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 Systèmes
Laboratoire d'Automatique, Génie Informatique et Signal
(LAGIS - UMR CNRS 8219
et Directeur de la recherche à École Polytechnique de Lille (Poltech’ lille)
mèl : Tel: (33) (0) , mobile : (33) (0)
Ce cours et bien d’autres sont disponibles à
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.

2. Few References 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.
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: , 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
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, Part II: On line implementation, CEP, Vol 14/1 pp 85-96,
B. Ould Bouamama et al. « Software for Supervision System Design In Process Engineering Industry. » 6th IFAC, SAFEPROCESS, , pp Beijing, China, 29-1 sept
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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, …)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

4. 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
CHAPTER 5: Application to industrial processes
Electrical systems
Mechanical and electromechanical systems
Process Engineering processes : power station
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

5. 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. Few References 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.
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: , 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
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, Part II: On line implementation, CEP, Vol 14/1 pp 85-96,
B. Ould Bouamama et al. « Software for Supervision System Design In Process Engineering Industry. » 6th IFAC, SAFEPROCESS, , pp Beijing, China, 29-1 sept
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

7. INTRODUCTION & MOTIVATIONS
PART 1
INTRODUCTION & MOTIVATIONS
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

8. 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

9. 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

10. 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

11. Introduction to integrated design of engineering systems
Chapter 1
Introduction to integrated design of engineering systems
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

12. 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

13. 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

14. Mechatronics ; Synergetic Effects
Information
technology
System theory
Automatic control
Computer engineering
Diagnosis
Artificial Intelligence
Software
MECHATRONICS
Electronics
Power electronics,
Networks,
converters AN/NA,
Micro controllers
Actuators,
Sensors
Mechanics
Hydraulics,
Thermal engineering,
Mechanism
Pneumatic
Mechanical elelents
Precision mechanics

15. 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. 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.
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. 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 electronic-mechanical systems with sensors, actuators and digital microelectronics.

18. Methodology for testing
Development of generic models and Control algorithms
Validation using SiL
Test
Validation using MiL
Validation using HiL
Test
Industrial validation

19. 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)

20. Cycle en V HiL (Hardware in the Loop) 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. Bond Graphs : Tools for Integrated Design
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

22. LEVELS OF MODELLING 1. Technological 3. Mathematical 4. Algorithmic
This level constructs the architecture of the system by the assembly of different sub-systems, which are the plant items (heat exchanger, boiler, pipe...). The technological level can be represented by the so-called word bond graph.
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
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

23. 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

24. WHAT WE CAN DO WITH BOND GRAPH ?
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

25. BOND GRAPH FOR ALARM FILTERING
National Project : EDF-LAIL
world-wide project: CHEM
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

26. THE EKOFISK JACKING OPERATION
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

27. A feasibility study in coordination with Phillips Petroleum Company
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 tons
Raising to take place in summer 1987
Expected shut down 28 days
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

28. TYPES OF INDUSTRIAL APLICATIONS
Electrochemical integrated with transport sytem
Nuclear power plant
FCC process : Refinery Catalytic Cracking.
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

29. Bond Graph for Integrated Supervision design
New instrumentation architecture
Structural Analysis
RRAs
Technical specifications
Sensor Placement
Diagnosis Results
P&ID
Process
Dynamic Models generation
RRAs generation
Real Time Implementation
Datas from process
Sensors

30. Dedied Software (FDiPad)

31. Graphical User Interface (1/4)
Data base
Architectural model
Behavioral model

32. Graphical User Interface (2/4)
Residuals
Fault signature

33. Architectural model

34. TECHNICAL SPECIFICATIONS AND MONITORABILITY ANALYSIS

35. Sensor placement

36. Simulation interface

37. Bond Graph Theory PART: 2 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. Founders
J. Thoma
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

39. THE FIRST IDEA The first paper
The first system used by Paynter teaching in the Civil Engineering Department at MIT and first ideas
The first paper
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

40. 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

41. DEFINITION, REPRESENTATION2 1
Mechanical power :  
REPRESENTATION
P = e.f e f
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

42. 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

43. 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

44. Bond Graph model in block diagramme
Information system
Energetic system
CORRECTOR
ACTUATOR
BOND GRAPH
MODEL
SENSOR C X Y
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

45. 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. E
vertex
Submodel (Component ) C
vertex
Submodel (Component)
Edge (bond) E C
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

46. Some definitions (2/2) Which generic variables are used ?
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

47. 1. 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 variables
Effort e(t) : voltage, temperature, pressure
Flow f(t) : mass flow, current, entropy flow,
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

48. How to select them Thermique Thermofluide Mécanique Hydraulique
Tamb
Hydraulique
Thermofluide
Mécanique
Électrique
(J,f)
Chimie , electrochimie
Thermodynamique
Economique
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

49. POWER VARIABLES FOR SEVERAL DOMAINS
Electrical
DOMAIN
Mechanical (rotation)
Hydraulic
Chemical
Thermal
Economic
Mechanical (translation)
FLOW (f)
EFFORT (e)
VOLTAGE
u [V]
CURRENT
i [A]
FORCE
F [N]
VELOCITY
v [m/s]
TORQUE
 [Nm]
ANGULAR VELOCITY
 [rad/s]
PRESSURE
P [pa]
VOLUME FLOW
dV/dt [m3/s]
CHEM. POTENTIAL
 [J/mole]
MOLAR FLOW
dn/dt [mole/s]
TEMPERATURE
T [K]
ENTROPY FLOW
dS/dt [J/s]
UNIT PRICE
Pu [$/unit]
FLOW OF ORDERS
fc [unit/period]
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

50. 2. ENERGY VARIABLES
The momentum or impulse p(t), (magnetic flow, integral of pressure, angular momentum, … )
The general displacement q(t), (mass, volume, charge … )
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

51. Why energy variables ?  ENERGY VARIABLES  Why energy variables ?
The momentum or impulse p(t), (magnetic flow, integral of pressure, angular momentum, … )
The general displacement q(t), (mass, volume, charge … )
 Why energy variables ?
Energy stored
by a spring
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

52. ENERGY VARIABLES FOR SEVERAL DOMAINS
Displacement (q)
Impulse (p)
Electrical
CHARGE
q [Coulomb]
FLUX
Φ [Wb]
Mechanical (translation)
DISPLACEMNT
x [m]
MOMENT
J [Ns]
Mechanical (rotation)
ANGLE
 [rad]
ANGULAR MOMENTUM
[Nms]
VOLUME
V [m3]
MOMENTUM pp
Ns/m2
Hydraulic
Nbr of MOLE
n [-] ?
Chemical
ENTROPY
S [J/K] ?
Thermal
accumulation of orders qe
Economic
Economic momentum Pe
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

53. Energy variables : analogy
P,V
u,q
Q,T
x, F
Displacement
F,
u,
Impulse
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

54. 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

55. PSEUDO BOND GRAPH FLOW (f) EFFORT (e) DOMAIN Hydraulic Chemical
PRESSURE
P [ pa ]
MASSE FLOW
[ Kg /s ]
Chemical
CONCENTRATION
C [ mole/m3]
MOLAR FLOW
[ mole/s]
TEMPERATURE
T [K]
HEAT FLOW
[W ]
CONDUCTION
Thermal
ENTHALPY FLOW
[ W ]
SPECIFIC ENTHALPY
h [ J/kg ]
CONVECTION
TEMPERATURE
T [K]
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

56. 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

57. Let us learn bond graph language
Go head

58. EXAMPLE1 : ELECTRICAL INDUCTION MOTORw ua ui ia
LOAD
(J,f)
ELECTRICAL PART
MECHANICAL PART 
Inductor Ra La ua ia  w
ELECTRICAL PART
MECHANICAL
PART
LOAD
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

59. EXAMPLE 2: POWER STATION
TURBINE
RECEIVER
STEAM
FEED WATER
HEATER
PUMP
BOILER TW PW
PUMP TR PP
PIPE TP PP TB PB
TURBINE
RECEIVER
HEATER TH U i
Load   U
source
MOTOR i
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

60. Where is the generecity ?

61. FEW ELEMENTS FOR A BIG PURPUSE
Tamb C Se Sf RS R I
(J,f) TF GY
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille
61\

62. BOND GRAPH ELEMENTS R C I TF, GY 0,1 Sf Se BOND GRAPH ELEMENTS
PASSIVE ELEMENTS
(transform received power into dissipated (R) or stored (C, I) energy R C I
JUNCTIONS
Connect different elements of the systems : are power conserving
TF, GY
0,1
They are not a material point (common effort (0) and common flow ((1)
Energy transformation or transformation from one domaine to another
ACTIVE ELEMENTS
Generate and Provide a power to the system Sf Se
One port element
R,C,I,
Se,Sf
0,1
Tree ports element
TF, GY
Two ports element
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

63. Bond graph well suited automated modelling
SYMBOLS
DEMOS
Junctions
Passive elements
Active elements
Junctions

64. Passive elements Representation 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

65. R element (resistor, hydraulic restriction, friction losses …)v1 v2 i
ELECTRICAL
HYDRAULIC p1 p2 T1 T2
THERMAL
R Constitutive equation : For modeling any physical phenomenon characterized by an effort-flow relation ship f
R:R1
Representation e
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

66. Examples of R elements
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

67. BUFFERS
A) C element (capacitance) Examples: tank, capacitor, compressibility
ELECTRIC i1 i2 C i
THERMAL m c T
HYDRAULIC h
A: section
h: level
: density
C= A/g p
C Constitutive equation (For modeling any physical phenomenon characterized by a relation ship between effort and  flow f
C:C1
Representation e
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

68. Examples of C elements
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

69. p : impulsion of pressure
Inertance : I element
ELECTRIC
HYDRAULIC
MECHANICAL l F V1 V2 i p1 p2
 : Magnetic flux
p : impulsion of pressure
Q : momentum
I Constitutive equation (For modeling any physical phenomenon characterized by a relation ship between flow and  effort f
I:I1
Representation e
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

70. Tetrahedron of State 4 variables : e, f, p, q 3 Bg elements : R, C, I
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

71. 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 f1 TF :m e1 f2 e2
Defining relation
e1 = m.e2,
f2 = m.f1
Where m : modulus
Modulated transformer (m is not cste) f1
MTF :m e1 f2 e2 u
Defining relation
e1 = m(u).e2,
f2 = m(u).f1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

72. EXAMPLES OF TRANSFORMERSu1 u2 i2 i1
Electrical transformer TF :m TF :A
Hydraulic power is transducted
into mechanical power
A : area of the piston
Hydraulic piston F2 F1 a b
Lever TF
:b/a F2 F1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

73. 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
Defining relation
e1 = rf2
e2 = rf1
Where r : modulus f1 GY :r e1 f2 e2
Modulated Gyrator (if r is not cste) u
Defining relation
e1 = r(u)f2
e2 = r(u)f1 e1 e2
MGY :r f1 f2
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

74. Example of gyrator : DC motor u  i GY :r u i  
 = ri
 = K(iind)i
MGY :r u i  
iind
r = K(iind)
MODULATED GYRATYOR
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

75. 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... f Se e
Se = e(t)
MSe
Modulated effort source u
Se = e(t,u)
Simple effort source
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

76. 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 e
Sf = f(t,u) u
MSf f
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

77. JUNCTIONS (1/5)  0 - JUNCTION “ Common effort junction”
Defining relation
Representation e2 f2 e1 e3
Power conservation f1 f3 e4 f4
ai = if
ai = if
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

78. Jonction 0 : Loi de conservation d’énérgie
Cas statique
Bilan énergétique
Bilan massique
.P3
.P1 P2
Cas dynamique
C:Ct
Bilan énergétique
C:Ch
Bilan massique
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

79. JUNCTIONS (2/5) : Examples of 0-junctionP E C R i i1 i2
Se:E
i = i1 + i2 Mc Mp
Se:Fr
C:1/k 1
I:Mp
Se:Fr
C:1/k 1
I:Mc

80. JUNCTIONS (3/5) : 1 JUNCTION
1 - JUNCTION “ Common flow junction”
Defining relation
Power conservation
ai = if
ai = if
Representation e2 f2 e1 e3 1 f1 f4 e4
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

81. JUNCTIONS (4/5) : Examples of 1-junction
R:R1
R:R2
P2 -P3 P3
P1 -P3 R1 R2 E C R L UR UL UC i
Se:E
E =UR + UL + UC k M
F(t) b F FR FC
C:1/k
I:M
R:b FM
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

82. Junction 1 : thermal system
Cas dynamique
Cas statique 1 T1 T2 R TR R TR T1 T2 1 TC C
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

83. Exercise R2 C2 L2 i3 R3 L1 i6 i1 R1 i4 i5 E C1 i2 k mg Mp

84. 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

85. Structural Model Se, Sf I , C 0, 1, TF, GY R De, Df u Din Dout y
Sources
Se, Sf u
Stockage
d’énergie
I , C
Structure de Jonction
0, 1, TF, GY
Din
Dissipation
d’énergie R
Dout y
Capteurs
De, Df
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

86. Summary
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

87. BUILDING ELECTRICAL MODELS
Fix a reference direction for the current, it will be used as power direction
For each node in circuit with a distinct potential create a 0-junction
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
Assign power directions to all bonds
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
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

88. Simplifications of Bond graphs1
Example of simplification 1 C 1 C R C R C 1 1 R
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

89. Electrical circuit : Example1b a g C 1
R:R1 C
Se:E a b g a b g
(1)
(2)
(3,4) 1
R:R1 C
Se:E a b 1
R:R1 C
Se:E
(6)
(5)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

90. Electrical circuit : EXAMPLE2
iR1
iC1
iL1 R2 L2 1
R:R1
uR1
iC1
C:C1
uC1
iR1 1
I:L1
iL1
uL1
uC1 1 TF
I:L2
R:R2
Se:E E
iR1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

91. Electrical circuit : Example3SE C1 R1
iR1
iC1 R2 C2 SF
iR2
iC2
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

92. BUILDING MECHANICAL MODELS
Fix a reference axis for velocities
Consider all different velocities ( absolute velocities for mass and inertia and relative velocities for others).
For each distinct velocity, establish a 1-junction, Attach to the 1-junction corresponding Bond graph elements
Express the relationships between velocities. Add 0-junction (used to represent those relationships) for each relationship between 1-junctions
Place sources
Link all junctions taking into account the power direction
Eliminate any zero velocity 1-junctions and their bonds
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

93. Mechanical system : EXAMPLE (1/2)g k f
Vref V1
(2) 1 Vk Vf
C:1/k
I:M
R:f
(3)
Relationship between velocities
(4)
Se:-Mg Sf
(5,6)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

94. Mechanical system : EXAMPLE (2/2) (Simplifications)1
Vref V1 Vk Vf
C:1/k
I:M
R:f
Se:-Mg Sf 1
Simplification 1
V1-Vref Sf
Vref Vf
R:f Vk
C:1/k V1
Se:-Mg
I:M
Se:-Mg 1
R:f
C:1/k
I:M
Eliminate any zero velocity 1-junctions and their bonds V1 Vf Vk
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

95. Exercise 1 : mechanical x f1 k2 k1 k3 f2 m1 m2 m3 R3 k1 k2 k3 F(t) +Mb 1
R:f1
C:1/k1
C:1/k3
R:f2
I:Mb
I:Ma
Se:-F(t)
C:1/k2
F(t) Ma k1 k3 f2 m1 m2 m3 R3 k1 k2 k3
F(t) +
Vref=0
m1,f1
m2,f2
m3,f3
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

96. Electro-mechanical sytem1
R:Ra
I:La
Se:UF IF UR UI IF 1
R:B
I:J
Se:Load m m  R I 1
R:Ra
I:La
Se:UA IA UR UI Um
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

97. Exercise 3 : Hydro-mechanical and suspensionSf R7 R5 R6
Air
Pompe P1
Piston
Cylindre
Compresseur
Atmosphère Se2:P0
Arbre
De:L Mc Mp
Sf:Fr
C:1/k
R:Ra Mp
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

98. BUILDING HYDRAULIC MODELS
Fix for the fluid a power direction
For each distinct pressure establish a 0-junction (usually there are tank, compressibility, ….)
Place a 1-junction between two 0-junctions and attach to this junction components submitted to the pressure difference
Add pressure and flow sources
Assign power directions
Define all pressures relative to reference (usually atmospheric) pressure, and eliminate the reference 0-junction and its bonds
Simplify the bond graph
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

99. Hydraulic system : EXAMPLE (1/2)
Inertia I
Resistance R1
Resistance R2
Pump P1 P2 P3 P4
Pat
Se:P1 1
R:R1 I
R:R2 C
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

100. EXAMPLES OF BG MODELS : Hydraulic
Valve 1 R2
Pump PP PR LC P0
I:l/A 1
P P -PR
C:CR 1
R:R2
PR -P0
Se:PP PP PR PR
Se:-P0 P0 De
PID
R:R1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

101. EXERCISES : Mechanical (pneumatic valve)
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
Vanne
u(t)
x(t)
Block diagramme
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

102. EXERCISES : Bond graph model of the pneumatic valve
C:1/ke Fk
I:m FI Pe
Pneumatic
energy
TF:A F
Mechanical
energy
Se:Pe Df x 1
R:f Ff
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

103. EXERCISES : Hydraulic control system
PID
0,2 -1 bar
psi Pe x LT PR P0
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

104. EXERCISES : Bond graph model of the hydraulic system1
R:RV
C:CR
C:ke Fk
De:P0 x Pe
TF:A F
I:m FI
R:f Ff
PID u
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

105. EXERCISES Hydraulic systems
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

106. EXAMPLES OF BG MODELS :ThermalTs Ta
Source of heat
C:Cb TS
R:Ra 1 TS
TS - Ta TS
Se:-Ta Ta
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

107. CAUSALITY PART 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
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

108. CAUSALITIES Definition Problematic Importance of causal proprieties
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

109. System A impose an effort e to system B
Convention A B
System A impose an effort e to system B e f A B e
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

110. PRINCIPLE
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

111. CALCULATION EXAMPLE P1 P2  P R:K PR P2 P1 PR 1 R:K  P PR P1 P1 1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

112. Remarks about causalities
 the orientation of the half arrow and the position of the causal stroke are independent e f A B
System A impose effort e to B
System A impose flow f to B
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

113. 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 u R i e F 1 ) ( = - f
Resistance causality Se Sf 
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

114. Integral and derivative causality
Preferred (integral)
causality
Derivative
causality C e f f C e e I f f I e
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

115. Causalities for 1-junction
Causal Bond Graph model
Strong bond
1-Junction e1 e4 e3 f2
Block diagram
Only 1 bond without causal stroke near 1 - junction
 Rule
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

116. Causalities for 0-junction
Block diagram e1 e3 e4 f1 e2 f4 f3 f2
Strong bond
Only 1 causal stroke near 0 - junction
 Rule
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

117.  2 CAUSALITY SITUATIONS
TF JUNCTION f1 TF :m e1 f2 e2
Defining relation
e1 = m.e2
f2 = m.f1
Where m : modulus
 2 CAUSALITY SITUATIONS
If e2 and f1 are known : e1 m e2 f2 f1 TF :m
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

118. CAUSALITY OF TF JUNCTION
If e1 and f2 are known : e2
1/m e1 f1 f2 e1 e2 TF :m f1 f2
 RULE : A symmetrical position of the causal stroke
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

119. CAUSALITY OF GY JUNCTION:r e1 f2 e2
Defining relation
e1 = r.f2
e2 = r.f1
Where r : modulus
 2 CAUSALITY SITUATIONS
If f2 and f1 are known : e2 e1 r f2 e2 f1 e1 GY :r f1 f2 f2
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

120. CAUSALITY OF GY JUNCTION
If e1 and e2 are known : f2 GY :r e2 e1 f1
1/r
 RULE : Skew - symmetrical position of the causal stroke
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

121. 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

122. Four Information given by BG
There exists a physical link between A and B A e f
Power variables show the type of energy B
Flow is input for B and effort is output
A supplies power to B
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

123. From BG to Bloc Diagram (1/2)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

124. From BG to Bloc Diagram (2/2)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

125. Application to Electrical system : BG model
E(t) L C R1 R2
V(t)
 1. BOND GRAPH MODEL
I:L 2
R:R2 5
De:e6
Se:E(t)
E(t) 1 4
R:R1 3 C 6
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

126. Application to Electrical system:State equationx y
 2. STATE EQUATIONS
Structural laws
- 1 junction
- 0 junction
Constitutive equations
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

127. Application to Electrical system : Block Diagram (1/2)
I:L
Se:E E 5
R:R2
R:R1 6 4 2 3 C E C L R2
U(t) R1
0-Junction
f6=f4-f5
e6=e4=e5
1-Junction
e2=e1-e3-e4
f2=f1=f3=f4 e6
e6(0)
Se:E e2 e3 + - e1 e4 f2
f2(0) f6 f5 -
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

128. Application to Electrical system : Block Diagram (2/2)
Causal graph
Bloc Diagram
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

129. Application to Hydraulic system: BG model
Pump P0 PC R2 R1 PP l 1
PI1
R:R1
I:I1
PR1 P0 1
R:R2
PR2
Se:-P0
Atmosphere PC
C:CR
Se:PP PP
De:PC
Pref PC + - u
PID
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

130. Application Hydraulic system: Block Diagram
1 junction
0 junction
Structural laws
Constitutive equations
I:I1
C:CR
R:R1
R:R2
Calcul de CR et I1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

131. Application Hydraulic system: Block Diagram1
PI1
R:R1
I:I1
PR1 1
R:R2
PR2 PC
C:CR
Se:-P0 P0
Atmosphere
Se:PP PP
De:PC
Pref PC + - u
PID + -
Se:PP PC
PR1 PP
Se:-P0
PR2
PI1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

132. EXAMPLE (How to avoid derivative causality ?)iC UC C E i UC
Se:E iC
Derivative causality
Current infinite ? R 1 E iR uR uC iC C
Se:E
Integral causality adding R E C R i iC UC
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

133. Derivative causality : example
I:M1
I:M2 TF
:b/a
Se:F(t) 1 1
C:1/k C
I:M1
I:M2 TF
:b/a
Se:F(t) 1 1
C:1/k
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

134. Transfer Function  Schematic  Causal Bond Graph Model 1 R:R1 C:C1iR iC
UC1
 Schematic
 Causal Bond Graph Model 1
R:R1
uR1
iR1
uC1
iR1
iC1
C:C1
Se:E E
iR1
 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
Junction 1
Junction 0
R element in conductance causality
iR1=UR1/R1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

135. System to be controlled
State Equations
System to be controlled M x yc u
ACTUATORS
CORRECTOR
PROCESS A
X-x y
SENSORS
Bond graph
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

136. 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.
Properties
the state vector does not appear on the Bond graph, but only its derivative
The dimension of the state vector is equal to the number of C- and I-elements in integral causality
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

137. 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

138. Application R:Ra R:f Se:Ua MGY Se:-L 1 1 :K I:J I:La uM ia uRa uLa
Df:im
Df:wm 1 L w
I:J
R:f
Se:-L f J
MGY :K  w
r = k(iF)
Se:Ua ia ua
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

139. 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- Junction
R element in conductance causality
State equation
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

140. SIMULATION Use of Symbols software
Automatic generation of the state equation
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

141. Application : do it R2 R:R1 C:C1 I:L1 R:R2 Se:E 1 1 1 C:C2 L1 C1 R1
E(t) C1 R1
iR1
iC1
iL1 R2
Us(t)
iR2 C2 1
R:R1
uR1
iC1
C:C1
uC1
iR1
uL1 1
I:L1
iL1
uC1
uR2
iR2 1
R:R2
De:Us(t) 1 2 3 4 5 6 7 8 9 10 11 12
Se:E E
iR1
TF :m
C:C2 us
COMPARAISON SYMBOLS_SIMULINK
BLOCK_DIAGRAM SIMULINK
S-FUNCTION FROM SYMBOLS
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

142. 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

143. INTRODUCTION TO MULTIPORT ELEMENT
 SINGLE BOND GRAPH : One energy e f
The constitutive relation is scalar
 MULTIBOND GRAPH : more than one energy
Representation : A bond coupled by a ring
The constitutive relation is matrix
e1 , e2 ...
f1, f2 ... e1 f1 en ei f2 fn
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

144. Constitutive equations
Coupled bond graph C
Chemical
Hydraulic
Thermal
Constitutive equations
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

145. Coupled Bond graphs Representation
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

146. Convection Heat transfer (1/2)
➽ General expression for convected energy
Internal specific energy
Pressure energy
Kinetic energy
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

147. Convection Heat transfer (2/2)
➽ Modeling Hypothesis
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

148. Coupling of thermofluid variables1 Rc
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

149. Pump as single flow source
Thermofluid pump
➽ Bond graph models
Pump as single flow source
A) Modulated source 1 Rc
B) Using R Multiport
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

150. C) Use of an activated element
Activated bonds d
C) Use of an activated element 1 1 f 1 e

151. SOFTWARE REPRESENTATION
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

152. How to modelise a sensor ?PI C 1 2 I 3 e
Hydraulic system case

153. SOFTWARE REPRESENTATIONd

154. How to represent it in Symbols2000 ?1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

155. Example of multiport elements
 R MULTIPORT
 Representation R 1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

156. Constitutive equation for R-multiport
 Physical law ( Continuity)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

157. Inertia of the fluid ➽ Impulse of pressure p R I 1 Rc Hydraulic power
Thermal power
Hydraulic power 1 R I
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

158. Dynamic bond graph model of the pipe
Fluid moving with inertia
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

159. Bond graph model of the pipe
Global Model
Step response for hydraulic model to pressure difference
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

160. Constitutive equations
C - MULTIPORTS
H,m
Heater C
Representation
Output
BG model
Input C
Constitutive equations
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

161. Thermofluid example : heated tank
State variables
I element : p Pe
Po=0
One ports C Q
H,m
Two ports C
Tex
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

162. Bond graph model C Environnement Se:P0=0 Rc2 Rc1 C 11 R:Re I:I1 R:Rs3 4 10
Environnement Se:P0=0
R:Rs 12 6 8 9
Rc2 11
De:L C 01 5 7
Rc1 15 16 14 02 13
De:T 13 14 03
R:Rex Rm
Ambiance C 17 18 19 20 21 22 23
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

163. Constitutive equations (1/4)
Jonction 11 
Elém ent R :Re 
Elément I:l/A
Jonction 01 
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

164. Constitutive equations (2/4)
Jonction 02 
Multiport C : CR
niveau dans le réservoir indiqué par le capteur De :L
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

165. Constitutive equations (3/4)
Capacité thermique
Température indiquée par le capteur De :T
Jonction 12 
Vanne de réglage R :Rs
Eléments R : Rm et R :Ra 
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

166. 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

167. Global Dynamic Model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

168. Simulation using State equations format
Simulink
Generation of S-function from Symbols2000
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

169. From BG to Block Diagram
EXO SUR SYMBOLS
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

170. SYSTEMES CHIMIQUES
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

171. Types of applications : distillation column, fuel cell,..
Physico chemical processes (1/4)
Types of applications : distillation column, fuel cell,..
nc constituents
Variables
Parameters
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

172. ➽ B) Mixture to constituents transformation ?
Physico chemical processes (2/4)
➽ A) Used variables
Chemical
Constituents
➽ B) Mixture to constituents transformation ?
Thermique
Hydraulique
Mixture
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

173. ➽ C) Use a bloc diagramme
Physico chemical processes (3/4)
Bloc
➽ C) Use a bloc diagramme 1 e
Mixture (gaz)
Specie 1
Specie i
Specie nc
➽ D) Use a transformer
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

174. Physico chemical processes (4/4)C 1 Rc O U T P 1 Rc I N P U T
Gaz (mixture)
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

175. Chemical system C:CA C:CC RS C:CD C:CB Rel 1 Recepteur 1 1
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

176. Electrochemical Process
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

177. Electrochemical Model
Chimique-électrique
Production H2O
Distribution de la tension
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

178. Integrated models
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

179. 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 , Ghent (Belgique), Mai 2000 ]
Heater
Market place
Reactor
Inlet
Outlet
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

180. Chemical model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

181. Thermofluid model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

182. Economic model C:C R:R I:I m & b 1 a From hydraulic modelFA m
& b
Reinvestment
R:R T DC 1 ÷ ø ö ç è æ / C UC P a SC
Supplier
Factory inventory IA
From
hydraulic
model
I:I A
C:C
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

183. Global integrated model
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

184. Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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

186. BG Methodology Of modeling complex system

187. Thermal system
Thermal system : bath of water heated by a source of temperature
Electrical analogy

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

189. Equations
Structural equations
Constitutive equations

190. State equations

191. Block diagram

192. 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.

193. STATE EQUATIONS

194. Automated modelling using Symbols

195. Link with Matlab-Simulink

196. Easy to derive a model adding new elements

197. Electrical system R2 R:R1 C:C1 I:L1 R:R2 Se:E 1 1 1 C:C2 L1 C1 R1 iR1
E(t) C1 R1
iR1
iC1
iL1 R2
Us(t)
iR2 C2 1
R:R1
uR1
iC1
C:C1
uC1
iR1
uL1 1
I:L1
iL1
uC1
uR2
iR2 1
R:R2
De:Us(t) 1 2 3 4 5 6 7 8 9 10 11 12
Se:E E
iR1
TF :m
C:C2 us
SIMULATION using MATLAB
SIMULATION using Symbols2000

198. Mechanical system 1 1 1 1 C:k1 F1 F1 C:k1 k1 x1 Fm1 Se:-m1g I:m1 Fm1
C:k1 F1 x1
Fm1
Se:-m1g 1
I:m1 m1
Se:-m1g
Fm1 1
I:m1 F2 k2 x2 F2
C:k2
C:k2
Fm2 m2
Fm2 1
I:m2 1
I:m2 Se g
Se:-m2g
Se:-m2g

199. Mechanical example 1 x1 x2 k1 k2 m2 m1 I:m2 I:m1 C:k2 C:k1 Se:m2g Fm2
I:m1
C:k2
C:k1
Se:m2g
Fm2
Fm1
Se:m1g
Fk1
Fk2

200. Do it

201. Building Tamb Tref Rlosses Sensor TROOM Rroom Rradiator TRAD + - PID
Source of heat
TROOM
Tamb
Tref
PID
Rradiator
TRAD
Rlosses
Rroom
Sensor + -

202. Automated modelling PART 6
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

203. 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
Bond graph suited for automatic modelling
Graphical tool
Unified language
Causal and structural properties
Systematic derivation of equations
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

204. 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

205. Main Softwares (2/5) ENPORT ( From RosenCode Associates, Inc) ARCHER
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. 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. 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. 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. Some demonstrations using SYMBOLS 2000
GUI interface
From BG model to Matlab S-function
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

210. Simulation in Matlab DEMONSTRATION Electrical system
Mechanical system : suspension
Electromechanical system : DC motor
Hydraulic system
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

211. PART 7 Conclusions
Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

212. 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

213. 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

214. 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