Cohen–Coon PID Tuning Calculator
Calculate Cohen–Coon tuning from a first order plus dead time (FOPDT) model obtained from an open loop step test. The method handles larger dead time ratios than Ziegler–Nichols.
- PID: Kc = (τ/Kθ)(4/3 + θ/4τ), Ti = θ(32 + 6θ/τ)/(13 + 8θ/τ), Td = 4θ/(11 + 2θ/τ)
Cohen–Coon settings (ideal form)
| Controller | Gain Kc | Proportional band | Ti | Td |
|---|---|---|---|---|
| P | 2.889 | 34.62 % | ∞ (off) | 0 |
| PI | 2.456 | 40.72 % | 2.196 | 0 |
| PID | 3.722 | 26.87 % | 2.233 | 0.3478 |
Cohen–Coon Formulas
PI: Kc = (τ/Kθ)(0.9 + θ/12τ), Ti = θ(30 + 3θ/τ)/(9 + 20θ/τ)
PID: Kc = (τ/Kθ)(4/3 + θ/4τ), Ti = θ(32 + 6θ/τ)/(13 + 8θ/τ), Td = 4θ/(11 + 2θ/τ)
K is the steady state process gain (change in PV % divided by change in output %), τ the time constant and θ the dead time, both from a step test.
Worked example
K = 1.5, τ = 4 min, θ = 1 min (θ/τ = 0.25): PID Kc = 3.72, Ti = 2.23 min, Td = 0.35 min.
Frequently Asked Questions
When should I use Cohen–Coon tuning?
For self regulating processes with noticeable dead time, roughly 0.1 < θ/τ < 1, where fast disturbance rejection matters.
How do I get the FOPDT model?
Put the loop in manual, make a step in output and record the PV. Process gain is ΔPV/ΔOP, dead time is the delay before PV moves and τ the time to 63 % of the change after that.
Is Cohen–Coon better than Ziegler–Nichols?
It accounts for dead time explicitly and suits larger θ/τ, but it is also aggressive. Lambda or IMC tuning is usually more robust.
Learn more on the blog
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