Reduction of friction drag in subsonic flow via feedback control

在研究组的第一个资助期内，子项目3研究了分布参数系统的主动减阻和随后的基于模型的控制策略。首先，将这些方法应用于一维样本系统，然后将它们转移到3D-Navier-Stokes情况。然而，到目前为止，只考虑了稳定的流入条件。这些结果将在第二个供资期间转移到依赖时间的流入条件下。首先，假定控制器已知流入条件。利用这些信息，可以建立开环干扰抑制。在第二步中，该信息将不被提供给控制器。流入条件成为一个未知的扰动，只能通过它对摩擦阻力的影响来确定。因此，工厂模型必须跨越可能流入条件的整个运行范围。对于伴随的模型降阶，除了已经使用的适当的正交分解之外，还研究了生成泛函基的不同方法。这种比较的结果将在下一步中用于建立参数降阶模型。该模型可以从全局基础上构建，也可以从一组局部基础之间的内插构建。控制器应该包括来自该扩展模型的知识。为此，研究了非线性方法和稳健方法。对于后者，减少设计中的保守性的一个想法是结合关于流入条件的概率分布的知识。

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.