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1、Advanced PID ControlAdvancedPID ControlKarl J. strm Tore HgglundDepartment of Automatic ControlLund Institute of TechnologyLund UniversityCopyright 2006 by ISA Instrumentation, Systems, and Automation Society67 Alexander DriveP.O. Box 12277Research Triangle Park, NC 27709All rights reserved.Printed

2、in the United States of America.1098765432ISBN 1-55617-942-1No 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.NoticeThe

3、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

4、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

5、 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 commerci

6、al 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 manufacturers instructions on use of any commercial p

7、roduct must be followed at all times, even if in conflict with the information in this publication.Library of Congress Cataloging-in-Publication Datastrm, Karl J. (Karl Johan), 1934-Advanced PID control / Karl Johan Astrom and Tore Hagglund.p. cm.Includes bibliographical references and index.ISBN 1-

8、55617-942-1 (pbk.)1. PID controllers. I. Hgglund, Tore. II. Title. TJ223.P55A85 2006629.83-dc222005014664PrefaceThe PID controller is the most common solution to practical control problems.Although controllers with proportional and integral action have been used fromthe time when windmills and steam

9、 engines were the dominant technologies,the current form of the PID controller emerged with the pneumatic controllersin the 1930s. The controllers have been implemented in many different waysusing mechanical, pneumatic, electronic, and computer technology. The devel opment accelerated when the micro

10、processor implementations appeared in the1980s. One reason was that the computer implementations made it possibleto add features like auto tuning and diagnostics, which are very beneficial forusers. From an engineering perspective, it is particularly interesting to ana lyze what happened at the tech

11、nology shifts, when some important featureswere 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 thiswork, we have been exposed to a large number of real industrial control

12、 prob lems. We have benefited much from participating in development, commission ing, and troubleshooting of industrial controllers. The practical work has alsoinspired research.This book is the last part of a trilogy. The first book, Automatic Tuning ofPID Controllers, 1988, which had 6 chapters, g

13、ave a short description of ourearly experiences with development of relay auto tuners. The second book, PIDControllers: Theory, Design, and Tuning, 1995, which has 7 chapters, grew outof the need for a broader coverage of many aspects of PID control. In particular,it reviews many design methods for

14、PID controllers that we investigated inconnection 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

15、assess ifdynamics is dead time or lag dominated. This question stimulated further re search. Because of the drastic increase in computing power, it was also possibleto use design algorithms that require more computations.Tuning and design of PID controllers have traditionally been based on spe cial

16、techniques. Robust control was a major development of control theory thatmatured in the late 1990s, resulting in powerful design methods based on ro bust loop shaping. This stimulated us to initiate a research program to adaptvPrefacethese methods to PID control. At the same time, it seemed natural

17、to bringPID 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 thecontroller, because it is no use to tune a controller if the process has severemalfunctions. The present book, Advanced PID Control, is the

18、result of thiseffort.With a total of 13 chapters, this new book substantially expands on some ofthe topics covered in the previous versions and provides several new chaptersthat deal with controller design, feedforward design, replacement of the Ziegler Nichols tuning rules, predictive control, loop

19、 and performance assessment, andinteraction. At this point in our book trilogy, we assume that the reader ishighly familiar with control theory.Our research has given a deeper understanding of the trade offs betweenload disturbance attenuation, injection of measurement noise, and set pointresponse.

20、We have also been able to answer questions like: Should a controllerbe tuned for response to load disturbances or set points? What information isrequired to design a PID controller? When can derivative action give signif icant improvements? When are more complicated controllers justified? Whenis it

21、justified to develop more accurate process models? With the knowledgedeveloped, it is now possible to design auto tuners that can make these assess ments autonomously. In addition, we have developed new simple methods fordesigning PID controllers.As an example of the insight gained we can mention th

22、at control theorytells that it is not necessary to make a compromise between tuning for loaddisturbance response and set point response. Both requirements can be satis fied by using a controller with two degrees of freedom, which combines feedbackand feedforward. The feedback gains should be chosen

23、to satisfy requirementson disturbance attenuation and robustness. The desired response to set pointchanges can then be obtained by proper use of feedforward. Set point weightingis a simple form of feedforward for PID control. In some cases, it is justified touse more elaborate feedforward. For this

24、reason, we have included a chapteron controller design and another chapter on feedforward in the new book.The robustness analysis also shows the advantage of having low controllergain at high frequency, high frequency roll off. This can be accomplished byfiltering the process output by a second orde

25、r filter. Based on the insight ob tained, we recommend extended use of set point weighting or more advancedfeedforward. We also recommend that the process output is filtered using asecond order filter.We would like to thank many people who have given knowledge, insight,and inspiration. Our interest

26、in PID control was inspired by Axel Westreniusand Mike Somerville of Eurotherm in the early 1980s. We have learned muchfrom working with students; particular thanks are due to Lars Gran Elfgren(Eurotherm), Gran Grnhammar (LTH), Ari Ingimundarson (UPC), OskarNordin (Volvo), Helene Panagopoulos (Volvo

27、), Per Persson (Volvo), Mikael Pe tersson (ABB), Ola Slttke (ABB), and Anders Walln (Ericsson Mobile Plat forms), who continue to give us valuable insight even if they are now pursuingcareers in industry.We are very grateful to Sune Larsson and Lars Bth, formerly of NAFviControls, with whom we devel

28、oped the first industrial relay auto tuner. Thecompany NAF Controls was merged several times and is now part of ABB,where we have enjoyed interactions with Gran Arinder, Alf Isaksson, Per ErikModn, Lars Pernebo, and Thomas Vonheim. We have shared the joy and chal lenges in moving techniques for auto

29、 tuning and diagnostics into a wide rangeof industrial products. Many stimulating discussions with our colleagues AntonCervin (LTH), Sebastian Dormido (UNED), Guy Dumont (UBC), Chang ChiehHang (NUS), Karl Henrik Johansson (KTH), Birgitta Kristiansson (CTH),Bengt Lennartsson (CTH), Manfred Morari (ET

30、H), Dale Seborg (UCSB), Sig urd Skogestad (NTNU), Bjrn Wittenmark (LTH), and Karl Erik rzn (LTH)from academia are also highly appreciated.Our friends in industry Bill Bialkowski, Terry Blevins, Greg McMillan,and Willy Wojsznis from Emerson, Edgar Bristol, Sigifredo Nio, and GregShinskey from Foxboro

31、, Brje Eriksson (M real), Krister Forsman (Perstorp),Ken Goff (Leeds and Northrup), Niklas Karlsson (Evolution Robotics), JosephLu (Honeywell), Tor Steinar Schei (Cybernetica), Stefan Rnnbck (Optima tion), have generously shared their knowledge and insight with us. We areparticularly grateful to Pet

32、er 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 andgave much assistance with TEX, Agneta Tuszynski who translated much of thetext to LATEX, and Eva Dagnegrd who drew several of the

33、 figures.Finally, we would like to thank the Swedish Research Council (VR), theSwedish Agency for Innovation Systems (VINNOVA), and the Swedish Foun dation for Strategic Research (SSF) who have supported our research for manyyears.KARL JOHAN STRMTORE HGGLUNDDepartment of Automatic ControlLund Instit

34、ute of TechnologyBox 118, SE 221 00 Lund, Swedenkarl_johan.astromcontrol.lth.setore.hagglundcontrol.lth.seviiContents1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Feedback . . . . . . . .

35、 . . . . . . . . . . . . . . . . . . . . . . 21.3 Simple Forms of Feedback . . . . . . . . . . . . . . . . . . . . 31.4 How the PID Controller Developed . . . . . . . . . . . . . . . 51.5 Technology Changes and Knowledge Transfer . . . . . . . . . 71.6 Outline of the Contents of the Book . . . . . .

36、 . . . . . . . . . 81.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.8 Notes and References . . . . . . . . . . . . . . . . . . . . . . . 102. Process Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1 Introduction . . . . . . . . . . . . . . . . . .

37、. . . . . . . . . . . 122.2 Static Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Dynamic Models . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Feature Based Models . . . . . . . . . . . . . . . . . . . . . . . 232.5 Typical Process Models . . . . . . . . . . . . . .

38、 . . . . . . . . 282.6 Models for Disturbances . . . . . . . . . . . . . . . . . . . . . . 442.7 How to Obtain the Models . . . . . . . . . . . . . . . . . . . . 472.8 Model Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 562.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . .

39、. . . . . 612.10 Notes and References . . . . . . . . . . . . . . . . . . . . . . . 623. PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.2 The PID Controller . . . . . . . . . . . . . . . . .

40、 . . . . . . . . 643.3 Filtering the Derivative . . . . . . . . . . . . . . . . . . . . . . 733.4 Set Point Weighting . . . . . . . . . . . . . . . . . . . . . . . . 743.5 Integrator Windup . . . . . . . . . . . . . . . . . . . . . . . . . 763.6 When Can PID Control Be Used? . . . . . . . . . . . .

41、. . . . 873.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.8 Notes and References . . . . . . . . . . . . . . . . . . . . . . . 934. Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .

42、 . . . . . 954.2 A Rich Variety of Control Problems . . . . . . . . . . . . . . . 964.3 Feedback Fundamentals . . . . . . . . . . . . . . . . . . . . . . 964.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102ixContents4.5 Closed Loop Poles and Zeros . . . . . . . . . . . .

43、 . . . . . . . 1094.6 The Sensitivity Functions . . . . . . . . . . . . . . . . . . . . . 1114.7 Robustness to Process Variations . . . . . . . . . . . . . . . . 1184.8 Quantifying the Requirements . . . . . . . . . . . . . . . . . . 1224.9 Classical Specifications . . . . . . . . . . . . . . . . .

44、. . . . . 1284.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1364.11 Notes and References . . . . . . . . . . . . . . . . . . . . . . . 1375. Feedforward Design . . . . . . . . . . . . . . . . . . . . . . . . . . 1395.1 Introduction . . . . . . . . . . . . . . . . . . . . .

45、. . . . . . . . 1395.2 Improved Set Point Response . . . . . . . . . . . . . . . . . . . 1395.3 Set Point Weighting . . . . . . . . . . . . . . . . . . . . . . . . 1455.4 Neutral Feedforward . . . . . . . . . . . . . . . . . . . . . . . . 1465.5 Fast Set Point Response . . . . . . . . . . . . . . .

46、. . . . . . . 1505.6 Disturbance Attenuation . . . . . . . . . . . . . . . . . . . . . 1545.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1565.8 Notes and References . . . . . . . . . . . . . . . . . . . . . . . 1576. PID Design . . . . . . . . . . . . . . . . . . . . . . . .

47、 . . . . . . . . 1586.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1586.2 Ziegler Nichols and Related Methods . . . . . . . . . . . . . . 1596.3 Rule Based Empirical Tuning . . . . . . . . . . . . . . . . . . . 1696.4 Pole Placement . . . . . . . . . . . . . . . . . . . .

48、 . . . . . . . 1746.5 Lambda Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . 1866.6 Algebraic Design . . . . . . . . . . . . . . . . . . . . . . . . . . 1896.7 Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . 1966.8 Robust Loop Shaping . . . . . . . . . . . . . . . . .

49、 . . . . . . 2066.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2216.10 Notes and References . . . . . . . . . . . . . . . . . . . . . . . 2227. A Ziegler Nichols Replacement . . . . . . . . . . . . . . . . . . . 2257.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2257.2 The Test Batch . . . . . . . . . . . . . . . . . . . . . . . . . . . 2267.3 PI Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2287.4 PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2307.5 Frequency R