Optimal Feedback Control of Vortex Shedding Using Proper Orthogonal Decomposition Models

Abstract

This paper treats the question of control of two-dimensional incompressible, unsteady wake flow behind a circular cylinder at Reynolds number Re=100. Two finite-dimensional lower order models based on proper orthogonal decomposition (POD) are considered for the control system design. Control action is achieved via cylinder rotation. Linear optimal control theory is used for obtaining stabilizing feedback control systems. An expression for the region of stability of the system is derived. Simulation results for 18-mode POD models obtained using the control function and penalty methods are presented. These results show that in the closed-loop system mode amplitudes asymptotically converge to the chosen equilibrium state for each flow model for large perturbations in the initial states.