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International Journal of Aerospace Engineering
Volume 2012, Article ID 860510, 12 pages
Research Article

On Singular Perturbations of Flexible and Variable-Speed Wind Turbines

1Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
2Team Modelling and Simulation of Mechanical Systems, Faculty of Sciences at Tetouan, University Abdelmalek Essaadi, BP 2121, M’Hannech, 93002 Tetouan, Morocco

Received 31 October 2011; Accepted 5 February 2012

Academic Editor: Paul Williams

Copyright © 2012 R. Oulad Ben Zarouala et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A model for the mechanical dynamics of a wind turbine is developed, which is the composition of three physical mechanisms: flexion, torsion, and rotational dynamics. A first contribution is the identification of the essential physical parameters that provide a time-scale separation of these three mechanisms. Under the assumption of singular perturbations the time-scale separation allows to work with a reduced model of order one. This reduction has been essential for the control of this system allowing to control designers to take into account only the reduced-order model. A second contribution consists in employing a measurement of the fore-aft nacelle acceleration with the reduced model, together with a Kalman filter to estimate the flexible DOFs of the system (tower and average blade deflection). The successful approach is tested on high-order nonlinear aeroelastic simulator (FAST).