Feedback Stabilization of an Oscillating Vertical Cylinder by POD Reduced‐Order Model

The objective of this paper is to demonstrate the use of Reduced‐Order Models (ROM) based on Proper Orthogonal Decomposition (POD) to stabilize by vertical oscillations the flow over a circular cylinder at a Reynolds number equal to 60. Since in Fluid‐Structure Interaction, the POD algorithm cannot be applied directly, we then implement the fictitious domain method of [1] where the solid domain is treated as a fluid undergoing an additional constraint. The POD‐ROM is classically obtained by projecting the Navier‐Stokes equations on a small number of POD modes. The cylinder movement is then enforced in the POD‐ROM through the introduction of Lagrange multipliers. A Linear Quadratic Regulator framework is used to determine the optimal control law, in our case the vertical velocity of the cylinder, such that the flow is stabilized. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)