Research on Instability Boundaries of Control Force for Trajectory Correction Projectiles

The balance of stability and maneuverability is the foundation of the trajectory correction projectile. For the terminal correction projectile without an attitude feedback loop, a larger control force is expected which may cause an instability. This paper proposes a novel method to derive instability boundaries for the control force magnitude. No additional coordinate system is needed in this method. By introducing the concept of angular compensation matrix, the exterior ballistic linearized equations considering control force are established. The necessary prerequisite for a stable flight under control is given by the Routh stability criterion. The instability boundaries for the control force magnitude are derived. The results of example flights are 13.5% more accurate compared with that in relevant research. Numerical simulations demonstrate that if the control force magnitude lies in the unstable scope derived in this paper, the projectile loses its stability. Furthermore, the effects of the projectile pitch, velocity, and roll rate on flight stability during correction are investigated using the proposed instability boundaries.