Dynamic hysteresis control of lift on a pitching wing

Dynamic hysteresis appearing in the lift force during pitching maneuvers is distinctly different from conventional static hysteresis. The size and shape of dynamic hysteresis loops are dependent on the degree of flow attachment, the dimensionless pitching frequency, and two time delays associated with the flow separation process. A linearized version of the Goman–Khrabrov model is derived and shown to capture the dynamic hysteresis characteristics when the pitching amplitude is small. Closed-loop control using a linearized version of the Goman–Khrabrov model is demonstrated, which incorporates a disturbance model into the feed-forward controller. The controller is shown to reduce the dynamic hysteresis during periodic pitching, step-up and step-down maneuvers, and quasi-random pitching maneuvers.