se 513 lecture_01.pdf
TRANSCRIPT
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Lecture 1
Introduction to Systems Identification
SE 513: System Identification
Dr. Sami El Ferik,KFUPM, Term 142.1
Objectives:
Dr. Sami El Ferik,KFUPM, Term 142.
Introduce the course
Introduce identification
Introduce the structure of the course
Present the grading policy
Discuss any concern you may have.
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Expected Outcomes
Dr. Sami El Ferik,KFUPM, Term 142.
Grasp the objective of the course
Grasp the background required from the course
Possess a clear idea on the grading policy
Form teams for the project (3/per team)
Grasp the structure of the book.
3
Lecture Outlines
What is Identification?
Modeling vs. Identification.
Types of models.
Steps of systems identification.
Problems in identification.
Dr. Sami El Ferik,KFUPM, Term 142.4
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Systems Identification
Identification is a process in which experimental data is
used to build a mathematical model describing the system
Identification is a process that uses u(t) and y(t) todetermine the dynamics of the system
unmeasured disturbances
System ?u y
w
v
Measured
disturbances
Dr. Sami El Ferik,KFUPM, Term 142.5
Why do we need models?
Models can be used to improve our understanding of theprocess.
Models are needed in designing better controllers
A Model can be a part of some controllers like feedforward controllers
A model can be very valuable in optimizing the operatingconditions to get the best performance of control systems
Dr. Sami El Ferik,KFUPM, Term 142.6
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Examples
Dr. Sami El Ferik,KFUPM, Term 142.7
Solar-heated Houseu y
w
v
Solarradiation
Pump
Velocity
Wind, outside
temperature
Storage
temperature
T1, w1, C1
T, w, cQ
Heater
Mixing
V
V: volume of liquid
T: temperature inside tank
temperature at outlet
Ti : temperature at inlet
wi : inlet mass flow rate
w: outlet mass flow rate
Example: Heated Stirred Tank
Dr. Sami El Ferik,KFUPM, Term 142.8
T2, w2, C2
Stirred Tanku w, c
w
vT1 and
T2
w1
and
w2
C1, C2
Storage
temperature
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The Four Problems of Identification
Representation
Measurement
Estimation
Validation
Dr. Sami El Ferik,KFUPM, Term 142.9
Representation
What types of models are used to representthe system?
Types of Models:
Mental, intuitive, verbal
Graphs and tables: step response, Bode plot
Mathematical models
Differential and difference equations
static/dynamic, linear/nonlinear, lumped/distributed,continuous/discrete, time-domain/frequency domain
Dr. Sami El Ferik,KFUPM, Term 142.10
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Representation:
Some of the issues
How to select the model structure.
Flexibility of the model.
Complexity of the model.
Dr. Sami El Ferik,KFUPM, Term 142.11
Measurement
Which physical quantities should be
measured?
How should we measure them? Some of the issues:
• Some variables of interest are difficult or impossible tomeasure
• Presence of noise in the measured data
Dr. Sami El Ferik,KFUPM, Term 142.12
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Estimation
How do we estimate the model
parameters from the measured data?
How do we estimate the nonparametric
model from the measured data?
Dr. Sami El Ferik,KFUPM, Term 142.13
Validation
• Can the model explain the measured
data?
• Are the confidence limits on the
model acceptable?
Dr. Sami El Ferik,KFUPM, Term 142.14
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The Four Problems of Identification
Representation
Measurement
Estimation
Validation
Dr. Sami El Ferik,KFUPM, Term 142.15
How do we obtain mathematical
models?
Modeling
Identification
Experimental)
Dr. Sami El Ferik,KFUPM, Term 142.16
(Theoretical) Construct a simplified
version using idealizedelements
Write element laws
Write interaction laws
Combine element lawsand interaction laws toobtain the model
Conduct an experiment
Collect data
Fit data to a model Verify the model
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Mathematical Modeling Mathematical Model (Eykhoff, 1974)
“a representation of the essential aspects of an existing
system (or a system to be constructed) which represents
knowledge of that system in a usable form”
Everything should be made as simple as possible,
but no simpler.
Dr. Sami El Ferik,KFUPM, Term 142.17
General Modeling Principles
• The model equations are at best an approximation to thereal process.
• Adage: “All models are wrong, but some are useful.”
• Modeling inherently involves a compromise between modelaccuracy and complexity on one hand, and the cost and
effort required to develop the model, on the other hand.
• Process modeling is both an art and a science. Creativity isrequired to make simplifying assumptions that result in anappropriate model.
• Dynamic models of chemical processes consist of ordinarydifferential equations (ODE) and/or partial differentialequations (PDE), plus related algebraic equations.
Dr. Sami El Ferik,KFUPM, Term 142.18
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A Systematic Approach for Developing
Dynamic Models
1. State the modeling objectives and the end use of themodel. They determine the required levels of modeldetail and model accuracy.
2. Draw a schematic diagram of the process and labelall process variables.
3. List all of the assumptions that are involved indeveloping the model. Try for parsimony; the modelshould be no more complicated than necessary to meetthe modeling objectives.
Dr. Sami El Ferik,KFUPM, Term 142.19
Dr. Sami El Ferik,KFUPM, Term 142.20
4. Determine whether spatial variations of processvariables are important. If so, a partial differentialequation model will be required.
5. Write appropriate conservation equations (mass,component, energy, and so forth).
6. Introduce equilibrium relations and other algebraicequations (from thermodynamics, transport phenomena,chemical kinetics, equipment geometry, etc.).
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Natural Laws in Modeling
In processing systems,
Conservation of energy
Conservation of mass
Conservation of individual components
Conservation of momentum
are useful in Obtaining mathematical models
Dr. Sami El Ferik,KFUPM, Term 142.23
Conservation Principle
over any time period,
the rate of accumulation of S within the system
= flow rate of S in the system
− flow rate of S out of the system
+ rate of the amount generated within the system
− rate of the amount consumed within the system
Dr. Sami El Ferik,KFUPM, Term 142.24
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Heated Stirred Tank
Conservation of mass and Energy
Dr. Sami El Ferik,KFUPM, Term 142.27
Heated Stirred Tank Model
Dr. Sami El Ferik,KFUPM, Term 142.28
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Heated Stirred Tank Model
further simplifications are possible : Example V is constant,
Dr. Sami El Ferik,KFUPM, Term 142.29
Electrically Heated Stirred Tank Model
Dr. Sami El Ferik,KFUPM, Term 142.30
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Modeling verses Identification Modeling:
To have some physical insight
In many cases modeling from basic laws may be too complex to be practical
In some cases the model derived from the basic laws may contain unknown
parameters
Identification: Limited validity models (depends operating point, input,…)
Little physical insight (some parameters have no physical meaning)
They are easy to construct and use
Dr. Sami El Ferik,KFUPM, Term 142.31
System Identification
Dr. Sami El Ferik,KFUPM, Term 142.32
Perform an experiment
Collect data
Assume a model
Use data to estimate unknown parameters
Validate model
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Flow Chart for System
Identification (Ljung)
Dr. Sami El Ferik,KFUPM, Term 142.33
Flow Chart for SystemIdentification (Soderstrom and and Stoica)
Start
Design of Experiment
New data
Model Validation
Choose Model Structure
Perform Experiment and Collect data
Choose method& Estimate parameters
Model Accepted? STOP
Apriori
Knowledge
No Yes
Dr. Sami El Ferik,KFUPM, Term 142.34
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Flow Chart for System
Identification (Ljung)
Dr. Sami El Ferik,KFUPM, Term 142.35
To master the flow graph the
user should be familiar with
1- available techniques and
their rationale as well as
available model sets.
2- properties of the identified
model
3-Numerical schemes for
computing the estimate.
4- how to make intelligent
choices of experiment design,
model set, and criterion.
Organization of the book
Dr. Sami El Ferik,KFUPM, Term 142.36
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Dr. Sami El Ferik,KFUPM, Term 142.43