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Smith-Geddes Criterion
This criterion is based on phase margin [36,37]. The theta loop should have sufficient phase margin to avoid PIO sensitivity. The pilot model is not required. The flight is PIO sensitive if the phase angle of F j) TF (at the open loop gain crossover frequency) is less than —165°. It is PIO prone if the angle is less than —180°. Also, for the normal acceleration TF, if fm = 180 + f(j«c) — 14.3 «c < 0, then the flight is PIO prone.
10.7.1.2 Phase Rate Criterion
Excessive phase lags are encountered in modern high-performance aircraft. APhR (average phase rate) is the pitch attitude phase per unit frequency; the range of frequency is up to 2«180. This would capture the HO effects. APhR is computed as
— (180 + f 2v180 )
«180
10.7.1.3 Loop Separation Parameter
During landing, the flight path and theta loops could be treated as independent of each other, since during the flare the pilot would concentrate rather on flight path control [40]. This means that pilot models could be different for each loop and also the dominant resonance frequencies. If loop separation parameter (LSP) = pilot-aircraft closed loop system resonance frequency (of pitch attitude minus of flight path) is less than 2 rad/s, then the aircraft is prone to PIO. Appropriate pilot models are required.
10.7.1.4 Neal-Smith Time-Domain Criterion
The criterion uses the pilot compensation model defined as [14,41-43]
de(s) _ 400Kp(rleads + 1)e-0 23s Ue(s) s2 + 28s + 400
This model includes the second-order lag filter and an equivalent time delay of 300 ms. The pitch attitude control task is monitored for 5 s. The theta-errror (of the closed loop control) rms value is minimized. The rms value of the second derivative of the theta-error is computed. If this is greater than 100, the prediction is that the aircraft is PIO prone.
10.7.1.5 Bandwidth PIO Criterion
Bandwidth PIO criterion is specified in terms of the PIO rating boundaries in terms of BW and phase delay of the theta TF [34,44,45]. UBC also uses the flight path BW and the time-domain theta dropback. The parameters are obtained from the Bode diagrams of theta, pitch rate, and the flight path. Also, step response of the pitch attitude is used. The unified BW PIO criterion boundaries are defined. Table 10.13 specifies the PIO conditions.
