// multi-utility computation suite · offline · instant · precise
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sci.PID-tuning-Ziegler-Nichols-step Calculator
Calculates Ziegler-Nichols PID parameters from open-loop step test: process gain K = Δy/Δu, dead time θ, and time constant τ from S-shaped response. ZN step-response method: Kp = 1.2τ/(Kθ); Ti = 2θ; Td = 0.5θ — valid only for stable, non-oscillatory processes.
Inputs
K Process
Reference formula or conversion factor shown for context.
Tau S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Theta S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Results
PID controller gain Kc
The improvement or increase over the baseline.
PID integral time Ti (s)
Area under the curve between the specified limits. In physics: integral of velocity = displacement; integral of force over time = impulse.
PID 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.
PI: Kc=0.9/(Kp·R), Ti=τ/0.3
Reference formula or conversion factor shown for context.
R = θ/τ (controllability ratio)
The proportional relationship between two quantities.