Rule of thumb · Control SystemsNº 110 / 122

The ratio of dead time to time constant decides everything

Below L/τ ≈ 0.2 PID is easy and forgiving. Past about 1.0 it will disappoint no matter how you tune it.

Why it works

Lag only slows a loop down, and a controller can watch it happening. During dead time there is nothing to watch: every correction is made blind and lands after the fact, so the controller keeps pushing at a target it has already reached. Two plants with the same time constant and different delays are completely different control problems, and no amount of gain tuning changes which one you have.

When it fails

It is a statement about PID, not about control. A Smith predictor models the delay explicitly and controls against the prediction, which restores useful performance well past L/τ = 1 — and reducing the delay itself, by moving a sensor or shortening a pipe run, usually beats any amount of clever tuning.

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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Can PID control this process?

Below L/τ ≈ 0.2 PID is easy and forgiving. Past about 1.0 it will disappoint no matter how you tune it. Lag only slows a loop down, and a controller can watch it happening.

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