A closed loop system has the characteristic equation given by s3+Ks2+(K+2)s+3=0. For this system to be stable, which one of the following conditions should be satisfied?
A
0 < K < 0.5
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B
0.5 < K < 1
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C
0 < K < 1
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D
K > 1
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Solution
The correct option is D K > 1 Characteristic equation is,
s3+Ks2+(K+2)s+3=0
For this system to be stable, using Routh's criterion, we can write,
3<K(K+2)
or K2+2K−3>0
or (K+3)(K−1)>0
Here, the valid answer will be out of all the options given.