TOPIC 1 ndash INTRODUCTION AND REVIEW

1

ENGI9496 Modeling and Simulation of Dynamic Systems Date Topic 1 ndash Introduction and Review of Undergraduate System Dynamics Course Goals Improve your ability to generate and simulation system models and increase your insight into numerical simulation challenges and troubleshooting simulation output Major Concept Mechanical Electrical Thermal Hydraulic systems are unified by the fact that their components exchange dissipate and supply energy Power P = dEdt Modeling and simulation for most people is restricted to systems within their specific area of expertise For example

automotive engineers typically use ADAMS for multibody system modeling electrical engineers may write their own Matlab code for motor models

In this increasingly interdisciplinary age accurate and efficient modeling and simulation-based design is easier if you

have knowledge of other domains understand what the different domains have in common

THE GENERAL MODELING PROCESS When you take a physical system and turn it into a system of equations herersquos what you really do (example mass hanging from a rubber tube)

1 Define system boundaries (boundary conditions are essentially inputs from the external environment)

2 ldquoReticulaterdquo (divide) continuous physical system into discrete ldquolumpedrdquo components Many simplifying assumptions will be made sometimes unconsciously

3 Define constitutive laws (equations) for each element 4 ldquoBondrdquo elements by gathering constitutive laws and arranging the equations in correct

input-output form noting variables that are shared among different elements

TOPIC 1 ndash INTRODUCTION AND REVIEW

2

ADVANTAGES OF BOND GRAPHS Mechanical engineers may be comfortable discussing masses springs and dampers while electrical engineers may be comfortable with inductors capacitors and resistors However they are using the same set of dynamic elements The bond graph formalism presented in this course and in the text uses the energy-based analogies between different types of engineering elements to represent all types of systems using the same general elements An electrical thermal hydraulic or mechanical bond graph uses the same symbols and therefore combining bond graphs of a motor linkage and pump can be done seamlessly and equations can be derived systematically for the entire system Other advantages

some systems are difficult to represent schematically with ldquocircuit diagramsrdquo generalized loops and nodes that are visible on electrical circuit diagrams are not easy to

visualize in mechanical systems for hydraulic systems the equivalent element to a mass is a long thin pipe ndash how do you

show this hydraulic ldquomassrdquo on a diagram visual inspection of bond graphs can alert you to algebraic loops or implicit equations

that are more difficult to integrate numerically insight into power-conserving nature of many physical transformations

We can express power as the product of generalized effort and flow P = e(t)f(t) ldquoGeneralizedrdquo quantities that can be defined specifically for each energy domain

effort e flow f momentum p (integral of effort) displacement q (integral of flow)

What bond graphs make very clear

You can identify power variables (always 2 of them) where two physical components are connected

Elements are connected at ports When two components are joined the two complementary power variables are

simultaneously constrained to be equal for both components

TOPIC 1 ndash INTRODUCTION AND REVIEW

3

GENERALIZED ELEMENTS Any dynamic lumped-parameter system can be modeled using the following set of generalized elements

Kirchoffrsquos ldquolooprdquo (all elements have same flow efforts sum to zero) Kirchoffrsquos ldquonoderdquo (all elements have same effort flows sum to zero) Dissipator (dumps energy to environment) Potential energy storage device (energy is a function of displacement) Kinetic energy storage device (energy is a function of momentum) Source (of effort or flow prescribed from the environment) Transformer (relates effort to effort flow to flow either within or between two different

energy domains) Gyrator (relates effort to flow flow to effort)

The following are examples of electrical mechanical and hydraulic systems that would have the same equation structure and response ndash these systems are dynamically identical Mechanical System Electrical System Hydraulic System

TOPIC 1 ndash INTRODUCTION AND REVIEW

2

ADVANTAGES OF BOND GRAPHS Mechanical engineers may be comfortable discussing masses springs and dampers while electrical engineers may be comfortable with inductors capacitors and resistors However they are using the same set of dynamic elements The bond graph formalism presented in this course and in the text uses the energy-based analogies between different types of engineering elements to represent all types of systems using the same general elements An electrical thermal hydraulic or mechanical bond graph uses the same symbols and therefore combining bond graphs of a motor linkage and pump can be done seamlessly and equations can be derived systematically for the entire system Other advantages

some systems are difficult to represent schematically with ldquocircuit diagramsrdquo generalized loops and nodes that are visible on electrical circuit diagrams are not easy to

visualize in mechanical systems for hydraulic systems the equivalent element to a mass is a long thin pipe ndash how do you

show this hydraulic ldquomassrdquo on a diagram visual inspection of bond graphs can alert you to algebraic loops or implicit equations

that are more difficult to integrate numerically insight into power-conserving nature of many physical transformations

We can express power as the product of generalized effort and flow P = e(t)f(t) ldquoGeneralizedrdquo quantities that can be defined specifically for each energy domain

effort e flow f momentum p (integral of effort) displacement q (integral of flow)

What bond graphs make very clear

You can identify power variables (always 2 of them) where two physical components are connected

Elements are connected at ports When two components are joined the two complementary power variables are

simultaneously constrained to be equal for both components

TOPIC 1 ndash INTRODUCTION AND REVIEW

3

GENERALIZED ELEMENTS Any dynamic lumped-parameter system can be modeled using the following set of generalized elements

Kirchoffrsquos ldquolooprdquo (all elements have same flow efforts sum to zero) Kirchoffrsquos ldquonoderdquo (all elements have same effort flows sum to zero) Dissipator (dumps energy to environment) Potential energy storage device (energy is a function of displacement) Kinetic energy storage device (energy is a function of momentum) Source (of effort or flow prescribed from the environment) Transformer (relates effort to effort flow to flow either within or between two different

energy domains) Gyrator (relates effort to flow flow to effort)

The following are examples of electrical mechanical and hydraulic systems that would have the same equation structure and response ndash these systems are dynamically identical Mechanical System Electrical System Hydraulic System

TOPIC 1 ndash INTRODUCTION AND REVIEW

3

GENERALIZED ELEMENTS Any dynamic lumped-parameter system can be modeled using the following set of generalized elements

Kirchoffrsquos ldquolooprdquo (all elements have same flow efforts sum to zero) Kirchoffrsquos ldquonoderdquo (all elements have same effort flows sum to zero) Dissipator (dumps energy to environment) Potential energy storage device (energy is a function of displacement) Kinetic energy storage device (energy is a function of momentum) Source (of effort or flow prescribed from the environment) Transformer (relates effort to effort flow to flow either within or between two different

energy domains) Gyrator (relates effort to flow flow to effort)

The following are examples of electrical mechanical and hydraulic systems that would have the same equation structure and response ndash these systems are dynamically identical Mechanical System Electrical System Hydraulic System

User

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ENGI9496 Modeling and Simulation of Dynamic Systems

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