Plz ask for Q1-3 I will give thumb up

Questions R(S) Y(s) Gp(s) + Figure 1: A negative feedback system Consider a negative feedback system shown in Fig. 1. Suppose 1 G,(s) 8 +s Ge(s) = K S + 10 where K varies from 0 to infinity. Please analyze the closed loop system by method of 1. root locus. (a) (40 %) Please draw the root locus of the the system. You must specify all impor- tant values, such as the breakaway points, the number, angles, and centroid of asymptotes, the critical value of K for the system to have poles in the imaginary axis or the origin, the value of poles in the imaginary axis or the origin, and the departure angles, and so on. (b) (5 %) According to the root locus, is it possible to stabilize the system with this controller? Are there any constraints? No points will be given if not reason is provided. (c) (5 %) When K = 10, the three closed-loop poles are s = {-0.45+0.89 i, -10.11}. Please estimate the settling time of this controlled system. 2. frequency domain analysis (a) (10 %) Please draw the Bode plot of the open-loop system Gc(s) (s) using asymptote approach, if K is not considered (by letting K = 1). (b) (10 %) Please draw the Nyquist plot of the open-loop system Ge(s) (s), if K is not considered (by letting K = 1). (C) (10 %) Please specify the gain margin and phase margin of the controlled system. (d) (5 %) According to your analysis, is it possible to stabilize the system with this controller? and why? No points will be given if not reason is provided. 3. state-space equations (a) (10 %) Please write Gp(s) in the controllable form and observable form, respec- tively. (b) (5 %) Please check the controllability of the system in the controllable form in Problem (3a)