`
`Fundamentals of
`
`Automatic Control
`
`
`
`Robert C.
`\_W't:_\-'1‘i{:k
`Community and Technical College
`The University of Akron
`
`McGraw-Hill Book Company
`
`New York
`St. Louis
`Dallas
`San Francisco
`
`Montrmul
`New Delhi
`Panama
`Paris
`
`TSMC et al v. Zond IPR2014-00799
`Page 1 Zond Ex. 2011
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`irary of Congress Cataloging in Publication Data
`
`Fundamentals of automatic control.
`
`1. Automatic control. I. Title.
`74-10896
`
`|
`l
`
`53
`
`134771
`
`JNDAMENTALS OF AUTOMATIC CONTROL
`ipyright © 1975 by McGraw-Hill, Inc. All rights reserved.
`-inked in the United States of America. No part of this publication
`:13; be reproduced, stored in a retrieval system, or transmitted, in
`13+ 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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`Introduction 11
`
`
`
`Figure 1-10 Moving summing point around a biocli
`
`a system diagram to effect simplification is termed blocli-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 + BC. 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 that
`the original and equivalent identities can be used interchangeably.
`
`l-7 CLOSED-LOOP TRANSFER FUNCTION
`.m_.
`
`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.
`
`1"1ll'1d3l'|'lt3l'lifllS of automatic control
`
`TCC*-
`
`Figure 1-8 Takeoff-point
`sentotion
`
`repre-
`
`Fhe quantities being 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
`)l’1il".1‘ a summing pr_ijn[_
`A takeoff point is used when the output of a block is applied to two
`it‘ more blocks. A tal<t:ofi' 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
`iC(‘.ii0l‘l. This system is shown in block-diagram form in Fig. 1-9. In this
`)El[‘tiCLl]ElI' diagram the various blocks may be identified with elements
`if the system. In atltlition the units associated with the transfer function
`3f Bach b1OC1< 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 blor.;l< diagrams are useful in pointing out the similarity
`between apparently unrelated systems. It should be emphasized that
`the lines connecting one b10Cl< 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.
`
`I-6 SIMPLIFICATIDN or BLOCK DIAGRAMS
`
`
`The block 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,
`or
`—- —
`
`Amplifier
`{Alva}
`
`
`
`
`
`Heater
`Current, A
`
`
`0
`0”“
`
`Heaterawen temperature, F
`EOFIA}
`
`
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`Introduction 13
`
` mmQEF)JJ‘§I§)_?.-
`
`‘C1 Reference input elements
`Control elements
`System elements or process
`Feedback elements
`Desired value
`
`Reference input
`Controlied output
`Manipulated variable
`Disturbance input
`Feedback signal
`Error or actuating signal
`
`Figure 1-11 General block diagram of control system
`
`The reference input B 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 controllerl.
`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 G” convert the desired value to a
`reference input signal.
`The control elements G1, sometimes called the controller, are the
`
`Fundamentals of automatic control
`
`TABLE 1-1 BLOCK-DIAGRAM IDENTITIES
`
`Equivalent
`
` R
`
`C C
`
`1'?
`
`i/loving summing point
`
`Moving summing point
`
`Moving takeoff point
`
`Moving takeoff point
`
`
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