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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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