I'm modeling a distillation column on black box principles. While doing so, I've encountered a issue I don't know ho to handle; the temperature in the bottom act as an "inverse" integrator when applying different manual level controller outputs(the level controller controls bottom outflow based on said temperature measurement). The feedflow into the column is constant. See attached figure. Note that the legend on the lower subplot should read "Temperature fraction" and NOT tank level.
The noisy start and end is neglible. Observe the steps in controller(at t=~1800, t=~7700 and t=~7900 output and the "inverse" integrator behavior. Modeling this as an integrator would give negative integral time, Ti, which does not makes sense. I don't know how to model this response. Anyone who could help me with this problem?