Root locus control

improving transient response

Question

How to calculate K?

Second-order poles for the second-order system.

adding PID (compensator) with an integrator ( $\frac{1}{s}$ ) in feed forward path.

proportional-plus-integral (PI) controller ⇒ causing error to go to zero.

Important

Add zero! on the pole near the origin at $s=-a$

\frac{K}{s}(s+a) = K_p + \frac{K_i}{s}

where $K_p$ is the proportional gain, and $K_i$ is the integral gain.

Implementation $G_c(s)$

$G_c(s) = K_p + \frac{K_i}{s} = \frac{K_p(s+\frac{K_i}{K_p})}{s}$