Robust Stabilizing Controllers for a Class of Nonlinear Flexible Mechanical Systems

In this paper, we treat the problem of robustness of stability with respect to unmodelled flexibilities for a class of mechanical systems subject to memoryless feedback controllers. We take a singular perturbation approach and first present some results for the robust stability of a class of nonlinear singularly perturbed systems containing marginally stable boundary systems. Using these results, we present a condition which guarantees that a stabilizing controller whose design is based on a rigidified model of a flexible mechanical system also stabilizes the flexible system, provided that the components, whose flexibilities are neglected in the rigidified model, are sufficiently stiff. This condition involves the location of the rate sensors and is independent of the location of the displacement sensors. The results are illustrated by an example.