Question: A second-order process is controlled by a PID controller. The desired closed-loop servo transfer function is and the process model is (a) Derive a control

A second-order process is controlled by a PID controller. The desired closed-loop servo transfer function is

and the process model is

(a) Derive a control law that shows how adjust Kc, ?I, and ?D based on variations in Kp, ?I and ?2 and the desired closed-loop time constant ?c.

(b) Suppose ?I = 3, ?2 = 5, and Kp, = 1. Calculate values of Kc,?I and ?D to achieve ?c =1.5. Show how the response deteriorates for change-s in the following model parameters when the controller remains unchanged:

i. Kp =2

ii. Kp = 0.5

iii. ?2 = 10

iv. ?2 = 1

(G, = Gn = 1) G,G %3! 1+ G,G (C. Is + 1 Ysp

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