  This paper presents advances towards the data-based control of periodic
oscillator flows, from their fully-developed regime to their equilibrium
stabilized in closed-loop, with linear time-invariant (LTI) controllers. The
proposed approach directly builds upon Leclercq et al. (2019) and provides
several improvements for an efficient online implementation, aimed at being
applicable in experiments. First, we use input-output data to construct an LTI
mean transfer functions of the flow. The model is subsequently used for the
design of an LTI controller with Linear Quadratic Gaussian (LQG) synthesis,
that is practical to automate online. Then, using the controller in a feedback
loop, the flow shifts in phase space and oscillations are damped. The procedure
is repeated until equilibrium is reached, by stacking controllers and
performing balanced truncation to deal with the increasing order of the
compound controller. In this article, we illustrate the method on the classic
flow past a cylinder at Reynolds number Re=100. Care has been taken such that
the method may be fully automated and hopefully used as a valuable tool in a
forthcoming experiment.
