Low-Dimensional Models for Feedback Flow Control. Part I: Empirical Galerkin Models

Abstract

A o w model which is accessible to control design must combine low dimension, robustness and a simple structure with an ample dynamic range to cover controlled transients. Key enablers are reviewed in the context of empirical Galerkin models and are exemplied for incompressible shear o ws. These enablers include ‘subgrid’ turbulence and pressure representations, hybrid models that combine multiple operating points, and actuation models. The range of model validity is identied in terms of invariant manifolds which can be exploited by observer design and has to be respected by controller design.