Advanced PID Control.pdf

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\) Advanced PID Control Karl J. Astrom Tore Hdgglund Department of Automatic Control Lund Institute of Technology Lund Uniuersity z\ Jlsnr ,? Systems, ISA-The Instrumentalion, and Automation Society

Copyright @ 2006 by ISA - Instrumentation, Systems, and Automation Society 67 Alexander Drive P.O. Box 12277 Research Triangle Park, NC 27709 All rights reserved. Printed in the United States of America. 1 0 9 8 7 6 5 4 3 2 ISBN r-55617-942-r No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. Notice The information presented in this publication is for the general education of the reader. Because neither the author nor the publisher has any control over the use of the information by the reader, both the author and the publisher disclaim any and all liability of any kind arising out of such use. The reader is expected to exercise sound professional judgment in using any of the information presented in a particular application. Additionally, neither the author nor the publisher have investigated or considered the effect of any patents on the ability of the reader to use any of the information in a particular application. The reader is responsible for reviewing any possible patents that may affect any particular use of the information presented. Any references to commercial products in the work are cited as examples only. Neither the author nor the publisher endorses any referenced commercial product. Any trademarks or tradenames referenced belong to the respective owner of the mark or name. Neither the author nor the publisher makes any representation regarding the availability of any referenced commercial product at any time. The manufacturer's instructions on use of any commercial product must be followed at all times, even if in conflict with the information in this publication. Library of Congress Cataloging-in-Publication Data Astrtjm, Karl J. (Karl Johan), lg34- Advanced PID control / Karl Johan Astrom and Tore Hagglund. p. cm. Includes bibliographical references and index. ISBN 1-55617-942-1 (pbk.) 1. PID controllers. I. Hrigglund, Tore. II. Title. TJ223.P55A85 2006 629.8'3--dc22 20050r4664

Preface The PID controller is the most common solution to practical control problems. Although controllers with proportional and integral action have been used from the time when windmills and steam engines were the dominant technologies, the current form of the PID controller emerged with the pneumatic controllers in the 1930s. The controllers have been implemented in many different ways using mechanical, pneumatic, electronic, and computer technolory. The devel- opment accelerated when the microprocessor implementations appeared in the 1980s. One reason was that the computer implementations made it possible to add features like auto-tuning and diagnostics, which are very beneficial for users. From an engineering perspective, it is particularly interesting to ana- lyze what happened at the technology shifts, when some important features were rediscovered and others were added. This book has grown out of more than 25 years of development of auto- tuners for PID controllers in close collaboration with industry. Through this work, we have been exposed to a large number of real industrial control prob- lems. We have benefited much from participating in development, commission- ing, and troubleshooting of industrial controllers. The practical work has also inspired research. This book is the last part of a trilogy. The first book, Automatic Tfu.ning of PID Controllers, 1988, which had 6 chapters, gave a short description of our early experiences with development of relay auto-tuners. The second book, PID Controllers: Theory, Design,, and Tfu.ning, 1995, which has 7 chapters, grew out of the need for a broader coverage of many aspects of PID control. In particular, it reviews many design methods for PID controllers that we investigated in connection with our work on auto-tuners. The knowledge about PID control in 1995 still was not satisfactory for de- sign of auto-tuners. One drawback was that the user had to provide the con- troller with design choices. It is particularly difficult for a user to assess if dynamics is dead-time or lag dominated. This question stimulated further re- search. Because of the drastic increase in computing power, it was also possible to use design algorithms that require more computations. Thning and design of PID controllers have traditionally been based on spe- cial techniques. Robust control was a major development of control theory that matured in the late 1990s, resulting in powerful design methods based on ro- bust loop shaping. This stimulated us to initiate a research program to adapt

Preface these methods to PID control. At the same time, it seemed natural to bring PID control closer to the mainstream ideas in control. When working with in- dustrial auto-tuners, we also saw a great need to include diagnostics in the controller, because it is no use to tune a controller if the process has severe malfunctions. The present book, Aduanced PID Control, is the result of this effort. With a total of 13 chapters, this new book substantially expands on some of the topics covered in the previous versions and provides several new chapters that deal with controller design, feedforward design, replacement of the Ziegler- Nichols tuning rules, predictive control, loop and performanee asqeqqrnnnr ?-i interaction. At this point in our book trilogy, we assume that the reader rb highly familiar with control theory. Our research has given a deeper understanding of the trade-offs between load disturbance attenuation, injection of measurement noise, and set-point response. We have also been able to answer questions like: Should a controller be tuned for response to load disturbances or set points? What information is required to design a PID controller? When can derivative action give signif- icant improvements? When are more complicated controllers justified? When is it justified to develop more accurate process models? With the knowledge developed, it is now possible to design auto-tuners that can make these assess- ments autonomously. In addition, we have developed new simple methods for designing PID controllers. As an example of the insight gained we can mention that control theory tells that it is not necessary to make a compromise between tuning for load disturbance response and set-point response. Both requirements can be satis- fied by using a controller with two degrees of freedom, which combines feedback and feedforward. The feedback gains should be chosen to satisfy requirements on disturbance attenuation and robustness. The desired response to set-point changes can then be obtained by proper use of feedforward. Set-point weighting is a simple form of feedforward for PID control. In some cases, it is justified to use more elaborate feedforward. For this reason, we have included a chapter on controller design and another chapter on feedforward in the new book. The robustness analysis also shows the advantage of having low controller gain at high frequency, high frequency roll-off. This can be accomplished by flltering the process output by a second order filter. Based on the insight ob- tained, we recommend extended use of set-point weighting or more advanced feedforward. We also recommend that the process output is fiItered using a second order filter. We would like to thank many people who have given knowledge, insight, and inspiration. Our interest in PID control was inspired by Axel Westrenius and Mike Somerville of Eurotherm in the early 1980s. We have learned much from working with students; particular thanks are due to Lars Gdran Elfgren (Eurotherm), Giiran Grtinhammar (LTH), Ari Ingimundarson (UPC), Oskar Nordin (Volvo), Helene Panagopoulos (Volvo), Per Persson (Volvo), Mikael Pe- tersson (ABB), Ola Slattke (ABB), and Anders Wall6n (Ericsson Mobile Plat- forms), who continue to give us valuable insight even if they are now pursuing careers in industry. We are very grateful to Sune Larsson and Lars Beath, formerly of NAF vi

Controls, with whom we developed the first industrial relay auto-tuner. The company NAF Controls was merged several times and is now part of ABB, where we have enjoyed interactions with Gdran Arinder, Alf Isaksson, Per Erik Mod6n, Lars Pernebo, and Thomas Vonheim. We have shared the joy and chal- lenges in moving techniques for auto-tuning and diagnostics into a wide range of industrial products. Many stimulating discussions with our colleagues Anton Cervin (LTH), Sebastian Dormido (UNED), Gty Dumont (UBC), Chang Chieh Hang (NUS), Karl Henrik Johansson (KTH), Birgitta Kristiansson (CTH), Bengt Lennartsson (CTH), Manfred Morari (ETH), Dale Seborg (UCSB), Sig- (LTH), and Karl-Erik Arz6n (LTH) urd Skogestad (NTNU), Bjiirn Wittenmark from academia are also highly appreciated. Our friends in industry Bill Bialkowski, Terry Blevins, Greg McMillan, and Willy Wojsznis from Emerson, Edgar Bristol, Sigifredo Niflo, and Greg Shinskey from Foxboro, Bdrje Eriksson (M-real), Krister Forsman (Perstorp), Ken Goff (Leeds and Northrup), Niklas Karlsson (Evolution Robotics), Joseph Lu (Honeywell), Tor Steinar Schei (Cybernetica), Stefan Rtrnnbiick (Optima- tion), have generously shared their knowledge and insight with us. We are particularly grateful to Peter Hansen, formerly of Foxboro, who read the com- plete manuscript and gave us very good feedback. We are very grateful to Leif Andersson who made the layout of the text and gave much assistance with TbX, Agneta T\rszyriski who translated much of the text to I4rIbX, and Eva Dagnegfird who drew several of the figures. Finally, we would like to thank the Swedish Research Council (VR), the Swedish Agency for Innovation Systems (VINNOVA), and the Swedish Foun- dation for Strategic Research (SSF) who have supported our research for many years. Kanr, JoHaN AsrnOnt Tonn HAccluNn Department of Automatic Control Lund Institute of Technology Box 118, SE-22I00 Lund, Sweden karl-j ohan. astrom@control . Ith. se tore . hagglund@control . lth. se vu

Contents 1 . 2. 3. 4. Technology Changes and Knowledge Thansfer Summary . Introduction . Static Models Feature-Based Models Tlpical Process Models . : . : . : . Introductio" Feedback Simple Forms of Feedback Introduction 1.1 1.2 1.3 1.4 How the PID Controller Developed 1.5 1.6 Outline of the Contents of the Book . I.7 1.8 Notes and References Process Models 2.1 2.2 2.3 Dynamic Models 2.4 2.5 2.6 Models for Disturbances . 2.7 How to Obtain the Models 2.8 Model Reduction 2.9 2.t0 Notes and References PID Control 3.1 3.2 3.3 3.4 3.5 3.6 When Can PID Control Be Used? 3.7 3.8 Notes and References Controller Design 4.1 4.2 4.3 4.4 Introduction . A Rich Variety of Control Problems Feedback Fundamentals . Stability Introduction . The PID Controller . Filtering the Derivative Set-Point Weighting Integrator Windup Summary . Summary 1 1 2 3 5 7 8 10 10 t2 t2 13 T4 23 28 44 47 56 6 1 62 64 64 64 73 74 76 87 92 93 95 95 96 96 r02 ix

Contents 6. 7. Classical Specifications Introduction . Improved Set-Point Response . Set-Point Weighting Fast Set-Point Response . Summary Notes and References Closed-Loop Poles and Zeros The Sensitivity Functions . Robustness to Process Variations Introduction . Ziegler-Nichols and Related Methods Rule-Based Empirical T\rning. Pole Placement Lambda T\rning . Algebraic Design 4.5 4.6 4.7 4.8 Quantifying the Requirements 4.9 4.10 Summary A.LI Notes and References Feedforward Design 5.1 5.2 5.3 5.4 Neutral Feedforward . 5.5 5.6 DisturbanceAttenuation 5.7 5.8 PID Design 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Optimization Methods Robust Loop Shaping 6.8 6.9 Summary 6.10 Notes and References A Ziegler-Nichols Replacement 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Measurement Noise and Filtering 7.9 Detuning . 7.10 Summary 7.1I Notes and References Predictive Control Introduction . 8.1 8.2 The Smith Predictor 8.3 Analysis of Smith Predictor Control . 8.4 The PPI Controller . 8.5 Predictors for Integrating Processes 8.6 Model Predictive Control 8.7 Summarv Introduction . The Test Batch PI Control . PID Control Frequency Response Methods PID Control Based on Second-Order Model Comparison of the Methods . 109 1 1 1 1 1 8 122 128 136 137 139 139 139 I45 I46 150 154 156 157 158 158 159 169 t74 186 189 196 206 221 222 225 225 226 228 230 238 242 247 251 253 262 265 266 266 267 271 279 283 285 291

Introduction . Integrated Ttrning and Diagnosis Introduction . Interaction of Simple Loops . . Notes and References Supervision of Adaptive Controllers Iterative Feedback Ttrning Commercial Products Summary 8.8 Automatic Thning and Adaptation Introduction . 9.1 Process Knowledge . 9.2 Adaptive Techniques . 9.3 9.4 Model-Based Methods 9.5 Rule-Based Methods 9.6 9.7 9.8 9.9 9.10 Notes and References Loop and Performance Assessment 10.1 I0.2 Valves 10.3 Loop Assessment 10.4 Performance Assessment 10.5 10.6 Summary 10.7 Notes and References Interaction 11.1 LI.2 11.3 Decoupling 1I.4 Parallel Systems 11.5 Summary 11.6 Notes and References Control Paradigms 12.1 Introduction I2.2 Bottom-Up and Top-Down Approaches 12.3 Repetitive Control 12.4 Cascade Control I2.5 Mid-Range and Split-Range Control . 12.6 Nonlinear Elements I2.7 Neural Network Control . I2.8 Fuzzy Control . I2.9 System Structuring 12.10 Summary t2.II Notes and References Implementation 13.1 I3.2 Analog Implementations 13.3 Computer Implementations . 13.4 Velocity Algorithms 13.5 OperationalAspects 13.6 Controller Outputs . L3.7 Summarv Introduction . 10. l l . 12. 13. Contents 292 293 293 294 295 298 302 304 3 1 3 3 1 6 327 327 329 329 329 334 336 344 345 346 347 347 347 354 360 364 365 366 366 367 368 373 378 3 8 1 389 392 398 404 406 407 407 408 4r2 420 423 427 43r xi

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