Stick Balancing with Feedback Delay, Sensory Dead Zone, Acceleration and Jerk Limitation

A simplified model of stick balancing on the fingertip subjected to predictor feedback is investigated, which accounts for three important modeling issues: (1) feedback delay; (2) the sensory dead zone; and (3) limitation of the control force corresponding to the maximum acceleration and the maximum jerk of human hand movement. Eight different cases (± sensory dead zone, ± acceleration limitation, ± jerk limitation) are compared by estimating the maximum balance time out of five time-domain simulations with different initial conditions. It is shown that the region of linear stability in the plane of control parameters is reduced by the presence of dead zone, not affected by limitations on hand acceleration, but is increased by limitations on the jerk.