Control input separation methods for reduced-order model-based feedback flow control

First-principle-based models of the dynamics of flow systems are often of limited use for model-based control design, not only because of their nonlinear and infinite-dimensional nature, but also because the control input is generally specified as a boundary condition. Proper orthogonal decomposition and Galerkin projection are among the most effective and commonly used methods to obtain reduced-order models of flow dynamics. However, the final form of these models may not account for the presence of a forcing or control input. From a control design perspective, it is desirable to obtain a reduced-order model in which the control input appears explicitly in the dynamic equations. In this paper, two methods for control input separation are introduced and comparatively evaluated in experimentally based reduced-order modeling of cavity flow, both in their ability to reconstruct the forced flowfield and to provide models suitable for feedback control design. The proposed methods, namely, 1) actuated proper orthogonal decomposition expansion and 2) L-2 optimization, extend the baseline flow model through the use of innovation vectors, which capture the deviation of the actuated flow from the baseline space. The new methods address some of the issues associated with the subdomain separation technique employed in our previous works. Linear-quadratic regulator controllers, built using models obtained from the new methods, have been tested on a cavity flow experiment. Although the new models perform satisfactorily and comparably to our previous models in terms of suppression of cavity tones, they offer a substantial advantage in terms of the required input power to achieve a similar or better performance.