Given G(s) = 1/[(s^2+s+4)(s+6)] and C(s) = k, find the limit of stability of k. Also, what is the range of k such that the settling time is between 10 and 20 seconds.
The Attempt at a Solution
I have attempted to set this up just as i would for any other control systems problem by finding the transfer function:
T(s) = CG/(1+CG) = k / (s^3 + 7s^2 + 10s + k + 24)
I am currently stuck because I have no idea how to deal with a higher order system. In the past, I have done similar questions only in first or 2nd order where I would change T(s) into the form of characteristic equations covered in class.
Any help will help appreciated!