Simulation of Physical Engineering Systems from Bond Graph Models

Those familiar with bond graphs know that models with no derivative causality nor causally unassigned bonds are guaranteed to produce state equations of the form. (x) over circle = f(x,u) When the model is nonlinear there is little hope of obtaining a solution other than with time step simulation which is straightforwardly performed on equations of the form (1). When simulation is the goal of the modeling effort then it is rarely necessary to cast equations into the form of Eqs. (1). It is sufficient to know that this form of the equations could be produced but the steps required to obtain this form are unnecessary. This paper presents a nonlinear physical system and shows how to construct the system bond graph and then use causality to derive a set of equations appropriate for simulation but hardly in the form of Eqs.(1). Simulation results are also presented. The example system is a nonlinear roll control system.