Bond Graph Representation Research Articles

Bond-graph representation of ideal constraints via the principle of virtual power

Bond-graph representation of ideal constraints via the principle of virtual power

Sensitivity analysis of biochemical systems using bond graphs.

The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.

Bond graph multi-physics modeling of encapsulating materials in power electronic modules

This paper focuses on multi-physics modeling of encapsulating gels in power electronic modules for transient and steady-state simulation. With the emergence of wide-bandgap semiconductors such as SiC or GaN, operating at a higher temperature than conventional Si power chips, this passive element of the packaging appears as a few studied element sensitive to thermal and mechanical stresses. A thermo-mechanical coupled modeling of the material, based on bond graph representation, is presented. This approach allows to establish, under the same formalism, an analogy between the different physical domains. From this analogy, a multi-physical nonlinear state space representation is built, allowing transient simulation of the thermo-mechanical behavior of the material. This way of modeling and simulating is particularly adapted for a preliminary study during the upstream phases of design of the power electronic modules. It quickly establishes the maximum temperature and mechanical strains experienced by the gel.

On the flat representation for a particular class of port-Hamiltonian systems

Abstract This paper pertains to the flat representation of a class of port-Hamiltonian (PH) systems and advocates the use of bicausality of Bond graphs for finding appropriate flat outputs. Systems which are differentially flat have several useful properties which can be exploited to generate, for example, optimal trajectories/profiles which ensure constraints satisfaction. For the special case of PH systems combining the power preserving property with the flatness properties leads to effective control strategies for multi-physical systems. Hence, the purpose of this paper is to explore the implications and features of a particular class of PH systems (which can be retrieved from a Bond Graph representation) in finding their flat output representation. We concentrate on the example of an electrical storage system of a DC microgrid to illustrate the proposed theory.

Bond Graph Modelling of Different Equivalent Models of Photovoltaic Cell

Abstract The photovoltaic (PV) generator current-voltage equation is nonlinear and need a powerful algorithm to solve it. In this paper a dynamic modelling approach of photovoltaic generator is presented by the bond graph (BD) methodology. The BD is a graphical methodology for modelling and analysis of physical systems. It’s based on decomposition of the system in subsystems and exchange energy. Therefore, using the single and double diode models representation of equivalent circuit of PV generator, the bond graph representation is derived. The mathematical model is obtained by applying the bond graph elements and rules. At the end, the simulation results of these obtained models using experimental points are plotted.

Bond Graph Representation of Chemical Reaction Networks

The Bond Graph approach and the Chemical Reaction Network approach for modeling the biomolecular systems were developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction network concept of complexes. Both closed and open systems are discussed. The method is illustrated using a simple enzyme-catalyzed reaction and a trans-membrane transporter.

Controllability and observability of LTV systems -bond graph approach-

In this paper, a new methodology is proposed to determinate the controllability and the observability matrices of linear time varying systems modeled by bond graph. As the bond graph model can be viewed as a state space representation and as a module (algebraic approach), the determination of controllability and observability matrices is presented with the graphical approach. The equivalence between the two approaches (Graphic, Mathematical) is proposed and a graphical methodology is pointed out directly on the bond graph representation.

Design, modeling and experimental validation of a novel finned reciprocating compressor for Isothermal Compressed Air Energy Storage applications

Considering the need for a reliable and environmentally friendly energy storage solution for addressing renewable energy intermittency issue and following the developments on Isothermal Compressed Air Energy Storage (I-CAES) systems, a new finned piston compressor which is characterized by increased heat transfer area and coefficient has been designed, analyzed, manufactured and experimentally tested. This compressor includes two sets of concentric annular fins with different diameters: the mobile fins are pushed into the space between the stationary fins through a driver shaft and compress the air trapped in the interconnecting annular chambers while keeping the air temperature close to ambient. Modeling of heat transfer and fluid flow in such a complicated geometry with a transient, non-linear, multi-layer, multi-dimensional nature can be best done by equivalent electric analogies with variable resistances and capacitors and employing a lumped method. Using bond graph representation method and based on a previously developed model for a classic reciprocating compressor, energy conversion has been modeled using a conjugate heat transfer and fluid flow model. Results of the simulation are presented and have been validated using an experimental test bench and to provide contrast to current technology, compared to a classic reciprocating compressor. The heat transfer along one cycle has increased in the finned compressor by 32 times compared to a classic piston compressor. The results also reveal that however the volumetric efficiency is decreased slightly in the finned compressor (−8%), the exergetic efficiency has increased from 55.1% in a classic piston to 78.4% in the finned piston.

A comparative study of energetic model-based fault detection using HBG and COG formalisms

Summary The problem of modeling and fault detection in an electromechanical system having a graphical representation is considered. For this system's dynamics, motivated by a desire to provide a precise fault detection procedure using a unified energy-based framework, 2 energy-based graphical formalisms are presented and compared: the Hamiltonian Bond Graph and the Causal Ordering Graph. Firstly, easily calculated from the Hamiltonian Bond Graph representation covering the causal energetic paths, the energetic residual generators are systematically deduced by comparing the energy quantity in both normal and faulty situations. Secondly, the causal and structural properties of the Causal Ordering Graph tool can be used to design an observer devoted to fault detection so as to derive directly energy-based residual generators in terms of faults. To highlight the effectiveness and applicability of 2 proposed approaches, simulation results on DC motor are provided and discussed. The performances of these fault detection schemes are compared and discussed in detail with respect to existing methods.

Modelling and structural observability of switching linear hybrid singular systems

This paper deals with the graphical modelling approach, and the structural observability of switching linear hybrid singular systems (SLHSS). First, this approach is based on switching bond graph representation of physical systems. Switching systems which are a particular case of hybrid systems are considered. Using energy considerations, hybrid automaton is built from switching bond graph (SBG) model. Second, we express different conditions for the structural observability of the continuous and discrete states, and structural observability of the switching times of SLHSS system. Our approach can be implemented in software such as Symbol2000 or 20sim, in order to observe and to control the SLHSS systems in real time.

Modelling and structural observability of switching linear hybrid singular systems

This paper deals with the graphical modelling approach, and the structural observability of switching linear hybrid singular systems (SLHSS). First, this approach is based on switching bond graph representation of physical systems. Switching systems which are a particular case of hybrid systems are considered. Using energy considerations, hybrid automaton is built from switching bond graph (SBG) model. Second, we express different conditions for the structural observability of the continuous and discrete states, and structural observability of the switching times of SLHSS system. Our approach can be implemented in software such as Symbol2000 or 20sim, in order to observe and to control the SLHSS systems in real time.

Quasi-steady-state model of a class of nonlinear singularly perturbed system in a bond graph approach

A particular class of nonlinear singularly perturbed systems by using a bond graph approach is proposed. The class of nonlinear systems is defined by terms of product of state variables whose bond graph representation is described by MTF or MGY elements modulated by state variables. The singular pertubations applied to the system permit the separation of time scales. When the assumptions of Tikhonov Theorem are satisfied, then a new bond graph called singularly perturbed nonlinear bond graph (SPNBG) to determine the quasi-steady-state model of the system is presented. The SPNBG is characterized by having an integral causality assignment for the storage elements that represent the slow dynamics, and the storage elements of the fast dynamics have a derivative causality assignment. Finally, the proposed methodology is applied to an illustrative example.

Control of Incoming H2/O2 Flows in a PEM Fuel Cell

It has become crucial, with the dwindling of energy resources related to the depletion risk of fossil and fissile resources, to find energy alternatives which have the same properties as those of a hydrocarbon in terms of transport and storage. In this context, the fuel cell appears as a very serious element both at the industrial and research levels. The aim of the manuscript is to highlight the bond graph representation in order to control energy systems incorporating renewable and electrochemical sources, particularly Proton Exchange Membrane (PEM) fuel cells. The main issue here is, to control the incoming hydrogen and oxygen flows to the electrodes based on a fuel cell bond graph model developed under 20-sim software and to regulate the output current delivered by the fuel cell while respecting its static characteristic curve and by adjusting the oxygen flow at the cathode and the hydrogen flow at the anode.

Bond graph modeling for fault diagnosis: the continuous stirred tank reactor case study

Supervision of chemical and biochemical processes is difficult due to various factors, for example the evolution of nonlinear state variables, uncertainties in parameters and disturbances, and system operating conditions. The complexities arise out of the energetic couplings in the model. In this work, the bond graph representation, as a unified and multidisciplinary tool, is used for dynamic modeling and diagnosis for process engineering, incorporating the chemical kinetics of an equilibrated reaction, heat and mass transport phenomena. A pseudo bond graph model technique is applied to a pilot reactor fitted with a mono-fluid heating/cooling system. A modeling structure has been implemented through process sub-units and validated through experimental observations. This technique is proposed to indicate physico-chemical failures, for example matter leakage, caloric isolation, or the occurrence of a secondary reaction or temperature runaway when a very exothermic reaction occurs. It provides the computational algorithms to eliminate unknown variables from coupled thermochemical models and thus generate analytical redundancy relations (ARRs) in terms of measurements and parameters for online diagnosis.

Bond graph representation of nuclear reactor point kinetics and nearly incompressible thermal hydraulics

This work presents a simplified 1D model for a pressurized water reactor core, suitable for very rapid transients like control rod ejection. The model is represented using the bond graph formalism, a technique for modeling engineering systems as combinations of connected elements. Bond graphs are a flexible way of presenting coupled physics problems by automating the computer science aspects of modeling and letting the modelers focus on the physics; they were introduced in earlier work.To help leverage the flexibility of bond graph representations of physical systems, a new bond graph processing code, BGSolver, is introduced. BGSolver has been developed by the authors over the past several years, and is now released as open source software.A rapid rod ejection benchmark is solved with both BGSolver and RELAP5-3D; BGSolver obtained full convergence with a 5ms time step, while RELAP5-3D required a 1ms time step, due to the fully coupled time integration that BGSolver employed, compared to an operator splitting-based time integrator of RELAP5-3D. BGSolver’s time integrator demonstrated 3rd-order convergence in time, a very desirable property. A single nonlinear solve was used to obtain the steady state with BGSolver.

Coupling Bond Graph and Energetic Macroscopic Representation for Electric Vehicle Simulation

This paper deals with the analysis and simulation of an electric vehicle, coupling functional and structural approaches in the same simulation environment. The Bond Graph model, the structural approach, is first deduced from the physical system, which in turn produces a direct correspondence between the system and its model. The control structure is then easily deduced from the Energetic Macroscopic Representation, the functional approach, of the vehicle using a systematic procedure. Simulation results are provided in order to analyze the performance of the closed-loop system.

Modelling of a robotic leg using bond graphs

This paper studies the bond graph model of a robotic leg mechanism, and discusses methods of extracting significant features of system dynamics through simpler models. The goal is to determine a set of simpler mechanisms with similar dynamic behaviour to that of the original leg in various phases of its motion. The paper is divided in two sections. In the first section, a modular bond-graph representation of the leg mechanism is determined. In the second section, two algorithms are applied to simplify the bond graph representation. The first algorithm determines the relevant dynamic elements of the system for each phase of motion, and the second algorithm finds the simple mechanism described by the remaining dynamic elements. In addition to greatly simplifying the control system of the robotic leg, using simpler mechanisms with similar behaviour provides a greater insight into the dynamics of the system.

Bond graphs for spatial kinetics analysis of nuclear reactors

This work proposes a simple and effective approach to modeling nuclear reactor multiphysics problems using bond graphs. The bond graph formalism is a technique for modeling engineering systems as combinations of connected elements. After the bond graph representation of a multiphysics system is constructed, it can be automatically converted into a state derivative vector and integrated. Bond graphs are a flexible way of presenting coupled physics problems by automating the computer science aspects of modeling and lettings the modelers focus on the physics.Additionally, the representation of a multiport resistive element is presented, which is necessary for coupling more than two types of physics.Bond graph representations of 2D multigroup neutron diffusion, delayed neutrons and thermal feedback were presented and tested using an LRA BWR control blade drop benchmark problem with a coarse mesh. The code demonstrated 3rd-order convergence in time, a very desirable property of fully coupled time integrators.

Bond graph modelling and simulation of fault scenarios in switched power electronic systems

A bond graph representation of switching devices known for a long time has been a modulated transformer with a modulus [Formula: see text] in conjunction with a resistor [Formula: see text] accounting for the ON-resistance of a switch considered non-ideal. Besides other representations, this simple model has been used in bond graphs for simulation of the dynamic behaviour of hybrid systems. A previous article of the author has proposed to use the transformer–resistor pair in bond graphs for fault diagnosis in hybrid systems. Advantages are a unique bond graph for all system modes, the application of the unmodified standard Sequential Causality Assignment Procedure, fixed computational causalities and the derivation of analytical redundancy relations incorporating ‘Boolean’ transformer moduli so that they hold for all system modes. Switches temporarily connect and disconnect model parts. As a result, some independent storage elements may temporarily become dependent, so that the number of state variables is not time-invariant. This article addresses this problem in the context of modelling and simulation of fault scenarios in hybrid systems. In order to keep time-invariant preferred integral causality at storage ports, residual sinks previously introduced by the author are used. When two storage elements become dependent at a switching time instance [Formula: see text], a residual sink is activated. It enforces that the outputs of two dependent storage elements become immediately equal by imposing the conjugate3 power variable of appropriate value on their inputs. The approach is illustrated by the bond graph modelling and simulation of some fault scenarios in a standard three-phase switched power inverter supplying power into an RL-load in a delta configuration. A well-developed approach to model-based fault detection and isolation is to evaluate the residual of analytical redundancy relations. In this article, analytical redundancy relation residuals have been computed numerically by coupling a bond graph of the faulty system to one of the non-faulty systems by means of residual sinks. The presented approach is not confined to power electronic systems but can be used for hybrid systems in other domains as well. In further work, the RL-load may be replaced by a bond graph model of an alternating current motor in order to study the effect of switch failures in the power inverter on to the dynamic behaviour of the motor.

Bond-graph-based fault detection and isolation for hybrid system models

For the case when the abstraction of instantaneous state transitions is adopted, this paper proposes to start fault detection and isolation in an engineering system from a single time-invariant causality bond graph representation of a hybrid model. To that end, the paper picks up on a long-known proposal to model switching devices by a transformer modulated by a Boolean variable and a resistor in fixed conductance causality accounting for its ON resistance. Bond graph representations of hybrid system models developed in this way have been used so far mainly for the purpose of simulation. The paper shows that they can well constitute an approach to the bond-graph-based quantitative fault detection and isolation of hybrid models. Advantages are that the standard sequential causality assignment procedure can be a used without modification. A single set of analytical redundancy relations valid for all physically feasible system modes can be (automatically) derived from the bond graph. Stiff model equations due to small values of the ON resistance in the switch model may be avoided by symbolic reformulation of equations and letting the ON resistance of some switches tend to zero, turning them into ideal switches. First, for two examples considered in the literature, it is shown that the approach proposed in this paper can produce the same analytical redundancy relations as were obtained from a hybrid bond graph with controlled junctions and the use of a sequential causality assignment procedure especially for fault detection and isolation purpose. Moreover, the usefulness of the proposed approach is illustrated in two case studies by its application to standard switching circuits extensively used in power electronic systems and by simulation of some fault scenarios. The approach, however, is not confined to the fault detection and isolation of such systems. Analytically validated simulation results obtained by means of the program Scilab give confidence in the approach.