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Descripción
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| Recently, some kind of control schemes via extended time-delay feebback has been carried out in different situation of physical or engineering interes. In all of them the main goal is the stabilization of unstable periodic orbits in low-dimensional dynamical systems. The origin of the unstable character should be found in different sources, depending on the case considered. However, the maximum effort are devoted to control chaotic system. One example of this kind of analysis can be found in [1] for a one degree of freedom system. There, a control low is described that can be used to stabilize the libration of a gravity-gradient satellite which is in an elliptical orbit. The libration dynamics of this kind of satellites is self-excited and in some regions of the parameter space strongly chaotic. Any electrodynamic tether working in an inclined orbit is affected by a dynamic instability generated by the continuos pumping of energy from electromagnetic forces into the tether attitude motion.The analysis carried out until now show that the instability source is a non linear resonance mechanism that pumps energy continually into the system. Thus, the attitude motion of the tether relative to the orbital frame becomes unstable after several orbits. This mechanism is different from others considered in the literature which are associated to chaotic motions but without a continually increase of the total energy of the system. This is probably the reason why the time-delayed feedback does not work in the case of the rigid tether. In order to overcome the difficulties associated with this instability, a new control scheme has been analyzed in this paper. The background strategy is as follows: we add appropriate forces to the system with the aim of converting an unstable periodic orbit of the governing equations into an asymptotically stable one. The idea is to take such a stabilized periodic orbit as the starting point for the operation of the electrodynamic tether. We use an extended time-delay feedback control scheme which has been used successfully in problems with one degree of freedom. In order to obtain results with broad validity, some simplifying assumptions have been introduced in the analysis. Thus, we assume a rigid tether with two end masses orbiting along a circular, inclined orbit. We also assume a constant tether current which does not depend on the attitude and orbital position of the tether. The Earth's magnetic field is modeled as a dipole aligned with the Earth's rotation axis. | |
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Internacional
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Si |
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Nombre congreso
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The 2007 AAS/AIAA Space Flight Mechanics Meeting |
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Tipo de participación
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960 |
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Lugar del congreso
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Sedona, Arizona (USA) |
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Revisores
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No |
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ISBN o ISSN
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978-0-87703-541 |
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DOI
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Fecha inicio congreso
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28/01/2007 |
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Fecha fin congreso
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01/02/2007 |
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