROACH
`L. S. Bobrow ELEMENTARY LINEAR CIRCUIT ANALYSIS
`L.
`S. Bobrow FUNDAMENTALS OF ELECTRICAL ENGINEERING
`C.
`T. Chen LINEAR SYSTEM THEORY AND DESIGN
`D.
`J. Comer DIGITAL LOGIC AND STATE MACHINE DESIGN
`D.
`J. Comer MICROPROCESSOR BASED SYSTEM DESIGN
`C. H. Durney, L. D. Harris, C. L. Alley ELECTRIC CIRCUITS: THEORY
`AND ENGINEERING APPLICATIONS
`M. S. Ghausi ELECTRONIC DEVICES AND CIRCUITS: DISCRETE AND
`INTEGRATED
`
`G. H. Hostetter, C. J. Savant, Jr., R. T. Stefani DESIGN OF
`FEEDBACK CONTROL SYSTEMS
`S. Karni and W. J. Byatt MATHEMATICAL METHODS IN
`CONTINUOUS AND DISCRETE SYSTEMS
`B. C. Kuo DIGITAL CONTROL SYSTEMS
`B. P. Lathi MODERN DIGITAL AND ANALOG COMMUNICATION
`SYSTEMS
`C. D. McGillem and G. R. Cooper CONTINUOUS AND DISCRETE
`SIGNAL AND SYSTEM ANALYSIS Second Edition
`. H. Navon SEMICONDUCTOR MICRODEVICES AND MATERIALS
`. Papoulis CIRCUITS AND SYSTEMS: A MODERN APPROACH
`. E. Schwarz and W. G. Oldham ELECTRICAL ENGINEERING: AN
`INTRODUCTION
`. S. Sedra and K. C. Smith MICROELECTRONIC CIRCUITS
`213
`. K. Sinha CONTROL SYSTEMS
`M. E. Van Valkenburg ANALOG FILTER DESIGN
`W. A. Wolovich ROBOTICS: BASIC ANALYSIS AND DESIGN
`
`Ul>U
`
`CONTROL
`SYSTEMS
`
`Mom K. Slit/la
`
`McMaSter University
`
`Hamilton, Ontario, Canada
`
`TSMC et a1 V. Zond
`
`IPR2014—00803
`
`Page 1 Zond EX. 2013
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`HOLT. RINEHART AND WINSTON
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`

`Acquisitions Editor: Deborah Moore
`Production Manager: Paul Nardi
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`Illustrations: Scientific Illustrators
`
`072137215
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`Copyright :5"; 19% CBS College Publishing
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`All rights reserved.
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`383 Madison Avenue. New York. NY 100]?
`
`Library of Congress Cataloging-in-Publication Data
`
`Sinlia. N. K. (Naresh Kumar)
`Control systems.
`
`Includes index.
`
`I. Title.
`|. Automatic control. 2. Control theory.
`'l‘JBI3.S47444
`1980
`629.8
`85-24796
`ISBN B-UB-Db‘IBS?-fi
`
`Printed in the United States of America
`Published simultaneously in Canada
`nit“)
`038
`98765-1321
`
`CBS COLLEGE PUBLISHING
`Holt. Rinehart and Winston
`The Dryden Press
`Saunders College Publishing
`
`PREFACE
`
`1.
`
`INTRODUCTION
`
`2. MATHEMATICAL MODELS OF
`
`PHYSICAL SYSTEMS
`
`2.]
`2.3
`
`Introduction
`Differential Equations and Transfer Functions for Physical
`Systems
`Electrical Analogs for Mechanical Systems
`2.3
`2.4 Modeling an ArtnaturenControllcd DC Seryotnotor
`2.5
`Simplification of Block Diagrams
`2.6
`A DC Position~Control System
`2.? Mason‘s Rule
`2.8
`Summary
`19
`References
`2.10
`Problems
`
`Page 2
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`Page 2
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`

`

`
`
`Introdudm
`
`The subject of control systems is of great inportance to all engineers.
`The objective is to free human beings from boring repetitive chores that can be
`done easily and more economically by automatic control devices. The recent
`developments in the large-scale integration of semiconductor devices and the
`resulting availability of inexpensive microprocessors has made it practical to
`use computers as integral parts of control systems, making them cheaper as
`well as more sophisticated.
`Historically. the first automatic control device used in the industry
`Was the Watt fly-ball governor. invented in 1767 by James Watt. who was also
`the inventor of the steam engine. The object of this device was to keep the
`
`Page 3
`
`

`

`
`
`2 Chapter1
`
`Introduction
`
`To steam valve
`
`FIGURE 1.1. The Watt fly-ball governor.
`
`It was found that by a proper design of the governor the speed
`could be kept within narrow limits of a specified value. It was also observed
`that if one tried to increase the sensitivity of the governor by increasing the
`gear ratio between the engine shaft and the governor, it tended to “hunt” or
`oscillate about the desired setting. It was about 100 years later that a complete
`mathematical analysis was made by James Clerk Maxwell (more well known
`for his contributions to electromagnetic field theory).
`Much later it was realized that all automatic control systems worked
`on the principle of feedback. By a coincidence, about the same time the theory
`of feedback amplifiers had been developed by electrical engineers who had
`been concerned with transmitting telephone signals over long distances. In
`particular, one may mention the Nyquist theory of stability developed about
`1930. A great impetus to the theory of automatic control came during World
`War II when servomechanisms were utilized for the control of anti-aircraft
`guns. After World War 11 many peacetime applications followed. Some of these
`are the “autopilot” for aircraft, automatic control of machine tools, automatic
`control of chemical processes, and automatic regulation of voltage at electric
`power plants. Although originally the theory was based on frequency response
`and Laplace transform methods, in the 19605 the impact of the digital com.
`puter led to the development of time-domain theory using state variables. This
`was especially useful as more sophisticated multivariable control systems were
`developed for more complex processes. As computers have become cheaper
`and more compact, they have been utilized as components of more advanced
`
`3 Chapter1 Introduction
`
`
`
`___—__ Reference
`:— voltage
`
`
`
`FIGURE 1 .3. Automatic voltage regulator.
`
`Let us consider some simple examples of control systems. Figure
`1.2 shows the scheme for controlling the voltage at an electric power station
`in the 1940s. A human operator was required to watch a voltmeter connected
`to the busbars and adjust the field rheostat in order to keep the voltage close
`to the specified value. A scheme for automatic voltage regulation is shown in
`Fig. 1.3 and shows that it works by comparing the actual value of the voltage
`with the desired value. The difference or “error” is applied to a servomotor,
`after suitable amplification. This servomotor drives a shaft coupled to the field
`rheostat to alter the resistance in the field winding in such a manner that the
`error is reduced. Hence, it may be said that “feedback” is utilized to obtain
`automatic control. As a matter of fact, all automatic control systems use feed-
`back and can be represented by the block diagram shown in Fig. 1.4. It can be
`seen that the controlled output is fed back and compared with the reference
`Input. The difference, called the “error," is then utilized to drive the system in
`such a manner that the output approaches the desired value lie, the reference
`input}.
`
`:1: I
`Reference
`input
`
`output
`
`C(l')
`Controlled
`
`FIGURE 1.4. Block diagram of automatic control system.
`
`Another example is the home heating system. A thermostat senses
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`Page 4
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`

`

`
`
`4 Chapter1 Introduction
`
`
`Heating
`
`temperature
`system
`
`
`House
`
`
`
`Measured
`
`temperature
`FIGURE 1.5. A home heating system.
`
`or hunting. It is caused by the fact that although the system is designed with
`negative feedback. due to inherent time lags, it may change into positive feed-
`back at some frequency. Therefore, oscillations may be produced at this fre-
`quency if the gain is increased sufficiently. The Nyquist criterion of stability.
`developed for feedback amplifiers, provides a good understanding of this. We
`later see how one can increase the sensitivity {or accuracy) without
`
`The components used for control systems are usually of a wide
`variety. For example,
`these may be electromechanical, electronic.
`thermal,
`hydraulic, or pneumatic. In order to analyze the response of the various
`components, we replace them by their mathematical models. Although the
`input and the output of these devices are generally related through nonlinear
`differential equations, it is customary to obtain simplified linear models about
`the operating points because such models are easier to analyze. Transfer func-
`tion and state-variable models are most commonly employed.
`In our development of control theory, we shall generally be carrying
`out the analysis and design in terms of the mathematical models. Although this
`approach may sometimes appear abstract. one must appreciate that
`these
`models represent real systems. To a certain extent
`this abstraction is neces-
`sary for developing a unified theory of automatic control systems despite the
`great variety of components. One important aspect is the problem of obtaining
`mathematical models for different types of physical systems. This will be discus-
`sed in Chapter 2. It will be assumed that the reader is familiar with the theory
`of Laplace transforms. For the sake of completeness, a review of Laplace trans-
`forms is given in Appendix A.
`We shall close this chapter by mentioning some areas in which the
`theory of control systems has been applied. These include robotics, automatic
`control of large—scale power systems. numerical control of machine tools, auto-
`pilots for aircraft. prosthetic devices for handicapped persons. and the steering
`
`
`
`
`
`Mathematical
`Mala/5 of
`P/zysiaa/Systems
`
`2.1
`
`INTRODUCTION
`
`A crucial problem in engineering design and analysis is the deter-
`.
`.
`minauon of a mathematical model of a given physical system. This model must
`relate in a quantitative manner the various variables in the system. A model
`may be defined as “a representation of the essential aspects of a system which
`Presents knowledge of that system in a usable manner.“ To be useful. a model
`must, not be so complicated that it cannot be understood and thereby be
`unsuitable for analysis; at
`the same time it must not be oversimplified and
`
`Page 5
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