What each term does
- Kp (proportional gain) reacts to the current error. A higher Kp makes the loop faster, but too high makes it overshoot and oscillate. With Kp alone the process value stays below the setpoint: this is the steady-state offset.
- Ti (integral time) adds up the error over time and removes the offset. A shorter Ti acts more strongly, and too short causes slow oscillations. Set Ti to 0 to switch the integral off.
- Td (derivative time) reacts to how fast the process value changes and brakes the loop before it overshoots. It’s sensitive to noise, so many real loops run as PI with Td = 0.
CV = Kp × (e + 1/Ti ∫e dt + Td × de/dt), with the output limited to 0–100 %. Like most PLC PID blocks, the derivative acts on the process value instead of the error, so setpoint steps don’t cause a kick, and the integral stops while the output is saturated (anti-windup).
Tuning rules used
For a process with gain K, time constant τ and dead time θ:This is a simplified first-order-plus-dead-time model without noise or valve limits beyond 0–100 %. Use the values as a starting point, then fine-tune on the real machine. Siemens
PID_Compact and other PLC blocks also have their own auto-tuning.Related
Analog scaling calculator
Scale the 4–20 mA signal from your transmitter before it goes into the PID.
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