Feedback control of vortex shedding using a resolvent-based modelling approach
Bo Jin, Simon J. Illingworth, Richard D. Sandberg
Abstract
An investigation of optimal feedback controllers’ performance and robustness is carried out for vortex shedding behind a two-dimensional cylinder at low Reynolds numbers. To facilitate controller design, we present an efficient modelling approach in which we utilise the resolvent operator to recast the linearised Navier–Stokes equations into an input–output form from which frequency responses can be computed. The difficulty of applying modern control design techniques to high-dimensional flow systems is overcome by using low-order models identified from frequency responses. These low-order models are used to design optimal controllers using , and we demonstrate why the performance of the resulting feedback controllers deteriorates more rapidly with increasing Reynolds number. The challenges of designing robust controllers for each control set-up are also analysed and discussed.