A table is used to position vials under a dispenser head, as shown in Figure DP8.3 (a). The objective is speed, accuracy, and smooth motion in order to eliminate spilling. The position control system is shown in Figure DP8.3 (b). Since we want small overshoot for a step input and yet desire a short settling time, we will limit 20 log Mpω to 3 dB for T (jω). Plot the Bode diagram for a gain K that will result in a stable system. Then adjust K until 20 log Mpω) - 3 dB, and determine the closed-loop system bandwidth. Determine the steady-state error for the system for the gain K selected to meet the requirement for Mpω.
