Structural analysis of switching systems modelled by bond graph

In this paper the modelling and controllability of switched linear singular systems (SLSS) are investigated. First a procedure to draw a hybrid automaton using bond graph approach is proposed. Then, graphical methods are derived in order to determine different conditions for the structural R-I-C-controllability of SLSS systems. These methods are based on simple causal paths and causal manipulations on the switching bond graph model.

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.

Formalization of bond graph using higher-order-logic theorem proving

<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>

Engineering systems modeling and analysis based on the bond graph approach has been applied to biomolecular systems. In this context, the notion of a Faraday-equivalent chemical potential is introduced which allows chemical potential to be expressed in an analogous manner to electrical volts thus allowing engineering intuition to be applied to biomolecular systems. Redox reactions, and their representation by half-reactions, are key components of biological systems which involve both electrical and chemical domains. A bond graph interpretation of redox reactions is given which combines bond graphs with the Faraday-equivalent chemical potential. This approach is particularly relevant when the biomolecular system implements chemoelectrical transduction - for example chemiosmosis within the key metabolic pathway of mitochondria: oxidative phosphorylation. An alternative way of implementing computational modularity using bond graphs is introduced and used to give a physically based model of the mitochondrial electron transport chain To illustrate the overall approach, this model is analyzed using the Faraday-equivalent chemical potential approach and engineering intuition is used to guide affinity equalisation: a energy based analysis of the mitochondrial electron transport chain.

In recent years, there has been a growing demand in the field of engineering systems for research on the vibration response of motor-gear systems under non-steady state conditions. However, conventional modeling and simulation techniques are primarily restricted to systems within a single energy domain. When dealing with intricate electromechanical coupling systems, the modeling process becomes increasingly intricate. Consequently, this study adopts bond graph theory as the foundation for analyzing the vibration characteristics of motor-gear coupling systems. In addressing the vibration issue of the motor-gear transmission system, a nonlinear bond graph model is established that takes into account the time-varying mesh stiffness, static errors, and tooth surface friction, among other nonlinear factors. Then, according to the coupling relationship between motor mechanical systems and electrical systems, the electromechanical coupling dynamic model of the motor-gear system is established using the method of bond graph. In addition, the state equation of the system is derived based on the bond graph model. Finally, the system is simulated using 20-sim software, and the electromechanical coupled vibration characteristics of the simulation results are analyzed. This article lays the foundation for the design and analysis of motor-gear coupling systems and multi-energy domain complex 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]

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

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.

System inversion is a concept that often appears either implicitly or explicitly in the design of control systems (e. g. decoupling, feedback linearization or feedforward control). This paper presents an algorithm for the representation of an inverse systems model using bond graph techniques. Structural invertibility conditions are investigated graphically and the structure of the inverse model is discussed. This graphical inversion method is carried out in parallel with classical inversion algorithms using causality manipulations in bond graphs. The physical approach adopted here is enhanced with applications presented in Part 2 which follows.

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.

Controllability of system is basic conception for analyzing and designing system with modern control theoly. Bond graph contains system structure properties and can determine state variables. A simple method of determining controllability with bond graph is introduced in the paper. Only by assigning causality form for all storages elements of system in bond graph, which comply with firstly assigning integral causality and then assigning derivative causality, the controllability condition can be determined. Comparing with conventional numerical matrix method, this method does not depend on parameters of state matrices A and B and overcome miscellaneous computation for obtaining controllability matrix .two examples analyzing with controllability and uncontrollability process verify the effectivenms of the method.