Find the range for K such that 1s4 25s3 15s2 25s k will

Find the range for K such that 1/s^4 + 25s^3 + 15s^2 + 25s + k will be stable.

Solution:

To check the stability of given function we need to check roots for charactistic equation

Here charactistic equation is s^4 + 25s^3 + 15s^3 + 25s + K

we can use Routh Hurwitz method here

matrix will form like this

s^4 1 15 k

S^3 25 25

s^2 14 k

S^1 (350-25K)/14

S^0 k

For equation to be stable there should not be any chang in sign in first column therefore

term

(350-25K)/14 & k should be greater than zero

therefore

14 > k and k>0

Ans. range of k become (0,14)