Experimental control of Tollmien-Schlichting waves using the Wiener-Hopf formalism*

Sensor and actuator arrangement may lead to a control law that depends on future sensor readings, and such information is not available in a real-time application. When the non-causal part of the control kernel is substantial, simply truncating the kernel to its causal part implies in suboptimal solutions that can result in a considerable degradation of the control. Optimal causal control (and estimation) laws can be obtained using the Wiener-Hopf formalism by imposing causality in the quadratic cost functional to be minimized. This technique has been used in this work for the experimental control of Tollmien-Schlichting (TS) waves over a NACA 0008 wing profile at zero angle of attack and freestream velocity of 10 m/s. A loudspeaker is used to trigger the TS waves, measurements are performed using microphones and the attenuation of the TS waves is accomplished with a plasma actuator. Experimental results show that the Wiener-Hopf technique can be successfully applied for the control of TS waves. It was also observed that as the actuator moves upstream a significant better performance can be obtained with the Wiener-Hopf technique compared to the truncated solution.