Bandwidth-Phase Delay Criteria

The insights furnished by the crossover model for compensatory operation lead to criteria that can be used in control system design, as in the Neal-Smith approach. An important example is the Hoh-Mitchell-Ashkenas bandwidth and phase delay criteria (Hoh, 1988), a combination of two individual metrics, illustrated in Figure 21.6.

The first metric is aircraft bandwidth, defined as the frequency at which the phase angle of attitude response to stick force input is -135 degrees. The aircraft bandwidth measures the frequency over which the pilot can control without the need for lead compensation. The second metric is phase delay, defined as the difference in response phase angle at twice the frequency for a -180-degree phase angle and 180 degrees, divided by twice the frequency for a -180-degree phase angle. The phase delay metric approximates the phase character­istics of the effective airplane dynamics, from the region of crossover to that for potential pilot-induced oscillations. Systems with large phase delays are prone to such oscillations.

Boundaries in aircraft bandwidth-phase delay space have been developed using flight and simulator pilot ratings and commentary. Similar boundaries have been especially useful for rotorcraft and special (translatory) modes of control. With these boundaries, designers are able to account for closed-loop pilot-airplane dynamics, using effective airplane dynamics alone. A related airplane-alone criterion based on the crossover model is the Smith-Geddes (1979) criterion frequency. Still another criterion based on airplane-alone dynamics places boundaries in the Nichols plane of the attitude frequency response (Gibson, 1995). The idea is to confine the attitude frequency response within boundaries defined by the best piloted closed-loop flying qualities. All of these boundary methods depend on simple correlation. They should be effective to the extent that new cases resemble those on which the boundaries are based.

Good design practice suggests using all of these criteria to examine airplane dynamics at issue.