  This work deals with the closed-loop control of streaky structures induced by
free-stream turbulence in a zero-pressure gradient, transitional boundary
layer, by means of localized sensors and actuators. A linear quadratic gaussian
regulator is considered along with a system identification technique to build
reduced-order models for control. Three actuators are developed with different
spatial supports, corresponding to a baseline shape with only vertical forcing,
and to two other shapes obtained by different optimization procedures. A
computationally efficient method is derived to obtain an actuator which aims to
induce the exact structures which are inside the boundary layer, given in terms
of their first spectral proper orthogonal decomposition mode, and an actuator
that maximizes the energy of induced downstream structures. Two free-stream
turbulence levels were evaluated, corresponding to 3.0% and 3.5%, and
closed-loop control is applied in large-eddy simulations of transitional
boundary layers. All three actuators lead to significant delays in the
transition to turbulence and were shown to be robust to mild variations in the
free-stream turbulence levels. Differences are understood in terms of the SPOD
of actuation and FST-induced fields along with the causality of the control
scheme. The actuator optimized to generate the leading downstream SPOD mode,
representing the streaks in the open-loop flow, leads to the highest transition
delay, which can be understood due to its capability of closely cancelling
structures in the boundary layer. However, it is shown that even with the
actuator located downstream of the input measurement it may become impossible
to cancel incoming disturbances in a causal way, depending on the wall-normal
position of the output and on the actuator considered, which limits sensor and
actuator placement capable of good closed-loop performance.
