Reduced-Order Adaptive Controllers for Fluid Flows Using POD

Authors:
S. S. Ravindran
Affiliations:
Department of Mathematical Sciences, University of Alabama, Huntsville, Alabama 35899/ ravindra@ultra.math.uah.edu/ www.math.uah.edu/ravindra
Venue:
Journal of Scientific Computing
Year:
2000

Citing 6
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Abstract

This article presents a reduced-order adaptive controller design for fluid flows. Frequently, reduced-order models are derived from low-order bases computed by applying proper orthogonal decomposition (POD) on an a priori ensemble of data of the Navier–Stokes model. This reduced-order model is then used to derive a reduced-order controller. The approach discussed here differ from these approaches. It uses an adaptive procedure that improves the reduced-order model by successively updating the ensemble of data. The idea is to begin with an ensemble to form a reduced-order control problem. The resulting control is then applied back to the Navier–Stokes model to generate a new ensemble. This new ensemble then replaces the previous ensemble to derive a new reduced-order model. This iteration is repeated until convergence is achieved. The adaptive reduced-order controllers effectiveness in flow control applications is shown on a recirculation control problem in channel flow using blowing (actuation) on the boundary. Optimal placement for actuators is explored. Numerical implementations and results are provided illustrating the various issues discussed.