PID controller tuning calculator
Compute the proportional, integral and derivative gains of a PID loop from either a Ziegler–Nichols closed-loop test (Ku, Tu) or a Cohen–Coon open-loop step response (K, τ, θ).
PID controller tuning
Tuning rule
Ziegler–Nichols: Kp = 0.6·Ku, Ti = Tu/2, Td = Tu/8. Cohen–Coon: Kp = (1/K)·(τ/θ)·(4/3 + θ/(4τ)), Ti = θ·(32 + 6·(θ/τ))/(13 + 8·(θ/τ)), Td = 4θ/(11 + 2·(θ/τ)). Treat these as a starting point — detune by 20–30% for processes with long dead time.
PID tuning starts from a process model, then the loop is trimmed on site. For temperature, pressure or flow loops that pair with our stocked parts:
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AO Ctrl provides this tool for reference only.
Frequently asked questions
How do I tune a PID controller with Ziegler-Nichols?
Run the loop in proportional-only mode and raise Kp until the output sustains a constant-amplitude oscillation. Record the ultimate gain Ku and the oscillation period Tu. The Ziegler–Nichols PID settings are then Kp = 0.6·Ku, Ki = Kp / (Tu/2) and Kd = Kp·(Tu/8). These give an aggressive, quarter-decay response that usually needs detuning by 20–30% for real processes.
What is Cohen-Coon tuning and when do I use it?
Cohen–Coon uses an open-loop process reaction curve: apply a step and fit the first-order-plus-dead-time model K, τ and θ. Kp = (1/K)·(τ/θ)·(4/3 + θ/(4τ)), with the integral and derivative times θ·(32+6·(θ/τ))/(13+8·(θ/τ)) and 4θ/(11+2·(θ/τ)). It handles processes with significant dead time better than Ziegler–Nichols, but still treat the result as a starting point.
What are typical Kp, Ki and Kd units?
Kp is dimensionless (or %/%) in a unity-feedback controller. Ki is Kp/Ti in units of per second (integral time Ti in seconds), and Kd is Kp·Td in seconds. The tool reports Ki and Kd directly in those rate units so you can enter them into most PLC or stand-alone PID controllers.
AO Ctrl provides this tool for reference only.