Nonlinear feedback control of the wake past a plate: From a low-order model to a higher-order model

A framework to estimate, with an intelligent and systematic approach, the applicability of a controller derived for a low-order model to a higher-order model is presented. This framework is applied to the test case of nonlinear feedback control of the two-dimensional unsteady separated flow past a plate perpendicular to the free-stream velocity. A hierarchy of models of increasing complexity is generated by using vortex methods. A low-order point vortex model and a high-order vortex blob model are used to simulate the roll-up of the separated shear layer. A nonlinear controller able to manipulate the wake by means of a suction point located on the downstream wall of the plate is given in closed form for the point vortex model. This controller is applied to the vortex blob model by defining a center of circulation. The topological equivalence of the phase spaces of the two models is verified. Finally, the two models are used to simulate the same flows using the same controller and the results are discussed.