(Solved): 2. Sketch the root loci for the following open-loop transfer functions of \( ...

???????

2. Sketch the root loci for the following open-loop transfer functions of \( \mathrm{GH} \) \[ G=\frac{K(s+2)}{s+1}, H=\frac{1}{s+1} \] a) Determine the number of pole and zeros of the system above. b) How many zeros are at infinity? c) How many branches? d) Determine the number of asymptotes and Centroid. e) Find the break-out points and sketch the root locus plot. f) Find the gain at the Break-out points. g) Find the closed loop pole location where the feedback gain \( K=2 \)