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Control system miscellaneous

  1. The feedback system shown below oscillates at 2 rad/s when

    1. K = 2 and a = 0.75
    2. K = 3 and a = 0.75
    3. K = 4 and a = 0.5
    4. K = 2 and a = 0.5
Correct Option: A

Characterisitic equation is
1 + G(s)H(s) = 0

∴ 1 +
k(s + 1)
= 0
s3 + as2 + 2s + 1

⇒ s3 + s2a + s(k + 2) + (k + 1) = 0

as2 + (k + 1) = 0 ; s = jω ; s2 = – ω2; ; ω = 2
– aω2 + (k + 1) = 0 ; aω2 = k + 1 ; 4a = k + 1 ;
From options, k = 2, a = 0.75



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