Stability of Single-Channel Homing Rolling Aerospace Vehicle

Abstract

This paper aims to analyze the stability of a special class of single-channel slow-rotating homing missiles using the Frank–Wall stability criterion. To achieve this, starting from the model of a slow-rolling missile with six degrees of freedom (6 DOFs) in the body frame, a 6-DOFs 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 flight quality parameters. The obtained linear model has a complex representation (with real and imaginary parts) due to the coupling between longitudinal channels for the rolling missile. Then, the kinematic guidance equations, the seeker equations and the actuator relations using a switching function, specific to the slow-rolling single-channel missile, are defined. 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 (k), and a minimum and possibly a maximum limit for the time to hit the target tgo is obtained. The stability range defined for the navigation constant in the linear model is finally validated in the nonlinear model in the body frame.

Keywords

• homing missile
• slow-rolling missile
• single-channel command missile
• proportional navigation
• characteristic polynomial with complex coefficients
• stability criterion