Ultimate period
Ultimate period is Pu: the time for one complete cycle at the ultimate gain. Closed-loop Ziegler-Nichols reset and derivative are fractions of it. Do not find it on a production loop.
What it means
The ultimate period is the other half of the closed-loop Ziegler-Nichols measurement: with the gain set to the ultimate gain, you time one complete cycle of the process variable and record its period. The reset and derivative of the Ziegler-Nichols rules are then simple fractions of it.
Measured carelessly, the period drags the whole tune with it. Reset and derivative scale directly off the number, so a reading taken from a single cycle on a noisy trend inherits every error of that one cycle.
The period is also where a mechanical problem disguises itself. A limit cycle from stiction or backlash has a period of its own, but it is not the oscillation the method means — it belongs to the valve, not to the gain you set.
Questions that come up
What is ultimate period in PID tuning?
Pu: the time for one complete cycle when the gain is at ultimate gain, integral and derivative off. Ziegler-Nichols reset and derivative are fractions of it. Finding it means cycling the loop.
Related
Where this comes up
Written by PIDSnap control engineering. Published 2026-08-01, last reviewed 2026-10-22.