102 ◾  Distillation Control, Optimization, and Tuning
the proportional gain may need to be in the range of 2 or
higher if a thermosiphon reboiler is used that requires a narrow range of liquid level for good operation.
9.9 Summary
This chapter described the concept of a self-regulating process response and an integrating process response. Several
methods were described for tuning a control loop while the
controller is in automatic output mode. These include the trialand-error method, the Ziegler–Nichols ultimate gain method,
and the Robbins pattern recognition methods.
Exercises
9.1 With a controller in automatic output, a proportional
gain of 1.0, an integral time constant of 3.0 min, and
a derivative of zero, the response to a step change in
setpoint gave a quarter amplitude decay, and it took 39
min to reach the first peak. What is the first indication
that the controller could be tuned better? What changes
would be recommended for the tuning constants?
9.2 When a step change was introduced to a controller
setpoint, the process response reached the first peak in
5 min, the proportional gain was 2.5, the integral time
constant was 20 min, the derivative was zero, and the
height between the first peak and valley was 95% of
the height of the step change. Should the integral time
constant be increased or decreased? Should the proportional gain be increased or decreased?
9.3 When the setpoint is changed 10% of span, the control valve moves from 60% to 100% controller output
and stays there for 10 min while the process variable