System Identification Toolbox User's Guide - Ladispewww.researchgate.net › post › attachment › download › S

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Lennart Ljung

Computation Visualization Programming

User’s Guide

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System Identification Toolbox User’s Guide  COPYRIGHT 1988 - 1997 by The MathWorks, Inc. All Rights Reserved. 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 reproduced in any form without prior written consent from The MathWorks, Inc. U.S. GOVERNMENT: If Licensee is acquiring the Programs on behalf of any unit or agency of the U.S. Government, the following shall apply: (a) For units of the Department of Defense: the Government shall have only the rights specified in the license under which the commercial computer software or commercial software documentation was obtained, as set forth in subparagraph (a) of the Rights in Commercial Computer Software or Commercial Software Documentation Clause at DFARS 227.7202-3, therefore the rights set forth herein shall apply; and (b) For any other unit or agency: NOTICE: Notwithstanding any other lease or license agreement that may pertain to, or accompany the delivery of, the computer software and accompanying documentation, the rights of the Government regarding its use, reproduction, and disclosure are as set forth in Clause 52.227-19 (c)(2) of the FAR. MATLAB, Simulink, Handle Graphics, and Real-Time Workshop are registered trademarks and Stateflow and Target Language Compiler are trademarks of The MathWorks, Inc. Other product or brand names are trademarks or registered trademarks of their respective holders.

Printing History: April 1988 July 1991 May 1995 August 1995

First printing Second printing Third printing Reprint

Contents The System Identification Problem

1

What is System Identification? . . . . . . . . . . . . . . . . . . . . . . . 1-2 How is that done? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 How do you know if the model is any good? . . . . . . . . . . . . . . 1-2 Can the quality of the model be tested in other ways? . . . . . 1-2 What models are most common? . . . . . . . . . . . . . . . . . . . . . . 1-2 Do you have to assume a model of a particular type? . . . . . . 1-2 What does the System Identification Toolbox contain? . . . . 1-2 Isn’t it a big limitation to work only with linear models? . . . 1-3 How do I get started? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 Is this really all there is to System Identification? . . . . . . . . 1-3 The Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5 The Basic Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6 Variants of Model Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . 1-6 How to Interpret the Noise Source . . . . . . . . . . . . . . . . . . . . . . . 1-7 Terms to Characterize the Model Properties . . . . . . . . . . . . . . . 1-9 Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 Step Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 Zeros and Poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 Model Unstable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13 Feedback in Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13 Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13 Model Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 Additional Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 Nonlinear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 Still Problems? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 Fit Between Simulated and Measured Output . . . . . . . . . . 1-15 Residual Analysis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15 Pole Zero Cancellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15 What Model Structures Should be Tested? . . . . . . . . . . . . . 1-15 Multivariable Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16 Available Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16 Working with Subsets of the Input Output Channels . . . . 1-17 Some Prac