Experimental Results and Bifurcation Analysis on Scaled Feedback Control for Subsonic Cavity Flows

In this paper, we present the latest results of our ongoing research activities in the development of reduced-order models based feedback control of subsonic cavity flows. The model was developed using the proper orthogonal decomposition of particle image velocimetry images in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. Stochastic estimation method was used to obtain the state estimation of the Galerkin system from real time surface pressure measurements. A linear-quadratic optimal controller was designed to reduce cavity flow resonance and tested in the experiments. Real-time implementation shows a significant reduction of the sound pressure level within the cavity, with a remarkable attenuation of the resonant tone and a redistribution of the energy into various modes with lower energy levels. A mathematical analysis of the performance of the LQ control, in agreement with the experimental results, is presented and discussed