Stability of Single Channel Homing Slow-Rolling Missile

Abstract

Starting from the model of a slow-rolling missile with six degrees of freedom (6 DOF) in the body frame, a 6 DOF model in the Resal frame is obtained, which is used to linearize the coupled commanded motion. Based on the linearized model, we obtain the structural scheme of the commanded object and define the quality parameters. The obtained parameters have a complex representation (with real and imaginary parts) due to the coupling between longitudinal channels. Then, the kinematic guidance equations, the seeker equations and the actuator specific to the slow-rolling single-channel missile are defined using a switching function. The guidance kinematic equations, the seeker equations and the actuator model are linearized in the Resal frame, and the structural diagram of the homing missile is constructed. Starting from this, the characteristic polynomial having complex coefficients is determined and then analyzed with the Frank-Wall stability criterion. Based on the analysis, a stability range is determined for the navigation constant and a minimum and possibly a maximum limit for the time to hit the target is obtained. The stability range defined for the navigation constant on the linear model is finally validated on the nonlinear model in the body frame.