The longitudinal steady-state control for goingfrom hovering to small speed flight of a model insect isstudied, using the method of computational fluid dynamicsto compute the aerodynamic derivatives and the techniquesbased on the linear theories of stability and control for determiningthe non-zero equilibrium points. Morphological andcertain kinematical data of droneflies are used for the modelinsect. A change in the mean stroke angle (δ(?)) results in ahorizontal forward or backward flight; a change in the strokeamplitude (δΦ)or a equal change in the down- and upstrokeangles of attack (δα1) results in a vertical climb or decent;a proper combination of δ(?) and δΦ controls (or δ(?) and δα1controls) can give a flight of any (small) speed in any desireddirection.
In the present paper, the lateral dynamic flight stability properties of two hovering model insects are predicted by an approximate theory based on the averaged model, and computed by numerical simulation that solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theoretical and simulational results provides a test to the validity of the assumptions made in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency (164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency (26 Hz). The following conclusion has been drawn. The theory based on the averaged model works well for the lateral motion of the dronefly. For the hawkmoth, relatively large quantitative differences exist between theory and simulation. This is because the lateral non-dimensional eigenvalues of the hawkmoth are not very small compared with the non-dimensional flapping frequency (the largest lateral non-dimensional eigenvalue is only about 10% smaller than the non-dimensional flapping frequency). Nevertheless, the theory can still correctly predict variational trends of the dynamic properties of the hawkmoth's lateral motion.
Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability (passive stability),because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion.Controllability analysis shows that although inherently unstable,the lateral disturbance motion is controllable.By feeding back the state variables (i.e.lateral translation velocity,yaw rate,roll rate and roll angle,which can be measured by the sensory system of the insect) to produce anti-symmetrical changes in stroke amplitude and/or in angle of attack between the left and right wings,the motion can be stabilized,explaining why the drone flies can fly stably even if the flight is passively unstable.
In the present paper,the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical simulation.The theory is based on the averaged model(which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion,so that the flapping wings' degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments);the simulation solves the complete equations of motion coupled with the Navier-Stokes equations.Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory.One of the insects is a model dronefly which has relatively high wingbeat frequency(164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency(26 Hz).The results show that the averaged model is valid for the hawkmoth as well as for the dronefly.Since the wingbeat frequency of the hawkmoth is relatively low(the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large) compared with many other insects,that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.
在前面的飞行的一只土蜂的纵的动态飞行稳定性被学习。计算液体动力学的方法被用来计算空气动力学的衍生物和特征值的技术，特徵向量分析为解决运动的方程被采用。主要调查结果作为下列。土蜂的前面的飞行不由于一个的存在是动态地稳定的(或二) 不稳定或近似中立马厩天赋模式打手势。在徘回到中等飞行速度[飞行速度 u e =(0 3.5 ) m s −1 ；预付比率 J = 0 0.44 ] ，飞行是弱不稳定的或近似中立马厩；以高速度(u e = 4.5 m s −1 ；J = 0.57 ) ，飞行变得强烈不稳定(在仅仅 3.5 翅膀的两倍它的价值打败的起始的骚乱) 。
Our previous study shows that the hovering andforward flight of a bumblebee do not have inherent stabil-ity(passive stability).But the bumblebees are observed tofly stably.Stabilization control must have been applied.Inthis study,we investigate the longitudinal stabilization con-trol of the bumblebee.The method of computational fluiddynamics is used to compute the control derivatives and thetechniques of eigenvalue and eigenvector analysis and modaldecomposition are used for solving the equations of motion.Controllability analysis shows that at all flight speeds consid-ered,although inherently unstable,the flight is controllable.By feedbacking the state variables,i.e.vertical and horizon-tal velocities,pitching rate and pitch angle(which can bemeasured by the sensory system of the insect),to producechanges in stroke angle and angle of attack of the wings,theflight can be stabilized,explaining why the bumblebees canfly stably even if they are passively unstable.
Yan Xiong Mao Sun Institute of Fluid Mechanics, Beihang University,Beijing 100083, China
