Single-element boiler drum level control. The process exhibits an integrating response with inverse response: a step increase in feedwater first collapses steam bubbles and lowers the level, then the level rises. Based on Module 9 of Process Control: Modeling, Design, and Simulation by B. Wayne Bequette.
Variables are dimensionless deviation variables from the nominal operating point: level 0 is the desired operating level, the controller output 0 means no change from the nominal feedwater flow, and ±1 represents a full-scale deviation. The feedwater valve icon displays 0 as 50% open (nominal), −1 as fully closed, and +1 as fully open.
Figure from Bequette Module 9: the LT/LC single-element loop that manipulates boiler feedwater to hold drum level against steam demand.
IMC-based PID for .
Drum level to feedwater flow rate.
Feedwater valve dynamics (valve opening −1 to +1, 0 = 50% open).
Drum level to steam flow rate disturbance.
The transfer function used for IMC PID design is
IMC-based PID design with integral action uses the filter
yielding ideal PID parameters