Simulation of control systems : selected papers from the IFAC symposium, Vienna, Austria, 22-26 September 1986

435 Pages·1987·18.044 MB·English

by  I Troch, Peter Kopacek, F Breitenecker, International Federation of Automatic Control. Technical Committee on Theory

IFAC PROCEEDINGSS ERIES
Editor-in-Chief
JANOS GERTLER,D epartmenotfC omputearn dE lectriEcnagli neering,
GeorgeM asonU niversiFtayi,r faVxi,r giniUSaA,
GERTLER KEVICZKY (General EdAi tBorrisd)g:Be e tweeCno ntroSlc iencaen dT echnology
&
(NintThr iennWioarll dC ongreisns , volumes)
6
Analysainsd S ynthesoifsC ontroSly stems No.
(1985,1 )
Identification, aAndda pSttiovceh asCtoinct rol No.
(1985,2 )
Large-scSaylset ems, Decision-making,o fMC aotnhtermoalt ics No.
(1985,3 )
ProcesIsn dustriPeosw,e rS ystems No.
(1985,4 )
ManufacturiMnagn,- MachinSey stemCso,m puterCso,m ponentTsr,a ffiCco ntrol,
SpaceA pplications No.
(1985,5 )
BiomedicAaplp licatiWoantse,r R esourceEsn,v ironmenEtn,e rgy SystDeemvse,l opmenSto,c ial
EffectSsW,I IS,E ducation No.
(1985,6 )
BARKER YOUNG: IdentificaatnidoS ny stem ParamEestteirm ation No.
& (1985()1 985,7 )
NORRIE TURNER: Automatifoonr M ineraRle sourcDee velopment No.
& (1986,1 )
CHRETIEN:A utomatiCco ntroiln S pace No.
(1986,2 )
DA CUNHA: Planninagn d OperatioofnE lectrEince rgyS ystems No.
(1986,3 )
V ALADARES TAVARES EVARISTO DA SILVA:S ystemAsn alysAipsp lietdo W atera ndR elated
&
LandR esources No.
(1986,4 )
LARSEN HANSEN: ComputAeird edD esiginn C ontroaln dE ngineering Systems No.
& (1986,5 )
PAUL:D igitCaolm puteArp plicatitoonP sr ocesCso ntrol No.
(1986,6 )
YANG JIACHI: Control aSncdiT eencchen olofogry Development No.
(1986,7 )
MANCINI,J OHANNSEN MARTENSSON: AnalysiDse,s igann d EvaluatioofnM an-Machine
&
Systems No.
(1986,8 )
BASANEZ,F ERRATE SARIDISR:o botC ontro"lS yroco No.
& '85"( 1986,9 )
JOHNSON: Modellianngd Controolf B iotechnoloPgrioccaels ses No.
(1986,1 0)
T AL':I nformatiCoonn troPlr oblemisn M anufacturTiencgh nology No.
(9J8 7, 1)
SINHA TELKSNYS: StochCaosnttirco l No.
& (1987,2 )
RAUCH: Controolf D istribuPtaerda metSeyrs tems No.
(1987,3 )
FLORIAN HAASE: Softwarfeo rC omputeCro ntrol No.
& (1987,4 )
MARTOS, PAU ZIERMANN: Modellainndg C ontroolf N ationEaclo nomies No.
& (1987,5 )
CENSER,E TSCHMAIER,H ASEGAWA STROBEL:C ontroiln T ransportatSiysotne ms No.
& (1987,6 )
ADALI TUNALI: Microcomputer ApipnlP ircoacteisosn Control No.
& (1987,7 )
WANG PINGYA NG: PowerS ystemasn dP owerP lanCto ntrol No.
(9J8 7, 8)
BALCHEN: Automatiaonnd DataP rocessiinnAg q uaculture No.
(1987,9 )
YOSHITANI:A utomatiionnM iningM,i neraaln dM etalP rocessing No.
(1987,1 0)
GEERING MANSOUR: LargeS calSey stemTsh;e orya nd Applications No.
& (1987,1 1)
ROOS: Economicasn d Artificial IntelligenNcoe.
(1987,1 2)
TROCH, KOPACEK BREITENECKER:S imulatioofnC ontroSly stems No.
& (1987,1 3)
KAYA WILLIAMS:I nstrumentaatnidoA nu tomatiionnt heP aperR,u bberP,l astaincd Polymerization
&
Industries No.
(9J8 7, 14)
NOTICET O READERS
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Copieosf a lplr evioupsulbyl ishveodl umeasr ea vailaAb lfeu.l ldye scripctaitvael ogwuielb le g ladlsye notn request.
ROBERT MAXWELL
Publisher
IFACR elatTeidt les
BROADBENT MASUBUCHI:M ultilinGgluoasls aorfyA utomatCiocn trTole chnology
&
EYKHOFF:T rendasn dP rogreisnsS ysteImd entification
ISERMANN:S ysteImd entificTauttioorni (alAsu tomaStpieccIais aslu e)
SIMULATION
OF
CONTROL SYSTEMS
SelPeacptfeerrdots mhI eF ASCy mposium,
VieAnunsa2t,2r -2i6Sa e,p t1e9m86b er,
Editbeyd
I.T ROCH
Technical Unifv Veiresnintay
o
P.K OPACEK
UniversfiL tiyn z
o
and
F.B REITENECKER
TechniUcnailv ersfi Vtiye nna
o
Publishfoerd the
INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL
by
PERGAMON PRESS
OXFOR·D N EWY ORK· BEIJI· NFGR ANKFURT
SAOP AULO· S YDNE· YT OKYO· T ORONTO
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Copyrig©h t1 987IF AC
AlRli ghRtess ervepda.ro tftN hopi usb licmaatybi ero enp rodsutcoeirdnea,r d e triseyvsatolert m r ansmiint ted
anfyo romrlry anmye anesl:e cterloencitcr,mo asgtnaettiicmc,e cthaapnepi,hc oatlo,c opyriencgo,r odroi tnhge r­
wisew,i thpoeurtm isisnwi roint firnogtm h ceo pyrhioglhdte rs.
Firsetd iti1o9n8 7
LibraorfCy o ngrCeastsa loging-inD-aPtuab lication
Simulatoifoc no ntrsoyls tems.
(IFACp roceedisnegrsi e;s 1987n,o .1 3)
"IFACS ymposiuomn SimulatoifoC no ntroSly stems
sponsorbeydI FA C-Committeoen Theory"-P.
Includes indexes.
1.A utomatciocn trol-Mathemmaotdieclasl­
Congress2e.sA .u tomatciocn trol-Data processing-:-­
Congress3e.Cs o.m puter-aiddeesdi gn-Congresses.
I.T rochI,. II.K opacePke,t erI.l lB.r eitenecker,
F.( FelixI)V..I FACS ymposiuomn Simulatoifo n
AutomatCiocn tro(l18 96 : ViennaA,u stria).
V.I nternatiFoendaelr atoifoA nu tomatCiocn trol.
TechnicCaolm mittoene TheoryV.I .S eries.
TJ221.2.S515958 7 629.8'072'847 -52718
ISBN0 -08-034349-X
Thepsreo ceewdeirnrege sp rodlryu mceeadno sft hpeh oto-porfofcsueesstist n hgme a nuscsruippptllrysi tehde
authooftr hsde i ffepraepneTtrh sem. a nuschraivpbetse etynp euds idnifgf ertyepnetw riatnedtyr pse faTchees .
lay-out.afnidtg aubrolefess so mpea pedrisnd o atg rceoem plweittethlhs yet andraerqdu irecmoennstesq:u ently
three produdcoteniso dotin spcloamyp luentifeo rmTioety n.s urraepp iudb lictahtdisii osnc recpoaunnldcyo bte
changneodcr:o utlhdEe n glbiesc hh ecckoemdp leTtheelrye.tf horere ea,d aerraess kteoed x cuasnedy e ficiencies
.
oft hipsu blicwahtiicmohan y b ed uet ot haeb ovmee ntiorneeasdo ns.
TheE ditors
PrintienGd r eaBtr itbya iAn. W heatonC o.L tdE.x,e ter
&
IFACS YMPOSIUM ON SIMULATIONO F
CONTROL SYSTEMS
Organbiyz ed
OsterreichiPsrcohdeusk tiviutnadt s-
Wirtscthlaifc hkeittsr-muZ enP WZ)
( 0
I
Sponsboyr ed
IFAC-Committeoen Theory( THEORY)
Co-spobnys ored
IFAC-Committeoen Application (APCOM)
IFAC-Committeoen Computer(sC OMPUT)
IFAC-Committeoen Educati(oEnD COM)
IMACS-InternatiAosnsaolc iatfoiro nM athematiacnsd C omputerisn S imulation
Suppobryt ed
TechnicUanli versiVtiye nna
EAi-Aachen
InternaPtrioognraCalom m mittee
I.T rochA,u stri(aC hairman) R.M ezencevF,r ance
S.A idaJ,a pan W. SchaufelberSgweirt,z erland
D. P.A thertoUnK, A. Sydow,G DR
P.B orneF,r ance B. Tamm, USSR
A. vanC auwenberghBee,l gium M. Thoma,F RG
K. H. FasolF,R G H. TokumaruJ,a pan
K. FurutaJ,a pan R. TuschakH,u ngary
E.G ottzeiFnR,G S.T zafestGarse,e ce
P.K opacekA,u stria A. WeinmannG,r eece
P.M . LarsenD,e nmark
L.L jungS,w eden
NatioOnragla niCzoimnmgi ttee
P.K opacek( Chairman)
I.T roch
W. Karner
PREFACE
Simulatiohna s been af olro ng timae v aluablaen d Consequentlyq,u estionso f modelling,o f model
widely used tool for the analysiso f systems. simplificationb ut also theoretic aspeocft s
Especially the controle ngineehra sb eenf amiliar modellingw ere discusseddu ringt he Symposiutmo
with this means for a longt ime. Simulatiowna s some extent. Papers dealing primaritlhyi sw ith
used not only for the analysis of plantsa nd subjecta re collectedi n 1 of these
Session
controllesdy stemsb uta lso- and may be primarily Proceedingsb ut the interestedr eader should
-as a valuablree medyf or controlledre sign. consulta lso whereh e may findpa pers
sessio2n
dealing basically with systems analysiasn d
Further, simulationha s turned out to be a design,b ut someo f them deali n a shortw ay also
valuable tool in the educatioonf under-graduate with interestingm odellinags pects.L astb ut not
post-graduatset udentosf controle ngineering. least modellinga spects are addressetdo oi n some
and
Simulationma y equallyw ellb e usedi n continuing of the invitedpa pers, especiallyi n those
educationp rograms. Thisi s due to the factt hat preparedb y LennartL junga nd SpyrosT zafestas.
it allowsa quicka nd instructivper esentatiaonnd
discussiono f phenomena methods.A t the same is devotedt o the analysiasn d designo f
time, simulation beand usedq uitee asilyi n a sSyesstsemsi.2o Inn controle ngineerintgh eA NALYSIoSf
laboratorya llowicann gt he studentt o testv arious SYSTEMS is of importance in two respects.F irstly,
types of controllerisn connectionwsi tha 'real' the analysiso f the plant has to be performeda,
plant,T o somee xtent,s imulatiomany evenr eplace· topic which is coveredb y many papers on
laboratorye quipment allowingt he analysiasn d modelling, especiallyb y papers presentinag c ase
design of systemsa t relativelyl ow costs study on thiss ubjectS.e condlyt,h e analysiosf
withoutr isksb y a largen umbero f students. and the controllesdy stemi s of intrinsiicm portance.
This is due to the factt hat it allowst o judge
Whereas in old times of controle ngineering, whethero.r not the proposed controlwlielrl b e
analogueh ardware was the main instrumentf or adequatef or the givenc ontrolt ask.
,performing such simulation,n owadaysma inly
digitale quipment is usedb ecauset he latterh as The problemo f CONTROLLER DESIGN can be termed as
become morec omfortabldeu e to special simulation the centralq uestiowni thint he papers collected
softwarea nd languages.F urther,i n mostc ases in Especiallyt he use of so-called
Sessio2n,
digitals imulations be performed now with advanced controlc onceptass e.g.A DAPTIVITY and
sufficienstp eed. can OPI'IMALITYo ften required etailed simulation
studies. This is not only due to the high
Neverthelesst,h e developmento f new softwarea s theoreticr equirementosf suchc onceptbsu t also
well as the improvemenotf existinsgo ftwarien to the complexityo f the plantsf or whichs uch
ordert o meeti n a betterw ay the needso f control controllerhsa vet o be designed.
engineersi s stillg oingo n and willc ontinufeo r
somey ears. dealsw itht heoretiacs pectsa s wella s
Sessio2n
with practicala pplication-sa s it was the case
For theser easonsi t is notama zing thatt he IFAC in Chapter Yet, the reader interestedi n
1.
committeeo n Theoryd ecidedt o sponsor a Symposium systemsa nalysisa nd designs houldn ot forgett o
on 'SIMULATIOOFN CONTROL SYSTEMS'a nd to ask the consult also the invitedpa pers especiallyt hose
IFAC committeeosn Applicationosn, Computerasn d by KatsuhiraF uruta et al., P.M. Breuti janl .,
on F.ducation as wella s IMACS( theI nternational D.P.A thertoann d GislainV ansteenkiste.
Associationf or Mathematics and Computersi n
Simulationt)o act as co-sponsors. alreadym entionetdh e improvement of existing
Asa nd the developmento f new simulatiotno olsi s of
Speaking about SIMULATIOmNe ansa good dealm ore actual and growingi nterest. Sutcoho lse xist
than solving some more or less complicated mainly in the formo f software packages
equations or computingm ore or lessu sefula nd or less specialiseds imulatiolna nguagandesN .emo vree r­
meaningful numbers. Simulationc onsists of theless,a lso the developmento f new hardwaroer
performing experimentsw ith a system- in most the combinatioonf existingh ardwareb y new
caseso n a compute-r of differenphty sical nature interfaceasr e of interest.
but with analogousb ehaviouwri thr espect to the
problemt o be investigataendd solved. 3 collectpaspe rs devotedt o theq uestion
Session
of adequate improved It is
One of the main goalso f a simulatiosnt udyi s to completedb y andth ei nvitedpaS peIr MULATprIeONpar edTO ObLSy. W alter
get INSIGHITN A SYSTEMS BEHAVIOUR, no matter Ameling.T he invited paper by Fischlient al.
A.
whethera controlleodr an uncontrollseyds temi s should albseo mentionedi n thisc onnectionw hich
investigatedC.o nsequentltyh,e t asko f MODELLING emphasizes alsoo n questionso f engineering
a givens ystemi n a satisfactowaryy is of primary education.
concerni n all simulationSsu.c ha modelh ast o be
establishedi n an adequatew ay.T hism eans The editors liket o all who assisteidn the
the model musta ccountf or all propertieso ft thahte organizationo f thethank S ymposium in the pre­
real systewmh ich are of importance for the paration of theseP roceedingWse,and J ;wpthea t these
problemt o be solved.B ut at the same timet he Proceedings will provide a uniue source of
model should not be toc omplicateidn ordern ot informationo n both the state-oqf-the-anardt new
only to facilitatteh e necessarcyompu tations but developmentisn the fieldo f OF
SIMULATION CONTROL
also to allowa sufficientlayc curatees timation SYSTEMS.
of all required parameters and exogeneous IngeTr och
functionosf time. PeterK opacek
Vienna, Autumn FelixB reitenecker
1986
vii
Copyrig©h tI FACS imulatoifo n INVITEDP APERS
Control Systems,A uVsitern1ni9aa8,,6
BUILDING MODELS FOR A SPECIFIED
PURPOSE USING SYSTEM IDENTIFICATION
L.L jung
DiviosfiA ount omCaotnitcDr eopla,r tomfE elnetc tErnigcianle Leirniknogp,i ng
UniveSr-s5i8ty83,1L inkopSiwnegd,e n
Atp resweintLtha borfaortI ofnoryr matainodDn e ciSsyitsoenmM sI,T C,a mibdrge,
MA 02139U,S A
AbstractM.o delsa nd modelq ualitya re primec oncernfso r mostd esigni ssuesi n control
ands ystemsa nalysisT.h e successo f a simulatiosnt udyh ingesu pont he reliabilitoyf
the modelu sed.I n thisc ontributiwoen discussh ow to build mathematmiocdaell st hat
givenc ertainc onstraintasr,e of optimumq ualityf or a prespecifie(ds imulatioanp)p ­
licationW.e thent akei ntoa ccountt he influencoef bothb iase rrorsa nd randome rrors
on the model.I t turnso ur thatf or a fairlyb roadc lasso f identificatiomne thodsi n
the predictioenr rorf amily,t he optimalc hoiceso f designv ariablecsa n be giveni n an
explicifto rm.
1 ITNRDOUCTION HereG0 (qi)s t hter ansofpeerr ator
iBunivlodlmmivaanetngpshy o e smsamitobidicaeloanlifcdldst hy ioneiasocm sfeidy sces astlie gmn G0(q)u(kIt=g0) l(= k[-)k ]qu(tkI)=g=0 l( k)-uk()t (2)
variabThleep sa.r ticruoluattrae k meanhy a vae
substainntfilauloe nnt cheqe u aloiftt yh ree ­
-1
sultmiondg,e a lnidt i so fc ourdsees irtaob le int hseh iofpte raqt[oqru (t+l))=q;u u((tt)=
makteh ceh oiscoet sh aatm odoefl" optiqmuaal­ =u-(1t)].
litiys"a chiegvievdte,hn ce o nstraA icnotmsp.­
licathieorines t hatth ewriel tlpy icableln yo Wet hudse scrtihbseey stiendm i scrteitmaeen d,
"ufnoirmgloyo dde"s igsnots h,me o dqeula lity fosri mplitchiseta ym,p ling iistn atketeronv al
concmeupstbt et ietdot hien tenadpepdl icatiobne.t htei muen iItn.( 1)v0,( ti)s a na dditive
disturbwahniciceshs, u ppotsobe eda s tantairoy
A complegteenletyrr aela tomfet nhtip sr obilse m stochapsrteoisccws itshp ectrum
nod oudbitf ficIuntl hti.cs o ntribwuest hiaolnl
formualnasdto el avs eu bpermow,bh letrhefe i rst (3)
ofp ossibihlaivtbeie eecsno nstraasif noeldl ows:
Thism eatnhsa {t0v( t)c}a bne r egaradsge edn e­
ratbeyd
Onllyi nemaord ewlislb lec onesriedd.
0 (4)
Thet rusey stweimlb lea sumsedt ob el inear
0 (bumta bye m ucmho rceo mpltehxa tnh e whe{r0ee( t)i}sw hintoei wsiet vha riance
Ao·
modeclosn sidered)
Fotrh sey st(1e )mw em agye neraanit nep ut
Them odceoln stornuw citlbileb ys ystem {u(ts)u}c,th h at
0 identifiicnaa c tliaoosnfsp rediction
N
errmoert h(otdbose p recidseefliyin ne d lim u(t()tu-i:)(=i;R)
Sect4i)o n �tI: = l u
N+o>
exifsotar l l and stpheec tirsu m
Thei ntenmdoeddae plp licwaitlibloes n i mu­
i;,
0 latiwoint h siingpnuoatfl g si vferne quency
characte(rsicpstetriac)s. (w)=R ()i;-r ii;w. (5)
<liu 't;=� u
Thea nalyissbi ass oendg eneral asymptotic re­
Wea lltohwpe o ssliibtoiyfo utpfuete dbianc k,
sulgtisv iennL ju(n1g9 a8b5a)n Wdha lbearngd
whiccahs teh cer oss-sp<lie(cw)ti rsnum o n-zero.
Lju(n1g9 8R6e)l.a dtiesdc usasrigeoi nvsie nn ue
Thusc ollectthidena gts ae t
Yunaa nLdj u(n1g9 8G5e)v,e arnsLd j u(n91g8 6a)n d
Lju(n1g9 8F6o)cr.o mprehternesaitvmseee net , N
z=u{ ( y(l),,u (Ny)N(,) } (6)
Lju(n1g9 8F7o)gr.e nedriaslc usosniS oytnsesm s 1), ••••
Identtiifoisnce,aae l sGooo dwainnPd a y(n1e9 77),
wem apyr octeoee ds timtahtteer afnesfru nctions
Ekyho(f1f9 7149,8 a1n)Ad s tral:linn Edky hoff
G0 anHd0 in( 1)(,4 ). thLreee ts ubledt e noted
(119)7.
by
N
(q() q,)Z)
2 PRBLOEMS ETUP � � (7)
N
Int hicso ntribwuest hiaoalnsl s ume thaits th�eN(rQe() �= (q,)Z)
trulei nesayrs temtsh agte nertahtoeeb ss erved
S, Wes hadlils cpursosc edfuorre st hSietsci oinn
datIaf.y (ta)n ud( td)e nottheoe u tpaunttd h e 4.
inpurte,s pectaittv iemileny s ttaw nett hus
assumteh at
y(t0)(=qG)u(0(tt))+v (1)
L.L jung
2
3 MEASRUESO FM OLDQE AULITY wherdee nottheceso nstraasisnotecsdiw aitth
t;
oudre sitrode o a tm os"tar easonaamboluoenf t
Thter usey staenmtd h meo del. workTh"e.s wei ltly picianlcllyau m daex imum
numbeorfs amplseisg,np aolw ceorn straniontt s,
Supptohsaett h ter usey stiessm u bjteoc( t1 )­ tocoom plneumxe ripcraolc edeutrcThe.es c onst­
(4)i,. et.h at raintcso uallds ion cltuhdaect e rtdaeisni gn
vari/;a sbilmepsal ryne o atv ailtaobt lheue s eirn
(8) thpea rticauplpalri ciantq iuoens tion.
whe{ree0 (its)w )h intoei wsiet vha ria�n0c.e Modaeplp licaStiimounl:a tion
Fosri mpnloetra twieos nh,aa llls uos e Supptohsaett h ter ansffuenrc tGii osun s etdo
simultahtieen put-opuatroptft.1.1 htse y tsewmi th
(9) inpuu*t( tT)h.me o dGe(lq ,t hepnr odutchees
'1))
output
Supptohsaewt eh avdee ciudpeodan l tlh dee sign
variablaesss ocwiiatttheh meo dceoln struc­y(t=)G (�q),u*(t)
:0, 'il?
tioann ads a r esuolbtt aitnhemedo del
whitlhete r usey stweomu glidv teh ceo rrect out­
0
(1) put
£)wilclo ntaaimno,on tgh tehri nNg,ts h neum ber y0(=tG )0 (q)u*(t).
ofc olledcattead.
Thee rrsoirg nal
As caldaers icgrni terion
A
[G (�q),- 0G(q)]u*(t)
Iti so fc ourdsees irtahbaltteh meo dTe(lq ,£))
isc lotsoeT 0(qTh)e.d ifrfeence hatsh sep ectrum
'l'(iew ;(iew. �-)To(e)iw (11) w(_wcV,> =�</iew,� )-G0i(we)2w (�w) (17)
.�)� y /
shouilndo ,t hwoerrd sb,es malLle.ut s d evelope
whewr(�ew i)s t hsep ectorf{u um* )()tTh. is,
af ormamle asoufrt eh sei zoef Depending on
"t. againa,r Aainsd foumn ctainoidnt ,es x pectation
thien tenudseoedf t hmeo daeg lo ofdi itn s ome
w.tr .G
frequreanncgyme asby e m oriem portthaanintn
otheTrosc .a pttuhriefs a cwte,i ntroadf urcee­
(18)
quenwceyi ghstceadlc arri terion
Ji('�<·.�)J)'l'= ( we,i�)C(T(w-e)i'l'w2.l,) dw (12) itisao dm neu taeos eo urfrtr ehoi aerntv s he merpoa edgGree.fl N .o orttdmeeha ganwrtcia,etd ha ­
-rt (15a)n d
whetrhe2e x m2a trfiuxn ction
C(w) :J (19)
C(w) (31)
descrtihbreee sl atiimvpeo rtoafan g coeof di att wec arne wr(i1t8ea) s
diffefrreenqtu eanscw ieelaslst h.er elative
importoaftn hcfeei itn G a nHd, r espectively'i'._ (wW,e=.Vt )rII (:i>w),C (w) (02)
y
shagleln eraaslslumyte h aCt( wi)sH ermitian,
ie..t hat Fianl,lt yhaev ervaagrei aJtYn2(cte() a veraged
oveur* (ats)w elalso verw ilble
G)
(21)
(thlea setq ualfiotlyl wohwestn h dee pendoenn ce
wi s veiiW.aW) e s haslhlo rgtilvyae ne xamopfl e
hoswu cwhe ighftuinncgt ciaobnne sd etermined.wh icihs a s pecciaasloe f( 14.)
Nowt,h sec alJ1a(r'T (•2,):0 isa r andom variaSbilneoc uefr o ciunst hicso ntribiusot nti ohne
duteo t hrea ndominnTe .sT soo btaair ne aliza­simulataipopnl ic(a1t9iw)oes n h acloln foiunre
tioinn deepneqtnu dalmietays uirtie s,n atutroa l interteots htfe o lloswpiencgci aasloe f( 13):
takteh eex pectoaftJ1 i aonnfd o rtmh cer iterion [cu(w) o
C(w=) O 0 (22)
J(:0) E 'l'e(iw�, )C('l'Tw()-eiw.;D, )dw J
SeLej u(n1g9 8f6o)r mgoerneetr raela tt.m en
J
-rt
tr[II�()wC,( w)]dw (14)
} 4 PERDICTEIRORIONEDR N ITFITCIAOMNTE HODS
-rt
Thmeo dseelt
whetrhe2e x m2a trIIi ix�g ivbeyn
Thep erhmaopssct o mmaopnp roianmc ohd eirdne nti­
(15) ficatiisto onp ostutlhaattteh ter ansffuenrc ­
tioinst ob es ougwhitt haic ne rtsaeitn:
Thep robolfec mh oosdiensgiv ganr iacbalnneo sw
bes tataesd (23)
d
min (16) HerDeMt ypiciasla ls yu bsoefRt . Ino rdteor
I�/). J( .,9) cilmupadrtseohs vrueeem spautiblitotoitu ,nscht s due is sttotumoraas brlpaysien oncc ­ter um
BuildMiondgef losr S peciPfiuerdp ose 3
a
�(w()s e(e)1 -(4I)t)i .sa ssutmoeb de lotnoag wheMr(eq ,a0r)te h fei rkst te rimnst hLea ruent
v k
set expanosfiH o(nq ,Th0e)u .s oef k -step parhee­ad
dictiosrt sh uesq uivatlope rnetf ilt(e(Lrqi)n g
iw 2 =
�v(w=)� H/(e,0);/H (eiwE£, 0) (2)4 Mk(q,0o)rt) o s elecatniontgnh oeirms oed seelt .
={ Hi(we,0)/M}0.E D Desivganr iables
Vf
Thism eans tshyastt ietsamh s es umteodb e Leuts l istth aev aildaebslievg anr iables:
descraisb ed
spectorftu hmee x tirnap uu t
y(t=)G (q,0)+uH ((tq), 0)e(t) (25) in( 5) (33a)
fosro m0eE DHeMr.e { e(ti)sa} s equeonfic ned e­ cross spectura umn edb etween
pendreanntd voamr iawbiltezhse rmoe avna luaensd (ersultfirnoogmut pufte dba(c3k3 b)
varia�n.ca ensGd a nHd raef unctoifot nhse
shiofpte raqt;o r ?t'={H(q,0}):s1 e0otEf Dn oimsoed els.
�
Thiisn cluadsew sen, o ted,
thpeo ssiboiflp irteyf ilter­
(26a)
inwgi tLhi n( 31a)n tdh e
usoef k -staehpe parde dict­
H(q,=0 )+1 hk(0-).qk (26b) or(ss e(e3 2)).
kr=l
Int hisst uwdeys hacloln fine
Theraer see vewraaylbs yw hitchhte r ansffuenrc ­ oursetlovf eisx neodi msoed els,
tioinns( 15c)a bne p arametCroimzmoeondne. s ie..t hsee t isa s inlgte:o n
inclsutdaet e-msopdaecAleRs M,mAX o deolust,p ut­ lf
errmoord eeltsc,. (3)3 c
Thees timamteitohno d Thec oiocfeM ish owever
Givtehne m od(e2l5 a)n idn p-ouuttpduattu apt o incluadmeo*dtn hgde e sivganr iables.
timte- 1w,ec adne tertmhipenr ee dicotuitopnu t
att imtea s Thesteh rietee wmisl hle ncefboedr etnho ted
collectbiytv hesely ym bol
Ay (0t) (1=- -H1( q,)y0 ()t -)(1+q H, 0)G(q,(02)7u)( t) ,fl).
I Othdeers ivganr iabsluecashs,N ,t hneum beorf
Att imte,w heyn( th)a bse erne corwdece adn colledcatteaadn, d thsee otf t ransffuenrc ­
computthepe r edicetrirotonhr a tth meo d(e2l5 ) tiomno de(lisn cel,ut,dh ime&o gd oerld ne)rw ill be
letdo : regaradsfe idx iendt hisst u.d y
A -1
Et(,0)=y(l0t))=-(Hyq(,t0)-(Gy(0(q)t,u)((t2)8))
5 ASMPYTOTPIRCO PEESRO TFTI HEETS IMATED
Wem asya tyh at the mios"d geoloi df(t" 2h 5e) TRANSFFUENROC NTSI
sequeEn(cte, 0),t,=Nil s," 2s,m "a.lI lna v ery
•.•
commcolnao sfsi dentifimceatthiotodhnse , Coenrvgence
sqrueasdum o fp redicetrirooinrsm s i nimtioz ed
fintdh "eb esmto"d el: Unedrw eacko nditiitco anbnse s hotwhna t
(29) 0N 0*= a rmgi Vn( 0w). pa.s1 (34)
+ 0EDM N>oo
where
Wit0hd etermiintn heidws a yt,h ter ansffuenrc ­
N
tioens timbaetceo mes V(0)l ilra N EE2 ( , t0 ) (35)
(03) N>oo Nt� = l
Seee,. gL.j u(n1g9 78).
Amomnegt htohdasct a bne e xpreasss( e2d9w )e
fintdh "em axilmiukme limheotohd(o ads"s uming ApplyPianrgs evraell'ast iotno(s 3h5ig)pi ves,
Gasuisadni sturbatnhc"eel se)as,sq tu amreets"h od aftseorm cea lcula(tsieLoejn us(n 1g9 87u)s)i,n g
anodt heSresLe.j u(n1g9 8a7n)Ad s tr(llm1 09)8f or als(o3 3c).
furtdhiesrc ussions.
0*=amrign t r[R(•Qw(,]w0d:il)) (36)
Someex tensions 0 J
""'1l
Itm aoytf e bne w orthwthoci olnes iadm eord ifiedw ith
crite(r2i9ow)nh etrhepe r edicetrirooEn(r ts ,0)
(ore,q uivaltehnietn lpyu t-osuetqpuuetn ces) R(,w0 T)T(= -ei w, )0T(iew,0 ) (37)
firasrtfe i elrtetdh roauf gihl tLe(rq ):
Q(,w0 )(�w)1/�( iew)2 1 (38)
X
EF(t,=0L )( q)E(t,0) (31)
Ntoet hafto orp elno oopp era(t�i(ow)n= O),
ue
Thisi sh,o weveeqru,i vatlore enptl atchien g
noimsoed He(lq ,b0yH) ( q,0)/SLe((eq2 )8a.)n d, "l'(q.[0G)(=q,0)�o((qq)) ]-T (39)
foarf urtdhiesrc usWsaiholnb,ae nrLdgj ung
(198P6r)e.f ilttehrdeia nttgah ucso rrestpoo ndsa nd
selecatniontgnh oeirms oed el set.
�( w) (04)
Alstoh e oufsk e-s taehpe parde dicitn(o 2r7s)
migbhetu sefAusle .l aboroanit neW da bhelragn d
Lju(n1g9 8k6-)s,t aehpe parde dicmteitohnao rdes thiesx pressspieocni atloi zes
equivatlore enptl aHc(iqn,gb0 y)
(41)
-1
H(q,k0( )qM,0) (32)
L.L jung
4
Variance 6 MINIZMIINTGH EBI ACSO NBTURTIION
Let Consindoetwrh p er obolfem mi nimitzhibeni ga s
distribiu.tei.o n,
T(*)q Tq(,0*) (42)
miJnB( ..V) (51)
wi0t*hd efiansea dob ve.
2lEt.
Undfeari rgleyn ecroanld itiitco antnsh ebne wheJr (e£) )i sd efibnye( d73 )(,4 9'Ih)e.f unc­
shotwhna t tdieonJoBnc�,fi)ne ) od fet hpleeoa nntd,Z>tsvf e iu0ran* c(ilJt )ii.'Ihnot e nud ,rei nps,e n­
(43) defibn,ft)ye ( d3 6w)h,i wcehw riatse
Here( 43m)e atnhsa tth rea ndvoamr iaobnl et he 0*.S()=amrign tr[R(•Qw (,JOw0),)]ct.> (52)
lefcto nveirngd eiss tribtuott hineoo nr mdails t­ 0 l
ributwiiotznhe rmoe aann cdo varimaantcrei x -'It
R(w,i0sd) e fibnye( d73 )a nQd b y( 38W)e.h ave
P(w)H.e rteh ien dned xe nottheoesr dert hoef
n appentdheaedr gum,&etnoQt , t os trehsasit t i s
moduesle idnT (q,0).
maduepf rotmh dee sivganr ia(b3l3eS)se. ae l so
Lju(n91g8 6a)n Gde vearnsLd j u(n1g9 86).
Resultssu,ca hs( 43g)ob actkot haJ!ey mptotic
normalititehpsea roafm eestteir0m Na,te es tab­ Compar(i52n)gw itthh mei nimizpartoib(ol51ne) m,
lishee.dg,i. nL juanngCd a in(e1s99 )7'Ih.e
(49i)ti si ntuitcilveealry t thbheea stct h oice
expresfsoiPro( nwi )s i ng enecromaplil cated.
n of shoubleod n teh amta kCew(s) a nQd( ,w,:V)
Fomro detlhsaa tr pea rametars"i bzleabdco kx es" pr:lJo pioorntaTlh.at th iissi ndetehdce a sies
weh avheo,w etvhefero llogweinnegrr easlu lt, provienYn u aann Ldj u(n1g9 8a5n)Ld j u(n1g89 6b).
Lju(n9lg8 b5). Wet huhsa vteh feo llorweisnugl t.
(44) Theo1r.eC mo nsitdheperr obtloem mi nim(i51z)e
witrhe spteoc0 t= {@( w@),( w)L,( eiw),
witha@n d@d efibnye( d3 a)n (d04 ),r esp-ecti�(e)i}w( se(e3 3u)n)� tehruae es sumpt(i2o2n)s.
v
vely. X The£Jno pits s ucthh at
Ap ragmaitnitce rpretation (53a)
Evetnh outghhce o varioafn cnTee endo cto nverge
N
(converignde inscter ibduotenisoo itnm ply (53b)
converigneL n)c,we es haallll oouwr setlov es
2
usteh ree su(l4t3- )( 44i)nt hfeo llomwoirneg
wheries a ncyo nsttahnamtta k.Ves belotnog
suggesvteirvsei on: thaead misssiebtl.e opt
(45)
D
Wes haallls aol ltohwae p proximation
Herea rien clutdhepedr efilitne( r31 )a Lsa n
E (iew)�Ti*w()e (46) explicit opttihoatnth. e arNresoe et viecrea l
�N ways of otbhotepa tiindmieanslgi Agnncy.o mbina­
tioonfsi npsupte ctarnumnd o imsoed tehla otb ey
(SeLej u(n1g9 8f7o)jr u stifoinc)sa .ti
(5b3)w ilgli vteh oep tibmiaalds i stribution.
Alsroe catlhlat th ceh oiocfne o imsoed �e(lq )
Wit(h4 5a)n (d4 6t)h eex proens( s1i5c)a bne
contatihnoesp tioofn predhiocrtiikzo (onesn e
rewreint t
(2 3)
)•
7 MIINMZIINTGH VE ARIACNOTCNRBEUI TION
Thper oblem
whetrhebe i acso ntribRu wtaidsoe nf iinne( d3 7).
}ieJ;i avhee raep pentdheaedr gum,0e(0n*t=0 *(,8),
Leuts n otwu rtnot hper oblem
0N=0N(:i))t)o s tretshsde e pendoentn hcdeee sign
variables.
(45)
Thcer ite(r41i)oc na tnh ubses pliintt aob ias
anadv arnicaceo ntribution: wheJrp(e.2:> )i sg iven( 05)b.Wy e s hagleln elrya l
assumteh atth ien ppuotw iesrc onstrained:
(48)
where t.:-rt J @u ( w)-<d�w (55)
Spelloiun(tg50 ) g ives
JB(,0)= trR (w,,V0)*C)(( w)ct.> (94)
j
-rt 'l'(,,Z}w),d:AJ
j
-rt
where
(05)
Int hfeo llotwwisone gc tiwoesn hsa dlils ctuhses
minimizoaftt hieotsnwe co o ntribtuott ihoen s
desicgrni terion. @•v(w) (65)
:J=J {@u,u@el (75)
BuildMiondgefo lrs SpeiceiPdfu rpose 5
a
Herew ed ispesnedw itht hes calinng/ Nw,h ich is estmiatioonf t rnasferf untciosn.
immataelr.i
Weh aves tudiedt hef maily opfr edtiicoenr ror
For thec ase( 22w)e o batin thep roblem identifciatiomne thso fdort hep arametere stima­
tio,n and maudseeo f sormeeec ntyl deriveadsy mp­
(58) totiecxp ressnisof orb iasa ndv arainceo ft he
transfefru ntcioens tmiate.U ndre certain asumsp­
tionss ome fairlye xpliciatdv icef ort hec hioce
subject tot hec onstraintth at ofi nputs petcr,a feebdackm echasnmisp,r eftielrs
andn oismeod elsh aveb eend erived.
-'JIj <I? u ( w) wd -< C (59) bAcenkeosnwu ldpgepeoemrnit.te nTpdh a rewt rbi yt tighn oeAf rt myh Riessa reatrciclheOh f fasi ec
From( 58)a ndt hef actt ha<l?t (w)d oesn ote nter undecro ntarctD AAG2-9-84--0K05a,n di np artb y
ue
thec onstrain,t itf ollowst hat theS wediNsaht iaolnB oarfdo rT echncialD eveolp­
ment( STFU).
(60)
REFEERNCES
Iti st huso pitmalt ou seo penlo ope xperitmse,n
andt heo ptmiali nputi se asyt oc omupteu sign Astrmtl,K J (198.0 Ma)ximmu likelihooadn dp reidc­
Schwarzs' inequaltiy: tione rrorm ethso.dA utoamticav,o l1 6,p p5 51-
574.
Lemm1a The soultiont o( 58-)(59)
Astrtlm,K J andP .E yhkoff( 197.1 )Sytsem idenit­
cp�Pt(w)= µ • I c11(w)• <l?v(w) (61) 4f7ic6at.i on- as urevy. Autmoaticav,o l1 3,p p4 57-
whereµ isa consta,n atdjusdt seot hat
Eyhkoff,P (197.4 )Sysmt eIdenitfciatio.n Wile,y
@0Pt(w} dw C (62) Lonodn.
u =
-'JIj
Eyhkoff,P (1981()E )d.T rnedsa ndp rogreisns
sysmt eIdenitfictaionP,er gmaonP res,s Oxofrd.
8 MINIMIGZ TIHNED ESIGCNR ITERIA
Gevres,M andL Ljung( 198.6 )Optimale xperiment
Let nuosw t urn tthoef ulld esigcnr iterio(n1 3­) desigwni thr espte tcot hei ntedned modela pplica­
(16)i ni tsp rgamatifco rm( 48-)(50.) Ourp artial tio.n Automaitca,v ol2 2,S etp 1986t,o a ppear.
resulotnsb isa-andv arainc-meiniimztaiotnh en
shwo thati t icner tainc aseiss p ossieb tlo Ljung, L( 197.8 )Convergencaen aylsis poafrm eat­
minizmeit het woc ontribiuotsn siumltaneosuly. rici dentifaiticonm ethso.d IETEraEn asctioonns
Theno fc oursteh ef ullc riteriiosan l smoi ni­ AutomtaicC otnrol,v olA C-23p,p 7 707-83.
mize.d For thec aseo fTh eorem1 we thuhs avet he
followign reslut. Ljung, L( 1985.a O)nt hee sitmtaioonf t ransfer
funtcion,s Autoamtica,v ol2 1,p p6 77-696.
Theor2e:mC osniedrt hep robletmom inimi(z4e8 )-
(50)w ithr espte tco Ljung, L( 198b5). Asypmtotivacr aincee xprseisosn
= <l?u(w)' u<l?e(w,) L(iew)' H*(eiw) } IfEoEriET de rantnisAf utiobe.mld Ca koc-bnotxrt, o rlnavsfoelr f uAnCptc-pio38 n03m4 ,o- e8dl4s.4 .
{
undetrh ea ssumptiso n(33-)(22,) ands ubjectto Ljung, L( 198.6 P)aarmetrci methosd fori dentif­i
thec ontsriant (59). Then opti sg ivne by catioonft rnasfefru nctsi onolfi neasry smtse. I�n
Advancse inC ontrvooll XX V,( C.L. Leoneds,E d},
<l?ue(w) 0 Academci PressN,.Y .1 986t,o a ppear.
=
(63) LjungL, ( 198.7 S)ytsemsI detnifaitcio-nT heoyr
fort heU sre,. Pretniec-Hall,E ngweolodC liffst,o
appear.
Ljung, L andP EC aine(s1 97.9 )Asympttoicn orma­
Hereµ isa cosntnat, adjutseds ot hatth el eft litoy fp redtiicoenr rore stmiaitonf ora pprxoi­
1
hands ied has Laa uretn expressitohnta strats mates ystemomde l.s Stohcastisc vo3l, p p2 9-46.
witha "1",a ndµ isa cosntanta dujsteds ot hat
2
thei nput powre constriant ism et. Wahbler,g B andL Ljung( 198.6 D)esignv airables
forb isa distribuitnit ornna sfefru cntione stima­
D
tio.n IEEET ransA utomC ontrovlo,l AC-F3e1b,
Notet hatth ef reoemdi nt hec hoiec onfoi sem odle 1986.
andp refilitesir m agniar,y sincet heya lways
appeair nt hec obmintaioLn( q/)H*(q)i n tchreti e­ Yuan,Z Da ndL Ljung( 198.5 U)nroeuidcied opitmal
rion. open lioonppu td esigfno ri dentifaitcioonf
transfefru ntciosn,A utomatica,v ol2 1,p p6 97-
The casweh ereo urp rimient eret sis itnh et rnas­ 708.
ferf unctioGn isp roabblyt hem ostc ommno one,
and theretfhoeor petm iald esigvna raibleso ffedr e
byT heorems ho2u lbde o fi nterets.T heo nly draw­
bacwki tht hiss oultionm ayb et hatt hec hoiec of
contsantn oismeod elm ayl eadt om orec aluclatiso n
int hen umreicalm iniimztaioonf tphree idction
errorc riterion.
9 CONCLUSIONS
Int hicso ntribiuotnw eh avef oucsedo uri nteerst
ont hed esigvna raiblse thta area vailbalef ort he