How do I calculate PID Controller Tuning (Ziegler-Nichols)?

To calculate PID Controller Tuning (Ziegler-Nichols): Enter Process gain K, Dead time Tu (L), Process time constant T and other values. Click Calculate. INDUGRID computes the result instantly using the formula: Kp = 1.2/a Ti = 2×Tu Td = 0.5×Tu where a = K×Tu/T (from step test). No registration required.

What units does the PID Controller Tuning (Ziegler-Nichols) calculator use?

The PID Controller Tuning (Ziegler-Nichols) calculator uses the following units: output/input, s. SI units are used by default.

Automation & Control

PID Controller Tuning (Ziegler-Nichols)

Calculate PID controller parameters using the Ziegler-Nichols open-loop method (step response) for industrial process control.

Units:

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💡Ziegler-Nichols gives aggressive tuning — fast response but may overshoot 25–30%. For tighter control, multiply Ti by 1.5 and Td by 0.5. For temperature control, use very long Ti (10–30× Tu). Always test in simulation or with reduced output limits first.

Kp = 1.2/a Ti = 2×Tu Td = 0.5×Tu where a = K×Tu/T (from step test)

Input

Process gain K iRatio of steady-state output change to input (step) change. From step test: K = Δy / Δu.

output/input

Dead time Tu (L) iTransport delay / dead time in seconds. From step response: time from step until output starts to respond.

Process time constant T iTime constant in seconds. From step response: time from start of response to 63.2% of final value minus dead time.

Controller type iSelect the controller structure. PID is recommended for most industrial processes.

Result

Factor a = K×Tu/T —

Proportional gain Kp —

Integral time Ti [s] —

Derivative time Td [s] —

Integral gain Ki (= Kp/Ti) [1/s] —

Derivative gain Kd (= Kp×Td) [s] —