  Aeroelastic structures, from insect wings to wind turbine blades, experience
transient unsteady aerodynamic loads that are coupled to their motion.
Effective real-time control of flexible structures relies on accurate and
efficient predictions of both the unsteady aeroelastic forces and airfoil
deformation. For rigid wings, classical unsteady aerodynamic models have
recently been reformulated in state-space for control and extended to include
viscous effects. Here we further extend this modeling framework to include the
deformation of a flexible wing in addition to the quasi-steady, added mass, and
unsteady viscous forces. 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 aggressive
maneuvers with model predictive control while constraining maximum wing
deformation. This system identification approach provides an interpretable,
accurate, and low-dimensional representation of an aeroelastic system that can
aid in system and controller design for applications where transients play an
important role.
