A certain servomechanism system has dynamics dominated by a pair of complex poles and no finite zeros. The time-domain specifications on the rise time (tr), percent overshoot (Mp), and settling time (ts) are given by

tr ≤ 0.6 sec,

Mp ≤ 17%,

ts ≤ 9.2 sec.

(a) Sketch the region in the s-plane where the poles could be placed so that the system will meet all three specifications.

(b) Indicate on your sketch the specific locations (denoted by ×) that will have the smallest rise time and also meet the settling time specification exactly.

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