Feedback stabilization of an oscillating vertical cylinder by POD Reduced-Order Model

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Tissot, Gilles^1 ; Cordier, Laurent^1 ; Noack, Bernd R.^1

PPRIME Institute, CEAT, 43 route de l'aérodrome, Poitiers

86036, France^1

关键词: 2D Navier Stokes equations;    Feedback stabilization;    Fictitious domain method;    Generalized algebraic riccati equations;    Linear feedback gain;    Linear quadratic regulator;    Optimal feedback control;    Proper orthogonal decompositions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012137/pdf
DOI  :  10.1088/1742-6596/574/1/012137

来源: IOP

【 摘 要 】

The objective is to demonstrate the use of reduced-order models (ROM) based on proper orthogonal decomposition (POD) to stabilize the flow over a vertically oscillating circular cylinder in the laminar regime (Reynolds number equal to 60). The 2D Navier-Stokes equations are first solved with a finite element method, in which the moving cylinder is introduced via an ALE method. Since in fluid-structure interaction, the POD algorithm cannot be applied directly, we implemented the fictitious domain method of Glowinski et al. [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 onto the first POD modes. At this level, the cylinder displacement is enforced in the POD-ROM through the introduction of Lagrange multipliers. For determining the optimal vertical velocity of the cylinder, a linear quadratic regulator framework is employed. After linearization of the POD-ROM around the steady flow state, the optimal linear feedback gain is obtained as solution of a generalized algebraic Riccati equation. Finally, when the optimal feedback control is applied, it is shown that the flow converges rapidly to the steady state. In addition, a vanishing control is obtained proving the efficiency of the control approach.