Optimal Control of Unsteady Stokes Flow Around a Cylinder and the Sensor/Actuator Placement Problem

摘要

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 colocated 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.