Question

The open-loop transfer function of a unity feedback control system is \(\frac{1}{(s+2)^2}\). The closed loop transfer function poles are located at:
1. -2, -2
2. -2, -1
3. -2, +2
4. -2 ± j1

Answer 1

Correct Answer - Option 4 : -2 ± j1

Given:

\(G(s)=\frac{1}{(s+2)^2}\) and H(s) = 1

Closed loop transfer function is given as:

\(CLTF=\frac{G(s)}{1+G(s)H(s)}\)

\(CLTF=\frac{\frac{1}{(s+2)^2}}{1+\frac{1}{(s+2)^2}}\)

\(CLTF=\frac{1}{s^2+4s+5}\)

∴ Closed-loop poles of this CLTF is given as:

s = -2 ± j1