Bond Graph Models for Fluid Networks Using Modal Approximation

1985 ◽  
Vol 107 (3) ◽  
pp. 169-175 ◽  
Author(s):  
D. L. Margolis ◽  
W. C. Yang
Keyword(s):  
Transmission Lines ◽  
Bond Graph ◽  
Bond Graphs ◽  
Graph Models ◽  
Graph Representations ◽  
Approximation Techniques ◽  
Fluid Networks ◽  
Simulation Results ◽  
Dissipative Model ◽  
Modal Approximation

Modal bond graph representations of the dissipative model of rigid, cylindrical fluid transmission lines with laminar flow are developed. Modal approximation techniques are used for both hydraulic and pneumatic lines. The modeling and simulation procedures for fluid networks coupled with nonlinear and dynamic systems are greatly facilitated using bond graphs. The physical interpretation of the model is preserved in this approach. Simulation results for hydraulic single lines are compared with results derived by the quasi-method of characteristics. The simulation results for fluid networds for various line and termination configurations are illustrated.

Comparative Study of Bond Graph Models for Hydraulic Transmission Lines With Transient Flow Dynamics

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Limin Yang ◽  
Jørgen Hals ◽  
Torgeir Moan
Keyword(s):  
Flow Rate ◽  
Transmission Lines ◽  
Transient Flow ◽  
Transfer Functions ◽  
Separation Of Variables ◽  
Bond Graph ◽  
Input Output ◽  
Bond Graphs ◽  
Graph Representations ◽  
Linear Resistance

The partial differential equation describing one-dimensional flow in a hydraulic pipeline with linear resistance can be approximated and solved numerically using different modal approaches. Modal models can be obtained either by using rational transfer functions (RTF) in the Laplace domain solution or by using separation of variables (SOV) techniques. The pipeline models have four possible input–output configurations: pressure inputs at both ends, flow rate inputs at both ends, and the two cases of mixed inputs. In this paper, modal bond graph representations for pipeline sections are reviewed, and new bond graphs are proposed for combinations of solution method and input–output configurations not yet presented in the literature. This includes bond graph representations for the two mixed input cases developed using the SOV technique, and bond graphs for the other two cases, pressure inputs or flow rate inputs, constructed on the basis of RTF solutions. Through numerical simulations of hydraulic single lines, the obtained models are compared to alternative models already established in the literature. It is shown that the modal models developed by the RTF and SOV methods have the same accuracy when the same number of modes is used. For both of these approaches, correction methods to maintain a high accuracy when truncating high-order modes are described, and also adapted to the bond graph form. Finally, simulation results for various line configurations are illustrated.

scholarly journals Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Raquel S. Rodríguez ◽  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Bond Graph ◽  
Physical Domain ◽  
Graph Models ◽  
Simple Task ◽  
Analysis And Synthesis ◽  
Simulation Results

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

scholarly journals Analysing and simulating energy-based models in biology using BondGraphTools

2021 ◽  
Author(s):  
Peter Cudmore ◽  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Edmund J. Crampin
Keyword(s):  
Systems Biology ◽  
Mathematical Models ◽  
Bond Graph ◽  
Experimental Measurements ◽  
Bond Graphs ◽  
Graph Models ◽  
Conservation Of Energy ◽  
Conservation Of Mass ◽  
Physical Systems ◽  
Complex Interactions

AbstractLike all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

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 graphs and object-oriented modelling—a comparison

2002 ◽  
Vol 216 (1) ◽  
pp. 21-33 ◽  
Author(s):  
W Borutzky
Keyword(s):  
Hydraulic Drive ◽  
Object Oriented ◽  
Bond Graph ◽  
Massachusetts Institute Of Technology ◽  
Bond Graphs ◽  
Graph Models ◽  
Electrical Systems ◽  
Generalized Networks ◽  
Institute Of Technology ◽  
Object Oriented Modelling

Bond graph modelling was devised by Professor Paynter at the Massachusetts Institute of Technology in 1959 and subsequently developed into a methodology for modelling multidisciplinary systems at a time when nobody was speaking of object-oriented modelling. On the other hand, so-called object-oriented modelling has become increasingly popular during the last few years. By relating the characteristics of both approaches, it is shown that bond graph modelling, although much older, may be viewed as a special form of object-oriented modelling. For that purpose the new object-oriented modelling language Modelica is used as a working language which aims at supporting multiple formalisms. Although it turns out that bond graph models can be described rather easily, it is obvious that Modelica started from generalized networks and was not designed to support bond graphs. The description of bond graph models in Modelica is illustrated by means of a hydraulic drive. Since VHDL-AMS as an important language standardized and supported by IEEE has been extended to support also modelling of non-electrical systems, it is briefly investigated as to whether it can be used for description of bond graphs. It turns out that currently it does not seem to be suitable.

Bond Graphs For Cvd Processes

1989 ◽  
Vol 168 ◽  
Author(s):  
Surya R. Kalidindi ◽  
Seshu B. Desu
Keyword(s):  
Computer Program ◽  
Bond Graph ◽  
Single Bond ◽  
Unified Approach ◽  
Bond Graphs ◽  
Graph Representations

AbstractA unified approach to model the general CVD process, utilizing the versatility and flexibility of bond graph methods, is presented. The bond graph representations for important CVD sub-processes are derived. The application of these elements is illustrated through hypothetical examples of CVD processes. It is also shown that several different CVD processes can be handled by a single bond graph computer program.

A Bond Graph Approach to the Analysis of Prosthesis for a Partially Impaired Hand

2006 ◽  
Vol 129 (1) ◽  
pp. 105-113 ◽  
Author(s):  
Anand Vaz ◽  
Shinichi Hirai
Keyword(s):  
Bond Graph ◽  
Relative Orientation ◽  
Bond Graphs ◽  
Graph Models ◽  
Prosthetic Devices ◽  
Actuation Mechanism ◽  
Prosthetic Joints ◽  
System Equations ◽  
Analysis Of Dynamics ◽  
Prosthetic Finger

A system dynamics approach, based on bond graphs, is presented for the analysis of prosthetic devices for a partially impaired hand. The partial impairment implies that the hand has lost one or more fingers but retains the ability of its remaining natural fingers. It is shown that the existing natural joints can be used for the actuation of prosthetic finger joints and enable performance of tasks that would not have been possible otherwise. This is a challenging task as motion has to be transmitted from the remaining natural joints to the prosthetic joints. The joint axes move with respect to each other during performance of tasks and do not have any fixed relative orientation. In this work, basic concepts for the actuation of the prosthesis required for such tasks are developed systematically. Based on these concepts, Bowden cable based joint actuation mechanisms for transmission of motion from natural joints to corresponding prosthetic joints are presented and analyzed. The analysis of dynamics of the resulting under-actuated prosthesis with joint actuation mechanism is based on bond graph models that are systematically developed. Using these models, system equations are derived and numerical simulations performed for the analysis. One- and two-joint actuated prototypes of the prosthesis have been presented and effectively demonstrate the proposed concepts.

HYBRSIM—a modelling and simulation environment for hybrid bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 35-46 ◽  
Author(s):  
P. J. Mosterman
Keyword(s):  
Numerical Analysis ◽  
Event Detection ◽  
Bond Graph ◽  
Modelling And Simulation ◽  
Simulation Environment ◽  
Dynamic Coupling ◽  
Bond Graphs ◽  
Switching Element ◽  
Graph Models ◽  
Physical Systems

Bond graphs are a powerful formalism to model continuous dynamics of physical systems. Hybrid bond graphs introduce an ideal switching element, the controlled junction, to approximate continuous behaviour that is too complex for numerical analysis (e.g. because of non-linearities or steep gradients). HYBRSIM is a tool for hybrid bond graph modelling and simulation implemented in Java and is documented in this paper. It performs event detection and location based on a bisectional search, handles run-time causality changes, including derivative causality, performs physically consistent (re-)initialization and supports two types of event iteration because of dynamic coupling. It exports hybrid bond graph models in Java and C/C++ code that includes discontinuities as switched equations (i.e. pre-enumeration is not required).

Dissipative Modal Approximation of Fluid Transmission Lines Using Linear Friction Model

1991 ◽  
Vol 113 (1) ◽  
pp. 152-162 ◽  
Author(s):  
W. C. Yang ◽  
W. E. Tobler
Keyword(s):  
Transmission Lines ◽  
Friction Model ◽  
Step Response ◽  
Frequency Dependent ◽  
Approximation Techniques ◽  
Linear Friction ◽  
Computer Calculations ◽  
Complex Fluid ◽  
Dependent Viscosity ◽  
Modal Approximation

For both hydraulic and pneumatic transmission lines, analytical dissipative modal approximation techniques, which take into account the frequency dependent viscosity and heat transfer effects, are developed by introducing frequency dependent damping and natural frequency modification factors to the quadratic modes obtained analytically from linear friction model. The main advantage over the existing dissipative modal approximations is that the modal parameters of the resulting modal transfer function matrices and modal state space equations can be determined analytically rather than determined by table and/or numerical computer calculations. This introduces modeling flexibilities and greatly alleviates the difficulties of modeling complex fluid networks but still maintaining the modal accuracy and complexities. Unit step response comparisons are made with quasi-method of characteristics showing good agreements for both hydraulic and pneumatic lines.

scholarly journals Simulation methods of rigid holonomic multibody systems with bond graphs

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983415 ◽  
Author(s):  
Benjamin Boudon ◽  
Thu Thuy Dang ◽  
Rebecca Margetts ◽  
Wolfgang Borutzky ◽  
François Malburet
Keyword(s):  
Software Package ◽  
Multibody Systems ◽  
Three Dimensional ◽  
Bond Graph ◽  
Compact Model ◽  
Simulation Methods ◽  
Bond Graphs ◽  
Graph Models ◽  
The Past ◽  
Practical Guidance

Bond graph software can simulate bond graph models without the user needing to manually derive equations. This offers the power to model larger and more complex systems than in the past. Multibond graphs (those with vector bonds) offer a compact model which further eases handling multibody systems. Although multibond graphs can be simulated successfully, the use of vector bonds can present difficulties. In addition, most qualitative, bond graph–based exploitation relies on the use of scalar bonds. This article discusses the main methods for simulating bond graphs of multibody systems, using a graphical software platform. The transformation between models with vector and scalar bonds is presented. The methods are then compared with respect to both time and accuracy, through simulation of two benchmark models. This article is a tutorial on the existing methods for simulating three-dimensional rigid and holonomic multibody systems using bond graphs and discusses the difficulties encountered. It then proposes and adapts methods for simulating this type of system directly from its bond graph within a software package. The value of this study is in giving practical guidance to modellers, so that they can implement the adapted method in software.

Sign in / Sign up

Export Citation Format

Share Document