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Modelling in bond graph to obtain reduced models of systems with singular perturbations is applied. This singularly perturbed system is characterized by having three timescales, i.e., slow, medium, and fast dynamics. From a bond graph whose storage elements have an integral causality assignment (BGI), the mathematical model of the complete system can be determined. By assigning a derivative causality assignment to the storage elements for the fast dynamics and maintaining an integral causality assignment for the slow and medium dynamics on the bond graph, reduced models for the slow and medium dynamics are obtained. When a derivative causality to the storage elements for the fast and medium dynamics is assigned and an integral causality assignment to the slow dynamics is applied, the most reduced model is determined. Finally, the proposed methodology to the Ward Leonard system is applied.

The singular perturbations theory for a class of nonlinear systems with a bond graph approach is proposed. Also, the state equation of a class of nonlinear systems with singular perturbations modelled by bond graphs is described. Hence, a new junction structure to get the quasi-steady state model for a class of nonlinear systems is proposed. This junction structure has the fast storage elements in derivative causality and the slow storage elements in integral causality. The proposed methodology is applied to a synchronous machine.