Extended Crossover Model for Human-Control of Fractional Order Plants

A data-driven generalization of the crossover model is proposed, characterizing the human control of systems with both integer and fractional-order plant dynamics. The model is developed and validated using data obtained from human subjects operating in compensatory and pursuit tracking tasks. From the model, it is inferred that humans possess a limited but consistent capability to compensate for fractional-order plant dynamics. Further, a review of potential sources of fractionality within such man–machine systems suggests that visual perception, based on visual cues that contain memory, and muscular dynamics are likely sources of fractional-order dynamics within humans themselves. Accordingly, a possible mechanism for fractional-order compensation, operating between visual and muscular sub-systems, is proposed. Deeper analysis of the data shows that human response is more highly correlated to fractional-order representations of visual cues, rather than directly to objective engineering variables, as is commonly proposed in human control models in the literature. These results are expected to underpin future design developments in human-in-the-loop cyber-physical systems, for example, in semi-autonomous highway driving.

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