Ziegler–Nichols PID Tuning Calculator
Calculate classic Ziegler–Nichols tuning for P, PI and PID controllers, either from a closed loop test (ultimate gain and period) or from an open loop step response.
- PID: Kc = 0.6 Ku, Ti = Pu/2, Td = Pu/8
Ziegler–Nichols settings (ideal form, time in the same unit as your inputs)
| Controller | Gain Kc | Proportional band | Ti | Td |
|---|---|---|---|---|
| P | 2 | 50 % | ∞ (off) | 0 |
| PI | 1.8 | 55.56 % | 1.667 | 0 |
| PID | 2.4 | 41.67 % | 1 | 0.25 |
Ziegler–Nichols Rules
Open loop: P Kc = T/(KL); PI Kc = 0.9T/(KL), Ti = 3.33L; PID Kc = 1.2T/(KL), Ti = 2L, Td = 0.5L
Ku is the proportional only gain that makes the loop oscillate steadily, Pu the period of that oscillation. In the open loop method K is the process gain, L the apparent dead time and T the time constant from a step test.
Worked example
A loop oscillates steadily at Ku = 4 with Pu = 2 min. ZN PID gives Kc = 2.4, Ti = 1.0 min and Td = 0.25 min.
Frequently Asked Questions
What is the Ziegler–Nichols method?
A 1942 empirical tuning method that sets PID parameters from either the ultimate gain and period or the step response of the process.
Why is Ziegler–Nichols tuning so aggressive?
It targets a quarter decay ratio, which gives fast response but large overshoot and low robustness for most process loops.
How do I find Ku and Pu?
With integral and derivative off, raise the proportional gain until the loop oscillates with constant amplitude. That gain is Ku and the oscillation period is Pu.
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