Optimal Cyclic Control of a Structurally Constrained Span-Morphing Underwater Kite in a Spatiotemporally Varying Flow

This work presents a control methodology for maximizing the net power generated by an underwater kite capable of adjusting wingspan in real time. Underwater kite systems generate energy by performing cross-current figure-eight flight maneuvers while tethered to a winch system. These systems generate net positive power through cyclic spooling: spooling out under high-tension cross-current flight and spooling in radially under low tension. In the presence of structural constraints, simultaneous variation in the kite's angle of attack and span is superior to simply reducing the angle of attack in order to stay within permissible structural loading. Furthermore, the optimal combination of these variables depends on the amount of tether spooled out and the spatiotemporally-varying flow field. Leveraging a multi-degree-of-freedom model previously developed by the authors, the performance of three kites- two with fixed span and one with variable span - was compared. To maximize the performance of the modeled kites, an optimal control framework was developed. For the fixed-span case, spool-out speeds and mean elevation angles for the kite were optimized to maximize energy generation over a spool-out cycle. For the morphing span case, spool-out speeds, mean elevation angle, and wingspan were optimized to maximize energy generation over a spool-out cycle while considering the energetic cost of morphing. Simulation results show that the kite capable of span-morphing generated 38.7% more energy than a fixed-span kite of maximum allowable span and 13.2% more energy than a kite of the optimal fixed-span.