Tuned POD Galerkin models for transient feedback regulation of the cylinder wake

Proper orthogonal decomposition (POD) Galerkin models are typically obtained from a single reference, such as an attractor. The POD model provides a very efficient representation of the reference but is often incapable to handle transient dynamics and other changes in flow conditions. These shortcomings are detrimental in feedback flow control applications. A novel concept of tuned Galerkin models is suggested, by which the global model interpolates a succession of similar-structure local models. The tuned model covers a controlled transient manifold, compensating for the gradual deformation of dominant flow structures, along such transients. The model is an enabler for both improved tracking performance, as well as for optimized control hardware placement, taking into account the entire dynamic range of interest. These concepts are demonstrated in the benchmark of stabilization of the wake flow behind a circular cylinder.