Exploiting the Concept of Causality in Bond Graph for Approximate Differentiation of Signals through Integration

Bond graph is a pictorial method for modeling multi-energy physical systems where power transaction between the subparts of a system is represented by a power bond. This power bond carries information of two variables, an effort and a flow, decided based on the notion of causality by different subsystems. Their summation is performed by using 1 and 0 junctions respectively. Nevertheless, in the bond graph, it is often required to compare signals which are not in the form of flow or effort. By Differentiation, these signals can be converted into flow or effort and then can be compared. In this work, the concept of causality is exploited to differentiate an analogue signal. The input signal required to be differentiated is considered in two different ways: an effort signal and a flow signal. Initially bond graphs for these two different cases were prepared having differential causalities and later modified to make them integrally causal. The respective bond graphs are then interpreted in terms of physical systems in the mechanical domain. Simulation code has been written directly from the respective bond graphs in an algorithmic manner using the computational software MATLAB. Different types of analogue signals such as sinusoidal, cosine, unit step, ramp and quadratic have been differentiated using both these cases and simulation results are presented.