To gain robust performance (see Section IV), φm ≥ 60◦ is specified, yielding the recommendation_
3/8 ≤ ζ ≤ 1. (For ζ = 1, φm = 76◦, which is ample.) The minimum IE is obtained for ζ = _ 3/8 ≈ 0.61 as IEmin = 3Δτl/(2α2 sJ).
Example 1: A 1DOF PI controller is designed, following the given recommendation. The closed-loop bandwidth αs is selected according to (14), where trc = 0.2tro = 44 ms. This leads to αs = 50 rad/s. The measurement noise n in the experiments is filtered using a 500-rad/s first-order low-pass filter. Performance is evaluated with a small reference step, from 0 to 0.15ωnom, to avoid application of maximum torque. A rated
load-torque step is applied at t = 0.55 s. Fig. 3 shows that a fairly large overshoot appears in the reference step response. The rise time is, in both cases, slightly below the 44 ms, which is due to the added I part