Aeroservoelastic Modeling and Stability Analysis

It is well known that the elasticity has a great impact on the performance of the slender missile. In this paper, the dynamics of the flexible missile is regarded as a combination of the rigid motion and the elastic vibration. To simplify the modeling, we focus on the influence of the rigid motion on the elastic vibration, instead of completely considering the coupling between rigidity and elasticity. Based on certain assumptions, the longitudinal models of the rigid and elastic missile are derived, and the model of a typical three-loop acceleration autopilot is designed in accordance with the rigid body dynamics. To evaluate the effects of elastic vibration on stability of the closed-loop system, two different sensor placements are simulated in our example. The numerical simulation demonstrates that the bending vibration may deteriorate the tracking performance of autopilot, although it works well for rigid model. In the worst case, the divergent response due to aeroservoelastic instability can be observed, and the unstable response turns into limit-cycle oscillations (LCO) finally for the nonlinear saturation of actuators.

A modified full velocity difference model with the consideration of velocity deviation

In this paper, a modified full velocity difference model (FVDM) based on car-following theory is proposed with the consideration of velocity deviation which represents the inexact judgement of velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow varies with the deviation extent of velocity. The Burgers, Korteweg-de Vries (KdV) and modified K-dV (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The numerical simulations show a good agreement with the analytical results, such as density wave, hysteresis loop, acceleration, deceleration and so on. The results show that traffic congestion can be suppressed by taking the positive effect of velocity deviation into account. By taking the positive effect of high estimate of velocity into account, the unrealistic high deceleration and negative velocity which occur in FVDM will be eliminated in the proposed model.