  We present a data-driven feedforward control to attenuate large transient
lift experienced by an airfoil disturbed by an extreme level of discrete vortex
gust. The current analysis uses a nonlinear machine-learning technique to
compress the high-dimensional flow dynamics onto a low-dimensional manifold.
While the interaction dynamics between the airfoil and extreme vortex gust are
parameterized by its size, gust ratio, and position, the wake responses are
well-captured on this simple manifold. The effect of extreme vortex disturbance
about the undisturbed baseline flows can be extracted in a
physically-interpretable manner. Furthermore, we call on phase-amplitude
reduction to model and control the complex nonlinear extreme aerodynamic flows.
The present phase-amplitude reduction model reveals the sensitivity of the
dynamical system in terms of the phase shift and amplitude change induced by
external forcing with respect to the baseline periodic orbit. By performing the
phase-amplitude analysis for a latent dynamical model identified by sparse
regression, the sensitivity functions of low-dimensionalized aerodynamic flows
for both phase and amplitude are derived. With the phase and amplitude
sensitivity functions, optimal forcing can be determined to quickly suppress
the effect of extreme vortex gusts towards the undisturbed states in a
low-order space. The present optimal flow modification built upon the
machine-learned low-dimensional subspace quickly alleviates the impact of
transient vortex gusts for a variety of extreme aerodynamic scenarios,
providing a potential foundation for flight of small-scale air vehicles in
adverse atmospheric conditions.
