PID Loop Tuning (Ziegler-Nichols Closed-Loop)
Starting PID gains from the Ziegler-Nichols closed-loop (ultimate-sensitivity) method: with I and D off, raise the proportional gain until the loop just oscillates steadily -- that is the ultimate gain Ku, and the oscillation period is Tu. Then PID starts at Kp = 0.6 Ku, Ti = 0.5 Tu, Td = 0.125 Tu; PI (for a noisy/fast loop) at Kp = 0.45 Ku, Ti = Tu/1.2; P-only at Kp = 0.5 Ku. With Ku 4, Tu 2 s a PID starts at Kp 2.4, Ti 1.0 s, Td 0.25 s (42% proportional band). A legacy controller may want proportional band PB = 100/Kp and reset in repeats/min (1/Ti); a parallel-form controller uses different Ki/Kd. Ziegler-Nichols is aggressive (quarter-amplitude decay, overshoots) -- back it off for a gentler loop. A starting point, not a final tune; the process, the controller algorithm form, and the technician govern.
Formula and source
PID: Kp = 0.6 Ku, Ti = 0.5 Tu, Td = 0.125 Tu; PI: Kp = 0.45 Ku, Ti = Tu/1.2; P: Kp = 0.5 Ku. Proportional band = 100/Kp. Ku, Tu = the gain and period at the stability limit (steady oscillation).
Ziegler-Nichols closed-loop (ultimate-sensitivity) tuning rules (Ziegler & Nichols, 1942), by name; the process dynamics, the controller's algorithm form, and the commissioning technician govern the final tune.
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