Now let's practice drawing and interpreting root$-$locus plots with MATLAB. For each of the plant transfer functions $G_{}(s)$ given below, assume the plant is being controlled using negative$-$unity$-$feedback control $($i$.$e$.,$ assume $H(s)=1$ in Figure $15\mathrm{.}1$ in the textbook$)$ with a simple proportional controller $G_c(s)=K_p,$ and plot the root$-$locus as $K_p$ is varied from zero to infinity. Turn in all of your root$-$locus plots, as well as a single $m-$file that plots them all. Finally, use MATLAB's rlocus tools to determine the range of $K_p$ for which the closed$-$loop system is stable for each system.

a$.\frac{s}{s+5}$

b$.\frac{s+3}{(s+2)(s-4)}$

c$.\frac{1}{s^2}$

d$.\frac{1}{(s+5)(s^2+4s+8)}$