Estimation of shallow-cable states for active feedback control

A non-collocated active feedback control strategy to reduce the spatial vibrations of suspended cables is proposed. The technical relevance of this problem is represented by the need of reducing the risk of fatigue ruptures, caused by large amplitude vibrations. Devices mounted transversely to the cable in the two directions, close to one of its ends, supply the feedback control actions. A proportional derivative control law is adopted, based on the observation of two in-plane and two out-of-plane modal amplitudes. A nonlinear state observer is designed in order to estimate the necessary modal amplitudes to be employed in the feedback control law. The observer is written in closed form, based on reduced Galerkin models of the cable. A discussion on minimal number of observations and asymptotic stability of the observer is performed at rst. Afterwards numerical simulations are carried out in order to test the eectiveness of the proposed control strategy to reduce the spatial vibrations of the cable. Both free and forced vibrations are considered in the analysis.