  Reactive flow control has been shown as a promising tool to improve, among
other aspects, the aerodynamic characteristics of an aircraft. This paper
focuses on the use of reactive flow control to attenuate Tollmien-Schlichting
(TS) waves over a wing profile. TS waves are an instability mechanism that is
one of the first stages of boundary layer transition to turbulence. The
Wiener-Hopf technique was used in this work for the experimental boundary layer
control. The approach improves previous wave-cancellation techniques that, by
constructing control kernels in the frequency domain, lead to control kernels
with a non-causal part, i.e., actuation would need future sensor information to
be constructed. In practical applications, it is unfeasible to access this type
of information. Ignoring the non-causal part of the kernel leads to suboptimal
solutions that might significantly degrade the performance of the controller.
The Wiener-Hopf formalism allows us to take into account causality constraints
in the formulation of the control problem, leading to an optimal realistic
solution and a control kernel that is causal by construction. Moreover, it is
possible to construct the control strategy based only on the power and
cross-spectra obtained experimentally, in a data-driven approach. The present
work shows how to apply experimentally the Wiener-Hopf resolvent-based
formalism using signals from a wind tunnel experiment, demonstrating that the
Tollmien-Schlichting waves can be effectively attenuated via a Wiener-Hopf
based controller, which yielded better results than a typical wave-cancellation
approach.
