Effective sensor placements for the estimation of proper orthogonal decomposition mode coefficients in von Karman vortex street

For feedback control using low-dimensional proper orthogonal decomposition (POD) models, the mode amplitudes of the POD mode coefficients need to be estimated based on sensor readings. This paper is aimed at suppressing the von Klrman vortex street in the wake of a circular cylinder using a low-dimensional approach based on POD. We compare sensor placement methods based on the spatial distribution of the POD modes to arbitrary ad hoc methods. Flow field data were obtained from Navier-Stokes simulation as well as particle image velocimetry (PIV) measurements. A low-dimensional POD was applied to the snapshot ensembles from the experiment and simulation. Linear stochastic estimation was used to map the sensor readings of the velocity field on the POD mode coefficients. We studied 53 sensor placement configurations, 32 of which were based on POD eigenfunctions and the others using ad hoc methods. The effectiveness of the sensor configurations was investigated at Re = 100 for the computational fluid dynamic data, and for a Reynolds number range of 82-99 for the water tunnel PIV data. Results show that a five-sensor configuration can keep the root mean square estimation error, for the amplitudes of the first two modes to within 4% for simulation data and within 10% for the PIV data. This level of error is acceptable for a moderately robust controller. The POD-based design was found to be simpler, more effective, and robust compared to the ad hoc methods examined.