Download Lecture-1: Introduction - Dr. Imtiaz Hussain

Modeling & Simulation of Dynamic
Systems (MSDS)
Lecture-1
Introduction
Dr. Imtiaz Hussain
Associate Professor
Department of Electronic Engineering
email: [email protected]
URL :http://imtiazhussainkalwar.weebly.com/
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Outline
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Course Outline
Recommended Books
Types of
Systems
Introduction to Modeling (Basic Concepts)
Introduction to Simulation (Basic Concepts)
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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
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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
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Types of Systems
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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.
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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 )
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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
𝑅2 𝑅3
𝑦 𝑡 =
𝑢 𝑡
𝑅1 𝑅1 + 𝑅3 + 𝑅2 𝑅3
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Static Systems
• Some of the non-electrical static system examples are
systems with no acceleration
• E.g.
Furniture, Bridges, Buildings, etc. (ignoring
vibration)
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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,
y( t )  [ u( ),0    t ]
u : Input, t : Time
Example: A moving mass
y
u
Model: Force=Mass x Acceleration
My  u
M
Dynamic Systems
examples: RC circuit, Bicycle, Car, Pendulum (in motion)
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Ways to Study a System
System
Experiment with a
model of the System
Experiment with actual
System
Mathematical Model
Physical Model
Analytical Solution
Simulation
Frequency Domain
Time Domain
Hybrid Domain
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Model
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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.
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Types of Models
Model
Mathematical
Physical
Static
Dynamic
Static
Dynamic
Computer
Static
Dynamic
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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
Classification of Mathematical Models
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Linear vs. Non-linear
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Deterministic vs. Probabilistic (Stochastic)
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Static vs. Dynamic
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Discrete vs. Continuous
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White box, black box and gray box
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Black Box Model
• When only input and output are known.
• Internal dynamics are either too complex or
unknown.
Input
Output
• Easy to Model
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Black Box Model
• Consider the example of a heat radiating system.
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Black Box Model
• Consider the example of a heat radiating system.
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3535
Temperature in Degree Celsius
Temperature in Degree Celsius (y)
Room
Valve
Temperature
Position
(oC)
Heat
Raadiating
System
Heat
Raadiating
System
Room Temperature
Room Temperature
quadratic Fit
3030
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y = 0.31*x 2 + 0.046*x + 0.64
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00
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Valve Position
Valve Position (x)
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Grey Box Model
• When input and output and some information
about the internal dynamics of the system is
known.
u(t)
y(t)
y[u(t), t]
• Easier than white box Modelling.
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White Box Model
• When input and output and internal dynamics
of the system is known.
u(t)
dy(t )
du(t ) d 2 y(t )
3

dt
dt
dt 2
y(t)
• One should know have complete knowledge
of the system to derive a white box model.
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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
System Type
Model Type
Nonlinear
Input-output differential equation
Linear
State equations
Linear Time
Invariant
Transfer function
Approach to dynamic systems
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Define the system and its components.
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Formulate the mathematical model and list the necessary
assumptions.
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Write the differential equations describing the model.
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Solve the equations for the desired output variables.
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Examine the solutions and the assumptions.
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If necessary, reanalyze or redesign the system.
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Simulation
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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.
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Advantages to Simulation
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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.
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Disadvantages to Simulation
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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.
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END OF LECTURES-1
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