Feedback control of vortex shedding using a full-order optimal compensator M. Carini a , J.O. Pralits b,n , P. Luchini c a Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano (Campus Bovisa), via La Masa 34, 20156 Milano, Italy b Dipartimento di Ingegneria Civile, Chimica e Ambientale, Università degli Studi di Genova, via Montallegro 1,16145 Genova, Italy c Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, via Ponte don Melillo 1, 84084 Fisciano (SA), Italy article info Article history: Received 9 October 2013 Accepted 30 November 2014 Available online 29 January 2015 Keywords: Vortex shedding Cylinder wake Global instability Optimal control abstract In the present study the linear feedback control of the unsteady cylinder wake is numerically investigated at low Reynolds numbers. The classical small-gain or minimal control energy (MCE) solution of the optimal control and estimation problems is used to design a full-dimensional stabilising compensator of the linearised Navier–Stokes equa- tions, thus bypassing the open-loop model reduction of the fluid plant. For such high- dimensional system, both the feedback and the observer gains are efficiently computed based on the knowledge of the unstable global modes only. The derived control technique provides us with a theoretical analysis tool to investigate the best performance achievable by a ‘perfect’ MCE compensator, i.e. a MCE compensator free from model-reduction errors, on the actual flow field. In our setup, a single-input-single-output (SISO) configuration is considered, the vortex-shedding being controlled by means of the unsteady angular rotation of the cylinder surface with a single velocity sensor located in the wake for the state estimation. For Re ¼ 50 the MCE compensator is able to completely suppress the cylinder vortex shedding, driving the flow from the natural limit cycle to the unstable basic state, which is finally restored. The effects of sensor placement on the compensator performance are then investigated and finally, as Re is increased, the upper bound on the delay of the instability threshold is assessed. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction The control of the vortex shedding occurring in the wake of a bluff body represents a great challenge for many engineering applications. The inherent low frequency unsteadiness of the flow field which results in higher aerodynamic loads, structural vibrations and acoustic noise, can indeed be significantly reduced by means of a suitable control action on the flow. A large number of investigations have been dedicated to this subject and various strategies have been proposed, as documented by the review of Choi et al. (2008). In particular, besides passive devices and open-loop techniques, active feedback controls have gained an increasing attention due to their ability to adapt to the actual flow conditions. So far the flow past a circular cylinder has been established as a model problem for the understanding of bluff-body flow dynamics, thus becoming a classical topic in fluid mechanics. Several feedback control studies aimed at mitigating and suppressing the cylinder vortex shedding have been described in the past literature. In his experiments Roussopoulos (1993) was Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jfs Journal of Fluids and Structures http://dx.doi.org/10.1016/j.jfluidstructs.2014.11.011 0889-9746/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail address: jan.pralits@unige.it (J.O. Pralits). Journal of Fluids and Structures 53 (2015) 15–25