Control of Wing Stroke Plane Angle for Stabilizing of a Hovering Flapping-Wing Air Vehicle

Abstract

The wing stroke plane angle is chosen as an effective control parameter to stabilize unstable longitudinal flight dynamics of a hovering flapping-wing air vehicle. The numerical model of such a hovering flapper is based on the hawkmoth Manduca sexta because its morphology, aerodynamics, wing kinematics and flight mechanics are well-known for flight simulation. To conduct a linear stability analysis, the linear time-invariant system model of the hovering flapping-wing air vehicle is successfully established by applying both small perturbation theory and cycle-averaging theory to full nonlinear equations of motion at trim. The linearized model is verified by comparing the linear response with the response obtained by the direct time integration of the original nonlinear model. Due to the negative values of stability derivatives in diagonal of the system matrix, small disturbances of the body velocity passively disappear without any additional control from the trimmed wing kinematics. Unlike tailed conventional aircrafts, the absence of the longitudinal static stability makes overall longitudinal flight dynamics of the hovering flapper unstable. A full-state feedback controller stabilizing such an unstable system is designed using the linearized system model. The closedloop response of the hovering flapping-wing air vehicle is obtained using the original nonlinear model to see the performance of the designed controller. A relative rotational motion of the stroke plane with respect to the body turns out to be one of the effective control efforts for the stabilization of the hovering flapper; in the closed-loop response, the stroke plane angle is kept almost the same in the cycle-averaged mean sense with respect to the horizontal plane.