Figure 8. Human bandwidth estimated from the bode integral.

Following Stein (Stein, 2003), it is assumed that the closed loop log sensitivity function is constant up to a limiting bandwidth frequency and is zero at higher frequencies. Here, sensitivity is plotted as a function of inverted pendulum time constant for bandwidths of 0.5, 0.75, 1.0, 1.25 and 1.5 Hz. Bandwidth increases with line thickness. In these experiments, the inverted pendulum time constant was varied from 1 s to 0.5 s, and 0.5 s was the limit at which subject struggled to maintain balance. A sensitivity of 3 ± 1, represents the sensitivity at which control of an unstable system become very difficult.