Wandering Subspaces and Reduced Order Models for Flow Control

Abstract

We develop a family of reduced-order models for the modeling and control of a flow system operating under varying fluid and actuation parameters. The parametric subspaces of the reduced-order models are formed by considering the angle between the reduced-order subspaces that span the velocity fields. This grouping is combined with a discrete switching law to form a switched dynamical system composed of a set of reduced-order models. This methodology is applied to the modeling of a lid-driven cavity under varying translation velocities and phase differentials between the upper and lower walls. It is shown that the subspace angle metric successfully partitions the parametric space and provides insight on the dominant parameters that characterize the flow fields. An open-loop simulation of the resulting switched dynamical system demonstrates its ability to capture the evolution of the flow and input parameters as it occurs in the full-order model.