Control input separation methods applied to cavity flow

Two control input separation methods for control-oriented reduced-order modeling of flow systems are developed and implemented in a cavity flow experimental facility. The proposed methods are 1) actuated POD expansion with stochastic estimation and 2) optimization on a Hilbert space, respectively. These methods extend the baseline flow model through the use of innovation vectors, which capture the distance of the actuated flow from the baseline space. This technique remedies certain gaps associated with the sub-domain separation method employed in our earlier works by 1) producing models that exactly reduce to baseline case under no input, 2) not requiring an identifiable control region and 3) improving the estimation of the control terms. The methods are evaluated in experiments to test their ability to achieve reconstruction of the flow. Also, the performance of closed loop controllers built from models based on these new techniques are analyzed. It is seen that these controllers perform satisfactorily in terms of resonance peak suppression, and compare favorably over the old one in terms of power consumption.