Computational issues in nonlinear cables observation

In this paper a nonlinear state observer for suspended cables is developed. The aim is to estimate both in-plane and out-of-plane cable states, to be adopted in a feedback control action. The observer is written in closed form, based on reduced Galerkin models of the cable. The external excitation is identified as the harmonic motion of one cable support. A discussion on minimal number of observations and asymptotic stability of the observer is performed at first. Afterwards the derivation of the necessary terms of the observer is shown, in a suitably dimensional Galerkin cable model. Numerical simulations are then performed with a variable order Runge-Kutta implicit method, to test the efficiency of the observer. Regions of error instability are evidenced and linked to the time integration scheme and to the region of external excitation. Particular attention is posed to the ability of the observer to follow bifurcated branches and multimodal cable motions.