(Solved): A PD controller is used in the system shown. A. Find the values of the proportional gain \( K_{P} ...

A PD controller is used in the system shown. A. Find the values of the proportional gain \( K_{P} \) and derivative gain \( K_{d} \) such that the response to a unit step reference input [at \( R(s) \) ] will have the following closed-loop characteristics: \( \tau \leq 1 \) sec and \( \zeta=0.5 \). [20 pts] B. What is the steady state error due to a unit step reference input if \( K_{P}=60 \) and \( K_{d}=15 \) ? [15 pts]