PID Loop Tuning (Ziegler-Nichols Closed-Loop)

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.

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.

The Ziegler-Nichols closed-loop tuning rules are public (a classic control-engineering result); Ku and Tu are measured on the actual loop at the stability limit.

Estimate. AHJ and licensed professional govern.

Field names used by the API: ultimate_gain_ku, ultimate_period_tu_sec, pid_kp, pid_ti_sec, pid_td_sec, proportional_band_pct

• Ziegler-Nichols closed-loop PID: Kp=0.6Ku, Ti=0.5Tu, Td=0.125Tu; PI: Kp=0.45Ku, Ti=Tu/1.2; P: Kp=0.5Ku; from the ultimate gain/period at the stability limitZiegler & Nichols 1942
• Starting point, aggressive quarter-amplitude-decay tuning (overshoots); watch PB=100/Kp / reset units and interacting-vs-parallel form; the technician trims on the processcontrol-tuning practice