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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
MathematicalRepresentation
Validation
Model Modification
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Modeling
Actual System
Modelers Perception
MathematicalRepresentation
Validation
mmmm1111
mmmm2222
f
xx &,
l
Model Modification
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Modeling
Actual System
Modelers Perception
MathematicalRepresentation
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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Modeling : Understanding of Actual Systems
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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Modeling : Understanding of Actual Systems
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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Modeling : Modelers Perception
DC MotorV
Pulleyradius r, inertia J
p
, ,t,
b,
m
Load monitoringsystem
Elevator carmass M
Counterweightmass m
y
Cable
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Modeling : Modelers Perception
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Modeling : Modelers Perception
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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
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