Reduced-order modeling and feedback control of a flexible wing at low Reynolds numbers

A state-space reduced-order model for the lift generated by the unsteady deflection of a two-dimensional flexible wing is presented. The wing’s deflection is decomposed using a truncated Fourier series in the contribution of single deflection modes; the global lift is then obtained using superposition. The presented model is an extension of the model introduced in Brunton et al. (2013) for rigid pitching and plunging. A realization of the model is obtained using lift pulse responses from Direct Numerical Simulation (DNS) at a Reynolds number of 100. The performance of the deflection modes are discussed from a feedback control point of view and controllers for mode 1, mode 2 and pitching are designed using loop-shaping techniques and tested, comparing the results with DNS. The performance limitations of mode 1 and mode 2 are overcome by using a multi-input controller that uses both deflection modes together. Finally, the controllers are tested in an off-design condition at a higher Reynolds number of 1000.