$ \mathrm G(\mathrm s)=\frac1{\mathrm s^2+3\mathrm s+2} $
$ \mathrm C\cdot\mathrm E=1+\frac{\mathrm k}{\mathrm s}\mathrm G(\mathrm s)\;\mathrm H(\mathrm s) $
Syatem is UFB so, H(s) = 1
$ \begin{array}{l}\therefore\mathrm C\cdot\mathrm E=1+\frac{\mathrm k}{\mathrm s}\cdot\frac1{\mathrm s^2+3\mathrm s+2}=0\\\Rightarrow\mathrm s(\mathrm s^2+3\mathrm s+2)+\mathrm k=0\\\Rightarrow\mathrm s^33\mathrm s^2+2\mathrm s+\mathrm k=0\end{array} $
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R-Array |
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s3 |
1 |
2 |
By applying the sufficient condition.
For stability k>0 and k<6
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s2 |
3 |
K |
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s1 |
$\frac{6-\mathrm k}3$ |
0 |
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s0 |
k |
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But system will have 2-poles on if auxiliary equation will be formed. Auxiliary equation will be formed if odd order row becomes zero.
if k = 6, s-1 row becomes zero.
So, k = 6
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