Causal Bond Graph Research Articles

Bond Graph Modeling of a Two-Stage Pressure Relief Valve

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.

Discussion around the Scattering Matrix Realization of a Microwave Filter using the Bond Graph Approach and Scattering Formalism

Problem statement: Further to research works made previously and which use collectively the scattering formalism and bond graph technique for the modeling of a physical systems often working in high frequencies, we propose, in this article, a comparative study (discussion) for the scattering matrix realization of a high-frequency physical system. Approach: This discussion is based, on the one hand, on a non-causal (acausal) bond graph model which represents the starting model for the determination of the scattering parameters. On the other hand, we shall use a causal bond graph model richer in information and to which we shall apply what we called in former articles: the analytical procedure of the scattering parameters exploitation with the aim of showing the importance of the causality notion in the physical systems study by the bond graph approach, as well as the importance of the ways and causal loops notion. Results: We will, initially, apply this discussion, to an elementary transmission line; in the second place, the application is carried out on the equivalent circuit of a band pass filter based on localized elements often used like microwave filters in high frequencies studies. Conclusion: We will finish this discussion by realizing the scattering bond graph model of a quadruple by pointing out the procedure used for the construction of this new type of bond graph model.

New extraction method of the scattering parameters of a physical system starting from its causal bond graph model: Application to a microwave filter

The general idea consists of using jointly the bond graph technique and the scattering formalism. For that, we propose to extract the scattering parameters of a microwave filter with localized or distributed elements from its causal bond graph model while starting with the determination of the integro-differentials operators which is based, in their determination, on the causal ways and causal loops present in the associated bond graph model, and which gives rise to the wave matrix which gathers the incident and reflected waves propagation of the studied filter. The scattering parameters, founded from the wave matrix, were checked by comparison of the simulation results. Thereafter, we used a procedure to model these scattering parameters on a particular type of bond graph model often named Scattering Bond Graph Model. Key words: Waves propagation, bond graph modelling, high frequency domain, scattering parameters, integro-differentials operators, microwave filter, modelling and simulation.

How to Find Wave-Scattering Parameters from the Causal Bond Graph Model of a High Frequency Filter

Problem statement: The aim of this study is to use the bond graph technique and the wave-scattering formalism, jointly, to determine the scattering matrix of a high frequency filter with cut-off frequency 10 GHz. Approach: The first step consist to model the high frequency filter by bond graph approach, afterward, we decomposed the obtained causal bond graph model under an elementary structures of a cascaded sub-model, where, each one containing only 0-junction (parallel admittance) and 1-junction (series impedance). The causal ways and algebraic loops present in each causal bond graph sub-model, allows us to derive the elementary wave matrix W(i) of each sub-model. Results: The total or global wave matrix W(T) of the high frequency filter is given by the product of all elementary wave matrixes W(i). Conclusion: The scattering matrix S of the studied filter can be inferred by use of the founded wave matrix W(T) which relates the incident and reflected waves at one port directly to the incident and reflected waves at the adjacent port and the relations linking the S coefficients to the W coefficients. Finally, the scattering parameters, founded from the wave matrix, will be checked by comparison of the simulation results.

Modeling Method of a Low-Pass Filter Based on Microstrip T-Lines with Cut-Off Frequency 10 GHz by the Extraction of its Wave-Scattering Parameters from its Causal Bond Graph Model

Problem statement: This study presented a jointly application of bond graph technique and wave-scattering formalism for a new realization called scattering bond graph model which has the main advantage to show up explicitly the different wave propagation. Approach: For that, we proposed to find the scattering matrix from the causal bond graph model of a low-pass filter based on Microstrip lines and with cut-off frequency 10 GHz, while starting with determination of the integro-differentials operators which is based, in their determination, on the causal ways and causal algebraic loops present in the associated bond graph model and which gives rise to the wave matrix which gathers the incident and reflected waves propagation of the studied filter. Results: The scattering parameters, founded from the wave matrix, will be checked by comparison of the simulation results. Conclusion: Thereafter, we use a procedure to model directly this scattering matrix under a special bond graph model form often called “Scattering Bond Graph Model”.

Bond Graph Based Stability Analysis of a Railway Traction System

This paper emphasises the interest of the Bond Graph approach for analysis and system design of heterogeneous and multi-field devices. In particular, the local stability analysis of non linear systems can be directly derived from the linearised Causal Bond Graph. This method is applied to a typical electrical engineering system: a railway traction device involving electromechanical couplings. Validity usefulness and originality of this approach are displayed.

Using trees to build non-singular bond graphs from electric circuit graphs

A commonly used method to build bond graphs for electric circuits can lead to causal bond graphs with unity gain causal loops. Deriving equations from such causal bond graphs is problematic. This paper shows that, for electric circuits, unity gain causal loops are not a property inherent in the system but rather are due to the nature of the causal bond graphs. A method is proposed for building an acausal bond graph to which a modified version of the sequential causality assignment procedure can be applied, in order to guarantee a non-singular causal bond graph. This approach can also be applied to the problem of joining sub-systems.

Bond-Graph-Based Computational Approach to Hybrid System Dynamics

For a class of hybrid systems frequently encountered in the engineering practice, the dynamics corresponding to each causal bond graph topology can be expressed in terms of a continuous semigroup of linear operators. Consequently any sequence of modes yields a composite map that allows deriving a closed form expression for arbitrary state space trajectories. This expression is particularized for the dynamics in the vicinity of the steady state. Some key points that are unanimously accepted by engineers, but do not have yet a mathematically rigorous support, are addressed on the basis of a conjecture. All the theoretical results are envisaging the development of computational tools for exploring both general and steady state dynamics. An example gives a brief overview of the applicability to the quantitative analysis of a physical system behavior, using standard software environments for scientific computation.

Bond graphs II: Causality and singularity

The concepts of causality and singularity for bond graphs are defined, and related through the idea of a singular (or nonsingular) causal assignment, which is one with zero (or nonzero) discriminant. Necessary and sufficient conditions are given for a bond graph to have a causal assignment. It is proved that every acausal bond graph is acausally equivalent to a nonsingular bond graph, and that every nonsingular acausal bond graph has at least one nonsingular causal assignment for each consistent choice of input variables. The strong components of a causal bond graph B are defined, and it is shown that the discriminant of B is the product of the discriminants of its strong components; in particular, a causal assignment is singular if and only if there is at least one singular strong component. The reduced bond graph R( B) of B is defined and, if B is nonsingular, R( B) is proved to be acausally equivalent to B. Mason's determinant rule and the Mason gain formula are proved, and a simpler way of calculating the discriminant is derived.

Simulation and Exploitation of the Dynamic Bond Graph Model of the RTX Robot

In this paper, we will develop, step by step, a systematic procedure to succeed finally to the bond graph model of the RTX robot. The simulation with a causal bond graph will allow us to calculate the evolution of the geometric, kinematics and dynamic sizes the long of the trajectory imposed by specification conditions. This allows to predict the dynamic behaviour that must have the robot in its operational environment The dimensionnement of the energy source of every articulation, in term of instantaneous useful power, is necessary to could carry away the mechanical structure and respect consequently the specification conditions. All the mentioned treatments, will be based on some conventional sizes such as strength, velocity, torque….

BOND GRAPH MODELLING—A GENERAL SYSTEM THEORY APPROACH

Abstract Bond graph models are studied with the frame of General Systems Theory. Bond graph models as conceptual systems belong to the “Structure” level of GST. The Structure level can be partitioned in a hierarchy of four epistemological sublevels. To the “third” sublevel belong physical net-systems obeying the generalized Kirchhoff laws, consisting from R, C, I 1-ports, TR and GY 2-ports and from junction N-ports. It is shown that the acausal bond graph is the shorthand notation of the physical net-system, belonging therefore to the same epistemological sublevel. The causal bond graph conveys more information than the acausal one, allowing the formulation of the state space system equations in a straightforward manner. It represents therefore the next, higher level of structural system specification.