ChBE Clemson
4 minutes
Finding the Ultimate Gain and Period with a Closed-Loop Test
The ultimate gain test finds the edge of stability on purpose. Safety first: the loop will swing hard, so set output limits and alarms. Do not run it where a large swing could damage gear or spoil product. Put the controller in auto with proportional action only. Turn integral off, often by setting the integral time to its largest value, and set derivative to zero. Make a small setpoint step. If the swing dies out, raise the gain, often by half again, and step again. Keep going until the measured value swings up and down by the same amount every cycle. That gain is the ultimate gain, Ku. The ultimate period, Pu, is the time from one peak to the next, read off the trend chart. Time several cycles and divide to get a better number. If the swings grow, you went past Ku, so lower the gain at once. If the output hits a limit during the swing, the numbers are off. A cycle with a square or saw-tooth shape may come from a sticky valve, not from the edge of stability. Some loops with almost no dead time never cycle at any gain. Ku and Pu feed the Ziegler-Nichols closed-loop table and other rules. After this Concept you can run a closed-loop test safely and read Ku and Pu from the chart.