126 ◾  Appendix: Solutions to Chapter Exercises
T i = (3.33)(1.5) = 5.0 min

These tuning constants would be expected to be much
more aggressive than K c = 4.08 and T i = 13 min.

Exercise 10.2
TFO = 21.9 min

Apparent DT = 1.8 min

K p = 1.0

The QDR recommended K c = (0.9)(21.9)/(1.0)(1.8) = 11.0

T i = (3.33)(1.8) = 6.0 min

The high gain of 11 is much more aggressive than 4.08,
and the T i = 6.0 min is much more aggressive than 13
min. The control loop would probably run with sustained
cycling.
Exercise 10.3
TFO = 21.9 min
Apparent DT = 1.8 min
K p = 1.0
The IMC recommended K c = (21.9/1.0)/(1.8+21.9/2) = 1.72
The low gain, K c , of 1.72 is much more sluggish than K c =
4.08
The IMC recommended T i = 21.9 min
The SIMC recommended T i = (8)(1.8) = 14.4 min
The lower T i of 14.4 min is nearly the same at 13 min so, on
balance, the SIMC calculated values would be expected to
be more sluggish than K c = 4.08 and T i = 13 min.