Suppose that a process can be adequately modeled by the first-order-plus-time-delay model in Eq. 12-10.

(a) Calculate PI controller settings using the Hagglund-Astrom tuning relations in Table 12.4.

(b) Cohen and Coon (1953) reported the following tuning relations to PI controllers:

These tuning relations were developed to provide closed-loop responses with a quarter decay ratio. Compare the PI settings calculated from these equations to the controller settings of part (a). Which would you expect to be more conservative?

(c) Simulate the controllers of parts (a) and (b) for a unit step change in set point, followed by a unit step disturbance at t = 40. Assume that the Gd(s) = G(s) and that the model parameters are K = 2, ? = 3 and ? = 1. Which controller pro-vides better control?

Ke-t G() (12-10) 7s +1 (0.9 + 0/12-) Ke a[30 + 3(0/7)| 9 + 20(0/) G(s) . Ke- 0.35 70 Ke TS +1 6.80r 0.14 0,28. OK 0.330 + 100 + T