Bond Graph Modelling, A Quick Learning: Part 1

Bond graph modelling is a graphical approach to represent the dynamics of any systems. By graphical approach, means that you do not need to derive any ordinary or partial differential equations when you decide to model a particular system. This is interesting as it saves time to think about the system equations. Rather, bond graph focuses more on the energy transfer between the elements of any system which is more fundamental and intuitive to represent the system dynamics. This is the first article to introduce the modelling of any system (electrical, mechanical or hydraulic etc.) with this approach.

Bond graph approach was first introduced by Professor H.M. Paynter  from MIT, back in the early sixties. He first realized that every differential equation representing a dynamical system could also be obtained if the energy transfer between the system components was correctly identified in a graphical forms. Bond graph is one of the coolest inventions of engineering discipline in the last century. The idea is very smart as you do not need to derive any system governing equation rather you just focus on the mapping of energy transfer between the connected elements. Moreover, there are only nine fundamental elements or components in this method by which you can literally model any system in any physical domain. These elements are source of effort (SE), source of flow (SF), inductive element (I), capacitive element (C), resistive element (R), transformer (TR), gyrator (GY), 1-junction, and 0-junction. 

So, what are these elements mean in bond graph physically? Because, each element plays a fundamental role in the overall bond graph model. For example, source of effort in mechanical domain is the force, torque etc.; but, in electrical domain, it is the voltage or magneto-motive force in electromechanical domain. Source of flow in mechanical domain is the velocity and in electrical domain, it is the current. Examples of inductive elements are the mass or moment of inertia in mechanical domain, and inductor in electrical domain and so on. Capacitive element is a capacitor in electrical domain, a spring in mechanical domain, a water tank in hydraulic domain and so forth. Resistive elements are the dampers, electric resistors in mechanical and electrical domain respectively. A transformer, like its name, is a cantilever or a pulley or a drive train in gear box in mechanical domain; and in electrical domain, it could simply be a transformer used in electrical power line to scale-up or down the voltage. A gyrator plays important role in multi-domain or multi-physics system modelling as it helps to convert from one energy state into another. For instance, a DC motor or a generator, is a perfect example of a gyrator where we see that the electrical energy is transferred into mechanical energy or vice versa.

We will discuss more on these fundamental bond graph elements in the next part, especially we will highlight the constitutive relationship of these elements which eventually provide deeper insights into the dynamics of a system. We will enlighten more on the basic energy transfer between the elements and how it is defined in a bond graph. The universal law of energy conservation will help us understand which is behind each step of developing a bond graph model. This chapter is more of a philosophical introduction of the bond graph method. There is actually a lot to learn when we will dig deeper into this area.Until then, enjoy this brief introduction of this modelling approach.

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