Bond graph and variable causality

Causality in vector bond graphs and its application to modeling of multi-body dynamic systems

Hybrid models are those containing continuous and discontinuous behaviour. In constructing dynamic systems models, it is frequently desirable to abstract rapidly changing, highly nonlinear behaviour to a discontinuity. Bond graphs lend themselves to systems modelling by being multi-disciplinary and reflecting the physics of the system. The causally dynamic hybrid bond graph is therefore suitable for simulation as well as providing engineering insight through analysis. There is a distinction between structural and parametric switching. The controlled junction is used for the former, and gives rise to dynamic causality. A controlled element is developed for the latter. Dynamic causality is unconstrained so as to aid insight. The junction structure matrix (JSM) for the hybrid bond graph features Boolean terms to reflect the controlled junctions in the graph structure. This hybrid JSM is used to generate a mixed-Boolean state equation. When storage elements are in dynamic causality, the resulting system equation is implicit. Control properties can be seen in the structure and causal assignment. An impulsive mode may occur when storage elements are in dynamic causality, but otherwise there are no energy losses associated with commutation because this method dictates the way discontinuities are abstracted. An impulsive model can be derived if required to further aid simulation. The mixed-Boolean mathematical model can be implemented in an environment such as Matlab.

<p><span>The design of a supervision system based on the external model by structuring the industrial process according to several modes of operation (degraded and normal). The disadvantage of this model is that it describes the industrial process components as functions regardless of their dynamics without going into detail. Hence the interest of the bond graph model to fill the external model limits. The performance of the proposed supervisory system using both models lies in the detection and location of faults for each mode of operation. The bond graph model enriched by the concept of causality and thanks to these structural properties can clearly display the elements of the physical system taking into account their dynamics in normal and abnormal operation. The results of our research have been applied to central air conditioning system; the development of the proposed project has proceeded from the modeling stage to the reconfiguration stage of the system.</span></p>

Multidisciplinary systems are described most suitably by bond graphs. In order to determine unnormalized frequency domain sensitivities in symbolic form, this paper proposes to construct in a systematic manner a bond graph from another bond graph, which is called the associated incremental bond graph in this paper. Contrary to other approaches reported in the literature the variables at the bonds of the incremental bond graph are not sensitivities but variations (incremental changes) in the power variables from their nominal values due to parameter changes. Thus their product is power. For linear elements their corresponding model in the incremental bond graph also has a linear characteristic. By deriving the system equations in symbolic state space form from the incremental bond graph in the same way as they are derived from the initial bond graph, the sensitivity matrix of the system can be set up in symbolic form. Its entries are transfer functions depending on the nominal parameter values and on the nominal states and the inputs of the original model. The sensitivities can be determined automatically by the bond graph preprocessor CAMP-G and the widely used program MATLAB together with the Symbolic Toolbox for symbolic mathematical calculation. No particular program is needed for the approach proposed. The initial bond graph model may be non-linear and may contain controlled sources and multiport elements. In that case the sensitivity model is linear time variant and must be solved in the time domain. The rationale and the generality of the proposed approach are presented. For illustration purposes a mechatronic example system, a load positioned by a constant-excitation d.c. motor, is presented and sensitivities are determined in symbolic form by means of CAMP-G/MATLAB.

A bond graph procedure to get the steady state value for linear time-invariant systems is presented. The general case of a singular state matrix is considered. The procedure is based on a junction structure configuration with derivative causality assignment, and on relationships of the bond graphs with integral and derivative causality assignments. It is shown that the structurally null modes, i.e. the poles at the origin, are cancelled for steady state. The key to cancel the poles at the origin is that the adjugate matrix of sIn − Ap multiplies Bp yielding the zeros at the origin with the same order that the structurally null modes, where ( Ap, Bp, Cp, Dp) is a state space realization of a linear time-invariant system, s is the Laplace operator and In, is an n × n identity matrix. Hence, this unstable part of the system is cancelled and the steady state can be obtained. Thus, the singularity of the state space matrix is avoided, and the steady state is obtained from the bond graph with derivative causality assignment. Since the singular state matrix is considered, it is shown that by using the bond graph with derivative causality assignment, an equivalent system with linearly independent state variables can be obtained. An example of an electrical system with an electrical transformer modelled by an I-field whose state matrix is singular is presented. Also, the proposed methodology for a load driven by two DC motors is applied.

This paper proposes a Bond Graph (BG) model of a multi-source system (Wind Turbine (WT) and Solar Photovoltaic Panels (PV)) used to produce hydrogen from the water electrolysis. BG, as an unified and multidisciplinary tool, is a well suited tool for representing multi-physic dynamical systems based on power exchange. In this work, the approach is adapted for the Hybrid Renewable Energy Systems (HRES) by defining new appropriate BG elements to the per-existent library, these new elements allow covering wide class of the HRES systems sharing common structural characteristics. A simulator is built from the BG model of the multi-source system. It allows testing different operating modes according to weather conditions, user needs and safety measures.

Switchable structured bond: A bond graph device for modeling power coupling/decoupling of physical systems

One of the challenges for designers of complex engineering systems is to interpret large volumes of data that arise from multiple simulation studies. Numerical results need to be presented in relation to the geometry of the physical system or schematic model in order to encourage understanding of the simulated behavior and promote insight for improving the design. This paper presents a three-dimensional enhanced design environment for a broad class of engineering systems which has been developed and implemented using the concepts of Scientific Visualization. The design environment is based on the Bond Graph, supplemented with block diagram elements, as a modeling representation. The Bond Graph captures the interconnectedness of the system components and shows power pathways as energy is transferred within the system. Previously, construction of Bond Graph models has been limited to two-dimensional representations. The enhanced design environment allows for 3-D representation of a Bond Graph, which more closely conforms to physical system geometry. Animation of simulation results directly on this 3-D Bond Graph is provided to aid the designer in comprehending the system’s behavior. This is done principally by color coding of bonds corresponding to selected results. The tool for visualization of variable values on a 3-D Bond Graph was developed as a pilot design environment (BGVis-3D). A bounce-pitch-roll model of an automotive vehicle was simulated in this environment. Its behavior when encountering a pothole was investigated using BGVis-3D, which demonstrated the effectiveness of the tool.

Bond graphs provide an energy-based methodology for modelling complex systems hierarchically; at the moment, the method allows biological systems with both chemical and electrical subsystems to be modelled. Herein, the bond graph approach is extended to include chemomechanical transduction thus extending the range of biological systems to be modelled. Actin filament polymerization and force generation is used as an example of chemomechanical transduction, and it is shown that the TF (transformer) bond graph component provides a practical, and conceptually simple, alternative to the Brownian ratchet approach of Peskin, Odell, Oster and Mogilner. Furthermore, it is shown that the bond graph approach leads to the same equation as the Brownian ratchet approach in the simplest case. The approach is illustrated by showing that flexibility and non-normal incidence can be modelled by simply adding additional bond graph components and that compliance leads to non-convexity of the force-velocity curve. Energy flows are fundamental to life; for this reason, the energy-based approach is utilized to investigate the power transmission by the actin filament and its corresponding efficiency. The bond graph model is fitted to experimental data by adjusting the model physical parameters.

An existing bond graph of a squirrel cage induction motor was modified to make the bond graph physically more representative. The intent was to form a one-to-one correspondence between motor components and bond graph elements. Components explicitly represented include the stator coils, the squirrel cage rotor bars, and the magnetic flux routing section. The final bond graph spans electrical, magnetic, and mechanical energy domains, and contains common motor faults. From this bond graph. state equations were extracted and simulations performed. Simulated were the response of healthy motors, and motors with shorted stator coils and broken rotor bars. [S0022-0434(00)01203-X]

Development of trajectory and force controllers for 3-joint string-tube actuated finger prosthesis based on bond graph modeling

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.

This paper considers the supervision of complex systems by bond graph (BG) and external models (EM). The bond graph is used for the detection and isolation of fault affecting sensors, actuators or physical components of the process. The external models structure the industrial process, according to several modes of operation (degraded and normal). The switching from one operated mode to another mode is described by a graph called management mode operation graph. It represents the man-machine interface system. The logic functions are controlled by the availability of services and therefore the state of technological components. Thus, the availability of services (necessary for conducting a mission) will be provided by the monitoring algorithm based on BG at management operation graph. The combined representation BG-EM as behavioral and functional modeling for supervision system design is applied to a three tanks system.

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.

This article presents a model for active hydro-pneumatic (AHP) suspension system. This is a relatively new suspension design, in which the system works without the classical mechanical parts of a suspension, such as steel springs and dampers. Instead, a hydraulic system is used which consists of a plunger cylinder, a flow resistance, a hydro-pneumatic capacitor and a strong hydraulic pump together with a fast response servo valve. At the heart of each AHP suspension system, there is a force controller, which is responsible for tracking a certain desired force. The modeling of the system has been made using the bond graph simulation technique. All of the components of the system have been replaced by their bond graph counterparts. The governing equations are written in terms of bond graph models, and are solved simultaneously.  Bond graph results are compared to the results of others. The bond graph method succeeds in reproducing the same outputs as the other methods. However, the ability of the bond graph modeling in adapting to new changes in the system components and physical models makes it a good choice for complex systems.http://dx.doi.org/10.5755/j01.mech.17.3.509