Transcript MODELISATION FONCTIONNELLE

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 Systèmes
http://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 et bien d’autres sont disponibles à
http://www.mocis-lagis.fr/membres/belkacem-ould-bouamama/
 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.
1
« Integrated Design of Mechatronic Systems using Bond Graphs »
Few References
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
2
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, …)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
4
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
5
Few References
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
6
PART 1
INTRODUCTION & MOTIVATIONS
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
7
« Integrated Design of Mechatronic Systems using Bond Graphs »
SKILLS 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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
8
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..)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
9
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
10
Chapter 1
Introduction to integrated design
of engineering systems
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
11
« Integrated Design of Mechatronic Systems using Bond Graphs »
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,
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
12
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
13
Mechatronics ; Synergetic Effects
Information
technology
Electronics
Power electronics,
Networks,
converters AN/NA,
Micro controllers
Actuators,
Sensors
MECHATRONICS
System theory
Automatic control
Computer engineering
Diagnosis
Artificial Intelligence
Software
Mechanics
Hydraulics,
Thermal engineering,
Mechanism
Pneumatic
Mechanical elelents
Precision mechanics
« Integrated Design of Mechatronic Systems using Bond Graphs.»
14
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
…;
« Integrated Design of Mechatronic Systems using Bond Graphs.»
15
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 Yaskawa
Electric Corporation
« Integrated Design of Mechatronic Systems using Bond Graphs.»
16
Definition of Mechatronics
 Definition given by Rolf Isermann:
 The new integrated systems changed from electro-mechanical systems
with discrete electrical and mechanical parts to integrated electronicmechanical systems with sensors, actuators and digital
microelectronics.
« Integrated Design of Mechatronic Systems using Bond Graphs.»
17
Methodology for testing
Development of generic models and Control algorithms
Validation using MiL
Test
Validation using SiL
Test
Validation using HiL
Test
Industrial validation
« Integrated Design of Mechatronic Systems using Bond Graphs.»
18
18\18
Tests in Mechatronic systems
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)
« Integrated Design of Mechatronic Systems using Bond Graphs.»
19
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
« Integrated Design of Mechatronic Systems using Bond Graphs.»
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,…) .
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
21
LEVELS OF MODELLING
What
to do ?
1. Technological
This level constructs the architecture of the system by the assembly of different subsystems, which are the plant items (heat exchanger, boiler, pipe...). The technological
level can be represented by the so-called word bond graph.
2. Physical
Energy description ( Storagee, dissipation, ….
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.
3. Mathematical
 xi   f ( x, y )dx 
Level is represented by the mathematical equations (algebraic and differential equations) which describe the system behavior.
4. Algorithmic
The algorithmic level is connected directly with information processing, indicates how the mathematical models are calculated
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
23
WHAT WE CAN DO WITH BOND
GRAPH ?
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
24
« Integrated Design of Mechatronic Systems using Bond Graphs »
BOND GRAPH FOR ALARM FILTERING
National Project : EDF-LAIL
world-wide project: CHEM
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
25
THE EKOFISK JACKING OPERATION
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
26
A feasibility study in coordination with
Phillips Petroleum Company. Norway,
during the second half of 1985
The 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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
27
TYPES OF INDUSTRIAL APLICATIONS
Electrochemical integrated
with transport sytem
Nuclear power plant
FCC process : Refinery Catalytic Cracking.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs.»
28
Bond Graph for Integrated Supervision design
Structural
Analysis
Sensor
Placement
Diagnosis Results
Technical
specifications
New
instrumentation
architecture
RRAs
P&ID
Process
Dynamic Models
generation
Sensors
Datas from process
RRAs generation
Real Time
Implementation
« Integrated Design of Mechatronic Systems using Bond Graphs.»
29
Dedied Software (FDiPad)
« Integrated Design of Mechatronic Systems using Bond Graphs.»
30
Graphical User Interface (1/4)
Data base
Architectural model
Behavioral model
« Integrated Design of Mechatronic Systems using Bond Graphs.»
31
Graphical User Interface (2/4)
Residuals
Fault signature
« Integrated Design of Mechatronic Systems using Bond Graphs.»
32
32\
Architectural model
« Integrated Design of Mechatronic Systems using Bond Graphs.»
33
TECHNICAL SPECIFICATIONS AND MONITORABILITY ANALYSIS
« Integrated Design of Mechatronic Systems using Bond Graphs.»
34
Sensor placement
« Integrated Design of Mechatronic Systems using Bond Graphs.»
35
Simulation interface
« Integrated Design of Mechatronic Systems using Bond Graphs.»
36
36\
PART: 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, …)
37
Founders
J. Thoma
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
38
THE FIRST IDEA
 The first system used by Paynter teaching in the Civil Engineering Department at MIT and first ideas
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
39
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)
Companies using this tool
 Automobile company : PSA, Renault
 Nuclear company : EDF, CEA, GEC Alsthom
 Electronic :Thomson, Aerospace company ....
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
40
DEFINITION, REPRESENTATION
DEFINITION
2
1

REPRESENTATION
Mechanical power :

e
f
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
P = e.f
« Integrated Design of Mechatronic Systems using Bond Graphs »
41
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
42
Bonds activation
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
43
Bond Graph model in block diagramme
Information system
Energetic system
X
C
CORRECTOR
ACTUATOR
BOND GRAPH
MODEL
Y
SENSOR
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
44
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.
vertex
vertex
E
C
C
Submodel
(Component)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Edge (bond)
E
Submodel
(Component )
« Integrated Design of Mechatronic Systems using Bond Graphs »
45
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 ?
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
46
1. Power variables
Two multiports are connected by power interactions using
Variables
P(t )  e(t ). f (t )
e(t )
f (t )
Power variables are classified in a universal scheme and to
describe all types of multiports in a common language.
Two conjugated variables
 Effort e(t) : voltage, temperature, pressure
 Flow f(t) : mass flow, current, entropy flow,
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
47
How to select them
Thermique
Tamb
Mécanique
Électrique
(J,f)
Thermofluide
Hydraulique
Chimie , electrochimie
Thermodynamique
Economique
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
48
POWER VARIABLES FOR SEVERAL DOMAINS
DOMAIN
Electrical
Mechanical
(translation)
Mechanical
(rotation)
Hydraulic
Chemical
Thermal
Economic
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
EFFORT (e)
FLOW (f)
VOLTAGE
CURRENT
u [V]
i [A]
FORCE
VELOCITY
F [N]
v [m/s]
TORQUE
ANGULAR VELOCITY
 [Nm]
 [rad/s]
PRESSURE
VOLUME FLOW
P [pa]
dV/dt [m3/s]
CHEM. POTENTIAL
MOLAR FLOW
 [J/mole]
dn/dt [mole/s]
TEMPERATURE
ENTROPY FLOW
T [K]
dS/dt [J/s]
UNIT PRICE
FLOW OF ORDERS
Pu [$/unit]
fc [unit/period]
« Integrated Design of Mechatronic Systems using Bond Graphs »
49
2. ENERGY VARIABLES
The momentum or impulse p(t), (magnetic flow, integral of
pressure, angular momentum, … )
t
p (t )   e( )d  p (t0 )
t0
t
Momentum : p (t )  mx   Fdt  F  mx
t0
The general displacement q(t), (mass, volume, charge … )
q (t ) 
t
 f ( )d  q(t0 )
t0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
50
Why energy variables ?
 ENERGY VARIABLES
The momentum or impulse p(t), (magnetic flow, integral of pressure,
angular momentum, … )
t
p (t )   e( )d  p (t0 )
t
0
The general displacement q(t), (mass, volume, charge … )
t
q(t )   f ( )d  q(t0 )
t
q
p
 Why energy variables ? E (t )   e( q)dq, E (t )   f ( p )dp
0


1 2
E p (t ) 
kx1  kx02
Energy stored
2
1 2
q1
q1
q1 q
by a spring
E p (t )  q e( q)dq  q u ( q)dq  q dq 
q1  q02
0
0
0 C
2C
q1
q0 e( q)dq
x1
 x k . xdx 
0

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
51

ENERGY VARIABLES FOR SEVERAL DOMAINS
DOMAIN
Electrical
Mechanical
(translation)
Mechanical
(rotation)
Hydraulic
Chemical
Thermal
Economic
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Displacement (q)
Impulse (p)
CHARGE
FLUX
q [Coulomb]
Φ [Wb]
DISPLACEMNT
MOMENT
x [m]
ANGLE
J [Ns]
ANGULAR MOMENTUM
 [rad]
[Nms]
VOLUME
MOMENTUM pp
V [m3]
Ns/m2
Nbr of MOLE
?
n [-]
ENTROPY
?
S [J/K]
accumulation of orders
qe
Economic momentum
Pe
« Integrated Design of Mechatronic Systems using Bond Graphs »
52
Energy variables : analogy
Displacement
V
Q
Q,T
u,q
P,V
e  P

 f  V
 x  V  Vdt


V
x
i
e  u

f i
 x  q  idt


x, F
e  T

 f  Q
 x  Q  Q dt


e  F

 f  x
 x  x  xdt


Impulse
u,
i
e  u

f i
 p    udt  Li


Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
F,
e  F

f  x
x 
 p    Fdt  Mx


« Integrated Design of Mechatronic Systems using Bond Graphs »
53
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
 ….
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
54
PSEUDO BOND GRAPH
DOMAIN
Hydraulic
Chemical
EFFORT (e)
FLOW (f)
MASSE FLOW
PRESSURE

m
P [ pa ]
MOLAR FLOW
CONCENTRATION
C [ mole/m3]
[ Kg /s ]
n
[ mole/s]
CONDUCTION
TEMPERATURE
Thermal
HEAT FLOW
Q
T [K]
[W ]
CONVECTION
SPECIFIC ENTHALPY
h [ J/kg ]
ENTHALPY FLOW
H
[W]
TEMPERATURE
T [K]
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
55
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
56
Let us learn bond graph language
Go head
57
EXAMPLE1 : ELECTRICAL INDUCTION MOTOR
ui
Inductor
ia
La
Ra

ua
(J,f)

LOAD
ELECTRICAL PART
ELECTRICAL
PART
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
ua
ia
MECHANICAL PART
MECHANICAL
PART


« Integrated Design of Mechatronic Systems using Bond Graphs »
LOAD
58
EXAMPLE 2: POWER STATION
TURBINE
RECEIVER
STEAM
FEED
WATER
HEATER
PUMP
PP
R
m
RECEIVER
TR
PUMP
H R
U
source
i
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille


MOTOR
PP
PW
P
m
TP
H P
m W
TW
PIPE
PB
BOILER
H W
TURB
INE
B
m
TB
H B
TH
U
Q H
HEATER
« Integrated Design of Mechatronic Systems using Bond Graphs »
Load
59
i
Where is the generecity ?
60
FEW ELEMENTS FOR A BIG PURPUSE
Tamb
C
R
RS
Se
I
R
I
(J,f)
Se
I
C
Sf
TF
GY
C
R
Sf
R
C
I
R
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
61\ 61
BOND GRAPH ELEMENTS
BOND GRAPH ELEMENTS
PASSIVE ELEMENTS
ACTIVE ELEMENTS
JUNCTIONS
(transform received power into
dissipated (R) or stored (C, I)
energy
Generate and Provide a power
to the system
Connect different elements of
the systems : are power
conserving
R
C
I
Se
One port element
Sf
0,1
They are not a material
point (common effort (0)
and common flow ((1)
TF, GY
Energy transformation or
transformation from one
domaine to another
R,C,I,
Se,Sf
Tree ports element
Two ports element
0,1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
TF, GY
62
Bond graph well suited automated modelling
SYMBOLS
DEMOS
Junctions
Passive elements
Active elements
Junctions
« Integrated Design of Mechatronic Systems using Bond Graphs »
63
Passive elements
Representation

e
f
R, C, I
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).
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
64
R element (resistor, hydraulic restriction, friction losses …)
ELECTRICAL
THERMAL
HYDRAULIC

T
v1
U  Ri  0
R
D 
128
4
Constitutive equation :
p2
V
i
v1  v2  U
R
p1
v2
P1  P2  RV  0
P1  P2   RV 2
1
Q
T1 T2   RQ  0
R
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e
f

A
 R e, f   0
For modeling any physical
phenomenon characterized by an effort-flow relation ship
Representation
T2
R:R1
« Integrated Design of Mechatronic Systems using Bond Graphs »
65
Examples of R elements
e
R
f
(a)
x
F
u
R
i
V
P1
P  P1  P2
P2
V
R
F
R
i
R:Re
(b)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
x
R:Rm
(c)
n
n

P
F
u
  1  2
1 R 2
R:Rh
V
(d)
« Integrated Design of Mechatronic Systems using Bond Graphs »
n
R:Rt
(e)
66
BUFFERS
A) C element (capacitance)
ELECTRIC
i1
THERMAL
HYDRAULIC
V1
i2
C
dq d (C.U )

dt
dt
1
q
U   idt 
C
C
Constitutive equation
V2
d ( Ah)
V  V1 V2 
, p  gh
dt
1 
V
p 
 Vdt 
C
C
(For modeling any physical phenomenon
characterized by a relation ship between effort and  flow
Representation
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
d ( mctT )
Q  Q1  Q 2 
.
dt
1
Q
T   Q dt 
C
C
C  mct
 e,  fdt    e, q  0
C
e
f
Q 2
m
c
T
p
h
i  i1  i2 
Q1
A: section
h: level
: density
C= A/g
i
C
Examples: tank, capacitor, compressibility
C
C:C1
« Integrated Design of Mechatronic Systems using Bond Graphs »
67
Examples of C elements
e
f 
F
(a)
dq
dt
C
x
u
P
i
g
k
V
F
C
F
u
C:C1
i
(b)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
C:1/k
x
P
C:A/(g)
V
(c)
« Integrated Design of Mechatronic Systems using Bond Graphs »
(d)
68
Inertance : I element
HYDRAULIC
ELECTRIC
MECHANICAL
l
F
V1
i
V2
1
 Udt  0
L
   Li  0
i
 : Magnetic flux
I
p1

F mV
dv
lA dV
P  P 

 2
A A dt
A dt
A
1
V   Pdt   Pdt
l
I
p  IV  0
I
Constitutive equation
l
A
p2
p : impulsion of
pressure
Q : momentum
(For modeling any physical
phenomenon characterized by a relation ship between flow and  effort
Representation
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e
f
dx
F m .
dt
1
1
Q
x   Fdt   Fdt 
m
I
I
Q  Ix  0
 I  f ,  edt    I  f , p  0
I:I1
« Integrated Design of Mechatronic Systems using Bond Graphs »
69
Tetrahedron of State
4 variables : e, f, p, q
3 Bg elements : R, C, I
C
CAPACITOR
Potential energy
q  C.e
1
e   f (t )dt
C
Potential
 C (e, q, C )  0
q

dq
 f
dt
C
R
 R ( e, f , R )  0
ENERGY
q
e
e
dp
e
dt
DISSIPATOR
Instantane ous
e  Rf

p
d
dt
I
 I ( f , p, I )  0
I
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
d
dt


f
f
f
Kinetic
p
POWER
INDUCTOR
Kinetic energy
p  I. f
1
f   e(t )dt
I
« Integrated Design of Mechatronic Systems using Bond Graphs »
70
e
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
Simple transformer
e1
f1
TF
:m
Defining relation
e1 = m.e2,
f2 = m.f1
e2
f2
Where m : modulus
Modulated transformer (m is not cste)
u
e1
f1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
MTF
:m
e2
f2
Defining relation
e1 = m(u).e2,
f2 = m(u).f1
« Integrated Design of Mechatronic Systems using Bond Graphs »
71
EXAMPLES OF TRANSFORMERS
Electrical transformer
u2
u1
i1
i2
u1
TF
:m
i1
Hydraulic piston
u2
U 1  mU 2

i2  mi1
i2
Hydraulic power is transducted
F , x
into mechanical power
P
P , V
V
TF
:A
F
x
1

P

F


A

 x  1 .V


A
A : area of the piston
Lever
a
x1
x 2
F2
F1
b
x1
TF
:b/a
F2
x 2
F1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
b

F

.F

 1 a 2

 x 2  b .x1


a
72
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
e1
e2
GY
:r
f1
Defining relation
e1 = rf2
e2 = rf1
f2
Where r : modulus
Modulated Gyrator (if r is not cste)
u
e1
f1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
MGY
:r
e2
Defining relation
e1 = r(u)f2
e2 = r(u)f1
f2
« Integrated Design of Mechatronic Systems using Bond Graphs »
73
Example of gyrator : DC motor


u
i
u
i
GY
:r

 = ri

MODULATED GYRATYOR
iind
u
i

MGY
:r

 = K(iind)i
r = K(iind)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
74
ACTIVATED ELEMENTS (1/2)
 EFFORT AND FLOW SOURCES Se, Sf
 A 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 Se
 Generator of voltage, gravity force, pump, battery...
Simple effort source
Se
e
Se = e(t)
f
Modulated effort source
u
MSe
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e
Se = e(t,u)
f
« Integrated Design of Mechatronic Systems using Bond Graphs »
75
ACTIVATED ELEMENTS (2/2)
2. Flow source Sf
 Current generator, applied velocity..
Representation
Simple flow source
e
Sf
Sf = f(t)
f
Modulated flow source
u
MSf
e
Sf = f(t,u)
f
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
76
JUNCTIONS (1/5)
 0 - JUNCTION “ Common effort junction”
Representation
e2
e1
f2
0
f1
e1  e2  e3  e4

 f1  f 4  f 3  f 2  0
e3
f3
e4
f4
Defining relation
Power conservation
n
 ai .ei fi  0
i 1
ai = +1
if
ai = -1
if
0
0
e1. f1  e2 . f 2  e3 . f 3  e4 . f 4  0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
77
Jonction 0 : Loi de conservation d’énérgie
m 3 , H 3 Bilan énergétique
Cas statique
Bilan massique
H 3



H 2  H 3  H1
m 1, H 1
.P1
.P3
P2
m 2 , H 2
Cas dynamique
H 3 ,m 3
Q1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
P1
0
H 1
H 2
Bilan énergétique
U  H 3  Q1  H 2
H 3
U
H 2 ;m 2
m 1
m 3 P3
P2
0
m 2
Bilan massique
m  m 3  m 2 m 3
0
Q1
T ,U
P, m
m 2  m 3  m 1
H 2
T
C:Ct
« Integrated Design of Mechatronic Systems using Bond Graphs »
0
m 2
m P
C:Ch
78
JUNCTIONS (2/5) : Examples of 0-junction
V2
V1
V3
P
V3
i
V1
i = i 1 + i2
R
E
C
E
E
Se:E
i2
E
0
C:1/k
I:Mp
C:1/k
Se:Fr
1
I:Mc
x3
x1
x1
R
i1
i
x 2
Se:Fr
V2
C
i2
Mp
P
0
i1
Mc
V1 V2  V3
P
x1
0
« Integrated Design of Mechatronic Systems using Bond Graphs »
x 2
x 2
1
79
JUNCTIONS (3/5) : 1 JUNCTION
1 - JUNCTION “ Common flow junction”
Defining relation
Representation
e1
f1
e2
f2
1
e3
 f1  f 2  f 3  f 4

e1  e2  e3  e4  0
Power conservation
n
 ai .ei  0
i 1
e4 f 4
ai = +1
if
ai = -1
if 0
0
e1. f1  e2 . f 2  e3 . f 3  e4 . f 4  0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
80
JUNCTIONS (4/5) : Examples of 1-junction
R1
R:R1
R2
P1
V1
V2
UR
V1
P1 -P3
P3
P2
P1
V3
R:R2
P2 -P3
P2
1
V1
R
E
E
L
i
C
Se:E
UC
i
UL
1
i
P3
E =UR + UL + UC
UR
R
V2
1
V3
UL
V1 V2 V3 V
i
i
UC
L
C
k
C:1/k
x
I:M
M
b
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
FC
F(t)
F
x
FM
1
« Integrated Design of Mechatronic Systems using Bond Graphs »
FR
x 2
R:b
81
Junction 1 : thermal system
T1
Q
T2
Cas dynamique
Cas statique
R
TR
T1
Q1
Q R
1
T1  TR  T2  0
Q R  Q1  Q 2  Q
T2
Q 2
R
TR
T1  TR  T2  TC  0
Q R  Q1  Q 2  Q C
Q R
T1
T2
1
Q 2
Q1
TC Q C
C
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
82
Exercise
i3
i1
R1
C1
R3
L1
i4
E
L2
C2
R2
i6
i5
i2
k
mg
Mp
« Integrated Design of Mechatronic Systems using Bond Graphs »
83
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
84
Structural Model
Sources
Se, Sf
u
xi
Stockage
d’énergie
I,C
zi
Structure de
Jonction
x d
zd
Din
Dissipation
d’énergie
Dout
0, 1, TF, GY
R
y
Capteurs
De, Df
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
85
Summary
Symbol
e
Se:e
Sources
f
e
Energy stores Dissipator
Sf:f
Junctions
Transducers
Passive elements
Constitutive equation
f
e
f
e
f
e
f
e1
:m
f1
e1
f1
Junctions
e1
f1
f3
e1
Sensors
Sensors
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e
f=0
e=0
f
Capacitance
I
 I  f , p  0
Inertance
e2
e1  me2

 f 2  mf1
Transformer
e1  rf 2

e2  rf1
Gyrator
e1  e2  e3

 f1  f 2  f 3  0
Zero junction :
common effort
junction
 f1  f 2  f 3

e1  e2  e3  0
One junction :
common
flowjunction
f2
e3
1
f1
 C e, q   0
e3
0
Source of flow
C
f2
f3
 f (t ) given by the source

 e(t ) arbitrary
Resistance
e2
:r
Source of effort
 R (e, f )  0
f2
GY
e(t ) given by the source

 f (t ) arbitrary
R
e2
TF
Name
e2
f2
De:e
e  e(t )

f 0
Df:f
 f  f (t )

e  0
Sensors (Detectors)
« Integrated Design of Mechatronic Systems using Bond Graphs »
86
BUILDING ELECTRICAL MODELS
1. Fix a reference direction for the current, it will be used as power direction
2. For each node in circuit with a distinct potential create a 0-junction
3. 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-junction
4. Assign power directions to all bonds
5. 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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
87
Simplifications of Bond graphs

0

1
Example of simplification
C
1
0
0
0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
1

1
0
0
C
R
0
1
C
R
C
1

R
C
1
0
C

0
« Integrated Design of Mechatronic Systems using Bond Graphs »
R
88
Electrical circuit : Example1
R:R1
b
a
R1
a
b
0
0
0
C
E
b
a
1
0
Se:E
g
g
0
C
1
1
g
(2)
(1)
0
(3,4)
R:R1
b
a
1
0
Se:E
Se:E
0
R:R1
1
(5)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
1
C
1
C
(6)
« Integrated Design of Mechatronic Systems using Bond Graphs »
89
Electrical circuit : EXAMPLE2
L1
iR1
R2
iL1
0
R1
L2
C1
E
iC1
C:C1
R:R1
uR1
Se:E
E
iC1
1
iR1
uC1
iR1
0
I:L1
uL1
uC1
iL1
I:L2
iL1
1
1
TF
R:R2
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
90
Electrical circuit : Example3
R1
L1
R2
iR2
iR1
SE
C1
C2
iC1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
SF
SF
iC2
« Integrated Design of Mechatronic Systems using Bond Graphs »
91
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
92
Mechanical system : EXAMPLE (1/2)
Vref
f
k
g
V1
(4)
Relationship
between velocities
(2)
Absolute velocitie s
Vref , V1
1
R:f
1
Vref
0
0
Se:-Mg
1
R:f
Vf
V1
V1
V f  V1  VREF
I:M
1 Vref
Sf
Vk
1
V1
Vref
C:1/k
Vf
1
C:1/k
Relative velocities
Vk , V f
(5,6)
Vref
Vk
Vk  V1  VREF
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
1
(3)
1
V1
I:M
« Integrated Design of Mechatronic Systems using Bond Graphs »
93
Mechanical system : EXAMPLE (2/2) (Simplifications)
1
Sf
(5,6)
Simplification
Vref
Vref
C:1/k
Vk
1
0
1
V1
1
Vref
R:f
Vf
Vref
0
V1
V1
Se:-Mg
1
0
0
1 Vref
Sf
C:1/k
I:M
Vk
Vk  Vref  V1
 Vk  VF

V

V

V
ref
1
 f
0
0
1
Se:-Mg
I:M
V1
Vref
1
0
Se:-Mg
V1
1
R:f
R:f
Vf
V1-Vref
1
C:1/k
Vk
I:M
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Vf
V1
V1
Sf
R:f
if Vref  0  Vk  V1  V f
Eliminate any zero
velocity 1-junctions and
their bonds
Vf
I:M
V1
1
C:1/k
Vk
Se:-Mg
« Integrated Design of Mechatronic Systems using Bond Graphs »
94
Exercise 1 : mechanical
x
x
f1
x
MA
MB
k2
C:1/k2
Mb
Ma
F(t)
I:Ma
R:f1
k1
k3
x k 2
I:Mb
0
f2
x k 1
x MB
x MA
x f 1
C:1/k1
Se:-F(t)
1
1
x k 3
0
x f 2
Vref=0
+
k1
m1,f 1
m1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
R:f2
C:1/k3
k2
m2,f 2
k3
R3
m2
« Integrated Design of Mechatronic Systems using Bond Graphs »
m3,f 3
F(t)
m3
95
Electro-mechanical sytem
R:Ra
UR
IF
1
Se:UF
UI
I:La
IF
R:Ra
UR
IA
1
Se:UA
UI
I:La
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
R:B
R
IA
Um
MGY
r (iF )
m
m
1
I
Se:Load

I:J
« Integrated Design of Mechatronic Systems using Bond Graphs »
96
Exercise 3 : Hydro-mechanical and suspension
Pompe P1
Sf
Se1
Piston
V2
C2
R6
R4
C3
V1
Air
R:Ra
C:1/k
R5
R7
V3
Atmosphère Se2:P0
C1
De:L
x 2
Mc
Compresseur
x1
Mp
Sf:Fr
Cylindre
Arbre
M
Prof. BelkacempOuld BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
97
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
98
Hydraulic system : EXAMPLE (1/2)
Resistance R1
Pump
P1
Inertia I Resistance R2
P2
P3
P4
C
Pat
V
R:R1
Se:P1
R:R1
Se:P1
0 P2
1
0 P1
R:R2
1
1
I
1
1
C
C
R:R2
I
0 P3
1
R:R2
0 P4
Pat
0
1
R:R1
Se:P1
1
C
0
I
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
99
EXAMPLES OF BG MODELS : Hydraulic
Valve 1
Pump
PP
PR
LC
R2
P0
I:l/A
C:CR
R:R2
PR -P0
P P -PR
Se:PP
PP
VR1
1
R:R1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
PR
VR1
0
De
PR
VR 2
1
P0
Se:-P0
VR 2
PID
« Integrated Design of Mechatronic Systems using Bond Graphs »
100
EXERCISES : Mechanical (pneumatic valve)
u
Controller
1
2
4
3
7
6
x
5
F
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 : valve
7 : pipe
Block diagramme
u(t)
x(t)
Vanne
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
101
EXERCISES : Bond graph model of the pneumatic valve
C:1/ke
Se:Pe
Pneumatic
Mechanical
energy
energy
Pe
V
TF:
A
I:m
Fk x
FI
F
1
x
Df
x

x
Ff
R:f
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
102
EXERCISES : Hydraulic control system
PID
0,2 -1 bar
3 - 15 psi
Pe
Ve
x
LT
Vs
PR
P0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
103
EXERCISES : Bond graph model of the hydraulic system
C:ke
R:f
I:m
Ff
Fk x
Pe
MSe : Pe
V
FI
F
TF:
A
1
x
Df : x
x
u
x
PID
C:CR
De:P0
Sf : Ve
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

R:RV
PR
0
PR
Vs
1
P0
« Integrated Design of Mechatronic Systems using Bond Graphs »
Se : P0
104
EXERCISES Hydraulic systems
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
105
EXAMPLES OF BG MODELS :Thermal
Ta
Source of heat
Ts
Q S
C:Cb
Q b
TS
Sf : Q S
TS
Q S
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
0
R:Ra
TS - Ta
TS
Q a
Q a
1
Ta
Q a
« Integrated Design of Mechatronic Systems using Bond Graphs »
Se:-Ta
106
PART 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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
107
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
108
Convention
e
A
f
B
A
e
B
System A impose an effort e to system B
The causal stroke is placed near (respectively far from) the bond graph
element for which the effort (respectively flow) in known.
Cause effect relation : effort pushes, response is a flow
Indicated by causal stroke on a bond
Effort pushes
Flow points
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
109
PRINCIPLE
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
110
CALCULATION EXAMPLE
P1
P2
P
V
R:K
PR
P1
P2
1
PR
V  K P
V
V
2

V 
P   
K
PR
R:K
P
P1
1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
P1
« Integrated Design of Mechatronic Systems using Bond Graphs »
111
Remarks about causalities
 the orientation of the half arrow and the position of the causal
stroke are independent
System A impose effort e to B
e
A
B
f
e
A
f
e
B
System A impose flow f to B
A
B
A
f
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e
« Integrated Design of Mechatronic Systems using Bond Graphs »
f
B
112
Causality for basic multiports
 Required causality
e
Se
e
Sf


f
f
The sources impose always one causality, imposed effort by effort sources
and imposed flow by flow sources.
 Indifferent causality (applied to R element)
e
R
f
e
f
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
R
1
i  FR ( e )
i
1
u
R
e  FR ( f )
u  R.i
e
FR 1
f
Conductance causality
f
FR
e
Resistance causality
« Integrated Design of Mechatronic Systems using Bond Graphs »
113
Integral and derivative causality
Preferred (integral)
causality
Derivative
causality
e
C
f

e  FC  fdt


1
u

i.dt


 C

e

 f  FI  e.dt

 1
i   u.dt
 L
f
e

I

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

1  de 
f

F

C 


 dt 

i  C . du


dt
f
e

f
C

1  df 
e

F

I 


dt
 

u  L di


dt
« Integrated Design of Mechatronic Systems using Bond Graphs »
e
f
d
dt
I
f
d
dt
e
114
Causalities for 1-junction
Causal Bond Graph model
Block diagram
Strong bond
e2
e1
f2
1
f1
e4
e1
f4
e2  e1  e4  e3
e3
e4
f3
e3
f1  f 2
f2
f3  f 2
1-Junction
f4  f2
 Rule
Only 1 bond without causal stroke near 1 - junction
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
115
Causalities for 0-junction
Block diagram
Strong bond
e2
f2
e1
e3
0
f1
e4
f1
f3
f4
f4
f 2  f1  f 4  f3
0-Junction
f3
e1  e2
e2
e3  e2
e4  e2
e1. f1  e2 . f 2  e3 . f 3  e4 . f 4  0
 Rule
Only 1 causal stroke near 0 - junction
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
116
TF JUNCTION
e1
f1
TF
:m
Defining relation
e2
e1 = m.e2
f2 = m.f1
f2
Where m : modulus
 2 CAUSALITY SITUATIONS
e1  me2

 f 2  mf1
If e2 and f1 are known :
e1
f1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e2
TF
:m
f2
e2
m
e1
f1
m
f2
« Integrated Design of Mechatronic Systems using Bond Graphs »
117
CAUSALITY OF TF JUNCTION
1

e2  e1


m

 f1  1 f 2


m
If e1 and f2 are known :
e2
e1
f1
TF
:m
e1
1/m
e2
f2
1/m
f1
f2
 RULE : A symmetrical position of the causal stroke
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
118
CAUSALITY OF GY JUNCTION
e1
f1
GY
:r
e2
Defining relation
e1 = r.f2
e2 = r.f1
f2
Where r : modulus
 2 CAUSALITY SITUATIONS
e1  rf 2

e2  rf1
If f2 and f1 are known :
e1
f1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e2
GY
:r
f2
f2
r
e1
f1
r
e2
« Integrated Design of Mechatronic Systems using Bond Graphs »
119
CAUSALITY OF GY JUNCTION
1

f 2  e1


r

 f1  1 e2


r
If e1 and e2 are known :
e2
e1
f1
GY
:r
e1
1/r
f2
e2
1/r
f1
f2
 RULE : Skew - symmetrical position of the causal stroke
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
120
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 …).
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
121
Four Information given by BG
There exists a physical link between A and B
A
e
B
f
A supplies power to B
Power variables show the type of energy
Flow is input for B and effort is output
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
122
From BG to Bloc Diagram (1/2)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
123
From BG to Bloc Diagram (2/2)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
124
Application to Electrical system : BG model
L
R1
E(t)
R2
 1. BOND GRAPH MODEL
I:L
e2  p 2
Se:E(t)
C
1
1
3
5
De:e6
4
0
f 6  q6
6
R:R1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
R:R2
2
E(t)
V(t)
C
« Integrated Design of Mechatronic Systems using Bond Graphs »
125
Application to Electrical system:State equation
 2. STATE EQUATIONS
u
•
x  Ax  Bu
y  Cx
x
y
 p   e 
x   2    2 , u  Se  E (t ) , y  e6
 q6    f 6 
Structural laws
- 1 junction
- 0 junction
 f1  f 2 , f 3  f 2 , f 4  f 2

e2  e1  e3  e4
e4  e6 , e5  e6

 f 6  f 4  f5
1
p2

f

e
dt


2
2
• Constitutive equations 
L
L

e  1 f dt  q6
 6
 6
C
C

e3  R1 f 3

f  1 e
 5 R 5

2
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
 R1

 p 2   L
 q    1
 6 
 L
1 
C   p2   1 E (t )
1   q  0
 6 

R2C 
1   p2 

y  e6  0
 
 C   q6 
« Integrated Design of Mechatronic Systems using Bond Graphs »

126
Application to Electrical system : Block Diagram (1/2)
R1
L
E
R2
U(t)
C
E
Se:E
I:L
R:R2
2
5
0
1
1
4
6
3
e2=e1-e3-e4
1-Junction
Se:E
+
e1
-
e4
f2=f1=f3=f4
e2
1

L
R1
C
R:R1
e6=e4=e5
f2(0)
e3
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
0-Junction
f6=f4-f5
e6(0)
f6
f2
-
f5
1

C
e6
1
R2
« Integrated Design of Mechatronic Systems using Bond Graphs »
127
Application to Electrical system : Block Diagram (2/2)
Causal graph
Bloc Diagram
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
128
Application to Hydraulic system: BG model
l
R1
P0
PP
Pump
PC
PC
I:I1
PI1
1
PC
VRC
0
VR1
PR2
VR 2
1
P0
Se:-P0
VR 2
PR1
De:PC
R:R1
u
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
+
PID
PC
-
Pref
« Integrated Design of Mechatronic Systems using Bond Graphs »
129
Atmosphere
Se:PP
PP
PC
P0
R:R2
C:CR
VR1
R2
Application Hydraulic system: Block Diagram
•
Structural laws
1 junction
PI 1  PP  PC  PR1
0 junction
VRC  VR1  VR 2
1 junction
PR 2  PC  P0
I:I1
• Constitutive equations
• Calcul de CR et I1
C:CR
1
VR1   P I1dt
I1
1 
PC 
 VRC dt
CR
R:R1
2
PR1  R1.VR1  (Bernoulli law)
R:R2
2
PR2  R2 VR2  (Bernoulli law)
d ( A.h) d ( A.PC /( g )
A d ( PC )
g 
VRC 


 PC 
 VRC dt
dt
dt
g dt
A
d VR1 / Ac 
, F  PI 1. Ac , m  lAc
dt
lAc d VR1 
A
PI 1. Ac 
.
 VR1  c  PI 1dt
Ac
dt
l
CR 
Newton law : F  m ,  
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
I1 
« Integrated Design of Mechatronic Systems using Bond Graphs »
A
g
l
Ac
130
Application Hydraulic system: Block Diagram
I:I1
PI1
Se:PP
VR1
1
PC
PC
VRC
0
VR1
PR2
P0
1
VR 2
Atmosphere
PP
R:R2
C:CR
VR 2
PR1
De:PC
R:R1
u
PP
Se:PP
-
PI1
-
+
PR1
R1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
PC
-
PID
PC
+
Se:-P0
1
dt

I
VR1 -
VR1 2
Pref
VRC
1
CR
+ VR 2

1
R2
« Integrated Design of Mechatronic Systems using Bond Graphs »
Se:-P0
+
PC
-
PR2
131
EXAMPLE (How to avoid derivative causality ?)
Derivative causality
i
C
UC
iC
E
C
UC
E
Se:E
iC
0
i
Se:E
E
iC
R
uR
R
C
UC
C
E
iR
« Integrated Design of Mechatronic Systems using Bond Graphs »
uC
iR
1
UC 
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
dE
dt
Current infinite ?
Integral causality adding R
i
iC  C.
uC
iC
0
iR
1
i dt
C R
132
Derivative causality : example
I:M1
Se:F(t)
1
I:M2
TF
:b/a
1
C:1/k
I:M1
Se:F(t)
1
C
0
I:M2
TF
:b/a
1
C:1/k
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
133
Transfer Function
 Schematic
 Causal Bond Graph Model
iR
R:R1
R1
C1
E
iC
UC1
uR1
1
iR1
uC1
iR1
E
Se:E
C:C1
uC1
iR1
iC1
0
 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
e
1
1
f
(
t
)
dt

U

iC1dt


C1
c
C1
R element in conductance causality
iR1=UR1/R1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Junction 1
U R1  E  U C1
Junction 0
i C1  iR1
dU C1
 U C1  E
dt
U ( p)
1
W ( p )  C1

E ( p)
R1C1 p  1
R1.C1.
« Integrated Design of Mechatronic Systems using Bond Graphs »
134
State Equations
System to be controlled
yc
M
CORRECTOR
u
A
x
ACTUATORS
PROCESS
X-x
y
 x  Ax  bu
Linear : 
 y  cx
 x  F ( x, u )
Nonlinear 
 y  C ( x)
A  nn , B  mn , C  rn
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
SENSORS
Bond graph
 PI    e(t )dt 
x  

q
f
(
t
)
dt
 C  

Se, Sf  Manual
u
MSe, MSf  Auto.
y  De, Df 
« Integrated Design of Mechatronic Systems using Bond Graphs »
135
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.
 PI 
x 
qC 
  e(t )dt 


  f (t )dt 
Properties
the state vector does not appear on the Bond graph, but only
its derivative
 e( t ) 
x  

 f (t )
The dimension of the state vector is equal to the number of C- and Ielements in integral causality
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
136
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
137
Application
R:Ra
R:f
Df:im
f
uRa
Se:Ua
ua
uM
1
ia
ia
uLa
I:La
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
ia
MGY
:K
r = k(iF)


1

L

Se:-L
Df:m
J
I:J
« Integrated Design of Mechatronic Systems using Bond Graphs »
138
STATE EQUATION
 Equations from causal BG
There is 2 I element in integral causality, so there is 2 state variable
I element in integral causality
MGY
  1  dt
 J

J
1
f (t )   e(t ) dt  
1
I
ia   U La dt

La
U M  K

  Kia
R element in conductance causality
State equation
x    j dt
u  U a
 U La dt   M m e 
 L 
y  im  m 
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
U Ra  ia Ra
FR (e, f )  0  
 f  f
1- Junction
U La U a U Ra U M

 J     f  L
ia  im
Sensor  
   m

 e  U La  U a  U Ra  U M   Ra Φ e  K M m  U a
x

Φ
1

La
J

x  M
 m   j     f  L  Kia  f  L  K Φ e  f M m  Γ L
2

La
J
1

y

i

Φe
1
m

La

y    1 M
m
m
 2
J
« Integrated Design of Mechatronic Systems using Bond Graphs »
139
SIMULATION
 Ra
 e   L
Φ
x  
   Ka

M m  
 La
1

y

i

 1 m L Φ e
a

y    1 M
m
m
 2
J
K
J  Φe    Ua 

f  M m   Γ L 

J

Use of Symbols software
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
 K

A   La
Ra


 La
1
C
 La
f
J  B   1
1
K
 
 
J

1
J 
A   nxn  (2  2)
B   nx  (2  2)
B   mxn  (2  2)
Automatic generation of the state equation
« Integrated Design of Mechatronic Systems using Bond Graphs »
140
Application : do it
iR1
L1
iL1
R2
iR2
Us(t)
R1
C1
E(t)
C2
iC1
C:C1
R:R1
Se:E
E
iR1
1
6
4
uR1
1
3
BLOCK_DIAGRAM
SIMULINK
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
iR1
uL1
iC1
2
uC1
R:R2
I:L1
0
uC1
5
iL1
uR2
iL1
1
7
S-FUNCTION
FROM SYMBOLS
TF
:m
8
De:Us(t)
9
11
1
10
iR2
0
12
us
COMPARAISON
SYMBOLS_SIMULINK
« Integrated Design of Mechatronic Systems using Bond Graphs »
C:C2
141
PART 4
COUPLED BOND GRAPHS
 CHAPTER 4: Coupled energy bond graph




Representation and complexity
Thermofluid sources ,
Thermofluid Multiport R, C
Examples
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
142
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
e1
f1
e1 , e2 ...
ei
f2
en
f1, f2 ...
e1 , e2 ...
f1, f2 ...
fn
 The constitutive relation is matrix
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
143
Coupled bond graph
Chemical
CC
T
H
n
C
C
P
m
Hydraulic
H , m , n

Thermal
T ,P, 
Constitutive equations
 c e, q   0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
q  n m H 
T
e  P T
 T
« Integrated Design of Mechatronic Systems using Bond Graphs »
  h P, m, H , n   0 
  T , m, H , n   0 
 t

 ch  , m, H , n   0
144
Coupled Bond graphs
Representation
e1
ei
fi
en
fn
E

f1
F
E
F
(b)
(a)
e11
e12
f 12
f 11
e21
f 21
MULTIPORT
(c)
e22
f 22
e12
e11
1
f 11
e21
f 21
f 12
Coupling
element
e22
f 22
(d)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
145
Convection Heat transfer (1/2)
)
( P, m
( H , T )
➽ General expression for convected energy
Internal specific energy
Pressure energy
Kinetic energy
2

P
v
 m

 u 
H





2


Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
146
Convection Heat transfer (2/2)
2

P
v

 u 
H  m





2


➽ Modeling Hypothesis
Specific enthalpy : h  u 
For low velocity v :
P

 c pT [ J / kg]
v2

0
2
 m
h  m
 c pT
H
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
147
Coupling of thermofluid variables

Sf : m
P

m
1

m
Se:T
T

H
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Rc
T
 m
 c pT
H
« Integrated Design of Mechatronic Systems using Bond Graphs »
148
Thermofluid pump
➽ Bond graph models
Pump as single flow source
A) Modulated source
Sf h : m
Se:T
B) Using R Multiport
MSf h
MSf t
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
P

m
Sf h : m
T

H
Se:T
P

m
T

H
« Integrated Design of Mechatronic Systems using Bond Graphs »
1
Rc

m

H
149
Activated bonds
C) Use of an activated element
Sf  f1

 e  e1
1
Sf
1
f
d
Sf
1
Sf
e
Sf  f1

 e1  0
Sf  0

 e  e1
« Integrated Design of Mechatronic Systems using Bond Graphs »
150
SOFTWARE REPRESENTATION
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
151
How to modelise a sensor ?
PI
Sf
C
e
2

3
1
Sf
1
e2 
C2
I
0
d
f 2 dt
Hydraulic system case
1
f3 
e3dt  0

I3
1
e3  e2 
C2

f 2 dt  K 2Q2
P
« Integrated Design of Mechatronic Systems using Bond Graphs »
g
A
V
152
SOFTWARE REPRESENTATION
d
« Integrated Design of Mechatronic Systems using Bond Graphs »
153
How to represent it in Symbols2000 ?
P1, m
T1, H
P2 , m
T2 , H
H , m
e1
TF
:b
f1
Sf h : m
P1

m
Se:T
P1  P2 , T1  T2
e2
f 2  b. f1
f2
e1  e2  0
P2
1

m
H  m c pT
e0
e
T
H
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
H  m c pT  bm
MTF
: Cp
e
H
« Integrated Design of Mechatronic Systems using Bond Graphs »
154
Example of multiport elements

R MULTIPORT
T11 ( h11 )
H 11
T2 ( h2 )
H 2
P11
m
11
P2
m
2
T : Temperature (K)
h : Enthalpy specific (Joule/kg)
P : Pressure (pa)
H : Enthalpy flow (Joule/sec.)
m
 1 : Mass flow (kg/s)
 Representation
P1
T1 , P1
R
H 1 , m
1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
T2 , P2
H 2 , m
2
1
m
1
T1
H 1
R
« Integrated Design of Mechatronic Systems using Bond Graphs »
P2
T2
H 2
155
Constitutive equation for R-multiport
 Constitutive equation

1 
m
  R1 ( P1, P2 , T1, T2 ) 
m


2 
    R 2 ( P1, P2 , T1, T2 ) 
 H 1 
  R 3 ( P1, P2 , T1, T2 ) 
  
 R 4 ( P1, P2 , T1, T2 ) 
H 2 
Physical law ( Continuity)
H 1  H 2  H , m
1  m
2  m

H m
 h1 ,
H m
 c pT1
1

sign
(
P

P
)
P

P
1
2
1
2

m   Rh

  1
 H   sign ( P  P ) P  P c T 
1
2
1
2 p 1
R
 h

D 4
Rh 
128
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
156
Inertia of the fluid
➽ Impulse of pressure p
R
l
I
Hydraulic power
P1
1
m 2
m 1
T1
H 1
P2
T2
Rc
 m 

d 

A
dv
F  P. Ac  mc
 lA2 c  c 
dt
dt
A
p
m  c  Pdt  I
l
I
H 2
Thermal power
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
157
Dynamic bond graph model of the pipe
 Fluid moving with inertia
R:Rh
PR m
R
P1
  Ax
m
m 1
T1
H 1
1
RC
I:
PI

Jonction 1 , P  P  P  P ,
I
1
2
R

Elément R, PR  Rh m ,

m 1
p
Elément I, V    PI dt 

 I
I

A
P2
m 2
m  Ax
x.M
p
A
T2
H 2
P1  P2 
dm 


m


dt
Rh


 

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
I


Rh ARh
« Integrated Design of Mechatronic Systems using Bond Graphs »
158
Bond graph model of the pipe
 Global Model
P1  P2 
  dm 



m

  dt 
Rh

 
 H  m c T
p 1

 Step response for hydraulic model to pressure difference
t


1
m (t ) 
Pe 1  e 

Rh

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

  m (0)


« Integrated Design of Mechatronic Systems using Bond Graphs »
159
C - MULTIPORTS
H o , m
o
Representation
h, P
H , m

H i , m
i
C
H o , m
o
H,m
BG model
0
Input
H i , m
i
Q
Heater
Constitutive equations
H o , m
o
To , Po
Ti , Pi
T
Output
T,P
H , m

C
Q
Sf :Q
1 n


a
m


 i i

m 
Ch i 1

H    1 
n
n
1  

 
  


Q

a
H
dt

Q

a
h
.
m






i i
i i
i  dt
 CT  
CT 

 
i 1
i 1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
160
Thermofluid example : heated tank
State variables
I element : p
x   p H m QT
T
u  Pe Q e Tex
l
Pe
One ports C
Two ports C
H,m
Q
Tex
Q e
Po=0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
161
Bond graph model
R:Re
Se: Pe
3
1
8
5
4
11
e
m
12
 P
m
7
e
m
Sft :Q e
9
6
01
Se:P0=0
2
R:Rs
De:L
10
s
m
C
14
Environnement
I:I1
13
H T
Rc1
16
12
02
H e
17
Rc2
H s
C
Rm
18
Q 18
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Q
19
T
03
H s
R:Rex
20
13
11
Ambiance
Se:Te
15
De:T
22
21
Q 20
14
« Integrated Design of Mechatronic Systems using Bond Graphs »
23
Se:Tex
162
Constitutive equations (1/4)
 Jonction 11
 Elém ent R :Re
Elément I:l/A
Jonction 01
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e3  e1  e2  e4  P3  Pe  P2  P4

m 1  m 3
 f1  f3

m  m
 f 2  f 3
 2
3


 f  f
3
m 4  m 3
 4
m 25  m 3
 f 25  f3
e2  ΦRe(f 2 )  Re. f32  P  P2  Rem
 32
1
1
f3   e3dt  f3 (0)  p3  m
 3 (0)  m
3
I
I
 f 7  f 4  f 6  m 7  m 4  m 6  m e  m s

 P4  P7
e4  e7


e

e

 P5  P7
 5 7
P  P
e6  e7
 6
7
« Integrated Design of Mechatronic Systems using Bond Graphs »
163
Constitutive equations (2/4)
 f13  f16  f14  f12  f18  U13  H 16  Q e (u2 )  H 12  Q18

e12  e13 T12  T13
e14  e13 T14  T13


e16  e13  T16  T13
e17  e13 T17  T13


T18  T13
e18  e13
 Jonction 02
 Multiport C : CR
C : CRh  e7  Ch (q7 , q13 )  Ch (  f7 dt,  f13dt) 
e7  P7  gL  g
 niveau dans le réservoir indiqué par le
capteur De :L
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
1
m7
f
dt

 P7 (0)  P7
 7
Ch
Ch
V7
m
m
g 7  7
A
A Ch
L
P7 m7

g A
« Integrated Design of Mechatronic Systems using Bond Graphs »
164
Constitutive equations (3/4)
Capacité thermique
C : CRt  e13  Ct (q7 , q13 )  Ct (  f7 dt,  f13dt)  T13 
Température indiquée par le capteur De :T
Jonction 12
Vanne de réglage
R :Rs
U13
cV m7
e8  e6  e9  P8  P6  Ps

 f 6  f9  f10  f8  m 6  m 9  m 10  m 8
f8 
1
u
u
.sign(e8 ). e8  1 sign(e8 ) e8  m 8  m s  1 sign( P8 ). P8
Rs (u1)
Rs
Rs
f19 
1
e18 e20   Q19 1 T18 T20 
Rm
Rm
f 23
1
e22 e24   Q 23 1 T22 Ta 
Ra
Ra
Eléments R : Rm et R :Ra
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
T13 
1
U13

U
dt

 T13 (0)
 13
Ct (m7 )
cV m7
« Integrated Design of Mechatronic Systems using Bond Graphs »
165
Constitutive equations (4/4)
J onction 13 et 14
 Elément C :Cm : stockage
d’énergie Q par le métal du
réservoir
 Jonction 03
 Eléments de
couplage RC1 et RC2
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e19  e18  e20  T19  T18  T20

 f18  f19 , f 20  f19  Q18  Q19 , Q 20  Q19
et
e23  e22  e24  T23  T22  Ta

 f 22  f 23 , f 24  f 23  Q 22  Q 23 , Q 24  Q 23
e21 
1
Q21
f
dt

e
(
0
)

T

 T21 (0)

21
21
21
Cm
Cm
 f 21  f 20  f 22  Q 21  Q 20  Q 22

e20  e21, e22  e21  T20  T21, T22  T21



R C1 : f16  f15  f 25c p e15  H16  H e  m 3c pTe




R C2 : f11  f12  f10c p e12  H11  H s  m 8c pT13
« Integrated Design of Mechatronic Systems using Bond Graphs »
166
Global Dynamic Model
2

 p3  m7
 p 3  Pe  Re   
 I  Ch


m 7  p3  u1 sign  m7  Ps  m7  Ps
C
 C

I Rs
 h

h

 m7
 m7
U13  1
u1

 p3 
U13   I c pTe  c m  R  c p R sign  C  Ps  C  Ps
 h

V 7 m
s
h


U13
Q21  1
1  Ta
Q 21 


  
m7cV Rm Cm  Rm Ra  Ra


 m7 

 L   A 
y      U 
T   13 


 cV m7 
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
 Q21

 Q e(u2 )
 RmCm

167
Simulation using State equations format
Simulink
x(0)
u
f ( x, u )
x
x

y
x
C (x )
Generation of S-function from Symbols2000
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
168
From BG to Block Diagram
Se : Ps
e7 /g 
-
Se : Pe
TC
e3
1
I1 
+ - 11
e4
e5
f6
-
e1
LC
f2
 Re ( f 3 )
e2
De:L
f7
f4 +
f3
e7
 Ch (  f 7 dt)
-
e6
e8
+
01
uc  Rs (e8 )
f8
f10
12
e4
f6
uc
De:T
f2
Se : Te
c p .Te . f 2
RC1
f16
+
-
f13
 Ct (  f 7 dt ,  f13dt )
02
-
+
MSf : Q e
f12=f11
e13
e18
+
e20
Se : Ta
-
e23
e22
14
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
+
e23
e20
e21
03
 Cm (  f 20 dt ,)
 Re x (e22 )
f23
Rc 2 : c p .e13 . f10
RC2
f18
e24
e17
e12
f20
f21
f22
-
+
f18
f19
-
13
EXO SUR
SYMBOLS
e19
 Rm ( f19 )
« Integrated Design of Mechatronic Systems using Bond Graphs »
169
SYSTEMES CHIMIQUES
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
170
Physico chemical processes (1/4)
Types of applications : distillation column, fuel cell,..
State variables :

X  n1 . . nnc 1
Tin

H
Gaz  in
 Pin
m in
nc constituents
Variables
Parameters
x j , in 
* 
p j  j  1, nc

n j , in 
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
M j
 j  1, nc
c pj 
nnc
H
Tout 

H out 
Gaz (mixture )
Pout 
m out 
x j , out 

p*j , out 
 j  1, nc (constituen ts)
n j , out 
Tout 
« Integrated Design of Mechatronic Systems using Bond Graphs »
171

Physico chemical processes (2/4)
➽ A) Used variables
➽ B) Mixture to constituents
transformation ?
P1*
n1
Pi*
ni
Chemical
Constituents
P
*
Pnc
m
n nc
T
H
ni  m
.
xi
Mi
P1*
n
(i  1, n ) 1 *
Pi
ni
*
Pnc
nnc
Thermique
Mixture
P
Hydraulique

m
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
172
Physico chemical processes (3/4)
xi ,in , M i
P1*
➽ C) Use a bloc diagramme
P

m
Bloc
n1
Pi*
ni
*
Pnc
n nc
➽ D) Use a transformer
e

m
TF
e
x1 / M1
n1
Specie 1
Mixture (gaz)

Sf : m
P

m
1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
e
TF

m
xi / M i
e
TF

m
.
ni  m
e
ni
Specie i
e
Specie nc
n nc
« Integrated Design
of Mechatronic Systems using Bond Graphs »
xn / M n
xi
(i  1, nc )
Mi
173
Physico chemical processes
C
C
xi ,in , M i
n1
P1*
n1, in
P
I
N
P
U
T
m in
1
ni , in
xi , M i
n1, out
0
ni Pi*
Gaz (mixture)
H
T
(4/4)
n n P *
n
0
ni , out
m out
m in
n nc, in
Tin
Rc
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
H in
0
1
m out
m out
n nc
0
H out
« Integrated Design of Mechatronic Systems using Bond Graphs »
Rc
H out
174
O
U
T
P
U
T
Chemical system
 A. A   B .B
Kf

 A.C   B .D
Kr

Rel
C:CA
A
1
Recepteur
E i
TF
: A

A
TF
AA
: nF
C
 G
Af
Ar
1
C:CB
B
B AB
TF
: B
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
1
T
C
TF
D
: C
C:CC
1
RS
S g
TF
D
: D
« Integrated Design of Mechatronic Systems using Bond Graphs »
C:CD
175
Electrochemical Process
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
176
Electrochemical Model
Chimique-électrique
Production
H2O
Distribution de la tension
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
177
Integrated models
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
178
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 ]
Reactor
Outlet
Inlet
Market
place
Heater
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
179
Chemical model
Reactants A and B
A
C:CA
n A
B
C:CB
n B
Transformation
Products of reaction
D
TF
TF
:1/A
AA
A
A
TF B
:1/B
B
Af
1
C:CD
:1/D
Ar
1

n D
1
TF C
:1/C
C:CC
n C
RS
S g
Tg
Dissipation
To thermofluid model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
180
Thermofluid model
From chemical model
Sf : m D , H D
C :CR
TR
H C
Sf : m A , H A
0
Sf : m B , H B
PR
De
m C
Sf : H C
To economic
model
Sf : Q ex
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
181
Economic model
b
Factory inventory
C:C
P
m
From
FA
FA
Supplier
P UC
hydraulic
R:R T
model
P
/ m
UC
C
1
P

÷
÷

m
C
SC
R:R
1
R:R DC
m
0


0
m
DC
a
P
m
IA
I:I A
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
FA
« Integrated Design of Mechatronic Systems using Bond Graphs »
SC
SC
IA
Reinvestment
182
Global integrated model
Chemical model
Reactants A and B
C:CA
A
Products of reaction
TF
:1/A
n A
B
C:CB
Transformation
TF
:1/B
n B
D
TF
AA
A
AB
B
Af
1

1
:1/D
Ar
C:CD
n D
1
C
TF
:1/C
C:CC
n C
RS
S g
Dissipation
Tg
b

 D,H
Sf : m
D

 A, H
Sf : m
A
factory
inventory
C :CR
TR

H
C
0

 B,H
Sf : m
B

Sf : Q
ex
R:RT m
C
C
m
0

0
Hydraulic and thermal model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
 FA
m
PFA
PUC
PR
De
C:CFA

Sf : H
C
C 
PUC / m

1

R:RDC 
m DC
a
Supplier
PSC
1
 SC
m
 IA
m
R:RSC
PIA
I:IA
Reinvestment
Economic model
« Integrated Design of Mechatronic Systems using Bond Graphs »
183
Chemical model
Reactants A and B
C:C
A
A
B
Products of reaction
TF
A
TF
AA
AB
B
:1/B
n B
D
TF
:1/A
n A
B
C:C
Transformation
1
Af
1

:1/D
Ar
n D
1
C:C
D
C
TF
:1/C
C:C
n C
C
R
Dissipation
S

S g Tg
b
C :CR
 D , H D
Sf : m
TR
 A , H A
Sf : m
H C
0
 B , H B
Sf : m
Sf : Q ex
Sf : H C
PUC
PR
De
R:RT
C
m
0

0
C
m
C 
PUC / m

1

R:RDC
a
factory
inventory
C:CFA
 FA PFA Supplier
m
PSC
R:RSC
1 
 DC
m
m SC
 IA
m
PIA
Reinvestment
I:IA
Economic
model
« Integrated Design of Mechatronic Systems using Bond Graphs »
Hydraulic and thermal model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
184
PART 5
Application to industrial processes
 CHAPTER 5: Application to industrial processes
 Electrical systems
 Mechanical and electromechanical systems
 Process Engineering processes : power station
« Integrated Design of Mechatronic Systems using Bond Graphs »
185
185
BG Methodology Of modeling complex system
Physical process
Word bon graph
Acausal bond graph
Causalities assignment
Data acquisition
Causality conflict
no
Improvement of the
model by adding
elements
bond graph R,C,I
Causalities
correctes ?
yes
Mathematical equations
+
no
Experimental
datas
Model outputs

-
 < ad ?
yes
Validated model
« Integrated Design of Mechatronic Systems using Bond Graphs.»
186
Thermal system
Ta(t)
Tp
TI
2
3
Thermal system : bath of water
heated by a source of
temperature
Tf
Tr
Tf
Temperature
source
1
Tf
i2
i1
R1
uf
C1
i3
R2
u1 C2
R3
u2
ua
Electrical analogy
« Integrated Design of Mechatronic Systems using Bond Graphs.»
187
Word bond graph of the thermal process
Hot fluid
Temperature
source
Tf
Q f
Wall of the Tp
tank
Q p
Bath Tr
of
water Q r
Ambient
environment
Ta
Q a
External
temperature
source
Cas 1 : Thermal bond graph of the process neglecting the thermal capacity of the
wall
R:Rp
1
3
4
2
Se:Tf
R:Ra
C:Cr
5
11
9
Df:Q p
6
0
8
12
Se:-Ta
7
De:Tr
« Integrated Design of Mechatronic Systems using Bond Graphs.»
188
Equations
Structural equations
Jonction 11 : T2  T f  T5 ,
Q1  Q 5  Q 9 Q p Q 2
Jonction 0 : Q 4  Q 5  Q 6 , T5  T6  T7  Tr  T4
Jonction 12 : T3  T6  Ta , Q 8 Q 6 Q 3
Constitutive equations
1
1
Elément R : R p , Q 2  T2  T f  T5 
Rp
Rp
1 t 
Q4  Q4 ( 0 )
Elément C : C R , T4  Tr 
Q
dt

T
(
0
)

 4
4
Cr 0
Cr
1
1
T6  Ta 
Elément R : R a , Q 3 
T3 
Ra
Ra
« Integrated Design of Mechatronic Systems using Bond Graphs.»
189
State equations
 x( t )  Ax( t )  Bu ( t )
Linear case : 
 y( t )  Cx( t )  Du( t )
 x( t )  F ( x ,u )
Nonlinear case : 
 y ( t )  C ( x ,u )
Q p 
T f 
x  Q4  Qr , u    , y   
 Ta 
 Tr 
 1
1 


x( t )  Qr ( t )  

Q (t )
R C R C  r
a r
 p r
 1 
 1
Q p ( t )  R pCr 
y( t )  

Qr ( t )  R p


 Tr ( t )   1 
 0
 Cr 
 1

 Rp
1

Ra
 T f ( t )


T
(
t
)


a

0 T f ( t )
  Ta ( t ) 
0
« Integrated Design of Mechatronic Systems using Bond Graphs.»
190
Block diagram
R:Rp
1
3
4
2
Se:Tf
R:Ra
C:Cr
5
11
6
0
8
Se:-Ta
12
7
9
Df:Q p
De:Tr
Se:Ta
De:Tr
J11
T2
Se:Tf
1
Rp
Q 5  Q 9 Q p Q 2
J0

Q
Q
2
5
J11
(-)
Q 9
T5
Df:Q p
Q 6 (-)
T7
Q4(0)
Q 4
T5  T6  T7  Tr  T4
1
Cr

T4
(-)
T3
T6
J0
J12
1
Ra
Q 3
J12
Q8  Q 6  Q 3
« Integrated Design of Mechatronic Systems using Bond Graphs.»
191
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
4
1
Se:Tf
5
R:R2
C:Cm
6
1
9
Df:Q p
0
3
11
2
7
R:Ra
C:Cr
1
8
10
12
0
12
Se:-Ta
13
De:Tr
« Integrated Design of Mechatronic Systems using Bond Graphs.»
CHAP4/
192
192
STATE EQUATIONS
  1

1 
1
1




 Q
R
Q m    R1Cm R2Cm 
R2Cr


m
1



 Q 
 1
1
1   Qr   0
 r 
 




R2Cm
 R2Cr Ra Cr 

 1 
1
 T
Q p ( t )  R1Cm  Qm  
0
 f


y( t )  


 1    R1

T 
Q
T
(
t
)




 r
 
 r
0 0  a 

 Cr 
« Integrated Design of Mechatronic Systems using Bond Graphs.»
0 
T f 
1   Ta 
 
Ra 
193
Automated modelling using Symbols
« Integrated Design of Mechatronic Systems using Bond Graphs.»
194
Link with Matlab-Simulink
« Integrated Design of Mechatronic Systems using Bond Graphs.»
195
Easy to derive a model adding new elements
« Integrated Design of Mechatronic Systems using Bond Graphs.»
196
Electrical system
iR1
L1
iL1
iR2
R2
Us(t)
R1
C1
E(t)
C2
iC1
C:C1
R:R1
Se:E
E
iR1
1
6
4
uR1
1
3
iR1
uL1
iC1
2
uC1
R:R2
I:L1
0
uC1
5
iL1
SIMULATION using
MATLAB
1
De:Us(t)
9
iL1
7
11
uR2
TF
:m
8
1
10
iR2
12
SIMULATION using
Symbols2000
« Integrated Design of Mechatronic Systems using Bond Graphs.»
0
us
C:C2
197
Mechanical system
x ref  0
x ref
Sf : x ref
k1
0
x1
m1
F1
x m1
Se:-m1g
x1
Fm1
1
x m1
C:k1
C:k1
x1
F1
Se:-m1g
I:m1
x2
F2
0
x m 2
m2
Fm2
1
x m 2
x
g
x 2
C:k2
I:m2
Se
Se:-m2g
« Integrated Design of Mechatronic Systems using Bond Graphs.»
I:m1
x m1
x m1
x m1
k2
Fm1
1
F2
0
x m 2
1
C:k2
x 2
Fm2
x m 2
Se:-m2g
198
I:m2
Mechanical example
Sf : x ref
Fm1  m1g  Fk1  Fk 2
C:k1
Fk 2  k2  xk 2 dt  k2   x1  x2 dt  k2  x1  x2 
k1
x1
m1
Fk1  k1  xk1dt  k1   x1 dt  k1 x1
Se:m1g
Fk1
x1
Fk2
x2
k2
 m1x1  m1g  K1 x1  K 2  x2  x1 
Fk2
0
Fk2
x2
C:k2
xk 2
Fm2
x2
m2 g  k2  x2  x1   m2 x2
Se:m2g
x
« Integrated Design of Mechatronic Systems using Bond Graphs.»
I:m1
x1
1
m2
g
Fm1
1
m1g  k2  x2  x1   k1  x1  0  m1x1
1
xm1 
 Fm1dt
m1
x k 1
199
I:m2
Do it
« Integrated Design of Mechatronic Systems using Bond Graphs.»
200
Building
Tamb
Tref
+
-
Rlosses
Sensor
TROOM
PID
Rradiator
Rroom
TRAD
Source of heat
« Integrated Design of Mechatronic Systems using Bond Graphs.»
201
PART 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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
202
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
203
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
204
Main Softwares (2/5)
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
205
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
206
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
207
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
208
Some demonstrations using SYMBOLS 2000
GUI interface
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
From BG model to Matlab S-function
« Integrated Design of Mechatronic Systems using Bond Graphs »
209
Simulation in Matlab
 DEMONSTRATION
 Electrical system
 Mechanical system : suspension
 Electromechanical system : DC motor
 Hydraulic system
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
210
PART 7
Conclusions
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
211
Why Bond graph is well suited
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
212
Why Bond graph is well suited
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
213
Why Bond graph is well suited
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
« Integrated Design of Mechatronic Systems using Bond Graphs »
214