Saturation limits the contribution of acceleration feedback to balancing against reaction delay

Abstract

A nonlinear model for human balancing subjected to a saturated delayed proportional–derivative–acceleration (PDA) feedback is analysed. Compared to the proportional–derivative (PD) controller, it is confirmed that the PDA controller improves local stability even for large feedback delays. However, it is shown that the saturated PDA controller typically introduces subcritical Hopf bifurcation into the system, which can also lead to falling for large enough perturbations. The subcriticality becomes stronger as the acceleration feedback gain increases or the saturation torque limit decreases. These explain some features of human balancing failure related to the increased reaction delay of inactive elderly people.