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First, since the two sum-of-sines inputs were statistically independent, two effective open-loop pilot-vehicle describing functions may be determined (ref. 41). One open-loop describing function applies to the target errors caused by target motion; it is determined by calculating the ratios of the Fourier coefficients of h(jω )/e(jω ) at the target input frequencies. The other describing function applies to target errors caused by the disturbance input; it is determined from the ratios of the Fourier coefficients of –δ c(jω )/ δ ctot(jω) at the disturbance input frequencies. These two describing functions are referred to the “target following” and “disturbance rejection” describing functions hereinafter.
From these describing functions, open-loop crossover frequencies and phase margins were determined by linear interpolation. Figure 55 shows the magnitude and phase responses of the disturbance-rejection describing function. The data for this example are from the full-motion run (V1) in figure 54. Linear interpolation between the data at the appropriate frequencies (shown in fig. 55) gives a crossover frequency of 3.3 rad/sec and a phase margin of 28°.
The above two measures provide useful information about the character of the pilot-vehicle response. In particular, the crossover frequency is a rough measure of how fast the error is initially zeroed; the higher the crossover frequency, the faster the initial nulling of the error. The
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phase margin is a rough measure of the damping ratio of the error response; the higher the phase margin, the more damped the error response.
Each of these open-loop describing functions includes a different combination of both the pilot’s internal visual and motion compensation applied to the visual error and to the acceleration feedback (refs. 26, 41). Although only the motion cues were changed here, the pilot’s internal compensation may change in an attempt to account for degradations in either the visual or motion cues. The overall effect of these changes on pilot-vehicle performance and opinion are given next.
Target Following. The target-following crossover frequencies are given in figure 56 for all of the config-urations. For easy reference, the motion-filter gain K and natural frequency ω , rounded to one decimal place, are indicated above each bar. The mean value (bar height) and standard deviation (horizontal line above bar) are shown, each determined from six values. Each of the six values corresponds to the individual average for each pilot across his runs. Upon examining the variance ratio, or F-test
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Figure 56.Target-following pilot-vehicle open-loop crossover frequencies.
(ref. 54), for these data, the differences among the config-urations were not significant at the 5% level. In addition, no coherent trend was present among the motion-filter variations. This result agrees with, and extends, the results of Bray (ref. 24), which indicated an invariance in target-following open-loop crossover frequency for motion filter natural frequencies between 0.2 and 1.25 rad/sec with K = 1 for all configurations. The results from the present experiment indicate that this invariance across natural frequency variations also holds for motion-gain changes. Thus, it appears that the initial quickness with which the pilot closes the target-tracking loop does not depend on the motion cue. That result is intuitive; it might be expected that the speed with which this loop is closed would be based on a pilot’s mental model of the speed
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