That is, the time constant of the first-order lag can be up to 23% of the closed-loop-system time constant 1/αs without significant performance deterioration. This is quite generous an allowance, which shows that unmodeled dynamics normally should not be a problem.
Example 4: The tests of Examples 2 and 3 are repeated (for ζ = _ 3/8 to get the worst case), this time with the inclusion of a first-order lag with L = 0.23/αs, to represent unmodeled dynamics. The first-order lag is obtained when the bandwidth of the torque-control loop is αc = αs/0.23 = 220 rad/s. Figs. 9 and 10 show that acceptable performance is obtained for both step and trapezoidal references.