Control Issues in Reduced-Order Feedback Flow Control

Technological advances in sensors, actuators, on-board computational capability, modeling and control sciences have offered a possibility of seriously considering closed-loop flow control for practical applications. We can now attempt to address problems that have over the years not been effectively been solved using passive means and /or open-loop techniques. The main strategies to closed-loop control are a model-independent approach, a full-order optimal control approach based on the Navier Stokes solution and a reduced order model strategy. The current effort emphasizes methodology based on low-dimensional, proper orthogonal decomposition applied to the suppression of periodic vortex shedding in the wake of a circular cylinder. Focus is on the validity of the low-dimensional model, selection of the important modes that need representation, incorporation of an ensemble of snapshots that reflect vital transient phenomena, selection of sensor placement and number, and linear stochastic estimation for mapping of sensor data onto modal information. Furthermore, additional issues surveyed include observability, controllability and stability of the closed-loop systems based on low-dimensional models. Examples based on computational and experimental studies on the cylinder wake benchmark are presented to illuminate some of the important issues. We achieved a drag reduction of close to 90% of the vortex-induced drag, and lowered the unsteady lift force by the same amount. Finally, the paper summarizes some of the important lessons learned and notes on open issues for future research. Nomenclature