Rule of thumb · Control SystemsNº 50 / 96
One τ is 63%; five is settled
A first-order system covers 63% of a step in one time constant and is effectively settled after 4–5.
Why it works
Follows directly from the exponential 1 − e^(−t/τ). Knowing τ tells you the whole response timeline.
Do it exactly
Estimate with the rule, then check it against the calculator that models it properly.
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