The key to the flight control of statically unstable aircraft (SUA) is to maintain attitude stability; however, some SUA use large boosters during the boost section to obtain a relatively high initial energy, which causes the centre of gravity biased to shift backwards and the projectile to exhibit certain static instability characteristics. This study proposes a combination of engineering practice and the characteristics of the SUA model. By analysing the root characteristics of polynomials and using numerical polynomial solving methods, the dynamic performance of SUA is studied. The mechanism analysis of overshoot time-domain step response without oscillation or finite time oscillation under attitude control parameter selection conditions is studied. For SUA attitude control in the PD controller, the closed-loop characteristics of SUA have a significant difference, which is mainly reflected in the general situation with overshooting characteristics. The selection range of PD control parameters that meet engineering practice has been determined to ensure that the closed-loop response of the system has specific quality requirements, as well as the selection conditions of control parameters at different poles. Finally, several numerical examples were provided to demonstrate the correctness of the results of this study.
Zhang et al. (Fri,) studied this question.