`
`RICHARD C. DORF
`
`University of California, Davis
`
`ROBERT H. BISHOP
`
`The University of Texas at Austin
`
`7" ADDISON-WESLEY
`
`An imprint of Addison Wesley Longman, Inc.
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`Menlo Park, California - Reading, Massachusetts - Harlow, England
`Berkeley, California ' Don Mills, Ontario ' Sydney - Bonn 0 Amsterdam - Tokyo 0 Mexico City
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`1
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`ION 1021
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`1
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`ION 1021
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`

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`Gene F. Franklin and J. David Powell
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`Multivariable Feedback Design
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`Library of Congress Cataloging-in-Publication Data
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`Dorf, Richard C.
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`Modern control systems / Richard C. Dorf, Robert H. Bishop. — 8th ed,
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`Includes bibliographical references and index.
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`ISBN 0—201 —30864—9
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`1. Feedback control systems.
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`1998
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`629.8'3—dc21
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`2. Control theory.
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`I. Bishop, Robert H., 1957— .
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`2
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`

`

`2
`
`Chapter '1
`
`Introduction to Control Systems
`
`q
`
`Finally, we introduce the Sequential Design Example: Disk Drive Read System. This
`example will be considered sequentially in each chapter of this book. It represents a very
`important and practical control system design problem while simultaneously serving as a
`useful learning tool.
`
`1.1 INTRODUCTION
`
`Engineering is concerned with understanding and controlling the materials and forces of
`nature for the benefit of humankind. Control system engineers are concerned with under-
`standing and controlling segments of their environment, often called systems, to provide
`useful economic products for society. The twin goals of understanding and control are
`cbmplementary because effective systems control requires that the systems be understood
`and modeled. Furthermore, control engineering must often consider the control of poorly
`understood systems such as chemical process systems. The present challenge to control
`engineers is the modeling and control of modern, complex, interrelated systems such as
`traffic control systems, chemical processes, and robotic systems. Simultaneously, the for-
`tunate engineer has the opportunity to control many very useful and interesting industrial
`automation systems. Perhaps the most characteristic quality of control engineering is the
`opportunity to control machines and industrial and economic processes for the benefit of
`society.
`'
`Control engineering is based on the foundations of feedback theory and linear sys—
`tem analysis, and it integrates the concepts of network theory and communication theory.
`Therefore control engineering is not limited to any engineering discipline but is equally
`applicable to aeronautical, chemical, mechanical, environmental, civil, and electrical engi-
`neering. For example, quite often a control system includes electrical, mechanical, and
`chemical components. Furthermore, as the understanding of the dynamics of business, so-
`cial, and political systems increases, the ability to control these systems will increase also.
`A control system is an interconnection of components forming a system configuration
`that will provide a desired system response. The basis for analysis of a system is the foun‘
`dation provided by linear system theory, which assumes a cause-effect relationship for the
`components of a system. Therefore a component or process to be controlled can be repre-
`sented by a block, as shown in Fig. 1.1. The input—output relationship represents the cause-
`and—efifect relationship of the process, which in turn represents a processing of the input
`signal to provide an output signal variable, often with a power amplification. An open-loop
`control system utilizes a controller or control actuator to obtain the desired response, as
`shown in Fig. 1.2. An open-loop system is a system without feedback.
`
`An open-loop. control system utilizes an actuating device to control the
`process directly without using feedback.
`
`FIGURE 1 .1
`Process to be
`controlled.
`
`Input
`
`,
`
`Procm
`
`Output
`
`3
`
`

`

`Section 1.1
`
`Introduction
`
`3
`
`FIGURE 1 .2
`Open-loop control
`system (without
`feedback).
`
`.
`Output
`Desrred output response
`
`
`Act
`
`tin
`
`FIGURE 1.3
`Closed-loop
`feedback control
`system (with
`feedback).
`
`Desired output
`response
`
`
`
`
`
`Output
`
`In contrast to an open-loop control system, a closed-loop control system utilizes an
`additional measure of the actual output to compare the actual output with the desired output
`response. The measure of the output is called the feedback signal. A simple closed-loop
`feedback control system is shown in Fig. 1.3. A feedback control system is a control
`system that tends to maintain a prescribed relationship of one system variable to another
`by comparing functions of these variables and using the difference as a means of control.
`A feedback control-system often uses a function of a prescribed relationship between
`the output and reference input to control the process. Often the difference between the
`output of the process under control and the reference input is amplified and used to control
`the process so that the difference is continually reduced. The feedback concept has been
`the foundation for control system analysis and design.
`
`A closed-loop control system uses a measurement of the output and
`feedback of this signal to compare it with the desired input (reference
`or command).
`
`Due to the increasing complexity of the system under control and the interest in achiev-
`ing optimum performance, the importance of control system engineering has grown in the
`past decade. Furthermore, as the systems become more complex, the interrelationship of
`many controlled variables must be considered in the control scheme. A block diagram
`depicting a multivariable control system is shown in Fig. 1.4.
`
`FIGURE 1.4
`Multivariable
`control system.
`
`Desired
`output
`response
`
`
`Controller — -
`_
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`Measurement
`
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`Vgggglits
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`4
`
`

`

`Chapter 1
`
`Introduction to Control Systems
`
`A common example of an open-loop control system is an electric toaster in the kitchen.
`An example of a closed—loop control system is a person steering an automobile (assuming
`his or her eyes are open) by looking at the auto’s location on the road and making the
`appropriate adjustments.
`The introduction of feedback enables us to control a desired output and can improve
`accuracy, but it requires attention to the issue of stability of response.
`
`1.2 HISTORY OF AUTOMATIC CONTROL
`
`The use of feedback to control a system has had a fascinating history. The first applications
`of feedback control appeared in the development of float regulator mechanisms in Greece
`in the period 300 to 1 B.C. [1, 2, 3]. The water clock of Ktesibios used a float regulator
`(refer to Problem 1.11). An oil lamp devised by Philon in approximately 250 B.C. used a
`float regulator in an oil lamp for maintaining a constant level of fuel oil. Heron of Alexan-
`dria, who lived in the first century A.D., published a book entitled Pneumatica, which out-
`lined several forms of water-level mechanisms using float regulators [l].
`The first feedback system to be invented in modern Europe was the temperature regu-
`latorlof Cornelis Drebbel (1572—1633) of Holland [1]. Dennis Papin [1647-1712] in-
`vented the first pressure regulator for steam boilers in 1681. Papin’s pressure regulator was
`a form of safety regulator similar to a pressure—cooker valve.
`The first automatic feedback controller used in an industrial. process is generally
`agreed to be James Watt’s flyball governor, developed in 1769 for controlling the speed of
`a steam engine [1, 2]. The all-mechanical device, shown in Fig. 15, measured the speed of
`the output shaft and utilized the movement of the flyball with speed to control the valve
`and therefore the amount of steam entering the engine. As the speed increases, the ball
`weights rise and move away from the shaft axis, thus closing the valve. The flyweights
`require power from the engine to turn and therefore cause the speed measurement to be less
`accurate.
`
`FIGURE 1 .5
`Watt's flyball
`governor.
`
`W Measured
`w
`Speed
`
`Boiler
`5:} {Steam
`
`
`
`5
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`

`

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`Section 1.5 Examples of Modern Control Systems -
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`. the Industrial Revolution has until recently resulted mainly in the displacement of human,
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`muscle power from the tasks of production. The current revolution in computer technology _
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`is causing an equally momentous social change: the expansion of information gathering
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`and information processing as computers extend the reach of the human brain [16].
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`Control systems are used to achieve (1) increased productivity and (2) improved
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`performance of a device or system. Automation is used to improve productivity and ob-
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`tain high—quality products. Automation is the automatic operation or control of a process,
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`device,xor system. We utilize automatic control of machines and processes to produce a
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`product within specified tolerances and to achieve high precision [28].
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`The term automation first became popular in the automobile industry. Transfer lines
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`were c0upled with automatic machine tools to create long machinery lines that could
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`produce engine parts, such as the cylinder block, virtually without operator intervention.
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`In body—parts manufacturing, automatic—feed mechanisms were coupled with high—speed
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`stamping presses to increase productivity in sheet-metal forming. In many other areas
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`where designs were relatively stable, such as radiator production, entire automated lines
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`replaced manual operations.
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`With the demand for flexible, custom production emerging in the 1990s, a need for
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`flexible automation and robotics is growing [17, 25].
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`There are about 150,000 control engineers in the United States and also in Japan and
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`in Europe. In the United States alone, the ,c0ntrol industry does a business of over $50
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`billion per year! The theory, practice, and application of automatic control is a large, excit-
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`ing, and extremely useful engineering discipline. One can readily understand the motiva-
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`tion for a study of modern control systems.
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`1.5 EXAMPLES OF MODERN CONTROL SYSTEMS
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`Feedback control is a fundamental fact of modern industry and society. Driving an auto-
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`mobile is a pleasant task when the auto responds rapidly to the driver’s commands. Many
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`cars have power steering and brakes, which utilize hydraulic amplifiers for amplification of
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`the force to the brakes or the steering wheel. A simple block diagram of an automobile
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`steering control system is shown in Fig. 1.8(a). The desired course is compared with a
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`measurement of the actual course in order to generate ameasure of the error, as shown in
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`Fig. 1.8(b). This measurement is obtained by visual and tactile, (body movement) feedback.
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`There is an additional feedback from the feel of the steering wheel by the hand (sensor).
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`This feedback system is a familiar version of the steering control system in an ocean liner
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`or the flight controls in a large airplane. A typical direction-of-travel response is shown in
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`Fig. 1.8(c).
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`Control systems operate in a closed-loop sequence, as shown in Fig. 1.9. With an
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`accurate sensor, the measured output is equal to the actual output of the system. The differ-
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`ence between the desired output and the actual output is equal to the error, which is then
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`adjusted by the control device (such as an amplifier). The output of the control device
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`causes the actuator to modulate the process in order to reduce the error. The sequence is
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`such, for instance, that if a ship is heading incorrectly to the right, the rudder is actuated to
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`direct the ship to the left. The system shown in Fig. 1.9 is a negative feedback control
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`system, because the output is subtracted from the input and the difference is used as the
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`input signal to the power amplifier.
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`
`
`6
`
`

`

`1 0
`
`Chapter 1
`
`introduction to Control Systems
`
`Desired
`course
`of travel
`
`.
`Steering
`_
`mechanism
`
`,
`Automobile
`
`
`
`of travel
`
`, Measurement.
`
`visual and tactile
`
`Actual
`‘
`course
`
`(a)
`
`
`Desired direction of travel
`
`Response —
`direction
`0‘ /
`travel
`Actual direction of travel
`
`(b)
`
`Time, ‘
`
`(c)
`
`
`
`FIGURE 1.8
`(a) Automobile
`steering control
`system. (b) The
`driver uses the
`difference between
`the actual and the
`fizigfgcgreohceugt‘ed
`a controlled
`adjustment of the
`steering wheel. (0)
`Typical direction-
`of-travel response.
`
`FIGURE 1.9 '
`A negative
`feedback system
`block diagram
`depicting a basic
`closed-loop control
`system. The
`control device is
`
`Input
`desired
`oulpm
`
`ouput
`
`Actual
`
`Measured output
`often called a
`"controller.”
`
`
`7
`
`

`

`
`
`Section 1.5 Examples of Modern Control Systems
`
`'
`
`1 1
`
`N
`Fluid input
`
`FIGURE 1 .10
`A manual control
`system for
`regulating the level
`of fluid in a tank by
`adjusting the
`output valve. The
`operatorviews the
`level of fluid
`through a port in
`the side of
`the tank.
`
` Fluid output
`
`A basic, manually controlled closed—loop system for regulating the level of fluid in a
`tank is shown in Fig. 1.10. The input is a reference level of fluid that the operator is in-
`structed to maintain. (This reference is memorized by the operator.) The power amplifier is
`the operator, and the sensor is visual. The operator compares the actual level with the de—
`sired level and opens or closes the valve (actuator), adjusting the fluid flow out, to maintain
`the desired level.
`
`Other familiar control systems have the same basic elements as the system shown in
`Fig. 1.9. A refrigerator has a temperature setting or desired temperature, a thermostat to
`measure the actual temperature and the error, and a compressor motor for power amplifi-
`cation. Other examples in the home are the oven, furnace, and water heater. In industry,
`there are speed controls, process temperature and pressure controls, position, thickness,
`composition, and quality controls, among many others [14, 17, 18].
`In its modern usage, automation can be defined as a technology that uses programmed
`commands to operate a given process, combined with feedback of information to determine
`that the commands have been properly executed. Automation is often used for processes
`that were previously operated by humans. When automated, the process can operate. with-
`out human assistance or interference. In fact, most automated systems are capable of per-
`forming their functions with greater accuracy and precision, and in less time, than humans
`are able to do. A semiautomated process is one that incorporates both humans and robots.
`For instance, many automobile assembly line operations require cooperation between a
`human operator and an intelligent robot.
`A robot is a computer-controlled machine and involves technology closely associated
`with automation. Industrial robotics can be defined as a particular field of automation in
`which the automated machine (that is, the robot) is designed to substitute for human labor
`[18, 27. 33]. Thus robots possess certain humanlike characteristics. Today, the most com-
`mon humanlike characteristic is a mechanical manipulator that is patterned somewhat after
`the human arm and wrist. We recognize that the automatic machine is well suited to some
`tasks. as noted in Table 1.2, and that other tasks are best carried out by humans.
`Another very important application of control technology is in the control of the mod:
`ern automobile [19, 20]. Control systems for suspension, steering, and engine control have
`been introduced. Many new autos have a four-wheel-steering system, as well as an antiskid
`control system.
`A three-axis control system for inspecting individual semiconductor wafers is shown
`in Fig. 1.11. This system uses a specific motor to drive each axis to the desired position in
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`8
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