Relations between two bond graph approaches to sensitivity analysis and study of robustness

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.

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.

Hybrid system models exploit the modelling abstraction that fast state transitions take place instantaneously so that they encompass discrete events and the continuous time behaviour for the while of a system mode. If a system is in a certain mode, e.g. two rigid bodies stick together, then residuals of analytical redundancy relations (ARRs) within certain small bounds indicate that the system is healthy. An unobserved mode change, however, invalidates the current model for the dynamic behaviour. As a result, ARR residuals may exceed current thresholds indicating faults in system components that have not happened. The paper shows that ARR residuals derived from a bond graph cannot only serve as fault indicators but may also be used for bond graph model-based system mode identification. ARR residuals are numerically computed in an off-line simulation by coupling a bond graph of the faulty system to a non-faulty system bond graph through residual sinks. In real-time simulation, the faulty system model is to be replaced by measurements from the real system. As parameter values are uncertain, it is important to determine adaptive ARR thresholds that, given uncertain parameters, allow to decide whether the dynamic behaviour in a current system mode is the one of the healthy system so that false alarms or overlooking of true faults can be avoided. The paper shows how incremental bond graphs can be used to determine adaptive mode-dependent ARR thresholds for switched linear time-invariant systems with uncertain parameters in order to support robust fault detection. Bond graph-based hybrid system mode identification as well as the determination of adaptive fault thresholds is illustrated by application to a power electronic system easy to survey. Some simulation results have been analytically validated.

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.

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.

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.

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

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

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.

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.

A mechanism involves a number of interconnected rigid bodies. To design and control a system, modeling of mechanism plays an important role .There are many methods used for modeling like Newton –Euler, Lagrange’s Euler and Hamiltonian method. These methods become very laborious and cumbersome for complex multibody systems. The above mention techniques however, do not expose the cause and effect relationship. In this paper, bond graph approach is used for modeling two link manipulator by considering the flexibility at the joints. Bond graph technique shows the pictorial representation of the dynamics of the system. Moreover it may also be used for modeling multi energy domain systems