How come does a system become more stable when a zero is added to a system.. I mean i doesn't not change the location of the pole, it is still the same?
An example: Looking a closed loop system consisting of an controller $G_c(s)$, and a system $G(s) = \frac{1}{s(s+1)}$
If the controller is a PD it the close cloop transfer function $T(s)$ will look like this.
$G_c(s) = Kp + Kds$ $T(s) = \frac{\frac{Kp}{s(s+1)} + \frac{Kds}{s(s+1)}}{1 + \frac{Kp}{s(s+1)} + \frac{Kds}{s(s+1)}}$
With adding a PD controller the close loop transfer function receives an zero, but how come does make a system more stable.