Efficient Modeling and Simulation of Multidisciplinary Systems across the Internet

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Efficient Modeling and Simulation of
Multidisciplinary Systemsacross the Internet
TUTORIAL

• Herman Mann
• Computing and Information Centre
• Czech Technical University in Prague

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Tutorial objectives

• After attending this tutorial you should be able
  to
• understand the difference between various
  approaches to modeling and their suitability to
  different tasks
• be able to apply the concepts of multipole
  modeling in different 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
  engineering dynamics at you school (if you are a
  teacher)
• interested in visiting the DynLAB web-based
  course on modeling 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 of computer 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
design space
trajectory of ideal design procedure (real one in
many loops)
blocks
multipoles
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Modeling simulation procedure

• System definition
• system separation from its surroundings
• system decomposition into subsystems
• identification of subsystem energy interactions
• Model development
• subsystem abstraction and idealization
• identification of subsystem parameters
• Formulation of
• equations for subsystems
• equations for subsystem interactions
• combined and reduced equations
• Equation solution
• Interpretation of the solution

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Simulation using Simulink

• System definition
• system separation from its surroundings
• system decomposition into subsystems
• Model development
• subsystem abstraction and idealization
• parameter identification
• Formulation of
• equations for subsystems
• equations for subsystem interactions
• combined and reduced equations
• Composition of a block diagram
• Block-diagram analysis
• 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)
force exerted by cylinder
master-shape waveform
workpiece-shape waveform
Behavioral description (block diagram for control
design)
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Copying lathe (3)
source of master- shape waveform r
source of pressure
cylinder mass
F
model of workpiece resistance
slide-bed friction
Topological description (multipole diagram for
physical design)
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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
  dynamic systems onto their topological
  configuration
• they portray graphically energy interactions
  between subsystems in the systems
• they can be combined with block diagrams, which
  represent 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 the system and between the
  subsystems and the surroundings
• by storing energy in the subsystems or releasing
  it later as well as by changes from one form to
  another.
• Therefore, before starting any dynamic
  investigation of a system we should clearly
• separate the system from its surroundings
• decompose the system into its disjoint subsystems

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Multidisciplinary system (1)
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Multipole models

• Multipole model approximates subsystem mutual
  energy interactions assuming that
• the interactions take place just in a limited
  number of interaction sites formed by adjacent
  energy entries into the subsystems
• the energy flow through each such entry can be
  expressed by a product of two complementary power
  variables

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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)
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)
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
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

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Power variables
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Measurement of variables
Direct measurement of through 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
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Postulate of Compatibility
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
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Simple rotational system
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Cold rolling mill
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Unified approach to modeling
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Other approaches (1)
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Other approaches (2)
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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

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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

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Jumping ball
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Translatory systems
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Quarter-car model
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Motor on vibration isolator
stop characteristic
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Impact of a long spring
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Torsional pendulums
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Weight-lifting mechanism
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Rotary-to-rotary coupling
Coupling ratio
Power consumption
Pure transformer
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Coupled gears
Pure transformer
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Gear trains (part 1)
Gear train Configuration n
External spur gears
Internal spur gears
Beveled gear pair
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Gear trains (part 2)
Gear train Configuration n
Planetgear
Skewgear pair
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Belt-and-pulley or chain-and sprocket
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Gear train with backlash
Backlash characteristics
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Rotary-to-linear couplings
Coupling ratio
Power consumption
Pure transformer
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Rotary-to-linear convertion
n - 1/r
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Rack-and-pinion gear-train
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Movable rack-and-pinion assembly
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Pulley or sprocket assembly
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Lead screw assembly
P screw pitch
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Slider crank
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Linear-to-linear coupling
Coupling ratio
Power consumption
Pure transformer
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Levers and pulleys
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Lever systems
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Planar oblique throw
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Central star and planet
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Math pendulums
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Planar systems
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Translatory joint fixed to frame
Multipole model
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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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Pulse-width modulator
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Astable multivibrator
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Three-phase thyristor rectifier
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Electro-mechanical systems
Conductor moving in a magnetic field
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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
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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
• 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

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DYNAST distributed simulation environment
Client
Server
Learning mng. system for course delivery
Web browser
DYNAST Shell for submitting diagrams or equations
and for plotting
DYNAST Solver for forming and solving equations
Internet
DYNAST Publisher for documenting simulation
experiments submodels
CORTONA for 3D animation of simulated systems
MATLAB for design of control for simulated systems
DYNAST Monitor for assisting learners in
modelling and simulation
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DYNAST Solver

• provides the computation power for the DYNAST
  system.
• It can
• compute transient and steady-state (static)
  solution of systems 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-state solution
• linearize nonlinear system models and provide
  system transfer functions and responses in a
  semisymbolic form
• compute frequency-domain characteristics in
  different forms

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DYNAST Solver
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Semisymbolic analysis
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DYNAST Shell

• provides a user-friendly working environment for
  DYNAST Solver.
• 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

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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
• 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.

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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 DYNAST
  Solver from their client computers.
• The supervisor can communicate with the users
  across the Internet and assist them in solving
  their problems.

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DYNAST in control design
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Modeling using MATLAB
Example 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
D. Tilbury, B. Messner Control Tutorials for
Matlab at http//www.engin.umich.edu/group/ctm/
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Inverse pendulum experiment
Multipole model of the open loop in DYNAST
working environment
pendulum model sensor of d2/dt cart
inertia source of force F cart friction
sensor of dx/dt integration of dx/dt
sensor of x
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DYNAST as modelling toolbox for Matlab
Validation of the open-loop model in DYNAST
Export of open-loop transfer functions to MATLAB
environment in M-file
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Analog PID control of inverse pendulum
Closed-loop model in DYNAST based on control
design in MATLAB
Closed-loop verification in DYNAST
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DYNAST MATLAB
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Current control curriculum criticised

• for
• exposing students to rigor math before motivating
  them by practical engineering issues
• presenting textbook problems carefully
  engineered to fit the underlying theory
• using computers to carry old exercises without
  exploiting them efficiently
• Future Directions in Control Education, IEEE
  Control Systems, October 1999

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Considerations for control education

• Automatic control education currently has a very
  narrow approach ...
• It is necessary to attach greater importance to
  all the design cycle of a control system
• Modelling and identification ... are a key factor
  for achieving a good design ...
• S. Dormido Bencomo Control Learning Present and
  Future, IFAC Congress, Barcelona 2002

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DynLAB web-based courseon modeling and simulation
Geez, Joe, now I wish I took that DynLAB course
!
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EU project DynLAB

• The goal of the project within the Leonardo da
  Vinci EU program
• is to develop the
• Course on modeling and simulation
• of controlled multidisciplinary systems
• in a virtual lab
• Project consortium
• Czech Technical University in Prague
• Ruhr-Universität, Bochum
• Institute of Technology Tallaght, Dublin
• EAS, Fraunhofer Institut, Dresden
• University of Sussex, Brighton
• Project website
  http//virtual.cvut.cz/dynlab/

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Innovative style of the course

• introducing learners to dynamics through simple
  examples to stimulate their interest before
  exposing them to rigor math
• exposing learners to a unified, systematic and
  efficient methodology for realistic modelling of
  multidisciplinary systems
• giving learners access to a powerful
  tutor-monitored simulation system across the
  Internet
• exploiting computers not only for equation
  solving, but also for their formulation to
  minimise learners distraction from dynamics
• giving learners a better feel for the topic by
  problem graphical visualisation and interactive
  virtual experiments
• allowing different target groups to select an
  individual paths through the course both for
  self-study and remote tutoring

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Visualization of system dynamics
3D movable model
multipole diagram robot-arm
trajectory visualized by CORTONA
set-up in DYNAST Shell simulated by
DYNAST
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Learning modes in DynLAB
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Ball-and-beam virtual experiment