Question $2$

the complete root locus of the system given below

Case $1$: If $G1(s)=\frac{k}{s(s+2)(s+4)}$ and $G2(s)=1$

Case $2$: If $G1(s)=\frac{k(s+1)}{s(s+2)(s+3)}$ and

Case $3$: $G1(s)=\frac{k(s+1)}{s(s+2)(s+3)(s+4)}$ and $G2(s)=1G2(s)=1$

Draw the poles and zeros on the $S$ plan and draw the segments of the root loci on the real axis

Determine the no$.$ of asymptotes

Determine the asymptotes intersection point $(A)$

Determine the asymptotes angels

Determine the $j$ intersection points

Determine the break in or break away points

Draw the complete root locus according to the previous steps