Calculates Ziegler-Nichols PID tuning parameters from ultimate gain Ku and ultimate period Pu: Kp = 0.6Ku, Ti = Pu/2, Td = Pu/8. ZN tuning gives aggressive, fast response with significant overshoot (~25%) — reduced-overshoot variants use Kp = 0.33Ku.
Inputs
Ku
Reference formula or conversion factor shown for context.
Pu S
Time for one complete cycle (s). Period = 1 / frequency. A 50 Hz signal has a 20 ms period.
Method
Reference formula or conversion factor shown for context.
Results
proportional gain Kp
The improvement or increase over the baseline.
integral time Ti (s)
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
derivative time Td (s)
The instantaneous rate of change — the slope of the tangent line at a point. In physics: derivative of position = velocity; derivative of velocity = acceleration.
Ki = Kp/Ti
Reference formula or conversion factor shown for context.
Kd = Kp·Td
Reference formula or conversion factor shown for context.