Abstract
Effective placement of sensors and actuators is of crucial importance in flow control. Instead of using combinatorial search to identify optimal locations, we pose a related problem of polynomial complexity. If one could sense everything and actuate everywhere, what should one do? Using the unsteady 2D Stokes flow around a cylinder as an example, we obtain the analytic solution of an optimal distributed control problem and describe its spatial structure. At low circumferential wavenumbers or close to the cylinder wall, boundary vortex generators are shown to be more effective than collocated vorticity damping. This analytic solution has also been used to test numerical methods, demonstrating the importance of using discretization which resolves all eigenfunctions of interest.
This research was partially supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1–19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), M/S 403, NASA Langley Research Center, Hampton, VA,23681–0001.
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Lončarić, J. (1998). Sensor/Actuator Placement via Optimal Distributed Control of Exterior Stokes Flow. In: Borggaard, J., Burns, J., Cliff, E., Schreck, S. (eds) Computational Methods for Optimal Design and Control. Progress in Systems and Control Theory, vol 24. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1780-0_17
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DOI: https://doi.org/10.1007/978-1-4612-1780-0_17
Publisher Name: Birkhäuser, Boston, MA
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