PID Tuning Calculator
Calculate PID controller gains using the Ziegler-Nichols tuning method from ultimate gain and period.
Proportional Gain (Kp)
6.000
Proportional Gain (Kp) vs Ultimate Gain (Ku)
Formule
## 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.
Exemple Résolu
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
Questions Fréquentes
What is the Ziegler-Nichols method?
It is a classical tuning technique where you increase the proportional gain until the system oscillates continuously. The gain and period at this point (Ku, Tu) are used to compute PID gains from empirical formulas.
Is Ziegler-Nichols tuning optimal?
No. ZN tuning typically produces aggressive response with 25% overshoot. It provides a good starting point, but most systems benefit from adjustment. Modern methods like IMC, lambda tuning, or auto-tuning often give better results.
What if I only want PI control?
For PI control (no derivative): Kp = 0.45 × Ku, Ti = Tu / 1.2. For P-only control: Kp = 0.5 × Ku. These are also from the Ziegler-Nichols table.
Apprendre