Optimal bang-bang control of a mechanical double oscillator using averaging methods

Abstract : This paper considers a semi-active Tuned Liquid Column Damper (TLCD) designed to damp a Floating Wind Turbine (FWT). This device contains a choke that can be controlled to damp the natural oscillations created by ocean waves on the FWT. The choke, which controls the flow inside the TLCD, defines, by construction, an input variable having bounded values (the restriction). These limitations spur an interest in optimal control strategies for this oscillating system subject to a sinusoidal wave. These strategies are the subject of the paper. First, we numerically solve an optimal control problem of interests for the application. When computed over long time horizons, the resulting control signal appears to be of periodic nature. To confirm this fact, we employ averaging methods on a simplified model. This study confirms that the optimal control is bang-bang, is periodic, and its frequency is the double of the incoming wave frequency.
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Christophe Coudurier, Olivier Lepreux, Nicolas Petit. Optimal bang-bang control of a mechanical double oscillator using averaging methods. 9th Vienna International Conference on Mathematical Modelling, Feb 2018, Vienne, Austria. pp.49 - 54, ⟨10.1016/j.ifacol.2018.03.009⟩. ⟨hal-01886007⟩

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