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Intersection Problem (intersection + problem)
Selected AbstractsClosed-loop identification of the time-varying dynamics of variable-speed wind turbinesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2009J. W. van Wingerden Abstract The trend with offshore wind turbines is to increase the rotor diameter as much as possible to decrease the costs per kWh. The increasing dimensions have led to the relative increase in the loads on the wind turbine structure. Because of the increasing rotor size and the spatial load variations along the blade, it is necessary to react to turbulence in a more detailed way: each blade separately and at several separate radial distances. This combined with the strong nonlinear behavior of wind turbines motivates the need for accurate linear parameter-varying (LPV) models for which advanced control synthesis techniques exist within the robust control framework. In this paper we present a closed-loop LPV identification algorithm that uses dedicated scheduling sequences to identify the rotational dynamics of a wind turbine. We assume that the system undergoes the same time variation several times, which makes it possible to use time-invariant identification methods as the input and the output data are chosen from the same point in the variation of the system. We use time-invariant techniques to identify a number of extended observability matrices and state sequences that are inherent to subspace identification identified in a different state basis. We show that by formulating an intersection problem all states can be reconstructed in a general state basis from which the system matrices can be estimated. The novel algorithm is applied on a wind turbine model operating in closed loop. Copyright © 2008 John Wiley & Sons, Ltd. [source] Mixing symbolic and numerical approaches for the surface-to-surface intersection problemPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Mario Fioravanti This paper shows how the efficiency of the current methodologies applied to the surface-to-surface intersection problem can be improved by combining an algebraic/symbolic framework with efficient and robust numerical techniques. The algebraic/symbolic framework is used to translate the computation of resultants, subresultants, discriminants, etc. to one or several generalized eigenvalue problems and SVD computations. The framework requires only the values of the involved polynomials at some set of points, and it will guide the numerical computations, providing thus a certificate of the topological correctness of the output. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On the Floer homology of cotangent bundlesCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2006Alberto Abbondandolo This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T* M of a compact orientable manifold M. The first result is a new L, estimate for the solutions of the Floer equation, which allows us to deal with a larger,and more natural,class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Floer homology and the singular homology of the free loop space of M in the periodic case, or of the based loop space of M in the Lagrangian intersection problem. The idea for the construction of such an isomorphism is to consider a Hamiltonian that is the Legendre transform of a Lagrangian on T M and to construct an isomorphism between the Floer complex and the Morse complex of the classical Lagrangian action functional on the space of W1,2 free or based loops on M. © 2005 Wiley Periodicals, Inc. [source] | ||||||||||