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B i e n v e n u e

Faculty of Engineering and Natural Sciences

220314 |

Merseburg Universityof Applied Sciences

Faculty of Engineeringand Natural Sciences

INW

Lecture

Prof Dr-Ing Manfred Lohoumlfener Dean of the Faculty for Engineering and Natural Sciences

Professor of Mechatronic Systemshttpwwwhs-merseburgdeinw

Model Based Design of Mechatronic Systems

Hochschule MerseburgUniversity of Applied Sciences

Faculty of Engineering and Natural Scienceshttpwwwhs-merseburgde

httpwebhs-merseburgde~lohoefenBrno05Lecture-2014pdf

220314 Prof Dr M Lohoumlfener 3

Content

1Introduction

2Mechatronic Systems and Design

3Software Tools

4Modelling

5Simulations


Merseburg

x


MerseburgOver 1000 years old

Residence of German kings

About 35000 inhabitants

Industrial centre


UniversityUniversity site since 60 years

About 2800 students

About 300 staff members with 111 professors and lecturers

4 faculties


International Partners


~700 Students~700 Students

30 Professors and 30 Professors and LecturersLecturers

70 Employees70 Employees



Profiles Associated Institutes Networks

Fluid and Pump Technology reg ass

Research- and Consulting Centre of Machines and Energy Systems reg ass

Institute of Polymer Materials reg ass

Mechatronics Physics Tech-nology

Mechanical Engineering Production and Energy Technology

Industrial Engineering and Business Studies

Chemical and Polymer En-gineering

Process and Environ-mental Engineering Competence Network of Applied

and Transfer Oriented Research

PlasticsCompetenceCentre


International Partners (Examples)

TU Brno (CZ)Faculty of

Mechanical Engineering

TU Łoacutedź (PL)Faculty of Civil Engineering Archi-tecture and Environmental Engin-eering

Uni Riga (LV)Faculty of Physicsand Mathematics

Teachers ExchangeStudents ExchangeResearch Projects

JTUT Changzhou (CN)


Study Courses


Mechatronics Physics

Technologies

Chemical and Environmental Engineering



Technologies


MasterMasterBachelorBachelor

Chemistry Chemical

Engineering Pharmacy TechnologyCooperation

6161

126126

Industrial Engineering

and Business Studies

(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535

The numbers are the beginners last year

~300 new students per year


Akaflieg self-constructed ULA Pilot School

Urban Concept Car NIOS

Shell Eco-Marathon

Special Students Projects

Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD


In VDI guide line 2206 are some defini-tions

In our German working group ldquoMechatronicsrdquo we often use the definition by Harashima Tomizuka and Fukuda

Mechatronics

copy VDI guideline 2206 Design methodology for mechatronic systems Berlin Beuth 2004copy Harashima F Tomizuka M Fukuda T Mechatronics ndash ldquoWhat Is It Why and Howrdquo An Editorial IEEEASME Transactions on Mechatronics 1 (1996) 1 pp14


Mechatronics

ldquoMechatronics is an interdis-ciplinary design methodsolving mainly mechanicaldirected product tasks by thesynergetic spatial and func-

tional integration of mechanicelectric and information pro-

cessing subsystemsrdquo

VDIVDE GMA Technical Committee Mechatronics 2003

Mecha-nics

Electrics Electronics

Infor-matics

Mecha-tronics

Aktua-torics Sensorics

Model-ling

Microcon-trollers


Design Process

Mechanical engineeringElectrical engineeringInformation technologyPrototype

Time axis rarr

Parallel development in different departments ndash requires use of models

Classical product development

What we need


Design Process


Time axis rarr



What we need

copy httpuploadwikimediaorgwikipediacommonsddeAirbus_A380jpg


Better ldquoA model is the representation of substan-tial aspects of an ab-stract a planned or an ex-isting systems A model can exist as a theoretical imagination as an ab-stract system of signs or in reality of a determined material-energetic basis rdquo (Brockhaus abc Automa-tisierung Leipzig 1975)

Model

Short in DIN ldquoA model renders substantial char-acteristics of an original in a suitable mannerrdquo


VDI 2206

1 Introduction

2 Introduction to the de-velopment of mechat-ronic systems

3 Development methodo-logy of mechatronics

4 Application examples


The V model in product development (according to VDI 2206 Design methodology for mechatronic systems Beuth Berlin 2004)

httpwwwbeuthdedetechnische-regelvdi-220673296956

V Model


Design Process

Cyclic design process again and again hellip


Steps to Get a Model

1 Design an overall structure pay at-tention to inter-faces signals in-put and output of subsystems

2 Design of subsys-tems eg from analytic modelling differential equa-tions or transfer functions in block diagrams pay at-tention to state variables

3 Setting of para-meters eg get-ting technical dates from design drawings or from experimental modelling

4 Verification of the model with the real object if available

copy httpenwikipediaorgwikiSegway_PT


Steps to Get a Model Example

a) Is a Functional Specification re-quired

b) Which domains are to be con-sidered

c) How can we get a block diagram with all necessary sig-nals

copy httpmediabestofmicrocom32156926originalsegway_i2_technik2jpg


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods

Solving differential equation systems

Block diagram simulation

MultiMultidomaindomain

modellingmodelling

Description with VHDL-AMS

State flow

graphs

Real-timesimulation

VHDL-AMS Very High Speed Integrated Circuit Hardware Description Languageanalogue and mixed-signal extensions standard IEEE 10761-1999


Software Tools Requirements Solve differential equations Transform equations Solve difference equations Script language Graphical user interface

GUI Compiler for PC and mi-

crocontrollers Plotting graphs

Block diagrams State flow graphs Physical modelling Standardized Interfaces

ndash Other tools

ndash Digital and analogue IO simulators

Import and export of mod-els C- and VHDL-AMS-code

Block libraries hellip


MathWorks MATLABSimulinkCompany The MathWorks Inc

Web httpwwwmathworkscom

Price on request student version 89 USD

MATrix LABoratory ndash MATLAB

Scripts to execute as m file

Also symbolic calculation (CAS) possible

SIMULINK

Graphical input of block diagrams stored as mdl file

mdl-file can be called in M-script

RTW Real Time Workshop

Compilation to real-time models for different processors microcontrollers and for different operating systems or run-time systems

ldquoThe MathWorks delivers a complete set of tools for model-based design of con-trol systems ndash from the development of concepts to the application of software in embedded systemsrdquo

Market Leader


MathWorks MATLABSimulink

Overview from August 2009copy ftpftpmathworkscompubsseminarsSimEventsStateflowWebinarFilesStateflowTechnicalKitProductOverviewpdf


Real-Time Workshop

Rapid Prototyping


Commercial and Open Source All called software tool are

commercial programs with the benefits

ndash (Very) Good professional support

ndash Broad use in industry

ndash Further development will be done

ndash Libraries available

ndash Warranty is understood

Open source software can give us some advantages

ndash No runtime license costs

ndash inexpensive development tools

ndash Open source code allows to be verified of anyone

ndash Open source code can readily be used in future projects

ndash Further development with other suppliers easily possible no dependence on a certain supplier


Author John W Eaton

Web httpwwwgnuorgsoftwareoctave

httpoctavesourceforgenetpackagesphp

Price free

GNU-Octave

Scripts can be executed as oct or m file (compatible to MATLAB m file)

Characteristics

ldquoGNU Octave is a high-level language primarily intended for numerical computations It provides a con-venient command line interface for solving linear and nonlinear problems numerically and for performing other numerical exper-iments using a language that is mostly compatible with Matlab It may also be used as a batch-oriented languagerdquo

Documentation httpwwwgnuorgsoftwareoctaveoctavepdf

hellip And a GUI Its under development and to be tested


ScilabXcosOrganization Scilab Enterprises SAS Orsay

Cedex France

Web httpwwwscilaborg

Price Free

Scilab

Scripts can be executed as sci file (not compatible to MATLAB)

Xcos Graphical input of block diagrams stored as xcos

file (not compatible to Simulink mdl file) XCOS file can be called in SCI Script Multi domain simulation is available for electrical

and mechanical systems and for thermo-hydraulic elements

Documentation

httpwwwscilaborgsupportdocumentation


ScilabXcosExample

Inverted pendu-lum from

Scilab Demos rarr Xcos rarr Control Systems rarr In-verted pendulum


Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example

Model of a car with lift nod and roll oscillations (too complex to solve it in this lecture)


Example UnicycleModelling in several

ways

Block diagram in

ndash time domain with a classical integrator chain and in

ndash Laplace domain with transfer func-tions

Scripts with transfer functions

System of differential equation with solution in state space domain

Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics

From basic physics eg Newtons 2nd law we know the links between forces acceleration velocity and position eg

In mechanical engineering we need dynamic models to describe the dynamic behaviour of constructions based on the above mentioned laws So we have time derivations like

The Laplace operator s simplifies it to

msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t

a s=ssdotv s =s2sdotx s


Equations

mAsdotx A(t)+d Asdotx A(t)+k Asdotx A(t )=d Asdotx R(t)+k Asdotx R(t )

mRsdotx R(t )+d Asdotx R(t)+(k A+k R)sdotx R(t )=d Asdotx A(t )+k Asdotx A(t)+k Rsdotx S (t)

Differential equations

Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =

k Rk Ak Rd AsdotsmRsdots

2

G AR s=X Rs

X As =

k Ad Asdots

k Ak Rd AsdotsmRsdots2

Differential equation system

Msdotx (t )+ Dsdotx (t)+ Ksdotx (t )= F e(t)

GSA s=X As

X S s =

GSRssdotG RA s

1minusG RAssdotG AR s


Algorithm

1st step

Transpose the differential equation of nth order to the highest derivation

will become

2nd step

Set up of a chain of n integrators

3rd step

Connect the input of the chain in or-der of the equation

Derivations of the output signal are put from the integrator chain

All other signals and its derivations are input signals

4th step

For differential equation systems steps 1 to 3 are to be done for each differential equation and the result-ing block diagrams are to be con-nected with its signals to an overall block diagram

x= f y d n x

d t n= f x y

d n x

d t n= f x y

Algorithm to get a block diagram from a differential equation


Block Diagram Time Domain

Solved with Xcos

httpwwwhs-merseburgde~lohoefenBrno05Unicyclexcos

x A(t)=d AmA

( x R(t)minus x A(t))+k AmA

( x R(t)minusx A(t))

x R(t)=d AmR

( x A(t)minus x R(t ))+k AmR

( x A(t )minusx R(t))+k RmR

( x S (t )minusx R(t))


Block Diagram Time Domainx A(t)=

d AmA



x R(t)=d AmR




Solved with Simulink

httpwwwhs-merseburgde~lohoefenBrno05unicyclemdl


Block Diagram Laplace Domain

httpwwwhs-merseburgde~lohoefenBrno05Einrad_G(s)xcos

Transfer function simulated with Xcos


Single Transfer Function

httpwwwhs-merseburgde~lohoefenBrno05Einradsce

Solution with Scilab script


Single Transfer FunctionSolution with M-script in MATLAB or Octave

httpwwwhs-merseburgde~lohoefenBrno05unicycle_tfm


Time and Laplace Domain

Features Solution in time domain Solution in Laplace domain

Signals variables Includes also steady state variables

Includes only necessary variables

Functions connections blocks

Many functions blocks and connections shown in detail

Clearly only a few functions or blocks required

Initial values Simulation can start with initial values

All initial values must be zero

Nonlinearity Nonlinear functions are allowed in equation system

No nonlinear functions allowed

Time range Whole time range allowed -infin lt t lt infin

Only positive time range allowed 0 le t lt infin


Differential Equation Systems1st Sketch of mechanical sys-

tem

Marking of masses and inertia

Marking of mechanical ele-ments

Drawing of deflections and its directions

Drawing of forces and its dir-ections

2nd Fixing of time variant de-flection vector

3rd Force balance for any de-flection x

i(t)

Inertia force = sum of acting forces

4th Force basic equations

for spring damper friction hellip

5th Using force basic equa-tions with force balance

Natural dynamics = acting forces

xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)


Differential Equation Systems

Msdotx (t)+ Dsdotx(t)+ Ksdotx (t )= F e(t)

6th Representation as differ-ential equation system in matrix form

with the constant matrices

massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(

d 11 ⋯ d 1j ⋯ d 1n⋮ ⋮ ⋮d i1 ⋯ d ij ⋯ d in⋮ ⋮ ⋮d n1 ⋯ d ni ⋯ d nn

)

K=(k 11 ⋯ k 1j ⋯ k 1n⋮ ⋮ ⋮k i1 ⋯ k ij ⋯ k in⋮ ⋮ ⋮k n1 ⋯ k nj ⋯ k nn

)stiffnessmatrix

and the time variant force vec-tor

F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))


Differential Equation Systems7th Transformation in state

space representation

State space equation

Output equation

xSS (t)= AsdotxSS (t)+ Bsdotu (t)

y (t )=CsdotxSS (t)+Dsdotu(t)

Input vector u(t) State variables vector x

SS(t)

Output vector y(t) System matrix A Input matrix B Output matrix C Transfer matrix D

From

we get with the substitution and

or simplified

M ODEsdotxODE (t)+ DODEsdotxODE (t )+ KODEsdotxODE (t)= F e(t)xODE (t)= v (t) F e(t)=K esdotu(t)

[ xODE (t)vODE (t) ]=[ 0 1minusM ODE

minus1 sdotKODE minusM ODEminus1 sdotDODE ]sdot[ xODE (t)vODE (t) ]+[ 0

M ODEminus1 sdotK e

]sdot[ u (t )]

[ y (t )]=[ 1 0 ]sdot[ xODE (t )vODE (t )]+ [ 0 ]sdot[ u (t )] [ y(t )]=[ 1 0 ]sdot[ xODE (t )vODE (t )]

and



After all we only need thetransformation rules

x SS (t)=[ xODE (t)vODE (t ) ]A=[ 0 1

minusM ODEminus1

sdotKODE minusM ODEminus1

sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]

Scilab program (wwwscilaborg) Steady state transformation Using matrices M D K Ke

[nrnc]=size(M)

A=[zeros(nrnc) eye(nrnc) -inv(M)K -inv(M)D]

B=[zeros(nr1) inv(M)Ke]

C=[eye(nrnc) zeros(nrnc)]

Model=syslin(cABC)instants=00054 time axisy=csim(stepinstantsModel)xtitle(SimulationsResponse)plot2d(instantsy)


State Space Solution Scilab program 1Radsci Prof Dr M Lohoumlfener 26503 Data inputkA=32500dA=10000mA=1300kR=50000mR=20xS=1 differential equation system M=[mA 0 0 mR]D=[dA -dA -dA dA]K=[kA -kA -kA kR+kA]Ke=[0 kR] Transformation in state space[nrnc]=size(M)A=[zeros(nrnc) eye(nrnc) -inv(M)K -inv(M)D]B=[zeros(nr1) inv(M)Ke]C=[eye(nrnc) zeros(nrnc)]Einrad=syslin(cABC)instants=00014y=csim(stepinstantsEinrad)xtitle(Simulation EinradZeit t in sSprungantwort)xgrid(32)plot2d(instantsy)


Step response of the unicycledue to a pavementblue ndash wheel position black ndash body position

httpwwwhs-merseburgde~lohoefenBrno051radsce



State Space Solution

httpwwwhs-merseburgde~lohoefenBrno051_SSxcos

Solution with Xcos


Physical Modelling

Unicycle with SimMechanics


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Use of SimulationsExpectations Save time in develop-

ment Rapid software proto-

typing Avoid failures during

implementation of res-ults

Make experiments bet-ter to be avoided in reality

Make automated exper-iments

Get reproducible res-ults

Make a lot more exper-iments in the same time

Reduce costs for exper-iments


Model and Reality

Environment

Model Real

Object to be developed

Model MiL SiL

Real HiL Final Test

1 MiL Model in the Loopno real-time requirements

2 SiL Software in the Loopwith hardware interface

3 HiL Hardware in the Loopwith hardware test-bench

4 Final Test


Software in the Loop ndash SiLExplanation

A mechanical or electron-ic component as a part of a system is first imple-mented (realized) as a computer model simula-tion in software The computer is connected to the real world ie to the other parts of the system with a special interface to be tested and optimized


Example dSpaceDrive control with a real-time control-ler board DS1104 (dSpace)

Students project in the mechatron-ics lab in Merseburg

httpwwwdspacecom


Example dSpaceDesign of the PID-controller with Sim-ulink and dSpace library to connect the simulated con-troller with the ap-plication


Example dSpaceChange parameters and plot results during real-time test using ControlDesk (dSpace)


Hardware in the Loop ndash HiLExplanation

A mechanical or electron-ic component as a part of a system is manufactured as a real prototype To in-vestigate this prototype a computer simulates a real world as a model with a special interface to test and optimize the proto-type

Use

HiL simulation makes it possible to test a real sys-tem instead of a model

A complete environment is simulated to the object in real-time and the ob-ject has to react to virtual environmental influences

Important is the simula-tion of failure situations to electronic devices like cable corruption etc


Simulation and HardwareTest-bench with configura-tions of real vehicles

httpwwwipgde


Example LABCAR LABCAR software

modules Hardware components

Product of ETAS devel-opment and application tools for electronic sys-tems in automotive in-dustry

httpwwwetascomenproductsapplications_ecu_development-testing-labcar_component_overviewphp


Code GenerationWe tried several toolchains

Classical waydiams MATLAB Simulink

RTW

Additional compilerdiams dSpace

Alternative OSdiams Linux

Other tooldiams LabVIEW

Open source tools diams Scilab Xcos

Environment diams RTAI-Lab RTAI-Linuxdiams Linux with RT patches

Last trial diams SCALE-RT


MATLAB rarr RTAI-Linux

copy Dr C Schroumlder Ilmenau httpwwwimmsdeen


Scilab rarr RTAI-Laba) Add a Comedi AD block and con-nect it Close the window

b) RTAI CodeGen on the Super Block

c) Execute the real-time task dcmot -v

d) xrtailab -v

e) xrtailab adjust unitsdiv and secdiv

f) Visualize the signal on an oscillo-scope (ensure all grounds are well connected)

The laptop is a Fujitsu P-2040

Data acquisition hardware National Instruments PCMCIA DAQCard-6024E

copy RTAI-Lab tutorial Scilab Comedi and real-time control

Signal generation and visualization

httpwwwrtaiorg


SCALE-RTCombination of host sys-tem on Win-dows with MATLAB Simulink ScilabScicos and Com-pilers and target system on RTAI-Linux

Free for uni-versities

In short It works

httpwwwscale-rtcom


Future Tasksradic More useful tool chains also

for open source software is necessary

radic Useful tools for different mi-crocontrollers and RT OS

radic More support for open source tools is needed

radic RTAI Linux is well suited and has a support also for drivers with the COMEDI project but is difficult to maintain with the kernel development

radic The introduction of RT pree-mpt patches to the standard Linux kernel substitutes RTAI but a new driver framework must be developed

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Lecture

Prof Dr-Ing Manfred Lohoumlfener Dean of the Faculty for Engineering and Natural Sciences

Professor of Mechatronic Systemshttpwwwhs-merseburgdeinw

Model Based Design of Mechatronic Systems

Hochschule MerseburgUniversity of Applied Sciences

Faculty of Engineering and Natural Scienceshttpwwwhs-merseburgde

httpwebhs-merseburgde~lohoefenBrno05Lecture-2014pdf


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Merseburg

x





Industrial centre



About 2800 students


4 faculties



























JTUT Changzhou (CN)


Study Courses



Technologies




Technologies



Chemistry Chemical


6161

126126



(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535






Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








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Content

1Introduction


3Software Tools

4Modelling

5Simulations


Merseburg

x





Industrial centre



About 2800 students


4 faculties



























JTUT Changzhou (CN)


Study Courses



Technologies




Technologies



Chemistry Chemical


6161

126126



(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535






Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Merseburg

x





Industrial centre



About 2800 students


4 faculties



























JTUT Changzhou (CN)


Study Courses



Technologies




Technologies



Chemistry Chemical


6161

126126



(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535






Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68





Industrial centre



About 2800 students


4 faculties



























JTUT Changzhou (CN)


Study Courses



Technologies




Technologies



Chemistry Chemical


6161

126126



(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535






Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



About 2800 students


4 faculties



























JTUT Changzhou (CN)


Study Courses



Technologies




Technologies



Chemistry Chemical


6161

126126



(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535






Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



























JTUT Changzhou (CN)


Study Courses



Technologies




Technologies



Chemistry Chemical


6161

126126



(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535






Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Study Courses



Technologies




Technologies



Chemistry Chemical


6161

126126



(Dual Course)

2121

Polymer Engineer-

ing1919

3333

3535






Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

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Folie 46

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Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68




Shell Eco-Marathon


Ultra Light A

irplane


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

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Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Content

1Introduction


3Software Tools

4Modelling

5Simulations


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Mechatronic Systems

ABSABSESPESPASRASR

EDSEDS

ACCACC

MSRMSR

CANCAN

EHBEHBEGASEGAS

EMSEMS

GDIGDI

FSIFSIGMAGMA

MotronicMotronic

MOSTMOST

OBDOBD




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68




Mechatronics



Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Mechatronics





Mecha-nics


Infor-matics

Mecha-tronics


Model-ling

Microcon-trollers


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

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Folie 68


Design Process


Time axis rarr



What we need


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

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Folie 14

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Folie 60

Folie 61

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Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Design Process


Time axis rarr



What we need




Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

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Folie 13

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Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



Model



VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

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Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


VDI 2206

1 Introduction







V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

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Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68




V Model


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

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Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Design Process
















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

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Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68















Content

1Introduction


3Software Tools

4Modelling

5Simulations


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Simulations Methods




modellingmodelling


State flow

graphs

Real-timesimulation







ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68






ndash Other tools











SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68








SIMULINK






Market Leader





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68





Real-Time Workshop

Rapid Prototyping
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68
















Author John W Eaton



Price free

GNU-Octave


Characteristics






Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



Cedex France


Price Free

Scilab





Documentation



ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

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Folie 68


ScilabXcosExample




Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

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Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

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Folie 36

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Folie 56

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Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Content

1Introduction


3Software Tools

4Modelling

5Simulations

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

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Folie 61

Folie 62

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Folie 64

Folie 65

Folie 66

Folie 67

Folie 68

Complex Example




ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

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Folie 24

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Folie 33

Folie 34

Folie 35

Folie 36

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Folie 38

Folie 39

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Folie 51

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Folie 53

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Folie 56

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Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



ways

Block diagram in





Physical modelling

mA

kA

dA

kR

xR

mR

xS

FR

FA

FA

FR

xA

shock absorber

tire

wheel

carbody

street


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

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Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

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Folie 49

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Folie 51

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Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Dynamics




msdota t =F t

a t =d v t dt

=v t =d 2 x t

dt 2= x t



Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Equations




Transfer functions

GRA s=X As

X Rs =

k Ad Asdots

k Ad AsdotsmAsdots2

GSRs=X Rs

X S s =


2

G AR s=X Rs

X As =

k Ad Asdots




GSA s=X As

X S s =

GSRssdotG RA s



Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Algorithm

1st step


will become

2nd step


3rd step




4th step


x= f y d n x

d t n= f x y

d n x

d t n= f x y




Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



Solved with Xcos


x A(t)=d AmA



x R(t)=d AmR






d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



d AmA



x R(t)=d AmR

































tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68




























tem







i(t)






xT (t)=( x1(t) ⋯ xi (t ) ⋯ xn(t ))

msdotx i t =sum F t

F i (t )= f ( x(t) ⋯)






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68






massmatrix

dampermatrix

M= (m1 ⋯ 0 ⋯ 0⋮ ⋮ ⋮0 ⋯ mi ⋯ 0⋮ ⋮ ⋮0 ⋯ 0 ⋯ mn

)D=(


)


)stiffnessmatrix


F eT(t)=(F 1(t) ⋯ F i(t) ⋯ F n (t ))





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68





Output equation




SS(t)


From


or simplified




M ODEminus1 sdotK e

]sdot[ u (t )]


and





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68





minusM ODEminus1


sdotDODE ]B= [ 0

M ODEminus1

sdotK e]

C= [ 1 0 ]

D=[ 0 ]


[nrnc]=size(M)














Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68










Solution with Xcos


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Physical Modelling



Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68


Content

1Introduction


3Software Tools

4Modelling

5Simulations












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68












Model and Reality

Environment

Model Real


Model MiL SiL

Real HiL Final Test




4 Final Test







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68







httpwwwdspacecom








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68








Use






httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68



httpwwwipgde









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68









RTW














d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

Folie 58

Folie 59

Folie 60

Folie 61

Folie 62

Folie 63

Folie 64

Folie 65

Folie 66

Folie 67

Folie 68








d) xrtailab -v







httpwwwrtaiorg




In short It works

httpwwwscale-rtcom








Folie 1

Folie 2

Folie 3

Folie 4

Folie 5

Folie 6

Folie 7

Folie 8

Folie 9

Folie 10

Folie 11

Folie 12

Folie 13

Folie 14

Folie 15

Folie 16

Folie 17

Folie 18

Folie 19

Folie 20

Folie 21

Folie 22

Folie 23

Folie 24

Folie 25

Folie 26

Folie 27

Folie 28

Folie 29

Folie 30

Folie 31

Folie 32

Folie 33

Folie 34

Folie 35

Folie 36

Folie 37

Folie 38

Folie 39

Folie 40

Folie 41

Folie 42

Folie 43

Folie 44

Folie 45

Folie 46

Folie 47

Folie 48

Folie 49

Folie 50

Folie 51

Folie 52

Folie 53

Folie 54

Folie 55

Folie 56

Folie 57

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In short It works

httpwwwscale-rtcom








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