The open loop transfer function of a unity feedback system is given by $G (s) = \frac{π e^{- 0.25 s}}{s}$ . In G(s) plane, the Nyquist plot of G(s) passes through the negative real axis at the point

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Answer 1

$G (s) = \frac{π e^{- 0.25 s}}{s}$

In G(s) plane, the Nyquist plot of G(S) passes through the negative real axis at the point (-a, j0)

a = magnitude of G(s) at ω = ω_pc

ω_pc is phase cross over frequency.

at $ω = ω_{p c}, ∠ G (j ω) = - 180^{\circ}$

⇒ -0.25 ω_pc – 90 = -180

⇒ ω_pc = 2π

${| G (j ω) |}_{ω = ω_{p c}} = \frac{π (1)}{2 π} = 0.5$

(-a, j0) = (0.5, j0)