Reduced order model for feedback control of cavity flow - The effects of control input separation

Abstract

This work is focused on the development of a new control separation approach for reduced-order model based feedback control and its implementation in subsonic cavity flows. The model is derived by applying Proper Orthogonal Decomposition in conjunction with Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. The new method adds the effect of the control input as an additional set of basis. The model is derived for the baseline and a forced flow condition. When the new model was tested numerically, the new separation method showed noticeable changes when the control input was introduced into the system. A feedback controller based on the LQR methodology was designed and tested experimentally in the GDTL subsonic cavity flow facility of The Ohio State University. For control design, 4 modes were sufficient to capture the main features of the cavity flow. While experimental result showed that the new separation approach has similar effect on the flow behavior as our previous approach, we believe that the new methodology is a more suitable procedure for deriving control-oriented models. Furthermore, the new model does not require identification of the control input region in the data used to derive the reduced order model, which is not possible in many flow control applications.