Problem 1 Sketch the approximate root locus diagrams for the systems with the open-loop transfer function shown below. In each case identify and box the following quantities: (a) Open loop poles and zeros, (b) Portions of the real axis that are root loci, (c) Asymptote angles, (d) Hub location (intersection point of the asymptotes, also known as centroid) (e) Angles of departure from the open loop poles, (f) Angles of arrival at open loop zeros, if they exist (g) Break in and break away point locations on the real axis, if they exist (h) Imaginary axis crossover point locations and the corresponding value of K, if it exists. Compare your results to MATLAB using the "rlocus" command in MATLAB: G(s)= K(s+2) s(s+10)(s+2s+2)