Natural observers for singularly perturbed mechanical systems

In this note, we consider vector second order mechanical systems having fast sensor dynamics, and the objective is to obtain accurate estimates of the unmeasurable slow system state variables that are generated by an appropriately designed model-based observer. Using a singular perturbation framework, the proposed observer is designed using the system dynamics that evolves on the slow manifold, and the dynamic behavior of the resulting estimation error is analyzed in the presence of the unmodel led fast sensor dynamics. We show that the observation error generated by neglecting the (unmodeled) fast sensor dynamics is of order 0(e), where e is the singular perturbation parameter and a measure of the relative speed/time-constant of the fast (sensor) and the slow component (vector second-order system) of the overall system dynamics. The performance of the proposed natural observer is evaluated in an example of a two-degree of freedom mechanical system.