.
`
`Fundamentals of
`
`Automatic Control
`
`
`
`Robert C. W'I:_\-'ri{:k
`Community and Technical (.It'rllege
`The University of Akron
`
`McGraw-Hill Book Company
`
`New York
`St. Louis
`Dailas
`San Francisco
`
`Montreal
`New Delhi
`Panama
`Paris
`
`TSMC et al v. Zond IPR2014-00803
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`irary of Congress Cataloging in Publication Data
`
`Fundamentals of automatic control.
`
`1. Automatic control. I. Title.
`74-10896
`
`I
`I
`
`99:
`
`134771
`
`JNDAMENTALS OF AUTOMATIC CONTROL
`ipyright © 1975 by McGraw-Hill, Inc. All rights reserved.
`'inted in the United States of America. No part of this publication
`it}; be reproduced. stored in a retrieval system, or transmitted, in
`1y form or by any means. electronic, mechanical, photocopying, recording.
`' otherwise, without the prior written permission of the publisher.
`
`234567390 KPKP 78321098765
`
`To my mother
`
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`

`

`[I Fundamentals of automatic control
`
`1
`
`C*—
`
`C
`
`Figure 1~8 Takeoff-point
`Sciitotion
`
`repre-
`
`F118 CillafliitiBS biting combined at a summing point must be in the same
`Inits; for example. two voltages may be combined but a voltage and
`1 current cannot be brought together. Any number of variables may
`actor a summing point.
`A takeoff point is used when the output of a block is applied to two
`N“ more bIOCkS- A takeoff point is simply represented by a dot as shown
`
`To illustrate the block-diagram representation of a system, let us
`again examine the oven-temperature control described in the preceding
`iCCliOl‘l. This system is shown in block-diagram form in Fig. 1-9. In this
`)articular diagram the various blocks may be identified with elements
`if the system. In addition the units associated with the transfer function
`3f BflCh block are shown in parentheses.
`The block diagram tends to clarify the physical understanding of the
`system and provides a convenient basis for system analysis. We shall
`also see that block diagrams are useful in pointing out the similarity
`between apparently unrelated systems. It should be emphasized that
`the lines connecting one block with another represent the flow of
`control information within the system. The main sources of energy for
`the system need not be included in the block diagram.
`
`SIMPLIFICATIUN [IF BLOCK DIAGRAMS
`l-fi
`
`
`The bIOCk diagram that is initially drawn for a system may contain
`a large number of blocks and signal paths and be more complicated
`than is desirable. in such cases a simplification may be performed to
`reduce the block diagram to a form with feWer blocks. Rearranging
`
`Error
`voltage,
`v”
`__ _
`
`
`Heater
`
`current, A
`Amplifier
`
`[Ali/e!
`
`0
`0V9“
`
`Heateratoven temperature, F
`[OWN
`
`
`
`Introduction 11
`
`
`
`Figure 1-10 Moving summing point around a block
`
`a system diagram to effect simplification is termed block—diagram
`algebra since it is analogous to simplifying algebraic equations. How-
`ever, reducing a block diagram has the advantage of providing a better
`understanding of the interrelationships of the various elements in the
`system as compared to simplifying the system equations.
`The combining of cascaded blocks into a single block. as described
`in Sec. 1-5,
`is obviously one step toward simplification. As another
`possibility, it is sometimes useful to move a summing point around a
`block as indicated in Fig. 1-10. Note that the inputs A and B are intro-
`duced through blocks incorporating the function G around which the
`summing point was moved. Applying the distributive property of
`algebra, we see that C = (A + B}G = AG + BG. Thus the two diagrams
`are equivalent.
`Table 1-1 gives a number of transformations useful in simplifying
`block diagrams. These transformations can be verified by showing that
`the Outputs from the two equivalent diagrams are the same. Note Ihat
`the original and equivalent identities can be used interchangeably.
`
`1-7 CLOSED-LOOP TRANSFER FUNCTION
`—_____—_.___——-
`
`Since certain functions and types of variables are commonly associ—
`ated with feedback control systems. a generalized block diagram may
`be formulated and the associated closed-loop transfer function derived.
`Some standardization of the symbols and terminology relating to feed-
`back control systems has been achieved and is used in this case.
`Figure 1-11 is a general block diagram of a closed-loop control system.
`is important that the terms used in this diagram be clearly under—
`It
`stood.
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`Fundamentals of automatic control
`
`TABLE 1-] 3L0 CK- D1 AURAM IDENTITIES
`
`Equivalent
`
`l/[oving summing point
`
`Moving summing point
`
`Moving takeoff point
`
`Moving takeoff point
`
`—'-_'C
`
`If
`
`—-—.c
`
` R
`
`
`
`
`
`Introduction 13
`
`E)g Reference input elements
`Control elements
`System elements or process
`Feedback. elements
`Desired value
`
`MWQEO-‘O‘QIQE Error or actuating signal
`Disturbance input
`
`Reference input
`Controlled output
`Manipulated variable
`
`Feedback signal
`
`Figure 1-11 General block diagram of control system
`
`The reference input H is derived from the desired value and is a signal
`external to the control loop. It serves as the reference of comparison
`for the feedback signal.
`The controlled output C is the process quantity being controlled.
`The manipulated variable M is the control signal which the control
`elements apply to the process.
`The feedback signal B is a signal which is a function of the conlrolled
`output and which is summed With the reference input.
`The error or actuating signal E is the algebraic difference between
`the reference input and feedback signals and provides the signal ap-
`plied to the control elements.
`The disturbance input U is an unwanted input signal to the system
`that tends to cause the controlled output to differ from the value
`commanded by the reference input. Disturbance inputs are due to
`changes in the load on the system. For example, a change in the ambient
`temperature surrounding the oven described in Sec. 1-3 is a disturbance
`since it changes the heat input required by the oven. Obviously the
`response of the system to a disturbance input should be minimal.
`
`System Elements
`
`The reference input elements GU convert the desired value to a
`reference input signal.
`The control elements GI. sometimes called the controller. are the
`
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