Assessment of Maximum Unnoticeable Added Lag-Lead or Lead-Lag Dynamics with a Cybernetic Approach

This paper investigates the human controllers’ sensitivity to added first-order lag-lead and lead-lag dy- namics in the controlled system dynamics using a cybernetic approach and a dedicated human-in-the-loop experiment. The extent to which human controllers will adapt their control dynamics to these added dynamics is objectively determined and explicitly compared to Maximum Unnoticeable Added Dynamics (MUAD) en- velopes from literature. Human control adaptation to added lag-lead and lead-lag dynamics is predicted for a wide range of lead and lag time-constants using offline human control model simulations, while a smaller subset of eight added dynamics settings, supplemented with a baseline condition, is tested in the experiment. Both the simulation predictions and experiment data show that human controllers will significantly adapt their control gains and lead time-constants to added lag-lead or lead-lag dynamics. Overall stronger adaptation is observed with added lag (i.e., high added dynamics lag time constants), which requires human controllers to generate more compensating lead equalization and results in degraded task performance. Collected sub- jective rating data also confirmed that added lag-lead dynamics were more noticeable for human controllers than added lead-lag. While overall these findings correspond well with literature, our experiment data shows that even for some conditions with added dynamics that remained within the MUAD boundaries statistically significant changes in human control gain and lead time-constants, compared to the baseline condition, occur.