Bond Graph Sign Conventions

1975 ◽  
Vol 97 (2) ◽  
pp. 184-188 ◽  
Author(s):  
A. S. Perelson
Keyword(s):  
Graph Model ◽  
Bond Graph ◽  
Equivalence Classes ◽  
Parameter System ◽  
Bond Graphs ◽  
Lumped Parameter ◽  
Oriented Object

The lack of arbitrariness in the choice of bond graph sign conventions is established. It is shown that an unoriented bond graph may have no unique meaning and that with certain choices of orientation a bond graph may not correspond to any lumped parameter system constructed from the same set of elements. Network interpretations of these two facts are given. Defining a bond graph as an oriented object leads to the consideration of equivalence classes of oriented bond graphs which represent the same system. It is also shown that only changes in the orientation of bonds connecting 0-junctions and 1-junctions can lead to changes in the observable properties of a bond graph model.

Application of Vector Bond Graphs to the Modeling of a Class of Hand Prostheses

Volume 3 ◽  
2004 ◽  
Author(s):  
Anand Vaz ◽  
Shinichi Hirai
Keyword(s):  
Three Dimensional ◽  
Graph Model ◽  
Systems Design ◽  
Bond Graph ◽  
Bond Graphs ◽  
Prosthetic Joints ◽  
Angular Velocities ◽  
Control Systems Design ◽  
And Control ◽  
Systematic Derivation

Vector bond graphs have been systematically applied to the modeling of prosthesis for a partially impaired hand. The partial impairment considered covers a category of the hand that has lost one or more fingers but retains the ability of its remaining natural fingers. The fingers and their prosthetic extensions are considered as rigid links. Rotation matrices which specify orientation of finger links are obtained from respective angular velocities. String-tube mechanism used to actuate prosthetic joints is modeled with the connection to joint variables of the mechanism. The vector bond graph approach enables the modeling of three dimensional movement of the hand mechanism. An example of a two joint string-tube actuated prosthetic mechanism is presented to describe the construction of the vector bond graph model. Systematic derivation of dynamics from the vector bond graphs is shown. The approach based on vector bond graphs presented here is useful for simulations and control systems design of such biomechanical systems.

A Distributed Parameter Pseudo Bond Graph for Heat Conduction Modelling: Notion of Cellular Bond Graph

2003 ◽  
Author(s):  
Aziz Nakrachi ◽  
Genevieve Dauphin-Tanguy
Keyword(s):  
Heat Conduction ◽  
Heat Flow ◽  
Finite Difference ◽  
Heat Conduction Equation ◽  
Graph Model ◽  
Bond Graph ◽  
Distributed Parameter ◽  
Heat Flow Rate ◽  
Finite Volume Schemes ◽  
Bond Graphs

The paper presents a new procedure for building a pseudo bond graph model representing 1D and 2D heat conduction phenomena, in their distributed parameter form. The heat conduction equation is written in such a way that conjugate variables, temperature T(t,x,y) and heat flow rate Q⃗˙(t,x,y), and their space derivatives appear explicitly in the equation. New conjugations between variables are introduced as (T,div(Q⃗˙)) and (gradT,Q⃗˙). We define new bond graph elements named “distributed C- and R-elements”, and we build a “Distributed Parameter Bond Graph” (DPBG), with a form slightly different from the classical one. The approximation of the space derivatives leads to submodels we call “cellular bond graphs”, new notion which could be compared to the cellular automata. Moreover, we show how this representation enables to easily build classical finite difference or finite volume schemes.

Singularly Perturbed Bond Graph Models for Simulation of Multibody Systems

1995 ◽  
Vol 117 (3) ◽  
pp. 401-410 ◽  
Author(s):  
A. A. Zeid ◽  
J. L. Overholt
Keyword(s):  
Time Scale ◽  
Multibody Systems ◽  
Graph Model ◽  
Bond Graph ◽  
Rigid Bodies ◽  
Singularly Perturbed ◽  
Bond Graphs ◽  
Graph Models ◽  
Multibody Modeling ◽  
Nonlinear Properties

This paper develops a bond graph-based formalism for modeling multibody systems in a singularly perturbed formulation. As opposed to classical multibody modeling methods, the singularly perturbed formulation is explicit, which makes it suitable for modular simulation. Kinematic joints that couple rigid bodies are described by a set of differential equations with an order of magnitude smaller time scale than that of the system. Singularly perturbed models of joints can be used to investigate nonlinear properties of joints, such as clearance and friction. The main restriction of this approach is that the simulation may need to be computed using 64 bits precision because of the two-time scale nature of the solution. The formalism is based on developing bond graph models of an elementary set of graphical velocity-based constraint functions. This set can be used to construct bond graphs of any type of mechanical joint. Here, this set is used to develop bond graphs of several joints used in multibody systems and spatial mechanisms. Complex models of multibody systems may now be built by graphically concatenating bond graphs of rigid bodies and bond graphs of joints. The dynamic equations of the system are automatically generated from the resulting bond graph model. The dynamic equation derived from the bond graph are in explicit state space form, ready for numerical integration, and exclude the computationally intensive terms that arise from acceleration analysis.

scholarly journals Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

2020 ◽  
Author(s):  
Shan Su ◽  
Pablo J. Blanco ◽  
Lucas O. Müller ◽  
Peter J. Hunter ◽  
Soroush Safaei
Keyword(s):  
Cerebral Circulation ◽  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
Lumped Parameter Model ◽  
Desktop Computer ◽  
Detailed Model ◽  
Simulation Speed ◽  
Lumped Parameter ◽  
Proposed Model

The primary paper Safaei et al. (2018) proposed an anatomically detailed model of the human cerebral circulation that runs faster than real-time on a desktop computer and is designed for use in clinical settings when the speed of response is important. Based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, a lumped parameter model was developed for 218 arterial segments. The proposed model improved simulation speed by approximately 200-fold while preserved accuracy. Bond graph formulation was used to ensure mass and energy conservation. The model predicted the pressure and flow signatures in the body.

Bond Graph Modeling of a Two-Stage Pressure Relief Valve

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Osama Gad
Keyword(s):  
Mathematical Model ◽  
Graph Model ◽  
Bond Graph ◽  
Fluid Power ◽  
Pressure Relief Valve ◽  
System Component ◽  
Bond Graphs ◽  
Relief Valve ◽  
Two Stage ◽  
Pressure Relief

This study examined the use of bond graphs for the modeling and simulation of a fluid power system component. A new method is presented for creating the bond graph model, based upon a previously developed mathematical model. A nonlinear dynamic bond graph model for a two-stage pressure relief valve has been developed in this paper. Bond graph submodels were constructed considering each element of the studied valve assembly. The overall bond graph model of the valve was developed by combining these submodels using junction structures. Causality was then assigned in order to obtain a computational model, which could be simulated. The simulation results of the causal bond graph model were compared with those of a mathematical model, which had been also developed in this paper based on the same assumptions. The results were found to correlate very well both in the shape of the curves, magnitude, and response times. The causal bond graph model was verified experimentally in the dynamic mode of operation. As a result of comparison, bond graphs can quickly and accurately model the dynamics in a fluid power control system component. During the simulation study, it was found that nonlinearity occur due to three factors: changes in pressure, which cause nonlinear velocity changes of the flow rate; changes in the throttling area of the valve restriction, which usually changes nonlinearly; and changes in the discharge coefficient of the throttling area of the valve restriction, which does not remain constant.

Systematic Model Decoupling Through Assessment of Power-Conserving Constraints: An Engine Dynamics Case Study

2004 ◽  
Author(s):  
Geoff Rideout ◽  
Jeffrey L. Stein ◽  
Loucas S. Louca
Keyword(s):  
Power Flow ◽  
Three Dimensional ◽  
Coupled Model ◽  
Graph Model ◽  
Bond Graph ◽  
Bond Graphs ◽  
Third Order ◽  
Engine Mount ◽  
The One

Simplified models for predicting engine mount forces have traditionally been developed based on the assumption that for a well-balanced low-speed engine, the reciprocating dynamics can be decoupled from the three-dimensional motion of the engine block. In this paper the simplification is done systematically, using a technique previously developed by the authors to search for decoupling within a model, and to partition models in which decoupling is found. Beginning with a fully-coupled bond graph model of a balanced in-line six-cylinder engine, bonds representing negligible constraint terms are found based on aggregate power flow, and are converted to modulated sources. Separate bond graphs joined by modulating signals result. The “driving” bond graph represents the reciprocating dynamics, and the “driven” bond graph represents motion of the block on its mounts. The partitions are smaller than the original model and are simulated individually to accurately predict the dominant third-order mount forces with significant computational savings. The decoupling is found without the modeler relying on traditional assumed forms of the one-way coupled model, and can be quantitatively tracked as the system parameters and inputs change.

Dynamical Systems Framework for Service Robot Navigation Using Bond Graphs

2012 ◽  
Vol 433-440 ◽  
pp. 6678-6682
Author(s):  
S. Veera Ragavan ◽  
Velappa Ganapathy ◽  
R.M. Kuppan Chetty
Keyword(s):  
Dynamical Systems ◽  
Systems Approach ◽  
Robot Navigation ◽  
Graph Model ◽  
Bond Graph ◽  
Service Robot ◽  
Simulation Environment ◽  
Bond Graphs ◽  
Embedded Devices ◽  
Systems Framework

This paper employs a Dynamical Systems Approach to a Wheeled Mobile Robot (WMR) Locomotion problem using an extended Bond Graph model. Bond Graph model of a WMR and its subsystems have been developed and the model and subsystems are validated using 20-Sim Simulation environment. The developed model provides a stable and computationally less intensive framework that can be deployed on resource constrained embedded devices for path planning, navigation and formation modeling.

Complementarity framework formulation from bond graphs to model a class of nonlinear systems and hybrid systems with fixed causality

SIMULATION ◽  
2018 ◽  
Vol 94 (9) ◽  
pp. 783-795 ◽  
Author(s):  
Noé Villa-Villaseñor ◽  
J Jesús Rico-Melgoza
Keyword(s):  
Nonlinear Systems ◽  
Modeling And Simulation ◽  
Hybrid Systems ◽  
Graph Model ◽  
Bond Graph ◽  
Switching Systems ◽  
Switching Converters ◽  
Bond Graphs ◽  
Systematic Method ◽  
Power Switching

A systematic method for constructing models in the complementarity framework from a bond graph is proposed. Bond graphs with and without storage elements in derivative causality are considered. The proposed method allows the study of switching systems represented by a bond graph model of fixed causality. The proposed methodology allows the complementarity framework to be exploited in different engineering areas by using bond graphs. The idea of representing a unidirectional switch with a model that is essentially the same as a diode is presented. By employing a similar representation for diodes and switches, the modeling and simulation of power switching converters are simplified and become more intuitive. Two application examples are shown. A non-inverting buck-boost converter and a zeta converter with an element in derivative causality are simulated.

scholarly journals Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

2020 ◽  
Author(s):  
Shan Su ◽  
Pablo J. Blanco ◽  
Lucas O. Müller ◽  
Peter J. Hunter ◽  
Soroush Safaei
Keyword(s):  
Cerebral Circulation ◽  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
Lumped Parameter Model ◽  
Desktop Computer ◽  
Detailed Model ◽  
Simulation Speed ◽  
Lumped Parameter ◽  
Proposed Model

The primary paper Safaei et al. (2018) proposed an anatomically detailed model of the human cerebral circulation that runs faster than real-time on a desktop computer and is designed for use in clinical settings when the speed of response is important. Based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, a lumped parameter model was developed for 218 arterial segments. The proposed model improved simulation speed by approximately 200-fold while preserved accuracy. Bond graph formulation was used to ensure mass and energy conservation. The model predicted the pressure and flow signatures in the body.

Ideal physical element representation from reduced bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 73-83 ◽  
Author(s):  
L. S. Louca ◽  
J. L. Stein
Keyword(s):  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
System Model ◽  
Bond Graphs ◽  
State Equations ◽  
Rigorous Approach ◽  
Reduction Techniques ◽  
Relative Value ◽  
Element Removal

Previous research has demonstrated that bond graphs are a natural and convenient representation to implement energy-based metrics that evaluate the relative ‘value’ of energy elements in a dynamic system model. Bond graphs also provide a framework for systematically reformulating a reduced bond graph model (and thus the state equations) of the system that results from eliminating the ‘unimportant’ elements. This paper shows that bond graphs also provide a natural and convenient representation for developing a rigorous approach for interpreting the removal of ideal energy elements from the system model. For example, when a generalized inductance in the mechanical domain is eliminated from a model, the bond graph shows whether the coordinate representing the motion of the body becomes free to move (zero inertia) or fixed to ground (infinite inertia). This systematic interpretation of element removal makes bond graphs an attractive modelling language for automated model reduction techniques. An illustrative example is provided to demonstrate how the developed approach can be applied to provide the physical interpretation of energy element removal from a mechanical system.

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