Computation of stability radius for a third-order control system

In general, autopilots are applied to improve the performance of missiles, which may be possibly contradictory to system robustness. This paper focuses on design and stability radius computation of the two-loop autopilot. At first, based on output feedback, two-loop autopilot is introduced and designed specifically using pole placement method. A criterion about poles selection is given as follow: the real part of autopilot poles should be no more than a third of fin poles. Secondly, in order to validate robustness of the designed autopilot, a lemma in the sense of Holder 2-norm is derived with the theory of polynomials family, by which stability radius for two-loop autopilot is obtained easily. Finally, an example of autopilot design is offered in great detail. Four different designs are compared for discussing the relationship of performance and robustness. Stability radius is computed by the new lemma, and stability regions are obtained respectively. The analysis and simulation results verify the feasibility of robustness validation. Moreover, it indicates that actuator bandwidth should be three times the autopilot bandwidth. It is proved to be a reasonable compromise between performance and robustness.