Characteristics That Make Linear Time-Invariant Dynamic Systems Difficult for Humans to Control

We present results from an experiment in which 55 human subjects interact with a dynamic system 40 times over a one-week period. The subjects are divided into five groups. For each interaction, a subject performs a command-following task, where the reference command is the same for all subjects and all trials; however, each group interacts with a different linear time-invariant dynamic system. We use a subsystem identification algorithm to estimate the control strategy that each subject uses on each trial. The experimental and identification results are used to examine the impact of the system characteristics (e.g., poles, zeros, relative degree, system order, phase lag) on the subjects' command-following performance and the control strategies that the subjects learn. Results demonstrate that phase lag (which arises from higher relative degree and nonminimum-phase zeros) tends to make dynamic systems more difficult for humans to control, whereas higher system order does not necessarily make a system more difficult to control. The identification results demonstrate that improvement in performance is attributed to: 1) using a comparatively accurate approximation of the inverse dynamics in feedforward; and 2) using a feedback controller with comparatively high gain. Results also demonstrate that system phase lag is an important impediment to a subject's ability to approximate the inverse dynamics in feedforward, and that a key aspect of approximating the inverse dynamics in feedforward is learning to use the correct amount of phase lead in feedforward.