Modeling of Two Link Flexible Manipulator using Bond Graph Technique

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 is the first part of a two-part paper developing a procedure for impedance synthesis and dynamic system conceptual design using a bond graph approach. The first part examines impedance synthesis with bond graphs and develops some useful properties of impedance related to bond graph structure. The second part of the paper uses the impedance synthesis approach as a tool in conceptual design for generating dynamic system solutions meeting frequency domain input-output specifications. In Part I, impedance and transfer functions are directly formulated from bond graphs. An invertible procedure is developed in order to allow for synthesis. Frequency domain properties of bond graphs are developed that will aid in impedance synthesis and the synthesis of bond graph structures from impedance specifications is formulated with a view toward conceptual design. The synthesis is not unique, a given impedance can be synthesized into multiple bond graph structures depending on its complexity. The work presented focuses on the synthesis of passive impedances but may be generalized for active systems.

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.

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.

Dynamics of a class of repeated systems with non-identical elastic and visco-elastic interconnections—a bond graph approach

This paper presents a new concept for calculating of the bond graph observer gains based on a graphical approach that investigates the Lyapunov Second Method in order to conclude about the observer stability and to search for the adequate gains that stabilize the observer. This new observer is used in the mode identification procedure. In fact, the observer’s residues allow the differentiation between the current mode and the other system modes. In order to guarantee the efficiency of the mode identification procedure, a new bond graph approach is proposed. It concerns the discernibility between the modes in bond graph language. First, it deals with the R-discernibility that introduces the definition of the discernibility through the structural parity residual then returns to a simple calculation of some matrices’ ranks in bond graph language. Second, another bond graph technique is applied to define the discernibility throughout the equivalency between the realizations.

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.

This research is dedicated to developing an analytical physics-based model of rolling element bearing, especially focused on ball bearing. The mathematical model is built on the dynamics of planner rigid bodies having body fixed frames that consider inner ring, eight balls and outer ring. The distinguishing feature of the model is the capability to accurately locate all contact points between inner ring-balls, and balls-outer ring during its entire operation. This is possible as we chose bond graph as the modelling tool that considers precise bearing geometry and magnificently connects each point of the multi-body system by calculating relative velocities at contact points of the corresponding contacting pairs. The model also shows the effect of load zone on bearing parts, where contact deformation is calculated using Hertz contact theory. The condition of contact is applied while considering the clearance as well. The effects of faults on bearing are investigated in the end. With the help of bond graph, a modular program has been developed, which efficiently considers the dynamics of all the bearing components simultaneously. The model is validated by conducting a virtual experiment in SOLIDWORKS and comparing results with a literature as well.

The analysis of a system with singular perturbations in a bond graph approach is presented. The bond graph model (BGI) of this system is described. Hence, the quasi steady state model (SPBG) changing the causality of the storage elements that represent the fast dynamic can be obtained. The steady state response of the quasi steady state model in a bond graph approach is proposed. In order to obtain this response a derivative causality to the storage elements of the slow dynamic on the bond graph (BGD) has to be assigned. Finally, the proposed methodology is applied to a RC network.

Network thermodynamics of biological systems: A bond graph approach

This paper proposes an approach for the design of vehicular active suspension system by Luenberger observer. The main idea is to use the observer to diagnose using a bond graph approach. The design of an observer by the bond graph model becomes easier and more generous. Simulation results are used to show the dynamic behavior of system variables and evaluate the performance of the observer for fault diagnosis.

Bond graph modeling of multibody systems: a library of three-dimensional joints

Intelligent vector control for a novel mechatronic modeling of a 1.5MW variable speed WECS using the bicausality concept under a real wind flow: A Bond Graph Approach

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.

Recently Borutzky and Granda proposed to construct a so-called incremental bond graph from an initial bond graph with nominal parameters in order to determine unnormalized first order frequency domain sensitivities in symbolic form. At the same time Dauphin-Tanguy and Kam presented a bond graph approach that allowed them to set up a specific form of state equations in symbolic form commonly used for a robustness study of models with uncertain parameters. Both approaches designed for different purposes have been developed independently. Nevertheless, this paper shows that they can be used to obtain each other's results under some reasonable assumptions. For illustration both approaches are applied to an example, which has been kept fairly small for didactic reasons.