Quasy steady state model determination using bond graph for a singularly perturbed LTI system

A bond graph model in a integral causality assignment (BGI) for a singularly perturbed system is presented. This system is characterized by fast and slow dynamics. When the singular perturbation method is applied, the fast dynamic differential equation degenerate to an algebraic equation, the real roots of this equation by using a proposed bond graph, called Singularly Perturbed Bond Graph (SPBG) can be obtained. This SPBG has the property that the storage elements of the fast state and slow state have a derivative and integral causality assignment, respectively. Hence, a quasi steady state model by using SPBG is obtained. A Lemma to determine the junction structure from SPBG is proposed. Finally, the proposed methodology to a classical example of a DC motor and RC network is applied.