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Ziegler-Nichols

The Ziegler-Nichols method gives quick starting values for a PID controller without having to model the process accurately. You first control with pure P action and raise the gain until the system just starts to oscillate continuously, at the ultimate gain $K_u$ with period $T_u$ . These two numbers are then plugged straight into a standard table to find $K_p$ , $T_i$ and $T_d$ .

K_p=0.6K_u,\ T_i=\dfrac{T_u}{2},\ T_d=\dfrac{T_u}{8}

Ziegler-Nichols ultimate-gain method, PID table

Symbols

$K_u$	ultimate (critical) gain
$T_u$	period at sustained oscillation	s

Example

$K_u=8$ , $T_u=1.2$ s:

$K_p=0.6\cdot8=4.8$ , $T_i=0.6$ s, $T_d=0.15$ s.

The formulas only apply right after you have found

K_u

and

T_u

– do not mix them with other tuning methods.

Practise pID control for free →

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Part of Control Engineering: PID control.