New approach in solving derivative causality problems in the bond-graph method

Abstract

From the bond-graph model of a dynamic system, the state equations can be obtained. When the system contains only energy storing elements in integral causality, the system of state equations is immediately and directly determined. When the model contains at least one energy storing element in derivative causality, the resulted system of differential-algebraic equations arises some difficulties in finding the final form of the system of state equations. The work presents a new method of deducing the state equations in case of bond-graph models with one, or several energy storing elements in derivative causality. This method is based on the kinetic energy of the system and offers the possibility to avoid a difficult mathematical calculus for the transition from a system of differential algebraic equations to the system of state equations.

The Dynamic Equations of a Mechanical System Using the Bond-Graph Method and the Kinetic Energy

“…This methodology has been applied to mechanical systems with only one degree of freedom and no storing energy elements in derivative causality (Ibănescu, 2021). Then, it has been applied to mechanical systems with one degree of freedom, but containing storing energy elements in derivative causality (Ibănescu, 2022).…”