(C). For the mechanical system, consider a feedback control shown as follows. Please apply Routh table to show the stability condition (i.e., the closed-loop must be stable). (5%) Mechanical System Plant R s) Y(s) Controller G (s (D). For the above system, where J 1 (kg-m2), D - 2(N-m-s/rad) and K 5(N-m/rad) are considered. Now consider a proportional-derivative (PD) controller in a feedback loop shown as follows. Please design Kp & Kd such that the closed-loop system can reach 5% overshoot and a settling time of 0.5 seconds. (MATLAB simulation result must be given!) (10%) (E). Based on the results in (D), for an unit step reference input, please derive the steady state value of the output response. (596) (MATLAB simulation result must be given!) (F). Based on the results in (D) and (E), design a control gain Kc (shown as follows) such that zero steady state error can be achieved. (5%) (MATLAB simulation result must be given!) Mechanical System Plant R(s) Controller G (s)