Modelling and Simulation

1
Introduction

• Modelling and Simulation
• AUE 2007
• Bo Rohde Pedersen

2
Why and What

• Why make a model?
• What will be modeled?
• Is a complex model the best?
• When linear and nonlinear?

3
Principle in Modeling and Simulation
4
TSTF

• Try
• Simple
• Things
• First

5
First Order System
A first order system can be -a capacitor and
resistor -a masse and friction
6
Physical Model

• The Model has physical relations
• Equations from physics N2 etc.
• Not a Black box model
• See and Identify

7
Course Content

• Modelling of mechanical systems (MM1 and MM2)
• Electro Mechanic systems and simulation (MM3)
• Linearization (MM5)
• Thermal systems, head flow (MM4) DE5
• Matlab (MM4) M5
• Open for projects (MM4)

8
Translation Rotation
MM1 Modelling and Simulation AUE 2006 Bo Rohde
Pedersen
9
Translatation
A masse is moving in a direction
10
Energi Storage Masse
F M a
11
Energi Storage Spring
F K (x2-x1)
12
Loss Dæmper/friktion
F B (V2-V1)
Tørfriktion Statisk/dynamisk Konstant Viscos
friktion I væsker eller gas f.eks. system smurt
med olie Afhængig af hastigheden. Normalt i
første potens, men ved meget høje hastigheder
i anden potens.
13
Newtons 2 law
m a ? F
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Rotation
A masse is rotating
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Energi Storage Masse
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Energi Storage Spring
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Loss
18
Gear
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Newtons 2 law for Rotation
J d?/dt ? t
20
Exercise 1 MM1 Translative
21
Exercise 2 MM1 Rotation
B er gnidningen K1 fjeder konstant K2 fjeder
konstant