Stability analysis of a missile control system with a dynamic inversion controller

This paper examines the closed-loop stability of a bank-to-turn, air-to-air missile with a dynamic inversion controller using a two time-scale separation assumption. A. state-space formulation for the alpha, beta, and phi dynamics of the missile, assuming the inner-loop dynamic inversion is performed exactly, is presented. It is then shown that, under certain assumptions, the exponential stability of the alpha, beta, and phi dynamics about the commanded values can be guaranteed if the inner loop design frequency is large enough. An example calculation of the required inner-loop frequency to guarantee stability is done for a particular bank-to-turn missile. Finally, nonlinear six degree-of-freedom simulation results of a maneuver performed with the dynamic inversion controller are presented.