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Control system miscellaneous

  1. The open loop transfer function of a system is
    G(s) H(s) =
    K(1 + s)2
    s3

    The Nyquist plot for this system is



Correct Option: B

G(jω) H(jω) =
K(1 + jω)2
(jω)3

|G(jω) H(jω)| =
K(1 + ω2)
ω3

∠ G(jω) H(jω) = – 270° + 2tan-1 ω
For ω = 0 , GH(jω) = ∞ ∠– 270°
For ω = 1 , ∠GH(jω) = – 180°
For ω = ∞ , GH(jω) = 0 ∠– 90°
As ω increases from 0 to ∞, phase goes – 270° to – 90° . Due to s3 term there will be 3 infinite semicircle.



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