se 513 lecture_01.pdf

8/9/2019 SE 513 Lecture_01.pdf

1/22

1/23/2015

1

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.

2


2/22

1/23/2015

2

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.



3/22

1/23/2015

3

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


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



4/22

1/23/2015

4

Examples


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


T2, w2, C2

Stirred Tanku w, c

w

vT1 and

T2

w1

and

w2

C1, C2

Storage

temperature


5/22

1/23/2015

5

The Four Problems of Identification

Representation

Measurement

Estimation

Validation


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



6/22

1/23/2015

6

Representation:

Some of the issues

How to select the model structure.

Flexibility of the model.

Complexity of the model.


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



7/22

1/23/2015

7

Estimation

How do we estimate the model

parameters from the measured data?

How do we estimate the nonparametric

model from the measured data?


Validation

• Can the model explain the measured

data?

• Are the confidence limits on the

model acceptable?



8/22

1/23/2015

8

The Four Problems of Identification

Representation

Measurement

Estimation

Validation


How do we obtain mathematical

models?

Modeling

Identification

Experimental)


(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


9/22

1/23/2015

9

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.


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.



10/22

1/23/2015

10

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.



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.).


11/22


12/22

1/23/2015

12

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


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



13/22


14/22

1/23/2015

14

Heated Stirred Tank

Conservation of mass and Energy


Heated Stirred Tank Model



15/22

1/23/2015

15

Heated Stirred Tank Model

further simplifications are possible : Example V is constant,


Electrically Heated Stirred Tank Model



16/22

1/23/2015

16

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


System Identification


Perform an experiment

Collect data

Assume a model

Use data to estimate unknown parameters

Validate model


17/22

1/23/2015

17

Flow Chart for System

Identification (Ljung)


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



18/22

1/23/2015

18

Flow Chart for System

Identification (Ljung)


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



19/22


20/22


21/22


22/22

1/23/2015


se 513 lecture_01.pdf

Documents