Longitudinal PIO Criteria

10.7.1.1 Ralph-Smith Criterion

The longitudinal PIOs are classified in three types [32-35]: Type IPIO is expected to occur when the pilot ‘‘switches’’ control tracking pitch attitude to tracking of the pilot-felt normal acceleration. Type II PIO is expected to occur as a result of an abrupt turbulence or nontracking abrupt maneuver. Type III PIO tendency is caused by the pitch attitude tracking only. The main idea is that the aggressive tracking behavior (of pilot-aircraft) should not result in pilot-aircraft closed loop instability. The conditions for the Ralph-Smith (RS) criterion (Types I and II) are

Here, f (j«R) is the phase angle of the normal acceleration TF and 14.3 vR

is the phase lag as a result of pilot delay of 0.25 s. The condition for Type III PIO is that the phase angle of pitch attitude TF (with respect to force input at the crossover frequency) would be less than —180°. «R is the resonance frequency of the power spectral density (PSD) of the normal acceleration due to the closed loop control of pitch angle. In the case of the Type II PIO the resonance frequency is from the PSD of the pilot-aircraft open loop system. The pilot model for normal acceleration is simple gain with a pure time delay of 0.25 s, and for the theta loop it is a lead/lag model with a 0.3 s time delay, the time constants of which are ‘‘adjusted’’ according to the crossover pilot model. The RS criterion requires an explicit pilot model.