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**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.

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**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

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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

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**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

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**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

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**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

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**INTRODUCTION & MOTIVATIONS**

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

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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

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**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

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**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

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**Introduction to integrated design of engineering systems**

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

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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

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**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

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**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

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**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 …;

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**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

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**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.

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**Methodology for testing**

Development of generic models and Control algorithms Validation using SiL Test Validation using MiL Validation using HiL Test Industrial validation

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**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)

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**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

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**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

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**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

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**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

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**WHAT WE CAN DO WITH BOND GRAPH ?**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**BOND GRAPH FOR ALARM FILTERING**

National Project : EDF-LAIL world-wide project: CHEM Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**THE EKOFISK JACKING OPERATION**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**TYPES OF INDUSTRIAL APLICATIONS**

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

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**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

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**Dedied Software (FDiPad)**

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

Data base Architectural model Behavioral model

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

Residuals Fault signature

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Architectural model

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**TECHNICAL SPECIFICATIONS AND MONITORABILITY ANALYSIS**

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Sensor placement

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Simulation interface

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**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, …)

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Founders J. Thoma Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**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

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**DEFINITION, REPRESENTATION**

2 1 Mechanical power : REPRESENTATION P = e.f e f Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**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

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**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

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**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

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**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

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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

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**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

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**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

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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

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**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

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**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

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**Energy variables : analogy**

P,V u,q Q,T x, F Displacement F, u, Impulse Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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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

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**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

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**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

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**Let us learn bond graph language**

Go head

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**EXAMPLE1 : ELECTRICAL INDUCTION MOTOR**

w 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

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**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

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**Where is the generecity ?**

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**FEW ELEMENTS FOR A BIG PURPUSE**

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

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**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

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**Bond graph well suited automated modelling**

SYMBOLS DEMOS Junctions Passive elements Active elements Junctions

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**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

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**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

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

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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

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

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**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

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**Tetrahedron of State 4 variables : e, f, p, q 3 Bg elements : R, C, I**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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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

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**EXAMPLES OF TRANSFORMERS**

u1 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

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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

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**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

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**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

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**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

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**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

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**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

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**JUNCTIONS (2/5) : Examples of 0-junction**

P 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

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**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

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**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

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**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

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

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**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

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**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

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Summary Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**Simplifications of Bond graphs**

1 Example of simplification 1 C 1 C R C R C 1 1 R Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Electrical circuit : Example1**

b 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

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**Electrical circuit : Example3**

SE C1 R1 iR1 iC1 R2 C2 SF iR2 iC2 Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**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

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**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

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**Electro-mechanical sytem**

1 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

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**Exercise 3 : Hydro-mechanical and suspension**

Sf 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

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**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

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**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

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**EXERCISES : Hydraulic control system**

PID 0,2 -1 bar psi Pe x LT PR P0 Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**EXERCISES : Bond graph model of the hydraulic system**

1 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

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**EXERCISES Hydraulic systems**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**EXAMPLES OF BG MODELS :Thermal**

Ts 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

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**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

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**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

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PRINCIPLE Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**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

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**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

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**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

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**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

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** 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

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**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

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**From BG to Bloc Diagram (1/2)**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**From BG to Bloc Diagram (2/2)**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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 equation**

x 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

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**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 Diagram**

1 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:C1**

iR 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

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**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

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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

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**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

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**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

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**Constitutive equations**

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

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**Coupled Bond graphs Representation**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Convection Heat transfer (1/2)**

➽ General expression for convected energy Internal specific energy Pressure energy Kinetic energy Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Convection Heat transfer (2/2)**

➽ Modeling Hypothesis Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Coupling of thermofluid variables**

1 Rc Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**C) Use of an activated element**

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

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**SOFTWARE REPRESENTATION**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**How to modelise a sensor ?**

PI C 1 2 I 3 e Hydraulic system case

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**SOFTWARE REPRESENTATION**

d

154
**How to represent it in Symbols2000 ?**

1 Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**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

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**Dynamic bond graph model of the pipe**

Fluid moving with inertia Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Bond graph model of the pipe**

Global Model Step response for hydraulic model to pressure difference Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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**Bond graph model C Environnement Se:P0=0 Rc2 Rc1 C 11 R:Re I:I1 R:Rs**

3 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

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**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

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**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

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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

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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

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**➽ 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

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**Chemical system C:CA C:CC RS C:CD C:CB Rel 1 Recepteur 1 1**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Electrochemical Process**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Electrochemical Model**

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

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Integrated models Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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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

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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 model**

FA 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

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**Global integrated model**

Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**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

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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

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**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

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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

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**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

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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

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**Some demonstrations using SYMBOLS 2000**

GUI interface From BG model to Matlab S-function Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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**Simulation in Matlab DEMONSTRATION Electrical system**

Mechanical system : suspension Electromechanical system : DC motor Hydraulic system Prof. Belkacem Ould BOUAMAMA, Polytech’Lille

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

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**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

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**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

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