DP8.3 A table is used to position vials under a dis

penser 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). Determine a K 

such that the bandwidth is maximized while keeping

P.O. ≤ 20% to a unit step input. What is the max

imum bandwidth, vb, when P.O. ≤ 20? Determine the range of K such that the closed-loop system is stable. 

FIGURE DP8.3 Automatic table and dispenser. Vials Dispenser y-axis motor and sensor x-axis motor and sensor (a) R(s) K Y(3) Position command s(+2) Position Sensor 7 (x+7) (b)