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For the following feedback system $G(s) = \dfrac{1}{(s+1)(s+2)}.$ The $2\%$-settling time of the step response is required to be less than $2$ seconds.

Which one of the following compensators $C(s)$ achieves this?

  1. $3\bigg(\dfrac{1}{s+5}\bigg) \\$
  2. $5\bigg(\dfrac{0.03}{s} + 1\bigg) \\$
  3. $2(s+4) \\$
  4. $4\bigg(\dfrac{s+8}{s+3}\bigg)$
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