Stability of spinning missile with homing proportional guidance law

The terminal proportional guidance loop has been employed by spinning missiles to improve the attacking accuracy. However, it has been observed that the miss distance increases dramatically during the design of the spinning missile with only a guidance loop. Meanwhile, the conventional stability criteria of the guidance loop applicable to the non-spinning missile are no longer valid in the event of the spinning. To address this problem, in this paper, the stability of the spinning missiles with only a 3D proportional guidance loop is analytically derived from system equations in a form of complex summation and the suitable design criteria for the whole proportional guidance loop are also established. Numerical simulations show that during the terminal guidance phase the stable region for the proportional navigation coefficient is reduced with the increase of flight time, which is also shrunk dramatically due to spinning, and the decrease of the critical stable time of spinning missiles results in the increase of miss distance, which exhibit great agreements to those derived from the analytical stability criteria.