Ideal physical element representation from reduced bond graphs

Abstract

Previous research has demonstrated that bond graphs are a natural and convenient representation to implement energy-based metrics that evaluate the relative ‘value’ of energy elements in a dynamic system model. Bond graphs also provide a framework for systematically reformulating a reduced bond graph model (and thus the state equations) of the system that results from eliminating the ‘unimportant’ elements. This paper shows that bond graphs also provide a natural and convenient representation for developing a rigorous approach for interpreting the removal of ideal energy elements from the system model. For example, when a generalized inductance in the mechanical domain is eliminated from a model, the bond graph shows whether the coordinate representing the motion of the body becomes free to move (zero inertia) or fixed to ground (infinite inertia). This systematic interpretation of element removal makes bond graphs an attractive modelling language for automated model reduction techniques. An illustrative example is provided to demonstrate how the developed approach can be applied to provide the physical interpretation of energy element removal from a mechanical system.