Question

The open – loop transfer function of a unity feedback control system is

\(G\left( s \right) = \frac{1}{{{{\left( {s + 2} \right)}^2}}}\)

The closed loop transfer function will have poles at
1. – 2, – 2 
2. – 2, – 1
3. – 2 ± i
4. – 2, 2

Answer 1

Correct Answer - Option 3 : – 2 ± i

Closed loop transfer function poles are nothing but roots of characteristic equation.

\(\begin{array}{l} 1 + G\left( s \right)H\left( s \right) = 0\\ 1 + \frac{1}{{{{\left( {s + 2} \right)}^2}}} = 0\\ \Rightarrow {s^2} + 4s + 5 = 0\\ \Rightarrow s = - 2 \pm i \end{array}\)