Applied Control Theory for Embedded Systems

321 Pages·2006·3.92 MB·English

by  Tim Wescott

Applied Control Theory
for Embedded Systems

Applied Control Theory
for Embedded Systems
by Tim Wescott
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
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Library of Congress Cataloging-in-Publication Data
Wescott, Tim.
Applied control theory for embedded systems / by Tim Wescott.
p. cm. -- (Embedded technology series)
ISBN-13: 978-0-7506-7839-1 (pbk. : alk. paper)
ISBN-10: 0-7506-7839-9 (pbk. : alk. paper) 1. Embedded computer
systems--Design and construction. 2. Digital control systems--Design and
construction. I. Title. II. Series.
TK7895.E42W47 2006
629.8’9--dc22
2006002692
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN-13: 978-0-7506-7839-1
ISBN-10: 0-7506-7839-9
For information on all Newnes publications
visit our Web site at www.books.elsevier.com
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For all my teachers

Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ix
What’s on the CD-ROM? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi
Chapter 1: The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Control Systems ......................................1
1.2 Anatomy of a Control System ............................. 2
1.3 Closed Loop Control ................................ ...4
1.4 Controllers ................................ .......... 6
1.5 About This Book ...................................... 8
Chapter 2: Z Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Signals and Systems ................................... 12
2.2 Difference Equations .... .............................. 15
2.3 The Z Transform ....................................18
2.4 The Inverse Z Transform ............................... 19
2.5 Some Z Transform Properties ............................ 25
2.6 Transfer Functions ...................................30
2.7 Stability in the Z Domain ..............................34
2.8 Frequency Response ................................... 37
2.9 Conclusion .........................................41
Chapter 3: Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1 Tracking ................ ...........................43
3.2 Frequency Response ................................... 55
3.3 Disturbance Rejection ........ ........................ . 61
3.4 Conclusion ......................................... 63
Chapter 4: Block Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1 The Language of Blocks ................................65
4.2 Analyzing Systems with Block Diagrams ....................74
4.3 Conclusion .........................................93
viii Contents
Chapter 5: Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.1 Root Locus .........................................96
5.2 Bode Plots ........................................107
5.3 Nyquist Plots ......................................113
5.4 Conclusion ........................................124
Chapter 6: Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.1 Controllers, Filters and Compensators ....................125
6.2 Compensation Topologies .............................. 126
6.3 Types of Compensators ...................... .......... 128
6.4 Design Flow .......................................147
6.5 Conclusion ........................................148
Chapter 7: Sampling Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.1 Sampling .........................................149
7.2 Aliasing ..........................................151
7.3 Reconstruction .....................................153
7.4 Orthogonal Signals and Power .......................... 156
7.5 Random Noise .....................................157
7.6 Nonideal Sampling .................................. 159
7.7 The Laplace Transform ...............................170
7.8 z Domain Models ................................... 175
7.9 Conclusion ........................................ 182
Chapter 8: Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . 183
8.1 Characteristics of Nonlinear Systems ......................184
8.2 Some Nonlinearities .................................187
8.3 Linear Approximation ................................ 193
8.4 Nonlinear Compensators .............................. 199
8.5 Conclusion ........................................ 223
Contents ix
Chapter 9: Measuring Frequency Response . . . . . . . . . . . . . 225
9.1 Overview ......................................... 225
9.2 Measuring in Isolation ...............................226
9.3 In-Loop Measurement ................................ 229
9.4 Real-World Issues ...................................234
9.5 Software ................................ .......... 238
9.6 Other Methods .. ...................................245
Chapter 10: Software Implications . . . . . . . . . . . . . . . . . . . . . 247
10.1 Data Types ........................................247
10.2 Quantization ................ ...................... 250
10.3 Overflow .........................................262
10.4 Resource Issues .....................................264
10.5 Implementation Examples ............................. 268
10.6 Conclusion ........................................ 292
Chapter 11: Afterword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
11.1 Tools ............................................293
11.2 Bibliography ....................................... 295
About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299