The value of derivative feedback constant a, which will

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The value of derivative feedback constant a, which will increase the damping ratio of the system to 0.7 is______

1. 0.00245
2. 402.5
3. 0.245
4. None of these

Correct Option: C

Reduction of the block diagram

∴	C(s)	=		8	=	8
				s² + (2 + 8a)s

	R(s)		1 +	8		s² + (2 + 8a)s + 8
				s² + (2 + 8a)s

Characteristic equation is s² + (2 + 8a) + 8 = 0
Equating with the equation
s² + 2ξ ω_n s + ω_n ² , we get
ω_n = 2 √2
∴ ω(2 + 8a) = 2ξ ω_n = 2 × 0.7 × 2 √2
⇒ a = 0.245