Instrumental Variable Methods for System Identification PDF
Preview Instrumental Variable Methods for System Identification
Lecture Notes ni Control and nottamrofnI Sciences Edited by .V.A and Balakrishnan .M Thoma 57 IIIIIIII IHIIIIIIII IIIIIIIIIIIIIII IHIIIIIIIII .T SSderstrSm .G.P Stoica Instrumental Variable Methods for System Identification II IIIIIIIIIII II I galreV-regnirpS Berlin Heidelberg New York oykoT 1983 Series Editors A. V, Balakrishnan • M. Thoma Advisory Board L D. Davisson • ,~ G..1. MacFarlane. H. Kwakernaak .J L Massey Ya. • Z. Tsypkin • A. .J Viterbi Authors Torsten SSderstr~m Dept. of Automatic Control and Systems Analysis Inst. of Technology Uppsala University Uppsala, Sweden Petre Gheorghe Stoica Dept. of Automatic Control Polytechnical Inst. of Bucharest Bucharest, Romania AMS Subject snoitacifissalC :)0891( 93 E12, 93 B 30, 90A16, 90A ,91 62 M 01 ISBN 3-540-12814-X galreV-regnirpS New Heidelberg Berlin kroY oykoT ISBN 0-387-12814-X galreV-regnirpS weN Berlin Heidelberg York oykoT Library of Congress Cataloging in Publication Data S6derstr6m, Torsten. Instrumental variable methods for system identification. (Lecture notesi n control and information sciences ; 57) Bibliography: p. Includes index. .1 System identification. 2. Parameter estimation. .I Stoica, .P G. (Petre Gheorghe) .1I Title. .1II Series. CIA402.$693 1983 003 83-13525 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © by Springer-Verlag Berlin Heidelberg 1983 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 206113020-543210 DROWEROF DNA STNEMEGDELWONKCA This book is about system identification dna parameter estimation using the instrumental variable (IV) approach. It sah grown out of our joint research in this field during the last five years. ruO attempt sah been not only to ezirammus our findings in a unified form dna extend them to emos degree but also to include practical hints for the users. eW have nesohc a mathematical level of the text which ew hope will appeal both to those interested in the technical details dna those merely interested in woh to apply VI sdohtem in practice. oT understand the book the reader is demussa to have emos basic egdelwonk of stochastic systems or time series analysis dna also to wonk a little about parameter estimation in models. dynamic In places ew emussa the reader to eb familiar with structures of multivariable systems. eW have included various other dnuorgkcab material in the appendices to ekam the book reasonably self-contained. roF readers ohw are only practically interested ew dnemmocer a first reading of Part I dna a careful reading of Part III, thus skipping the erem theoretical Part II where the analysis is developed. eW have deliberately used rather wef references in the text. Instead ew evah included emos bibliographical notes in the dne of the chapters. Since instrumental variable sdohtem have u~ed been for quite a long time dna in diverse areas it should eb needless to yas that yna attempt to give a full dna perfect (historical) list of references is demood to fail. eW hope that ew have dedeeccus in giving the yek references dna emos more. Moreover, our purpose sah been to present a unified analysis rather than tracing the exact historical background of every single variant of the instrumental variable approach. eW wish to express our sincere thanks to the ynam persons ohw helped ekam this koob possible. Several colleagues detnemmoc no the text. eW would like to mention Professor Lennart Ljung in particular ohw edam valuable suggestions based no a preliminary version of the manuscript. eW also thank Professor Peter gnuoY for his helpful stnemmoc no our work dna for providing several references. Professor namroN hguoG sah suggested ynam stnemevorpmi to the English. ehT responsibility for the re- maining errors, English or technical, remains of course ours. eW also thank VI Professor Manfred ,amohT the editor of this series, ohw after preliminary discussions sah degaruocne su to write the .koob Most of our joint publications over the past years have been expertly typed by Miss Ingrid RingArd. eW are very grateful to her dna srM Lis Timner ohw jointly have typed the text os nicely with great care dna patience. srM Timner sah also skilfully prepared the figures. eW thank rD reP Erik n~doM ohw provided su with the drum drier data which ew evah desu in Section 9.2. ehT first author saw given a scholarship yb the Swedish Institute within na official exchange margorp between nedewS dna .ainamoR This grant edam possible a very fruitful stay in Bucharest. There ew worked efficiently together no the spot thus avoiding the more emosrebmuc communication yb mail. Last, but not least ew thank our families for their moral support during our work no this book. ELBAT FO STNETNOC TRAP I: SEIRANIMILERP DNA SNOITINIFED retpahC i .N OITCUDORTNI retpahC 2. SEIRANIMILERP .2 I Mod~ er~t~u~t~ 6 2.2 Sgst~ 21 3.2 latnemirepxE condit~n 81 2.4 emoS hOt--hal snoitnevnoc 02 2.5 Remarks and 51JoZiog~p~ not~ 12 retpahC 3. CISAB DNA DEDNETXE S VIMHTIROGLA 1.3 Basic VI varian~ 32 3.2 dedne~xE VI u~ia~t~ 13 3.3 Boo~t~p IV ua~ 73 3.4 R~k~ dna 6ibliographical not~ 83 PART : I I ANALYSIS Chapter 4. YCNETSISNOC .4 I Gcn~al co~ideratio~ 74 4.2 Analys~ of VI varian~ for ~alac~ ~yst~ 55 4.3 Anat4~/~ of IV v ~ for m~v~able ~yste~ 06 4.4 Converg~ce ~aZysi~ of bootstrap IV variant~ 76 4.5 skran1PR dna bib~.ioga~pl~te(zt not~ 47 Chapter 5. YCARUCCA 1.5 A~pt~t~ dist~ution of VI ~ t ~ 57 5.2 A~ympt~t~ d~tri6ut~n of bootstrap VI e~t~r~ 58 5.3 R~ar~ dna 6i61iographical not~ 88 retpahC 6. LAMITPO VISROTAMITSE 1.6 tncmet~t& fo opt/~y proble~ 98 6.2 emoS opti~iz~n exampl~ 39 6.3 Optimal IV ~t~o~ and app~m~tz implem~ntatio~ 69 lV 6.4 Analys~ of the approxi~e noitu~t~emelpm~ of o~cimal IV ~t~r6 601 6.5 Re~r~ dna bibliographical note6 t19 retpahC .7 LAMITPO TUPNI NGISED I 7. St~tcmc~t of ~¢ melborp 021 2.7 Inpu~ noitmzLcct~m~uJep 221 3.7 ¢cn~J~euoC rccUzmtion 521 4.7 cinu/tJJ~og~JA ~tJeep~ 231 5.7 R ~ dna bib~Log~pkiccZ seton 141 TRAP III: LACITCARP STCEPSA DNA ESAC SEIDUTS retpahC .8 YRAMMUS FO EHT SISYLANA DNA STNIH ROF EHT RESU 1.8 Basic fact~ no IV ~t~m~tLon 541 8.2 Hint~ for choosing the IV variant 051 8.3 Hints for input d~ign 651 4.8 Hin~ for ledom structure selection 751 retpahC .9 ESAC SEIDUTS .9 I Z~Je~G ~Ioce~ 561' 2.9 A murd ~L~Jd 861 3.9 nA cimonoc¢ p~oc~s 271 4.9 k ~m9 f~e 571 5.9 k tu~bo-~nctor 181 SECIDNEPPA xidneppA I. YLTNETSISREP GNITICXE SLANGIS 981 xidneppA .2 EMOS STLUSER S LNAOIMONYLOP DNA CITYLANA SNOITCNUF 591 xidneppA .3 EMOS XIRTAM STLUSER 002 xidneppA .4 EMOS YTILIBABORP STLUSER 312 xidneppA .5 NEIHBTRUD-NOSNIVEL MHTIROGLA 612 xidneppA .6 EMO SYGOLONIMRET DETAICOSSA HTIW LANOITAR SECIRTAM 225 iiV REFERENCES 722 TCEJBUS XEDNI 932 iI o I m l B m~ z rrl cs~ IT imw4 z tim4 o z retpahC I I NTRODUCT I NO ehT area of "system identification", in particular "parameter estimation in dynamical models", is na important eno in ynam fields, such sa control engineering, econometrics dna signal processing. There is certainly na overwhelming literature in this area. roF na introduction to dna a general survey of the area metsys identification ew refer the reader to Astr~m dna Eykhoff (1971), xoB dna Jenkins (1976), Eykhoff (1974), niwdooG dna enyaP (1977), arheM dna Lainiotis (1976). ehT present state of the art nac eb studied for example in Eykhoff (1981) dna recent proceedings of the CAFI aisopmyS no Identification dna metsyS retemaraP Estimation. ehT area of identification is, sa already indicated, related to other areas such sa time series analysis, statistics dna econometrics. A lot of various identification sdohtem have proposed been dna are in current use. A systematic yaw of nosirapmoc neewteb various sdohtem sah been given to emos degree but it is far from complete. There smees to eb na increasing interest in parametric methods, i.e. identification sdohtem which sa a crucial part include parameter estimation from experimental data. owT well-known parametric sdohtem are the least-squares dohtem )MSL( dna the prediction error dohtem (PEM). ehT MSL nac eb traced back to ssuaG (1809). It is desab no a simple algorithm. In fact, na analytic formo f the estimate nac eb given once the data are .nwonk A disadvantage of the MSL is that na asymptotic bias often occurs. This snaem that the estimated parameters often contain systematic errors that od not vanish even if the data series semoceb infinitly long. oT avoid the asymptotic bias eno possibility is to esu a MEP in a model structure that also describes the properties of the noise. This leads to a more xelpmoc dohtem dna requires a numerical optimization of a nonlinear function that sdneped no the recorded data. ehT advantage of using such a dohtem is that the estimated ledom often will give quite doog a description of the data. In particular the bias obstacle is on longer a problem sa for the simple .MSL oS far the discussion sah indicated that the user must face a trade-off neewteb algorithm complexity dna the properties of the estimated parameters. It would of course eb suoegatnavda to have estimation sdohtem that enibmoc the small algorithmic
The list of books you might like
