Rule of thumb · Control SystemsNº 109 / 122

One step test gives you all three numbers

Step the input and wait. The delay before anything moves is L, the total change over the input change is K, and the time from the end of the delay to 63.2% of the final value is τ.

Why it works

63.2% is not a convention, it is 1 − e⁻¹ — exact, and independent of how large a step you made. Every further time constant closes 63.2% of the gap that remains, which is why four or five of them counts as settled and why nobody quotes a 100% time. Those three numbers feed every open-loop tuning rule there is, so one experiment replaces a day of trial and error.

When it fails

Only if the process really is first order. A curve that starts shallow and steepens is at least second order, and reading 63.2% off it gives a time constant that describes nothing. A step test taken while the plant was still drifting, or while a disturbance arrived, fits a model of the disturbance instead — which is why the test is run twice, in both directions.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open First-Order Lag & Dead Time →

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How do I get a process model from a step test?

Step the input and wait. The delay before anything moves is L, the total change over the input change is K, and the time from the end of the delay to 63.2% of the final value is τ. 63.2% is not a convention, it is 1 − e⁻¹ — exact, and independent of how large a step you made.

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