Quasi-steady state model determination for systems with singular perturbations modelled by bond graphs

Abstract

A bond graph model for a singularly perturbed system is presented. This system is characterized by fast and slow dynamics. In addition, the bond graph can have storage elements with derivative and integral causality assignments for both dynamics. When the singular perturbation method is applied, the fast dynamic differential equation degenerates to an algebraic equation; the real roots of this equation can be determined by using another bond graph called singularly perturbed bond graph (SPBG). This SPBG has the characteristic that storage elements of the fast state and slow state have a derivative and integral causality assignment, respectively. Thus, a quasi-steady state model by using SPBG is obtained. A Lemma to get the junction structure from SPBG is proposed. Finally, the proposed methodology is applied to two examples.