Stability of Spinning Missiles with an Acceleration Autopilot

The lateral acceleration autopilot with a rate loop is the most commonly implemented autopilot, which has been extensively applied to high-performance command and homing guidance missiles. However, for spinning missiles, the autopilot may be dynamically unstable in the form of a divergent coning motion caused by crosscoupling effects. Conventional methods, without taking into account these effects, fail to produce stable autopilots. In this paper, the mathematical models for each component of the autopilot are formulated, and the system equation in the form of complex summation is finally obtained. The sufficient and necessary condition of coning motion stability for spinning missiles with lateral acceleration autopilots is analytically derived and further verified by numerical simulations. It is noticed that the stable region of the design parameters for the autopilot shrinks significantly under the spinning condition. It is also observed that the stable region for design parameters is further narrowed when an integrator is introduced into the acceleration loop while the steady-state accuracy is dramatically improved. A simple decoupling method of setting a lead angle for the commands to the servosystem is demonstrated to be effective to correct the crosscoupling and to extend the stability region for design parameters of the autopilot.