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

Chapter , Problem 8.43

(choose chapter or problem)

The following model has a dominant root of \(s=-3 \pm 5 j\) as long as the parameter \(\mu\) is no less than 3.

(\frac{d^{3} y}{d t^{3}}+(6+\mu) \frac{d^{2} y}{d t^{2}}+(34+6 \mu) \frac{d y}{d t}+34 \mu y=u_{s}(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) \(\mu=30\),

(b) \(\mu=6\), and

(c) \(\mu=3\). Discuss the effect of \(\mu\) on these predictions.