A system with the open loop transfer function is connected in a negative feedback gain of unity. What is the value of K for which the system is unstable.a)60b)70c)80d)90Correct answer is option 'D'. Can you explain this answer? - EduRev Electronics and Communication Engineering (ECE) Question

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A system with the open loop transfer function

is connected in a negative feedback gain of unity. What is the value of K for which the system is unstable.

a)
60
b)
70
c)
80
d)
90

Correct answer is option 'D'. Can you explain this answer?

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Verified Answer

A system with the open loop transfer function is connected in a negat...

The characteristic equation

S (S³ 8S² 24S 32) K = 0

Routh – Hurwitz array

S⁴ 1 24 K

S³ 8 32 O

S² 20 K

(20×32-8K) 0

S⁰ K

So for stable system,

K > 0

and 20×32 - 8K > 0

K < 80

So for unstable system K > 80

i.e. K = 90

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