Dynamic Modeling of a Three-Phase BLDC Motor Using Bond Graph Methodology

An important aspect of mechatronic systems is that the synergy realized by a clever combination of a mechanical system and its embedded control system leads to superior solutions and performances that could not be obtained by solutions in one domain. Models of mechatronic systems are often large and complicated, with many parameters, making the physical interpretation of the model outputs, even by domain experts, difficult. This is particularly true when unnecessary features are included in the model. In mechatronics, where a controlled system is designed as a whole, it is advantageous that model structure and parameters are directly related to physical structure in order to have a direct connection between design or modeling decisions and physical parameters. The bond graph methodology is a convenient and useful complimentary tool for obtaining both the behavioral and the diagnostic models. Moreover, the method presents the unique feature of being able to model systems in different energy domains using the same approach with a single model, thus it becomes ideal for modeling and simulation of mechatronics and control systems. Because of the multi-domain energies involved in the actuators, the bond graph methodology as a multidisciplinary and unified modeling language proves a convenient tool for the given purpose. The advantage of the bond graph modeling compared to other methods is the good visibility of power transfers between all elements, and even between several subsystems in which we can measure efficiency of the system. The proposed model guarantees the reversibility of power flows, at the opposite of other approach for example transfer function. By the bond graph method, it is easy to see the impact of changing one parameter in the complete model of the actuator system. The model structure can also be modified, taking care of the causality. Respecting the causality, computing convergence troubles due to causality conflicts are avoided. The analysis of causal paths highlights variable links. This is an advantage of bond graph method, in order to have a view of energetic dependences and resonances in the model. In this chapter, firstly, the pump-displacement-controlled actuator system with applications in aerospace industries is modeled using the bond graph methodology. Secondly, an 5

The most important single linear integrated circuit is the operational amplifier. Operational amplifiers (op-amp) are available as inexpensive circuit modules, and they are capable of performing a wide variety of linear and nonlinear signal processing functions (Stanley, 1994). In simple cases, where the interest is the configuration gain, the ideal op-amp in linear circuits, is used. However, the frequency response and transient response of operational amplifiers using a dynamic model can be obtained. The bond graph methodology is a way to get an op-amp model with important parameters to know the performance. A bond graph is an abstract representation of a system where a collection of components interact with each other through energy ports and are place in the system where energy is exchanged (Karnopp & Rosenberg, 1975). Bond graph modelling is largely employed nowadays, and new techniques for structural analysis, model reduction as well as a certain number of software packages using bond graph have been developed. In (Gawthrop & Lorcan, 1996) an ideal operational amplifier model using the bond graph technique has been given. This model only considers the open loop voltage gain and show an application of active bonds. In (Gawthrop & Palmer, 2003), the `virtual earth' concept has a natural bicausal bond graph interpretation, leading to simplified and intuitive models of systems containing active analogue electronic circuits. However, this approach does not take account the type of the op-amp to consider their internal parameters. In this work, a bond graph model of an op-amp to obtain the time and frequency responses is proposed. The input and output resistances, the open loop voltage gain, the slew rate and the supply voltages of the operational amplifier are the internal parameters of the proposed bond graph model. In the develop of this work, the Bond Graph model in an Integral causality assignment (BGI) to determine the properties of the state variables of a system is used (Wellstead, 1979; Sueur & Dauphin-Tanguy, 1991). Also, the symbolic determination of the steady state of the variables of a system based on the Bond Graph model in a Derivative causality assignment (BGD) is applied (Gonzalez et al., 2005). Finally, the simulations of the systems represented

Bond Graph Modelling of Different Equivalent Models of Photovoltaic Cell

Building performance simulation is crucial for the design and optimization of sustainable buildings. However, the increasing complexity of building systems necessitates advanced modeling techniques capable of handling multi-domain interactions. This paper presents a novel application of the bond graph (BG) methodology to simulate and analyze the thermal behavior of an integrated trigeneration system within an experimental test cell. Unlike conventional simulation approaches, the BG framework enables unified modeling of thermal and hydraulic subsystems, offering a physically consistent and energy-based representation of system dynamics. The study investigates the system’s performance under both dynamic and steady-state conditions across two distinct climatic periods. Validation against experimental data reveals strong agreement between measured and simulated temperatures in heating and cooling scenarios, with minimal deviations. This confirms the method’s reliability and its capacity to capture transient thermal behaviors. The results also demonstrate the BG model’s effectiveness in supporting predictive control strategies, optimizing energy efficiency, and maintaining thermal comfort. By integrating hydraulic circuits and thermal exchange processes within a single modeling framework, this work highlights the potential of bond graphs as a robust and scalable tool for advanced building performance simulation.

<div>Bond graph framework, established with MATLAB/Simulink, has a dual objective: analyze the system using bond graph and develop the system equations in symbolic form. This approach is a combination of the simulation skill of the MATLAB/Simulink and the modelling skill of the bond graph. In this analysis, a nine-degrees-of-freedom (9 DoF) three-wheeled vehicle model integrated with a 5 DoF human subject model is formulated using bond graph methodology and simulated using the Simulink toolbox. The present work is divided into two linear and nonlinear analyses of the dynamic behavior of sprung mass subjected to random and bumps inputs, respectively. The linear analysis evaluates the ride comfort of the vehicle and human subject model under the International Organization for Standardization (ISO) and ISO-2631-1 criterion, and the stability of the vehicle is evaluated through on eigenvalues obtained from a single-order state-space form of differential equations obtained from the Simulink toolbox. The nonlinear analysis excludes the human biodynamic model and evaluates the sprung mass bounce acceleration and displacement response and pitch acceleration response under bump inputs. From the linear analysis, vehicle ride is found to be in the “very uncomfortable” range, and above 74 km/h vehicle is found to be unstable. The nonlinear analysis suggests that a semi-active magnetorheological (MR) damper with a fuzzy logic control policy is superior compared to a conventional passive suspension when the vehicle is subjected to bump inputs. The present work is validated with a comparison between the vehicle sprung mass center vertical-lateral power spectral density (PSD) acceleration response simulated through the Simulink software tool and the same received from field tests.</div>

An important aspect of modern engineering systems is their great diversity. Often they include interactions among different physical domains, contain control subsystems, and are large-scale and complex. The bond graph is a powerful and versatile tool that can help the engineer to design modern engineering systems. Three issues are explored from a bond graph perspective: modeling of engineering systems, simulation of their behavior, and teaching about engineering systems. It is the author’s observation that bond graph methodology is one of the most useful engineering system techniques available and belongs in the problem-solving tool kit of every mechanical engineer. This paper develops a rationale for this viewpoint both for readers familiar with bond graph methods and for readers to whom they are new.

Photovoltaic systems are composed of several elements as PV source, DC/DC or DC/AC converters, DC or AC machines, accumulators, pumps, fans, and refrigerators. These systems are therefore of hybrid type and their modelling is complex. This is why we used the bond graph methodology. The photovoltaic generator is a special source of finite energy with a non-linear current-voltage characteristic. Thus, performances of linear electrical circuits and systems supplied by conventional sources must be re-evaluated when a PV generator is used as energy source. In the first objective of simulation, we use an averaged bond graph model of a photovoltaic system composed of a PV generator coupled to a DC motor-pump through a buck-boost converter. This converter assures a MPPT (maximum power point tracking) behaviour of the system. In the second objective of stability study of the PV system, a direct linearization of the bond graph model is done. The results show a non minimality of phase of the velocity response. So the PV generator voltage is chosen as variable to be controlled in order to assure an MPPT functioning.

Objectives: Methods: To model and simulate the pumping system by using as a source the PV and by the vectorial and scalar commands. The photovoltaic system modelling is complex; so we propose the use of bond graph (BG) methodology which permits the decomposition of the system into subsystems exchanging energy, and to represent several physic domains (electricity, mechanical, etc.) with an joined way. Findings: We represent a method based on the input-output causal inversion of the bond graph of the system which consists in deducing the laws from input-output control directly on bond graph. A new technique that consists on using a PWM bloc with three phases inverters is employed in order to optimize this bloc and to have better results. Applications: The modeling of photovoltaic system elements is an important step that should be preceded all application of sizing, identification or simulation. Keywords: Bond Graph Modeling, Induction Motor, MPPT, Photovoltaic, PWM, Scalar and Vector Control

Mechatronic design deals with the integrated design of a mechanical system and its embedded control system. This definition implies that it is important, as far as possible, that the system be designed as a whole. This requires a system approach to the design problem. An important aspect of mechatronic systems is that the synergy realized by a clever combination of a mechanical system and its embedded control system leads to superior solutions and performances that could not be obtained by solutions in one domain. The bond graph methodology is a convenient and useful complimentary tool for obtaining both the behavioral and the diagnostic models. Moreover, the causal properties of the bond graph methodology can help to design fault detection and isolation (FDI) algorithms. In this paper, the bond graph modeling in the interest of actuator monitoring is given. Then the method to associate the bond graph description to the model, in order to complete the equipment description, is explained.

One of the most important features in the analysis of the singular perturbation methods is the reduction of models. Likewise, the bond graph methodology in dynamic system modeling has been widely used. In this paper, the bond graph modeling of nonlinear systems with singular perturbations is presented. The class of nonlinear systems is the product of state variables on three time scales (fast, medium, and slow). Through this paper, the symmetry of mathematical modeling and graphical modeling can be established. A main characteristic of the bond graph is the application of causality to its elements. When an integral causality is assigned to the storage elements that determine the state variables, the dynamic model is obtained. If the storage elements of the fast dynamics have a derivative causality and the storage elements of the medium and slow dynamics an integral causality is assigned, a reduced model is obtained, which consists of a dynamic model for the medium and slow time scales and a stationary model of the fast time scale. By applying derivative causality to the storage elements of the fast and medium dynamics and an integral causality to the storage elements of the slow dynamics, the quasi-steady-state model for the slow dynamics is obtained and stationary models for the fast and medium dynamics are defined. The exact and reduced models of singularly perturbed systems can be interpreted as another symmetry in the development of this paper. Finally, the proposed methodology was applied to a system with three time scales in a bond graph approach, and simulation results are shown in order to indicate the effectiveness of the proposed methodology.

The dynamics of intermittent load systems fed from a PV source are explored, led by the expanding application of PV power in diverse areas. Most actual loads in small-scale village industry are intermittent and pulsating. For successful application of photovoltaics in these areas, the dynamical behaviour of such systems must be understood. This requires the formulation of dynamical models of PV-fed intermittent load systems. Bond graph methodology has recently emerged as a very convenient tool for dynamic modelling. This is the first application of this methodology in modelling photovoltaic systems. The spice-pounding operation is taken as a typical example of a pulsating load that can be fed from PV power. It is shown that the standard equivalent circuit of the PV cell gives rise to algebraic looping problems when expressed in the language of the bond graph. Means of overcoming the problem have been suggested. This is the first report of modelling the spice-pounding machine with the bond graph technique. The model has been simulated with COSMO–KGP software (developed at the I.I.T., Kharagpur, India) and the results reported. It is found that the dynamic behaviour of the PV-fed spice-pounding system differs significantly from that of a system fed from a constant voltage supply. Performance is compared for a shunt motor, a series motor and a separately excited motor, and three types of cam profiles, namely parabolic, cycloidal and half harmonic plus constant velocity. © 1997 by John Wiley & Sons, Ltd.

The paper presents a procedure for direct passivation of nonlinear systems using the bond graph methodology. The different steps of the passivation approach are carried out straightforwardly in the bond graph domain, including: relative degree and zero dynamics calculation, stabilization and tracking via feedback. The energy aspect of the bond graph representation highlights the choice of the appropriate Lyapunov function as the total energy in the storage elements while its orbital derivative is equal to the power supplied by the sources minus the power in the dissipative elements. Finally, the application of the proposed procedure is illustrated on the current fed-induction motor.

In this paper, non-regular static state feedback solutions of the row-by-row decoupling problem (RBRDP) with stability are investigated by the bond graph approach for the class of non-square linear models. More precisely, the aim is to study the problem of the non-regular static state feedback designing, firstly, when the model is not decouplable with a regular static state feedback and, secondly, when the model is decouplable with a regular static state feedback but not with stability. The bond graph methodology is used in order to characterize the structure of non-square models and the modification of the infinite structure that arises when a regular control law cannot exist. A new graphical methodology is proposed. Finally, when row-by-row decoupling with stability is possible for non-square bond graph models, a formal expression of the control is given using simultaneously the bond graph and the geometric approaches.

In this chapter, firstly, the pump-displacement-controlled actuator system with applications in aerospace industries is modeled using the bond graph methodology. Secondly, an approach is developed towards simplification and model order reduction for bond graph models that can usually use in conceptual representation or design procedures. The model order reduction process indicates which system components have the most bearing on the frequency response, and the final model retains structural information. Finally, the state space form of mathematical model of the system based on the bond graph model is presented. By associating bond graph model, it becomes possible to design fault detection and isolation (FDI) algorithms, i.e. the generation of fault indicators, and to improve monitoring of the actuator.

Bond graph aided design of controlled systems