1 « integrated design of mechatronic systems using bond graphs » prof. belkacem ould bouamama...
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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/
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
3 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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, …)
4 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
5 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
6 « 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
7« Integrated Design of Mechatronic Systems using Bond Graphs »
PART 1PART 1
INTRODUCTION & MOTIVATIONS
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
8 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
9 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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..)
10 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
11« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Chapter 1Chapter 1
Introduction to integrated design of engineering systems
12 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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,
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
13 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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.
14 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
15 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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 …;
16 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
17 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
19 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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)
20 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
21 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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,…) .
22 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
23 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
24« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
WHAT WE CAN DO WITH BOND GRAPH ?
WHAT WE CAN DO WITH BOND GRAPH ?
25 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
BOND GRAPH FOR ALARM FILTERING
National Project : EDF-LAIL
world-wide project: CHEM
26 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
THE EKOFISK JACKING OPERATIONTHE EKOFISK JACKING OPERATION
27 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
28 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
TYPES OF INDUSTRIAL APLICATIONS
TYPES OF INDUSTRIAL APLICATIONS
Electrochemical integrated with transport sytem
Nuclear power plant
FCC process : Refinery Catalytic Cracking.
29 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
30 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Dedied Software (FDiPad)
Dedied Software (FDiPad)
31 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
33 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Architectural model
Architectural model
34 « Integrated Design of Mechatronic Systems using Bond Graphs.»
TECHNICAL SPECIFICATIONS AND MONITORABILITY ANALYSIS
TECHNICAL SPECIFICATIONS AND MONITORABILITY ANALYSIS
35 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
39« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
40« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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 ....
41« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
DEFINITION, REPRESENTATION
DEFINITION, REPRESENTATION
DEFINITION
REPRESENTATION
P = e.f
e
f
1 2
Mechanical power :
42« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
43« Integrated Design of Mechatronic Systems using Bond Graphs »
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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
44« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Bond Graph model in block diagramme
Bond Graph model in block diagramme
CORRECTOR ACTUATOR BOND GRAPH
MODEL
SENSOR
CX
Y
Information system Energetic system
45« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Some definitions (1/2)
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
46« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Some definitions (2/2)
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 ?
47« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
48« Integrated Design of Mechatronic Systems using Bond Graphs »
How to select them
How to select them
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Tamb
(J,f)
Chimie , electrochimie
Mécanique
Thermique
Électrique
Economique
Hydraulique
Thermofluide
Thermodynamique
49« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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]
50« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
51« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
xx
qqC
dqC
qdqqudqqet
kxkxxdxkdqqet Energy stored
by a spring
52« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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]
?
53« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
54« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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 ….
55« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
56« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
58« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
59« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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 ?
61« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
62« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
63« Integrated Design of Mechatronic Systems using Bond Graphs »
Bond graph well suited automated modelling
Bond graph well suited automated modelling
JunctionsJunctions
Passive elementsPassive elements
Active elementsActive elements
JunctionsJunctions
SYMBOLS
DEMOS
64« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
65« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
66« Integrated Design of Mechatronic Systems using Bond Graphs »
Examples of R elements
Examples of R elements
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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)
67« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
68« Integrated Design of Mechatronic Systems using Bond Graphs »
Examples of C elements
Examples of C elements
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
69« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
70« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
71« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
72« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
73« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
74« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
75« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
ACTIVATED ELEMENTS (1/2)
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
76« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
ACTIVATED ELEMENTS (2/2)
ACTIVATED ELEMENTS (2/2)
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
77« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
78« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
79« Integrated Design of Mechatronic Systems using Bond Graphs »
JUNCTIONS (2/5) : Examples of 0-junction
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
80« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
81« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
JUNCTIONS (4/5) : Examples of 1-junction
JUNCTIONS (4/5) : Examples of 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
82« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
83« Integrated Design of Mechatronic Systems using Bond Graphs »
Exercise
Exercise
L1
E C1
R1
i1
i2
i4
R3
L2
i3 i6
R2 C2
k
mg
Mp
i5
84« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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.
85« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
86« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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)(
source by thegiven )(
te
tf
One junction :common
flowjunction
Constitutive equation Name
Source of effort
Symbol
Resistance
Capacitance
Inertance
Transformer
Zero junction :common effort
junction
arbitrary)(
source by thegiven )(
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)(
source by thegiven )(
te
tf
One junction :common
flowjunction
Constitutive equation Name
Source of effort
87« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
88« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
89« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Electrical circuit : Example1
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)
90« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
91« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Electrical circuit : Example3
Electrical circuit : Example3
L1
SE C1
R1
iR1
iC1
R2
C2 SF
iR2
iC2
SF
92« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
93« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
94« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
95« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
96« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
97« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
98« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
99« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
100« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
101« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
102« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
103« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
EXERCISES : Hydraulic control system
EXERCISES : Hydraulic control system
PID0,2 -1 bar 3 - 15 psi Pe
xLT PR sV
eV
P0
104« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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 :
105« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
EXERCISES Hydraulic systems
EXERCISES Hydraulic systems
106« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
108« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
109« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
110« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
PRINCIPLE
PRINCIPLE
111« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
112« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
113« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
114« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
115« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Causalities for 1-junction
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
116« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Causalities for 0-junction
Causalities for 0-junction
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
117« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
118« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
119« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
CAUSALITY OF GY JUNCTION
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
120« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
CAUSALITY OF GY JUNCTION
CAUSALITY OF GY JUNCTION
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
121« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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 …).
122« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
123« Integrated Design of Mechatronic Systems using Bond Graphs »
From BG to Bloc Diagram (1/2)
From BG to Bloc Diagram (1/2)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
124« Integrated Design of Mechatronic Systems using Bond Graphs »
From BG to Bloc Diagram (2/2)
From BG to Bloc Diagram (2/2)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
125« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
126« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
127« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Application to Electrical system : Block Diagram (1/2)
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
128« Integrated Design of Mechatronic Systems using Bond Graphs »
Application to Electrical system : Block Diagram (2/2)
Application to Electrical system : Block Diagram (2/2)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Causal graphCausal graph
Bloc DiagramBloc Diagram
129« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
130« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
131« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Application Hydraulic system: Block Diagram
Application Hydraulic system: Block Diagram
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
132« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
133« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
134« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
135« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
136« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
137« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
138« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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)
139« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
140« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
141« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
142« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
COUPLED BOND GRAPHSCOUPLED BOND GRAPHS
CHAPTER 4: Coupled energy bond graph Representation and complexity Thermofluid sources , Thermofluid Multiport R, C Examples
PART 4PART 4
143« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
144« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
145« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
146« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Convection Heat transfer (1/2)
Convection Heat transfer (1/2)
2
2vPumH
➽ General expression for convected energy
Internal specific energy Pressure energy Kinetic energy
),( mP
),( TH
147« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Convection Heat transfer (2/2)
Convection Heat transfer (2/2)
➽ Modeling Hypothesis
2
2vPumH
TcmhmH p
02
: v velocity lowFor 2
v
]/[: kgJTcP
uh p
enthalpy Specific
148« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Coupling of thermofluid variables
Coupling of thermofluid variables
TcmH p
T
Pm
mSf : 1
m
RcT
HTSe:
149« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
150« Integrated Design of Mechatronic Systems using Bond Graphs »
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
151« Integrated Design of Mechatronic Systems using Bond Graphs »
SOFTWARE REPRESENTATION
SOFTWARE REPRESENTATION
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
152« Integrated Design of Mechatronic Systems using Bond Graphs »
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
153« Integrated Design of Mechatronic Systems using Bond Graphs »
d
SOFTWARE REPRESENTATION
SOFTWARE REPRESENTATION
154« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
155« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
156« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
157« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
158« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
159« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
160« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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 ,
Constitutive equations
161« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
162« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
163« Integrated Design of Mechatronic Systems using Bond Graphs »
Constitutive equations (1/4)
Constitutive equations (1/4)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
164« Integrated Design of Mechatronic Systems using Bond Graphs »
Constitutive equations (2/4)
Constitutive equations (2/4)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
165« Integrated Design of Mechatronic Systems using Bond Graphs »
Constitutive equations (3/4)
Constitutive equations (3/4)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
166« Integrated Design of Mechatronic Systems using Bond Graphs »
Constitutive equations (4/4)
Constitutive equations (4/4)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
167« Integrated Design of Mechatronic Systems using Bond Graphs »
Global Dynamic Model
Global Dynamic Model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
168« Integrated Design of Mechatronic Systems using Bond Graphs »
Simulation using State equations format
Simulation using State equations format
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
),( uxfu x
x(0)
)(xCyx
x
SimulinkSimulink
Generation of S-function from Symbols2000Generation of S-function from Symbols2000
169« Integrated Design of Mechatronic Systems using Bond Graphs »
From BG to Block Diagram
From BG to Block Diagram
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
-
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
170« Integrated Design of Mechatronic Systems using Bond Graphs »
SYSTEMES CHIMIQUESSYSTEMES CHIMIQUES
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
171« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
172« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
173« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
174« Integrated Design of Mechatronic Systems using Bond Graphs »
Physico chemical processes (4/4)
Physico chemical processes (4/4)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
175« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
176« Integrated Design of Mechatronic Systems using Bond Graphs »
Electrochemical Process
Electrochemical Process
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
177« Integrated Design of Mechatronic Systems using Bond Graphs »
Electrochemical Model
Electrochemical Model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Chimique-électrique
Production H2O
Distribution de la tension
178« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Integrated modelsIntegrated models
179« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
180« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
181« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
182« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
183« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
184« Integrated Design of Mechatronic Systems using Bond Graphs »
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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« Integrated Design of Mechatronic Systems using Bond Graphs »
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
186 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
-
187 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
188 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
189 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
Constitutive equations
190 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
191 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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:
192 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
193 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
194 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Automated modelling using Symbols
Automated modelling using Symbols
195 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Link with Matlab-Simulink
Link with Matlab-Simulink
196 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Easy to derive a model adding new elements
Easy to derive a model adding new elements
197 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
198 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
199 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
200 « Integrated Design of Mechatronic Systems using Bond Graphs.»
Do it
Do it
201 « Integrated Design of Mechatronic Systems using Bond Graphs.»
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
203« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Why Bond graph is well suited
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
204« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Main Softwares (1/5)
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
205« Integrated Design of Mechatronic Systems using Bond Graphs »
Main Softwares (2/5)
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
206« Integrated Design of Mechatronic Systems using Bond Graphs »
Main Softwares (3/5)
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
207« Integrated Design of Mechatronic Systems using Bond Graphs »
Main Softwares (4/5)
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
208« Integrated Design of Mechatronic Systems using Bond Graphs »
Main Softwares (5/5)
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
209« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
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
210« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Simulation in Matlab
Simulation in Matlab
DEMONSTRATION
Electrical system
Mechanical system : suspension
Electromechanical system : DC motor
Hydraulic system
211« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
PART 7
Conclusions
PART 7
Conclusions
212« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Why Bond graph is well suited
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
213« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Why Bond graph is well suited
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
214« Integrated Design of Mechatronic Systems using Bond Graphs »Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
Why Bond graph is well suited
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