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.

中文翻译：

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使线性时不变动态系统难以控制的特性

我们提供了一个实验的结果，其中55个人体对象在一个星期的时间内与动态系统进行了40次交互。主题分为五个组。对于每次交互，受试者将执行命令跟踪任务，其中所有受试者和所有试验的参考命令均相同；但是，每个组都与不同的线性时不变动力系统相互作用。我们使用子系统识别算法来估计每个受试者在每个试验中使用的控制策略。实验和识别结果用于检查系统特性（例如，极点，零点，相对程度，系统阶数，相位滞后）对受试者的命令遵循性能和受试者学习的控制策略的影响。结果表明，相位滞后（由较高的相对度和非最小相位零引起）趋向于使动态系统更难以控制，而较高的系统阶数并不一定会使系统更难以控制。识别结果表明，性能的提高归因于：1）使用前馈逆动力学的相对准确的近似值；2）使用增益较高的反馈控制器。结果还表明，系统相位滞后是影响受试者近似前馈逆动力学的能力的重要障碍，并且近似于前馈逆动力学的关键方面是学习在前馈中使用正确量的相位超前。