1) Given the following open loop: 1 s(s2 + 2s + 10) (a) Sketch the pole-zero map Determine: (b) the number of infinite zeros (c) region where the root locus crosses the real axis (d) center of gravity (e) angle of asymptotes (f) break-away or break-in point (g) range of values of k for which the system is stable (h) angular frequency at which the root locus crosses the imaginary axis (i) phase cross-over frequency (i) gain margin (k) gain cross-over frequency (1) phase margin 2) Design a Pl compensator, Gc(s), for the following system and specifications: Zero steady state error due to a step input; a pair of dominant closed-loop poles with a time constant of 0.25 seconds and; a damping ratio of 0.8. Obtain the compensated system step response. X(s) E(s) Y(s) Ge(s) G(s) G(s) = 1 (s + 2)(s + 6)