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Question

Consider a unity feedback system with forward path transfer function G(s) = K(s+3)(s+5)(s2)(s4)
The range of K to ensure stability is

A
K>34
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B
K<1 (or) K>34
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C
k < - 1
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D
1< K<34
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Solution

The correct option is B K<1 (or) K>34
Closed loop transfer function is,

T(s)=G(s)1+G(s)=K(s+3)(s+5)(K+1)s2+(8K6)s+(15K+8)

For stability all coefficients should be positive or all negative
Case-I: All coefficient are positive,
K+1>0K>1
8 K6>0K>0.75
15 K+8>0K>815
K > 0.75

Case-II : All coefficients are negative:

K+1<0K<1
8K6<0K<0.75
15 K+8<0K<815
K < - 1
So, for stability either K > 0.75 or K < - 1

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