Problem 2: (20 points)
Consider the closed-loop system in Figure 2 with
\begin{equation}
G_c(s) = K, \quad G_p(s) = \frac{1}{s(s+4)(s+6)}, \quad H(s) = 1.
\end{equation}
(1) Sketch the root locus;
(2) With $K = 28$, the closed-loop system poles are $s = -1.37 \pm j1.39$ and $-6.20$. Hence, for the complex poles,
the damping ratio is approximately 0.707. Find the steady-state error for a unit ramp input;
(3) Design a phase-lag compensator that will decrease steady-state error by a factor of 4 such that the closed-loop
poles will not be changed significantly;
(4) Find the steady-state error for the compensated system of (3);
(5) Use Matlab to verify the results in (2) - (4).
