Stability analysis of spinning missiles induced by seeker disturbance rejection rate parasitical loop

This paper focuses on the dynamic stability of spinning missiles equipped with two-loop autopilot considering the seeker disturbance rejection rate parasitical loop (DRRPL)effect induced by attitude disturbance of projectile. The representative mathematical model of spinning missiles in the non-spinning coordinate system is established, and the cross-coupling effect between the pitch and yaw induced by the rotation motion of missile body is analyzed and decoupled. The two-loop acceleration autopilot for each channel is designed with the conventional design method, and the relationship between the autopilot gains and the expected design indexes is deduced. A proportional navigation guidance (PNG)system model with consideration for the seeker DRRPL is further proposed in the form of complex summation. After strict mathematic deduction, the sufficient and necessary condition of the dynamic stability for spinning missiles is obtained. Numerical simulations and discussions under different cases are conducted to demonstrate the validity of stability condition. The results indicate that the stability of a spinning missile is closely related to the amplitude of the seeker DRR, the rolling rate, and the autopilot design indices. The stable region of the autopilot design frequency is obtained by solving the dynamic stability condition. To meet the requirement of stable controlling at a constant spinning rate, it was found to be effective to decrease the amplitude of the seeker DRR for spinning missiles, employ the lead angle decoupling approach to the commands for the servo system, and guarantee that the autopilot design frequency is lower than the critical value. The dynamic stability condition derived in this paper is useful for evaluating the stability of a spinning missile with consideration for the seeker DRRPL, and the conclusions obtained can provide guidance for the autopilot design of spinning missiles.