Vibration control for flexible mechanical systems with bounded input

The aim of this paper is to develop a boundary control for attenuating the vibration of a flexible beam and string system in the presence of input restriction. To this end, a boundary control is developed to attenuate the vibration and mitigate the effect of the restricted input employing smooth hyperbolic tangent function. Under the proposed control, the stability of the controlled system is achieved through rigorous analysis without resorting to discretization of the system infinite-dimensional model, and the controlled system is ensured to be asymptotically stable. Finally, the simulations verify the results.