PID algorithm form converter
The same three numbers behave differently depending on which equation the controller solves. Moving a tuning set between systems without converting for form is a common way for a loop that worked on one plant to misbehave on another.
This converter handles all three forms in every direction, and tells you when a conversion is impossible rather than returning a number that looks plausible.
The three forms
Series (interacting): the derivative term multiplies the proportional-plus-integral term. Changing rate also changes the effective gain and reset, so the parameters are not independent.
Ideal (non-interacting): the three terms are added, with gain scaling all of them. This is the form most published tuning guidance assumes.
Parallel (independent): the three gains are entirely separate. Changing the proportional gain does not affect integral or derivative action at all, which makes tuning rules written for the ideal form inapplicable.
When a conversion is impossible
Ideal-to-series conversion has a real constraint: it requires the integral time to be at least four times the derivative time. An ideal tuning set with more derivative than that has no series equivalent, because the series structure physically cannot produce that combination.
This tool says so rather than returning a number. A converter that quietly produced something for an impossible input would be worse than useless — you would take the number to a plant.
Questions that come up
Does the form matter if derivative is zero?
No. With no derivative action, the interaction factor is exactly one and all three forms are identical. This is one reason the distinction causes so little trouble on flow loops and so much on temperature loops.
Related
Last reviewed 2026-08-01.