Quasi-steady-state model of a class of nonlinear singularly perturbed system in a bond graph approach

A particular class of nonlinear singularly perturbed systems by using a bond graph approach is proposed. The class of nonlinear systems is defined by terms of product of state variables whose bond graph representation is described by MTF or MGY elements modulated by state variables. The singular pertubations applied to the system permit the separation of time scales. When the assumptions of Tikhonov Theorem are satisfied, then a new bond graph called singularly perturbed nonlinear bond graph (SPNBG) to determine the quasi-steady-state model of the system is presented. The SPNBG is characterized by having an integral causality assignment for the storage elements that represent the slow dynamics, and the storage elements of the fast dynamics have a derivative causality assignment. Finally, the proposed methodology is applied to an illustrative example.