 Delayed cursor feedback experiment

Can feedback delay change correction timing even when the physical task stays the same? Susilaradeya and colleagues tested this in a human tracking experiment. Participants pressed with both index fingers against fixed force sensors; the two forces controlled a screen cursor along two diagonal axes. A target moved in slow circular motion, usually at $0.2$ rotations per second. The researchers sampled the forces at $50$ samples per second and inserted an additional delay of $0$, $100$, $200$, $300$, or $400$ milliseconds before displaying the cursor. Each trial lasted $20$ seconds; the $70$ trials included $14$ per delay, in pseudorandom order. ^[ref]

The readout was fluctuation in cursor angular velocity, analyzed by Fourier transforms over approximately $10$ seconds from the middle of each trial. The principal peak was around $2$ hertz without added delay, around $1.4$ hertz with $100$ milliseconds, and around $1$ hertz with $200$ milliseconds. Thus changing observation timing changed the timing of corrective motion. ^[ref] This is an empirical motivation for taking stale observations seriously. Human feedback control includes prediction and other dynamics; these observations do not measure $k$ in the ideal integrator model or test its $k\tau =\pi /2$ boundary.