systems identification - ???????? - fumcpanelprofsite.um.ac.ir/~karimpor/iden/sysiden_lec1.pdf ·...

SYSTEMSSYSTEMSIdentificationIdentification

Ali KarimpourAssistant Professor

Ferdowsi University of Mashhad

Reference: “System Identification Theory For The User” Lennart Ljung(1999)“Practical Issues of System Identification” Lennart Ljung (2007)“Perspectives on System Identification” Lennart Ljung (2009)

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Ali Karimpour Sep 2010

Lecture 1

Perspective on System IdentificationPerspective on System Identification

Topics to be covered include:

� System Identification.

� Place System Identification on the global map. Who are our neighbors in this part of universe?

� Discuss some open areas in System Identification.

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System Identification

System Identification: The art and science of building mathematical models of dynamic systems from observed input-output data.

System Identification is look for sustainable description by proper decision on:

Model complexity

Information contents in the

data

Effective Validation

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Dynamic systems

System: An object in which variables of different kinds interact and produce observable signals.

Stimuli: External signals that affects system.

Dynamic System: A system that the current output value depends not only on the current external stimuli but also on their earlier value.

Time series: A dynamic system whose external stimuli are not observed.

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Dynamic systems

Stimuli

It can be manipulated by the observer.

Input DisturbanceIt can not be manipulated

by the observer.

Measured Unmeasured

Dynamic system

Inputu

Measured disturbance

w

Unmeasured disturbancev

Output

y

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A solar heated house

Dynamic system

Pumpvelocity

u

Solar radiation

w

Wind, outdoor temperaturev

Storage temperature

y

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Speech generation

Dynamic system

chord, vibarationairflowv

Sound

y

Time series: A dynamic system whose external stimuli are not observed.

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Models

Model: Relationship among observed signals.

Model types

1- Mental models

2- Graphical models

3- Mathematical (analytical) models

4- Software models• Split up system into subsystems,

• Joined subsystems mathematically, 1- Modeling

2- System identification

• Does not necessarily involve any experimentation on the actual system.Building

models • It is directly based on experimentation.

• Input and output signals from the system are recorded.

3- Combined

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The fiction of a true model

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The Core

The Core: The core of estimating models is statistical theory.

• Model: m

• True Description: S

• Model Class: M

• Complexity (Flexibility): C

• Information: Z

• Estimation

• Validation

• Model Fit: F(m,Z)

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Estimation

A template problem: Curve fitting

Squeeze out the relevant information

in data.

No more satisfaction

All data contains signal and noise.

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[ ])),((),(minargˆ NmChZmFm NeMm

+=∈

Estimation

The simplest explanation is usually the correct one. So the conceptual process for estimation is:

Fit measuregood agreement with data

Complexity measureNot too complex

m̂ is a random variable since of irrelevant part of data (noise).

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The System Identification Problem

1- Select an input signal to apply to the process.

2- Collect the corresponding output data.

3- Scrutinize the corresponding output data to find out if some preprocessing …

4- Specify a model structure.

5- Find the best model in this structure.

6- Evaluate the property of model.

7- Test a new structure, go to step 4.

8- If the model is not adequate, go tostep 3 or 1.

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The System Identification Problem

1- Choice of Input Signals.

2- Preprocessing Data.

3- Selecting Model Structures.

• Filtered Gaussian White Noise. • Random Binary Noise.

• Pseudo Random Binary Noise, PRBS. • Multi-Sines.

• Chirp Signals or Swept Sinusoids. • Periodic Inputs.

• Drifts and Detrending. • Prefiltering.

• Looking at the Data. • Getting a Feel for the Difficulties.

• Examining the Difficulties. • Fine Tuning Orders and Noise Structures .

• Accepting the Models .

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The Communities around the core

1- Statistics. ML Methods, Bootstrap method,…

2- Econometrics and time series analysis.

3- Statistical learning theory.

4- Machine learning.

5- Manifold learning.

6- Chemo metrics.

7- Data Mining.

8- Artificial Neural Network.

9- Fitting Ordinary Differential equation to data.

10- System Identification.

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Some Open Areas in System Identification

• Spend more time with neighbors.

• Model Reduction and System Identification.

• Issues in Identification of Non-linear Systems.

• Meet Demand from Industry.

• Convexification.

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Model Reduction

System identification is really “system approximation” and therefore closely related to model reduction.

Linear systems – Linear models. Divide, conquer and reunite.

Non-linear systems – Linear models. Is it good for control?

Non-linear systems – nonlinear reduced models. Much work remains.

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Linear Systems – Linear ModelsDivide-Conquer-Reunite

Helicopter data: 1 pulse input; 8 outputs (only 3 shown here)

State space of order 20 wanted.

18 is 208 is102 is 2002 is

××+=××+=

dCduCxybAbuAxx&

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Next fit 8 SISO models of order 12, one for each output

11 is 121 is121 is 1221 is i

××+=××+=

iiiii

iiiii

dcudxcybAubxAx& 8,...,2,1=i

duCxybuAxx

+=+=&

189681969696

××××

dCbA

Reunite

Order reduction

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Reduce model from 96 to 20

duCxybuAxx

+=+=&

189681969696

××××

dCbA

udxCy

ubxAxˆˆˆ

ˆˆˆˆ

+=

+=&

18ˆ208ˆ120ˆ2020ˆ

××

××

dC

bA

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Convexification

systems identification - ???????? - fumcpanelprofsite.um.ac.ir/~karimpor/iden/sysiden_lec1.pdf ·...

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