This paper investigates the crossover-regression phenomenon in compensatory manual-control tasks. The adjustment, between-subject variation, and accuracy of linear human-operator models are analyzed in detail. A theoretical investigation into closed-loop error minimization will be presented. Our main hypothesis was that crossover regression is caused by an operator's inability to sufficiently decrease the time delays required to limit forcing-function resonance. To test the hypothesis and explore the use of linear-operator models in regressed conditions, an experiment very similar to McRuer's landmark 1965 experiment was conducted. A comparison between regressive and nonregressive conditions revealed that crossover regression is indeed a strategy to reduce forcing-function resonance. The bandwidth of the forcing-function signal at which participants regressed their crossover frequency was found to vary considerably between participants. In regressed conditions, the betweensubject variability in frequency-domain performance increased. Additionally, the operator control behavior became increasingly nonlinear, resulting in larger uncertainties and a higher between-subject variability in the linear-model parameter estimates. Nomenclature et = tracking error, in. K c = controlled dynamics gain, in:=in: nt = operator remnant activity, deg T = measurement time, s ut = stick deflection, deg Y c j! = controlled element dynamics Y p j! = pilot describing function yt = system output, in. = damping ratio 2 ! = squared correlation coefficient 2 a = squared relative remnant i = forcing-function standard deviation, in. e = effective time delay, s d = pure time delay, s I = lag-time constant, s L = lead-time constant, s ' M = phase margin, deg '! = phase shift, deg ! c = gain crossover frequency, rad=s ! i = forcing-function bandwidth, rad=s ! nm = neuromuscular break frequency, rad=s
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