PID - Ziegler-Nichols Ultimate Tuning
Classical Ziegler-Nichols PID gains from ultimate gain K_u and ultimate period T_u - an on-line tuning recipe for level, pressure and flow loops.
Proportional gain Kp
2.400 -
Integral time Ti
12.5s
Derivative time Td
3.13s
Formula, assumptions, and limits
$$K_p = 0.6 K_u,\ T_i = 0.5 T_u,\ T_d = 0.125 T_u$$
Classical Z-N produces aggressive response (25 % overshoot). For less-oscillatory tuning use Tyreus-Luyben ($K_p$ = 0.45 $K_u$, $T_i$ = 2.2 $T_u$).
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $K_u$ | Ultimate (critical) gain | - | P-only closed loop |
| $T_u$ | Ultimate period of oscillation | s | P-only closed loop |
Spotted an error in this calculation? . We acknowledge editorial corrections within two working days.