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Find the range of K for the system to be stable s4+7s3+10s2+2ks+k=0.

Mumbai University > Electronics Engineering > Sem 4 > Linear Control Systems

Topic: Stability Analysis in Time Domain

Difficulty : High

Marks : 5M

1 Answer
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Given, s4+7s3+10s2+2ks+k=0

s4|110k

s3|72k0

s2|702k7k0

s1|(702k7)2k7k(702k7)00

s0|k00

At s0k>0

For s1=(702k7)2k7k(702k7)>0

k[2(702k7)7]>0

[1404k497]>0

1404k49=0

91=4k

914=k

22.75>k

For s2=702k7>0

702k>0

k<35

Combining the condition, k should be in the range of 0<k<35.

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