Data-driven aeroelastic modeling for control

From insect wings to wind turbines, flows over flexible structures encounter broad operating regimes that may include viscous separated flow and dynamic stall. Effective real-time control of these structures relies on accurate and efficient estimates of unsteady aeroelastic forces. Traditional models, such as Theodorsen's model, typically involve quasi-steady or idealized unsteady aerodynamic forces and do not describe transients. For rigid wings, reduced order unsteady aerodynamic models have recently been extended to include viscous effects at low Reynolds numbers. Here we further extend this modeling procedure to include the effects of a flexible wing, incorporating wing deformation in addition to the quasi-steady forces, added mass forces, and large unsteady transients due to viscous effects. We develop low order linear models based on data from direct numerical simulations of flow past a flexible wing at low Reynolds number. We demonstrate the effectiveness of these models to track an aggressive reference lift maneuver with model predictive control while constraining maximum wing deformation. This modeling procedure could enable agile control for aerodynamic systems with deforming surfaces.