Upload
alexandra-mcfadden
View
48
Download
1
Embed Size (px)
DESCRIPTION
SYSTEMS Identification. Ali Karimpour Assistant Professor Ferdowsi University of Mashhad. Reference: “System Identification Theory For The User” Lennart Ljung(1999) “Practical Issues of System Identification” Lennart Ljung (2007) - PowerPoint PPT Presentation
Citation preview
SYSTEMSSYSTEMSIdentificationIdentification
Ali Karimpour
Assistant 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)
2
lecture 1
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.
3
lecture 1
Ali Karimpour Sep 2010
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
4
lecture 1
Ali Karimpour Sep 2010
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.
5
lecture 1
Ali Karimpour Sep 2010
Dynamic systems
Stimuli
It can be manipulated by the observer.
Input Disturbance
It can not be manipulated by the observer.
Measured Unmeasured
Dynamic system
Inputu
Measured disturbance
w
Unmeasured disturbance
v
Output
y
6
lecture 1
Ali Karimpour Sep 2010
A solar heated house
Dynamic system
Pumpvelocity
u
Solar radiation
w
Wind, outdoor temperature
v
Storage temperature
y
7
lecture 1
Ali Karimpour Sep 2010
Speech generation
Dynamic system
chord, vibarationairflow
v
Sound
y
Time series: A dynamic system whose external stimuli are not observed.
8
lecture 1
Ali Karimpour Sep 2010
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
9
lecture 1
Ali Karimpour Sep 2010
The fiction of a true model
10
lecture 1
Ali Karimpour Sep 2010
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)
11
lecture 1
Ali Karimpour Sep 2010
Estimation
A template problem: Curve fitting
Squeeze out the relevant information
in data.
No more satisfaction
All data contains signal and noise.
12
lecture 1
Ali Karimpour Sep 2010
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).
13
lecture 1
Ali Karimpour Sep 2010
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 to step 3 or 1.
14
lecture 1
Ali Karimpour Sep 2010
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 .
15
lecture 1
Ali Karimpour Sep 2010
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.
16
lecture 1
Ali Karimpour Sep 2010
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.
17
lecture 1
Ali Karimpour Sep 2010
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.
18
lecture 1
Ali Karimpour Sep 2010
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 is
102 is 2002 is
dCduCxy
bAbuAxx
19
lecture 1
Ali Karimpour Sep 2010
Linear Systems – Linear ModelsDivide-Conquer-Reunite
Next fit 8 SISO models of order 12, one for each output
11 is 121 is
121 is 1221 is i
iiiii
iiiii
dcudxcy
bAubxAx8,...,2,1i
duCxy
buAxx
18968
1969696
dC
bA
Reunite
Order reduction
20
lecture 1
Ali Karimpour Sep 2010
Linear Systems – Linear ModelsDivide-Conquer-Reunite
Reduce model from 96 to 20
duCxy
buAxx
18968
1969696
dC
bA
udxCy
ubxAx
ˆˆˆ
ˆˆˆˆ
18ˆ208ˆ
120ˆ2020ˆ
dC
bA
21
lecture 1
Ali Karimpour Sep 2010
Convexification