PID Tuning Calculator

Calculate PID controller gains using the Ziegler-Nichols tuning method from ultimate gain and period.

s

Proportional Gain (Kp)

6.000

Integral Gain (Ki)6.000
Derivative Gain (Kd)1.5000
Integral Time (Ti)1.000 s
Derivative Time (Td)0.2500 s

Proportional Gain (Kp) vs Ultimate Gain (Ku)

Vedi formula →

Formula

## 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.

Esempio Risolto

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

  1. 01Kp = 0.6 × 10 = 6.0
  2. 02Ti = 2 / 2 = 1.0 s, Ki = 1.2 × 10 / 2 = 6.0
  3. 03Td = 2 / 8 = 0.25 s, Kd = 0.075 × 10 × 2 = 1.5