Feedback control of vortex shedding using data driven modelling with minimal sensing

This work details the data-driven modelling and control of vortex shedding past a circular cylinder at Re_D=1000. Training data of velocity magnitude snapshots, generated by 2D unsteady simulations, are used to obtain linear reduced-order state-space models of the system through dynamic mode decomposition with control. Actuators are modelled as opposing wake jets. A Linear Quadratic Gaussian controller is implemented using a Kalman filter with a single direct lift coefficient measurement. The influence of model order on controller performance, whose objective is to minimise lift, is studied. At least a 4th-order model is required to achieve suppression of vortex shedding. Maximum suppression is achieved using 11 modes. Using the Bode Integral Theorem, it is argued that when higher-order models & controllers are deployed (>11), the loop shape of the sensitivity transfer function results in amplification of disturbances at lower frequency passbands, resulting in poorer controller performance. In the best case, using direct lift measurements, an 11 dB reduction in lift variance is achieved, resulting in a 26% reduction in drag, which represents a controller efficiency of 75% compared to complete suppression. Normalised recirculation length (L_R/D) increases from 1.05 to 1.92. The controller rejects external disturbances and sensor noise. The 2D trained controller is validated against a 3D DDES simulation with controller performance dropping to 11.5% drag reduction due to secondary instabilities.