KEY POINTS
to remember in modeling physical systems.
MODELING IS MORE THAN WRITING DOWN EQUATIONS.
Standard engineering formulations make implicit
assumptions.
Standard boundary conditions in different domains
may be incompatible.
Equation derivation may usefully be postponed.
Mod. Sim. Dyn. Sys.
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page 1
INSIGHT IS THE FOREMOST GOAL OF MODELING.
Start by identifying the behavior to be modeled,
then identify the responsible physical phenomena.
Start coarse, refine later.
Don’t start fine hoping to simplify later.
Mod. Sim. Dyn. Sys.
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page 2
ENERGY-BASED MODELING
a systematic approach to modeling physical system
dynamics.
DYNAMICS COMES FROM ENERGY STORAGE, POWER
EXCHANGE AND (FREE) ENERGY DISSIPATION.
There's only one energy.
It is the same in all domains.
The same energy-based approach may be used to
construct models in all domains.
Mod. Sim. Dyn. Sys.
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page 3
“BOND-GRAPH MODELING”.... ???
Bond graphs are NOT the point.
Drawing bond graphs is not modeling!
Energy-based modeling does not require bond graphs.
Bond graphs provide one unambiguous, domainindependent network notation. Equally useful alternative notations might be devised. Bond graphs are a tool, one among many. Mod. Sim. Dyn. Sys.
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page 4
COMMON (MIS-)PERCEPTION
Energy-based modeling dictates
a unique choice of variables
a unique equation derivation procedure
Energy-based modeling is NOT an equation
derivation procedure.
Mod. Sim. Dyn. Sys.
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page 5
STEPS IN THE MODELING PROCESS
Identify the behavior to be modeled.
—and how to determine the competence of a model
Construct (formulate, synthesize) a model.
—and identify the assumptions needed to define it
Choose state variables.
Derive (state and output) equations.
Analyze the model behavior.
—and check its competence
Mod. Sim. Dyn. Sys.
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page 6
PHENOMENA, NOT OBJECTS! A network model is a collection of connected pieces (elements). Model elements are NOT physical system components.
Model elements describe kinds of behavior
e.g., storage of energy, transmission of power, etc.
Mod. Sim. Dyn. Sys.
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page 7
PHYSICAL SYSTEMS INTER-ACT.
Power flow requires a bilateral interaction.
—influences go both ways
In contrast, signal flows are unilateral.
—influences go one way
A “PORT” IS THE KEY CONCEPT OF ENERGY-BASED NETWORK
MODELING.
—describes interaction between (sub)systems
Mod. Sim. Dyn. Sys.
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page 8
ENERGETIC INTERACTIONS
constrain the computational structure of equations
i.e. how variables of one element depend on those
of others
Boundary conditions assumed for one element
constrain the boundary conditions of others.
That's what is displayed by causality assignment.
Mod. Sim. Dyn. Sys.
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page 9
ENERGY-BASED APPROACH:
Identify energy storage elements
—defined at equilibrium.
Identify dissipation elements
—defined in steady state.
COMBINED THEY MODEL DYNAMICS.
Identify connection elements
—defined to be power-continuous.
Mod. Sim. Dyn. Sys.
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page 10
THOU SHALT NOT MODULATE
STORAGE ELEMENTS!
(unless first thou maketh sure that the related power
flow hath no importance unto thee or thine system
and the sub-systems therein, even unto the third
and fourth generation.)
Every variable argument of an energy storage function
identifies a port with a corresponding power flow.
Mod. Sim. Dyn. Sys.
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page 11
CONNECTION ELEMENTS MAY BE MODULATED. —But modulated connection elements (junction
structures) can gives rise to remarkably complex
behavior.
Modulated transformers (or gyrators) may make
elements of one kind appear to behave as elements of
another kind.
e.g., force sources may look like springs
That’s why kinematics, not dynamics, makes
mechanics difficult.
Mod. Sim. Dyn. Sys.
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page 12
THERMODYNAMIC CONSIDERATIONS:
Connectors and energy storage elements conserve
energy.
—These elements satisfy the first law.
Dissipators create entropy and destroy free energy.
—These elements satisfy the second law.
Source elements (or boundary conditions) may violate
either law.
(and almost always do)
AVOID CONTROLLED-SOURCE ELEMENTS.
Mod. Sim. Dyn. Sys.
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page 13
NEVER TRUST A COMPUTER! COMPUTERS INTRODUCE NEW WAYS TO BE WRONG.
Computational algorithms
Finite sampling frequencies
Finite word-length
introduce new (and usually subtle) ways to violate key
constraints of modeling physical systems
e.g., energy conservation, entropy production, etc.
Mod. Sim. Dyn. Sys.
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page 14
Junction structures may be hidden.
modulated (switched) zero or one junctions
Mechanical systems are unique. Mechanical displacement variables may be arguments of energy storage functions (energy variables) configuration variables (describing system geometry) or both Geometry is fundamental! gradients identify efforts efforts are equilibrating variables OK ... that means velocity is an effort ... and force is a flow ... ? (junction structure) some coupling may be “embedded” in “dissipation” phenomena identify (steady state) dissipation function Mod. Sim. Dyn. Sys.
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page 15