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.

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).

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.

Zero Dynamics of Physical Systems From Bond Graph Models—Part I: SISO Systems

1999 ◽  
Vol 121 (1) ◽  
pp. 10-17 ◽  
Author(s):  
S. Y. Huang ◽  
K. Youcef-Toumi
Keyword(s):  
System Analysis ◽  
Mimo Systems ◽  
Geometric Approach ◽  
Bond Graph ◽  
Graph Representation ◽  
Zero Dynamics ◽  
Feedback Systems ◽  
State Equations ◽  
Graph Models ◽  
Physical Systems

Zero dynamics is an important feature in system analysis and controller design. Its behavior plays a major role in determining the performance limits of certain feedback systems. Since the intrinsic zero dynamics can not be influenced by feedback compensation, it is important to design physical systems so that they possess desired zero dynamics. However, the calculation of the zero dynamics is usually complicated, especially if a form which is closely related to the physical system and suitable for design is required. In this paper, a method is proposed to derive the zero dynamics of physical systems from bond graph models. This method incorporates the definition of zero dynamics in the differential geometric approach and the causality manipulation in the bond graph representation. By doing so, the state equations of the zero dynamics can be easily obtained. The system elements which are responsible for the zero dynamics can be identified. In addition, if isolated subsystems which exhibit the zero dynamics exist, they can be found. Thus, the design of physical systems including the consideration of the zero dynamics become straightforward. This approach is generalized for MIMO systems in the Part II paper.

Lagrange’s Equations for Complex Bond Graph Systems

1977 ◽  
Vol 99 (4) ◽  
pp. 300-306 ◽  
Author(s):  
Dean Karnopp
Keyword(s):  
Bond Graph ◽  
Writing System ◽  
Complex Mechanism ◽  
State Equations ◽  
Graph Models ◽  
Physical Systems ◽  
Lagrange’S Equations ◽  
Alternative Means ◽  
Lagrange's Equations ◽  
State Functions

The standard means of imposing causality to extract state equations for bond graph models of physical systems can be inconvenient when algebraic loops and derivative causality in combination with nonlinear constraints are present. This paper presents an alternative means of writing system differential equations using energy and coenergy state functions and Lagrange’s equations. For certain types of systems, particularly mechanical and electromechanical systems, this indirect means of finding state equations turns out to be very convenient. In this technique, causality is used in a new way to establish generalized coordinates and generalized efforts for nonconservative elements. Finally, it is shown that in some cases in which a Lagrangian can be written by inspection for a complex mechanism, a detailed bond graph for this component is unnecessary and yet the equations of the mechanism can be easily coupled to the bond graph equations for the remainder of the system.

scholarly journals BOND GRAPH METHODOLOGY IN THE RLC CIRCUIT ANALYSIS

2019 ◽  
pp. 261-270
Author(s):  
Darina Hroncová
Keyword(s):  
General Class ◽  
Bond Graph ◽  
Operating Conditions ◽  
Coupled Systems ◽  
System Model ◽  
Electrical System ◽  
Bond Graphs ◽  
State Equations ◽  
Mechatronic Systems ◽  
Physical Systems

Urgency of the research. The bond graphs theory aim for to formulate general class physical systems over power interactions. The factors of power are effort and flow. They have different interpretations in different physical domains. Yet, power can always be used as a generalized resource to model coupled systems residing in several energy domains. Target setting. Formalism of power graphs enables to describe different physical systems and their interactions in a uniform, algorithmizable way and transform them into state space description. This is useful when analyzing mechatronic systems transforming various forms of energy (electrical, fluid, mechanical) by means of information signals to the resulting mechanical energy. Actual scientific researches and issues analysis. Over the past two decades the theory of Bond Graphs has been paying attention to universities around the world, and bond graphs have been part of study programs at an ever-increasing number of universities. In the last decade, their industrial use is becoming increasingly important. The Bond Graphs method was introduced by Henry M. Paynter (1923-2002), a professor at MIT & UT Austin, who started publishing his works since 1959 and gradually worked out the terminology and formalism known today as Bond Graphs translated as binding graphs or performance graphs. Uninvestigated parts of general matters defining. The electrical system model is solved with the help of the above mentioned bond graphs formalism. Gradually, the theory of power graphs in the above example is explained up to the construction of state equations of the electrical system. The state equations are then solved in Matlab / Simulink. The statement of basic materials. Using bond graphs theory to simulate electrical system and verify its suitability for simulating electrical models. In various versions of the parameters of model we can monitor its behavior under different operating conditions. The language of bond graphs aspires to express general class physical systems through power interactions. The factors of power i.e., effort and flow, have different interpretations in different physical domains. Yet, power can always be used as a generalized coordinate to model coupled systems residing in several energy domains. Conclusions. We introduced a method of systematically constructing a bond graph of an electrical system model using Bond graphs. A practical example of an electrical model is given as an application of this methodology. Causal analysis also provides information about the correctness of the model. Differential equations describing the dynamics of the system in terms of system states were derived from a simple electrical system coupling graph. The results correspond to the equations obtained by the classical manual method, where first the equations for individual components are created and then a simulation scheme is derived based on them. The presented methodology uses the reverse procedure. However, manually deriving equations for more complex systems is not so simple. Bond charts prove to be a suitable means of analysis, among other systems and electrical systems.

scholarly journals Torsional Vibration Analysis by Bondgraph Modelling. A practical approach

2018 ◽  
Author(s):  
T Heeringa
Keyword(s):  
Computer Technology ◽  
Bond Graph ◽  
Symbolic Manipulation ◽  
Bond Graphs ◽  
Late Professor ◽  
Physical Systems ◽  
Modern Computer ◽  
Direct Input ◽  
User Friendly ◽  
Modern Computer Technology

The traditional modeling approach in engineering is mathematical, but thanks to the advances in computer technology it is now possible for the practical engineer to model physical systems in a more “user friendly” way. This paper will demonstrate the power and simplicity of Bond Graphs in modelling technique. Bond Graph modelling was original developed in the late 1950s by the late Professor Henry M. Paynter of MIT. Professor Paynter acted well before his time as the main advantage of his creation, other than the modeling insight that it provides and the ability of effectively dealing with mechatronics, came into fruition only with the recent advent of modern computer technology and the tools derived as a result of it, including symbolic manipulation, MATLAB and SIMULINK and the simulation package 20sim, see:  www.20sim.com , which allows direct input of the Bond Graph.

Some Bond Graph Identities Involving Junction Structures

1975 ◽  
Vol 97 (4) ◽  
pp. 439-441 ◽  
Author(s):  
D. Karnopp
Keyword(s):  
Bond Graph ◽  
The Other ◽  
Bond Graphs ◽  
Physical Systems ◽  
Other Hand ◽  
Sign Convention ◽  
Flow Variables ◽  
Junction Structure

When bond graphs are generated from reasonable physical systems according to standard rules, there are only rare cases in which power loops arise that yield singular algebraic relations among effort and flow variables. On the other hand, if one assembles bond graphs from subsystem models, paradoxical situations may arise in which sign conventions and causality interact strangely and in which physically impossible situations seemingly occur. Some useful bond graph identities are shown which often eliminate such paradoxes. The general conclusion is that a bond graph containing a junction structure power loop should be carefully examined with respect to sign convention and to see whether a simplifying identity can be used before causality is applied and equations are formulated.

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.

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