Stability of a Single-Channel Rolling Aerospace Vehicle with Semi-Automatic Command to Line of Sight

This paper presents a stability analysis of single-channel, slow-rolling, Semi-Automatic Command to Line of Sight (SACLOS) missiles using a comparison of the Routh–Hurwitz and the Frank–Wall stability criteria and a nonlinear analysis. Beginning with a six-degree-of-freedom (6-DOF) model in the Resal frame, a linearized model for the commanded motion is developed. This linearized model, which features complex coefficients due to the coupling of longitudinal channels in rolling missiles, is used to define the structural scheme of the commanded object and its flight quality parameters. The guidance kinematic relations, guidance device equations, and actuator relations, incorporating a switching function specific to slow-rolling, single-channel missiles, are also defined and linearized within the Resal frame to construct a comprehensive structural diagram of the SACLOS missile. From this, the characteristic polynomial with complex coefficients is derived and analyzed by comparing the Routh–Hurwitz and the Frank–Wall stability criteria. This analysis determines a stability domain for the guidance gain and establishes a minimum limit for the guidance time. The stability domain defined through the linear model is then validated using a nonlinear model in the body frame.