Question

The forward path transfer function of a unity negative feedback system is given by G(s) = K/((s + 2)(s - 1))

The value of K which will place both the poles of the closed-loop system at the same location, is ______. 

 

Answer 1

Given G(s) = k/((s + 2)(s - 1))

H(s) = 1

Characteristic equation: 1 + G(s)H(s) = 0

1 + K/((s + 2)(s - 1)) = 0

The poles are s_1,2 = - 1± √(9/4 - 4k)

If 9/k - k = 0, then both poles of the closed loop system at the same location.

So, K = 9/4  ⇒ 2.25