lecture-1-_introduction_modelling_&_simulation (2).pptx

1
Modeling & Simulation of Dynamic Systems
(MSDS)
Dr. Imtiaz Hussain
Associate Professor
Department of Electronic Engineering
email: imtiaz.hussain@faculty.muet.edu.pk
URL :http://imtiazhussainkalwar.weebly.com/
Lecture-1
Introduction

2
Outline
• Course Outline
• Recommended Books
• Types of
• Systems
• Introduction to Modeling (Basic Concepts)
• Introduction to Simulation (Basic Concepts)

3
Course Outline
• Introduction to Modeling & Simulation
• Modeling of
• Mechanical Systems
• Electrical Systems
• Electronic Systems
• Electromechanical Systems
• Hydraulic Systems
• Thermal Systems
• Transfer Function Models
• State Space Models
• Discrete models
• Modeling non-linear systems
• Simulation of Mechanical, Electrical and Electronic
Systems

4
Recommended Books
1. Burns R. “Advanced Control Engineering, Butterworth
Heinemann”, Latest edition.
2. Mutanmbara A.G.O.; Design and analysis of Control
Systems, Taylor and Francis, Latest Edition
3. Modern Control Engineering, (5th
Edition)
By: Katsuhiko Ogata.
4. Control Systems Engineering, (6th
Edition)
By: Norman S. Nise

5
Types of Systems
•
Static System: If a system does not change
with time, it is called a static system.
•
Dynamic System: If a system changes with
time, it is called a dynamic system.

6
Static Systems
• A system is said to be static if its output y(t) depends only
on the input u(t) at the present time t, mathematically
described as
𝑦 (𝑡 )=𝒉(𝑢(𝑡 ))
𝑦 (𝑡 )=𝒉(𝑢1(𝑡),𝑢2 (𝑡),…,𝑢𝑚 (𝑡))

7
Static Systems
• Following figure gives an example of static systems, which is a
resistive circuit excited by an input voltage u(t).
• Let the output be the voltage across the resistance R3,
and according to the circuit theory, we have
𝑦 (𝑡 )=
𝑅2 𝑅3
𝑅1 (𝑅1 +𝑅3)+𝑅2 𝑅3
𝑢(𝑡)

8
Static Systems
• Some of the non-electrical static system examples are
systems with no acceleration
• E.g. Furniture, Bridges, Buildings, etc. (ignoring
vibration)

Dynamic Systems
• A system is said to be dynamic if its current output may depend on
the past history as well as the present values of the input variables.
• Mathematically,
Time
Input, :
:
]
),
(
[
)
(
t
u
t
u
t
y 

 

 0
Example: A moving mass
M
y
u
Model: Force=Mass x Acceleration
u
y
M 



10
Dynamic Systems
examples: RC circuit, Bicycle, Car, Pendulum (in motion)

11
Ways to Study a System
System
Experiment with a
model of the System
Experiment with
actual System
Physical Model Mathematical Model
Analytical Solution
Simulation
Frequency Domain Time Domain Hybrid Domain

12
Model
•
A model is a simplified representation or
abstraction of reality.
•
Reality is generally too complex to copy
exactly.
•
Much of the complexity is actually irrelevant
in problem solving.

13
Types of Models
Model
Physical Mathematical Computer
Static Dynamic Static Dynamic
Static Dynamic

What is Mathematical Model?
A set of mathematical equations (e.g., differential eqs.) that
describes the input-output behavior of a system.
What is a model used for?
• Simulation
• Prediction/Forecasting
• Prognostics/Diagnostics
• Design/Performance Evaluation
• Control System Design

15
Classification of Mathematical Models
•
Linear vs. Non-linear
•
Deterministic vs. Probabilistic (Stochastic)
•
Static vs. Dynamic
•
Discrete vs. Continuous
•
White box, black box and gray box

16
Black Box Model
• When only input and output are known.
• Internal dynamics are either too complex or
unknown.
• Easy to Model
Input Output

17
Black Box Model
• Consider the example of a heat radiating system.

18
Black Box Model
• Consider the example of a heat radiating system.
Valve
Position
Room
Temperature
(o
C)
0 0
2 3
4 6
6 12
8 20
10 33
0 2 4 6 8 10
0
5
10
15
20
25
30
35
Valve Position
Temperature
in
Degree
Celsius
Heat Raadiating System
Room Temperature
0 2 4 6 8 10
0
5
10
15
20
25
30
35
Valve Position (x)
Temperature
in
Degree
Celsius
(y)
Heat Raadiating System
y = 0.31*x2 + 0.046*x + 0.64
Room Temperature
quadratic Fit

19
Grey Box Model
• When input and output and some information
about the internal dynamics of the system is
known.
• Easier than white box Modelling.
u(t) y(t)
y[u(t), t]

20
White Box Model
• When input and output and internal dynamics
of the system is known.
• One should know have complete knowledge
of the system to derive a white box model.
u(t) y(t)
2
2
3
dt
t
y
d
dt
t
du
dt
t
dy )
(
)
(
)
(



Mathematical Modelling Basics
Mathematical model of a real world system is derived using a
combination of physical laws and/or experimental means
• Physical laws are used to determine the model structure (linear
or nonlinear) and order.
• The parameters of the model are often estimated and/or
validated experimentally.
• Mathematical model of a dynamic system can often be expressed
as a system of differential (difference in the case of discrete-time
systems) equations

Different Types of Lumped-Parameter
Models
Input-output differential equation
State equations
Transfer function
Nonlinear
Linear
Linear Time
Invariant
System Type Model Type

23
Approach to dynamic systems
• Define the system and its components.
• Formulate the mathematical model and list the necessary
assumptions.
• Write the differential equations describing the model.
• Solve the equations for the desired output variables.
• Examine the solutions and the assumptions.
• If necessary, reanalyze or redesign the system.

24
Simulation
•
Computer simulation is the discipline of
designing a model of an actual or theoretical
physical system, executing the model on a
digital computer, and analyzing the execution
output.
•
Simulation embodies the principle of
``learning by doing'' --- to learn about the
system we must first build a model of some
sort and then operate the model.

25
Advantages to Simulation

Can be used to study existing systems without
disrupting the ongoing operations.

Proposed systems can be “tested” before committing
resources.

Allows us to control time.

Allows us to gain insight into which variables are
most important to system performance.

26
Disadvantages to Simulation

Model building is an art as well as a science. The
quality of the analysis depends on the quality of the
model and the skill of the modeler.

Simulation results are sometimes hard to interpret.

Simulation analysis can be time consuming and
expensive.

Should not be used when an analytical method would
provide for quicker results.

27
END OF LECTURES-1
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lecture-1-_introduction_modelling_&_simulation (2).pptx

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