Reduced Order Modeling for Feedback Control of a Flexible Wing at Low Reynolds Numbers

A variety of unsteady aerodynamic models for a twodimensional rigid plate undergoing pitching and plunging motion is present in the literature. For a two-dimensional flexible wing, unsteady forces are generated by the wing deflection in time. Hence the necessity of unsteady models that also take into account the flexible degrees of freedom of the wing. In the present work, the deflection of a flexible wing immersed in a uniform free-stream has been decomposed using a truncated Fourier series. The effects of a prescribed deflection of the flexible wing on the flowfield in terms of each one of the leading modes (from 1 to 10) have been investigated using high-fidelity Direct Numerical Simulation (DNS) for viscous, compressible flows at low Reynolds numbers. System identification techniques are applied to obtain reduced order state-space models that relate the deflection of the wing to the measured lift. The system identification procedure is presented and the accuracy and validity of the reduced order models are discussed. Finally, the characteristics and the performance of the reduced order models are addressed from a feedback control point of view.