Dynamic Flight Stability of a Hovering Flapping-Rotary-Wing Vehicle

The aerodynamic performance and mechanisms of the compound layout of flapping-rotary-wing (FRW) vehicles have been studied extensively in the literature, but open-loop stability has rarely been involved. To bridge this gap, a hovering stability analysis of a 30 g FRW prototype has been conducted. Averaged-model assumptions and small-disturbance linearization method were used to formulate the model, in which the stability derivatives were calculated using numerical simulation. The modal characteristics and physical causes were studied with the techniques of eigenvalue and eigenvector analysis and compared with those of a helicopter. The results show that the FRW has two unstable modes: an unstable oscillatory mode and a slow divergence mode. The former mode features a horizontally circling trace of the center of gravity, coupled with a periodic oscillation of pitch and roll angles, which is dominated by a coupling roll (or pitch) moment produced by a forward (or sideward) speed perturbance. The latter mode features a decreased (or increased) wing rotation speed accompanied by an increasing downward (or upward) motion speed of the body owing to a strong dependence between the aerodynamics and the passive rotation of the wing. Longitudinal–lateral coupling and rotational–vertical coupling mark the distinction in modal characteristics between the FRW and the helicopter. The model and results of this study may offer a reference for the stability analysis and control design for FRW vehicles.