Question

The frequency at which the Nyquist plot of a unity feedback system with the open loop transfer function \(G(s) = \frac {25s}{\sqrt {(s+1)}(s+1)^4}\) crosses the negative real axis is
1. 1 rad / s
2. √2 rad / s
3. √3 rad / s
4. 5 rad / s

Answer 1

Correct Answer - Option 3 : √3 rad / s

Concept:

• Nyquist plot crosses the negative real axis at phase cross over frequency (ω_pc)
• The phase crossover frequency is the frequency at which the phase angle first reaches −180°
• i.e., ∠(G(ω_pc)) = -180⁰

Calculation:

Given G(s) = \(\frac{{25s}}{{\sqrt {s + 1} {{\left( {s + 1} \right)}^4}}}\)

∠(G(ω_pc)) = 90⁰ – 0.5 tan^-1(ω_pc) – 4 tan^-1(ω_pc) = -180⁰

By solving we get ω_pc = \(\sqrt 3 \) rad/sec