Free PID Tuning Calculator
Calculate PID controller gains using the Ziegler-Nichols tuning method from ultimate gain and period.
Proportional Gain (Kp)
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Proportional Gain (Kp) vs Ultimate Gain (Ku)
Ziegler-Nichols PID Tuning
The Ziegler-Nichols closed-loop method determines PID gains from two measurements: the ultimate gain Ku (gain at which the system oscillates) and the ultimate period Tu (period of those oscillations).
Formulas
Kp = 0.6 × Ku
Ti = Tu / 2, so Ki = Kp / Ti = 1.2 × Ku / Tu
Td = Tu / 8, so Kd = Kp × Td = 0.075 × Ku × Tu
These gains provide a starting point; fine-tuning is usually needed to balance response speed, overshoot, and stability.
Example Calculation
A system oscillates at Ku = 10 with period Tu = 2 seconds.
- 01Kp = 0.6 × 10 = 6.0
- 02Ti = 2 / 2 = 1.0 s, Ki = 1.2 × 10 / 2 = 6.0
- 03Td = 2 / 8 = 0.25 s, Kd = 0.075 × 10 × 2 = 1.5
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