modeling 03
TRANSCRIPT
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Efficient Modeling and Simulation
of Multidisciplinary Systems
across the Internet
Heman Mann
Computing and Information Centre
Czech Technical Universi ty in Prague
TUTORIAL
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Tutorial objectives
After attending this tutorial you should be able to:
understand the difference between various approaches tomodeling and their suitability to different tasks
be able to apply the concepts of multipole modeling indifferent physical domains
be motivated to try the simulation software system DYNAST
freely accessible across the Internet be aware of the importance of physical-level simulation for
reliable control design
be prepared to introduce a unified approach to engineeringdynamics at you school (if you are a teacher)
interested in visiting the DynLAB web-based course onmodeling and simulation (to be fully completed soon)
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Kernel engineering tools
Modeling = procedure to simplify investigation of their dynamic behavior
Simulation = imitation of dynamic behavior of real systems
Analysis = relating system behavior to a changing variable or parameter
Diagnostics = indicating the reason for a system failure
Why engineers need these tools?
to better understand behavior of existing dynamic systems
to predict, verify and optimize behavior of designed systems
to detect, localize and diagnose faults in engineering products
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Multidisciplinary approach
Contemporary engineering crosses borders between traditional
disciplines: different physical domains
electrical, magnetic, mechanical, fluid, thermal, ...
different levels of modeling abstraction
conceptual, functional, physical, virtual prototyping, (digital) control,diagnossis, ...
different levels of modeling idealization
(non)linear, time (in)variable, parameter (in)dependent,
different model descriptions
equations, transfer functions, block diagrams, multipoles, ...
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Efficiency of simulation
In the past:
efficiency of simulation was evaluated with regard to its demand ofcomputer time only
Nowadays: the computer time is so inexpensive that the cost of simulation is
dominated by the cost of personnel qualified to be able
to prepare the input data
to supervise the computation
to interpret the results
Therefore: efficient simulation software should provide
automated equation formulation
robust computational algorithms user-friendly interface
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Design procedure
Design proceeds through several levels of abstraction
conceptual functional (e.g., control design)
physical (e.g., real or virtual prototyping)
technological
Different system descriptions are used
geometric (blue
topological (geometric dimensions of subsystems are not shown, only
their interactions)
behavioral (internal interactions of subsystems are not shown, only
their external behavior)
Design proceeds through several levels of granularity
(perpendicular to the design-space diagram)
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Design space
trajectory of ideal design procedure (real one in many loops)
blocks multipoles
design space
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Modeling & simulation procedure
1. System definition
system separation from its surroundings system decomposition into subsystems
identification of subsystem energy interactions
2. Model development subsystem abstraction and idealization
identification of subsystem parameters3. Formulation of
equations for subsystems
equations for subsystem interactions
combined and reduced equations
4. Equation solution5. Interpretation of the solution
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Simulation using Simulink
1. System definition
system separation from its surroundings system decomposition into subsystems
2. Model development subsystem abstraction and idealization
parameter identification
3. Formulation of equations for subsystems
equations for subsystem interactions
combined and reduced equations
4. Composition of a block diagram
5. Block-diagram analysis6. Interpretation of the solution
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Block Diagram Algebra
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Block diagram applications
Graphical representation of
causes-effects relations
inputs: causes
outputs: effects
explicit equations
inputs: independent variables outputs: dependent variables
control structures
inputs: excitations, disturbances
outputs: desired variables
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Copying lathe (1)
Geometric description
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Copying lathe (2)
Behavioral description (blockdiagram for control design)
master-shape
waveform
workpiece-shape
waveform
force exerted bycylinder
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Copying lathe (3)
Topological description (multipolediagram for physical design)
source of
pressure
source of master-
shape waveform r
cylinder mass
model of workpiece resistance
slide-bed friction
F
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Multipole diagrams
can be set up based on mere inspection of the modeled
real systems without any equation formulation or block-diagram construction
equations underlying the system models can be not only
solved, but also formed automatically by the computer
they project geometric configuration of real dynamicsystems onto their topological configuration
they portray graphically energy interactions between
subsystems in the systems
they can be combined with block diagrams, whichrepresent a special case of multipole diagrams)
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Multipole modeling
Principles of multipole modeling
Concept of across and through variables
Postulates of continuity and compatibility
Advantages of multipole modeling
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Investigation of dynamic behavior
Dynamic behavior of a dynamic system is governed
by the flow of energy and matter between subsystems of thesystem and between the subsystems and the surroundings
by storing energy in the subsystems or releasing it later aswell as by changes from one form to another.
Therefore, before starting any dynamic investigation of a systemwe should clearly
separate the system from its surroundings
decompose the system into its disjoint subsystems
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Multidisciplinary system (1)
Tachometer
Busline
Electronicamplifier
Hydraulicmotor
Outputsynchro
Inputsynchro
Compensatingnetwork
Hydraulicvalve
Load
Demodulator
Gear
Control
Source ofpressure
Shaft
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Multipole models
Multipole model approximates subsystem mutual energy
interactions assuming that
the interactions take place just in a limited number ofinteraction sites formed by adjacent energy entries into the
subsystems
the energy flow through each such entry can be expressed
by a product of two complementarypower variables
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Tachometer
Busline
Electronicamplifier
Hydraulicmotor
Outputsynchro
Inputsynchro
Compensatingnetwork
Hydraulicvalve
Load
Demodulator
Gear
Control
Source ofpressure
Shaft
Multidisciplinary system (2)
Subsystems are separated by energy boundaries,
sites of energy interactions are denoted by small circles
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Multidisciplinary system (3)
Tachometer
Busline
Electronicamplifier
Hydraulicmotor
Outputsynchro
Inputsynchro
Compensatingnetwork
Hyd
raulic
valve
Load
Demodulator
Gear
Sourceof
pressure
Shaft
Energy interactions between subsystems are characterized exclusively by
energy flows through the sites of interactions at the energy boundaries
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Multidisciplinary system (4)
Tachometer
Busline
Electronicamplifier
Hydraulicmotor
Outputsynchro
Inputsynchro
Compensatingnetwork
Hydraulic
valve
Load
Demodulator
Gear
Sourceof
pressure
Shaft
The energy boundaries are detached and the energy interactions are
interconnected with the energy entries of subsystems by ideal links
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Multipole constitutive relation
vB vC
vDvE
A D
CB
EvA
iB iC
iD
iE
A D
CB
EiA
( )c( )b
A D
CB
E
( )a
5 - pole across variables through variables
Each multipole can be characterized by a constitutive relation
between its across and through variables expressed by means
of a combination of
physical elements
blocks equations
look-up tables
Power variables
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Power variables
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Measurement of variables
Direct measurement ofthrough variables requires
including the measuring
instrument between
disconnected adjacent
energy entries
Across variables are measured
between distant energy entries
without disconnecting them
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Postulate of Continuity
a
b
c
Through variables a, b, c:
a + b + c =0
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Postulate of Compatibility
a
b
c
Across variables a, b, c:
a + b + c =0
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Reference across-variables
Measurement of reference
across variables
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Non-mechanical elements
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Simple electrical system
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Simple hydraulic system
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Mechanical elements
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Simple translational system
Si l t ti l t
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Simple rotational system
Cold rolling mill
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Cold rolling mill
U ifi d h t d li
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Unified approach to modeling
Oth h (1)
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Other approaches (1)
Other approaches (2)
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Other approaches (2)
Additional advantages
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Additional advantages
multipole models can be developed once for the individual
subsystems and stored to be used any time later this job can be done for different types of subsystems by
specialists in the field
submodels can be represented by different descriptions
suiting best to the related engineering discipline or application
submodel refinement or subsystem replacement can be taken
into account without interfering with the rest of the system
model
mixed-level modeling is allowed
Mechanical systems
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Mechanical systems
Translational systems
Rotational systems
Coupled mechanical systems
Rotary-to-rotary couplings Rotary-to-linear couplings
Linear-to-linear couplings
Planar systems
Jumping ball
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Jumping ball
Translatory systems
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Translatory systems
y
k dmg
yAA
y
ydyS
yA
mA
( )a ( )b
yS
mg
yd
k
m
d
m2
m1
FdF
v2
v1
l l
F
kR
kB
0 l0
d2 d1
Fd
CAR 2CAR 1
m1 m2
lF
v1 v2( )c( )b( )a
Quarter-car model
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Quarter-car model
Motor on vibration isolator
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Motor on vibration isolator
stop characteristic
Impact of a long spring
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Impact of a long spring
Torsional pendulums
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Torsional pendulums
Weight-lifting mechanism
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Weight lifting mechanism
Rotary-to-rotary coupling
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Rotary to rotary coupling
B
A
A
B
n
Pure transformer
Coupling ratio:
Power consumption:
0BBAA
P
Coupled gears
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Coupled gears
B
A
A
B
n
Coupling ratio:
Power consumption:
0BBAA
P
Pure transformer
Gear trains (part 1)
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Gear trains (part 1)
Gear train Configuration n
External
spur gears
Internal
spur gears
Beveled
gear pair
b
a
r
r
b
a
r
r
b
a
rr
Model
Gear trains (part 2)
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(p )
Gear train Configuration n
Planet
gear
Skew
gear pair
b
a
r
r
b
a
r
r
Model
Belt-and-pulley or chain-and sprocket
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ba rrn / barrn
Gear train with backlash
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Backlash
characteristics
Rotary-to-linear couplings
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y p g
B
A
A
B
F
xn
Coupling ratio:
Power consumption:
0 BBAA xFP Pure transformer
Rotary-to-linear convertion
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y
mg
y
A
r
m, J
A
mgm
Ay An J
n r
( )a ( )b
J,mA
( )a
A
AxxA
A
mgsinmxAA
n
( )bn = - 1/r
Rack-and-pinion gear-train
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rn /1
Movable rack-and-pinion assembly
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rn /1
Pulley or sprocket assembly
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rn
Lead screw assembly
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Pn P screw pitch
Slider crank
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2
0
2
0
)sin(
)sincos(sin
1
yrl
yrrr
x
n
A
A
A
A
BA
Linear-to-linear coupling
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B
A
A
B
F
F
x
xn
Coupling ratio:
Power consumption:
0 BBAA xFxFP Pure transformer
Levers and pulleys
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Lever systems
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k
k
mg
mCB
A
l
y
mg
By
CyAy
mk
( )a ( )b
n kl
k
mg
m
A B C
D
B'
l1 l2
l3v t( )
y
Ayna Cy
By B'y
m mg( )a ( )b
nal /l1 2
nb
nbl /l2 3
Planar oblique throw
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Central star and planet
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Math pendulums
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n
m mmg
Ax
xAB yAB
Ay
Bx Byx
y mA
B
mg
( )a ( )b
n yAB
xAB
xy
A
B
C
xB xC0
C2
n1
m1
m1
m2
m2 m2g
m1g
n2
Cx xC
xB
yB
yC
By
Cy
n1 yBxB
n 2 y y BC
x x BC
( )b( )a
Planar systems
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x
y
mC
mA
B
mg BxdC
xB
mC
( )a ( )b
n
m mg
Ax
xAB
yAB
Ay
By
mn
yAB
xAB
mg
m
A
B
k
n yAB
xAB
( )a ( )b
m mg
yAB
xAB
n
BxAy
kyAB
xAB
Translatory joint fixed to frame
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Multipole model
Translatory joint between bodies
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Revolute joints
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Body with revolute joints
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Two-link planar robot
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Physical 2-pendulum with friction
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Truck with active damping
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Truck model
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Electrical & electronic systems
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CMOS inverter
Pulse-width modulator
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Astable multivibrator
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Three-phase thyristor rectifier
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Electro-mechanical systems
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Conductor moving in a magnetic field
Coils in a magnetic field
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ac rotational transducer
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Movable-core solenoid
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Permanent magnet DC machine
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Chopper-driven dc motor
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Movable-plate condenser
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Reluctance machine
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Three-phase stepping motor
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Electromagnetic relay
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Magnetic levitation of a ball
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Chopper-driven dc motor
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Fluid-power systems
QCf1 Cf2
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Q
( ) ( )a b
Gf
Q
pB
f1 f2
Lf
Valve for flow control
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Fluid-mechanical transducers
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Fluid-damped car suspension
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Two-stage relief valve
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Relief valve in a system
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Spool valves
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FPN simulation benchmark
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DYNAST software system
for efficient simulation of multidisciplinary engineering systems
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y g g y
freely accessible across the Internet at
http://virtual.cvut.cz/dyn/
DYNAST has been designed
for practicing engineers to enhance efficiency and quality of
their work
for engineering students to accelerate and deepen their
understanding of system dynamics
for remote engineering teams to support their collaboration
DYNAST distributed simulation environment
Client Server
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Web browser
DYNAST Shellfor submitting diagrams or
equations and for plotting
CORTONAfor 3D animation
of simulated systems
MATLABfor design of control for
simulated systems
Learning mng. systemfor course delivery
DYNAST Solverfor forming and solving
equations
DYNAST Publisherfor documenting simulation
experiments & submodels
DYNAST Monitorfor assisting learners in
modelling and simulation
I nternet
DYNAST Solver
provides the computation power for the DYNAST system.
It
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It can
compute transient and steady-state (static) solution ofsystems of nonlinear algebro-differential equations
formulate these equations for multipole diagrams that may be
combined with block diagrams and/or equations
compute Fourrier analysis of the periodic steady-statesolution
linearize nonlinear system models and provide system
transfer functions and responses in a semisymbolic form
compute frequency-domain characteristics in different forms
DYNAST Solver
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Semisymbolic analysis
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DYNAST Shell
provides a user-friendly working environment for DYNAST Solver.
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Thanks to its wizard dialogs, users do not need to learn a
simulation language.
DYNAST Shell allows for
submitting equations in textual and diagrams in graphical form
syntax analysis of the submitted problem for errors processing the submitted problem by DYNAST Solver
plotting the resulting data in different graphical forms
creating graphical symbols and models for new components
processing of reports on simulation experiments and models communication with the clients Matlab control-design toolset
Submitting a component model
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DYNAST Shell -- symbol editor
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DYNAST Publisher
is a LaTeX-based documentation system installed on
the server for automated publishing of
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the server for automated publishing of
reports on simulation experiments and descriptions of library submodels
Publisher extracts automatically the relevant parts of
the input data and captures the submitted multipole or
block diagrams as well as the resulting output plots and
includes them into the documents.
The documents can be converted by the server into
PostScript, PDF and HTML formats.
DYNAST Monitor
allows design managers or tutors to observe from any site on the
Internet the data files and diagrams the users are submitting to
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DYNAST Solver from their client computers.
The supervisor can communicate with the users across the Internet
and assist them in solving their problems.
DYNAST in control design
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functional level
physical level
Control
synthesis
Control design
verification
Controlled
system
Control
objectives
Plant to be
controlled
Model
reduction
Real-partsimplementation
MATLAB domain
DYNAST domain
Modeling using MATLABExample of the paper-and-pencil procedure necessary for the equation formulation and their
transformation before MATLAB can be used to compute the open-loop response:
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D. Tilbury, B. Messner: Control Tutorials for Matlab at http://www.engin.umich.edu/group/ctm/
Inverse pendulum experiment
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Multipole model of the open loop inDYNAST working environment
pendulum model
sensor ofd2/dt
cart inertia
source of force F
cart friction
sensor ofdx/dt integration ofdx/dt sensor ofx
DYNAST as modelling toolbox for Matlab
Validation of the open-loop model in DYNAST
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p p
Export of open-loop transfer functions to
MATLAB environment in M-file
Analog PID control of inverse pendulum
Closed-loop
model in
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DYNAST basedon control
design in
MATLAB
Closed-loop
verification in
DYNAST
DYNAST & MATLAB
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Current control curriculum criticised
for
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exposing students to rigor math before motivating them bypractical engineering issues
presenting textbook problems carefully engineered to fit
the underlying theory
using computers to carry old exercises without exploitingthem efficiently
Future Directions in Control Education, IEEE Control Systems, October 1999
Considerations for control education
1. Automatic control education currently has a very
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1. Automatic control education currently has a very
narrow approach ...
2. It is necessary to attach greater importance to all the
design cycle of a control system
3. Modelling and identification ... are a key factor for
achieving a good design ...
S. Dormido Bencomo: Control Learning: Present and Future, IFAC Congress, Barcelona 2002
DynLAB web-based courseon modeling and simulation
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Geez, Joe, now I wish I took that DynLAB course !
EU project DynLAB
The goal of the project within the Leonardo da Vinci EU program
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is to develop the
Course on modeling and simulationof controlled multidisciplinary systems
in a virtual lab
Project consortium: Czech Technical University in Prague Ruhr-Universitt, Bochum Institute of Technology Tallaght, Dublin EAS, Fraunhofer Institut, Dresden University of Sussex, Brighton
Project website: http://virtual.cvut.cz/dynlab/
Innovative style of the course
introducing learners to dynamics through simple examples to stimulatetheirinterestbefore exposing them to rigormath
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exposing learners to a unified, systematic and efficient methodology forrealistic modelling of multidisciplinary systems
giving learners access to a powerful tutor-monitored simulation systemacross the Internet
exploiting computers not only forequation solving, but also for theirformulationto minimise learners distraction from dynamics
giving learners a better feel for the topic by problem graphicalvisualisation and interactive virtual experiments
allowing different target groups to select an individual paths through the
course both for self-study and remote tutoring
Visualization of system dynamics
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3D movable model multipole diagram robot-arm trajectory
visualized by CORTONA set-up in DYNAST Shell simulated by DYNAST
Learning modes in DynLAB
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Ball-and-beam virtual experiment
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