How to Use the PID Tuning Gain Calculator
The hardest part of commissioning a loop is deciding what numbers to type in first. Put the controller in manual, bump the output by a small step, and the curve the process variable draws gives you everything an open loop tuning rule needs.
Three numbers come off that curve. Process gain K is the change in PV as a percent of span divided by the change in MV in percent, dead time L is how long the PV stays still after the bump, and time constant T is how long it then takes to cover 63.2 percent of the total change. The Ziegler-Nichols reaction curve values for PID are Kc = 1.2T รท (K ร L), Ti = 2L and Td = 0.5L.
These are empirical rules rather than derived results, and Ziegler-Nichols was designed for disturbance rejection, so setpoint changes usually overshoot noticeably. If the loop cycles, halve Kc and lengthen Ti; if it crawls, move the other way. Whatever the rule, the output here is a starting point that has to be retuned against the real process under real operating conditions.
Frequently Asked Questions
It is dimensionless: express both PV and MV as a percent of their spans and divide. If opening a valve 10 percent raises temperature by 20 percent of span, K is 2. Mixing engineering units with percent changes the gain by orders of magnitude.
Cohen-Coon adds correction terms aimed at processes with significant dead time, so it behaves better when L/T is large. Ziegler-Nichols is simpler but more aggressive and often produces heavy overshoot on setpoint changes.
On noisy loops such as flow and pressure, derivative action amplifies noise and makes the valve chatter, so PI alone is normal. Derivative helps on slow, quiet loops like temperature, and even there it is usually paired with a derivative filter.