ResearchDirector at Ecole Polytechnique de Lille http

Prof. B. Ould Bouamama Polytech Lille « Integrated Design of Mechatronic Systems using Bond Graphs» 1

Research Director at Ecole Polytechnique de Lille http://www.polytech-lille.fr/Head of the research group “Bond Graphs”, CRIStAL UMR CNRS9189»

Contact : [email protected] Web site : https://wikis.univ‐lille1.fr/ci2s/membres/belkacem‐ould‐bouamama

Prof. B. Ould Bouamama Polytech Lille « Integrated Design of Mechatronic Systems using Bond Graphs»

SKILLS and OBJECTIVES Systemic approach for global analysis of complex multiphysic

systems .

Dynamic modelling and simulation of complex systems

Training with new software's tools for integrated design and simulation of industrial systems.

Managing of multidisciplinary teams.

Keywords : Bond Graphs, Mechatronics, Integrated design, Simulation,

Dynamic Modelling, Automatic Control

2


Complexity associated with design of new systems Exchange of information and energy flows for control Complex Multiphysic Energetic Systems (complexity du of coupling of

several energies ): nedd of unified approach

Scientific and economical context Need of accurate model for virtual prototyping Energetic approach for design and monitoring of innovate systems

Economical challenge

3


ORGANISATION OF THE LECTURE Lecture

Illustrated by pedagogical examples and real systems Case Studies : Dynamic vehicle Simulation, Active suspension active, Robotics, Power

station, Hydraulic platform, …).

Case Study Integrated design of simulation platform of multiphysical system using specific

software's (Symbols2000, Matlab-Simulink..)

Required Knowledge : Physics :

• Conservative laws of mass, energy and momentum, thermal transfer, basis of mechanics, hydraulic, electricity, ….

Basis of simulation : • notion of causality, numerical simulation, …

Differential calculus and integral

4


Some References of the lecturer1. Bond graphs for modelling

J. Thoma et B. Ould Bouamama « Modelling and simulation in thermal and chemical engineering » Bond graph Approach , Springer Verlag, 2000.

B. Ould Bouamama et G. Dauphin-Tanguy. « Modélisation par Bond Graph. Eléments de Base pour l'énergétique ». Techniques de l'Ingénieurs, 16 pages BE8280

B. Ould Bouamama et G. Dauphin-Tanguy. « Modélisation par Bond Graph. Application aux systèmes énergétiques ». Techniques de l'Ingénieurs, 16 pages BE8281.

B. Ould-Bouamama. La conception intégrée pour la surveillance robuste des systemes. Approche Bond Graph. Techniques de l'Ingénieurs AG3550. 24 pages 2013.

B. Ould-Bouamama. Contrôle en ligne d'une installation de générateur de vapeur par Bond Graph. Techniques de l'Ingénieurs AG3551. 28 p., 2014

2. Bond graphs for Supervision Systems Design A.K. Samantaray and B. Ould Bouamama « Model-based Process Supervision. A Bond Graph Approach» . Springer Verlag, Series: Advances

in Industrial Control, 490 p. ISBN: 978-1-84800-158-9, Berlin 2008. B. Ould Bouamama et al.. «Model builder using Functional and bond graph tools for FDI design». Control Engineering Practice, CEP, Vol.

13/7 pp. 875-891. B. Ould Bouamama et al.. "Supervision of an industrial steam generator. Part I: Bond graph modelling". Control Engineering Practice, CEP,

Vol 14/1 pp 71-83, 2005. Part II: On line implementation, CEP, Vol 14/1 pp 85-96, 2005.. B. Ould Bouamama et al. « Software for Supervision System Design In Process Engineering Industry. » 6th IFAC, SAFEPROCESS, , pp.

691-695.Beijing, China, 29-1 sept. 2006.

5

Publications and co publications in the BG and FDI domain

6


CONTENTS (1/2) CHAPTER 1: Introduction to integrated design of engineering systems

Definitions, context Why an unified language and systemic approach Different representations of complex systems, Levels of Modelling Modeling tools for mechatronics Why bond graph ? What we can do with bond graphs. Methodology of Fast prototyping , Hardware in the Loop (HIL), Software in the Loop (SIL) Interest of Bond graph for Prototyping

CHAPTER 2: Bond Graph Theory Historic of bond graphs, Definition, representation Power variables, Energy Variables True and pseudo bond graph Bond graph and block diagram Basic elements of bond graph (R, C, I, TF, GY, Se, Sf, Junctions,….) Model Structure Knowledge Construction of Bond Graph Models in different domains (electrical, mechanical, hydraulic, …)

7


CONTENTS (2/2)

CHAPTER 3: Causalities and dynamic model Definitions and causality principle Sequential Causality Assignment Procedure (SCAP) Bicausal Bond Graph From Bond Graph to bloc diagram, State-Space equations generation Examples

CHAPTER 4: Coupled energy bond graph Representation and complexity Thermofluid sources , Thermofluid Multiport R, C Examples

CHAPTER 5: Automated Modeling and Structural analysis Bond Graph Software's for dynamic model generation Integrated Design for Engineering systems Bond Graph for Structural analysis (Diagnosis, Control, …) Application

8


Chapter 1

Introduction to integrated design of engineering systems

9


Motivations

Complexity of systems are due of coupling of multi energies (mechanical, electrical, thermal, hydraulic, …). Example : Power station :

Why dynamic modeling ? Design, Analysis , Decision, Control, diagnosis, ….

Which skills for this task Multidisciplinary project management

Which kind of tool I is needed ? Structured, unified, generic,

10


What is Mechatronic Systems

Mecatronics (« Meca »+ « Tronics » Engineering systems putting in evidence multiple skills

• Mechanics : Hydraulics, Thermal engineering, Mechanism, pneumatic• Electronics : power electronics, Networks, converters AN/NA, Micro controllers, • Automatic control : Linear and nonlinear control, Advanced control, Stability, … • Computer Engineering : Real time implementation

Why Mechatronics ? Integrating harmoniously those technologies , mechatronics allows to design new

and innovative industrial products simpler, more economical, reliable and versatile (flexible) systems.

Définition : « Utilisation simultanée et en étroite symbiose des techniques du génie mécanique, de l'électronique, de l'automatisme et de la micro-informatique pour envisager de nouvelles façons de concevoir et de produire, créer de nouveaux produits plus performants et de nouvelles machines ».

11


Mechatronics ; Synergetic Effects

Informationtechnology

System theoryAutomatic controlComputer engineeringDiagnosisArtificial IntelligenceSoftware

ElectronicsPower electronics,Networks, converters AN/NA,Micro controllersActuators,Sensors

MechanicsHydraulics, Thermal engineering,MechanismPneumaticMechanical elelentsPrecision mechanics

MECHATRONICS

12


Examples of Mechatronic systems Examples of Mechatronic systems include:

Remotely controlled vehicles such as the Mars Rover• A rover is a space exploration vehicle designed to move across the surface of a planet or other

astronomical body.– Control of Take- off and up to exploration of Mars planet– Remote control– Embeded supervision,, net work communication– Virtual simulation ….;

design of Hybrid vehicle• Electrical part;• Mechanical energy• Electrochemical part• Control (software, sensor, …)• Network

13


From Electromecanical to Mechatronic systems

Before 1950 Complex systems are studied as electromechanical sub systems

Around 1950 Emergence of semi conductors, electronic control and power

electronics. 1960-1970 Design of microcontrollers because of appearance of computer

engineering. Possibility to design embedded control systems more efficient

1969 : “Mechatronics” was first introduced in Japan YaskawaElectric Corporation

14


Methodology for Fast prototyping

15

Development of generic models and Control algorithms

Industrial validation

Validation using HiL

Test

Validation using SiL

Test

Test

Validation using MiL


Tests in Mechatronic systems (1/2) Tests can be executed using

Dynamic models (Model-in-the-Loop, MiL), Existing function (Software-in-the-Loop, SiL), Or a real industrial computer (Hardware-in-the-Loop, HiL)

MiL (Model in the Loop)• Test object : model• Input signals are simulated• Output signal values are saved to be compared to the expected values• Automatic test execution through:

– – The development environment used for modeling– Specific software's (MATLAB/Simulink)

16


Tests in Mechatronic systems (2/2) SiL (Software in the Loop)

• Test object: generated code• Environment is simulated• The inputs and outputs of the test object are connected to the test system• The generated code is executed on a PC or on an evaluation board• Automatic test execution through:

– – use of MATLAB/Simulink with Realtime Workshop)– – Interfaces to external tools

HiL (Hardware in the Loop)• Test object: real ECU• Environment simulation through environment models (e.g.: MATLAB/Simulink)• Inputs and Outputs are connected to the HiL-Simulator• Comparison of the ECU output values to the expected values• Automatic test execution through the control software of the HiL-Simulator

17


Steps in fast prototyping

ECU : Electronic Control Unit

ECU Tests by HIL simulation

System/Component Design & Simulation

Rapid Prototyping

Tests Plans

Final testsFinal tests

FunctionalAnalysis

Models

ECU

OutilsIntegration/validation on hybrid bench

TechnicalSpecifications

System equirements

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RequirementsOverall functionsvaluesCosts & milestones

SpecificationsFulfilment of requirementsLimitationsReliability and safety

System designPartinioningMulti-physics componentWord Bong GraphPower exchange

Modeling & SimulationModels of componentsKinematic & dynamic behaviorsSimulation according to the requirements

Component DesignPhysical component: mechanics, electronics, ….Mechanical CADController, HMI,…Space optimisation

Hardware IntegrationAssemblingCouplingOptimisation

Software IntegrationSignal analysisFiltringTest of algorithms

System testingBehavioral testsStress testingReliability and safetyMonitoring and supervision

Field TestingFinal productNorm & certificationStatistics

ProductionSimultanousplanningTechnologiesQuality control

MechatronicComponents

Mechanics, Electronics, Control, Software (HMI)

Component Tests & AnalysisHardware in the loopsimulation,Stress Analysis,..

PrototypesLaboratory test benches

Test and measurementsAlgorithms

i mplementation

Integrated design : From modellingto industrial test

19

Deming wheel - PDCA cycle : Tool for quality management : W. Edwards Deming (1950)

PlanIdentify objectives

Formulate hypothesisDefine validation criteria

Plan

DoCheck

Act

DoBuild model

CheckCausal analysis

Structural analysisSimulation

ActCriticize simulation

resultsIdentify further needs

P

DC

ARoue Deming

Interest of using bond graph tool for new product designing or improvement of existing productsDeming wheel

20


Bond Graphs : Tools for Integrated Design Bond graphs Bond graph is an unified graphical language used for any

kind of physical domain. The tool is confirmed as a structured approach for modeling and simulation of multidisciplinary systems.

Bond graphs for modelling and more… Because of its architectural representation, causal and

structural properties, bond graph modelling is used not only for modelling but for : • Control analysis, diagnosis , supervision, alarm filtering • Automatic generation of dynamic modelling and supervision algorithms• Sizing • Used today by industrial companies (PSA, Renault, EDF, IFP, CEA, Airbus,…) .

21


LEVELS OF MODELLING

WhatWhat

to do ?to do ?WhatWhat

to do ?to do ?1. Technological

2. Physical Energy description ( Storagee, dissipation, ….

3. Mathematical dxyxfxi ),(

4. Algorithmic

This level constructs the architecture of the system by the assembly of different sub-systems, which are the plant items (heat exchanger, boiler, pipe...). The technological level can be represented by the so-called word bond graph.

The modelling uses an energy description of the physical phenomena based on basic concepts of physics such as dissipation of energy, transformation, accumulation, sources , …). Here, the bond graph is used as a universal language for all the domains of physics.

Level is represented by the mathematical equations (algebraic and differential equations) which describe the system behavior.

22


THE FOUR LEVELS IN THE BG REPRESENTATION A Word bond graph : technological level

is used to make initial decisions about the representation of dynamic systems Indicates the major subsystems to be considered As opposite to block diagram the input and outputs are not a signals but a power

variables to be used in the dynamic model

A bond graph is a graphical model : physical level The phenomena are represented by bond graph elements (storage, dissipation, inertia

etc..)

From this graphical model (but having a deep physical knowledge) is deduced Dynamic equations (algebraic or differential) : mathematical level Simulation program (how the dynamic model will be calculated) is shown by causality

assignment : Algorithmic level

23


Chapter 2 : Bond Graph Theory

CHAPTER 2: Bond Graph Theory Historic of bond graphs, Definition, representationPower variables, Energy VariablesTrue and pseudo bond graphBond graph and block diagramBasic elements of bond graph (R, C, I, TF, GY, Se, Sf,

Junctions,….)Model Structure KnowledgeConstruction of Bond Graph Models in different domains

(electrical, mechanical, hydraulic, …)

24


Founders

J. Thoma

25

Paynter and Einshtein

26

THE FIRST IDEA The first system used by Paynter teaching in the Civil Engineering Department at MIT and first ideas

27


(The Gestation and Birth of Bond Graphs by Prof. H.M. Paytner (c. 2000) My efforts were also strongly motivated by a preoccupation with the logical

philosophy underlying analogies in general.” When these analogous devices were reduced to equations for computer simulation, distinctions became completely blurred. We lay down a fundamental principle of generalization by abstraction: “

Mes efforts ont également été fortement motivés par une préoccupation avec une philosophie de la logique qui sous-tend les analogies en général. "Lorsque les dispositifs analogues ont été réduits à des équations pour la simulation par ordinateur, les distinctions deviennet complètement floues. Nous établissons un principe fondamental de généralisation par abstraction:

28


HISTORIC OF BOND GRAPH MODELLING

Founder of BG : Henry Paynter (MIT Boston) The Bond graph tool was first developed since 1961 at MIT, Boston, USA by

Paynter ‘April, 24 , 1959) Symbolism and rules development :

• Karnopp (university of California), Rosenberg (Michigan university), Jean Thoma (Waterloo)

Introduced in Europe only since 1971. Netherlands and France ( Alsthom)

Teaching in Europe , USA … France : Univ LyonI, INSA LYON, EC Lille, ESE Rennes, Univ. Mulhouse, Polytech’Lille, ….. University of London, University of Enshede (The Netherlands), Waterloo..;

Companies using this tool• Automobile company : PSA, Renault• Nuclear company : EDF, CEA, GEC Alsthom• Electronic :Thomson, Aerospace company ....

29


DEFINITION, REPRESENTATION DEFINITION

REPRESENTATION

Exchanged Power is P = e.fe

f

1 2

Mechanical power :

30


Bond as power connectionThe power is represented by the BOND

Bond

The direction of positive power is noted bythe half-arrow at the end of the bond

direction of power

31

INFORMATION BONDS The signal is represented as

information bonds: no power

Example : Sensors• Detector of effort such as pressure,

voltage, temperature

• Detector of flow such as current, hydraulic flow

Information Bonds for signal exchange

Dee

f=0

Dee=0

f 32


Some definitions (1/2) BOND GRAPH MODELING

Is the representation (by a bond) of power flows as products of efforts and flows with elements acting between. These variables and junction structures to put the system together.

Bond graphs are labeled and directed graphs, in which the vertices represent submodels and the edges represent an ideal energy connection between power ports.

CEdge (bond)

Exchanged powerC

vertex

Submodel(Component)

capacitor

E

vertex

Submodel(Component )

Battery

E

33


Some definitions (2/2) The vertices are idealized descriptions of physical phenomena: they are

concepts, denoting the relevant aspects of the dynamic behavior of the system.

The edges are called bonds. They denote point-to-point connections between submodel ports.

The bond transports a power as product of two generic energy variables

Which generic variables are used ?

34


1. Power variables

Power variables are classified in a universal scheme and to describe all types of multiports in a common language.

35

Power variables

Intensive variable• Temperature• Pressure• Voltage.

Effort variable e(t) Flow f(t)

Derivative of extensive variable• Entropy flow• Volume flow• current

POWER VARIABLES FOR SEVERAL DOMAINS

Electrical

DOMAIN

Mechanical (rotation)

Hydraulic

Chemical

Thermal

Economic

Mechanical(translation)

VOLTAGE

u [V]

CURRENT

i [A]FORCE

F [N]

VELOCITY

v [m/s]

FLOW (f)EFFORT (e)

TORQUE

[Nm]

ANGULAR VELOCITY

[rad/s]

UNIT PRICE

Pu [$/unit]

FLOW OF ORDERS

fc [unit/period]

PRESSURE

P [pa]

VOLUME FLOW

dV/dt [m3/s]

TEMPERATURE

T [K]

ENTROPY FLOW

dS/dt [J/s]

CHEM. POTENTIAL

[J/mole]

MOLAR FLOW

dn/dt [mole/s]

36


Why pseudo bond graph in proccess engineering ?

In process engineering systems, each plant item is associated with a set of process variables. The number of variables is higher than DOF

• For hydraulic : Pressure-mass flow, volume flow• For thermal: température, specific enthalpy _entropy flow, enthalpy flow,

thermal flow, quality of steam….• For chemical : chemical potential, chemical affinity, molar flow…

Complexity of used variables• Use pseudo bond graphs allows to manipulate more intuitive variables and

easily measurable (concentration, enthaly flow, …) therefore easy to simulate.

• Entropy is not conserved • ….

37


PSEUDO BOND GRAPH

Thermal

HydraulicPRESSURE

P [ pa ]

MASSE FLOW

[ Kg /s ]m

ChemicalCONCENTRATION

C [ mole/m3]

MOLAR FLOW

[ mole/s]n

TEMPERATURE

T [K]

HEAT FLOW

[W ]Q

CONDUCTION

ENTHALPY FLOW

[ W ]HSPECIFIC ENTHALPY

h [ J/kg ]

CONVECTION

TEMPERATURE

T [K]

FLOW (f)EFFORT (e)DOMAIN

38

2. ENERGY VARIABLES The momentum or impulse p(t), (magnetic flow, integral of pressure,

angular momentum, … )

The general displacement q(t), (mass, volume, charge … )

)()()( 00

tpdetpt

t

)()()( 00

tqdftqt

t

t

txmFFdtxmtp

0

)(:Momentum

39


Why energy variables ?

pq dppftdqqet )()(,)()( EE

ENERGY VARIABLESThe momentum or impulse p(t), (magnetic flow, integral of pressure, angular momentum, … )

)()()( 00

tpdetpt

t

The general displacement q(t), (mass, volume, charge … )

)()()( 00

tqdftqt

t

Why energy variables ?

1

0

1

0

1

0

1

0

1

0

20

21p

20

21p

21)()()(E

21.)()(E

qq

qq

qq

xx

qq

qqC

dqCqdqqudqqet

kxkxxdxkdqqetEnergy stored

by a spring

40


Energy variables : analogy

dtVVxVfPe

idtqxifue

dtQQxQf

Te

dtxxxxf

Fe

Liudtpifue

xMFdtpxf

Fe

P,V u,q

iQ

Q,T

x

x, F

Displacement

xF,

u,

i

Impulse

41

ENERGY VARIABLES FOR SEVERAL DOMAINS

Electrical

DOMAIN

Mechanical (rotation)

Hydraulic

Chemical

Thermal

Economic

Mechanical (translation)

CHARGE

q [Coulomb]

FLUX

Φ [Wb]DISPLACEMNT

x [m]

MOMENT

J [Ns]

Impulse (p)Displacement (q)

ANGLE

[rad]

ANGULAR MOMENTUM

[Nms]

accumulation of orders qe

Economic momentum Pe

VOLUME

V [m3]

MOMENTUM pp

Ns/m2

Nbr of MOLE

n [-]

?

ENTROPY

S [J/K]

?

42

p y yPower variables: How to select them in multiphysic system ?

43

Chemical, Electrochemical

The

rmod

ynam

ic

Economic

Electrical

ThermalMechanical

Hydraulic

Is used just a pair of variables:1. Intensive variable : effort variable e(t))2. Derivative of extensive variable : flow variable f(t)

43

44

H2

H2O

O2Anode CathodeElectrolyte

Oxydation2H2 → 4H+ + 4e-

-

H+

ReductionO2 + 4e- + 4H+ → 2H2O

+

e-

H+

1) The FC is based on oxidation-reduction principle. It produces electricity from fuel, which react in the presence of a catalyst. A hydrogen FC cell uses H2 as its fuel and O2 as its oxidant.2) At the anode, a platinum catalyst causes the hydrogen to split into positive hydrogen ions(protons) and negatively charged electrons

3) The Polymer Electrolyte Membrane (PEM) allows only the positively charged protons to pass through it to the cathode while the negatively charged electrons must travel along an external circuit to the cathode, creating an electrical current.

4) At the cathode, the electrons and positively charged hydrogen ions combine with oxygen to form water, which flows out of the cell.

Fuel Cell system

45

How th electricity is producedThe enthalpy1 of this global reaction is the difference between the enthalpy of products and the reactants, so:

Enthalpy is a measurement of energy in a thermodynamic system. It is the thermodynamic quantity equivalent to the total heat content of a system. It equals to the internal energy of the system plus the product of pressure and volume.

H=U+PV

The negative sign in here means this amount of energy is released in this reaction, so for this exothermic reaction, 286kJ of energy is released per mole of H2 consumed during the overall reaction

46

How th electricity is producedHowever, not 100% of the enthalpy can be converted into electricity. A certainamount of enthalpy is inherent cannot be converted into work, i.e., only part of the286kJ being released per mole H consumed during operation may betransferred to electricity.

This part of energy is the Gibbs free energy ΔG, where,

Gibbs free energy : The greatest amount of mechanical work which can be obtainedfrom a given quantity of a certain substance in a given initial state, withoutincreasing its total volume or allowing heat to pass to or from external bodies

The electrical work is the product of charge and potential, the theoretical potentialthat could be driven from this energy is:

F is the faraday constant, valued as 96485 (C/mol), n stands for the number ofelectrons involved in the overall reaction per mole of hydrogen being consumed

47

How th electricity is producedIn fact, electrochemically, the potential the electrodes could provide would be deviatedfrom 1.23 V if it is not working in the standard condition:

where a stand for the activity of different species

Generally, the losses can be categorized to three partsActivation losses due to the electrode kinetics in order to providecontinuous electrical current by giving necessary activation energy duringthe electrochemical reaction. Basically, the activation loss could be deduced from the Tafelequation on the electrodes, and may have the formulation of:

48

How th electricity is producedwhere α is the transfer coefficient, i is the current density, and the ih is the exchange current density on the electrode. It may be in a form of

Ohmic losses : caused by the resistance either to the flow of the ions in the proton electrolyte membrane, or of the electrons in the electrically conductive parts in the fuel cell such as the bipolar plates, GDL, etc.

R' is the total cell internal resistance.Concentration losses :usually happening when the reactant gases areconsumed rapidly.

49

How th electricity is produced

These three voltage losses happened on each cell would considerably influence theoutput performance of the PEMFC stack. They are dominated in zone I, II,

50

Word Bon dgraph and Which power variables are usedWord Bon dgraph and Which power variables are used

Source of H2

Source of O2

Electro chemical reaction

Thermo -chemical reaction

Mechanical part

Pump

Pipe

ReactorEconomical market

Resistor Ambiance

Pm

P

m

nT

H

µ

Electrical Part

Thermal source

U i

TQ

C

Voltage source

G H

Faraday Phenomena

U

i

U

i

PmTH

pu

fc

Ui

H T PmQ T

51


EXAMPLE1 : ELECTRICAL INDUCTION MOTOR

ua

ia

LOAD

(J,f)

ELECTRICAL PART MECHANICAL PART

RaLa

ELECTRICAL PART

ua

ia

MECHANICAL

PART

LOAD

52

EXAMPLE 2: POWER STATION

RECEIVER

HEATER

TH HQ

BOILERTW

WH

PW

WmTB

BH

PB

Bm TURBINETR

RH

RmPP

PUMP PIPETP

PH

PP

Pm

FEED WATER

STEAM

HEATER

TURBINE

PUMPRECEIVER

U i

LoadMOTOR

U

isource

53

Each subsystem can be détailled

SG Liquidephase T1

P1

1m

1HT2

P2

2m

2HT3

P3

3m

3H

P4

T4

P5

T5

P6P7

P8

T6T7

T8

4H5H6H7H

8H

4m5m6m

7m

8m

HP turbine

Condenser

LP turbine

Condensa-te PumpPreheaterFeed

pump

SG Vapor phase

54

What about physical phenomena : Generic Physical elements R,C,I, TF,GY, Se,Sf

Se

Sf

Sf

Se

R

R

R

R

R

GY

TF

I

II

I

C

C

C

C

C

55

BOND GRAPH ELEMENTS

ACTIVE ELEMENTSGenerate and Provide a power

to the system

SfSe

One port element

R,C,I,Se,Sf 0,1

Tree ports element

BOND GRAPH ELEMENTS

PASSIVE ELEMENTS(transform received power into dissipated (R) or stored (C, I)

energy

R C I

TF, GYTwo ports element

JUNCTIONSConnect different elements of

the systems : are power conserving

TF, GY0,1

They are not a material point (common effort (0)

and common flow ((1)

Energy transformation or transformation from one

domaine to another

56

Structural Model

u

y

ein fin

Dout

Sources

Se, Sf

Structure de Jonction

0, 1, TF, GY

Dissipation

d’énergie

R

Stockage

d’énergie

I , C

Capteurs

De, Df

eout fout

57

First examples (1/3)

L1

Se C1

R1

iR1

iC1

1

R:R1

iUR

Uc

ii

ESe

I:L1

C:C1

MSe:mg

k

Friction : f

x

1x 1

R:fFR

FcmgSe

I:M

UL i

FI

x

x

xx

Spring

M

Friction

C:kSpring

Inertia of mass

Force

58



E

R1

g

C

i

Uc

UR

1

R:R1

iUR

C:C1Uc

iSe:E

i

E

59



T2

On-Off

V o

QOPI

T1

60

Bond graph model of an hydraulic system

Tank2

0

C:C1

De2

6

Tank1

0

C:C1

De1

2

Pump

MSf11

T2

On-Off

Valve1

1

R:R1

43 5

Valve 2

1

R:R2

Se17

89

PIu1

On-off

USER

u3

PI

T1

Vo

QO

Out

flow

to c

onsu

mer

61


Bond graph well suited for automated modelling : softwares

JunctionsJunctions

Passive elementsPassive elements

Active elementsActive elements

JunctionsJunctions

62

63

Specific softwares for Bond graphg automatic modelling

Symbols Shakti software 20sim software

Only Bond Graph tool can be used for automatic generation of dynamic models !!!


Lets’ Learn Bond Graph theory

64


Passive elements Definition The bond graph elements are called passive because they transform

received power into dissipated power (R-element), stored under potential energy (C-element) or kinetic (I-element).

Representation

65

R:R1feΣ

C:C1feΣ

I:LfeΣ

R: means R element

R1: Name of the element

Resistive R element

66

v1 v2

i

021

RiUUvv

128

4DR

p1

p2

V

0 xRF

x

F

R

0P RV 0T RQ

Tr

Ta

0, feRR Constitutive equation : For modeling any physical phenomenon characterized by an effort-flow relation ship

fR:R1Representation e

AR

Capacitive C element (capacitance)

C Constitutive equation (For modeling any physical phenomenon characterized by a relation ship between effort and flow

Electric Hydraulic

h

t

t

mcCCQdtQ

CT

dtTmcdQQQ

1

.)(21

0,, qefdte CC

fC:C1Representation e

Thermal

mcT

1Q 2Q

Cqidt

CU

dtUCd

dtdqiii

1

).(21

p

A: sectionh: level: densityCh= A/g

i

V

,

h

d AhV P gh

dtg Vp Vdt

A C

F

F

1 ,dFxK dt

F K xdt Kx

x

Mechanical

67

Mechanical and electrical capacity

1 2

v

1i 2i

0C

K

1 2C K dt 1 20

1v i i dtC

C

0

C:1/K

0

C:C0

1 2i i

1 2 1i2i

1 2 vc

68

Inertial I element (Inertia) Electric Hydraulic Mechanical Thermal

p1 p2

V

l

AlI

VIp

PdtI

Pdtl

AV

dtVd

AlA

dtdv

Am

AFPP

0

1

2

p : impulsion of pressure0

01

Li

UdtL

i

: Magnetic flux

V1 V2i

0

11

.

xIQ

IQFdt

IFdt

mx

dtxdmF

F

Q : momentum

????

0,, pfedtf II

fI:I1Representation e

I Constitutive equation (For modeling any physical phenomenon characterized by a relation ship between flow and effort

69

Mechanical and electrical inertia

1C 2C

1v 2v

iJ L

1 21 c c dtJ

1 21i v v dtL

11C

2C

I:J

1 2C C

11v

2v

I:L

1 2v v i

i i

70


Two ports power conservative element(with out storage and dissipation)

71

f1

TF:m

e1

f2

e2

f1

GY:m

e1

f2

e2

2211 .. fefe

TRANSFORMER Convert energy as well in one physical domain as well between one physical

domain and another Examples: lever, pulley stem, gear pair, electrical transformer, change of physical

domain….

Representation

f1

TF:m

e1

f2

e2Defining relation

e1 = m.e2,f2 = m.f1

Where m : modulus

Simple transformer

Modulated transformer (m is not cste)

f1

MTF:m

e1

f2

e2u

Defining relatione1 = m(u).e2,f2 = m(u).f1

72

EXAMPLES OF TRANSFORMERS

TF:m

1u

1i

2u

2i

u1 u2

i2i1

Electrical transformer

xF ,

VP ,

Hydraulic piston

TF:1/A

P

V

F

x

VA

x

FA

P

.1

1

Hydraulic power is transducted

into mechanical power

A : area of the piston

TF:b/a

12

21

.

.

xabx

FabF

F2F1

1x 2x

F2

F1

2x

1x

a b

Lever

1 1 2 2F x F x

1 1 2 2u i u i

1 2

2 1

u mui mi

73

Examples of TF elements

74

12 1

2

11 2

2

RRRR

1

2:

TFRR

1

12

2

Gearing

,

power conservation : xF

Rack and pinion R

,x F

:TF

R

x

F1 xRRF

1 1 2 2

1 1 2

2 2 1

RiR

i<1 i=1 i>1Reducer of the velocity No change of speed Speed increase

Increase in torque No change of torque Decresae in torque

4. GYRATOR Convert energy as well in one physical domain as well between one

physical domain and another Examples: Gyroscope, Hall effect sensor, change of physical domain….

Representation

f1

GY:r

e1

f2

e2

Defining relatione1 = rf2e2 = rf1

Where r : modulus

f1

MGY:r

e1

f2

e2

u

Modulated Gyrator (if r is not cste)

Defining relatione1 = r(u)f2e2 = r(u)f1

75

Example of gyrator : DC motor

u

i

GY:r

Electrical Power ui Mechanical

Power

Ui = Defining relation

= kiu= k

Where k : modulus

Power Conservation :

76

GY:r

u

i


ACTIVE ELEMENTS

Elements that provide powerThey provide effort or flow:

Se or Sf

77

Source of effort, Source of flow

78

EFFORT AND FLOW SOURCES Se, SfA source maintains one of power variables constant or a specified function of time no matter how large the other variable may be.

fSf:f(t) e

Sf = f(t) = cste

Current generator, applied velocity..

Source of flow

fSe:e(t)

e

Se = e(t) = cste

Generator of voltage, gravity force, pump, battery

Source of effort

Sources can be modulated (controlled)

T1

PC

T1

Tank1

0

C:C1

De1

De1

Pump

MSf1

PIu

Pump

Sf1

Tank1

0

C:C1

De1

De1

u

( )V F u

( )V F u V cste

V cste

PI

79


Junctions

How to connect different subsystems ?

80


JUNCTIONS (1/6)

0 - JUNCTION “ Common effort junction”

0.... 44332211 fefefefe

Power conservation

0.1

n

iiii fea

ai = +1 if 0

ai = -1 if 0

0e1

e2e3

e4

f1

f2

f4

Representation

f3

Defining relation

02341

4321

ffffeeee

81

JUNCTIONS (2/6) : Examples of 0-junction

EC

R

i i1

i2

0E

i i1

Ei2

E

R

C

Se:E

i = i1 + i2

0

C:1/k

3x

1V

2V

3V 0P

1V

P 2V

3VP

321 VVV

2x 1

I:Mc

2x

Mc

Mp

2x

1x

Se:Fr

C:1/k

1

I:Mp

1xSe:Fr

1x

R:RV

C:Ch

Rv

Ch

:Sf V

82

( ) gyJonction (3/6) : Conservative energy laws

aQ

UT

0 sce mmm

0

C:Ch

aQ cmPUT

,,

ee

eePTmH

,,

ss mH ;sm

emSf :

P

sH

❶ Only hydraulic energy isconsidered

0hemSf :

0t

C:Cht

eTSe :sHeH

em

Cm

CmP

PP

TT

sm

00UHQH

mmm

sae

sce

❷ hydraulic and thermal energies are considered

83


JUNCTIONS (4/6) : 1 JUNCTION

1e1

e2e3

e4

f1

f2

f4

1 – JUNCTION Common flow junction

Representation

0.... 44332211 fefefefe

04321

4321

eeeeffff

Defining relation

Power conservation

0.1

n

iii ea

ai = +1 if 0

ai = -1 if 0

f3

84

JUNCTIONS (5/6) : Examples of 1-junction

1P1

R:R1

C:Ch

PR1

P1P2

R1

Q

P2

Q

EC

R L

UR UL

UCi1

E

i i

i

Se:E

E =UR + UL + UC

UR

R

L

C

UL

UC i

1

FRFC

C:k

I:ma

R:f

0 11

I:mb

k x

maFafmb

Fb

Se:FaSe:Fb

ax rk

xb

xFaFb

85

Pressure loss

Hydraulic losses

R:fb R:fa

mb

ma

fa fb


Junction (6/6) : thermal system

1T1

T2

R

TR

2Q1Q

RQ

T1 T2

Q

TQR

2

: thermal flow

1

: hermal conductibility / .

:

e=wall thickness

ec

TQ WR

S WattKR e Kelvin

T W m K

S m

m

QQQQTTT

R

R

21

21 0

Static case Dynamic case

1T1 T2

R

TR

2Q1QRQ

CR

CR

QQQQTTTT

21

21 0

CQTC

C

86


SUMMARY

87

1TF

:m

I:L2

R:R2

iR2

iR2

UL2

UR2

UST

iR2

Exercises : Example1

1

R:R1

uR1

Se:EE

iR1

iC1

0

C:C1

uC1

iR1

1

I:L1

iL1

uL1uC1

iL1

UET

iL1

L1

E C1

R1

0iR1

iC1

iL1 R2

L2

iR2

m

88

Exercise : do it

L 1

E C 1

R 1

i1

i2

i4

R3

L2

i3 i6

R 2 C 2

i5

L 1

SE C 1

R 1

iR1

iC1

R 2

C 2 SF

iR2

iC2

SF

m

89


How to construct multiphysic Systems ?

Thermal, Hydraulic, mechanical, electrical ….

90


BUILDING MECHANICAL MODELS1. Fix a reference axis for velocities

2. Consider all different velocities ( absolute velocities for mass and inertia and relative velocities for others).

3. For each distinct velocity, establish a 1-junction, Attach to the 1-junction corresponding Bond graph elements

4. Express the relationships between velocities. Add 0-junction (used to represent those relationships) for each relationship between 1-junctions

5. Place sources

6. Link all junctions taking into account the power direction

7. Eliminate any zero velocity 1-junctions and their bonds

8. Simplify bond graph by condensing 2-ports 0 and 1-junctions into bonds : for example : 1 0 1 is replaced by 1 1

91

92

c fc

1J

f

tc2 2,c

K

2J

c E

1 1J LR fU c

f R

2 2J Li 2 2i

2 2c U1 CK t cc U

fc

2tc

I:J

1Se:c(t)

R:f

0

C:1/K I:J2

1 Se:c2(t)

gyMechanical and electrical analogy

Exercise 1 : mechanical

Mak1

Mb

x

F(t)

MAx

I:Ma

1Se;F(t)

MaF

MAx

R:fa

RF

fa fa

C:1/k1 R:R11

RKx

1RFCF

1

R:fb

MBx

I:Mb

MbF

MbF

fb fb

0

C:1/k1

1kx

MBx

CF

Ma

k1

Mb

x

F(t)

R1

MBx

0

I:Ma

1 1

I:Mb

Se;F(t)

MaF

MBx

R:fa

R:fb

RF

MAx

MbFMAx

93

A quart of vehicle : longitudinal dynamics

0

: roadSf x

R:Rs10

1I:MCarcx

carxC:1/ks

Se:-Mcg

RsF

KsF

Road

Car body

R:Rst1

C:1/kst

stF

1I:Mtire

Se:-Mtg

stx

Suspension

Rst

Kst Tire Mtire

Tire structure

rx

tirex

stx

Car Mcar

tirexsuspx suspx

+

94

A half : longitudinal dynamics

95

: roadSf x

0 R:Rp

1

Se:-mpg

1

I:Mp

C:1/kp

10

1C:1/ks

R:Rs 1

1

0 0

I:McSe:-mcg

1:TF

d1

2:TF

d

I:Jc

Se: t g

0

: roaSf x

1

01

I:Mw

1

C:1/ks

Se;-Mwg

1

C:1/kp

R:Rs

R:Rp

96


Electro-mechanical sytem

)( FirMGY

IF

1

R:Ra

I:La

Se:UF

IFUR

UI

1

R:Ra

I:La

Se:UA

IAUR

UI

Um

IA1

R:B

I:J

Se:Loadm

m

R

I

97


Exercise 1 : mechanical

1

R:f1

C:1/k1

C:1/k3 R:f2

I:Mb

0

0

1

I:Ma

Se:-F(t)

C:1/k2

1fx

1kx

3kx2fx

MBxMAx

2kx

x MAx MBx

Ma

k2

k3k1

f1

f2

MbF(t)

m1 m2 m3

R3k1 k2 k3 F(t)

+Vref=0m1,f1 m2,f2 m3,f3

98


BUILDING HYDRAULIC MODELS1. Fix for the fluid a power direction

2. For each distinct pressure establish a 0-junction (usually there are tank, compressibility, ….)

3. Place a 1-junction between two 0-junctions and attach to this junction components submitted to the pressure difference

4. Add pressure and flow sources

5. Assign power directions

6. Define all pressures relative to reference (usually atmospheric) pressure, and eliminate the reference 0-junction and its bonds

7. Simplify the bond graph

99


Hydraulic system : ExampleInertia IResistance R1 Resistance R2Pump

P1 P2 P3 P4 Pat

Se:P1 0P10P2 0P3 0P4

Pat01 1 1

R:R1 I

1

R:R2 C

CV

Se:P1 1

R:R1

1 1

IR:R2

0

C

Se:P1

R:R1

1

I

R:R2

C

100


EXAMPLES OF BG MODELS : Hydraulic

0

C:CR

R:R1

Se:PP

PP

1RV

I:l/A

1

P P -PR

PR

1RV 2RV

PR Se:-P0

2RV

P01

R:R2

PR -P0

Valve 1

R2PumpPP

PRLC

P0

De

PID

101

EXERCISES : Mechanical (pneumatic valve)

102

Vanneu(t) x(t)

Block diagramme

Pe : pressure from controller (0,2 -1 bar )x : valve position [0-6 mm]f : friction m : mass of part in motion [kg]1 : Rubbery membrane of section A [m²]2 : Spring of elasticity coefficient Ke [kgf/m]3 : Stem,4 : packing of watertightness, 5 : seating of valve,6 : valve7 : pipe

u

6

4

5

3

2

1

7 x

F

Controlleru

6

4

5

3

2

1

7 x

F

Controller

DEMO


EXERCISES : Bond graph model of the pneumatic valve

Se:Pe 1

C:1/ke

xFk

R:f

Ff

Df x xPe

V

Pneumatic

energy

TF:A

F

x

Mechanical

energy

I:m

FI

103

EXERCISES : Hydraulic control system

104

PID0,2 -1 bar 3 - 15 psi Pe

xsV

eV

P0

LT

T1

De1u

PR


EXERCISES : Bond graph model of the hydraulic system

eVSf : 0 1

R:RV

0: PSe

C:CR

sV

RPRP 0P

1

C:ke

xFk

De:P0

x

x

Pe

VTF:A

F

x

I:m

FI

R:fFf

xDf :

PID

u

ePMSe :

105


EXERCISES Hydraulic systems

106

Patm

F1 F4

P2P1

P3

P4

P5

V1

V2

V3

V4

V6

V5

F3

F2

F5 F6

F7

F8

1) Bond Graph Model

2) Electrical equivalent scheme

R1R2

R3

R4

R5


JUNCTIONS (5/5) : Physical interpretation of the junction elements

Electrical circuits 0-junction : Kirchoff’s currents law 1-junction : Kirchoff’s voltage law

Mechanical systems 0-junction : Geometric compatibility for a situation involving a single force and several

velocities which algebraically sum to zero 1-junction : Dynamic equilibrium of forces associated with a single velocity (Newton’s

law when an inertia element is involved). Hydraulic systems

0-junction : Conservation of volume flow rate 1-junction : requirement that the sum of pressure drops around a circuit involving a

single flow must sum algebraically to zero.

107


EXAMPLES OF BG MODELS :Thermal

C:Cb

0

bQTS

R:Ra

1aQ

TS

TS - TaaQ

Se:-TaTa

aQ

TS

SQSQSf :

Ts

Ta

Source of heat

SQ

108

Electro Mechanical Actuators (EMA)

109

Servo Hydraulic Valve (SHV) : how iy works An electrohydraulic servo valve (EHSV) is an electrically operated valve that controls

how hydraulic fluid is ported to an actuator.

Pipe P: Input pressure(Pressure source) Pipe T: Exhaust

(output to the tank)Patm

Verin

Postion 1:P is connected to A And T to B

Position 2:P is connected to B and T to A

Postion 0:A and B are plugged

Controlled distributor


Simple and double acting cylinder : how it works

Compressed air supply : P=PaExhaust : P=0

http://geea.org.pagesperso-orange.fr/PNEUM/distrib_3_2.swf

1) Simple acting

Double acting Cylinder

Se:PaSe:0

xF ,(0,1)u Signal

control

111

Controlled servo valve with two positions cylinder

0

verP

R:R2(u)

xF ,

Se:Pa Se:0

A B

P T

1

1

R:R1(u)

:TF

A

F1

I:MR:f

:TF

A

cF

RF

u

1 u

aP

1P

verP

0

Se:0

0

Se:0

verP

verP

xSe:Pa

Se:Load

Cylinder-Piston

aP

V

V

(0,1)uServo Valve

Signal control

xController

refx

:Df x

0,1u

+

-

C

C: k

Load

112

Application

113

Exercise 2 : Servo valve and suspension

Set point

xx

Controller

To atmosphere

0 TFA

aV

aPx

aF1

C:Cc I:M

:R

C:k:Msf q

xController

Set point

114


Exercises Word Bond graph Bond graph model

115


Chapter 3

CAUSALITY CHAPTER 3: Causalities and dynamic model

• Definitions and causality principle• Sequential Causality Assignment Procedure (SCAP)• Bicausal Bond Graph • From Bond Graph to bloc diagram,• State-Space equations generation• Examples

116


CAUSALITIES Definition

Causal analysis is the determination of the direction of the efforts and flows in a BG model. The result is a causal BG which can be considered as a compact block diagram. From causal BG we can directly derive an equivalent block diagram. It is algorithmic level of the modeling.

Problematic Importance of causal proprieties Simulation Alarm filtering Monitoringability Controllability Observability

117

Convention

118

A BeA B

e

The causal stroke is placed near (respectively far from) the bond graphelement for which the effort (respectively flow) is known.The causal stroke is placed near (respectively far from) the bond graphelement for which the effort (respectively flow) is known.

f

Cause effect relation : effort pushes, response is a flow

Indicated by causal stroke on a bond

Effort pushes

Flow points

A BfA B

f e

(a)

(b)

PRINCIPLE

119

ER1

i UR

Se:E R11

RUiR

R1

i UR

i

Se:E R:R1i

UR

R1Sf:i1RU R i

1 0RU R i

Sf:i R:R1i

UR


CALCULATION EXAMPLE

PR

V

PKV

PR2

KVPV

P1

P

P2

V

R:K

1P1

P2

PR

R:K

1P1

P1

P

120


Remarks about causalities

the orientation of the half arrow and the position of the causalstroke are independent

e

f A B

e

f A B

A Be

System A impose effort e to B

A Bf

System A impose flow f to B e

f

121


Causality for basic multiports Required causality

The sources impose always one causality, imposed effort by effort sources

and imposed flow by flow sources.

Indifferent causality (applied to R element)

Conductance causality

1RF

uR

i

eFi R1

)(1

fR

e fe

ef

f

eR

iRufFe R

.)(

Resistance causality

RF

fSe

e

fSf

e

122


Integral and derivative causalityPreferred (integral)

causality

fC

dti

Cu

fdtFe C

.1e

f

eI

dtu

Li

dteFf I

.1

. e

f

Ce

dtduCi

dtdeFf C

.

1 fdtde

f I

dtdiLu

dtdfFe I

1 fdtd e

Derivativecausality

123


Causalities for 1-junction

Only 1 bond without causal stroke near 1 - junction

Rule

1e1

e2

e3

e4

f1

f2

f4

f3

Causal Bond Graph model

24

23

21

ffffff

3412 eeee 1-Junction

e1

e4

e3

f2

Block diagramStrong bond

24

23

21

ffffff

3412 eeee e1

e4e3

+

+-

Causality

124


Causalities for 0-junction

Only 1 causal stroke near 0 - junction

Rule

0e1

e2

e3

e4

f1

f2

f4

f3

Causal Bond Graph model

1 2

3 2

4 2

e ee ee e

3412 ffff 0-Junction

f1

f4

f3

e2

Block diagramStrong bond

24

23

21

eeeeee

3412 ffff f1

f4f3

+

+-

Causality

125

Causality for TF element 2 CAUSALITY SITUATIONS

2 1

1 2

..

f m fe me

f1

TF:m

e1 e2

f2

1mf1

e2

f2

e1

1 2

2 1

1 .

1 .

f fm

e em

f1TF: m

e1

f2

e2

e1

f2

e2

f1

If e2 and f1 are known : If e1 and f2 are known :

m

m1m 126

Causality for GY element 2 CAUSALITY SITUATIONS

1 2

2 1

1/

1/

f r e

f r e

If e2 and e1 are known

f1

GY:r

e1

f2

e2

f2

If f2 and f1 are known

1 2

2 1

..

e r fe r f

f1

GY:r

e1e2

f2

e1

f2e2

f11/r

1/r

e1

f2 e2

f1 r

r

127


Sequential Causality Assignment Procedure (SCAP)

Apply a fixed causality to the source elements Se and Sf

Apply a preferred causality to C and I elements. With simulation, we prefer to avoid differentiation. In other words, with the C-element the

effort-out causality is prefered and with I -element the effort in causality is preferred.

Extend the causality through the nearly junction , 0, 1, TF an GY

Assign a causality to R element which have indifferent causality .

!!! It these operations give a derivative causality on one element, It is usually betterto add other elements (R) in order to avoid causal conflicts. This elements musthave a physical means (thermal losses, resistance …).

128


Four Information given by BG

e

f

Power variables show the type of energy

A B

There exists a physical link between A and B

A supplies power to B

Flow is input for B and effort is output

129

Covering causal path Définion (Causal path)

A causal path between two ports is an alternation of bonds and basic bond graph elements (named nodes) such that (i) all nodes have a correct and complete causality, and (ii) two bonds of the path have in the same node opposite causal stroke direction.

Simple direct Causal path : covered following only one variable (effort or flow).

Indirect causal path : one element (R,C, I) should be crossed along the path

Mixad causal path : it comprises a gyrator (GY) imposing the change of followed variable

130

e1 0 1

f

e0 1 0

f

Passive element (R, C, I

f

e f

f

e1 GY

f

e

f

131

Effort source

0f3

f2

f4

f1

e3

e2

e4

e1

e known

Flow source

Se:e System

Se:e

f Output of Se (of Sf) is aneffort (flow) and is aninput for the system.Rule : The causality is

compulsorySf:f f known System

Sf:fe

Junction 0

ffff ee

eeee

4321

14

13

12 2f

3f 1f(-)

(+)

(-)4f

14

13

12

eeeeee

1e

4

3

2

eee

Junction 1 1f3

f2

f4

f1

e3

e2

e4

e1

eeee ff,ff

ff

4321

14

13

12

Only one flow is allowed to be an input. All others are outputs (here f1 ).

Rule: Only one bond havenot a causal stroke near a 1junction.

Only one effort is allowedto be an input. All othersare outputs (here e1 ).

Rule: Only one bond havecausal stroke near a 0junction.

TF

m:TF1e 2e

2f1f

2f1fm:

TF1e 2e

,mffmee

12

21

,fm

f

em

e

21

12

1

1

Only one effort and oneflow may be inputs

Rule : One causalstroke near TF

r:GY1e 2e

2f1f

r:GY1e 2e

2f1f

,rferfe

12

21

,er

f

er

f

21

12

1

1

Two efforts or two flowsmay be inputs

Rule : Two causal strokeor no one near GY

GY

I

ef

I:I1

I:I1e

f

R ef

R:R1

R:R1ef

Resistance causality:output is an effort

Conductance causality: flow is an output

)( fe R

)(1 ef R

CC:C1

ef

fe

Integral causality:effort is an output

f e

f e

fe

qfdte CC

14

13

12

ffffff

1f

4

3

2

fff

2e

3e 1e(-)

(+)

(-)4e

m

m0

02e 1e

2f1f

f )( fR e

f)(1 eRe

r

r10

01 2f

1f

1e

2e

r

r0

0

2e

1e2f

1f

m

m10

01 2e1e

2f1f

Derivative causality :flow is an output

Integral causality :flow is an output

eC:C1

Element Bond graph Causal equation Bloc diagrams Rule

edtdf C

1

pedtf II

fdtde I

1

fdtC

edtd

C1

edtI

fdtd

I1 Derivative causality :

effort is an output


How to generate simulation diagram from the bond graph model ?

132


From Causal BG to Bloc Diagram (1/3)

1

1R

133


From Causal BG to Bloc Diagram (2/3)

e21/me1

f1f2 1/m

e1me2

f2mf1f1

TF:m

e1

f2

e2

f1

TF:m

e1

f2

e2

f1

GY:r f2

f1

GY:r

e1

f2

e2

e1rf2

e2rf1

f11/re2

f2e1 1/r

f1

e1

f2

e2

e1 e2

134


From BG to Bloc Diagram (3/3)

f6=f4-f5

135

How causal path can help for simulation !

E

R1

g

C

iUc

UR

1

R:R1

C:C1Se:E

EUR

Uc

ie ic

ir

1

1R

For R elemntUR

irURR:R1 1

1R

Ui Rr

For C elementUc

ic

C:C1 1

1C

dtiC

U cc 1

1ic

For 1 junction ❶E

Uc

UR

+

-E

Uc

UR

136

Steps for bloc diagram generation

1

R:R1

C:C1Se:EE

UR

Uc

ie ic

ir

❶Causal graph❶ Causal graph❷ Expansion of causal bonds

to bilateral signal❷ Expansion of causal bonds

to bilateral signal

❸Write constitutive equationfor each element and replace

junction by operators

❸Write constitutive equationfor each element and replace

junction by operators

1

R1

Se C1

URir

ic

UcE

+Se UR

1

1R

ir

Uc -

1

1C

Uc

❹ Use Simulink Software❹ Use Simulink Software

137

Application to Electrical system : BG model

E(t)

L

C

R1

R2V(t)

Se:E(t)E(t)

11

I:L

2

R:R1

3

40

R:R2

5

C

6

22 pe

66 qf

1. BOND GRAPH MODEL

De:e6

138


Application to Electrical system : Block Diagram

E CL

R2 U(t)R1

1

I:L

Se:EE

1

5

0

R:R2

R:R1

64

2

3

C

2

1R

f6

f5

-Se:E

e2

e3

+

-

-

e1

e4

L1 f2

f2(0)

C1 e6

e6(0)

1-Junction e2=e1-e3-e4

f2=f1=f3=f4

0-Junctionf6=f4-f5

e6=e4=e5

1R

139

1

I:L

Se:EE

1

5

0

R:R2

R:R1

64

2

3

C:C1

1

R1 C1

0

L R2

Se

1. Causal graph1. Causal graph 2. Expansion of causal bonds to bilateral signal

2. Expansion of causal bonds to bilateral signal

1R1

1C

:Se E

1L

2 4 3f f f

3f

6e

6 4 5e e e

2f2e

5f2

1R

5e

6f

1e

3e

4f

+ -

-

-

+

3. Write constitutive equationfor each element

3. Write constitutive equationfor each element

2e 2f

4f

4e5e 5f

6f6e3e 3f

140

Application to Hydraulic system: BG model

Se:PP

PP

De:PC

uPID Pref

PC+ -

Pump

P0

PC

P0

PCR2

R1

PP

l

1

PI1

R:R1

I:I1

PR1

1RV PC

0

C:CR

1RV

PCRCV

P0

2RV2RV1

R:R2

PR2

Se:-P0

Atm

osphere

141

Application Hydraulic system: Block Diagram1 junction 11 RCPI PPPP

0 junction 21 RRRC VVV

1 junction 02 PPP CR • Structural laws

• Calcul de CR et I1

dtVAgP

dtPd

gA

dtgPAd

dthAdV RCC

CCRC

)()/(.().(

gAC R

dtPl

AVdtVd

AlAAP

lAmAPFdt

AVdmFe

Ic

RR

cc

cI

ccIcR

111

1

11

..

,.,/, :lawwton N

cAlI

1

• Constitutive equations

I:I1

C:CR

dtPI

V IR 111

1

dtVC

P RCR

C 1

law) (Bernoulli. 2111 RR VRP

law) (Bernoulli2222 RR VRP

R:R1

R:R2

142

Application Hydraulic system: Block Diagram

Se:PPPP

De:PC

uPID Pref

PC+ -

1

PI1

R:R1

I:I1

PR1

1RV PC

0

C:CR

1RV

PCRCV

2RV 1

R:R2

PR2

Se:-P0

2RV

P0

Atm

osphere

+ +-

dtI1Se:PP

PC

PR1

PP

1RV

1R

RC

1

2RV

2

1R

Se:-P0

PR2

PC

--

+ -PI1 RCV

21RV

143

Insulin Pump

cPVoltage source

DC motor

Pinion + Rack Orifice

2

2CF 0P1u

i 1Shaft Piston +

cylinder

End user

1

R:Ra

I:La

R:Rp

:KeGY c1

I:Jp

0

C:1/Kp

:RpTF 1

I:Mc

:ApTF 0

C:Cyl

1 Se:P0Se:u

R:Ror

r

j

ru

Lu

eu2

mc

1

IFu

cQ

0P0rP

i

R:Rc

cv

cQ

cP

orQ

cyQ

orQ

cvCF

RcF

RPFc

c

orQ

144

1

I:Jm

C:1/k

1

R:Ra

I:La

aURU

eU mc

IU aiTF

:1/N0 1

R:fm R:fr Se:-Fp

m sr

I:Jr

Ircr

cfmc

erc srcfrc

m

pc

Imc

: rRTF

Se:Ua:Ke

GY

Voltage source

Electrical part Mechanical part

Reducer Whell

ai

mc

mContact force

aU eU srcsr

pcr

g gModelling and control of Intelligent vehicle

src

145

EXAMPLE (How to avoid derivative causality ?)

E C

i

iC UC

dtdECiC .

E C

Ri

iC UC

C

0E

i

UC

Se:E

iC

Derivative causality

Current infinite ?

dtiC

U RC 1

R

1E

iR

uR iR

0uC

iR

iC

C

uC

Se:E

Integral causality adding R

146

Derivative causality : example

1 TF:b/a 1

I:M1 I:M2

C:1/k

Se:F(t)

Add of elasticity of the body

TF:b/a 1

I:M2

C:1/k

0

C

1

I:M1

Se:F(t)

147


State equations : Définition

Objectif Une représentation d'état permet de modéliser un système dynamique sous

forme matricielle en utilisant des variables d'état. On se place alors dans un espace d'état.

Cette représentation, qui peut être linéaire ou non-linéaire, doit rendre compte de l'état du système à n'importe quel instant futur si l'on possède les valeurs initiales. Cette représentation peut être continue ou discrète.

Un système peut être entièrement décrit à l'aide d'un ensemble de variables minimal. Les variables d'état sont des grandeurs physiques continues du système (elles doivent être dérivables) et doivent être indépendantes les unes des autres.

148


Un vecteur d’état ensemble minimal de variables d’état, c’est-à-dire de grandeurs temporelles,

nécessaires et suffisantes pour déterminer l’évolution future d’un système quand on connaît les équations qui décrivent le fonctionnement du système et les entrées de ce système.

les variables d’état constituent les supports des "souvenirs" du système.

Plus généralement, les variables d’état dans les systèmes physiques sont les éléments aptes à emmagasiner de l’énergie sous forme cinétique ou potentielle : inductances, capacités, masses, ressorts... Ce sont les éléments ayant une capacité de "mémoire".

149


L’idée de base des représentations d’état est que le futur d’un système dépend de son

passé, de son présent et de ses entrées : le futur peut alors être décrit à partir d’un ensemble de variables bien choisies.

Contrairement à l’analyse classique des systèmes qui fait appel à la représentation de Laplace, dans le cas des représentations d’état, l’analyse a lieu dans le domaine temporel. De fait, au cadre de l’analyse des fonctions de la variable complexe se substitue le cadre de l’algèbre matricielle.

150


Intérêt d’une représentation d’état La fonction de transfert Relation entrée/sortie qui n’apporte aucune connaissance sur la structure

interne d’un système. Deux systèmes différents peuvent très bien avoir la même fonction de

transfert., la représentation d’état contient des informations accessibles à lamesure et directement liées aux grandeurs physiques des systèmes. Elleoffre de ce fait des possibilités nouvelles en termes d’analyse et decommande des systèmes.

Un même système complexe pouvant être décomposé de différentesmanières, la représentation d’état n’est pas unique. Bien au contraire, pourun système donné, il en existe une infinité.

le dénominateur de la fonction de transfert correspond au polynômecaractéristique de la matrice d’état : Den[H(p)] = det(pI − A) = QA(p)

151

Représentation d’état et de fonction de transfert

152

Y((s)U(s)W(s)

DuCxy

BuAxdtdx

uxCy

uxfdtdx

,),(

),(PROCESS Capteursx(t) y(t)u(t)

State Equations

nrnmnn CBA

xCyuxFx

cxybuAxx

,,

)(),(

Nonlinear:Linear

SENSORS

ACTUATORSu

CORRECTOR PROCESS

x

y

yc

X-x

System to be controlled

M

A

DfDey

MSfMSeSfSe

u

dttfdtte

qP

xC

I

,Auto. ,

Manual,

)()(

Bond graph

153


STATE EQUATIONThe state vector, denoted by x, is composed by the variables p (impulse) and q (displacement) , the energy variables of C- and I-elements.

Properties the state vector does not appear on the Bond graph, but

only its derivative

The dimension of the state vector is equal to the number of C- and I-elements in integral causality

dttf

dtteqP

xC

I

)(

)(

)(

)(tf

tex

154


HOW TO OBTAIN STATE EQUATION❶. Start from a graph without flow/effort variables marked on bonds

. Fix key variables : input u, state variables x and measurements y

u : Se and Sf x : the derivative of state variables is marked on flow bond for C

element and on effort bond for I element : y: De and Df elements

. Determine unknowns via constitutive relations, junction constraints based on fixed causality (use the equation from the strong bond )

155

State equations : RC Electrical system (1/2)

E

R1

g

C

i

Uc

UR

1

R:R1

C:C1Se:EE

1 C:C1Se:EE

❶ Start from a graph without flow/effort variables marked on bonds

❷ Fix key variables

1x

R:R1

Df:m

Df:m

y 1 1( ) ( ) ( ) ( )

( ): m

x i t x t i t dt q t

u Se ty Df i

The state variable is the charge q(t) but in the Bond graph appears only its derivative (the current)

156

State equations : RC Electrical system (2/2)

1 C:C1Se:E E

R:R1 ❸ determine unknowns (I, Ur and

Uc), via constitutive relations, junction constraints

11R x

1 1/x C

1x1x

1x

1 1

1

1 11 1

1 1 1 1 1 1

1

1 1

1 1 1

1

x xR x E x E x EC R C R C R

xy E xR C

Use of Software for automatic generation of state equation

State equation

Df:m

157

State equations : RLC Electrical system (1/2)

1 C:C1Se:E E

R:R1 ❸determine unknowns via constitutive relations, junction constraints21 /R x L

1 1/x C

1x

I:L

1 12 2

1

21

2

R xx E xL C

xxL

xyL

2 /x L

2 /x L

2x1x

Df:im

y

The state variables are the charge and flux but in the Bond graph appears only their derivatives (the current and voltage)

idtdqxqx

UdtdiLxx

11

22

Cx

CqU

LxUdt

Li

1

21

158

State equations : RLC Electrical system (1/2)

1 C:C1Se:E E

R:R1 ❸determine unknowns via constitutive relations, junction constraints21 /R x L

1 1/x C

1x

I:L

1 12 2

1

21

2

R xx E xL C

xxL

xyL

2 /x L

2 /x L

2x1x

y

The state variables are the charge and flux but in the Bond graph appears only their derivatives (the current and voltage)

idtdqxqx

UdtdiLxx

11

22

Cx

CqU

LxUdt

Li

1

21

159

Se:Ua 1

I:Jm

R:Rm

Se:-L1

R:Ra

I:La

Df:im

Df:m

GY:K

))(()(

)()(

2

1

tttU

x

MJLi

dttdtte

xx

x

Application to DC motor (1/2)

1

2

State variables are:

: Electrical flux=Li

:angular moment=J mm

dx Udt

dJx Jdt

1x U2x

LaU

160

Application to DC motor (2/2)

Se:Ua 1

I:J

R:Rm

Se:-L1

R:Ra

I:La

Df:imDf:m

GY:K

2/mR x J

1 /x L

1 /x L1 /aR x L

1 /x L

2 /x J

2 /x J

1( / )x L k

2 /x J

2( / )x J k

1 1

2 2

1 1

2 2

1 00 1

1 0

10

a

a

Lm

R kx x UL Jx xk R

L J

y xLy x

J

1y 2y

1 21

1 22

11

22

aa

mL

R x xx U kL J

x R xx kL JxyLxyJ

1x 2x

LaU

161

Simulation using state equation

1 1

2 2

1 1

2 2

1 00 1

1 0

10

a

a

Lm

R kx x UL Jx xk R

L J

y xLy x

J

DuCxyBuAxx

Ua y

Cxy x

1 0,

0 1

1 0, 0

10

a

m

R kL JA B

k RL J

LC D

J

162

Simulation using block Diagram

+-

dtLa

1

aR-

Se:Ua

Se:Ua

1

I:Jm

R:Rm

Se:-L1

R:Ra

I:La

Df:im

Df:m

GY:K

aURU

eU m

JIU

IU

RU

i

ik m J dt

Jm1

-mR

kSe:L

-+

2y1y

f

163

Exercises

E CL

R2 U(t)R1

1

I:L

Se:EE

1

5

0

R:R2

R:R1

64

2

3

C

De:e6

CxyBuAxx

u x

y6

6

2

6

2 ,)(, eytESeufe

qp

x

2. STATE EQUATIONS

164

Mechanical system

x1

x2

k1

k2

m2

m1

refxSf :

1

F2

I:m2

2x0

1 I:m1

0

C:k2

C:k1

Se:-m2g

1mx

1x

2mx

Fm2

Se

Fm1

F1

1mx

refx0refx

2mx

1mx

xg

1

F2

I:m2

2x0

1 I:m1

C:k2

C:k1

Se:-m2g

1mx

1x

2mx

Fm2

Fm1

F1

2mx

1mx

Se:-m1g

Se:-m1g

165

Application : do it

1

R:R1

uR1

Se:EE

iR1

iC1

0

C:C1

uC1

iR1

uL1

1

I:L1

iL1

uC1

iL1

TF :m

uR2

iR2

1

R:R2

C:C2

us

L1

E(t) C1

R1

iR1

iC1

iL1 R2 iR2iR2

C2

Df:iR2

12

3

4

5

6

7 8

9

10

S-FUNCTION FROM SYMBOLS

BLOCK_DIAGRAM SIMULINK

COMPARAISON SYMBOLS_SIMULINK 166

Mechanical example

11111221 0 xmxkxxkgm

221222 xmxxkgm

x1

x2

k1

k2

m2

m1

refxSf :

xg

2111 kkm FFgmF

1 I:m2

2kx0

1 I:m1

C:k2

C:k1

Se:m2g

2x

Fm2

Fm1Se:m1g

1kx

1x1x

2x

Fk1

Fk2

Fk2

Fk2

1111111

212212222

xkdtxkdtxkFxxkdtxxkdtxkF

kk

kk

12211111

11

11

xxKxKgmxm

dtFm

x mm

167

Building

Source of heat

TROOM

Tamb

Tref

P I DRradiator

TRAD

Rlosses

Rroom

Sensor

+ -

168

Exercise : Modelling and simulation

11,c 1 2tc22 , cfc

1J 2J

Kf

1J1f

m2f

2J

11,c

22,c

1mc

2mc

169


COUPLED BOND GRAPHS

• CHAPTER 4: Coupled energy bond graph • Representation and complexity• Thermofluid sources , • Thermofluid Multiport R, C• Examples

Chapter 4Chapter 4

170


INTRODUCTION TO MULTIPORT ELEMENT SINGLE BOND GRAPH : One energy

e

f

The constitutive relation is scalar

MULTIBOND GRAPH : more than one energy Representation : A bond coupled by a ring

The constitutive relation is matrix

e1 , e2 ...

f1, f2 ...

e1 , e2 ...

f1, f2 ...

e1

f1

en

eif2

fn

171


Coupled bond graph

Constitutive equations

0, qec T

T

TPe

Hmnq

0,,,0,,,0,,,

nHmnHmTnHmP

ch

t

h

,,PT

CnmH ,, T

CH

P

m

n

Chemical

Hyd

raul

ic

The

rmal

172


Coupled Bond graphs Representation

E

F

1e1f

ifie

nfne

E

F

(a) (b)

(c)

1

Couplingelement

11e

11f

21e

21f

12e

22e

22f

12f11e

11f

MULTIPORT21e

21f

12e

12f

22e

22f

(d)

E

F

1e1f

ifie

nfne

E

F

(a) (b)

(c)

1

Couplingelement

11e

11f

21e

21f

12e

22e

22f

12f1

Couplingelement

11e

11f

21e

21f

12e

22e

22f

12f11e

11f

MULTIPORT21e

21f

12e

12f

22e

22f

11e

11f

MULTIPORT21e

21f

12e

12f

22e

22f

(d)

173

Convection Heat transfer

174

),( mP

),( TH

➽ Modeling Hypothesis

2

2vPumH

TcmhmH p 0

2 : v velocity lowFor

2

v

]/[: kgJTcPuh p

enthalpy Specific


Coupling of thermofluid variables

TcmH p

T

Pm

mSf : 1

m

RcTH

TSe :

Pump as single flow sourcemSfh :

TSe:

1

Rc

Pm

T

H

B) Using R Multiport

H

m

175

TcmH p

T

Pm

mSf : 1

m

CETFTH

TSe :

CETF : Coupling Element for Thermofluid


Example of multiport elements

R MULTIPORT

Representation

(kg/s)flowMass:.)(Joule/secflowEnthalpy:

(pa)Pressure:(Joule/kg)specificEnthalpy :h

(K)eTemperatur:

1mHP

T

1

1

1

11 )(

mPH

hT

2

2

2

22 )(

mPH

hT

1

1

1

11 )(

mPH

hT

11, PT

11, mH R

22 , PT

22 , mH

1P

1HR

2T

2H

1

1T1m

2P

176


Constitutive equation for R-multiport

mmmHHH 2121 , 11 , TcmHhmH p

Physical law ( Continuity)

Constitutive equation

),,,(),,,(),,,(),,,(

2121421213

21212

21211

2

1

2

1

TTPPTTPPTTPPTTPP

HHmm

RR

R

R

12121

2121

)(1

)(1

TcPPPPsignR

PPPPsignR

Hm

ph

h

128

4DRh

177


Inertia of the fluid

IpPdt

lAm

dtAmd

lAdtdvmAPF

Ic

cccc

2.

1HRc

2T

2H1T

Thermal power

Hydraulic power

1P1

1m

2P

2m

RI

➽ Impulse of pressure p l

178


Dynamic bond graph model of the pipe Fluid moving with inertia

11m

2m

1H2H

RC

2P

R:Rh

1T

1P

AI :

RP IP

2T

Rm

11m

2m

1H2H

RC

2P

R:Rh

1T

1P

AI :

RP IP

2T

Rm

IpdtP

ImV

mRPPPPP

I

hR

RI

1 I,Elément

, R,Elément , , 1Jonction 21

AMxp

xAm.

xAm

hRPPm

dtmd 21

hh RARI

:Where

179


Bond graph model of the pipe Global Model

Step response for hydraulic model to pressure difference

1

21

TcmHR

PPmdtmd

p

h

)0(11)( mePR

tmt

eh

180


Thermofluid C multiport : Saturated regim boiler (2/2)

0hl

Deh,p

0tl

Deh,l

QSf t:

1

01ext TSe :

RfmRme

Cm

0hv

0tvDet

2 3

16

17

1418

20

21

22

2324

5 6

8

9

10 11

15

25

26

Thermal losses

Liquide phase

Steam phase

Evaporation

RC:CL C:CV

❷❷ Two separated phase


Thermofluid C multiport : Saturated regim boiler (1/2)

X : Steam quality [0, 1]P : Pressure in the boilerT : Temperature of the mixtureL : Level of the waterhi(P): Thermodynamic function (of vaport and liquid)

aQ

cHT

0hemSf :

0t

C:Cht

eTSe :sHeH

emC

mP

PP

TT

sm

saec

sec

HQHHmmm

dtHQHH

dtmmm

saec

sec

em

eHaQ

sH

cm

cH

( ) ( )(1 )

( ) ( )(1 )

cc v L

c

cc v L

c

Hh h P X h P Xmm P X P XV

P

X

( )T P

(1 ) cX m

T

L

e e p eH m c T

s s vH m c T

,,e e

e

H mTe P

,,s sH m

T P

c

c

Hm

❶❶ Monophase mixture


Thermofluid example : heated tank (undersaturated)

Pe

l

eQ

Po=0

H,m

Two ports C

Tex

One ports C

Q

Te

T

TexQPeu

QmHpx

State variablesI element : p

183

Bond graph model

De:T

De:L

ePSe:

C

Pm

01

5

7

T

02

H13

et QSf : 14

eTSe:eH

Rc115 16

em

exTSe:

13

1403

R:RexRm

Am

bian

ce

C

Q T18Q

20Q

17

18

19

20

21

22

23

sm10

Envi

ronn

emen

t

Se:P

0=0

R:Rs

12

6

8

9

Rc21112

sH sH

11

R:ReI:I1

1

2 3

4

em

184

Constitutive equations (1/4)

Jonction 11

325

34

32

31

325

34

32

31

4234213

mmmmmmmm

ffffffff

PPPPeeee e

Elém ent R :Re 232

23.2Re2 mRPPfR)(fΦe ee

333333 )0(1)0(1 mmpI

fdteI

f

Jonction 01

76

75

74

76

75

74

647647

PPPPPP

eeeeee

mmmmmfff se

Elément I:l/A

185


Jonction 02

1318

1317

1316

1314

1312

1318

1317

1316

1314

1312

1812216131812141613 )(

TTTTTTTTTT

eeeeeeeeee

QHuQHUfffff e

Multiport C : CR 777

71371377Rh )0(1),(),(C:C PPCmdtf

Cdtfdtfqqe

hhChCh

hCm

Amg

AVggLPe 777

77

niveau dans le réservoir indiqué par le capteur De :L

Am

gPL 77

186


Capacité thermique

)0()(

1),(),(C:C 137

1313

71313713713Rt T

mcUdtU

mCTdtfdtfqqe

VtCtCt

Température indiquée par le capteur De :T 7

1313 mc

UTV

Jonction 12

8109681096

68968 mmmmffff

PPPeee s

Vanne de réglage R :Rs

).()().(.)(

188

1888

188

18 PPsign

Rummeesign

Rueesign

uRf

ss

ss

Eléments R : Rm et R :Ra

aaa

mm

TTR

QeeR

f

TTR

QeeR

f

2223242223

201819201819

11

11

187


J onction 13 et 14

2324232223242322

2223242223

1920191819201918

201819201819

,,

et,,

QQQQffffTTTeee

QQQQffffTTTeee

a

Elément C :Cm : stockage d’énergie Q par le métal du réservoir

)0()0(121

2121212121 T

CQTedtf

Ce

mm

Jonction 03

2122212021222120

222021222021

,,

TTTTeeeeQQQfff

Eléments de couplage RC1 et RC2

1381112101211C2

31615251516C1

:R

:R

TcmHHecfff

TcmHHecfff

psp

epep

188


Global Dynamic Model

7

13

7

21

7

1321

221771

7

13313

77137

72

33

11

1

mcUAm

TL

y

RT

RRCQ

RcmUQ

)(uQCR

QPCmP

Cmsign

Ruc

RmcUTc

IpU

PCmP

Cmsign

Ru

Ipm

Cm

IpRPp

V

a

a

ammmV

emm

sh

shs

pmV

ep

sh

shs

hee

189


Simulation using State equations format

),( uxfu x

x(0)

)(xCyx

x

SimulinkSimulink

Generation of S-function from Symbols2000Generation of S-function from Symbols2000

190

From BG to Block Diagram

-

1

1IePSe :

e2

f2)( 3Re f

f3e3 )( 7 dtfCh

e4

e8

-e7e1 f4

f7

f6

)( 8eu Rscf8

f6-+

sPSe :

),( 137 dtfdtfCte13

e6

e17f13

f12=f11

2.. fTc epeTSe :f2 f16

10132 ..: fecR pc

)( 19fRm),( 20 dtfCm

e20

e19f20 f19e22

+-

f21e21

e12

f22

e23

+

)( 22Re exe23

TaSe :-

+

-

f18

f18

-

e24

+e4

-+ f10

-+

f23

De:L ge /7

De:T

11 01

LC

uce5

12

RC1 RC2e18

03

13

14

e20

02

eQMSf :+

TC

-

1

1IePSe :

e2

f2)( 3Re f

f3e3 )( 7 dtfCh

e4

e8

-e7e1 f4

f7

f6

)( 8eu Rscf8

f6-+

sPSe :

),( 137 dtfdtfCte13

e6

e17f13

f12=f11

2.. fTc epeTSe :f2 f16

10132 ..: fecR pc

)( 19fRm),( 20 dtfCm

e20

e19f20 f19e22

+-

f21e21

e12

f22

e23

+

)( 22Re exe23

TaSe :-

+

-

f18

f18

-

e24

+e4

-+ f10

-+

f23

De:L ge /7

De:T

11 01

LC

uce5

12

RC1 RC2e18

03

13

14

e20

02

eQMSf :+

TC

191


SYSTEMES CHIMIQUES

192


Physico chemical processes (1/4)

in

in

in

in

mPHT

Gaz

)(,1

)(

,

*,

,

tsconstituennj

T

n

p

x

mixtureGaz

mPHT

c

out

outj

outj

outj

out

out

out

out

HnnnXcc nn 11 ..

:variablesState

nc constituents

Types of applications : distillation column, fuel cell,..

c

inj

j

inj

nj

n

p

x

,1

,

*

,

cpj

j njc

M,1

Variables Parameters

193


H

T

m

P

Thermique

Hydraulique

Mixture

➽ A) Used variables

*ncP

ncn

Chemical

*1P

1n

*iP

inConstituents

➽ B) Mixture to constituents transformation ?

ncn

),1(. niMxmn

i

ii *

iPin

*1P

mP 1n

*ncP

194


1

TFMx 11 /

TFii Mx /

TFnn Mx /

m

e

e

e

e

Mixture (gaz)

Specie 1

Specie i

Specie nc

e

e

1n

in

ncn

m

m

m

),1(. ci

ii ni

Mxmn

➽ D) Use a transformer

mSf : P

ncn

*ncP

1n*

iP

in

*1P

m

PBloc

iini Mx ,,

➽ C) Use a bloc diagramme

195


P

inm1

Rc

INPUT

inT

inH

Gaz (mixture)

inm

iini Mx ,,

inn ,1

inncn ,

inin ,

outn ,1T H

outin ,

ncn

0

C

0

0

0

0

nn

1n

in

*1P

*iP

*nP

1

Rc

OUTPUT

ii Mx ,

outm

outH

outm

outm

outH

196

Chemical system

. . . .fK

A B C DKrA B C D

gS T

RS

fA rA1 1

E

nFTF:

Recepteur

i

Rel 1

G

ATF:

AAAC:CA

A

BTF:

BABC:CB

B

C:CC

C:CD

CTF:

DTF:

1

C

D

C

D

197


Electrochemical Process

198

Electrochemical Model

Chimique-électrique

Production H2O

Distribution de la tension

199


Integrated models: Thermoéconomie Thermoéconomie : modeste contribution [cf. réfence : Oud bouamama « Integrated Bond graph modelling in

Process Engineering linked with Economic System ». European Simulation Multiconference ESM'2000, pp. 23-26, Ghent (Belgique), Mai 2000 ]

B

A

B

A

B

A

H

H

mmCC

D

C

D

C

D

C

H

H

mmCC

DCBA DCK

K

BAr

f

MarketplaceexQ

Heater

Market place

Reactor

Inlet

Outlet

200

Chemical modelTransformation Products of reactionReactants A and B

TF:1/A

A

TF:1/D

TF:1/B

TF:1/C

C

DA

nDAAnA ArAf

nC

11

Dissipation

RS

C:CD

ABB

BnB

1

C:CA

C:CCC:CB

TggS

To thermofluid model201


Thermofluid model

BB HmSf ,:

exQSf :

De

0

C :CRDD HmSf ,:

CHSf :

PR

Cm

TR

CHAA HmSf ,:

From chemical model

To economicmodel

202


Economic model

FAm

Reinvestment

R:RT

R:RDC

1

FA

÷÷

10

/0CUC

mP

R:RSC

Supplier

Factory inventory

PUC

Cm

PSC

PFA

PIA

DCm SC

m

IAm

From hydraulic

model

I:IA

C:C

203

Global integrated model

BB HmSf ,:

FAm

I:IAexQSf :

D e

0

C :C R

R :R T R :R D C 1

C :C FADD HmSf ,:

CHSf :

P R

Cm

10/0 CUC mP

R :R S C

S u pp lier

fac to ry in ven to ry

H yd rau lic a nd the rm a l m o d e l E co no m ic m o d e l

C he m ica l m o d e l

T ran s fo rm atio n P ro du cts o f reac tio nR eac tan ts A an d B

T F:1 / A

A

T F:1 / D

T F:1 / B

T F:1 / C

C

D A

n DA An A ArA f

n C

11

D issip a tio nR S

C :C D

A B B

Bn B

1

C :C A

C :C CC :C B

T ggS

P U C

Cm

T R

CHP SC

P F A

P IA

DCm SCmIAm

AA HmSf ,:

R ein vestm en t

204


BB HmSf ,:

FAm

I:IA exQSf :

De

0

C :CR

R:RT R:RDC 1

C:CFADD HmSf ,:

CHSf :

PR

Cm

10/0 CUC mP

R:RSC

Supplier

factory inventory

Hydraulic and thermal model Economic

Chemical model Transformation Products of reaction Reactants A and B

TF :1/A

A

TF :1/D

TF :1/B

TF :1/C

C

D A n D

A An A ArA f

nC

11

Dissipation R

C:C

AB B Bn B

1

C:C

C:CC:C

TggS

PUC

Cm

TR

CH

PSC

PFA

PIA

DCm SCmIAm

AA HmSf ,:

Reinvestment

205


PART 5

Automated modellingCHAPTER 5: Automated Modeling and Structural analysis

Bond Graph Software's for dynamic model generationIntegrated Design for Engineering systemsBond Graph for Structural analysis (Diagnosis, Control, …)Application

206


Why Bond graph is well suited The bond graph model :

can be supported by specific software: the model can be graphically introduced in the software and generate

automatically the dynamic model. It can be completely and automatically transformed into a simulation

program for the problem to be analyzed or controlled or monitored. See http://www.arizona.edu/bondgraphs.com/software.html

Bond graph suited for automatic modelling Graphical tool Unified language Causal and structural properties Systematic derivation of equations

207


Main Softwares (3/5)

CAMP-G : The Universal Bond Graph Preprocessor for Modeling and Simulation of Mechatronics Systems.

is a model generating tool that interfaces with Languages such as MATLAB® / SIMULINK®, ACSL® and others to perform computer simulations of physical and control systems

Based on a good GUI, doesn't support object based modeling. Equations derived are neither completely reduced nor sorted properly.

20-sim : Twente Sim the simulation package from the University of Twente. Modeling and simulation program that runs under Windows. Advanced modeling and simulation package for dynamic systems that supports

iconic diagrams, bond graphs, block diagrams, equation models or any combination of these. allows interaction with SIMULINK®.

good product recommended for modeling of small to medium sized systems. The graphics and hard copy output quality is poor.

Not control analysis support.

208


Main Softwares (4/5)

Bond graph tool box for Mathematica this toolbox features a complete embedding of graphical bond graph in the

Mathematica symbolic environment and notebook interface Till review, the tool box did only support basic bond graph elements and junction

structures. Recommended for tutorial use in modeling of very small simple systems.

MS1 : BG modeling software from Lorenz Simulation is a modeling workbench developed in partnership with EDF (Electricité de France),

which allows free combination of Bond Graph, Block Diagram and Equations for enhanced flexibility in model development.

Models can be introduced in Bond Graph, Block Diagram or directly as equations MS1 performs a symbolic manipulation of the model (using a powerful causality

analysis engine) and generates the corresponding simulation code.

209


Main Softwares (5/5) Modelica : Object-Oriented Physical System Modeling Language

This is a language designed for multi domain modeling developed by the Modelica Association, a non-profit organization with seat in Linköping, Sweden.

Models in Modelica are mathematically described by differential, algebraic and discrete equations.

SYMBOLS 2000 : SYstem Modeling in BOndgraph Language and Simulation Allows users to create models using bond graph, block-diagram and equation models.

Large number of advanced sub-models called Capsules are available for different engineering and modeling domains.

has a well-developed controls module, that automatically transforms state-space modules from BG or block diagram models and converts them to analog or digital transfer functions. Most control charts and high-level control analysis can be performed. This software is recommended for use in research and industrial modeling of large systems.

FDI analysis tool boox is developed by B. OUL DBOUAMAMA & A.K. Samantaray

210


Some demonstrations using SYMBOLS 2000 and 20sim

From BG model to Matlab S-functionFrom BG model to Matlab S-functionGUI interfaceGUI interface

211


CONCLUSIONS Modelling

Unified representation language Shows up explicitly the power flows Makes possible the energetic study Structures the modeling procedure Makes easier the dialog between specialists of differents physical domains Makes simpler the building of models for multi-disiplinary systems Shows up explicitly the cause - to efect relations (causality) Leads to a systematic writing of mathematical models (linear or non linear associated

Simulation Specific softwares (CAMAS, CAMP+ASCL, ARCHER, 20 SIM) A priori knowledge of the numerical problems which may happen (algebraic-differential

equation, implicit equation) by the means of causality Physical meaning of the variables associated with the bon-graph mode For fast Prototypage

Control, monitoring

212


Many Thanks

213

Any comments are [email protected]

Documents

ResearchDirector at Ecole Polytechnique de Lille http