Correct Answer - Option 3 : -2 + j, - 2 - j
Concept:
The closed-loop transfer function for unity feedback is
\(TF = \frac{{G\left( s \right)}}{{1 + G\left( s \right)}}\)
G(s) = open loop gain
for closed loop poles 1 + G(s) = 0
Calculation:
Given that
\(G\left( s \right) = \frac{1}{{{{\left( {s + 2} \right)}^2}}}\)
Now closed-loop transfer function is
\(TF = \frac{{\frac{1}{{{{\left( {s + 2} \right)}^2}}}}}{{1 + \frac{1}{{{{\left( {s + 2} \right)}^2}}}}} = \frac{1}{{{{\left( {s + 2} \right)}^2} + 1}}\)
\(TF = \frac{1}{{{s^2} + 4s + 5}}\)
Now for close loop pole 1 + G(s) = 0
s2 + 4s + 5 = 0
s = -2 ± j = -2 + j, -2 - j