The FOPDT model

First order plus dead time: three numbers describe how a loop answers a step. A gain, a time constant, and a dead time. It is a rough model on purpose – most process loops are not first order, but a first-order fit captures enough to tune them without pretending to more precision than the data holds.

The three parameters

Gain K is how far the output moves per unit of input, once everything settles. Time constant T is how fast it gets there – the time to reach about 63% of the final change. Dead time L is the flat stretch before anything happens at all: transport delay, sampling, a slow sensor.

The step response Flintloop draws is the model G(s) = K · e^(−Ls) / (T·s + 1) laid over your data. The fit minimises the residual between that curve and the capture; the residual is shown as a percentage so you can see when the loop is not first order and the number is lying to you.

When it does not fit

Integrating loops (level in a tank with no self-regulation) and strongly nonlinear loops (valves near their seat, pH near neutral) will not sit under a FOPDT curve. Flintloop flags a high residual rather than fitting anyway, because tuning from a wrong model is how a loop ends up oscillating after a "successful" tune.