For a process with the transfer function,

$G_{(s)}=\frac{k(s+1)}{s({}_{1}s+1)({}_{2}s+1)({}_{3}s+1)}$

With ${}_2>{}_1>0,k>0,$ which is controlled with a Proportional controller. Sketch the root$-$locus

diagram for the following cases and check your results with MATLAB showing all your codes:

a$.>{}_1>{}_2>0$

b$.{}_1>>{}_2>0$

c$.{}_1>{}_2>>0$

d$.=0$

e$.<mn\; id="EditorElement\_5579283">0</mn>$

f$.$ Discuss the relevance of the results in $($a$-$e$)$ above.