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sci.PID-tuning-Cohen-Coon Calculator
Calculates Cohen-Coon PID parameters from FOPDT step response (K, τ, θ) for quarter-decay-ratio response. Cohen-Coon gives better tuning than ZN for processes with large dead time — it is recommended when θ/τ > 0.5.
Inputs
K Process
Reference formula or conversion factor shown for context.
Tau S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Theta S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Results
PID gain Kc (Cohen-Coon)
The improvement or increase over the baseline.
integral time Ti (s)
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
derivative time Td (s)
The instantaneous rate of change — the slope of the tangent line at a point. In physics: derivative of position = velocity; derivative of velocity = acceleration.
Cohen & Coon 1953 — accounts for large dead time better than Ziegler-Nichols
Total number of items or occurrences.
r = θ/τ
Reference formula or conversion factor shown for context.