Transcript Document

INTELLIGENT POWERTRAIN DESIGN
The BOND GRAPH Methodology for Modeling of Continuous
Dynamic Systems
Jimmy C. Mathews
Advisors: Dr. Joseph Picone
Dr. David Gao
Powertrain Design Tools Project
Outline
• Dynamic Systems and Modeling
• Bond Graph Modeling Concepts
• Sample Applications of Bond Graph Modeling
• The Generic Modeling Environment (GME) and
Bond Graph Modeling
• Future Concepts
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Dynamic Systems and Modeling
• Dynamic Systems
Related sets of processes and reservoirs (forms in which matter or energy exists) through
which material or energy flows, characterized by continual change.
• Common Dynamic Systems
electrical, mechanical, hydraulic, thermal among numerous others.
• Real-time Examples
moving automobiles, miniature electric circuits, satellite positioning systems
• Physical systems
Interact, store energy, transport or dissipate energy among subsystems
• Ideal Physical Model (IPM)
The starting point of modeling a physical system is mostly the IPM.
• To perform simulations, the IPM must first be transformed into
mathematical descriptions, either using Block diagrams or Equation
descriptions
• Downsides – laborious procedure, complete derivation of the mathematical
description has to be repeated in case of any modification to the IPM [3].
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Computer Aided Modeling and Design of Dynamic Systems
• Basic Concepts
STEP 1: Develop an ‘engineering model’
Physical
System
STEP 2: Write differential equations
STEP 3: Determine a solution
Schematic
Model
STEP 4: Write a program
The Big
Question??
Classical Methods, Block
Diagrams OR Bond
Graphs
Differential
Equations
Fig 1. Modeling Dynamic Systems [1]
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GME +
Matlab/Simulink
Output
Data Tables &
Graphs
Simulation and
Analysis
Software
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Bond Graphs vs. Block Diagrams [5, 8]
• Block Diagrams
Early attempt to deal with heterogeneity, closely related to the emergence of automatic control,
nice example of information hiding, very successful and good environments like Simulink,
Easy V, and VisSim available presently.
• Familiar and versatile graphical notation to represent Signal Flow.
• Downsides
i. Do not provide a suitable notation for depicting physical system models because not all
block diagrams represent physical processes.
ii. Energetic Coupling between elements/systems - - - energy exchange implies interaction, i.e.
a bilateral, two-way influence of each system on the other.
Block diagrams fundamentally depict a unilateral influence of one system on another. Hence,
to describe energetic interaction of two systems/elements in terms of signal flow, the output of
one should be the input of another and vice versa.
iii. When two systems interact energetically, we must have
the block representation as in figure 2 (or its converse). In
contrast, the block diagrams shown below might represent
Fig 2. Block Diagram of Energetic
possible operations on signals or information, but neither
Interaction [8]
represents any possible energetic interaction.
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Bond Graphs vs. Block Diagrams (contd..)
• Bond Graphs
Close correspondence between the bond graph and the physical system it represents.
• Conserves the physical structural information as well as the nature of sub-systems which are
often lost in a block diagram.
• Can be directly derived from the IPM. When the IPM is changed, only the corresponding part
of a bond graph has to be changed. Advantage of making the model very amenable to
modification for ‘model development’ and ‘what if?’ situations.
• Account for all the energy in physical systems and provide a common link among various
engineering systems. Use analogous power and energy variables in all domains, but allow the
special features of the separate fields to be represented.
• The only physical variables required to represent all energetic systems are power variables
[effort (e) & flow (f)] and energy variables [momentum ε(t) and displacement F(t)].
• The dynamics of physical systems are derived by the application of instant-by-instant energy
conservation. Actual inputs are exposed.
• Linear and non-linear elements are represented with the same symbols; non-linear kinematics
equations can also be shown.
• Provision for active bonds. Physical information involving information transfer, accompanied by
negligible amounts of energy transfer are modeled as active bonds.
Some more advantages will be discussed after dealing with the concept of causality.
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Bond Graph Methodology
• Invented by Henry Paynter in the 1961, later elaborated by his students Dean C. Karnopp and
Ronald C. Rosenberg
• A Bond Graph is an abstract representation of a system where a collection of components
interact with each other through energy ports and are placed in a system where energy is
exchanged [2].
• A bond-graph model consists of subsystems which can
either describe idealized elementary processes or nonidealized processes. Non-idealized processes can either
be non-linear equation models or bond graph sub models
[3].
• Subsystems can have two type of ports: power ports
and signal ports.
• Power ports specify both an effort variable and flow
variable. Signal ports specify only one variable, a flow or
Fig 3. Subsystems of a bond graph [3]
an effort or a mathematical variable.
• Two types of knots in bond graphs, 0 junctions and 1 junctions; represent domainindependent generalizations of Kirchoff’s laws.
• Connects are called bonds, indicate power between various subsystems. The half arrows
indicates positive power flow orientation. The full arrows indicate signal flows.
• Bond is characterized by the value of an instantaneous power, computed as the product of
effort and flow variables (e.g. voltage and current in the electrical domain).
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The Bond Graph Modeling Formalism
• Bond Graph’s Reach?
Mechanical
Rotation
Hydraulic/Pneumatic
Mechanical
Translation
Electrical
Magnetic
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Thermal
Chemical/Process
Engineering
Fig 4. Multi-Energy Systems Modeling using
Bond Graphs
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The Bond Graph Modeling Formalism (contd..)
• Two different physical domains are considered: the Electrical and the Mechanical domains.
• Electrical Domain
To facilitate conversion of electrical circuits to bond graphs, represent different elements
(Voltage Source, Resistor, Capacitor, Inductor) with visible ports (figure 5).
To these ports, we connect power bonds denoting energy exchange between elements.
Fig. 5 Electric elements with power ports [4]
• Mechanical Domain
Mechanical elements like Force, Spring, Mass, Damper are similarly dealt with.
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The Bond Graph Modeling Formalism (contd..)
The R – L - C circuit
The power being exchanged by a port with the rest of the system is a product of the voltage
and the current:
P=u*i
The equations for the resistor, capacitor and inductor are:
u_R = i * R
u_C = 1/C * (∫idt)
u_L = L * (di/dt); or i = 1/L * (∫u_L dt)
1
Fig 6. The RLC Circuit [4]
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The Bond Graph Modeling Formalism (contd..)
The Spring-Mass-Damper System
Port variables on the bond graph elements are force on the element port and velocity of the
element port.
P=F*v
The equations for the damper (damping coefficient, α), spring (coefficient, KS) and mass are:
F_d = α * v
F_s = KS * (∫v dt) = 1/CS * (∫ vdt)
F_m = m * (dv/dt); or v = 1/m * (∫F_m dt); Also, F_a = force
Fig 7. The Spring Mass Damper System [4]
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The Bond Graph Modeling Formalism (contd..)
Analogies!
Lets compare! We see the following analogies between the mechanical and electrical
elements:
•
•
•
•
•
The Damper is analogous to the Resistor.
The Spring is analogous to the Capacitor, the mechanical compliance corresponds with the
electrical capacity.
The Mass is analogous to the Inductor.
The Force source is analogous to the Voltage source.
The common Velocity is analogous to the loop Current.
Notice that the bond graphs of both the RLC circuit and the Spring-mass-damper system are
identical. Still wondering how??
•
•
•
Various physical domains are distinguished that each is characterized by a particular
conserved quantity. Table 1 illustrates these domains with corresponding flow (f), effort (e),
generalized displacement (q), and generalized momentum (p).
Note that power = effort x flow in each case.
Also note, the bond graph modeling language is domain-independent.
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The Bond Graph Modeling Formalism (contd..)
Table 1. Domains with corresponding flow, effort, generalized displacement and generalized
momentum
f
flow
e
effort
q = ∫f dt
generalized
displacement
p = ∫e dt
generalized
momentum
Electromagnetic
i
current
u
voltage
q = ∫i dt
charge
λ = ∫u dt
magnetic flux
linkage
Mechanical
Translation
v
velocity
f
force
x = ∫v dt
displacement
p = ∫f dt
momentum
ω
angular velocity
T
torque
θ = ∫ω dt
angular displacement
b = ∫T dt
angular
momentum
Hydraulic /
Pneumatic
φ
volume flow
P
pressure
V = ∫φ dt
volume
τ = ∫P dt
momentum of a
flow tube
Thermal
T
temperature
FS
entropy flow
S = ∫fS dt
entropy
Chemical
μ
chemical potential
FN
molar flow
N = ∫fN dt
number of moles
Mechanical Rotation
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The Bond Graph Modeling Formalism (contd..)
• Foundations of Bond Graphs
Based on the assumptions that satisfy basic principles of physics;
a. Law of Energy Conservation is applicable
b. Positive Entropy production
c. Power Continuity
• Closer look at Bonds and Ports
Fig. 8 Energy flow
between two sub models
represented by a bond [4]
Power port or port: The contact point of a sub model where an ideal connection will be
connected.
Power bond or bond: The connection between two sub models; drawn by a single line (Fig. 8)
Bond denotes ideal energy flow between two sub models; the energy entering the bond on
one side immediately leaves the bond at the other side (power continuity).
Energy flow along the bond has the physical dimension of power, being the product of two
variables; called power-conjugated variables.
A
e
f
B
(directed bond from A to B)
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The Bond Graph Modeling Formalism (contd..)
• Two views of Interpretation of Power Bond
1. As an interaction of energy; connected subsystems for a load to each other by their energy
exchange; embodies an exchange of a physical quantity.
2. As a bilateral signal flow; interpreted as effort and flow flowing in opposite direction, thus
determining the computational direction of the bond variables; w.r.t. one of the sub models,
effort is the input and flow is the output and vice versa for the other sub model.
• Determining the direction of Effort and Flow
During modeling it need not be decided what the computational direction of the bond variables
is, however it is necessary to derive the mathematical model (set of differential equations)
from the graph.
Process of determining the computational direction of the bond variables is called causal
analysis; indicated in the graph by the so-called causal stroke, (indicating the direction of the
effort), called the causality of the bond (figure 9).
Fig. 9 Why is the Power direction not shown? [4]
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The Bond Graph Modeling Formalism (contd..)
• Bond Graph Elements
Bond graph elements are drawn as letter combinations (mnemonic codes) indicating the type
of element. The bond graph elements are the following:
C
storage element for a q-type variable,
e.g. capacitor (stores charge), spring (stores displacement)
L
storage element for a p-type variable,
e.g. inductor (stores flux linkage), mass (stores momentum)
R
resistor dissipating free energy,
e.g. electric resistor, mechanical friction
Se, Sf
sources,
e.g. electric mains (voltage source), gravity (force source),
pump (flow source)
TF
transformer,
e.g. an electric transformer, toothed wheels, lever
GY
gyrator,
e.g. electromotor, centrifugal pump
0, 1
0 and 1–junctions, for ideal connecting two or more sub models
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The Bond Graph Modeling Formalism (contd..)
• Storage Elements
Two types; C – elements & I – elements; q–type and p–type variables are conserved
quantities and are the result of an accumulation (or integration) process; they are the state
variables of the system.
C – element
(capacitor, spring, etc.)
q is the conserved quantity, stored by accumulating the net flow, f to the storage element.
resulting balance equation
dq/dt = f
Equations for linear capacitor
and linear spring:
u = (1/C) * q
dq/dt = i,
dx/dt = v,
F = k * x = (1/C) * x
Fig. 10 Examples of C - elements [4]
For a capacitor, C [F] is the capacitance and for a spring, K [N/m] is the stiffness and C [m/N]
the compliance.
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The Bond Graph Modeling Formalism (contd..)
I – element
(inductor, mass, etc.)
p is the conserved quantity, stored by accumulating the net effort, e to the storage element.
resulting balance equation
dp/dt = f
Fig. 11 Examples of I - elements [4]
Equations for linear inductor and linear mass:
dλ/dt = u,
i = (1/L) * λ
dp/dt = F,
V = (1/m) * p
For an inductor, L [H] is the inductance and for a mass, m [kg] is the mass. For all other
domains, an I – element can be defined.
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The Bond Graph Modeling Formalism (contd..)
R – element
(electric resistors, dampers, frictions, etc.)
R – elements dissipate free energy and energy flow towards the resistor is always positive.
Algebraic relation between effort and flow, lies principally in 1st or 3rd quadrant.
e = r (f)
Fig. 12 Examples of Resistors [4]
Electrical resistance value [Ω] given by Ohm’s law;
u=R*I
If the resistance value can be controlled by an external signal, the resistor is a modulated
resistor, with mnemonic MR. E.g. hydraulic tap: the position of the tap is controlled from the
outside, and it determines the value of the resistance parameter.
In the thermal domain, the dissipator irreversibly produces thermal energy, the thermal port is
drawn as a kind of source of thermal energy. The R becomes an RS.
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The Bond Graph Modeling Formalism (contd..)
Sources
(voltage sources, current sources, external forces, ideal motors, etc.)
Sources represent the system-interaction with its environment. Depending on the type of the
imposed variable, these elements are drawn as Se or Sf.
Source elements are used to give a variable a fixed value, for example, in case of a point in a
mechanical system with a fixed position, a Sf with value 0 is used (fixed position means
velocity zero).
Fig. 13 Examples of Sources [4]
When a system part needs to be excited, often a known signal form is needed, which can be
modeled by a modulated source driven by some signal form (figure 14).
Fig. 14 Example of Modulated Voltage
Source [4]
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The Bond Graph Modeling Formalism (contd..)
Transformers
(toothed wheel, electromotor, etc.)
An ideal transformer is represented by TF and is power continuous (i.e. no power is stored or
dissipated). The transformations can be within the same domain (toothed wheel, lever) or
between different domains (electromotor, winch).
e1 = n * e2
&
f2 = n * f1
Efforts are transduced to efforts and flows to flows; n is the transformer ratio. Only one
dimensionless parameter n is required to describe effort transduction and flow transduction.
n is a defined as follows: e1 and f1 belong to the bond pointing towards TF.
Fig. 15 Examples of Transformers [4]
If n is not constant, it becomes an input signal to the modulated transformer, MTF.
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The Bond Graph Modeling Formalism (contd..)
Gyrators
(electromotor, pump, turbine)
An ideal gyrator is represented by GY and is power continuous (i.e. no power is stored or
dissipated). Real-life realizations of gyrators are mostly transducers representing a domaintransformation.
e1 = r * f2
&
e2 = r * f1
r is the gyrator ratio and is the only parameter required to describe both equations. R has a
physical dimension (same as R-element), since r is the relation between effort and flow.
Fig. 16 Examples of Gyrators [4]
Gyrator is defined by one bond pointing towards and other bond pointing away.
If r is not constant, the gyrator is a modulated gyrator, a MGY.
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The Bond Graph Modeling Formalism (contd..)
Junctions
Junctions couple two or more elements in a power continuous way; there is no storage or
dissipation at a junction.
0 – junction
Represents a node at which all efforts of the connecting bonds are equal. E.g. a parallel
connection in an electrical circuit.
The sum of flows of the connecting bonds is zero, considering the sign. The power direction
determines the sign of flows: all inward pointing bonds get a plus and all outward pointing
bonds get a minus.
0 – junction can be interpreted as the generalized Kirchoff’s Current Law.
Additionally, equality of efforts (like electrical voltage) at a parallel connection.
Fig. 17 Example of a 0Junction [4]
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The Bond Graph Modeling Formalism (contd..)
1 – junction
Is the dual form of the 0-junction (roles of effort and flow are exchanged).
Represents a node at which all flows of the connecting bonds are equal. E.g. a series
connection in an electrical circuit.
The efforts of the connecting bonds sum to zero. Again, the power direction determines the
sign of flows: all inward pointing bonds get a plus and all outward pointing bonds get a minus.
1- junction can be interpreted as the generalized Kirchoff’s Voltage Law.
In the mechanical domain, 1-junction represents a force-balance, and is a generalization of
Newton’ third law.
Additionally, equality of flows (like electrical current) through a series connection.
Fig. 18 Example of a 1-Junction [4]
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The Bond Graph Modeling Formalism (contd..)
Some Miscellaneous Stuff!
Power Direction: The power is positive in the direction of the power bond. A port that has
incoming power bond consumes power. E.g. R, C. If power is negative, it flows in the opposite
direction of the half-arrow.
R, C, and I elements have an incoming bond (half arrow towards the element) as standard,
which results in positive parameters when modeling real–life components.
For source elements, the standard is outgoing, as sources mostly deliver power to the rest of
the system.
For TF– and GY–elements (transformers and gyrators), the standard is to have one bond
incoming and one bond outgoing, to show the ‘natural’ flow of energy.
These are constraints on the model!
Duality:
The role of effort and flow in the storage elements (C, I) are interchanged. They are each
other’s dual form.
A gyrator can be used to decompose an I-element to a GY and C element and vice versa.
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The Bond Graph Modeling Formalism (contd..)
• Causal Analysis
Causal analysis is the determination of the signal direction of the bonds. The energetic
connection (bond) is now interpreted as a bi-directional signal flow. The result is a causal bond
graph, which can be seen as a compact block diagram.
Causal analysis covered by modeling and simulation software packages that support bond
graphs; Enport, MS1, CAMP-G, 20 SIM
Four different types of constraints need to be discussed prior to following a systematic
procedure for bond graph formation and causal analysis.]
• Causal Constraints
Fixed Causality (Se, Sf)
Fixed causality is the case when equations allow only one of the two port variables to be the
outgoing variable. An effort source (Se) has by definition always its effort variable as signal
output, and has the causal stroke outwards. This causality is called effort-out causality or effort
causality. A flow source (Sf) clearly has a flow-out causality or flow causality.
May occur at non-linear elements, where the equations for that port cannot be inverted (e.g.
division by zero).
e
e
Se
e
f
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Sf
Se
f
e
f
Sf
f
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The Bond Graph Modeling Formalism (contd..)
Constrained Causality
(TF, GY, 0-junction, 1-junction)
Constrained causality is defined when a relations exist between the causalities of the different
ports of the element. At a TF, one of the ports has effort-out causality and the other has flowout causality.
e2
e1
e2
e1
OR
TF
f1
n
TF
f2
f1
n
f2
Similarly, at a GY, both ports have either effort-out causality or flow-out causality.
At a 0–junction, where all efforts are the same, exactly one bond must bring in the effort. This
implies that 0–junctions always have exactly one causal stroke at the side of the junction.
The causal condition at a 1–junction is the dual form of the 0-junction. All flows are equal, thus
exactly one bond will bring in the flow, implying that exactly one bond has the causal stroke
away from the 1–junction.
Preferred Causality
(C, I)
Causality determines whether an integration or differentiation w.r.t time is adopted in storage
elements. Integration has a preference over differentiation because:
1. At integrating form, initial condition must be specified.
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The Bond Graph Modeling Formalism (contd..)
2. Integration w.r.t. time can be realized physically; Numerical differentiation is not physically
realizable, since information at future time points is needed.
3. Another drawback of differentiation: When the input contains a step function, the output will
then become infinite.
Therefore, integrating causality is the preferred causality. C-element will have effort-out
causality and I-element will have flow-out causality. (figures 10 & 11).
Indifferent causality
(Linear R)
Indifferent causality is used, when there are no causal constraints! At a linear R, it does not
matter which of the port variables is the output.
There is no difference choosing the current as incoming variable and the voltage as outgoing
variable, or the other way around.
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Examples
•
Electrical Circuit # 1 (R-L-C) and its Bond Graph model
U1
U2
U3
+
-
U0
STEP 1: Determine which physical domains exist in the system and identify all basic
elements like C, I, R, Se, Sf, TF, GY. Give each element a unique name.
STEP 2: Indicate a reference effort for each domain in the Ideal Physical Model (reference
velocity with positive direction for the mechanical domains). Note that references in the
mechanical domain have a direction.
Generation of the connection / junction structure.
STEP 3: Identify all other efforts (mechanical domains: velocities) and give them unique
names.
STEP 4: Draw these efforts (mechanical: velocities), and not the references, graphically by
0–junctions (mechanical: 1–junctions). Keep if possible, the same layout as the IPM.
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Examples (contd..)
STEP 5: Identify all effort differences (mechanical velocity(=flow) differences) needed to
connect the ports of all elements enumerated in Step 1. Differences have a unique name.
STEP 6: Construct the effort differences using a 1–junction (mechanical: flow differences
with a 0–junction) and draw them as such in the graph.
STEP 4:
0
0
0
U1
U2
U3
0: U12
STEP 5, 6:
0
U1
1
0:
0
U2
U23
1
0
U3
STEP 7: The junction structure is now ready and the elements can be connected. Connect
the port of all elements found at step 1 with the 0–junctions of the corresponding efforts or
effort differences (mechanical: 1–junctions of the corresponding flows or flow differences).
STEP 8: Simplify the resulting graph by applying the following simplification rules:
1. A junction between two bonds can be left out, if the bonds have a ‘through’ power direction (one bond
incoming, the other outgoing).
2. A bond between two the same junctions can be left out, and the junctions can join into one junction.
3. Two separately constructed identical effort or flow differences can join into one effort or flow
difference.
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Examples (contd..)
STEP 7:
Se : U
0
R:R
I:L
0: U12
0: U23
1
0
1
0
U3
U2
U1
C:C
STEP 8:
R:R
Se : U
1
I:L
C:C
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Examples (contd..)
The Causality Assignment Algorithm:
STEP 1a. Chose a fixed causality of a source
element, assign its causality, and propagate this
assignment through the graph using the causal
constraints. Go on until all sources have their
causalities assigned.
STEP 1b. Chose a not yet causal port with fixed
causality (non-invertible equations), assign its
causality, and propagate this assignment
through the graph using the causal constraints.
Go on until all ports with fixed causality have
their causalities assigned.
STEP 2: Chose a not yet causal port with
preferred causality (storage elements), assign
its causality, and propagate this assignment
through the graph using the causal constraints.
Go on until all ports with preferred causality
have their causalities assigned.
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1a.
Se : U
R:R
1
I:L
C:C
2.
Se : U
R:R
I:L
1
C:C
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Examples (contd..)
STEP 3: Chose a not yet causal port with
indifferent causality, assign its causality, and
propagate this assignment through the graph
using the causal constraints. Go on until all
ports with indifferent causality have their
causalities assigned.
R:R
3.
1
Se : U
I:L
C:C
•
Electrical Circuit # 2 and its Bond Graph model
R1
C1
L1
C2
C2
L1
C1
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R2
R3
R1
R2
R3
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Examples (contd..)
•
A DC Motor and its Bond Graph model
Se2:τ
Se1:Ua
Km
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Generation of Equations from Bond Graphs
Se : U
R:R
•
2
•
1
1
4
I:L
3
•
•
C:C
Fig. 19 Bond Graph of a series RLC
circuit
•
A causal bond graph contains all information to derive the
set of state equations.
Either a set of Ordinary first-order Differential Equations
(ODE) or a set of Differential and Algebraic Equations
(DAE).
Write the set of mixed differential and algebraic equations.
For a bond graph with n bonds, 2n equations can be
formed, n equations each to compute effort and flow or
their derivatives.
Then, the algebraic equations are eliminated, to get final
equations in state-variable form.
For the given RLC circuit, Se = e1= U;
Hence,
e2 = R * f2;
(de3/dt) = (1/C) * f3;
(df4/dt) = (1/L) * e4;
f1 = f4; f2 = f4; f3 = f4;
e4 = e1 - e2 - e3
e1 - e2 - e3 = U – (R * f2) – e3 = U – (R * f4) – e3
(df4/dt) = (1/L) * (U – (R * f4) – e3)
- - - - - - - (i)
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Generation of Equations from Bond Graphs (contd..)
Also,
(de3/dt) = (1/C) * f3 = (1/C) * f4
- - - - - - - - (ii)
In matrix form, (dx/dt) = Ax + Bu
(de3/dt)
0
1/C
e3
=
(df4/dt)
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0
+
-1/L
-R/L
f4
U
1/L
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Generation of Equations from Bond Graphs (contd..)
Some Points to Note:
One of the most important features of bond graphs is ‘easy determination of causality’.
For computer algorithms to solve equations, representing the physics of real systems, it is
essential that proper input and output causality be maintained.
State variables and computational problems are known completely after assigning causality,
even before the modeler derives a single equation.
Modeling in terms of bond graphs helps one focus on modeling the physical effects without
bothering about the computational issues such as generation of a consistent system of
equations.
B.G. on one hand relate closely to the structure of the system being modeled, while on the
other hand, they contain enough information to derive other system representations like statespace equations.
B.G can be drawn or a B.G. description of the system can be created before causality is
considered. In contrast, causality has to be considered before a block diagram can be drawn.
E.g. the decision as to whether a resistor has a voltage or current as output has to be made
before a block diagram can be constructed. In B.G., causality can be automatically assigned
after the system has been described.
Intelligent Powertrain Design
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The Bond Graph Metamodeling Environment in GME
Intelligent Powertrain Design
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Applications in GME Metamodeling Environment
•
RLC Circuit
Intelligent Powertrain Design
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Applications in GME Metamodeling Environment (contd..)
DC Motor model
Intelligent Powertrain Design
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Future Concepts
•
Defining the GME Approach for analysis of Bond Graphs [1]
Conventional Approach
Probable GME / Matlab Approach
1. Determination of Physical System
and specifications from the
requirements.
2. Draw a functional Block Diagram.
3. Transform the physical system into a
schematic.
4. Use Schematic and obtain a
mathematical model, a block diagram
or a state representation.
5. Reduce the block diagram to a close
loop system.
6. Analyze, design and test.
1. Identify the physical system elements
and represent a word Bond Graph.
2. Represent a bond graph model in
GME.
3. GME interpreters generate equations
in a suitable form (e.g. state space
variable matrix form) suitable for
analysis in Matlab.
4. Use Matlab, to analyze, design and
test.
Intelligent Powertrain Design
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Future Concepts (contd..)
•
Creating Bond Graph Interpreters
Bond Graph Interpreters
in GME ??
Fig. The Simulation Generation Process [7]
Intelligent Powertrain Design
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Future Concepts (contd..)
•
Advanced Bond Graph Techniques
Expansion of Bond Graphs to Block Diagrams
Bond Graph Modeling of Switching Devices
Bond Graphs as Object-oriented physical-systems modeling
Hierarchical modeling using Bond Graphs
Use of port-based approach for Co-simulation
Intelligent Powertrain Design
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References
1.
Granda J. J, “Computer Aided Design of Dynamic Systems” http://gaia.csus.edu/~grandajj/
2.
Wong Y. K., Rad A. B., “Bond Graph Simulations of Electrical Systems,” The Hong Kong
Polytechnic University, 1998
3.
http://www.ce.utwente.nl/bnk/bondgraphs/bond.htm
4.
Broenink
J.
F.,
"Introduction
to
Physical
Systems
Modeling
with
Bond
Graphs,"
University of Twente, Dept. EE, Netherlands.
5.
Granda J., Reus J., "New developments in Bond Graph Modeling Software Tools: The Computer
Aided
Modeling
Program
CAMP-G
and
MATLAB,"
California
State
University, Sacramento
6.
http://www.bondgraphs.com/about2.html
7.
Vashishtha D., “Modeling And Simulation of Large Scale Real Time Embedded Systems,” M.S.
Thesis, Vanderbilt University, May 2004
8.
Hogan
N.
"Bond
Graph
notation
for
Physical
System
models,"
Modeling of Physical System Dynamics
Intelligent Powertrain Design
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Integrated