First-order plus dead time (FOPDT)
A three-number description of a process — gain, time constant and dead time — that most tuning rules start from.
What it means
First-order plus dead time is the working shorthand for a process: how far the measurement moves, how fast it moves once it starts, and how long it waits before it starts at all. Those three numbers — process gain, time constant and dead time — carry most of what tuning theory actually reasons about.
The model is never exactly true. Real processes carry extra lags, distributed elements and nonlinearity, and the FOPDT form ignores all of them. It survives anyway, because the three numbers are exactly the constraints that matter, and because the reaction-curve rules — open-loop Ziegler-Nichols, Cohen-Coon, lambda tuning — are formulas written against it.
A bump test is how you obtain the numbers: step the output in manual and read the dead time, the time constant and the gain straight off the response. The fit is honest wherever the process settles; it breaks where the process will not settle, or where something the three numbers cannot describe dominates the response.
Related
Where this comes up
Last reviewed 2026-09-18.