A system with the open loop transfer function G(s) = K s(s

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A system with the open loop transfer function G(s) = K
s(s + 2)(s² + 2s + 2)

is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of K is ____

1. 2
2. 3
3. 4
4. 5

Correct Option: D

Characteristic equation is, 1 + G(s)H(s) = 0
⇒ 1 + G(s) = 0 (∴ H(s) = 1)

⇒ 1 +	k	= 0
	s(s + 2)(s² + 2s + 2)

⇒ s⁴ + 4s³ + 6s² + 4s + k = 0
Constructing Routh- array, we have

For the closed loop system to be marginally stable, 20 – 4k = 0
⇒ k = 5