Reduction of friction drag in subsonic flow via feedback control

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During the first funding period of the research group ¿Active drag reduction via wavy surface oscillation¿ model reduction for distributed parameter systems and subsequent model based control strategies have been investigated by subproject 3. First, the methods were applied to onedimensional sample systems and then, they have been transferred to the 3D-Navier-Stokes case. However, only steady inflow conditions have been considered so far. These results are to be transferred to time dependent inflow conditions in the second funding period. At first, the inflow conditions are assumed to be known to the controller. Using this information an open-loop disturbance rejection can be established. In a second step, this information will not be provided to the controller. The inflow condition becomes an unknown disturbance, which can be only determined from its influence on the friction drag. Thus, the plant model has to span the whole operating range of possible inflow conditions. For the accompanying model reduction, different methods to generate a functional basis are investigated additionally to the Proper Orthogonal Decomposition, which has already been used. The results from this comparison are used in the next step to set up a parametric reduced-order model. This model can either be built from a global basis or from an interpolation between set of local bases. The controller should include the knowledge from this extended model. For this purpose, nonlinear methods are investigated as well as robust approaches. For the latter, one idea to reduce the conservatism in the design is to incorporate knowledge about the probability distribution of the inflow condition.