System Identification Toolbox.pdf

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System Identification
Toolbox
For Use with M ATLAB ®
Lennart Ljung
Compu tation
Visuali zation
Program ming
User’s Guide
Version 5
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For contact information about worldwide offices, see the MathWorks Web site.
System Identification Toolbox User’s Guide
COPYRIGHT 1988 - 2002 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc .
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by
or for the federal government of the United States. By accepting delivery of the Program, the government
hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR
Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part
252.227-7014. The terms and conditions of The MathWorks, Inc. Software License Agreement shall pertain
to the government’s use and disclosure of the Program and Documentation, and shall supersede any
conflicting contractual terms or conditions. If this license fails to meet the government’s minimum needs or
is inconsistent in any respect with federal procurement law, the government agrees to return the Program
and Documentation, unused, to MathWorks.
MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks, and
TargetBox is a trademark of The MathWorks, Inc.
Other product or brand names are trademarks or registered trademarks of their respective holders.
Printing History: April 1988
First printing
July 1991
Second printing
May 1995
Third printing
November 2000
Fourth printing
Revised for Version 5.0 (Release 12)
April 2001
Fifth printing
July 2002
Online only
Version 5.0.2 (Release 13)
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Contents
Preface
What Is the System Identification Toolbox? . . . . . . . . . . . . . viii
Using This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
The System Identification Problem
1
Basic Questions About System Identification . . . . . . . . . . . . 1-2
Common Terms Used in System Identification . . . . . . . . . . 1-4
Basic Information About Dynamic Models . . . . . . . . . . . . . . 1-6
The Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
The Basic Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Variants of Model Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
How to Interpret the Noise Source . . . . . . . . . . . . . . . . . . . . . . . 1-8
Terms to Characterize the Model Properties . . . . . . . . . . . . . . 1-10
The Basic Steps of System Identification . . . . . . . . . . . . . . . 1-12
A Startup Identification Procedure . . . . . . . . . . . . . . . . . . . . 1-14
Step 1: Looking at the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
Step 2: Getting a Feel for the Difficulties . . . . . . . . . . . . . . . . 1-14
i
 
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Step 3: Examining the Difficulties . . . . . . . . . . . . . . . . . . . . . . 1-15
Step 4: Fine Tuning Orders and Disturbance Structures . . . . 1-16
Multivariable Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Reading More About System Identification . . . . . . . . . . . . . 1-21
The Graphical User Interface
2
The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
The Model and Data Boards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
The Working Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
The Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
The Validation Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
The Work Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Management Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
Workspace Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Help Texts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Handling Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
Data Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
Getting Input-Output Data into the GUI . . . . . . . . . . . . . . . . . . 2-8
Taking a Look at the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10
Preprocessing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11
Checklist for Data Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
Simulating Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
Estimating Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15
The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15
Direct Estimation of the Impulse Response . . . . . . . . . . . . . . . 2-15
Direct Estimation of the Frequency Response . . . . . . . . . . . . . 2-16
Estimation of Parametric Models . . . . . . . . . . . . . . . . . . . . . . . 2-17
ARX Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21
ARMAX, Output-Error and Box-Jenkins Models . . . . . . . . . . . 2-23
State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25
User Defined Model Structures . . . . . . . . . . . . . . . . . . . . . . . . . 2-26
ii
Contents
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Examining Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28
Views and Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28
The Plot Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29
Frequency Response and Disturbance Spectra . . . . . . . . . . . . 2-30
Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30
Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31
Compare Measured and Model Output . . . . . . . . . . . . . . . . . . . 2-31
Residual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32
Text Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33
LTI Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33
Further Analysis in the MATLAB Workspace . . . . . . . . . . . . . 2-34
Some Further GUI Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-35
Mouse Buttons and Hotkeys . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-35
Troubleshooting in Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-36
Layout Questions and idprefs.mat . . . . . . . . . . . . . . . . . . . . . . 2-36
Customized Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-37
What Cannot be Done Using the GUI . . . . . . . . . . . . . . . . . . . 2-37
Tutorial
3
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
The Toolbox Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
An Introductory Example to Command Mode . . . . . . . . . . . . 3-5
The System Identification Problem . . . . . . . . . . . . . . . . . . . . . 3-9
Impulse Responses, Frequency Functions, and Spectra . . . . . . 3-9
Polynomial Representation of Transfer Functions . . . . . . . . . 3-11
State-Space Representation of Transfer Functions . . . . . . . . . 3-13
Continuous-Time State-Space Models . . . . . . . . . . . . . . . . . . . 3-14
Estimating Impulse Responses . . . . . . . . . . . . . . . . . . . . . . . . . 3-15
Estimating Spectra and Frequency Functions . . . . . . . . . . . . . 3-15
Estimating Parametric Models . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
Subspace Methods for Estimating State-Space Models . . . . . . 3-17
iii
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