Appendix: Solutions to Chapter Exercises ◾  125
Exercise 8.3
The controller gain, K c = 100/25 = 4.
The time to change the controller output as much as the
gain would change the controller outlet is T i = 1/ repeats/
minute = 1/0.05 = 20 min.
Exercise 9.1
The integral time constant of 3 min is 13 times smaller than
the response time of 39 min. Increase the proportional
gain from 1 to 13, and increase the integral time constant
from 3 to 39 min.
Exercise 9.2
The integral time constant should be reduced to about 7
min, and the proportional gain should be reduced to
about 1.2.
Exercise 9.3
Use a smaller setpoint change, so that the controller output
does not saturate at 100%. Repeat the test with, say, a 5%
setpoint change in the opposite direction.
Exercise 10.1
(52 − 51)/(6.7 − 4.1) = 1/2.6 = 0.385% PV change/minute

Apparent DT = 4.1 − 2.6 = 1.5 min

K p = 1.0

The Z-N recommended K c = (0.9)(10)/(0.385)(1.5) = 15.6