Consider the frequency response of a minimum-phase loop transfer function G(s) shown in the Bode plot in Figure 4. We want to design a lag compensator achieving at least 45 phase margin and 8 dB gain margin with static velocity error constant K = 4, which is in the form of C(s) = K Ts+1 BTS1 Answer the following questions. (a) Setting K = 4, draw the Bode plot of the gain compensated system KG(s) on the semilog paper (download it from the class Moodle page). Find the gain and phase margins of the gain compensated system from the sketch. (b) Find the frequency at which KG(w) = -125 and set this as the target gain crossover fre- quency. Find the required attenuation and compute the value of . (c) Set T = 10 and draw the Bode plot of the compensated system C(s)G(s). Do NOT use a new semilog paper. Draw the Bode plot on the same semilog paper used above. (d) Find the gain and phase margin of the compensated system from the sketch and show that all the given stability margin specifications are achieved.