Department of Applied Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary.
Chaos. 2022 May;32(5):053108. doi: 10.1063/5.0087019.
Human stick balancing is investigated in terms of reaction time delay and sensory dead zones for position and velocity perception using a special combination of delayed state feedback and mismatched predictor feedback as a control model. The corresponding mathematical model is a delay-differential equation with event-driven switching in the control action. Due to the sensory dead zones, initial conditions of the actual state cannot always be provided for an internal-model-based prediction, which indicates that (1) perfect prediction is not possible and (2) the delay in the switching condition cannot be compensated. The imperfection of the predictor is described by the delay mismatch, which is treated as a lumped parameter that creates a transition between perfect predictor feedback (zero delay mismatch) and delayed state feedback (mismatch equal to switching delay). The maximum admissible switching delay (critical delay) is determined numerically based on a practical stabilizability concept. This critical delay is compared to a realistic reference value of 230 ms in order to assess the possible regions of the threshold values for position and velocity perception. The ratio of the angular position and angular velocity for 44 successful balancing trials by 8 human subjects was used to validate the numerical results. Comparison of actual human stick balancing data and numerical simulations based on the mismatched predictor feedback model provided a plausible range of parameters: position detection threshold 1°, velocity detection threshold between 4.24 and 9.35°/s, and delay mismatch around 100-150 ms.
采用一种特殊的时滞状态反馈和失配预测器反馈组合，研究了人类棒平衡的反应时滞和位置与速度感知的感觉死区，作为控制模型。相应的数学模型是一个带有事件驱动控制作用切换的时滞微分方程。由于存在感觉死区，基于内部模型的预测无法始终提供实际状态的初始条件，这表明（1）不可能实现完美预测，（2）切换条件中的时滞无法补偿。预测器的不完美性由时滞失配来描述，时滞失配被视为一个集中参数，它在完美预测器反馈（零时滞失配）和时滞状态反馈（失配等于切换时滞）之间产生过渡。根据实际稳定性概念，通过数值方法确定最大允许切换时滞（临界时滞）。将该临界时滞与 230ms 的实际参考值进行比较，以评估位置和速度感知的阈值可能区域。8 位人类受试者的 44 次成功棒平衡试验的角位置和角速度比值被用来验证数值结果。实际人类棒平衡数据与基于失配预测器反馈模型的数值模拟的比较提供了一个合理的参数范围：位置检测阈值为 1°，速度检测阈值在 4.24 到 9.35°/s 之间，时滞失配约为 100-150ms。
