System Identification. Discrete-time parametric methods

Andrzej Królikowski, Dariusz Horla, Joanna Ziętkiewicz

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ISBN/ISSN:

978-83-7775-579-2

DOI:

Wydawnictwo:

Wydawnictwo Politechniki Poznańskiej

Rok wydania:

2020

Liczba stron:

131

XML:ISBN/ISSN:

ONIX MARC21

Bibliografia:

Królikowski, Andrzej; Horla, Dariusz; Ziętkiewicz, Joanna. System Identification. Discrete-time parametric methods. Red. . : Wydawnictwo Politechniki Poznańskiej, 2020, 131 s. ISBN 978-83-7775-579-2

Bibliografia refWorks:

RT Book, Whole

SR Electronic(1)

A1 Królikowski, A.

A1 Horla, D.

A1 Ziętkiewicz, J.

T1 System Identification. Discrete-time parametric methods

PB Wydawnictwo Politechniki Poznańskiej

YR 2020

SN 978-83-7775-579-2

Bibliografia BibTex:

@Book{ 240038, author = "Królikowski, Andrzej and Horla, Dariusz and Ziętkiewicz, Joanna", editor = "", title = "System Identification. Discrete-time parametric methods", publisher = "Wydawnictwo Politechniki Poznańskiej", year = "2020", address = "", isbn = "978-83-7775-579-2" }

Bibliografia endNote:

TY - BOOK

AU - Królikowski, Andrzej

AU - Horla, Dariusz

AU - Ziętkiewicz, Joanna

ED -

TI - System Identification. Discrete-time parametric methods

PB - Wydawnictwo Politechniki Poznańskiej

CY -

PY - 2020

SN - 978-83-7775-579-2

ER -

Netografia (standard APA):

Królikowski, Andrzej; Horla, Dariusz; Ziętkiewicz, Joanna. System Identification. Discrete-time parametric methods [baza danych online] : Wydawnictwo Politechniki Poznańskiej, 2020 [dostęp: 25 08 2024]. Dostęp w Ibuk Libra: https://libra.ibuk.pl/reader/system-identification-discrete-time-parametric-methods-andrzej-krolikowski-dariusz-240038.

algorytmy, MATLAB, automatyka

Podręcznik jest materiałem pomocniczym przygotowanym na potrzeby wykładów i ćwiczeń laboratoryjnych z przedmiotu identyfikacja obiektów sterowania prowadzonych na kierunku automatyka i robotyka. Przedstawiono w nim podstawowe metody i algorytmy id...

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ISBN/ISSN:

978-83-7775-579-2

DOI:

Wydawnictwo:

Wydawnictwo Politechniki Poznańskiej

Rok wydania:

2020

Liczba stron:

131

XML:ISBN/ISSN:

ONIX MARC21

4.4.6. Projection method with dead zone7
Preface8
1. Introduction 10
1.1. The concept of system identification10
1.2. Classification of identification methods13
2. Systemmodels14
2.1. Introduction14
2.1.1. Discrete-time models14
2.1.2. Discretisation using the zero-order hold method15
2.1.3. Tustin’s method16
2.1.4. Finite difference method16
2.2. Deterministic models17
2.2.1. FIR model17
2.2.2. ARMA model18
2.2.3. State-space model20
2.3. Stochastic models24
2.3.1. ARMAX and ARIMAX models24
2.3.2. ARX and ARIX models25
2.3.3. Output error model27
2.3.4. State-space model28
2.4. Bounded noise models2931
2.4.1. Model with simple disturbance input31
2.4.2. Model with compound disturbance input31
2.5. Model properties33
2.4.3. State-space mode l3133
2.5.1. Controllability, reachability, observability and detectability33
2.5.2. Identifiability34
3. Direct estimationmethods36
3.1. Introduction36
3.2.Order of persistent excitation37
3.2.1. Definition37
3.2.2. Order of persistent excitation of typical signal38
3.2.3. Persistent excitation and parameter estimation39
3.3.Deterministic models and the least-squares method40
3.4. Stochastic models and the least-squares method41
3.4.1. Least-squares method for stochastic models41
3.4.2. Weighted least-squares method49
3.4.3. Bias-eliminated least-squares method49
3.4.4. Instrumental variables method52
3.4.5. Maximum likelihood method53
3.5. Bounded noise models and the least-squares method56
3.6.Model order estimation57
4. Recursive estimationmethods59
4.1. Introduction59
4.2. Deterministic models59
4.2.1. Least-squares method59
4.2.2. Projection method63
4.2.3. Modified projection method63
4.2.4. Modified projection method for prediction model65
4.2.5. Modified least-squares method for prediction model65
4.3. Stochastic models66
4.3.1. Least-squares method66
4.3.2. Bias-eliminated least-squares method66
4.3.3. Kalman filter method68
4.3.5. Instrumental variables method68
4.3.6. Extended least-squares method69
4.3.7. Maximum likelihood method69
4.3.8. Extended Kalman predictor70
4.3.9. Second-order filter72
4.4. Bounded noise models73
4.4.1. Least-squares method73
4.4.2. Least-squares method for prediction model74
4.4.3. EW-RLS algorithm75
4.4.4. MVSA algorithm75
4.4.5. Fixed dead zone method76
4.5. Recursive estimation of the order and parameters79
4.5.1. Introduction79
4.5.2. Preliminary assumptions80
4.5.3. Recursive estimation of the degrees and coefficients81
4.5.4. Recursive algorithm for the simultaneous degrees and parameters estimation84
4.6. Model delay estimation87
5. Time-variant systemidentification90
5.1. Introduction90
5.2. Weighted least-squares method91
5.3. Forgetting factor and windup in estimation91
5.4. Modifications of recursive least-squares method93
5.4.1. Investigation of persistent excitation condition93
5.4.2. Adaptation to noise95
5.4.3. Robust estimation96
6. Closed-loop systemidentification 98
6.1. Introduction98
6.2. Example of first-order inertia system98
6.3. General conditions for identifiability99
6.4. Identifiability of LQG control system100
6.5.Model order estimation in a closed-loop system102
7. Selection of excitationsignal104
7.1. Introduction104
7.2. FIR model104
7.3. ARX bounded noise model105
7.4. Stochastic ARX model108
7.5. Selection of excitation signal and uniqueness of estimation108
8.Multivariable systemidentification110
9.1.Analitical method120
9. Case study – simple identificationexperiment120
9.2. The ’real’ experiment121
10. Experiment implementationinMatlab 124
10.1. Parameter estimation124
10.2. Creating model structure125
10.3. Model conversion126
10.4. Selected additional functions126
10.5. Simulink126
Summary127
References128

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

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