Optimal feedback control of vortex shedding using proper orthogonal decomposition models

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 decomp osition (POD) are considered for the control system design. Control action is achieved via cylinder rotation. Linear optimal control theory is used fo r obtaining stabilizing feedback control systems. Ali expression for the re gion of stability of the system is derived. Simulation results for 18-mode POD models obtained using the control,function and penalty methods are pres ented. These results show that ill the closed-loop system mode amplitudes a symptotically Converge to the chosen equilibrium state for each flow model for large perturbations in the initial states.