FOPDT calculator
A first-order-plus-dead-time model is three numbers: how much the measurement moves per unit of output, how long before it starts, and how long it takes to get most of the way. Those three numbers are what every open-loop tuning rule eats, and they come from a bump you already know how to run.
This calculator does the arithmetic. Process gain is the settled change in PV divided by the change in output. Dead time is the delay to first movement. The time constant is the time to 63% of the settled change, minus the dead time.
What you have to measure
With the loop in manual and the process steady, step the output a few percent and hold it. Record the output before and after, the PV before and after it settles, the time until the PV first moves, and the time until it has covered 63% of its settled change. Both times are measured from the instant of the step, not from each other.
If the PV never settles — it keeps drifting — the process is integrating and this model does not apply. Level loops are the usual case. Do not force a time constant onto a tank.
What the 63% point is
A first-order lag covers 63% of its final change in one time constant. That is the definition, not an approximation. If you cannot pick the 63% point cleanly off the trend, the response is not first-order enough for the model, and the PID calculator will still give you a number. It will just be a number for a process you do not have.
Questions that come up
Can I take these numbers straight to the PID calculator?
Yes. The Lambda, Cohen-Coon and open-loop Ziegler-Nichols methods take exactly K, L and T. Whether you should type the result into a live controller is a different question — the model has to be a fair picture of the loop first.
What if the PV moved the opposite way to the output?
Then the process gain is negative, which is a reverse-acting process. The calculator keeps the sign. The PID methods use the magnitude for the gain formula; you still have to set controller action to match the process.
Related
These tools assume a self-regulating loop and a bump you have not shown us. Photograph the trend and the faceplate if you want a check against the loop in front of you, not a formula.
Last reviewed 2026-09-10.