1 « Integrated Design of Mechatronic Systems using Bond Graphs » Prof. Belkacem OULD BOUAMAMA Responsable de léquipe MOCIS Méthodes et Outils pour la conception

1« Integrated Design of Mechatronic Systems using Bond Graphs »

Prof. Belkacem OULD BOUAMAMA

Responsable de l’équipe MOCIS Méthodes et Outils pour la conception Intégrée des Systèmeshttp://www.mocis-lagis.fr/membres/belkacem-ould-bouamama/

Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS - UMR CNRS 8219

et Directeur de la recherche à École Polytechnique de Lille (Poltech’ lille)----------------------------------------------------------

mèl : [email protected], Tel: (33) (0) 3 28 76 73 87 , mobile : (33) (0) 6 67 12 30 20

Ce cours est dispensé aux élèves de niveau Master 2 et ingénieurs 5ème année. Plusieurs transparents proviennent de conférences internationales : ils sont alors rédigés

en anglais . Toutes vos remarques pour l’amélioration de ce cours sont les bienvenues.

Integrated Design of Mechatronic Systems using

Bond Graphs.

Ce cours et bien d’autres sont disponibles à http://www.mocis-lagis.fr/membres/belkacem-ould-bouamama/

http://www.mocis-lagis.fr/membres/belkacem-ould-bouamama/

mailto:[email protected]



2 « Integrated Design of Mechatronic Systems using Bond Graphs.»

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

1. Bond graphs for modelling J. Thoma et B. Ould Bouamama « Modelling and simulation in thermal and chemical engineering » Bond graph Approach , Springer

Verlag, 2000.

« Les Bond Graphs » sous la direction de Geneviève Dauphin-Tanguy. Collection IC2 Systèmes Automatisés Informatique Commande et

Communication, Edition Hermes, 383 pages, Paris 2002.

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 BE8281.2. 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.

Few References

Few References



CONTENTS (1/3)

CONTENTS (1/3) 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, …)



CONTENTS (2/3)

CONTENTS (2/3)

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: Application to industrial processes Electrical systems Mechanical and electromechanical systems Process Engineering processes : power station


CONTENTS (3/3)

CONTENTS (3/3)

CHAPTER 6: 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

ANNEXE1: Case studies Symbols2000 Software Tutorial and How to create Capsules ? Case Studies Application des Bond graphs en énergétique

ANNEXE2: A paper (in French) published in “Techniques de l’ingénieur” : Copyright please : do not diffuse

B. Ould Bouamama et G. Dauphin-Tanguy. "Modélisation par Bond Graph. Application aux systèmes énergétiques". Techniques de l'Ingénieurs, 16 pages BE8281, 2006.

B. Ould Bouamama et G. Dauphin-Tanguy. "Modélisation par Bond Graph. Eléments de Base pour l'énergétique". Techniques de l'Ingénieurs, 16 pages BE8280, 2006.




1. Bond graphs for modelling J. Thoma et B. Ould Bouamama « Modelling and simulation in thermal and chemical engineering » Bond graph Approach , Springer

Verlag, 2000.

« Les Bond Graphs » sous la direction de Geneviève Dauphin-Tanguy. Collection IC2 Systèmes Automatisés Informatique Commande et

Communication, Edition Hermes, 383 pages, Paris 2002.

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 BE8281.2. 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.

Few References

Few References


PART 1PART 1

INTRODUCTION & MOTIVATIONS




SKILLS and OBJECTIVESSKILLS and OBJECTIVES Systemic approach for global analysis of complex multiphysic systems .

Finding innovative solutions

Reasoning based on analogy .

Transversal skills on dynamic modeling of Engineering systems independently of their physical nature.

Deduction in a systematic way state equations and their simulation diagram for nonlinear 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



ORGANISATION OF THE LECTURE

ORGANISATION OF THE LECTURE

Lecture : 16h Illustrated by pedagogical examples and real systems Case Studies : Dynamic vehicle Simulation, Active suspension active,

Robotics, Power station, Hydraulic platform, …).

Case Study : 14h Integrated design of simulation platform of multiphysical system using

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



Objectifs et organisation du cours 5/5

Objectifs et organisation du cours 5/5

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



Chapter 1Chapter 1

Introduction to integrated design of engineering systems


Motivations

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 taskMultidisciplinary project management

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




What is Mechatronic Systems

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.


Mechatronics ; Synergetic Effects

Mechatronics ; Synergetic Effects

Information technologySystem theoryAutomatic controlComputer engineeringDiagnosisArtificial IntelligenceSoftware

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

MechanicsHydraulics, Thermal engineering,MechanismPneumaticMechanical elelentsPrecision mechanics

MECHATRONICS


Examples of Mechatronic systems

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 ….;

Automation systems : Vehicle stability control; Automated landing of aircraft in adverse weather; Precision control of robots, Design of hybrid vehicle …;


From Electromecanical to Mechatronic systems

From Electromecanical to Mechatronic systems

Before 1950Complex systems are studied as electromechanical sub systems

Around 1950Emergence 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 Yaskawa Electric Corporation


Definition of MechatronicsDefinition of Mechatronics

Definition given by Rolf Isermann: The new integrated systems changed from electro-mechanical systems

with discrete electrical and mechanical parts to integrated electronic-mechanical systems with sensors, actuators and digital microelectronics.

18 « Integrated Design of Mechatronic Systems using Bond Graphs.» 18\18

Methodology for testing

Methodology for testing

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

Tests in Mechatronic systems

Tests can be executed usingDynamic 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)


Cycle en V

Cycle en V

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



Bond Graphs : Tools for Integrated Design

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,…) .



LEVELS OF MODELLINGLEVELS OF MODELLING

1. Technological

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

3. Mathematical dxyxfxi ),(

4. Algorithmic

WhatWhat

to do ?to do ?

WhatWhat

to do ?to do ?

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.

The algorithmic level is connected directly with information processing, indicates how the mathematical models are calculated



THE FOUR LEVELS IN THE BG REPRESENTATION

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



WHAT WE CAN DO WITH BOND GRAPH ?

WHAT WE CAN DO WITH BOND GRAPH ?



BOND GRAPH FOR ALARM FILTERING

National Project : EDF-LAIL

world-wide project: CHEM



THE EKOFISK JACKING OPERATIONTHE EKOFISK JACKING OPERATION



Raising of 6 decks and their interconnecting bridges simultaneously by 6,5 meters

Heaviest platforms deck 10.000 tons

Raising to take place in summer 1987

Expected shut down 28 days

A feasibility study in coordination with Phillips Petroleum Company. Norway, during the second half of 1985

The jacking operation



TYPES OF INDUSTRIAL APLICATIONS

TYPES OF INDUSTRIAL APLICATIONS

Electrochemical integrated with transport sytem

Nuclear power plant

FCC process : Refinery Catalytic Cracking.


Bond Graph for Integrated Supervision designBond Graph for Integrated Supervision design

Dynamic Models generation

RRAs generation

Sensor Placement

Diagnosis Results

New instrumentation architecture

Process

Real Time ImplementationReal Time Implementation

Datas from process

Sensors

P&ID

Structural Analysis

RRAs

Technical specifications


Dedied Software (FDiPad)

Dedied Software (FDiPad)


Graphical User Interface (1/4)Graphical User Interface (1/4)

Architectural model

Behavioral model

Data base

32 « Integrated Design of Mechatronic Systems using Bond Graphs.» 32\

Graphical User Interface (2/4)Graphical User Interface (2/4)

Fault signature

Residuals


Architectural model

Architectural model


TECHNICAL SPECIFICATIONS AND MONITORABILITY ANALYSIS

TECHNICAL SPECIFICATIONS AND MONITORABILITY ANALYSIS


Sensor placement

Sensor placement

36 « Integrated Design of Mechatronic Systems using Bond Graphs.» 36\

Simulation interface

Simulation interface

37

PART: 2PART: 2

Bond Graph Theory

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, …)

38« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

FoundersFounders

J. Thoma


THE FIRST IDEA

THE FIRST IDEA

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

The first paper


HISTORIC OF BOND GRAPH MODELLING

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 LondonUniversity of Enshede (The Netherlands)

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


DEFINITION, REPRESENTATION

DEFINITION, REPRESENTATION

DEFINITION

REPRESENTATION

P = e.f

e

f

1 2

Mechanical power :


Bond as power connection

Bond as power connection

The power is represented by the BOND

Bond

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

direction of power


Bonds activation

Bonds activation

INFORMATION BONDSThe 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



Bond Graph model in block diagramme

Bond Graph model in block diagramme

CORRECTOR ACTUATOR BOND GRAPH

MODEL

SENSOR

CX

Y

Information system Energetic system


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)

C

vertex

Submodel (Component)

E

vertex

Submodel (Component )

E




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 ?


1. Power variables1. Power variables

Two multiports are connected by power interactions using Variables

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

Two conjugated variablesEffort e(t) : voltage, temperature, pressure Flow f(t) : mass flow, current, entropy flow,

)(tf

)(te

)().()( tftetP


How to select them

How to select them


Tamb

(J,f)

Chimie , electrochimie

Mécanique

Thermique

Électrique

Economique

Hydraulique

Thermofluide

Thermodynamique


Electrical

DOMAIN

Mechanical (rotation)

Hydraulic

Chemical

Thermal

Economic

Mechanical (translation)

POWER VARIABLES FOR SEVERAL DOMAINS

POWER VARIABLES FOR SEVERAL DOMAINS

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]


2. ENERGY VARIABLES2. ENERGY VARIABLES

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

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

)()()( 0

0

tpdetpt

t

)()()( 0

0

tqdftqt

t

t

txmFFdtxmtp

0

)(:Momentum


Why energy variables ?

Why energy variables ?

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

pq

dppftdqqet )()(,)()( EE Why energy variables ?

1

0

1

0

1

0

1

0

1

0

20

21p

20

21p

2

1)()()(E

2

1.)()(E

qq

qq

qq

xx

qq

qqC

dqC

qdqqudqqet

kxkxxdxkdqqet Energy stored

by a spring


Electrical

DOMAIN

Mechanical (rotation)

Hydraulic

Chemical

Thermal

Economic

Mechanical (translation)

ENERGY VARIABLES FOR SEVERAL DOMAINS

ENERGY VARIABLES FOR SEVERAL DOMAINS

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]

?


Energy variables : analogy

Energy variables : analogy

V

dtVVx

Vf

Pe

idtqx

if

ue

dtQQx

Qf

Te

dtxxx

xf

Fe

Liudtp

if

ue

xMFdtp

xf

Fe

P,V u,q

iQ

Q,T

x

x, F

Displacement

xF,

u,

i

Impulse

V


Why pseudo bond graph?

Why pseudo bond graph?

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 ….


PSEUDO BOND GRAPH

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


Pseudo energy variables

Pseudo energy variables

Mass m stored by any accumulator,

Total enthalpy (or internal energy) U stored by any heated tank,

Number of moles n accumulated in a reactor.

Thermal energy Q stored by any metallic body.

57

Let us learn bond graph language

Let us learn bond graph language

Go head


EXAMPLE1 : ELECTRICAL INDUCTION MOTOR

EXAMPLE1 : ELECTRICAL INDUCTION MOTOR

wua

ui

ia

LOAD

(J,f)

ELECTRICAL PART MECHANICAL PART

Inductor

RaLa

ELECTRICAL PART

ua

ia

MECHANICAL

PART

w LOAD


EXAMPLE 2: POWER STATION

EXAMPLE 2: POWER STATION

FEED WATER

RECEIVER

HEATER

TH HQ

BOILER TW

WH

PW

Wm

MOTOR

TB

BH

PB

Bm TURBINE

STEAM

HEATER

TURBINE

PUMP TR

RH

Rm

PP

PIPE TP

PH

PP

Pm

PUMP

RECEIVER

U i

Load U

isource

60

Where is the generecity ?Where is the generecity ?


FEW ELEMENTS FOR A BIG PURPUSE

FEW ELEMENTS FOR A BIG PURPUSE

61\

Tamb

(J,f)Se

Sf

Sf

SeRS

R

R

R

R

R

TF

GY

II

I

I

C

C

C

C


BOND GRAPH ELEMENTS

BOND GRAPH ELEMENTS

ACTIVE ELEMENTSGenerate and Provide a power

to the system

SfSe

One port element

R,C,I,

Se,Sf0,1

Tree ports element

BOND GRAPH ELEMENTS

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

energy

R C I

TF, GY

Two 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


Bond graph well suited automated modelling

Bond graph well suited automated modelling

JunctionsJunctions

Passive elementsPassive elements

Active elementsActive elements

JunctionsJunctions

SYMBOLS

DEMOS


Passive elementsPassive

elementsRepresentation

DefinitionThe 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).

R, C, Ie

f R, C, I

e

f


R element (resistor, hydraulic restriction,

friction losses …) R element (resistor, hydraulic restriction,

friction losses …)

0, feR

v1v2

i

ELECTRICAL

R Constitutive equation : For modeling any physical

phenomenon characterized by an effort-flow relation ship

fR:R1Representation e

HYDRAULIC

2

21

21 0

VRPP

VRPP

p1 p2V

128

4DR

021 QRTT

T1 T2

Q

THERMAL

AR

021

RiU

Uvv


Examples of R elements

Examples of R elements


R1

2

nn

21

R

u

i

R:Re

u

i

xF

F

R

R:Rm

F

xR:Rt

n

Re

f

(a)

(b) (c)

R

1P 2P21 PPP

V V

R:Rh

P

V(d) (e)


BUFFERS

BUFFERS

C Constitutive equation (For modeling any physical phenomenon

characterized by a relation ship between effort and flow

A) C element (capacitance) Examples: tank, capacitor, compressibility

ELECTRIC

i1 i2

C

i

CV

dtVC

p

ghpdtAhd

VVV

1

,)(

21

HYDRAULIC

1V

h

A: sectionh: level: densityC= A/g

p

2V

t

t

mcCCQ

dtQC

T

dtTmcd

QQQ

1

.)(

21

0,, qefdteCC

fC:C1Representation e

THERMAL

mcT

1Q 2Q

Cq

idtC

U

dt

UCd

dt

dqiii

1

).(21


Examples of C elements

Examples of C elements


xF

FC

u

i k

C:C1

u

iC:1/k

F

xC:A/(g)

P

V

(a)

(b) (c) (d)

V

P g

Ce

dt

dqf


0,, pfedtf II

fI:I1 Representation

e

I Constitutive equation (For modeling any physical

phenomenon characterized by a relation ship between flow and effort

Inertance : I element

Inertance : I element

ELECTRIC

V1 V2i

0

01

Li

UdtL

i

p1 p2

V

HYDRAULIC

l

A

lI

VIp

PdtI

Pdtl

AV

dt

Vd

A

lA

dt

dv

A

m

A

FPP

0

1

2

0

11

.

xIQ

IQ

FdtI

Fdtm

x

dtxd

mF

MECHANICAL

F

: Magnetic flux p : impulsion of pressure

Q : momentum


Tetrahedron of State

Tetrahedron of State

C

I

R

0),,( CqeC

fdt

dq e

dt

dp

0),,( IpfI

e

q

f p

0),,( RfeR

C

I

C

I

R

0),,( CqeC

fdt

dq e

dt

dp

0),,( IpfI

e

q

f p

0),,( RfeR

C

I

4 variables : e, f, p, q 3 Bg elements : R, C, I

dttfC

e

eCq

)(1

.

energy Potential CAPACITOR

Rfe ousInstantane

DISSIPATOR

dtteI

f

fIp

)(1

.

energy KineticINDUCTOR

ENERGY

POWER

dt

d

ef

fq

e pPotential Kinetic

dt

d

ENERGY

POWER

dt

d

eef

ffqq

ee ppPotential Kinetic

dt

d


TRANSFORMER

TRANSFORMERConvert energy as well in one physical domain as well between

one physical domain and anotherExamples: 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

e2

u

Defining relation e1 = m(u).e2,

f2 = m(u).f1


EXAMPLES OF TRANSFORMERSEXAMPLES OF

TRANSFORMERS

TF:m

1u

1i

2u

2i

12

21

mii

mUU

TF:b/a

12

21

.

.

xa

bx

Fa

bF

F2F1

1x 2x

u1u2

i2i1

Electrical transformer

xF ,

VP ,

Hydraulic piston

TF:A

P

V

F

x

VA

x

FA

P

.1

1

Hydraulic power is transducted

into mechanical power

A : area of the piston

F2

F1

2x

1x

a b

Lever


4. GYRATOR

4. GYRATORConvert 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 relation e1 = rf2

e2 = rf1

Where r : modulus

f1

MGY:r

e1

f2

e2

u

Modulated Gyrator (if r is not cste)

Defining relation e1 = r(u)f2

e2 = r(u)f1


u

i

GY:r

u

i

= ri

= K(iind)iMGY:r

u

i

iind

r = K(iind)

MODULATED GYRATYOR

Example of gyrator : DC motor

Example of gyrator : DC motor


ACTIVATED ELEMENTS (1/2)


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.

1. Effort source SeGenerator of voltage, gravity force, pump, battery...

fSe

eSe = e(t)

fMSe

e

Modulated effort source

u Se = e(t,u)

Simple effort source




2. Flow source SfCurrent generator, applied velocity..

Representation

fSf e

Sf = f(t)

fMSf

e Modulated flow source

u Sf = f(t,u)

Simple flow source


0 - JUNCTION “ Common effort junction”

0.... 44332211 fefefefe

Power conservation

0.1

n

iiii fea

ai = +1 if 0

ai = -1 if 0

0e1

e2

e3

e4

f1

f2

f4

Representation

f3

JUNCTIONS (1/5)

JUNCTIONS (1/5)

Defining relation

02341

4321

ffff

eeee


Jonction 0 : Loi de conservation d’énérgie

Jonction 0 : Loi de conservation d’énérgie

213 HQHU

2H0

3H

1Q

C:Ct

U T

Bilan énergétique

23 mmm

2m0

3m

C:Ch

m P

Bilan massique

1QmP

UT

,

,

33,mH

22 ;mH

Cas dynamique

0

3m 3P

1P2P

132 mmm

Bilan massique

1m 2m.P3.P1 P2

Cas statique

11, Hm 22 , Hm

33, Hm

0

3H

2H1H

Bilan énergétique

132 HHH


JUNCTIONS (2/5) : 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

3V

P

321 VVV

2x 1

I:Mc

2x

Mc

Mp

2x

1x

Se:Fr

C:1/k

1

I:Mp

1xSe:Fr

1x


1e1

e2e3

e4

f1

f2

f4

1 - JUNCTION “ Common flow junction”

Representation

0.... 44332211 fefefefe

04321

4321

eeee

ffff

Defining relation

Power conservation

0.1

n

iii ea

ai = +1 if 0

ai = -1 if 0

JUNCTIONS (3/5) : 1 JUNCTION

JUNCTIONS (3/5) : 1 JUNCTION




VVVV 321

1P1

2VP2 1

3V

R:R1 R:R2

P2 -P31V

1V

P3

P1 -P3P1 P2P3

R1 R2

1V 2V 3V

EC

R L

UR UL

UCi 1

E

i i

i

Se:E

E =UR + UL + UC

UR

R

L

C

UL

UC i

k x

M

F(t)b 1F FR

FC

C:1/k

2xx

I:M

R:b

FM


Junction 1 : thermal system

Junction 1 : thermal system

1T1

T2

R

TR

2Q1Q

RQ

T1T2

Q

QQQQ

TTT

R

R

21

21 0

Cas statiqueCas dynamique

1T1 T2

R

TR

2Q1Q

RQCR

CR

QQQQ

TTTT

21

21 0

CQTC

C


Exercise

Exercise

L1

E C1

R1

i1

i2

i4

R3

L2

i3 i6

R2 C2

k

mg

Mp

i5


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

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.


Structural Model

Structural Model

u

y

Din

Dout

ix

dx

iz

dz

Sources

Se, Sf

Structure de Jonction

0, 1, TF, GY

Dissipation

d’énergie

R

Stockage

d’énergie

I , C

Capteurs

De, Df


Summary

Summary

Symbol

Resistance

Capacitance

Inertance

Transformer

Zero junction :common effort

junction

arbitrary)(

source by thegiven )(

tf

te

Source of flow

0),( feRf

eR

0, qeC

0, pfI

m :TF

e1 e2

f2f1

12

21

mff

mee

Gyratorr :

GYe1 e2

f2f1

12

21

rfe

rfe

e1 e2

f2f1

0

e3f3

0321

321

fff

eee

e1 e2

f2f1

1

e3f3

0321

321

eee

fff

Sour

ces

Ene

rgy

stor

esT

rans

duce

rsJu

ncti

ons

Sen

sors

Dis

sipa

tor

Pas

sive

elem

ents

Junc

tion

s

Sensors (Detectors)e

f=0De:e

Df:ff

e=0

Sen

sors

Se:e

e

fSf:f

e

f

f

eC

f

eI

0

)(

f

tee

0

)(

e

tff

arbitrary)(


te

tf

One junction :common

flowjunction

Constitutive equation Name

Source of effort

Symbol

Resistance

Capacitance

Inertance

Transformer

Zero junction :common effort

junction

arbitrary)(


tf

te

Source of flow

0),( feRf

eR

f

eR

0, qeC

0, pfI

m :TF

e1 e2

f2f1

12

21

mff

mee

Gyratorr :

GYe1 e2

f2f1

12

21

rfe

rfe

e1 e2

f2f1

0

e3f3

e1 e2

f2f1

0

e3f3

0321

321

fff

eee

e1 e2

f2f1

1

e3f3

0321

321

eee

fff

Sour

ces

Ene

rgy

stor

esT

rans

duce

rsJu

ncti

ons

Sen

sors

Dis

sipa

tor

Pas

sive

elem

ents

Junc

tion

s

Sensors (Detectors)e

f=0De:e

Df:ff

e=0Df:f

f

e=0

Sen

sors

Se:e

e

fSf:f

e

fSe:e

e

f

e

fSf:f

e

f

e

f

f

eC

f

eC

f

eI

f

eI

0

)(

f

tee

0

)(

e

tff

arbitrary)(


te

tf

One junction :common

flowjunction

Constitutive equation Name

Source of effort


BUILDING ELECTRICAL MODELS

BUILDING ELECTRICAL MODELS

1. Fix a reference direction for the current, it will be used as power direction2. For each node in circuit with a distinct potential create a 0-junction3. Insert 1-junction between two 0-junctions, attach all bond graph elements

submitted to the potential difference (C,I,R,Se,Sf elements) to this 1-junction4. Assign power directions to all bonds5. For explicit ground potential, delete corresponding 0-junction and its

adjacent bonds. If non explicit ground potential is shown, choose any 0-junction and delete it

6. Simplify resulting bond graph (remove extraneous junctions); for example 1 0 1 is replaced by 1 1

Hydraulic, thermal systems similar, but mechanical different


Simplifications of Bond graphs

Simplifications of Bond graphs

0 1 Example of simplification

01

C

0

C

1 0 0

C

1

R

C

0 1

R

1 0 1

C

0

R

C

0 R


Electrical circuit : Example1


E

R1

ba

g

C

b

0

g

0

(2)

a0

1

1

1

R:R1

C

Se:E

a0

b

0

g

0

(3,4)

1

1

1

R:R1

C

Se:E

a0

b

0

(5)

1

R:R1

CSe:E

(6)

(1)


Electrical circuit : EXAMPLE2

Electrical circuit : EXAMPLE2

1

R:R1

uR1

Se:EE

iR1

iC1

0

C:C1

uC1

iR1

1

I:L1

iL1

uL1

uC1

iL1

1TF

I:L2

R:R2

L1

E C1

R1

0iR1

iC1

iL1 R2

L2




L1

SE C1

R1

iR1

iC1

R2

C2 SF

iR2

iC2

SF


BUILDING MECHANICAL MODELS

BUILDING MECHANICAL MODELS

1. 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


Mechanical system : EXAMPLE (1/2)

Mechanical system : EXAMPLE (1/2)

fk

ref

VV

VV

,

, 1

es velocitiRelative

s velocitieAbsolute

g

k f

Vref

V1

(2) 1

1

Vref

V1

1Vk

1Vf

C:1/k

I:M

R:f

(3)

REFf

REFk

VVV

VVV

1

1

Relationship between velocities

(4)

1

1

Vref

V1

1Vk

1Vf

C:1/k

I:M

R:f0

Se:-Mg

Sf(5,6)

0

V1

Vref

Vref

V1


Mechanical system : EXAMPLE (2/2) (Simplifications)

Mechanical system : EXAMPLE (2/2) (Simplifications)

1

1

Vref

V1

VkVf

C:1/k

I:M

R:f0

Se:-Mg

Sf

0

V1

Vref

Vref

V1

1V1

1Vk

1Vf

C:1/k

I:M

R:f0

Se:-Mg

Sf(5,6)

0

V1

Vref

Vref

V1

1

1V1

1Vk

1Vf

C:1/k

I:M

R:f0

Se:-Mg

Sf(5,6)

0

V1

Vref

Vref

V1

1

Fkreff

refkVV

VVV

VVV

1

1

1

V1-Vref

Sf

Vref

0 1Vf

R:f

Vk

C:1/k

1V1

Se:-Mg I:M Se:-Mg

1

R:f

C:1/kI:M

Eliminate any zero velocity 1-junctions and

their bonds

V1

Vf

Vk

fkref VVVV 10 if

0 1

0

Simplification


Exercise 1 : mechanicalExercise 1 : mechanical

1

R:f1

C:1/k1

C:1/k3R:f2

I:Mb

0

0

1

I:Ma

Se:-F(t)

C:1/k2

1fx

1kx

3kx

2fx

MBxMAx

2kx

x MAx MB

x

Ma

k2

k3k1

f1

f2

Mb

F(t)

m1 m2 m3

R3k1 k2

k3 F(t)

+Vref=0

m1,f1 m2,f2 m3,f3


Electro-mechanical sytem

Electro-mechanical sytem

)( FirMGY

IF

1

R:Ra

I:La

Se:UF

IFUR

UI

1

R:Ra

I:La

Se:UA

IAUR

UI

Um

IA 1

R:B

I:J

Se:Loadm

m

R

I


Exercise 3 : Hydro-mechanical and suspension

Exercise 3 : Hydro-mechanical and suspension

R4

1V

C1

C2

C3

Se1

Sf

R7

R5

R6

Air

Pompe P1

Piston

Cylindre

Compresseur

3V

2V

Atm

osph

ère

Se2:

P0

Arbre

De:L

Mp

Mc

Mp

2x

1x

Sf:Fr

C:1/k R:Ra


BUILDING HYDRAULIC MODELS

BUILDING HYDRAULIC MODELS

1. 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


Hydraulic system : EXAMPLE (1/2)

Hydraulic system : EXAMPLE (1/2)

Inertia IResistance R1 Resistance R2Pump

P1 P2 P3 P4 Pat

Se:P1 0P10P2 0P3 0P4

Pat

01 1 1

R:R1 I

1

R:R2C

C

V

Se:P1 1

R:R1

1 1

IR:R2

0

C

Se:P1

R:R1

1

I

R:R2

C


EXAMPLES OF BG MODELS : Hydraulic

EXAMPLES OF BG MODELS : Hydraulic

0

C:CR

R:R1

Se:PP

PP

1RV

I:l/A

1

P P -PR

PR

1RV 2RV

PRSe:-P0

2RV

P0

1

R:R2

PR -P0

Valve 1

R2PumpPP

PRLC

P0

De

PID


EXERCISES : Mechanical (pneumatic valve)

EXERCISES : Mechanical (pneumatic valve)

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


EXERCISES : Bond graph model of the pneumatic valve

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


EXERCISES : Hydraulic control system

EXERCISES : Hydraulic control system

PID0,2 -1 bar 3 - 15 psi Pe

xLT PR sV

eV

P0


EXERCISES : Bond graph model of the hydraulic system

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

V

TF:A

F

x

I:m

FI

R:f

Ff

xDf :

PID

u

ePMSe :


EXERCISES Hydraulic systems

EXERCISES Hydraulic systems


EXAMPLES OF BG MODELS :ThermalEXAMPLES OF BG MODELS :Thermal

C:Cb

0

bQTS

R:Ra

1aQ

TS

TS - Ta

aQ

Se:-Ta

Ta

aQ

TS

SQSQSf :

Ts

Ta

Source of heat

SQ

107« Integrated Design of Mechatronic Systems using

Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

PART 3PART 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



CAUSALITIES

CAUSALITIES

DefinitionCausal 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 proprietiesSimulation Alarm filtering MonitoringabilityControllabilityObservability



Convention

Convention

A B e A B

System A impose an effort e to system B

e

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

f

Cause effect relation : effort pushes, response is a flow

Indicated by causal stroke on a bond

Effort pushes

Flow points



PRINCIPLE

PRINCIPLE



CALCULATION EXAMPLE

CALCULATION EXAMPLE

PR

V

PKV

PR2

K

VP

V

P1

P

P2

V

R:K

1P1

P2

PR

R:K

1P1

P1

P



Remarks about causalities

Remarks about causalities

the orientation of the half arrow and the position of the causal stroke are independent

e

f

A B

e

f

A B

A B e

System A impose effort e to B

A B f

System A impose flow f to Be

f



Causality for basic multiports

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 R

1

)(1

=

=

fR

e fe

ef

f

eR

iRu

fFe R

.

)(

Resistance causality

RF

fSe

e

fSf

e



Integral and derivative causality

Integral and derivative causality

Preferred (integral) causality

fC

dti

Cu

fdtFe C

.1

e

f

eI

dtu

Li

dteFf I

.1

. e

f

Ce

dt

duCi

dt

deFf C

.

1 fdt

de

fI

dt

diLu

dt

dfFe I

1f

dt

d e

Derivative causality



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

Strong bond

24

23

21

ff

ff

ff

3412 eeee 1-Junction

e1

e4

e3

f2

Block diagram





Only 1 causal stroke near 0 - junction

Rule

0e1 e3

e4

f1

e2

f4

f3

f2

24

23

21

ee

ee

ee

3412 ffff 0-Junction

f1

f4

f3

e2

Block diagram

0.... 44332211 fefefefe

Strong bond



TF JUNCTION

TF JUNCTION

f1

TF:m

e1

f2

e2Defining relation

e1 = m.e2

f2 = m.f1

Where m : modulus 2 CAUSALITY SITUATIONS

12

21

mff

mee If e2 and f1 are known :

e1me2

f2mf1

f1

TF:m

e1

f2

e2

f2



CAUSALITY OF TF JUNCTION

CAUSALITY OF TF JUNCTION

21

12

1

1

fm

f

em

eIf e1 and f2 are known :

f2

TF:m

e2e1

f1

e21/me1

f1f2 1/m

RULE : A symmetrical position of the causal stroke



CAUSALITY OF GY JUNCTION


2 CAUSALITY SITUATIONS

12

21

rfe

rfe If f2 and f1 are known :

e1rf2

e2rf1

f1

GY:r

e1

f2

e2

f2

f1

GY:r

e1

f2

e2 Defining relation e1 = r.f2

e2 = r.f1

Where r : modulus





21

12

1

1

er

f

er

f If e1 and e2 are known :

f2

GY:r

e2e1

f1

f21/re1

f1e2 1/r

RULE : Skew - symmetrical position of the causal stroke



Sequential Causality Assignment Procedure (SCAP)

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 better to add other elements (R) in order to avoid causal conflicts. This elements must have a physical means (thermal losses, resistance …).



e

f

Power variables show the type of energy

Four Information given by BG

Four Information given by BG

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


From BG to Bloc Diagram (1/2)









Application to Electrical system : BG model

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



Application to Electrical system:State equation

Application to Electrical system:State equation

Cxy

BuAxx

u x

y6

6

2

6

2 ,)(, eytESeuf

e

q

px

2. STATE EQUATIONS

• Structural laws

- 1 junction

4312

242321 ,,

eeee

ffffff

- 0 junction

546

6564 ,

fff

eeee

• Constitutive equations

52

5

313

666

222

1

1

1

eR

f

fReC

qdtf

Ce

L

pdte

Lf

6

26

6

2

2

1

6

2

10

)(0

111

1

q

p

Cey

tEq

p

CRL

CL

R

q

p



Application to Electrical system : Block Diagram (1/2)


E CL

R2U(t)

R1

1

I:L

Se:EE

1

5

0

R:R2

R:R1

6

4

2

3

C

2

1

R

f6

f5

-

Se:Ee2

e3

+

-

-

e1

e4

L

1 f2

f2(0)

C

1 e6

e6(0)

1-Junction

e2=e1-e3-e4

f2=f1=f3=f

4

0-Junctionf6=f4-f5

e6=e4=e5

1R





Causal graphCausal graph

Bloc DiagramBloc Diagram



Application to Hydraulic system: BG model

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

PC

RCVP0

2RV2RV1

R:R2

PR2

Se:-P0

Atm

osp

here



Application Hydraulic system: Block Diagram

Application Hydraulic system: Block Diagram 1 junction 11 RCPI PPPP

0 junction 21 RRRC VVV

1 junction 02 PPP CR

• Structural laws

• Calcul de CR et I1

dtVA

gP

dt

Pd

g

A

dt

gPAd

dt

hAdV RCC

CCRC

)()/(.().(

g

ACR

dtPl

AV

dt

Vd

A

lAAP

lAmAPFdt

AVdmFe

Ic

RR

c

ccI

ccIcR

111

1

11

..

,.,/

, :lawwton N

cA

lI

1

• Constitutive equations

I:I1

C:CR

dtPI

VIR 1

11

1

dtVC

P RCR

C 1

law) (Bernoulli. 2111 RR VRP

law) (Bernoulli2222 RR VRP

R:R1

R:R2





Se:PP

PP

De:PC

uPID Pref

PC+ -

1

PI1

R:R1

I:I1

PR1

1RV PC

0

C:CR

1RV

PC

RCV

2RV 1

R:R2

PR2

Se:-P0

2RV

P0

Atm

osp

her

e

+ --

dtI

1Se:PP

PC

PR1

PP

1RV

1R

RC

1

2RV

2

1

R

Se:-P0

PR2

PC

+-

+ -PI1 RCV

21RV



EXAMPLE (How to avoid derivative causality ?)

EXAMPLE (How to avoid derivative causality ?)

E C

i

iC UC

dt

dECiC .

E C

Ri

iC UC

C

0E

i

UC

Se:E

iC

Derivative causality

Current infinite ?

dtiC

URC

1

R

1E

iR

uR iR

0uC

iR

iC

C

uC

Se:E

Integral causality adding R



Derivative causality : example

Derivative causality : example

1 TF:b/a 1Se:F(t)

I:M1 I:M2

C:1/k

1Se:F(t)

I:M1

TF:b/a

1

I:M2

C:1/k

0

C



Transfer FunctionTransfer Function

Se:EE

iR1

dtiC

Udttfc

e CC 11

11

)(1

1

R:R1

uR1 iR1

0uC1

iR1

iC1

C:C1

uC1

Causal Bond Graph Model

E C1

R1

iR

iC

UC1

Schematic

Equations from causal BG There is one C element in integral causality, so the differntial

equation is the 1st order (one state variable)

C element in integral causality

R element in conductance causality

iR1=UR1/R1

Junction 1 11 CR UEU

Junction 0 11 RC ii

1

1

)(

)()(

..

11

1

11

11

pCRpE

pUpW

EUdt

dUCR

C

CC



State Equations

State Equations

nrnmnn CBA

xCy

uxFx

cxy

buAxx

,,

)(

),(Nonlinear:Linear

SENSORS

ACTUATORSu

CORRECTOR PROCESS

x

y

yc

X-x

System to be controlled

M

A

DfDey

MSfMSe

SfSeu

dttf

dtte

q

Px

C

I

,

Auto. ,

Manual,

)(

)(

Bond graph



STATE EQUATION

STATE EQUATION

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

Propertiesthe 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

dtte

q

Px

C

I

)(

)(

)(

)(

tf

tex



HOW TO OBTAIN STATE EQUATION

HOW TO OBTAIN STATE EQUATION

WRITE STRUCTURAL LAWS ASSOCIAED WITH JUNCTION (0,1, TF, GY)

CONSTITUTIVES EQUATIONS OF EACH ELEMENT (R, C, I)

TO COMBINE THOSE DIFFERENTS LAWS TO OBTAIN STATE EQUATION



Application

Application

Se:Ua

ia

ua 1L

w

I:J

w

R:f

Se:-L

f

J

1

R:Ra

I:La

uM

ia

uRa

uLa

ia

Df:im

Df:wm

MGY:K

w

r = k(iF)



STATE EQUATION

STATE EQUATION

dtUL

i

dtJ

dtteI

tf

Laa

a

J

1

1

)(1

)(

Equations from causal BG

There is 2 I element in integral causality, so there is 2 state variable

I element in integral causality

R element in conductance causality

f

RiUfeF

f

aaRaR

0),(

MGY

a

M

Ki

KU 1- Junction

LfJ

MRaaLa UUUU

mm

La

emLaj

iy

Uu

MdtUdtx

m

ma iiSensor

m

e

Lmem

amee

M

Φ

ΓMΦM

UMΦΦ

Jy

Liy

J

f

La

KfKix

J

K

L

RUUUUx

m

am

LaLfj

a

aMRaaLa

1

1

2

1

2

1

State equation



SIMULATION

SIMULATION

m

e

L

a

m

e

m

e

M

Φ

Γ

U

M

Φ

M

Φ

Jy

Liy

J

f

La

KJ

K

L

R

x

m

am

a

a

1

1

2

1

Use of Symbols softwareAutomatic generation of the state

equation

JLC

B

JK

LR

Jf

LaK

A

a

a

a

11

1

1

)22(

)22(

)22(

mxn

nx

nxn

B

B

A



Application : do it

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

0

us

L1

E(t) C1

R1

iR1

iC1

iL1 R2

Us(t)

iR2

C2

De:Us(t)

1

2

3

4

5

6

7 8

9

10

11

12

S-FUNCTION FROM SYMBOLS

S-FUNCTION FROM SYMBOLS

BLOCK_DIAGRAM SIMULINK

BLOCK_DIAGRAM SIMULINK

COMPARAISON SYMBOLS_SIMULINK

COMPARAISON SYMBOLS_SIMULINK


COUPLED BOND GRAPHSCOUPLED BOND GRAPHS

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

PART 4PART 4



INTRODUCTION TO MULTIPORT ELEMENT

INTRODUCTION TO MULTIPORT ELEMENT

SINGLE BOND GRAPH : One energye

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

ei

f2

fn



Coupled bond graph

Coupled bond graph

Constitutive equations

0, qec

T

T

TPe

Hmnq

0,,,

0,,,

0,,,

nHm

nHmT

nHmP

ch

t

h

,,PT

CnmH ,, T

CH

P

m

n

Chemical

Hyd

rau

lic

Th

erm

al

CC



Coupled Bond graphs

Coupled Bond graphs

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)

Representation



Convection Heat transfer (1/2)


2

2vPumH

➽ General expression for convected energy

Internal specific energy Pressure energy Kinetic energy

),( mP

),( TH





➽ Modeling Hypothesis

2

2vPumH

TcmhmH p

02

: v velocity lowFor 2

v

]/[: kgJTcP

uh p

enthalpy Specific



Coupling of thermofluid variables

Coupling of thermofluid variables

TcmH p

T

Pm

mSf : 1

m

RcT

HTSe:



Thermofluid pump

Thermofluid pump

➽ Bond graph models

H

mhMSf

tMSf

mSfh :

TSe:

P

T

A) Modulated source

Pump as single flow source

mSfh :

TSe:

1

Rc

Pm

T

H

B) Using R Multiport

H

m


d

Activated bonds

Activated bonds

C) Use of an activated element

Sf

1

1

ee

fSf

01

1

e

fSff

1

Sf1

eSf

1

1

0

ee

Sf


SOFTWARE REPRESENTATION




d

How to modelise a sensor ?

How to modelise a sensor ?

Sf

0

C

Sf1

2

I

3

e

2222

23

33

3

22

2

1

01

1

QKdtfC

ee

dteI

f

dtfC

e

VA

gP

Hydraulic system case

PI


d





How to represent it in Symbols2000 ?

How to represent it in Symbols2000 ?

0

.

21

12

ee

fbf

1f

1e 2e

2fb

TF:

2121 , TTPP

mbTcmH p

mH ,HT

mP

,

,

1

1

HT

mP

,

,

2

2

CpMTF:H

mSfh :

TSe:

1m

T

m

ee

H

0

e

TcmH p1P 2P



Example of multiport elements

Example of multiport elements

R MULTIPORT

Representation

(kg/s)flowMass:

.)(Joule/secflowEnthalpy:

(pa)Pressure:

(Joule/kg)specificEnthalpy :h

(K)eTemperatur:

1m

H

P

T

1

1

1

11 )(

m

P

H

hT

2

2

2

22 )(

m

P

H

hT

1

1

1

11 )(

m

P

H

hT

11, PT

11,mH R

22 , PT

22 ,mH

1P

1HR

2T

2H

1

1T

1m

2P



Constitutive equation for R-multiport

Constitutive equation for R-multiport

mmmHHH 2121 , 11 , TcmHhmH p

Physical law ( Continuity)

Constitutive equation

),,,(),,,(

),,,(

),,,(

21214

21213

21212

21211

2

1

2

1

TTPPTTPP

TTPP

TTPP

H

H

m

m

R

R

R

R

12121

2121

)(1

)(1

TcPPPPsignR

PPPPsignR

H

m

ph

h

128

4DRh



Inertia of the fluid

Inertia of the fluid

I

pPdt

l

Am

dt

A

md

lAdt

dvmAPF

Ic

cccc

2.

1HRc

2T

2H

1T

Thermal power

Hydraulic power

1P1

1m

2P

2m

RI

➽ Impulse of pressure p l



Dynamic bond graph model of the pipe

Dynamic bond graph model of the pipe

Fluid moving with inertia

I

pdtP

I

mV

mRP

PPPP

I

hR

RI

1 I,Elément

, R,Elément

, , 1Jonction 21

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

A

Mxp

xAm

.

xAm

hR

PPm

dt

md 21

hh RAR

I



Bond graph model of the pipe

Bond graph model of the pipe

Global Model

Step response for hydraulic model to pressure difference

1

21

TcmH

R

PPm

dt

md

p

h

)0(11

)( mePR

tmt

eh



C - MULTIPORTS

C - MULTIPORTS

dtmhaQC

dtHaQC

maC

H

mn

iiii

T

n

iii

T

n

iii

h

11

1

.11

1

ii mH ,

oo mH ,

H,m

QHeater

Ph,

CmH ,

Representation

PT ,

mH ,C0

BG model

ii mH ,

ii PT ,

Input

QSf :

T Q

oo mH ,Output

oo PT , oo mH ,




Thermofluid example : heated tank

Thermofluid example : heated tank

Pe

l

eQ

Po=0

H,m

Two ports C

Tex

One ports C

Q

Te

T

TexQPeu

QmHpx

State variablesI element : p



Bond graph model

Bond graph model

De:T

De:L

ePSe:

C

Pm

01

5

7

T

02

H13

et QSf : 14

eTSe:eH

Rc1

15 16

em

exTSe:

13

1403

R:RexRm

Am

bian

ce

C

Q T

18Q

20Q

17

18

19

20

21

22

23

sm10

Env

iron

nem

ent

S

e:P

0=0

R:Rs

12

6

8

9

Rc2

1112

sH sH

11

R:ReI:I1

1

23

4

em


Constitutive equations (1/4)



Jonction 11

325

34

32

31

325

34

32

31

4234213

mm

mm

mm

mm

ff

ff

ff

ff

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

PP

PP

PP

ee

ee

ee

mmmmmfff se

Elément I:l/A





Jonction 02

1318

1317

1316

1314

1312

1318

1317

1316

1314

1312

1812216131812141613 )(

TT

TT

TT

TT

TT

ee

ee

ee

ee

ee

QHuQHUfffff e

Multiport C : CR 777

71371377Rh )0(1

),(),(C:C PPC

mdtf

Cdtfdtfqqe

hhChCh

hC

m

A

mg

A

VggLPe 777

77

niveau dans le réservoir indiqué par le capteur De :L

A

m

g

PL 77





Capacité thermique

)0()(

1),(),(C:C 13

7

1313

71313713713Rt T

mc

UdtU

mCTdtfdtfqqe

VtCtCt

Température indiquée par le capteur De :T 7

1313 mc

UT

V

Jonction 12

8109681096

68968 mmmmffff

PPPeee s

Vanne de réglage R :Rs

).()().(.)(

188

1888

188

18 PPsign

R

ummeesign

R

ueesign

uRf

ss

ss

Eléments R : Rm et R :Ra

aaa

mm

TTR

QeeR

f

TTR

QeeR

f

2223242223

201819201819

11

11





J onction 13 et 14

2324232223242322

2223242223

1920191819201918

201819201819

,,

et

,,

QQQQffff

TTTeee

QQQQffff

TTTeee

a

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

)0()0(1

2121

21212121 TC

QTedtf

Ce

mm

Jonction 03

2122212021222120

222021222021

,,

TTTTeeee

QQQfff

Eléments de couplage RC1 et RC2

1381112101211C2

31615251516C1

:R

:R

TcmHHecfff

TcmHHecfff

psp

epep


Global Dynamic Model

Global Dynamic Model


7

13

7

21

7

1321

221771

7

13313

77137

72

33

11

1

mc

UA

m

T

Ly

R

T

RRC

Q

Rcm

UQ

)(uQCR

QP

C

mP

C

msign

R

uc

Rmc

UTc

I

pU

PC

mP

C

msign

R

u

I

pm

C

m

I

pRPp

V

a

a

ammmV

emm

sh

shs

pmV

ep

sh

shs

hee


Simulation using State equations format

Simulation using State equations format


),( uxfu x

x(0)

)(xCyx

x

SimulinkSimulink

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


From BG to Block Diagram

From BG to Block Diagram


-

1

1

IePSe :

e2

f2)( 3Re f

f3e3 )( 7 dtfCh

e4

e8

-e7e1 f4

f7

f6

)( 8eu Rscf8

f6-+

sPSe :

),( 137 dtfdtfCt

e13

e6

e17

f13

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 RC2

e18

03

13

14

e20

02

eQMSf :+

TC

-

1

1

IePSe :

e2

f2)( 3Re f

f3e3 )( 7 dtfCh

e4

e8

-e7e1 f4

f7

f6

)( 8eu Rscf8

f6-+

sPSe :

),( 137 dtfdtfCt

e13

e6

e17

f13

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 RC2

e18

03

13

14

e20

02

eQMSf :+

TC

EXO SUR SYMBOLS


SYSTEMES CHIMIQUESSYSTEMES CHIMIQUES




in

in

in

in

m

P

H

T

Gaz

Physico chemical processes (1/4) Physico chemical processes (1/4)

)(,1

)(

,

*,

,

tsconstituennj

T

n

p

x

mixtureGaz

m

P

H

T

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

jnj

c

M,1

Variables Parameters



Physico chemical processes (2/4)Physico chemical processes (2/4)

H

T

m

P

Thermique

Hydraulique

Mixture

➽ A) Used variables

*ncP

ncn

Chemical

*1P

1n

*iP

inConstituents

➽ B) Mixture to constituents transformation ?

ncn

),1(. niM

xmn

i

ii *

iP

in

*1P

m

P 1n

*ncP



Physico chemical processes (3/4)Physico chemical processes (3/4)

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

M

xmn

➽ D) Use a transformer

mSf :P

ncn

*ncP

1n*iP

in

*1P

m

PBloc

iini Mx ,,

➽ C) Use a bloc diagramme


Physico chemical processes (4/4)

Physico chemical processes (4/4)


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

C

1

Rc

OUTPUT

ii Mx ,

outm

outH

outm

outm

outH



Chemical system

Chemical system

DCBA BAKr

K

BA

f

....

gS T

RS

fA rA1 1

E

nFTF:

Recepteur

i

Rel 1

G

ATF:

AAAC:CA

A

BTF:

BAB

C:CB

B

C:CC

C:CD

CTF:

DTF:

1

C

D

C

D


Electrochemical Process

Electrochemical Process



Electrochemical Model

Electrochemical Model


Chimique-électrique

Production H2O

Distribution de la tension


Integrated modelsIntegrated models



Thermoéconomie

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

m

m

C

C

D

C

D

C

D

C

H

H

m

m

C

C

DCBA DCK

K

BAr

f

Marketplace

exQ

Heater

Market place

Reactor

Inlet

Outlet



Chemical model

Chemical modelTransformation Products of reactionReactants A and B

TF:1/A

A

TF:1/D

TF:1/B

TF:1/C

C

DAnD

AAnA ArAf

nC

11

Dissipation

RS

C:CD

ABBBnB

1

C:CA

C:CCC:CB

TggS

To thermofluid model



Thermofluid model

Thermofluid model

BB HmSf ,:

exQSf :

D e

0

C : C RDD HmSf ,:

CHSf :

P R

Cm

T R

CHAA HmSf ,:

F r o m c h e m i c a l m o d e l

T o e c o n o m i cm o d e l



Economic model

Economic model

FAm&

b

Reinvestment

R:RT

R:RDC

1

FA

10

/0CUC

mP & a

R:RSC

Supplier

Factory inventory

PUC

Cm&

PSC

PFA

PIA

DCm& SC

m&

IAm&

From hydraulic

model

I:IA

C:C



BB HmS f ,:

FAm

b

I : I AexQS f :

D e

0

C : C R

R : R T R : R D C 1

C : C F ADD HmS f ,:

CHS f :

P R

Cm

10

/0 CUC mP a

R : R S C

S u p p l i e r

f a c t o r y i n v e n t o r y

H y d r a u l i c a n d t h e r m a l m o d e l E c o n o m i c m o d e l

C h e m i c a l m o d e l

T r a n s f o r m a t i o n P r o d u c t s o f r e a c t i o nR e a c t a n t s A a n 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 A rA f

n C

11

D i s s i p a t i o 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

CH

P S C

P F A

P I A

DCm SCm

I Am

AA HmS f ,:

R e i n v e s t m e n t

Global integrated model

Global integrated model



BB HmSf ,:

FAm

b

I:IA exQSf :

De

0

C :CR

R:RT R:RDC 1

C:CFA DD HmSf ,:

CHSf :

PR

Cm

10

/0 CUC mP a

R:RSC

Supplier

factory inventory

Hydraulic and thermal model Economic model

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

nD AA nA Ar A f

nC

1 1

Dissipation RS

C:CD

AB B B nB

1

C:CA

C:CC

C:CB

Tg gS

PUC

Cm

TR

CH PSC

PFA

PIA

DCm SCm IAm

AA HmSf ,:

Reinvestment


185

PART 5PART 5

Application to industrial processes

CHAPTER 5: Application to industrial processes Electrical systems Mechanical and electromechanical systems Process Engineering processes : power station


BG Methodology Of modeling complex system

BG Methodology Of modeling complex system

Improvement of the model by adding

elementsbond graph R,C,I

Physical process

Word bon graph

Acausal bond graph

Causalities assignment

Mathematical equationsExperimentaldatas

no

no

Data acquisition

yes

yes

< ad ?

Model outputs+

Causalitiescorrectes ?

Causality conflict

Validated model

-

Improvement of the model by adding

elementsbond graph R,C,I

Physical process

Word bon graph

Acausal bond graph

Causalities assignment

Mathematical equationsExperimentaldatas

no

no

Data acquisition

yes

yes

< ad ? < ad ?

Model outputs+

Causalitiescorrectes ?Causalitiescorrectes ?

Causality conflict

Validated model

-


Thermal system

Thermal system

Ta(t)

Tf

Tf

Tp2

3

1

TrTf

R1

u2

i3i2i1

u1uf uaC2C1

R2 R3

TI

Temperature source

Ta(t)Ta(t)

Tf

Tf

Tp2

3

1

TrTf

R1

u2

i3i2i1

u1uf uaC2C1

R2 R3

TI

Temperature source

Electrical analogy

Thermal system : bath of water heated by a source of temperature


Word bond graph of the thermal process

Word bond graph of the thermal process

TrTfBath

of water

Wall of the tank

Hot fluidTemperature

source

Ambient environment

fQ

External temperature

source

Tp Ta

aQpQ rQ

TrTfBath

of water

Wall of the tank

Hot fluidTemperature

source

Ambient environment

fQ

External temperature

source

Tp Ta

aQpQ rQ

R:Rp

Se:Tf

C:Cr

0 1211

R:Ra

Se:-Ta

De:Tr

1

234

5 6

7

8

9

pQDf:

R:Rp

Se:Tf

C:Cr

0 1211

R:Ra

Se:-Ta

De:Tr

1

234

5 6

7

8

9

pQDf:

Cas 1 : Thermal bond graph of the process neglecting the thermal capacity of the wall


Equations

Equations

368632

4765654

2951521

1 Jonction

0Jonction

1 Jonction

QQQ,TTT:

TTTTT,QQQ:

QQQQQ,TTT:

a

r

pf

aaa

r

t

rr

fpp

TTR

TR

Q,

C)(QQ

)(TdtQC

TT,

TTR

TR

Q,

633a

444

044R

522p

11R:RElément

00

1C:CElément

11R:RElément

Structural equations



State equations

State equations

r

p

a

fr

T

Qy,

T

Tu,QQx

4

)u,x(C)t(y

)u,x(F)t(x

)t(Du)t(Cx)t(y

)t(Bu)t(Ax)t(x

:caseNonlinear

: caseLinear

)t(T

)t(TR)t(Q

C

CR

)t(T

)t(Q)t(y

)t(T

)t(T

RR)t(Q

CRCR)t(Q)t(x

a

fpr

r

rp

r

p

a

f

apr

rarpr

00

01

1

1

1111


Block diagram

Block diagram

pR

1

rC

1

aR

1Se:Tf

T2

T5

(-)

Se:Ta

(-)(-)

Q4(0)

4765 TTTTT r

pQDf:

J11 J0

J12J11

J0

J12

4Q

rDe:T

T3

6Q

3Q2Q295 QQQQ p

9Q

T4

368 QQQ

7T

5Q 6T

pR

1

rC

1

aR

1Se:Tf

T2

T5

(-)

Se:Ta

(-)(-)

Q4(0)

4765 TTTTT r

pQDf:

J11 J0

J12J11

J0

J12

4Q

rDe:T

T3

6Q

3Q2Q295 QQQQ p

9Q

T4

368 QQQ

7T

5Q 6T

R:Rp

Se:Tf

C:Cr

0 1211

R:Ra

Se:-Ta

De:Tr

1

234

5 6

7

8

9

pQDf:

R:Rp

Se:Tf

C:Cr

0 1211

R:Ra

Se:-Ta

De:Tr

1

234

5 6

7

8

9

pQDf:


CHAP4/ 192

Refinement of the model by adding bond graph elements

Refinement of the model by adding bond graph elements

As an example, we can include the thermal capacity of the wall of the bath 1.

R:Rp

Se:Tf

C:Cm

0 121

R:Ra

Se:-Ta5

134

6 12 10

9

pQDf:

C:Cr

0

De:Tr

11

7

R:R2

2

18

13

R:Rp

Se:Tf

C:Cm

0 121

R:Ra

Se:-Ta5

134

6 12 10

9

pQDf:

C:Cr

0

De:Tr

11

7

R:R2

2

18

13


STATE EQUATIONS

STATE EQUATIONS

a

f

r

m

r

m

r

p

a

f

a

r

m

rarm

rmm

r

m

T

TR

Q

Q

C

CR

)t(T

)t(Q)t(y

T

T

R

RQ

Q

CRCRCR

CRCRCR

Q

Q

00

01

1

1

10

01

111

111

11

1

22

221


Automated modelling using Symbols

Automated modelling using Symbols


Link with Matlab-Simulink

Link with Matlab-Simulink


Easy to derive a model adding new elements

Easy to derive a model adding new elements


Electrical system

Electrical system

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

0

us

L1

E(t) C1

R1

iR1

iC1

iL1 R2

Us(t)

iR2

C2

De:Us(t)

1

2

3

4

5

6

7 8

9

10

11

12

SIMULATION using MATLABSIMULATION using MATLAB

SIMULATION using Symbols2000SIMULATION using Symbols2000


Mechanical system

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


Mechanical example

Mechanical example

11111221 0 xmxkxxkgm

221222 xmxxkgm

x1

x2

k1

k2

m2

m1

refxSf :

x

g

2111 kkm FFgmF

1 I:m2

2kx0

1 I:m1

C:k2

C:k1

Se:m2g

2x

Fm2

Fm1Se:m1g

1kx

1x

1x

2x

Fk1

Fk2

Fk2

Fk2

1111111

212212222

xkdtxkdtxkF

xxkdtxxkdtxkF

kk

kk

12211111

11

11

xxKxKgmxm

dtFm

x mm


Do it

Do it


Building

Building

Source of heat

TROOM

Tamb

Tref

PIDRradiator

TRAD

Rlosses

Rroom

Sensor

+ -

202« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA,

Polytech’Lille

PART 6PART 6

Automated modelling

CHAPTER 6: 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


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 modellingGraphical toolUnified languageCausal and structural propertiesSystematic derivation of equations


Main Softwares (1/5)


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

20-sim : Twente Sim the simulation package from the University of Twente.

Dymola : BG modeling software from Dynasim AB

MS1 : BG modeling software from Lorenz Simulation SYMBOLS 2000 : SYstem Modeling in BOndgraph Language

and Simulation

http://www.bondgraph.com/



http://www.20sim.com/




http://www.dynasim.se/

http://www.dynasim.se/

http://www.lorsim.be/eng/index.htm





ENPORT ( From RosenCode Associates, Inc) The is the first bond graph modeling and simulation software written in the early

seventies by Prof. R.C.Rosenberg Sftware did not request causalities to be specified, and it transformed the topological

input description into a branch admittance matrix which could then be solved. Not available in a commercial

ARCHER determination of structural controllability, observability and invertibily of linear

models. It is a high quality academic work based on the research at the "Ecole Centrale de Lille" catering mostly to automatic control theory

Not commercially available.


mailto:[email protected]

http://bondgraphs.com/software.html




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.







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.


http://www.virtualdynamics.fr/

http://www.wolfram.com/products/mathematica/





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


http://www.modelica.org/

http://www.modelica.org/

http://www.symbols2000.com/

http://www.symbols2000.com/

http://www.symbols2000.com/capsuleso.html


Some demonstrations using SYMBOLS 2000

Some demonstrations using SYMBOLS 2000

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


Simulation in Matlab

Simulation in Matlab

DEMONSTRATION

Electrical system

Mechanical system : suspension

Electromechanical system : DC motor

Hydraulic system


PART 7

Conclusions

PART 7

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

Identification No “black box” model identification of unknown parameters, but knowledge of the associated physical phenomena Physical meaning for the obtained model




Analysis Putting to the fore the causality problems, and therefore the numerical problems Estimation of the dynamic of the model and identification of the slow and fast variables Study of structural properties

choice and positioning of sensors and actuators help for control system design

Functioning in faulty mode

Control Physical meaning of the state variables, even if they are not always measurable Possibility to build a state observer from the model Design of control laws from simplified models




Monitoring Graphical determination of the “monitorability” conditions and of the number and location of

sensors to make the faults localisable and detectable Design of software monitoring systems Determination of “sensitive” parts of a system

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

Documents

1 « Integrated Design of Mechatronic Systems using Bond Graphs » Prof. Belkacem OULD BOUAMAMA Responsable de léquipe MOCIS Méthodes et Outils pour la conception