1. Given the unity feedback system of Figure P9.1, R(s) + E(s) G(s) with K(s + 6) G(s) FIGURE P9.1 (s+3)(s+4) (s+7) (s+9) a) Sketch the root locus of the original system, and identify the asymptotes. b) Using the operating point of -3.2 + j2.38 that sits on the = 0.8 line (143.13 deg), show that the gain K of the closed loop transfer function T(s) = C(s)/R(s) at this operating point is 4.60. c) Design a proportional derivative compensator so that T₁ =1 sec. What is Ge(s), and what is the new Gn (s) = Ge(s) G(s), Where should the new zero be added at? d) BONUS: (10 points) What is the new gain value K, of the new fully compensated system with the G₁ (s) calculated in part c)? C(s)