AP2.8 Consider the cable reel control system given in Figure AP2.8. Find the value of Kt and Ka such that the percent overshoot is P.O. ≤ 15% and a zero steady state error to a unit step is achieved. Compute the closed-loop response y(t) analytically and confirm that the steady-state response and P.O. meet the specifications.

FIGURE AP2.8 Cable reel control system. Desired Amplifier Motor Reel dynamics Actual cable velocity + 100 Torque 1 velocity R(s) Ka V(s) s+2 s(s+10) Measured velocity Tachometer K