Ziegler-Nichols PID Tuning Calculator
Compute classical Ziegler-Nichols closed-loop PID tuning parameters from the ultimate gain Ku and ultimate period Tu.
How to Use the Ziegler-Nichols PID Tuning Calculator
- Identify Ku by gradually increasing proportional gain until sustained oscillation.
- Measure Tu as the period of that oscillation.
- Enter Ku and Tu, then click Calculate.
使用场景
- •Initial PID tuning of industrial loops.
- •Teaching control systems.
- •Robot motion controller setup.
公式
Kp = 0.6 · Ku; Ti = 0.5 · Tu; Td = 0.125 · Tu; Ki = Kp / Ti; Kd = Kp · Td.
常见问题
Where does this method come from?
John G. Ziegler and Nathaniel B. Nichols published the closed-loop (ultimate sensitivity) method in 1942. It is still the standard starting point for PID tuning.
How do I find Ku and Tu?
Set Ki and Kd to zero, increase Kp until the loop oscillates continuously but without diverging. The critical Kp is Ku and the oscillation period is Tu.
Is the result optimal?
Ziegler-Nichols is aggressive — it produces a ~25% decay ratio and moderate overshoot. For smoother response, Tyreus-Luyben or Chien-Hrones-Reswick settings are gentler.