A system for dispensing radioactive fluid into capsules is shown in Figure AP3.8(a).The horizontal axis moving the

Question:

A system for dispensing radioactive fluid into capsules is shown in Figure AP3.8(a).The horizontal axis moving the tray of capsules is actuated by a linear motor. The x-axis control is shown in Figure AP3.8(b).
(a) Obtain a state variable model of the closed-loop system with input r(t) and output y(t).
(b) Determine the characteristic roots of the system and compute K such that the characteristic values are all co-located at s1 = -2, s2 = -2, and s3 = -2.
(c) Determine analytically the unit step-response of the closed-loop system.