(Solved): L(s)=s(s+10)(s2+2s+2)(s+3) (a) Calculate the OL poles and OL zeros (b) Calculate the number of z ...

$L(s)=\frac{(s+3)}{s(s+10)\left(s^2+2s+2\right)}$ (a) Calculate the OL poles and OL zeros (b) Calculate the number of zeros at infinity (c) Calculate the asymptotes (i) center and (ii) angles of the asymptotes (d) Calculate the breakaway points on the real axis (e) For each OL pole calculate the angle of departure (f) For each finite $\mathrm{OL}$ zero calculate the angle of arrival (g) Calculate the value of $k$ when (if) the root locus crosses the $jw$-axis (h) Calculate frequency of oscillation of the system when the root locus crosses the jw-axis (i) Sketch the root locus by hand (j) Plot the root locus using MATLAB