Derivation of control inputs for deep stall recovery using nonlinear frequency analysis

Although the problem of locked-in deep stall is well documented over many years, there currently exists no consistent procedure that can guarantee recovery. Past studies have suggested that it might be possible to rock the aircraft in pitch to destabilise the statically stable deep stall trim point, thereby gaining enough momentum to push the nose down. However, the methods used in these studies are either of preliminary or empirical nature and cannot guarantee recovery. In this paper, we use bifurcation analysis to derive a recovery manoeuvre, specifically by assessing the aircraft’s nonlinear frequency response under an elevator forcing. The ensuing nonlinear Bode plot detects unstable (divergent) solutions near resonance that contribute to a successful deep stall recovery. Moreover, the nonlinear resonant frequency is slightly lower than the result obtained using linear analysis, and time simulation shows that relying on the linear result does not lead to a successful recovery. It is also found that at the high angles of attack associated with deep stall, the frequency separation between the short period and phugoid mode is significantly reduced, leading to only one visible peak in the frequency response. This feature is also reflected in the time-domain step response.