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Technical report from Automatic Control at Linköpings universitet Practical Issues of System Identification Lennart Ljung Division of Automatic Control E-mail: [email protected] 29th June 2007 Report no.: LiTH-ISY-R-2810 Accepted for publication in UNESCO encyclopedia EOLSS: Encyclope- dia of LifeSupport Systems Address: Department of Electrical Engineering Linköpings universitet SE-581 83 Linköping, Sweden WWW: http://www.control.isy.liu.se AUTOMATIC CONTROL REGLERTEKNIK LINKÖPINGS UNIVERSITET Technical reports from the Automatic Control group in Linköping are available from http://www.control.isy.liu.se/publications.

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Technical report from Automatic Control at Linköpings universitet

Practical Issues of System Identification

Lennart LjungDivision of Automatic ControlE-mail: [email protected]

29th June 2007

Report no.: LiTH-ISY-R-2810Accepted for publication in UNESCO encyclopedia EOLSS: Encyclope-dia of LifeSupport Systems

Address:Department of Electrical EngineeringLinköpings universitetSE-581 83 Linköping, Sweden

WWW: http://www.control.isy.liu.se

AUTOMATIC CONTROLREGLERTEKNIK

LINKÖPINGS UNIVERSITET

Technical reports from the Automatic Control group in Linköping are available fromhttp://www.control.isy.liu.se/publications.

Abstract

This is a survey of practical issues in System Identi�cation.

Keywords: identi�cation

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Best Fits

arx441: 0.0030537

100 120 140 160 180

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Measured and 10 step predicted output

Time

 �PMSR��?U9 ± ­�§�93=@_Q�-?U9On¾GR��AD;���A �¼n>=@_Q�Jcan-G8AUAD9On¿KMPTF-9C��=8F-nh3�Wca_QAU9<;�=@�-93=8n�;-?Q9<n-PTNOAD9On¿GR��AU;-��A��Â_QGRKMPTn�KTPMF-9H�H¼GR?]=@PM?QN<?U=8H�A�^8=@KMPTn>=8ADPTGRF�n-=8A�=�5��-_UPTF-S�=8F����]��CEGJn�9<Kkl]P¯AD� � � ! ± ' � )� ! ± ' � )) !"hF'�- ! hF'�¤ '�j

G@H]?U9O;-?UG)n-�-NOPMF-S¿F�9Ol C�9<=@_U��?U9<CE9<F AU_�Òz�-PTAU9�l³9<KMK�5L=8A©AD�-9�_D=@CE9�AUPMCE9�P¯A¡PT_¡F-G@A©HÂ=@KM_QPT�>9On¬ `�?U9<_QPMn-�-=@K=@F>=@K¯`J_QPM_O�

100 120 140 160 180

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Measured and 10 step predicted output

Time

Best Fits

arx411: 0.0018472

n4s4: 0.0035842

amx4121: 0.0018923arx811: 0.0019366arx441: 0.0030537

 �PMS@�-?U9�e)­'��_��>SR�-?Q9 ± ¬-�JA�H¼G@?�_U9O^@9<?U=@K6n-P:�[9<?Q9<F A�C�G)n-9<KT_<�

Best Fits

arx411: 0.0018472

100 120 140 160 180

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Measured and 10 step predicted output

Time

 �PTSR�-?Q9 ² ­L��_]�>SR��?U9 ± ¬-��A]H¼GR?�AD��9¦¬19<_BA��:����caCEG)n-9<K��

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Model Fit vs # of par’s

# of par’s

% U

nexp

lain

ed o

f out

put v

aria

nce

Red: Best Fit

Blue: AIC Choice

Blue: MDL Choice

 �PMSR��?U9 � ­*°mGRCE;>=@?QPM_UG@F-_6G@H�AU�-9�h¢ca_QAU9<;¡=@�-93=8n©;-?Q9<n-PTNOAUPMGRF¦9<?Q?UGR?XH¼GR?ih3��� �]���]��caCEGJn�9<KM_pH¼G@?6AU�-9³=@PM?QN<?D=rH�An>=8A�=J�

−0.4

−0.2

0

0.2

0.4Autocorrelation of residuals for output 1

−20 −15 −10 −5 0 5 10 15 20−0.4

−0.2

0

0.2

0.4Cross corr for input 1and output 1 resids

Samples

 �PMS@�-?U9�gJ­i��9O_UPMn��>=@K6=@F>=8KT`)_UPT_�AD�-9�¬19<_QA����]��caCEGJn-9OKkH¼GR?�AU�-9�^@=8KMPMn-=8ADPTGRFÅ=@PT?UNO?D=8H�A�n-=8A�=��

0 20 40 60 80 100 1205

10

15

20

25 κ−number of Inflow

0 20 40 60 80 100 1208

10

12

14

16

18

20

22 κ−number of Outflow

0 20 40 60 80 100 1200

20

40

60

80Inflow

0 20 40 60 80 100 1200

50

100

150

200Vessel Level

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Avdelning, Institution

Division, Department

Division of Automatic ControlDepartment of Electrical Engineering

Datum

Date

2007-06-29

Språk

Language

� Svenska/Swedish

� Engelska/English

Rapporttyp

Report category

� Licentiatavhandling

� Examensarbete

� C-uppsats

� D-uppsats

� Övrig rapport

URL för elektronisk version

http://www.control.isy.liu.se

ISBN

ISRN

Serietitel och serienummer

Title of series, numberingISSN

1400-3902

LiTH-ISY-R-2810

Titel

TitlePractical Issues of System Identi�cation

Författare

AuthorLennart Ljung

Sammanfattning

Abstract

This is a survey of practical issues in System Identi�cation.

Nyckelord

Keywords identi�cation