Gust mitigation of a plunging-pitching airfoil by an adjoint-based approach

Gust encounters during the flight of Micro-air vehicles (MAVs) can be detrimental and an effective method for gust mitigation is highly desirable to help MAVs operating under extreme conditions. In this study, facing the problem's large control space, an adjoint-based approach is developed to achieve the gust mitigation of a heaving-pitching airfoil. Two kinds of gust are considered: the horizontal gust by changing the velocity of incoming flow, and the vertical gust by inducing an additional flow from the bottom. Mitigation is realized by first designing an objective function to assess force difference before and after gusts, then using an adjoint-based approach to minimize the function. Two different adjoint-based algorithms are developed: one uses direct numerical simulation (DNS) and its adjoint simulation of an incompressible flow, and the other uses a Galerkin-projection reduced-order model (ROM) and its adjoint ROM. It is shown that both adjoint-based algorithms can effectively mitigate the influence of gusts by tuning the motion of airfoil accordingly. The adjoint-based DNS algorithm is a high-fidelity method with reasonable computational cost, and the adjoint-based ROM algorithm is a low-fidelity method but its online computation is fast enough for real-time control.