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Control Loop Sample Time Calculator

Work out control loop sample time instantly with clear inputs, formula shown and shareable results.

About Control Loop Sample Time Calculator

A digital loop should sample at least ten times per process time constant and about twenty times the desired closed-loop bandwidth, and at least twice per dead time. Sampling too slowly adds effective dead time of half a sample period, which directly erodes phase margin.

Formula

Sample time

Ts <= tau/10, Ts <= 1/(20 x closed-loop bandwidth), Ts <= theta/2

Worked example

With the default values below, Control Loop Sample Time Calculator returns Recommended sample time of 0.17. Change any input above and every figure here is recalculated in your browser.

Inputs used

Process time constant
8 s
Dead time
1.5 s
Desired closed-loop bandwidth
0.3 Hz

Results

Recommended sample time
0.17 s
Sample rate
6.00 Hz
Samples per time constant
48.00 samples
Nyquist limit for the bandwidth
3.00 Hz

Step by step

  1. 1Values used
  2. 2Sample time
  3. 3Recommended sample time= 0.17 s
  4. 4Sample rate= 6.00 Hz
  5. 5Samples per time constant= 48.00 samples
  6. 6Nyquist limit for the bandwidth= 3.00 Hz

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does slow sampling destabilise a loop?

Zero-order hold adds an effective dead time of half the sample period. Extra dead time reduces phase margin, and enough of it makes the loop oscillate.

Is faster sampling always better?

Beyond about twenty times bandwidth there is little benefit, and derivative action starts amplifying quantisation noise. Filter the measurement instead.

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