Equivalence of PI(D) and predictive functional control for aperiodic processes without dead time

PFC (Predictive Functional Control) algorithm is a very effective simple SISO (Single Input, Single Output) controller. PFC controller parameters have a physical meaning and they are easy to tune. PI(D) controllers are very widespread in the industry although their tuning is not easy. It is a common opinion that predictive controller is much better than PI(D) controller. However PI(D) controllers can be tuned in such a way that they (or extended by some filter) are equivalent to the predictive PFC controller. The relations between the PFC and PI(D) controller (extended with a filter) are derived analytically and confirmed by simulations for the control of the hot air blower pilot plant.