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The characteristic equation of the above closed-loop system is:

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  1. s2 + 11s + 10 = 0
  2. s2 + 11s + 130 = 0
  3. s2 + 10s + 120 = 0
  4. s2 + 10s + 12 = 0

Answer (Detailed Solution Below)

Option 2 : s2 + 11s + 130 = 0
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Detailed Solution

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Concept:

Characteristic equation “q(s)” is Numerator part of 1 + G(s)H(s) = 0

Where G(s)H(s) is open loop transfer function

Let,

     -----(1)

So, 1 + G(s)H(s) = 0 can be written as:

⇒ q(s) = p(s) + z(s) = 0 is characteristic equation.       -----(2)

Analysis:

G(s) = 4 × (3/s+1)

H(s) = 10/(s+10)

The characteristic equation is given as:

1+ G(s) H(s) = 0

(s+1)(s+10) + 120 = 0

s2 + 11s + 130 = 0

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