Adaptive systems in control and signal processing : proceedings

433 Pages·1987·19.998 MB·English

by  Björn Wittenmark, Karl Johan °Aström, International Federation of Automatic Control, International Federation of Automatic Control Technical Committee on Theory

OtherI AFC Publications
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ADAPTIVE SYSTEMS IN
CONTROL AND SIGNAL
PROCESSING1 986
Proceoeftd h2iennI dFgA sCW orkshop
LunSdw,e d1-e3J nu,1l 9y86
Editbeyd
K.J . ASTROM
and
WITTENMARK
B.
LunIdn stoifTt eucthgyen, So wleoden
Publishedt he
for
INTERNATIFOENDAELR ATOIFOA NU TOMATCIOCN TROL
by
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holders.
First ed1i9t8i7o n
LibroafCr oyn gress iCnPa utballiDaoctaga itinogn
Adaptisvyes teimnsc ontraonld s ignparlo cess1i9n8g6,.
"SeconIdF ACW orkshoopn AdaptiSvyes temisn
Controaln dS ignaPlr ocess1i9n8g6,o; r ganizbeyd
LundI nstitouftT ee chnoloLguyn,d ,S wedens;p onsored
byI FACT heorCyo mmitteceo;- sponsobryeS dw edisIhF AC
Committee"-P.
Includiensd ex.
1.A dapticvoen trsoyls tems-Congresses.
2.A daptisvieg nparlo cessing-CongrIe.As ssterso.m ,
KarlJ .( KarJlo han)1,9 34- . II.W ittenmark,
BjornI.l lI.n ternatiFoendaelr atoifoA nu tomatic
ControlI.V .I FACW orkshoopn AdaptiSvyes temisn
Controaln dS ignaPlr ocessi(n2gn d1:9 86L:u nd,
Sweden)V . Teknishkoag skolia Lnu nd.V I.I nter­
nationFaeld eratoifoA nu tomatCiocn troTle.c hnical
Committoene Theory.
TJ217.A32171 987 629.8'368 7-25733
ISBN0 -08-034085-7
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threep rodudcotenisood tni spcloaym pulneiftoerm iTtyoe. n surraepp iudb lictahdtiiisso cnr epcaoncyun ldo bte
changneodcr:o utldh Een glisbhec hecckoemdp leTtheelrye.tf horere eader,sa raes keedx causnedy e ficiencies
to
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to
TheE ditors
PrintiendG reBarti tlJ'ja inW heatoCno . Exeter
A. f$ Ltd.,
SECOND IFACW ORKSHOP ON ADAPTIVES YSTEMS
IN CONTROL AND SIGNALP ROCESSING1 986
Organbiyz ed
LundI nstitouftT ee chnoloLguyn,d ,S weden
Sponsboyr ed
IFA C TheorCyo mmittee
Co-spobnys ored
SwedisIhFA C Committee
InternaPtrioognrCaaolmm mittee
K.J .A stromS,w eden( Chairman)
A.B envenisFtrea,n ce
B.E gardStw,e den
P.E rikssSowne,d en
P.G awthroApu,s tralia
G.G oodwinA,u stralia
R.I sermanFnR,G
R.J ohnson, USA
S.J � rgenseDne,n mark
L.K eviczkHyu,n gary
P.K okotovUiScA,
I.L andauF,r anc(eC hairman)
L.L jungS,w eden
MacchFir,a nce
0.
E.M oscaI,t aly
K.N arendrUaS,A
PeterkCaz,e choslovakia
V.
G.S aridUiSsA,
W. Schaufelberger, Switzerland
Sunahara,Japan
Y.
M.T omizukUaS,A
TsypkiUnS,S R
Y.
H.U nbehaueFnR,G
B.W idrow, USA
B.W ittenmaSrwke,d en
E. dstiUeS,A
Y
LocOarlg aniCzoimnmgi ttee
G.O lsso(nC hairman)
K. Astrom
].
P.H agander
R.J ohansson
B.W ittenmark
Ms.E .S childt
Ms.A -B.M adsen
Copyhrt©i IgFAACd aptivei nCS oynsttreomls
anSdi gPnraolc essiSnwge,d 1eL9nu,8n 6d ,
PREFACE
The firsts peciaIlF AC activitoyn adaptivceo ntrolw as a Symposium on
Optimizatiaonnd Adaptive Contirno lR ome This was followebdy a
1962.
symposiumo n Theoryo f Self-AdaptiSvyes temsi n Teddingtoinn and the
1965
symposium on SystemS ensitivaintdy A daptiviitny D ubrovniki n Aftert hat
1968.
adaptivceo ntrowla s discusseidn others ymposiam ainlyt he very successful
symposiums erieosn Identificaatnido Pnr ocessP arameteErs timatiionni tiatiend
Praguei n
1967.
In the Theory Committeoef IFAC createda workingg roup on adaptive
1981
controclh airebdy profL andau.T hisg roupi nitiatseedv eraalc tivitiine asd aptive
controlO.n e goalw as to try to bringt he communitieosf controaln d signal
processincgl osetro getheAr .r esulotf thea ctiviwtays to organize workshops.
The first workswhaosp c alleAdd aptivSey stemsi nC ontroaln d SignaPlr ocessing
Itw as heldi n San FranciscoT.h isp roceedingi s from the thsee cond
1983.
workshopi nt hes eriewsh ichw as heldi nL und.
Therew ere threep lenarys essionasn d submittepda pers.W e believteh at
192
thisr eflectthse i ncreasiinngt ereisnt adaptivceo ntrolT.h e papersw ere selected
on the basiso f extendeadb stractOsf. thes ubmittepda pers were accepted.
83
Fivep apersw ere withdrawnl aterT.o maintaian w orkshops piriitn spitoef the
largen umber of papersw e decidetdo run two applicatisoensss ionisn parallel
and we alsoi ntroducetdw o posters essionTsh.e y were heldi n two rooms each
witha bout papers.T he sessionwse re very wella ttendeadn d very well
10
receivedt,h erew as a livelsyp iriwti thl otso f discussiopnasr ticularilny t he
posters essionMsa.n y participasnatisd t hatn extt imet heyw ouldp refert o have
theipra perp resenteadt a postesre ssion.
Therew ere participafnrtosm countrieAsu,s traliBae,l giumB,r azilC,a nada,
188 24
China,C zechoslovakDiean,m ark,F inlandF,r ance,F RG, Hungary,I sraelI,t aly,
Japan,M exico,t he NetherlandNso,r way,P ortugalS,w eden,T urkey UK, USA,
USSR,a nd Yugoslavia.
We would liket o thank the !PC,t he speakersa nd alla ttendeefso r their
contributitoon a good workshop.B ecauseo f thel argei nteresitth as now been
decidetdo e xpandt hew orkshopt o symposiumT.h e nextm eeting thiss eries
a in
wilble helda tt heU niversiotfy S trathclyde.
KarlJ ohan strllm GustafO lsson
A
Chairmano ft he! PC Chairmano ft heL OC
vii
Copyrig©h tIFACA daptiSvyes temisnC ontrol PLENARYP APERS
andS ignaPlr ocessiLnugn,d ,S weden1, 986
ADAPTIVE INVERSEC ONTROL
BernaWridd row
DepartomfEe lnetc tEingcianle eIrnofirnmga,tS iyosntL eambso raSttofaorrndy ,
UnisvietrSyt,faor ndC,A 9 430U5S,A
AbstractA.d apticvoen troilss eenas a twop arptr oblecmo,n troolf p landty namiacnsd c ontroolf
plannto iseT.h ep artasre treatseedp arately.
An unknowpnl anwti ltlr acakn i npucto mmansdi gniaflt hep lanitsd rivebny a controlwlheors e
transffeurn ctiaopnp roximattheeis n verosfe t hep lanttr ansffeurn ctioAnn. a daptiivnev erse
identificpartocieosncs a nb eu setdo o btaai snt abcloen trolleerv,e ni ft hep lanitsn onminimpuhma se.
A model-refevreernscieoo fn t hiisd eaa llowssy stem dynatmoic clso sealpyp roximdaetsei red
referemnodceel dynamicNso. d irect feiesdu bsaecdek,x ceptth atth ep lanotu tpuitsm onitored and
utiliiznoe dr detroa djutshtep arametoeftr sh ec ontroller.
Controofli nternpalla nnto isiesa ccompliwsihteahdn o ptimaadla ptnivoei scea ncellTehrec. a nceller
doesn ota ffecptl andty namicbsu,tfe edsb ackp lannto isiena wayt hamti nimizpelsa notu tpnuoti se
power.
KeywordsA.d aptivceo ntromlod,e lingi,d entificaitnivoenr,s meod elingn,o isec ancelling,
deconvoluatdiaopnt,ii vnev ercsoen trol.
INTRODUCTION
Thipsa peprr esean tvse ryb riedfe scripotfia o mne anos f
usinagd aptifivlet ertiencgh niqfoure sso lutoifoa nd aptive
controplr oblemThse. emphasoifst hipsa peri so n sys­
temsc onceprtast hetrh anm athematiacn alysiAs f.u ll
papebry B .W idroawn dE .W alacihsi np reparawthiiocnh
wilald dretshsei ssumeosr ec ompletely.
Manyp robleimnsa dapticvoen trcoalnb ed ividiendt tow o R·E·Sor()E"SSIt.;R"E D
L"rt:f
parts(:a )c ontrooflp landty namicasn,d( b)c ontroofl
plannto iseV.e ryo ftean ,s inglsey steims u tilitzoe d (aA)D APTIVTER ANSVERSFAlTLLE R
achiebvoet ohf t hesceo ntlro objectiTvheesa .p proaocfh
thipsa pert reatesa cphr oblesme paratCeolnytr.o olf p lant
INPUT ADAPTIVE OUTPUT
dynamiccasn b ea chievbeydp recedtihnegp lanwti tha n FILTER
adaptivceo ntrowlhloesrte r ansfufnecrt iiosnt hei nverosfe
that thoepf l anCto.n troolf p lannto iscea nb ea chievbeyd, ERROR
an adaptifveee dbapcrkoc estsh amti nimizpelsa notu tput
noiswei thoaultt erpilnagnd ty namics. ··orSIRf:D
Kl'\:EPl"ST PO'.S.E
ADAPTIVEF ILTERS (bSlY MBOLRIECP RESENTATION
An adaptidvieg ifitlatle srh,o wni nF ig. hasa ni npuatn, FIGI. AN ADAPTIVFEI LTER
1,
outpuatn,d a nothesrp eciianlp ucta lletdh e" desired
responsTeh.e'd 'e sirreeds ponsien puitss ometimceasl led etertsom inimiszoem efu nctioonfth e error( usuamlelayn
the" trainsiinggn al." square error)T.h e errori sd efineads thed ifference
betwetehne d esirreesdpo nsea ndt hea ctufiallte rre sponse.
Thea daptifivlet ecro ntaiandsj ustapbarlaem etetrhsa cto n­ Many sucha lgorithemxsi sat ,n umbero f whicha re
troilt si mpulsree sponseT.h esep arametceorsu ldfo,r descriibnet dh et extboobkyW idroanwd Steam[sl ].
examplbee,v ariabwleei ghctosn nectteotd h et aposf a
tappedd elalyi noer t oi nternpoailn tso fa lattificltee r. Fort hep urposeosf t hipsa perth,e adaptifivlete rm aybe
Theraer em anyw ayst oc onfigusruec ah fi lter. considerbeedl itktoeh eo nes howin nF igl.a ,an adaptive
tappedd elalyi noer tr ansverfislatle Wri.t hfi xedw eights,
Thea daptifivlet earl soi ncorporaatne "sa daptiavleg o­ thiiss a linefiarn ite-impulse-(reFIRs)pond sieg itfiall ter
rithmw"h ospeu rpoisset oa utomatiacdajlultsyht ep aram- havinag tr ansffuenrc tiowni tohn lzye ronso,po lesi nth e
BernaWriddo rw
2
finite z-Tphliawsni el.ble t heb asibcu ildibnlgoc kf ort he
adaptisvyes tetmosb ed escribbeeldo w.
p
/ /
DIRECT PLANTID ENTIFICATION PLANT DEL.\ YEO
PL \.\;T
!:"VERSE
Adaptipvlea nmtod elinogr i dentificiasta ino inm portant
functiFoing.u r2ei llustrhaotwet sh icsa nb ed onew itahn
DELAY
adaptivFeIR filteTrh.ep lanitn pusti gniaslt hei nputto FIG. DELAYEDI NVERSIED ENTIFICATION
thea daptifivlet erT.h ep lanotu tpusti gniaslt hed esired 4
responsfoer thea daptifviel teTrh.e a daptiavleg orithm Thec hoiciesg eneranloltcy r itical.
minimizmeesa ns quaree rror,c ausitnhge m odel tob ea
P
beslte asstq uaremsa tch thep lanPt fo r theg iveinn put Thei nverfislet eirs u seda s a controlilnet rhe p resent
to
signaanld fo r theg ivesne tof . weigahltlsoc atteoPd . schemes,ot ha!!.t becometsh er espondseel aoyf t hec on­
/PLANT trollpelda ntM.a king smalils g eneradlelsyi rabbluet,
!!.
theq ualiotfyc ontrdoelp endusp ont hea ccuraocfy the
•INPUT inverspiroonc ewshsi csho metimreesq uiretsob eo ft he
__t--- _._-..RD.E!ESSPO\II .-SREE D ordeorfh altfh el engotfht hea daptifivlet e!!.r .
p
A computer simulation heaxsbp eeernid moennett o i llus­
tratteh ee ffectiveonfe ssti hnev ersion pFriocgeusrsSe.a
c-P����/ o,OU,TPUT showst hei mpulrsees ponosfea nonminimpuhma spel ant
;; 'o havinag smallt ranspdoerlta yF.i gurSeb showst he
'-..ADAPTIVE impulsree sponsoef t heb eslte asstq uaresi nverwsiet ha
FILTER
FIG DIRECTI DENTIFICATION delaoyf samplpeer iods.T hee rrorpo wer wasl ess
2. !!. = 26
thaSn% oft hep lanitn pupto werF.i gurSeci sa convolu­
tioonf t hep lanatn di tsi nverismep ulsrees ponseT.h e
INVERSE PLANTI DENTIFICATION resuilste ssentiaa ulnliyit m pulsaeta delaoyf 2 6w,i th
smal"ls idelobeelss"e where.
Anotheirm portafnutn ctiiosin n verpslea nitd entification.
Thitse chniiqsui el lustriatnFe idg . Thep lanitn puitsa s
3.
beforeT.h ep lanotu tpuitst hei nputtot hea daptifivlet er.
Thed esirreesdpo nsefo r thea daptifviel tiesrt hep lant
input thicsa s&1e. inimizimnega ns quare errorc auses
in
thea daptifviel tert ob ea beslte asstq uariensv ertsoe
P-
thep lanPt fo r theg iveinn pustp ectruamn dfo r theg iven
(aP)LA NTI MPULSER ESPONES
seto fw eightosft hea daptifviel teTrh.e a daptiavleg o­
rithamt tempttosm aket hec ascaodfep lanatn da daptive
inverbseeh avlei kae unigta in.T hisp rocesiss o ften
calldeedc onvolution.
0
TIME
P/L pANT
FIG3. INVERISDEE NTIIFCATION
Fors akeo fa rgumentth,ep lancta nb ea ssumetdo h ave
polesa ndz erosA.n inverisfei ,ta lshoa dpo lesa ndz eros,
wouldn eedt oh avez erowsh eret hep lanhta dpo lesa nd ( ) 40-WEIGDHETL AY EO INVERSE
b
polesw heret hep lanhta dz eros. Maaknii nngy erwsoeu ld IMPULSER ESPONSE
be nop robleemx cepfotr t hec asoef a nonminimum phase li=26
plantI.tw oulds eemt hastu chan inverwsoeu ldn eedt o
haveu nstabploel easn,d this bew otruuledi ft hei nverse
werec ausaIlf.t hei nvercsoeu lbed noncausaaswl e lals
causal howtehveeanr t ,w o-sisdteadb ilnev erwsoeu ledx ist
fotrh eaolryoll f ti wnoe-atsrii mdee-du nLvtaarprpalilnaaascnnfoettirm ssn .a ccorwdi th the 0 I II TIME
'I r 1
A causaFlIR filtcearna pproximaa dteel ayveedr sioonf
thet wo-sidpeladn itn veransde ,an adaptiFvIeRf iltcearn
selafd justt hifusn ctionT.h em ethodi si llustraitne d
to
Fig4.. T het imsep ano ft hea daptifviel t(etrhn eu mbeorf
weighmtusl tiplbiye tdh es amplipenrgi od)c an bem ade
adequatellyo nsgo t hatth em ean square eorrfo rto hpet im­
inversweo uldb ea smalflr actoifot nh ep lanitn put
ized
power. To achievteh iosb jectiwvieth a nonminimum
phaspel antth,ed elayn eeds be choseanp propriately. FIG.5 AP LANTA ND ITDSE LAYEDI NVERSE
tJ. to
AdaptIivnveer Csoen trol 3
PLANT
NOISE
(LPA)NT*( EDLYAEIDV NESRE) l----- PLA:\T
p OUTPCT
PLA�N'-T-- ----'
CASCADEDI MPULSER ESPONSE
(c )
0
TIEM
SYNTIJETIC
l\=26 NOISE
FIG. 5 (CONT'AD P)L ANATN DI TS DELAYIENDV ERSE REFERENCE
._MODEL
OFFL INEP ROCESS
A model-refereinncvee rspiroocne siss s howni nF ig6.. A
referenmcodee l isu sedi np lacoef t hed elaoyf F ig4. .
Minimizinmge an square errotrh esw yisttheo mf F ig6.
causetsh ec ascaodfet hep lanatn di ts" model-reference 7M ODEL-REFERENCEI NVERSOEF NOISYP '...ANT
FIG.
inversteoc' l'o sealpyp roximtahtere e sponsoefa model
M.
Muchi skn own aboutth ed esigonf m odel referenscyes ­
tems[ 2]T.h em odeli sc hosetnog ivae d esirarbelsepo nse ADAPTIVE CONTROL OF PLANTD YNAMICS
tot heo veraslyls temS.o med elamya yn eedt ob ei ncor­
Now havintgh ep lanitn veristce ,a nb eu sed a controller
porateidn ttoh em odeli no rdetroa chielvoew e rror. as
top roviad ed rivifnugn ctifoorn t hep lantTh.i s simple
ideias i llustinr aFtiegd8. . E rroarn alyfosri tsh isstr ucture
hasb eend onea ndw ilble presentiendt hep aperb y
Widrowa ndW alachM.a ny simulation examples have
beend onew,i th consgioods ternets ulTthse.i dewao rks.
p Thep lanmtu stb es tablaen,dt hep lanzte ross houlndo tb e
veryc losteo t hej ro-aixnit sh es -plane (aonrat loto hge)
PL/ANT IN/VE RSE unicti rclien t hez -pla(ndei gital), oat vheerrylw oinsge
inverfislet ewro ulbde r equired.
FIG.M ODEL-REFERENCPEL ANTI NVERSE
6
INPUT
COMMAND
PLANT
p OUTPUT
MODEL-REFERENCE
Thusf ar,t hep lanhta sb eenn oisfree e.P lannto iscer eates PLANTI NVERSE PLANT
difficufolrty t hei nvermsodee linsgc hemeosf F igs3., 4 ,
and6 .T hen oise will ibnivaesrs seot lhueti onWsi.e ner
FIG8.D YNAMICC ONTROLO FN OISYP LANT
filtetrh eotreyl wlhsy :P lanotu tpunto isgeoe sd irecitnltyo
thei npuotfst hea daptifivlet erbsi,a sitnhgei npucto vari­
ancmea triceosft hesfiel ters.
ADAPTIVE PLANT-NOICSAEN CELLING
To avoitdh ipsr obletmh,es chemoef F ig. can beu sed.
A diremcodte linpgroc essy ields Wien7e firl tetrh eory Thes ysteomf F ig8. onlyc ontrolasn dc ompensatfoers
P.
showwsh yP i su nbiaseTdh:ep lannto isdeoe s nota ffect plandty namicTsh.e n oisaep pearsa tt hep lanotu tpuutn a­
thei nputto andt herefodreoe s noti nfluenictecs o vari­ batedT.h eo nlyw ayt hatth ep lanotu tputn oiscea nb e
P
ancem atrixT.h en oisiesa ddetdo t hed esirreesdpo nseo f reduceidst oo btaitnh inso isfero m thep lanotu tputa nd
P,i. et.ot hep lant ouBtuptut th.ep lanotu tpnuoti siesn ot procesist t,h efene di tb ack ithnet pol ant inTphuest y.s ­
correlatweidt ht hep lanitn putT.h ere sulits t hafotr the tems howni nF ig.d oetsh is.
9
adaptivfiel tert,h ep lannto ised oes nota ffectth e
crosscorrelbaettiwoente hne d esired reasnpdto hnesa ed ap­ InF ig9., a ne xaccto pyo fP i sf edt hes amei npusti gnal
tivfiel teirn putT.h erefotrheeW, i enesro lutifoorn P is ast hep lanPt. Theo utpuotf t hiPs copyi ss ubtracted
unbiased. fromt hep lanotu tputA.s sumintgh aPt hasa dynamic
responesses entiaildleyn titoc atlh aotf t hep lant the
P,
Now usinagn e xaccto pyo f inp lacoef ano ffl ine differencien t heo utpuitssa closees timaotef t hep lant
P P,
procesiss s howni nF ig. whichc alculattheems o del noiseT.h inso isiesfi lterbeyd and thesnu btracfrtoemd
7 Q
referenpclea nitn versTeh.eo ff linper ocescsa nru n faster thep lanitn putT.h efi lteri sg eneratbeyda no ff line
Q
tharne atli mes,o t haats isc alculattheemd od,e lr efer­ procestsh adte livenresw v alueosf almositn stantane­
P Q
encien versiesi mmediatoebltya ined. ouslwyi tnhe wv aluoefsP .
4 BernaWridd row
Thefi lteirs t hbee sitn ve(rwsiet hdoeultao yf) essen­
Q P,
tiatlhlbeye sitn veorsfeP (withdoeulta yTh)e. " synthetic
noisseh"o uhladv ae spectraclh aracltiektreh aotf t he
plannoti sIetw. i lble s howinn t hWei droawn dW alach I inputstc:p
papert hatth neo icsaen celslyisntgoe fmF ig9. a dapatnsd
convertgome isn imtihzpeel annoti saett hpel aonutt put.
Ass ucihti, s a no ptilmialn elaeras sqtu asreyss teTmh.e re
isn ow ayt ofu rthreerd utchepe l annoti se.
noiselcss--sptlrceansp1p nse
Thes ystoefmF ig9. a ppeatrobs e a feedbascyks tem.
Howeveirf, i sd ynamictahlesl aym ea sP ,t hetr ansfer
P
functarioounn dt hel oopi sze ro.T hetr ansffeurn ction
fromt he" contrsoilg nailn"p pouti ntt ot he" plaonutt ­
putpo'i'n its t haotft hpel aanlto nTeh.u st,h neo icsaen ­
\! \
celldoeesrn oatf fectthpe l adnytn amics.
\i
l!
PLANT
NOISE slc:rpe spOonf.n "ioC:i spyl am
wiatdh:i punvoei scea nceller
FIG.I O CANCELLING
\-------- PLANT OPTIMAALD APTIVNEO ISE WITH
+ p OUTPUT A MINIMUMP HASEP LANT
ESTIMATIO:-.:
COpPY OPNFLO AINSTE
Q
COPY
-;:Ji-
INPUT CCPY
COMMAND
SIGNAL
SYNTIIETIC
NOISE
CpOPY Q CCQPY
OFFL INEP ROCESS
FIG.A DAPTIVNEO ISCEA NCELLER
9F ORN OISPYL ANT
""' OFF /
LINE
Figu1re0 s howress ulotfas c omputern opilcsaaenn tc ella­ PROCESS
tioenx perimeTnhte.p lanitnt hicsa swea sm inimum
phasAel.m opesrtf ecnto icsaen celliaspot sisoinbw lietha FIG1. A1D APTIVIEN VERSCEO NTROL
minimupmh aspel anatn,dt hiisse vidfernottm h eex peri­
ment.
CONCLUSION
Methodfosr adapticvoen trool fp landty namiacnsdfo r
ADAPTIVE INVECROSNET ROL
controolf plnaonitsh ea veb eend escribFeodrt. h eir
propearp plicatthipeol nam,nu ts t stabalnedt, h pel ant
The syosftF eimg1 .1 c ombinaeloslf t hpea rtasl,l owing be
zeross hounlodtb ee xtremecllyo tsoet hej m-aoxifts h e
controoflp ladnytn amiacnsdc ontrooflp lannoti sTeh.e
s-ploarnt eh uen icti rcolfte h ze- plaAnneu .n stapbllaen t
entisryes tiescm a ll"eadd aptiinvveec rosnetr ol."
coulfidr sbtes tabiwliitzfhee de dbtahckea,nd apticvoenl­y
trolleTdh.ef eedbaapcpkr ocaocuhla dl sboeu setdom ove
InF ig1.1 d,i thneori siesu seidn t hep laindte ntification
plaznetr iofsr equirPreodpe.rd esiogfsn u cfhe edbiasac k
procestsoo btainT hissh oubledd onien c asewsh ere
P. subjoefcc tu rrenrets earch.
thep lanitn pusti gniasln otpe rsistoerni tso therwise
unsuitfoarbp lleai ndte ntificAaltsiionoF ni.g1 .1 o,n ec an
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P
model woulredq uiret imteo c atcuhp ,a ndi nt he ProcessiNnegwJ. e rsePyr:e ntice-Hall.
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AdaptIivnveer se Control
5
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0.
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�
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On
invecrosnetr oFli.f teAesnitlho Cmoanrf eroennC cier cuits,s quartreasn,s versfaillt foerr asd aptfiilvtee riIEnEgE.
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IFAC WorkshoonpA daptSiyvset eimnCs o ntroaln dS ig­
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On
regulaAtuotrosm.a Vtoilc9.a,N o.2 .
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self-turneignugl afotro nro nminimpuhma ssey stems.
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AstromK,. J .a ndW ittenmBa.r k(,1 980S)e.l f-tuning
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LandaIu.D, . (1976U)n.b iasreedc ursiidveen tification
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tioonnsA utomaCtoinct rVooll2,.1 .
Martin-SanJc.Mh .e (z1,9 76A) n.e ws oluttioao dna ptive
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64,
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ApplicaFtlioornisd,a .
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Tansactions on
AutomaCtoinctr oplp.3. 8 -51.
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1692-1716.
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NewY orkA,c ademPirce ss.
KailaTt.h( ,1 980L)i.n eSayrs temPsr,e ntice-Hall.
D.T .L .,M orfM,. ,a ndF riedlaBn.d (e1r9,8 1).
Lee,
Recursilveeas sqtu arleasd deesrt imaatligoonr itIEhEmEs .
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CT,
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