Exploiting Bond Graph Causality in Physical System Models

1987 ◽  
Vol 109 (4) ◽  
pp. 378-383 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
Physical System ◽  
Dynamic Structure ◽  
Bond Graph ◽  
Additional Research ◽  
Bond Graphs ◽  
State Equations ◽  
Design Assessment ◽  
Direct Interpretation ◽  
Junction Structure ◽  
Structure Properties

Causality as a concept and a tool associated with bond graphs has seen use for more than twenty years. Our principal purpose in this paper is to bring together several different views and applications of causality in order to suggest how valuable it can be in understanding the dynamic structure of models. The topics considered include causality assignment, both traditional and nontraditional, and state equations; design assessment of models based on direct interpretation; and junction structure properties. The topics are illustrated by examples. Some opportunities for additional research into causality properties and applications are suggested.

Fault indicators and unique mode-dependent state equations from a fixed-causality diagnostic bond graph of linear models with ideal switches

2018 ◽  
Vol 232 (6) ◽  
pp. 695-708 ◽  
Author(s):  
Wolfgang Borutzky
Keyword(s):  
Linear Time ◽  
Bond Graph ◽  
Differential Algebraic Equations ◽  
Fault Detection And Isolation ◽  
Mode Switching ◽  
State Transitions ◽  
Algebraic Equations ◽  
State Equations ◽  
Analytical Redundancy ◽  
Junction Structure

Analytical redundancy relations are fundamental in model-based fault detection and isolation. Their numerical evaluation yields a residual that may serve as a fault indicator. Considering switching linear time-invariant system models that use ideal switches, it is shown that analytical redundancy relations can be systematically deduced from a diagnostic bond graph with fixed causalities that hold for all modes of operation. Moreover, as to a faultless system, the presented bond graph–based approach enables to deduce a unique implicit state equation with coefficients that are functions of the discrete switch states. Devices or phenomena with fast state transitions, for example, electronic diodes and transistors, clutches, or hard mechanical stops are often represented by ideal switches which give rise to variable causalities. However, in the presented approach, fixed causalities are assigned only once to a diagnostic bond graph. That is, causal strokes at switch ports in the diagnostic bond graph reflect only the switch-state configuration in a specific system mode. The actual discrete switch states are implicitly taken into account by the discrete values of the switch moduli. The presented approach starts from a diagnostic bond graph with fixed causalities and from a partitioning of the bond graph junction structure and systematically deduces a set of equations that determines the wanted residuals. Elimination steps result in analytical redundancy relations in which the states of the storage elements and the outputs of the ideal switches are unknowns. For the later two unknowns, the approach produces an implicit differential algebraic equations system. For illustration of the general matrix-based approach, an electromechanical system and two small electronic circuits are considered. Their equations are directly derived from a diagnostic bond graph by following causal paths and are reformulated so that they conform with the matrix equations obtained by the formal approach based on a partitioning of the bond graph junction structure. For one of the three mode-switching examples, a fault scenario has been simulated.

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.

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.

Non-iterative evaluation of multiphase thermal compliances in bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 13-19 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Bond Graph ◽  
The State ◽  
Refrigeration Cycle ◽  
State Variables ◽  
Unfinished Business ◽  
Bond Graphs ◽  
State Equations ◽  
Efficient Simulation ◽  
Multiple Phase ◽  
Iterative Evaluation

The practical use of bond graphs to organize the efficient simulation of multiple-phase thermodynamic systems is perhaps the most significant piece of unfinished business regarding the evolution of bond graphs. The most widely recognized form for these cases, called the pseudo bond graph, dictates particular causalities that require iteration, assuming the use of available state equations. This paper shows how the alternative convection bond graphs can direct non-iterative evaluation of state properties of multiphase thermal compliances. The state variables of a compliance become temperature, mass and volume. A refrigeration cycle is used as an example.

The Properties of Bond Graph Junction Structure Matrices

1973 ◽  
Vol 95 (4) ◽  
pp. 362-367 ◽  
Author(s):  
J. R. Ort ◽  
H. R. Martens
Keyword(s):  
Sufficient Conditions ◽  
Bond Graph ◽  
Bond Graphs ◽  
Flow Equations ◽  
Correct Number ◽  
Constraint Equations ◽  
Necessary And Sufficient ◽  
Fundamental Theorems ◽  
Junction Structure ◽  
The Relationship

Some fundamental theorems concerning the relationship between the junction structure of bond graphs and the effort and flow equations, are presented. Necessary and sufficient conditions are stipulated to guarantee the correct number of constraint equations. The structure and rank of the coefficient matrices of the effort and flow equations are examined. An orthogonality relationship between effort and flow equations is established. The development yields the result that the number of effort and flow equations corresponding to a causal assignment are sufficient and their coefficient matrices are of maximum rank.

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.

Automating physical system modelling using bond graphs

1989 ◽  
Vol 21 (9) ◽  
pp. 584-588
Author(s):  
S.J. Hood ◽  
E.R. Palmer ◽  
D.H. Withers
Keyword(s):  
Physical System ◽  
System Modelling ◽  
Bond Graphs

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.

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