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Question

Consider a negative unity feedback system with the forward path transfer function s2+s+1s3+2s2+2s+k, where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is

A
8
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B
9
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C
6
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D
7
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Solution

The correct option is A 8
CE is
1+G(s)H(s)=0

1+s2+s+1s3+2s2+2s+K=0

s3+3s2+3s+(1+K)=0

R.H. criteria:

s3s2s1∣ ∣ ∣133(1+K)9(1+K)0

For marginal stability,

9(1+K)=0

K=8

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