Step Test FOPDT Model Calculator
Turn an open loop step test into a first order plus dead time model. Enter the output step, the PV change and the times when the PV reached 28 % and 63 % of its change.
- K = ΔPV ÷ ΔOP = 15 ÷ 10
- τ = 1.5 × (t63 − t28)
- θ = t63 − τ
Two Point Method (Smith)
τ = 1.5 (t₆₃ − t₂₈)
θ = t₆₃ − τ
t₂₈ and t₆₃ are the times, measured from the output step, when the PV has completed 28.3 % and 63.2 % of its total change. ΔPV and ΔOP in % of range.
Worked example
OP step 10 %, PV 40 → 55 %, t₂₈ = 2.5 min, t₆₃ = 4 min: K = 1.5, τ = 2.25 min, θ = 1.75 min.
Frequently Asked Questions
What is a FOPDT model?
First order plus dead time: a process described by gain, time constant and dead time, used by most tuning rules.
Why use 28 % and 63 %?
For a first order response these points give τ and θ with simple formulas (Smith method).
What if the PV keeps ramping?
The process is integrating (like level); use integrating tuning rules instead.
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