Time Delay in the Lift Response to Actuation and Its Effect on Controller Bandwidth

The transient lift responses of two- and three-dimensional wings subjected to pulse-like disturbances are used to obtain a measure of the separated flow system time delay. Data from different investigators (Amitay{\&}Glezer, 2002, Darabi{\&}Wygnanski, 2004, Williams, et al. 2009) using different wing geometries and different actuators are compared, which show that the transient lift measurements share certain common features. All the data scale with the convective time scale, t+=tU/c. An initial reversal in lift occurs immediately after actuation, which is followed by a rapid growth in lift to reach maximum lift at t+=3. A slow relaxation from maximum lift back to the undisturbed separated flow state occurs by t+=15. The initial lift reversal is associated with a time delay in the plant (separated flow system.) The time delay is related to the formation of a leading edge vortex and its convection time. The transient lift time delay limits the bandwidth for a given control architecture, which results in two important implications. First there is a practical upper limit for actuator bandwidth, and second, a different control architecture will be necessary to achieve closed-loop control on the shorter fluid-dynamic time scales.