SnS-SD-02!3!10 Modeling of Dynamics Systems

8/3/2019 SnS-SD-02!3!10 Modeling of Dynamics Systems

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Modeling and SimulationMCT 6101

Lecture #2: Modeling of Dynamic Systems

Dr. Shahrul Naim Sidek

Department of Mechatronics Engineering

International Islamic University Malaysia


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Previously


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Definition of System Dynamics

System Definition

Modeling

System Analysis

Recommendations

System dynamics


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System Dynamics

System Definition

Modeling

Actual System

Modelers Perception

Simulation

Recommendations

MathematicalRepresentation

Validation


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Modeling

Mathematical

models?


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Modeling

How to develop the mathematical model?


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Modeling

What is re uired to develo

mathematical model of a system?


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Modeling

Laws of Conservation(energy, momentum, mass, charge)

Laws of Properties

Model Representation:

Differential Equation. , Transfer Function,

State Space, Block Diagram, Linear Graph


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Modeling : Mechanical Systems

Newtons LawsMass

Damper

Spring

Mechanical Systems

Laws of Conservation(mechanical energy, momentum)

Laws of Properties


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Modeling : Electrical Systems

Khircoffs LawsResistance

Inductance

Capacitance

Electrical Systems

Laws of Conservation(energy, charge)

Laws of Properties


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Modeling : Thermal Systems

Conservation

of Thermal EnergyResistance Capacitance

Thermal System

Laws of Conservation Laws of Properties


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Modeling : Fluid Systems

Conservation of massResistance

Inductance

Capacitance

Fluid System

Laws of Conservation Laws of Properties


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Modeling

Actual System

Modelers Perception


Validation

Model Modification


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Modeling

Actual System

Modelers Perception


Validation

mmmm1111

mmmm2222

f

xx &,

l

Model Modification


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Modeling

Actual System

Modelers Perception


Validation( ) ( ) flmlmlmxmm =++++ sincos2sincos

2

221&&&&&&&&&

0sincos2 =+++ gxll &&&&&&

frT =

Model Modification


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Modeling : Understanding of Actual Systems

Often helpful hints:

What signals are we interested in modeling?

What parameters are important for describing the system?

Which parameters are time-varying, and which are constant?

What quantities influence others?


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A way of structuring problems :

what belongs to the system, and what does not

inputs, outputs and internal dynamics

Example of systems view of cruise control in a car


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Try to make subsystems which reflect logical relations, physicalprinciples, cause-and-effect.

Example Systems view of cruise control in a car


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Modeling : Modelers Perception

Based on modeler perception, transform the actual systeminto schematic representation, based on the assumed basic

elements to build the actual system.xx &

mmmm1111

mmmm2222

f

l


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DC MotorV

Pulleyradius r, inertia J

p

, ,t,

b,

m

Load monitoringsystem

Elevator carmass M

Counterweightmass m

y

Cable


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Modeling : Mathematical Representation

From schematics diagram, we use laws of conservation and lawof properties to develop analytical models.


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First choice: validate against real data (experiment) Second option: soft validation

verify that equations are dimensionally correct

Modeling : Model Validation

verify that equations describe qualitatively correct behavior


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Modeling : Model Modification

Model Simplification

Neglect minor effects Use idealized relationships

Model Detailing Take into account the neglected effects

Consider non-linearities

etc

SnS-SD-02!3!10 Modeling of Dynamics Systems

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