Question

For a unit feedback system with G(s)= K(s+α)​/s(s+3)(s+6)

find the values of α and K that will yield a second order closed loop pair of poles at −1±j100.

Answer 1

To find the values of α and K that will yield a second order closed-loop pair of poles at −1±j100, we need to solve for α and K.

Step-by-step explanation:

To find the values of α and K that will yield a second-order closed-loop pair of poles at -1±j100, we need to solve for α and K. The characteristic equation of the closed-loop system can be written as (s+1+100i)(s+1-100i) = 0. Expanding this equation and comparing it with the given transfer function G(s), we can determine the values of α and K.

By comparing the coefficients of s^2, s, and the constant term, we get the following equations: α = 6, K = -8820.