Search results for: nonlinear finite element

Authors: Maria de Fátima Lambert

Abstract:

Following previous studies about Writing and Seeing, this paper focuses on the aesthetic assumptions within the concept of Winter Journey (Voyage d’Hiver/Winterreise) both in Georges Perec’s Saga and the Oulipo Group vis-à-vis with the creations by William Kentridge and Michael Borremans. The aesthetic and artistic connections are widespread. Nevertheless, we can identify common poetical principles shared by these different authors, not only according to the notion of ekphrasis, but also following the procedures of contemporary creation in literature and visual arts. The analysis of the ongoing process of the French writers as individuals and as group and the visual artists’ acting might contribute for another crossed definition of contemporary conception. The same title/theme was a challenge and a goal for them. Let’s wonder how deep the concept encouraged them and which symbolic upbringings were directing their poetical achievements. The idea of an inner journey became the main point, and got “over” and “across” a shared path worth to be followed. The authors were chosen due to the resilient contents of their visual and written images, and looking for the reasons that might had driven their conceptual basis to be. In Pérec’s “Winter Journey” as for the following fictions by Jacques Roubaud, Hervé le Tellier, Jacques Jouet and Hugo Vernier (that emerges from Perec’s fiction and becomes a real author) powerful aesthetic and enigmatic reflections grow connected with a poetic (and aesthetic) understanding of Walkscapes. They might be assumed as ironic fictions and poetical drifts. Outstanding from different logics, the overwhelming impact of Winterreise Lied by Schubert after Wilhelm Müller’s poems is a major reference in present authorship creations. Both Perec and Oulipo’s author’s texts are powerfully ekphrastic, although we should not forget they follow goals, frameworks and identities. When acting as a reader, they induce powerful imageries - cinematic or cinematographic - that flow in our minds. It was well-matched with William Kentridge animated video Winter Journey (2014) and the creations (sharing the same title) of Michael Borremans (2014) for the KlaraFestival, Bozar, Cité de la musique, in Belgium. Both were taken by the foremost Schubert’s Winterreise. Several metaphors fulfil new Winter Journeys (or Travels) that were achieved in contemporary art and literature, as it once succeeded in the 19^th century. Maybe the contemporary authors and artists were compelled by the consciousness of nothingness, although outstanding different aesthetics and ontological sources. The unbearable knowledge of the road’s end, and also the urge of fulfilling the void might be a common element to all of them. As Schopenhauer once wrote, after all, Art is the only human subjective power that we can call upon in life. These newer aesthetic meanings, released from these winter journeys are surely open to wider approaches that might happen in other poetic makings to be.

Keywords: Aesthetic, Voyage d’Hiver, Georges Perec & Oulipo, Schubert's Winterreise, William Kentridge & Michael Borremans.

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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