One arm of a space robot is shown. The block diagram for the control of the arm is shown. The transfer function of the motor and arm is

(a) If Gc(s) = K, determine the gain necessary for an overshoot of 4.5%, and plot the step response, (b) Design a proportional plus derivative (PD) controller using the ITAE method and ωn = 10. Determine the required prefilter Gp(s). (c) Design a PI controller and a prefilter using the ITAE method, (d) Design a PID controller and a prefilter using the ITAE method with ωn - 10. (e) Determine the effect of a unit step disturbance for each design. Record the maximum value of y(t) and the final value of y(t) for the disturbance input, (f) Determine the overshoot, peak time, and settling time (with a 2% criterion) step R(s) for each design above, (g) The process is subject to variation due to load changes. Find the magnitude of the sensitivity at a) = 5, |STG(j5)|, where

(h) Based on the results of parts (e), (f), and (g), select the best controller.

G(s) = s(s +10). T Ge()G(S