Chen Jingtian, Lu Shaoyi, Zhang Li, Insperger Tamas, Stepan Gabor
State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, People's Republic of China.
Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary.
J R Soc Interface. 2025 Jun;22(227):20240843. doi: 10.1098/rsif.2024.0843. Epub 2025 Jun 18.
The inverted pendulum, a classical mechanical system, often serves as a platform for studying stability and control algorithms. Modelling human standing balance as an inverted pendulum controlled by the time-delayed proportional-derivative (PD) feedback controller can be used effectively to study the related biomechanical mechanisms. In this study, to investigate the human balance control strategy, an adjoint sensitivity analysis method and a corresponding optimizer are implemented to directly determine system parameters, control gains and the time delay in the human balancing model. This study validates the accuracy of the optimizer through numerical simulations and experimental verification based on the physical model of the inverted pendulum on a cart. The experimental results confirm the performance of the identification algorithm for systems involving non-smooth dynamics and inherent time delays. Moreover, the identification based on human balance data indicates that the time-delayed PD feedback controller effectively represents the human balance control strategy. Additionally, the identification reveals a tendency in the control strategy: the control gains are located in the lower-left region of the stability diagram, indicating that the human body tends to adopt an optimal control strategy that minimizes energy consumption.
倒立摆作为一种经典的机械系统，常被用作研究稳定性和控制算法的平台。将人体站立平衡建模为由时滞比例-微分（PD）反馈控制器控制的倒立摆，可有效地用于研究相关的生物力学机制。在本研究中，为了探究人体平衡控制策略，实施了一种伴随灵敏度分析方法和相应的优化器，以直接确定人体平衡模型中的系统参数、控制增益和时间延迟。本研究通过基于小车上倒立摆物理模型的数值模拟和实验验证，验证了优化器的准确性。实验结果证实了该识别算法对于涉及非光滑动力学和固有时间延迟的系统的性能。此外，基于人体平衡数据的识别表明，时滞PD反馈控制器有效地代表了人体平衡控制策略。此外，该识别揭示了控制策略中的一种趋势：控制增益位于稳定性图的左下方区域，表明人体倾向于采用使能量消耗最小化的最优控制策略。
