Nonlinear state observation for cable dynamics

We explore the applicability of non-linear state observation to cable dynamics. The aim is to capture from the minimal number of measurements a larger description of the state to be employed in active or semi-active control policies. To this end, a non-linear state observer is designed analytically, in the space of modal amplitudes, following relevant literature results. The main theory of non-linear state observation is preliminary reviewed and the applicability to the dynamics of structural cables is discussed, including asymptotic stability and minimal number of measurements. Next a sample non-resonant cable is considered and numerical simulations are carried out in order to test the observation error stability under different conditions. A non-collocated feedback control strategy, based on transversal actuation, is finally considered, in which the control algorithm is based on the estimated state variables. The with-observer control solution is compared with the ideal case in which the entire state of the system is known, thus highlighting the limits and potentialities of the proposed approach.