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Anidentificationexperimentisbasicallydoneinanopen-loopsystem,butitis
onlypossiblewhenthesystemisstable.Thegeneralblockdiagramoftheexperi-
mentispresentedinFigure1.1.
Accordingtothegivendiagram,severalstagescanbedistinguishedintheexper-
iment:
•Planningoftheexperimentandgatheringdata
Thisstagerelieson,e.g.,defininginputsandoutputs,choosingthemethod
ofmeasurement,determiningtheoperatingpoint,choosingthesampletime,
choosing(ifpossible)theidentificationsignal,i.e.,persistentlyexcitinginput
signal(ofappropriateorder)and,consequently,gatheringthemeasureddata.
Themostcommonidentificationsignalsare:randomsignals,pseudo-random
signals,e.g.,pseudo-randombinarysequence(PRBS),stepwisesignalsand
sumsofsines.Theidentificationsignalcanalsobetheresultofoptimisation,
withthemostaccurateestimationofsystemparametersasanoptimisationcri-
terion–suchanapproachisdescribedinChapter7.Itshouldbenotedthat
planningtheexperimentandgatheringdatacomprisethemostexpensivepart
ofthewholeexperiment.Theremainingstagesonlyinvolvetheprocessingof
data.
•Choosingtheclassandstructureofthemodel
Forinstance,formodelsofclassesARXorARMAX,thestructureadditionally
determinestheordersofpolynomialsandthedelayvalue.
•Choosingafitcriterion
Thedecisionisrelatedtothechoiceofamethodformodelparametersestima-
tion,e.g.,theleast-squaresormaximumlikelihoodmethod.
•Modelverification
Thephaseofverificationreliesonsubjectingtheobtainedmodeltoselected
tests,forinstance,confirmingthecorrectnessofthemodelforadifferentset
ofmeasureddata.Theresultofverificationdeterminesthedecisionofthe
model!sacceptance,oroftheexperiment!srepetition.Anegativeresultinver-
ificationoftenresultsinthechoiceofamorecomplexstructureofthemodelor
achangeofthemodeltype.
Thisbookbasicallyconcernsthestageofmodelcalculation.Withinthebook,
algorithmsformodelparametersestimation(estimationalgorithms,inshort)are
described.Ablockdiagramofparameterassessmentˆ
Btofthemodelisshownin
Figure1.2.However,itshouldbekeptinmindthatthewholeidentificationexper-
imentofthesystemisacomplexanditerativeprocessofthestructurepresentedin
Figure1.1.
Identificationcanalsobeappliedinaclosed-loopsystem,whichmaybeneces-
sary,forinstance,ifthesystemthatistobecontrolledisunstable.Closed-loopiden-
tificationisalsoappliedinthecaseofadaptivecontrolsystems,whencontrolsystem
parametersareautomaticallytrimmeddependingontheresultofidentification.In
thesekindsofcontrolsystems,calledself-adjustingsystems[2,19,50],itisnecessary