r: CO TROL SENSORS
`AND ACTUATORS
`
`0
`(Measurement) Primary
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`Coil
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`Insulating
`Form
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`Core
`Displacement
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`(Measurand)
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`rsmvTirn•
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`Ferromagnetic Core
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`•
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`Secondary
`Coil
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`Secondary
`Coil
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`Displacement x
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`EXHIBIT
`0
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`24/
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`1•1111111/ (cid:9)
`
`MOW Ali
`
`CLARENCE W. de SILVA
`
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`

`
`RELEASED °I -1-3 -1A '
`JAMES WHITE LIBRARY
`ANDREWS UNIVERSITY
`REPREN SPRINGS, MICH
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`Control Sensors
`and Actuators
`
`CLARENCE W. DE SILVA
`
`It
`
`PRENTICE HALL, Englewood Cliffs, New Jersey 07632
`
`JAMES WHITE LIBRARY
`ANDREWS UNIVERSITY
`BERRIEN SPRINGS, MI 49104
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`

`
`De Silva, Clarence W.
`Control Sensors and actuators.
`Includes bibliographies and index.
`1. Automatic control. 2. Detectors. 3. Actuators.
`I. Title.
`TJ213.D38 1989 (cid:9)
`ISBN 0-13-171745-6
`
`88-28998
`
`629.8 (cid:9)
`
`To Charmaine, C.J., and Cheryl—as their senses develop
`and as they become increasingly active.
`
`Editorial/production supervision and
`interior design: David Ershun
`Cover design: Ben Santora
`Manufacturing buyer: Mary Ann Gloriande
`
`© 1989 by Prentice-Hall, Inc.
`A Division of Simon & Schuster
`Englewood Cliffs, New Jersey 07632
`
`All rights reserved. No part of this book may be
`reproduced, in any form or by any means,
`without permission in writing from the publisher.
`
`The publisher offers discounts on this book when ordered
`in bulk quantities. For more information, write:
`Special Sales/College Marketing
`Prentice Hall
`College Technical and Reference Division
`Englewood Cliffs, NJ 07632
`
`Printed in the United States of America
`
`10 9 8 7 6 5 4 3 2 1
`
`ISBN 0-13-171745-6
`
`PRENTICE-HALL INTERNATIONAL (UK) LIMITED, London
`PRENTICE-HALL OF AUSTRALIA PTY. LIMITED, Sydney
`PRENTICE-HALL CANADA INC. , Toronto
`PRENTICE-HALL HISPANOAMERICANA, S.A. , Mexico
`PRENTICE-HALL OF INDIA PRIVATE LIMITED, New Delhi
`PRENTICE-HALL OF JAPAN, INC. , Tokyo
`SIMON & SCHUSTER ASIA PTE. LTD. , Singapore
`EDITORA PRENTICE-HALL DO BRASIL, LTDA. , Rio de Janeiro
`
`T- T
`I 3
`D3
`193 (1
`
`513414
`
`-411s5 )(/Jt(_,
`
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`

`
`Contents
`
`PREFACE (cid:9)
`
`1 CONTROL, INSTRUMENTATION, AND DESIGN (cid:9)
`
`1.1 (cid:9)
`1.2 (cid:9)
`1.3 (cid:9)
`1.4 (cid:9)
`1.5 (cid:9)
`1.6 (cid:9)
`1.7 (cid:9)
`
`Introduction 1
`Control System Architecture 2
`Digital Control 3
`Signal Classification in Control Systems 5
`Advantages of Digital Control 8
`Feedforward Control 9
`Instrumentation and Design 11
`Problems 12
`References 16
`
`2 PERFORMANCE SPECIFICATION AND
`COMPONENT MATCHING
`
`2. 1 (cid:9)
`2.2 (cid:9)
`
`Introduction 17
`Sensors and Transducers 19
`
`vii
`
`1
`
`17
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`2.3 (cid:9)
`2.4 (cid:9)
`2.5 (cid:9)
`2.6 (cid:9)
`2.7 (cid:9)
`
`Transfer Function Models for Transducers 20
`Parameters for Performance Specification 26
`Impedance Characteristics 36
`Instrument Ratings 50
`Error Analysis 55
`Problems 75
`References 83
`
`3 ANALOG SENSORS FOR MOTION MEASUREMENT (cid:9)
`
`84
`
`Introduction 84
`3.1 (cid:9)
`3.2 (cid:9)
`Motion Transducers 85
`3.3 (cid:9)
`Potentiometers 87
`3.4 (cid:9)
`Variable-Inductance Transducers 95
`Permanent-Magnet Transducers 108
`3.5 (cid:9)
`Eddy Current Transducers 112
`3.6 (cid:9)
`Variable-Capacitance Transducers 113
`3.7 (cid:9)
`Piezoelectric Transducers 118
`3.8 (cid:9)
`Other Types of Sensors 126
`3.9 (cid:9)
`3.10 A Design Criterion for Control Systems 132
`Problems 134
`References 142
`
`4 TORQUE, FORCE, AND TACTILE SENSORS (cid:9)
`
`144
`
`4.1 (cid:9)
`4.2 (cid:9)
`4.3 (cid:9)
`4.4 (cid:9)
`4.5 (cid:9)
`4.6 (cid:9)
`4.7 (cid:9)
`
`Introduction 144
`Force Control 145
`Strain Gages 153
`Semiconductor Strain Gages 167
`Torque Sensors 174
`Force Sensors 196
`Tactile Sensing 199
`
`iv (cid:9)
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`Contents
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`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`

`
`Problems 206
`References 216
`
`5 DIGITAL TRANSDUCERS (cid:9)
`
`218
`
`Introduction 218
`5 .1 (cid:9)
`Shaft Encoders 219
`5.2 (cid:9)
`5.3 (cid:9)
`Incremental Optical Encoders 225
`5.4 (cid:9)
`Absolute Optical Encoders 235
`Encoder Error 238
`5.5 (cid:9)
`Digital Resolvers 243
`5.6 (cid:9)
`Digital Tachometers 244
`5.7 (cid:9)
`Hall Effect Sensors 245
`5.8 (cid:9)
`Measurement of Translatory Motions 247
`5.9 (cid:9)
`5.10 Limit Switches 249
`Problems 249
`References 252
`
`6 STEPPER MOTORS (cid:9)
`
`253
`
`Introduction 253
`6. 1 (cid:9)
`Principle of Operation 254
`6.2 (cid:9)
`Stepper Motor Classification 262
`6.3 (cid:9)
`Single-Stack Stepper Motors 263
`6.4 (cid:9)
`Multiple-Stack Stepper Motors 273
`6.5 (cid:9)
`Open-Loop Control of Stepping Motors 275
`6.6 (cid:9)
`Stepper Motor Response 277
`6.7 (cid:9)
`Static Position Error 284
`6.8 (cid:9)
`Damping of Stepper Motors 286
`6.9 (cid:9)
`6.10 Feedback Control of Stepper Motors 293
`6.11 (cid:9)
`Stepper Motor Models 299
`Stepper Motor Selection and Applications 304
`6.12 (cid:9)
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`Contents
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`Problems 311
`References 322
`
`7 CONTINUOUS-DRIVE ACTUATORS (cid:9)
`
`323
`
`Introduction 323
`7.1 (cid:9)
`DC Motors 324
`7.2 (cid:9)
`Brushless DC Motors 327
`7.3 (cid:9)
`DC Motor Equations 330
`7.4 (cid:9)
`7.5 (cid:9)
`Control of DC Motors 342
`Torque Motors 359
`7.6 (cid:9)
`Motor Selection Considerations 363
`7.7 (cid:9)
`Induction Motors 365
`7,8 (cid:9)
`Induction Motor Control 375
`7.9 (cid:9)
`7.10 Synchronous Motors 387
`Hydraulic Actuators 390
`7.11 (cid:9)
`Hydraulic Control Systems 401
`7.12 (cid:9)
`Problems 416
`References 428
`
`ANSWERS TO NUMERICAL PROBLEMS
`
`INDEX
`
`429
`
`431
`
`vi (cid:9)
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`Contents
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`
`Preface
`
`This book is suitable for a course in control system instrumentation or for a second
`course in feedback control systems. There is adequate material in the book for two
`fifteen-week courses, one at the senior (fourth-year undergraduate) level and the
`other at the first-year graduate level. Also, the book can serve as a useful reference
`tool for practicing engineers in the field of control engineering.
`The manuscript for the book evolved from the notes I developed for an under-
`graduate course entitled Instrumentation and Design of Control Systems and for a
`graduate course entitled Control System Instrumentation at Carnegie Mellon Univer-
`sity. The undergraduate course is a senior elective, but it is a popular course that
`usually is taken by approximately half of the senior class. The graduate course is of-
`fered for electrical and computer engineering, mechanical engineering, and chemical
`engineering students. The prerequisite for both courses is a conventional undergrad-
`uate course in feedback control theory, as well as the consent of the instructor. Dur-
`ing the development of the material for this book, a deliberate attempt was made to
`cover a major part of the syllabuses for two courses—Analog and Digital Control
`System Synthesis, and Computer Controlled Experimentation—offered in the De-
`partment of Mechanical Engineering at the Massachusetts Institute of Technology.
`A control system is a dynamic system that contains a controller as an integral
`part. The purpose of the controller is to generate control signals that will drive the
`process to be controlled (the plant) in the desired manner. Actuators are needed to
`perform control actions as well as to drive the plant directly. Sensors and transducers
`are necessary to measure output signals for feedback control, to measure input sig-
`nals for feedforward control, to measure process variables for system monitoring,
`and for a variety of other purposes. Since many different types and levels of signals
`
`vii
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`are present in a control system, signal modification (including signal conditioning
`and signal conversion) is indeed a crucial function associated with any control sys-
`tem. In particular, signal modification is an important consideration in component
`interfacing. It is clear that a course in control system instrumentation should deal
`with sensors and transducers, actuators, signal modification, and controllers.
`Specifically, the course should address the identification of control system compo-
`nents with respect to functions, operation and interaction, and proper selection and
`interfacing of these components for various control applications .. Parameter selection
`(including system tuning) is an important step as well. Design is a necessary part of
`control system instrumentation, for it is design that enables us to build a control sys-
`tem that meets the performance requirements—starting, perhaps, with basic compo-
`nents such as sensors, actuators, controllers, compensators, and signal modification
`devices.
`The approach taken in this book is to treat the basic types of control sensors
`and actuators in separate chapters, but without losing sight of the fact that various
`components in a control system have to function as an interdependent and intercon-
`nected group in accomplishing the specific control objective. Operating principles,
`modeling, design considerations, ratings, specifications, and applications of the indi-
`vidual components are discussed. Component integration and design considerations
`are addressed primarily through examples and problems, which are drawn from such
`application systems as robotic manipulators, machine tools, ground transit vehicles,
`aircraft, thermal and fluid process plants, and digital computer components. It is im-
`possible to discuss every available control system component in a textbook of this
`nature; for example, thick volumes have been written on measurement devices
`alone. In this book, some types of sensors and actuators are studied in great detail,
`whereas some others are treated superficially. Once students are exposed to an in-
`depth study of some components, it should be relatively easy for them to extend the
`same concepts and the same study approach to other components that are function-
`ally or physically similar. Augmenting their traditional role, the problems at the end
`of each chapter serve as a valuable source of information not found in the main text.
`In fact, the student is strongly advised to read carefully all problems in addition to
`the main text.
`The book consists of seven chapters. Chapter I provides an introduction to the
`subject of control system instrumentation. Component modeling, rating, and match-
`ing aspects are discussed early, in chapter 2, so that the relevance and significance of
`these considerations can be explored in the subsequent chapters. The next three
`chapters of the book are devoted to sensors and transducers, and the last two chap-
`ters consider actuators. Because of space restrictions, signal modification and mi-
`croprocessor-based control are not covered in the book, even though these are im-
`portant topics of control system instrumentation. Although solutions are available for
`all problems included in the book, answers to only the numerical problems are given
`at the end of the book, in order to encourage independent thinking.
`The planning of the course syllabus is left to the instructor, but proper consid-
`eration should be given to the course level (undergraduate or graduate), the depart-
`ment (mechanical, electrical, chemical, aerospace, etc.), and the instructor's own
`
`viii (cid:9)
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`background. My general advice, however, is that all seven chapters be covered, re-
`gardless of the course level. A basic treatment of the main topics is appropriate at
`the undergraduate level, and an in-depth treatment of selected topics from each
`chapter could be undertaken at the graduate level.
`The objective of this book is to provide an introductory course in control sys-
`tem instrumentation, emphasizing sensors and actuators. The book does not claim
`the virtually impossible undertaking of transforming a student into an expert in con-
`trol system instrumentation during a fifteen-week period. Rather, the introductory
`material presented here will serve as a firm foundation for building up expertise in
`the subject later—perhaps in an industrial setting or in an academic research labora-
`tory—with further knowledge of control hardware and analytical skills (along with
`the essential hands-on experience) gained during the process. Undoubtedly, for best
`results, a course in control sensors and actuators should be accompanied by a labora-
`tory component and/or class projects.
`
`Acknowledgments
`
`Many people deserve special mention for making this project possible. Professor
`David Wormley, head of the Mechanical Engineering Department at MIT—who is
`an authority on the subject of control systems—and Professor Alistair MacFarlane,
`head of the Information Engineering Division at the University of Cambridge, have
`advised and guided me throughout my professional career. A special sense of grati-
`tude is extended to Professor Ian McCausland, professor of electrical engineering at
`the University of Toronto, who has provided constant support and encouragement
`during the past fifteen years. Professor Arthur Murphy, presently a Departmental
`Fellow at DuPont, hired me for his department at Carnegie Mellon University in
`1978 and encouraged me to teach a course on control system instrumentation. Writ-
`ing this book would have been impossible without the support and encouragement
`given by Professor William Sirignano, presently the dean of engineering at the Uni-
`versity of California, Irvine. Those students who attempted some of the problems in
`the book during the evolutionary period of the manuscript contributed to the book in
`no uncertain terms. I am grateful to Mr. Bernard Goodwin, executive editor and as-
`sistant vice-president of Prentice Hall, for undertaking to publish the manuscript.
`The two reviewers who provided constructive criticism during the proposal stage and
`the final manuscript stage have helped in improving the quality of the manuscript.
`The instrumentation experience I gained at places such as IBM Corporation, West-
`inghouse Electric Corporation, Bruel and Kjaer, and NASA's Lewis and Langley
`Research Centers was quite valuable in developing the material for the book. Ms.
`Mildred Gibb, who painstakingly and carefully generated the final copy of the
`manuscript on her word processor, deserves special thanks.
`
`Preface (cid:9)
`
`ix
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`But as artificers do not work with perfect accuracy, it comes to
`pass that mechanics is so distinguished from geometry that
`what is perfectly accurate is called geometrical; what is less
`so, is called mechanical. However, the errors are not in the
`art, but in the artificers.
`
`Sir Isaac Newton, Principia Mathematica,
`Cambridge University, May 8, 1686
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`7
`Control,
`Instrumentation, and
`Design
`
`1.1 INTRODUCTION
`
`The demand for servomechanisms in military applications during World War II pro-
`vided much incentive and many resources for the growth of control technology.
`Early efforts were devoted to the development of analog controllers, which are elec-
`tronic devices or circuits that generate proper drive signals for a plant (process). Par-
`allel advances were necessary in actuating devices such as motors, solenoids, and
`valves that drive the plant. For feedback control, further developments in sensors
`and transducers became essential. With added sophistication in control systems, it
`was soon apparent that analog control techniques had serious limitations. In particu-
`lar, linear assumptions were used to develop controllers even for highly nonlinear
`plants. Furthermore, complex and costly circuitry was often needed to generate even
`simple control signals. Consequently, most analog controllers were limited to on/off
`and proportional-integral-derivative (PID) actions, and lead and lag compensation
`networks were employed to compenstate for weaknesses in such simple control ac-
`tions.
`The digital computer, first developed for large number-crunching jobs, was
`employed as a controller in complex control systems in the 1950s and 1960s. Origi-
`nally, cost constraints restricted its use primarily to aerospace applications that re-
`quired the manipulation of large amounts of data (complex models, several hundred
`signals, and thousands of system parameters) for control and that did not face serious
`cost restraints. Real-time control requires fast computation, and this speed of com-
`putation is determined by the required control bandwidth (or the speed of control)
`and parameters (e.g., time constants, natural frequencies, and damping constants) of
`the process that is being controlled. For instance, prelaunch monitoring and control
`of a space vehicle would require digital data acquisition at very high sampling rates
`(e.g., 50,000 samples/second). As a result of a favorable decline of computation cost
`(both hardware and software) in subsequent years, widespread application of digital
`computers as control devices (i.e., digital control) has become feasible. Dramatic
`developments in large-scale integration (LSI) technology and microprocessors in the
`
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`1970s resulted in very significant drops in digital processing costs, which made digi-
`tal control a very attractive alternative to analog control. Today, digital control has
`become an integral part of numerous systems and applications, including machine
`tools, robotic manipulators, automobiles, aircraft autopilots, nuclear power plants,
`traffic control systems, and chemical process plants.
`Control engineers should be able to identify or select components for a control
`system, model and analyze individual components or overall systems, and choose
`parameter values so as to perform the intended functions of the particular system in
`accordance with some specifications. Component identification, analysis, selection,
`matching and interfacing, and system tuning (adjusting parameters to obtain the re-
`quired response) are essential tasks in the instrumentation and design of a control
`system.
`
`1.2 CONTROL SYSTEM ARCHITECTURE
`
`Let us examine the generalized control system represented by the block diagram in
`figure 1.1. We have identified several discrete blocks, depending on various func-
`tions that take place in a typical control system. Before proceeding, we must keep in
`mind that in a practical control system, this type of clear demarcation of components
`might be difficult; one piece of hardware might perform several functions, or more
`than one distinct unit of equipment might be associated with one function. Neverthe-
`less, figure 1.1 is useful in understanding the architecture of a general control sys-
`tem. This is an analog control system because the associated signals depend on the
`continuous time variable; no signal sampling or data encoding is involved in the sys-
`tem.
`
`Plant is the system or "process" that we are interested in controlling. By con-
`trol, we mean making the system respond in a desired manner. To be able to accom-
`plish this, we must have access to the drive system or actuator of the plant. We apply
`certain command signals, or input, to the controller and expect the plant to behave
`in a desirable manner. This is the open-loop control situation. In this case, we do not
`use current information on system response to determine the control signals. In feed-
`back control systems, the control loop has to be closed; closed-loop control means
`making measurements of system response and employing that information to gener-
`ate control signals so as to correct any output errors. The output measurements are
`made primarily using analog devices, typically consisting of sensor-transducer units.
`
`Reference
`Input Signal
`
`Signal
`Conditioning
`
`Analog
`Control
`Hardware
`
`Actuator
`
`Plant
`
`(cid:9) Outputs
`
`Signal
`Conditioning
`
`Analog Sensors-
`Transducers
`
`Figure 1.1. Components of a typical analog control system.
`
`2 (cid:9)
`
`Control, Instrumentation, and Design (cid:9)
`
`Chap. 1
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`An important factor that we must consider in any practical control system is noise,
`including external disturbances. Noise may represent actual contamination of signals
`or the presence of other unknowns, uncertainties, and errors, such as parameter
`variations and modeling errors. Furthermore, weak signals will have to be am-
`plified, and the form of a signal might have to be modified at various points of inter-
`action. In these respects, signal-conditioning methods such as filtering, amplification,
`and modulation become important.
`Identification of the hardware components (perhaps commercially available
`off-the-shelf items) corresponding to each functional block in figure 1.1 is one of the
`first steps of instrumentation. For example, in process control applications off-the-
`shelf analog proportional-integral-derivative (PID) controllers may be used. These
`controllers for process control applications have knobs or dials for control parameter
`settings—that is, proportional band or gain, reset rate (in repeats of the proportional
`action per unit time), and rate time constant. The control bandwidth (frequency
`range of operation) of these devices is specified. Various control modes—such as
`on/off, proportional, integral, and derivative, or combinations—are provided by the
`same control box.
`Actuating devices (actuators) include DC motors, AC motors, stepper motors,
`solenoids, valves, and relays, which are also commercially available to various
`specifications. Potentiometers, differential transformers, resolvers, synchros, strain
`gauges, tachometers, piezoelectric devices, thermocouples, thermistors, and resis-
`tance temperature detectors (RTDs) are examples of sensors used to measure process
`response for monitoring performance and possible feedback. Charge amplifiers,
`lock-in amplifiers, power amplifiers, switching amplifiers, linear amplifiers, tracking
`filters, low-pass filters, high-pass filters, and notch filters are some of the signal-
`conditioning devices used in analog control systems. Additional components, such
`as power supplies and surge-protection units, are often needed in control, but they
`are not indicated in figure 1.1 because they are only indirectly related to control
`functions. Relays and other switching devices and modulators and demodulators may
`also be included.
`
`1.3 DIGITAL CONTROL
`
`Direct digital control (DDC) systems are quite similar to analog control systems.
`The main difference in a DDC system is that a digital computer takes the place of
`the analog controller in figure 1.1. Control computers have to be dedicated machines
`for real-time operation where processing has to be synchronized with plant operation
`and actuation requirements. This also requires a real-time clock. Apart from these
`requirements, control computers are basically no different from general-purpose dig-
`ital computers. They consist of a processor to perform computations and to oversee
`data transfer, memory for program and data storage during processing, mass storage
`devices to store information that is not immediately needed, and input/output devices
`to read in and send out information. Digital control systems might utilize digital in-
`struments and additional processors for actuating, signal-conditioning, or measuring
`functions, as well. For example, a stepper motor that responds with incremental mo-
`
`Sec. 1.3 (cid:9)
`
`Digital Control
`
`3
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`tion steps when driven by pulse signals can be considered a digital actuator. Further-
`more, it usually contains digital logic circuitry in its drive system. Similarly, a two-
`position solenoid is a digital (binary) actuator. Digital flow control may be
`accomplished using a digital control valve. A typical digital valve consists of a
`bank of orifices, each sized in proportion to a place value of a binary word
`0, 1, 2, . . . , n). Each orifice is actuated by a separate rapid-acting on/off so-
`(2', i
`lenoid. In this manner, many digital combinations of flow values can be obtained.
`Direct digital measurement of displacements and velocities can be made using shaft
`encoders. These are digital transducers that generate coded outputs (e.g., in binary
`or gray-scale representation) or pulse signals that can be coded using counting cir-
`cuitry. Such outputs can be read in by the control computer with relative ease. Fre-
`quency counters also generate digital signals that can be fed directly into a digital
`controller. When measured signals are in the analog form, an analog front end is
`necessary to interface the transducer and the digital controller. Input/output interface
`boards that can take both analog and digital signals are available with digital con-
`trollers.
`A block diagram of a direct digital control system is shown in figure 1.2. Note
`that the functions of this control system are quite similar to those shown in figure
`1.1 for an analog control system. The primary difference is the digital controller
`(processor), which is used to generate the control signals. Therefore, analog mea-
`surements and reference signals have to be sampled and encoded prior to digital pro-
`cessing within the controller. Digital processing can be conveniently used for signal
`conditioning as well. Alternatively, digital signal processing (DSP) chips can func-
`tion as digital controllers. However, analog signals are preconditioned, using analog
`circuitry prior to digitizing in order to eliminate or minimize problems due to alias-
`ing distortion (high-frequency components above half the sampling frequency ap-
`pearing as low-frequency components) and leakage (error due to signal truncation)
`as well as to improve the signal level and filter out extraneous noise. The drive sys-
`
`Reference input
`
`ADC
`
`Real-time
`clock
`
`Digital
`control
`processor
`
`Address
`
`I I
`(cid:9) I I (cid:9)
`Analog (cid:9)
`multiplexing
`
`I
`
`L
`- I Add r es s
`
`L.i (cid:9)
`
`L. (cid:9)
`
`igital
`multiplexer F--
`
`
`DAC
`
`Drive
`system
`
`Plant
`
`Outputs
`
`Signal"
`conditioning
`
`Analog
`sensors/
`ransducers
`
`r- - -
`I (cid:9)
`Digital (cid:9)
`I
`—I sensors/ I-4— — — — — —
`I transducers I
`_j
`
`Figure 1.2. Block diagram of a direct digital control system.
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`4 (cid:9)
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`tern of a plant typically takes in analog signals. Often, the digital output from con-
`troller has to be converted into analog form for this reason. Both analog-to-digital
`conversion (ADC) and digital-to-analog conversion (DAC) can be interpreted as
`signal-conditioning (modification) procedures. If more than one output signal is
`measured, each signal will have to be conditioned and processed separately. Ideally,
`this will require separate conditioning and processing hardware for each signal chan-
`nel. A less expensive (but slower) alternative would be to time-share this expensive
`equipment by using a multiplexer. This device will pick one channel of data from a
`bank of data channels in a sequential manner and connect it to a common input
`device. Both analog and digital multiplexers are available. In a digital multiplexer,
`the input signals come from a bank of digital sensors, and the output signal itself,
`which would be in digital form, goes directly into the digital controller. High-speed
`multiplexers (e.g., over 50,000 switchings/second) use electronic switching.
`For complex processes with a large number of input/output variables (e.g., a
`nuclear power plant) and with systems that have various operating requirements
`(e.g., the space shuttle), centralized direct digital control is quite difficult to imple-
`ment. Some form of distributed control is appropriate in large systems such as man-
`ufacturing cells, factories, and multicomponent process plants. A favorite distributed
`control architecture is provided by heirarchical control. Here, distribution of control
`is available both geographically and functionally. An example for a three-level hier-
`archy is shown in figure 1.3. Management decisions, supervisory control, and coor-
`dination between plants are provided by the management (supervisory) computer,
`which is at the highest level (level 3) of the hierarchy. The next lower level computer
`generates control settings (or reference inputs) for each control region in the corre-
`sponding plant. Set points and reference signals are inputs to the direct digital con-
`trol (DDC) computers that control each control region. The computers communicate
`using a suitable information network. Information transfer in both directions (up and
`down) should be possible for best performance and flexibility. In master—slave dis-
`tributed control, only downloading of information is available.
`
`1.4 SIGNAL CLASSIFICATION IN CONTROL SYSTEMS
`
`A digital control system can be loosely interpreted as one that uses a digital com-
`puter as the controller. It is more appropriate, however, to understand the nature of
`the signals that are present in a control system when identifying it as a digital con-
`trol system.
`Analog signals are continuous in time. They are typically generated as outputs
`of a dynamic system. (Note that the dynamic system could be a signal generator or
`any other device, equipment, or physical system.) Analytically, analog signals are
`represented as functions of the continuous time variable t.
`Sampled data are, in fact, pulse amplitude—modulated signals. In this case, in-
`formation is carried by the amplitude of each pulse, with the width of the pulses
`kept constant. For constant sampling rate, the distance between adjacent pulses
`is also kept constant. In a physical situation, a pulse amplitude—modulated signal is
`generated through a sample-and-hold operation, in which the signal is sampled at
`
`Sec. 1.4 (cid:9)
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`Level 3
`
`Geographic Distribution
`
`Superviso ry
`(Management)
`Computer
`
`Process Plant 1
`
`o
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`21 • • • P
`
`Level 2
`
`Control-Setting
`Computer
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`Local Control System 1
`
`Set
`Points
`Inputs)
`(Reference
`
`Functional
`Distribution
`
`Level 1
`
`DDC
`Computer
`
`Control
`Actuator
`
`Plant
`Subsystem
`
`Outputs
`
`Feedback
`Signals
`
`Measurement
`Instruments
`
`Figure 1.3. A three -level hierarchical control scheme.
`the beginning of the sampling period and kept constant at that value, irrespective of
`the true value of the signal over that period. An important advantage of sampling is
`that expensive equipment can be shared among many signals. Furthermore, sam-
`pling is necessary in real-time digital processing to allow for the processing time.
`Analytically, sampled data consist of a sequence of numbers (or a function of integer
`variable).
`Digital data are coded numerical data. For example, a binary code or ASCII
`(American Standard Code for Information Interchange) may be used to represent
`each value in a sequence of digital data. The code itself determines the actual value
`of a particular unit of digital information. Typically, digital data are generated by
`digital processors, digital transducers, counters, encoders, and other such digital
`devices.
`Table 1.1 summarizes the identifying characteristics of these three types of
`data. Analog systems generate analog signals only. Sampled-data systems depend on
`analog data as well as sampled data. Digital systems, however, utilize all three types
`of signals, generally at different levels of interaction. Sampled-data systems and dig-
`ital systems may be modeled using discrete-time models (see table 1.2).
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`TABLE 1.1 SIGNAL CATEGORIES FOR IDENTIFYING CONTROL SYSTEM TYPES
`
`Signal (data)
`category
`
`Analog signals (data)
`
`Sampled data
`
`Digital data
`
`Description
`
`Continuous in time t; typically represents an output of a dynamic
`system
`Pulse amplitude—modulated signals
`Information carried by pulse amplitude
`Typically generated by sample-and-hold process
`Coded numerical data; the particular code determines the numerical
`value
`Typically generated by digital processors, digital transducers, and
`counters
`
`TABLE 1.2 REPRESENTATIVE ANAL