PID Tuning Rechner — Formel

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.

Lösungsbeispiel

A system oscillates at Ku = 10 with period Tu = 2 seconds.

  1. Kp = 0.6 × 10 = 6.0
  2. Ti = 2 / 2 = 1.0 s, Ki = 1.2 × 10 / 2 = 6.0
  3. Td = 2 / 8 = 0.25 s, Kd = 0.075 × 10 × 2 = 1.5