Data-Driven Controller Design and Sensor Selection for Flow Around a Circular Cylinder

We propose a data-driven method to design feedback controllers and select sensor positions for real-time particle image velocimetry (PIV). The proposed method is divided into two steps. First, we acquire data of an optimal feedback controller that is designed based on the Navier-Stokes equations. Second, we derive a sparse map between the flow velocity field and the optimal control input from the data. The sparse map is regarded as a real-time feedback controller. This feedback controller uses information of the flow velocity at so a few points that PIV processing can be implemented in real time. The processing points are selected via a greedy algorithm that is developed for a simultaneous optimization problem of controller gain and processing point positions. The greedy algorithm takes into account that PIV measures two components of a flow velocity vector per processing point. We deal with a benchmark problem of flow around a circular cylinder at the Reynolds number 100 to verify the effectiveness of the proposed method. A numerical simulation reveals that a controller that is designed with the proposed method successfully mitigates vortex shedding by the feedback of the flow velocity at only a few dozen points.