A bond graph model for a closed-loop linear time invariant multiple input multiple output system with singular perturbations is presented. This system is formed by a plant, an observer and the feedback. Hence, the storage elements that represent the slow dynamics of the observer determine the feedback control. Also, a junction structure of the bond graph model for the closed-loop system with singular perturbations is proposed. A new bond graph to obtain the observer and controller gains of the closed-loop system is presented. This new bond graph has the characteristic that storage elements of the fast dynamics and slow dynamics have a derivative and integral causality assignment, respectively. Thus, a quasi-steady state model of a singularly perturbed system with a slow state estimated feedback is obtained. Finally, the proposed methodology is applied to an illustrative example.
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