Problem 2
A closed-loop system with the plant being the dynamic system of Problem 1, and a PID compensator having
the transfer function
$D_c(s) = \frac{G_1 + G_2s + G_3s^2}{s}$
(a) Determine the transfer function $H(s)$ of the closed-loop system.
(b) The \"nominal value\" of the sensor scale factor $c = 1$. For this value of $c$, the parameters $G_1, G_2, G_3$ are
to be designed such that the closed loop poles are located at
$s = -4, -1 + j, -1 - j$
Determine the values of the parameters $G_1, G_2, G_3$ for which the poles achieve these values.