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Transcript of Start of presentation Advanced Simulation Technologies Conference April 18-22, 2004 François E....
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
François E. Cellier, Ph.D.Professor and Director of Undergraduate Studies
Department of Electrical & Computer EngineeringUniversity of Arizona
Smart Product Modeling:Dealing with the Issuesof System Complexity
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Smart Product Modeling
• Smart Product Modeling (SPM) is a term that has been coined to denote modeling support for the design and development of complex systems.
• It is often used in the context of rapid prototyping of alternate system designs.
• In SPM, models of alternate system components become interchangeable in ways that resemble physical system components.
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Manufacturing Life Cycle• In car manufacturing, the development life cycle of
a new model is now two years. In the first year, the features of the new model are designed, whereas in the second year, the production of the new model is being designed.
• Many of the components of a car are prefabricated, and they are often outsourced. Your new “all-American” car may feature a German engine and a Japanese transmission.
• Design alternatives must be chosen, before even a real prototype of the new model has been produced.
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
SPM and Life Cycle Reduction• Complex systems can only be designed in a
short time and with limited resources, if many design decisions can be made on the basis of simulation models alone.
• Components are supposed to be delivered together with simulation models describing them.
• The object-oriented modeling of physical systems provides a means to accomplish that goal.
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Detaileddescription
Iconicrepresentation
Taxonomy
Organization of KnowledgeLet us consider the example of an electrical resistor :
va vb
Potentials: va, vb
u
Voltage: u : u = va vb
Ri
Current: i : u = R · i
The object-oriented modeling paradigm stores the four items characterizing an object in a single place. These are: the taxonomy (naming and organization), the iconic representation (for graphical modeling), the detailed mathematical description (either in the form of equations or in the form of a topology), and the lexical information (a verbal description).
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
The Causality of the Model EquationsU 0
i+
R
I 0
I0
R
U0 = f(t)
i = U0 / R
I0 = f(t)
u = R· I0
Identical Objects
Different Equations
The causality of the equations must not be predetermined. It can only be decided upon after the analysis of the system topology.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Basic Requirements of OO Modeling
• Physical objects should be representable by mathematical graphical objects.
• The graphical objects should be topologically connectable.
• The mathematical models should be hierarchically describable. To this end, it must be possible to represent networks of coupled objects again as graphical objects.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Example of a Topological Description
model Circuit1 SineVoltage U0(V=10, freqHz=2500); Resistor R1(R=100); Resistor R2(R=20); Capacitor C(C=1E-6); Inductor L(L=0.0015); Ground Ground; equation connect(U0.p, R1.p); connect(R1.n, C.p); connect(R2.p, R1.n); connect(U0.n, C.n); connect(Ground.p, C.n); connect(L.p, R1.p); connect(L1.n, Ground.p); connect(R2.n, L.n);end Circuit1;
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Graphical Information (Annotation)package CircuitLib annotation (Coordsys( extent=[0, 0; 504, 364], grid=[2, 2], component=[20, 20])); model Circuit1 annotation (Coordsys( extent=[-100, -100; 100, 100], grid=[2, 2], component=[20, 20])); Modelica.Electrical.Analog.Sources.SineVoltage U0(V=10, freqHz=2500) annotation (extent=[-80, -20; -40, 20], rotation=-90); Modelica.Electrical.Analog.Basic.Resistor R1(R=100) annotation (extent=[ -40, 20; 0, 60], rotation=-90); Modelica.Electrical.Analog.Basic.Capacitor C(C=1E-6) annotation (extent=[-40, -60; 0, -20], rotation=-90); Modelica.Electrical.Analog.Basic.Resistor R2(R=20) annotation (extent=[0, -20; 40, 20]); Modelica.Electrical.Analog.Basic.Inductor L(L=0.0015) annotation (extent=[40, 20; 80, 60], rotation=-90); Modelica.Electrical.Analog.Basic.Ground Ground annotation (extent=[0, -100; 40, -60]); equation connect(U0.p, R1.p) annotation (points=[-60, 20; -60, 60; -20, 60], style(color=3)); connect(R1.n, C.p) annotation (points=[-20, 20; -20, -20], style(color=3)); connect(R2.p, R1.n) annotation (points=[0, 0; -20, 0; -20, 20], style(color=3)); connect(U0.n, C.n) annotation (points=[-60, -20; -60, -60; -20, -60], style(color=3)); connect(Ground.p, C.n) annotation (points=[20, -60; -20, -60], style(color=3)); connect(L.p, R1.p) annotation (points=[60, 60; -20, 60], style(color=3)); connect(L.n, Ground.p) annotation (points=[60, 20; 60, -60; 20, -60], style(color=3)); connect(R2.n, L.n) annotation (points=[40, 0; 60, 0; 60, 20], style(color=3)); end Circuit1;end CircuitLib;
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Advanced Simulation Technologies Conference
April 18-22, 2004
Models in Modelica
• Models in Modelica consist of a description of their model structure as well as a description of their embedding in the model environment:
model Model name Description of the model embedding; equations Description of the model structure;end Model name;
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Advanced Simulation Technologies Conference
April 18-22, 2004
Model Structure in Modelica• The model structure in Modelica consists either of a set of
equations, a description of the model topology, or a combination of the two types of model structure descriptions.
• A topological model description is usually done by dragging and dropping model icons from graphical model libraries into the modeling window. These models are then graphically interconnected among each other.
• The stored textual version of the topological model consists of a declaration of its sub-models (model embedding), a declaration of its connections (model structure), as well as a declaration of the graphical description elements (Annotation).
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Advanced Simulation Technologies Conference
April 18-22, 2004
Model Topology in Modelica
Class name
Instance name
Modifier
Connection
Connector
model MotorDrive PI controller; Motor motor; Gearbox gearbox(n=100); Shaft Jl(J=10); Tachometer wl; equation connect(controller.out, motor.inp); connect(motor.flange , gearbox.a); connect(gearbox.b , Jl.a); connect(Jl.b , wl.a); connect(wl.w , controller.inp);end MotorDrive;
motor
controller
PIn=100
Jl=10
w l
w r
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Advanced Simulation Technologies Conference
April 18-22, 2004
Resistors in Modelica
Rivp vn
u
connector Pin Voltage v; flow Current i;end Pin;
model Resistor "Ideal resistor" Pin p, n; Voltage u; parameter Resistance R; equation u = p.v - n.v; p.i + n.i = 0; R*p.i = u;end Resistor;
Voltage
type ElectricPotential = Real (final quantity="ElectricPotential", final unit="V");type Voltage = ElectricPotential;
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Advanced Simulation Technologies Conference
April 18-22, 2004
Similarity Between Different Elements
Rivp vn
u
model Resistor "Ideal resistor" Pin p, n; Voltage u; parameter Resistance R; equation u = p.v - n.v; p.i + n.i = 0; R*p.i = u;end Resistor;
model Capacitor "Ideal capacitor" Pin p, n; Voltage u; parameter Capacitance C; equation u = p.v - n.v; p.i + n.i = 0; C*der(u) = p.i;end Capacitor;
Civp vn
u
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Advanced Simulation Technologies Conference
April 18-22, 2004
Partial Models and Inheritance
ivp vn
u
partial model OnePort Pin p, n; Voltage u; equation u = p.v - n.v; p.i + n.i = 0; end OnePort;
model Resistor "Ideal resistor" extends OnePort; parameter Resistance R; equation R*p.i = u;end Resistor;
model Capacitor "Ideal capacitor" extends OnePort; parameter Capacitance C; equation C*der(u) = p.i;end Capacitor;
ivp vn
u
R
ivp vn
u
C
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Decomposition and Abstraction
planetary1=110/50
C4=0.12 C5=0.12
planetary2=110/50
C6=0.1
2
bearing2
C8=0.1
2
dem
ultip
lex
shaftS=2e-3
S
planetary3=120/44
C11=0.12
shaftS1=2e-3
S
C12=0.1
2
bearing1bearing4
Cou
rtes
y T
oyot
a T
ecno
-Ser
vice
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Heterogeneous Modeling Formalisms
inertialx
y
axis1
axis2
axis3
axis4
axis5
axis6r3Drive1
1
r3Motorr3ControlqdRef
1
S
qRef
1
S
k2
i
k1
i
qddRef cut joint
q: angleqd: angular velocity
qdd: angular acceleration
qd
tn
Jmotor=J
gear=i
spring=c
fric
=R
v0
Srel
joint=0
S
Vs
-
+diff
-
+pow er
emf
La=(2
50
/(2*D
*wm
))R
a=250
Rd2=100
C=0.004*D/w m
-
+OpI
Rd1=100
Ri=10
Rp1=200
Rp2=50
Rd4=100
hall2
Rd3=100
g1
g2
g3
hall1
g4
g5
rw
cut in
iRef
qd q
rate2
b(s)
a(s)
rate3
340.8
S
rate1
b(s)
a(s)
tacho1
PT1
Kd
0.03
w Sum
-
sum
+1
+1
pSum
-
Kv
0.3
tacho2
b(s)
a(s)
q qd
iRefqRef
qdRef
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Mechanical Connectors
connector Frame Position r0[3] "Distance of the frame from the inertial system"; Real S[3, 3] "Transformation matrix of the frame to the inertial system"; Velocity v[3] "Absolute velocity of the frame"; AngularVelocity w[3] "Absolute angular velocity of the frame"; Acceleration a[3] "Absolute acceleration of the frame"; AngularAcceleration z[3]"Absolute angular acceleration of the frame "; flow Force f[3] "Force acting on the frame"; flow Torque t[3] "Torque acting on the frame";end Frame;
Because of the sign conventions, an empty output frame ( ) must always be connected to a full input frame ( ).
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Mechanical Bodies I• Mechanical bodies define the D’Alembert
Principle for the sum of acting forces and torques.model BodyBase "Inertia and mass properties of a rigid body"; extends Frame a; Mass m; Position rCM[3] "Distance from frame to center of gravity"; Inertia I[3, 3]; equation f = m*(a + cross(z, rCM) + cross(w, cross(w, rCM))); t = I*z + cross(w, I*w) + cross(rCM, f);end BodyBase;
FrameCenter of Gravity
rCM
The coordinates of the frames are first converted to the center of gravity.
The D’Alembert Principle is then formulated for the center of gravity.
The resulting force f and torque t are finally transformed back to the frame by means of their relative movement under introduction of the accompanying centripetal and Coriolis forces.
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Mechanical Bodies IImodel Body "Rigid body with one cut"; extends Frame_a; parameter Position rCM[3]={0,0,0} "Vector from frame_a to center of mass, resolved in frame_a; parameter Mass m=0 "Mass of body [kg]"; parameter Inertia I11=0 "(1,1) element of inertia tensor"; parameter Inertia I22=0 "(2,2) element of inertia tensor"; parameter Inertia I33=0 "(3,3) element of inertia tensor"; parameter Inertia I21=0 "(2,1) element of inertia tensor"; parameter Inertia I31=0 "(3,1) element of inertia tensor"; parameter Inertia I32=0 "(3,2) element of inertia tensor"; BodyBase body; equation connect (frame_a, body.frame_a); body.m = m; body.rCM = rCM; body.I = [I11, I21, I31; I21, I22, I32; I31, I32, I33];end Body
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Mechanical Bodies IIImodel Body "Rigid body with one cut"; extends Frame_a; parameter Position rCM[3]={0,0,0} "Vector from frame_a to center of mass, resolved in frame_a; parameter Mass m=0 "Mass of body [kg]"; parameter Inertia I11=0 "(1,1) element of inertia tensor"; parameter Inertia I22=0 "(2,2) element of inertia tensor"; parameter Inertia I33=0 "(3,3) element of inertia tensor"; parameter Inertia I21=0 "(2,1) element of inertia tensor"; parameter Inertia I31=0 "(3,1) element of inertia tensor"; parameter Inertia I32=0 "(3,2) element of inertia tensor"; BodyBase body; equation connect (frame_a, body.frame_a); body.m = m; body.rCM = rCM; body.I = [I11, I21, I31; I21, I22, I32; I31, I32, I33];end Body
Information extracted from type declaration
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Advanced Simulation Technologies Conference
April 18-22, 2004
Mechanical Bodies IV
Coordinate transformation frame a frame b
Body calculated relative to frame a
Bodies with more than two joints have to be constructed by the modeler using additional frame translations. Such elements are not available in the MBS library as pre-designed modules.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Mechanical Bodies V
Geometry for the animation.
Geometry for the computation of mass and inertia matrix (not represented graphically, since modeled by means of equations).
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Advanced Simulation Technologies Conference
April 18-22, 2004
An Example I
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Advanced Simulation Technologies Conference
April 18-22, 2004
An Example II
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Advanced Simulation Technologies Conference
April 18-22, 2004
An Example III
Cut joint
Kinematic loop
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Advanced Simulation Technologies Conference
April 18-22, 2004
An Example IV
Equations after expansion of the matrix expressions
Elimination of trivial equations of the type: a = b
Remaining equations after the symbolic transformation.
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Advanced Simulation Technologies Conference
April 18-22, 2004
An Example V
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Advanced Simulation Technologies Conference
April 18-22, 2004
Multi-body Systems• A multi-body system (MBS) consists of a combination of
mechanical parts, connected to each other to support motion in three-dimensional space.
Hmm! Maybe this is not yet the most luxurious model… but abstraction is everything after all.
Start of presentation
Advanced Simulation Technologies Conference
April 18-22, 2004
Properties of OO Modeling Environment• The object-oriented modeling environment supports
both flexible topological and hierarchical interconnection mechanisms.
• The environment lends itself to information hiding. The details of the models are hidden behind iconic model representations.
• The environment contains no domain-specific knowledge. The entire domain-specific knowledge is encoded in the domain libraries, such as the MBS library.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Passive Solar Space Heating• An experimental building
with passive solar heating is shown here from three sides.
• Solar radiation through the walls, the windows, and the ceiling is to be modeled.
• Losses are also being modeled, including the losses through the slab.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Top-level Model
Iconic representation Topological representation
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April 18-22, 2004
Living Room Model
Iconic representation Topological representation
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April 18-22, 2004
The Interior Wall
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April 18-22, 2004
The Window
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April 18-22, 2004
The Solar Position
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April 18-22, 2004
The Solar-House Package
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April 18-22, 2004
Simulation Results
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Advanced Simulation Technologies Conference
April 18-22, 2004
Knowledge Abstraction• The object-oriented modeling metaphor lends
itself to knowledge abstraction.
• Thereby, it enables the modeler to formulate domain-specific knowledge in the language of the domain expert.
• Object-oriented models are thus well suited for communication of knowledge between modelers and domain experts.
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Advanced Simulation Technologies Conference
April 18-22, 2004
The Hemodynamic SystemThe heart chambers and blood vessels are containers of blood. Each container is a storage of mass, thus contains a C-element.
The C-elements are partly non-linear, and in the case of the heart chambers even time-dependent.
The mSE-element on the left side represents the residual volume of the vessel.
The mSE-element on the right side represents the thoracic pressure, which is influenced by the breathing.
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Advanced Simulation Technologies Conference
April 18-22, 2004
The Hemodynamic System II
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Advanced Simulation Technologies Conference
April 18-22, 2004
The Hemodynamic System III
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Advanced Simulation Technologies Conference
April 18-22, 2004
The HeartThe heart contains the four chambers, as well as the four major heart valves, the pulmonary and aorta valves at the exits of the ventricula, and the mitral and triscuspid valves between the atria and the corresponding ventricula.
The sinus rhythm block programs the contraction and relaxation of the heart muscle.
The heart muscle flow symbolizes the coronary blood vessels that are responsible for supplying the heart muscle with oxygen.
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Advanced Simulation Technologies Conference
April 18-22, 2004
The ThoraxThe thorax contains the heart and the major blood vessels.
The table lookup function at the bottom computes the thoracic pressure as a function of the breathing.
The arterial blood is drawn in red, whereas the venous blood is drawn in blue.
Shown on the left are the central nervous control signals.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Summary• The Object-oriented modeling paradigm enables us
to organize and encapsulate knowledge about a system.
• The methodology allows us to manage and communicate this knowledge in natural ways, using terminology that is familiar to the domain expert.
• Each individual component model, be it a leaf model or a topological description of subsystems, can be kept small and manageable.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Summary• In the process of compilation, the models are
merged to form a large and monolithic set of equations.
• To obtain efficient simulation models, it may even be necessary to merge the model equations and the simulator equations (integration algorithms).
• These equations are then further processed by pruning out knowledge that is not needed for the task at hand.
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Advanced Simulation Technologies Conference
April 18-22, 2004
Summary• The resulting simulation codes are as efficient
as if not more efficient than the best spaghetti code special-purpose simulators of the past.
• The technology is already widely used in the automotive industries, but is also making headway in other application domains.
• At the University of Arizona, the technology is taught in a senior/graduate level class to roughly 25 students per year.