$11\mathrm{.}8$ PID control action is applied to the plant

$G_p(s)=\frac{s+10}{(s+2)(s+5)}$

The PID controller has the transfer function

$G_c(s)=K_P(1+\frac{1}{T_{\text{I}}s}+T_{D}s)$

Use the values $T_{\text{I}}=0\mathrm{.}2$ and $T_D=0\mathrm{.}5.$ Plot the root locus with the proportional gain $K_P$ as the parameter.Using the "series" command in Matlab to combine two transfer functions in Matlab and then use "rlocus" with the combined transfer function. Use "help series" in Matlab to understand the command.

Import both transfer functions into "sisotool".