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Journal of Vibration and Control
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Nonlinear State Observation for Cable Dynamics

Lucia Faravelli

Department of Structural Mechanics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy, lucia{at}dipmec.unipv.it

Filippo Ubertini

Department of Structural Mechanics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy, filippo.ubertini{at}unipv.it

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.

Key Words: Non-linear observer • state estimation • non-linear cables • feedback control.

This version was published on July 1, 2009

Journal of Vibration and Control, Vol. 15, No. 7, 1049-1077 (2009)
DOI: 10.1177/1077546308094253
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