Flight stabilization control of a hovering model insect

The longitudinal stabilization control of a hovering model insect was studied using the method of computational fluid dynamics to compute the stability and control derivatives, and the techniques of eigenvalue and eigenvector analysis and modal decomposition, for solving the equations of motion (morphological and certain kinematical data of hoverflies were used for the model insect). The model insect has the same three natural modes of motion as those reported recently for a hovering bumblebee: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. Controllability analysis shows that although unstable, the flight is controllable. For stable hovering, the unstable oscillatory mode needs to be stabilized and the slow subsidence mode needs stability augmentation. The former can be accomplished by feeding back pitch attitude, pitch rate and horizontal velocity to produce δφ or δα₂; the latter by feeding back vertical velocity to produce δΦ or δα ₁ (δΦ, δφ, δα₁ and δα₂ denote control inputs: δΦ and δφ represent changes in stroke amplitude and mean stroke angle, respectively; δα₁ represents an equal change whilst δα₂ a differential change in the geometrical angles of attack of the downstroke and upstroke).