The following model has a dominant root of s 3 5j as long as the parameter is no less than 3 d3y dt3 (6 ) d2y dt2 (34 6) dy dt 34y us(t) Investigate the accuracy of the estimate of the maximum overshoot, the peak time, the 100 rise time, and the 2 settling time based on the dominant root, for the f...

The factor of the given root pair is s3 2 25 s 2 6s34 To find the third root s A expand the ...

The following model has a dominant root of s = - 3 5j as long as

Question:

The following model has a dominant root of s = - 3 ± 5j as long as the parameter μ is no less than 3.
d3y/dt3 + (6 + μ) d2y/dt2 + (34 + 6μ) dy/dt + 34μy = us(t)
Investigate the accuracy of the estimate of the maximum overshoot, the peak time, the 100% rise time, and the 2% settling time based on the dominant root, for the following three cases: (a) μ = 30, (b) μ = 6, and (c) μ = 3. Discuss the effect of μ on these predictions.