// multi-utility computation suite · offline · instant · precise
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eng.PID-Ziegler-Nichols-tuning Calculator
Calculates Ziegler-Nichols PID gains from the closed-loop oscillation test (ultimate gain Ku and ultimate period Tu). The Ziegler-Nichols frequency response method doesn't require a process model — it uses the gain at which the closed loop just oscillates.
Inputs
Ku Gain
Reference formula or conversion factor shown for context.
Tu S
Time for one complete cycle (s). Period = 1 / frequency. A 50 Hz signal has a 20 ms period.
Controller Type
Reference formula or conversion factor shown for context.
Results
proportional gain Kp
The improvement or increase over the baseline.
integral gain Ki = Kp/Ti
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
derivative gain Kd = Kp·Td
The instantaneous rate of change — the slope of the tangent line at a point. In physics: derivative of position = velocity; derivative of velocity = acceleration.
integral time Ti (s)
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
Ziegler-Nichols closed-loop tuning (1942)
LOS (length of stay) -- the number of days from admission to discharge. A key hospital efficiency metric.
expected overshoot
Reference formula or conversion factor shown for context.