Stability of Moving Mass Control Spinning Missiles with Angular Rate Loops

Moving mass control (MMC) is a new control method in control field. It is a potential way to solve the problem of aerodynamic rudder control insufficiency caused by the low density of upper atmosphere, to reduce the high speed missile aerodynamic thermal load, and to solve the problem of rudder surface ablation. However, the spinning of the airframe and the movement of internal moving mass induce the serious dynamic cross-coupling between pitch and yaw channels, which may lead to system instability in the form of a divergent coning motion. In this paper, the mathematical model of the MMC missile is established, and the angular motion equation is finally obtained by some linearized assumptions. Then, the sufficient and necessary conditions of coning motion stability for MMC missiles with angular rate loops under fast and slow spinning rates are analytically derived and further verified by numerical simulations. It is noticed that the upper bound of the control gain is affected by the location of the moving mass and the spinning rate of the missile.