First-order plus dead time (FOPDT)

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, or export the same trend as a CSV of time, PV and OP and let the FOPDT calculator pick those points. 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.

Read them in order. Dead time is the wait before first movement. The time constant is the climb to about 63% of the settled change, minus that wait. Process gain is settled ΔPV over ΔOP. If the process does not settle, you do not have an FOPDT model — you have an integrator or a limit, and the reaction-curve rules do not apply.

Questions that come up

What is a first-order plus dead time model?

Three numbers from a bump: process gain (how far the PV moves), dead time (the wait before it starts), and the time constant (how fast it climbs once it starts). Most open-loop tuning rules — Ziegler-Nichols, Cohen-Coon, lambda — eat those three.

Related

Where this comes up

• DeltaV PID parameters explained
• PID calculator
• FOPDT calculator
• Dead time
• Time constant
• Bump test
• Cohen-Coon tuning
• Internal model control (IMC)
• Sample time
• Smith predictor