Noise, Filtering, and Actuator Movement

The Core Idea

Measurement noise is variation in a reading that may not reflect useful process movement. A controller can turn that variation into changing output commands, so filtering and tuning must be judged together.

What you will learn

  • Distinguish a noisy measurement from a rapidly moving process.

  • Compare output movement with and without a measurement filter.

  • Meet a temperature goal and an output-movement goal together.

Why it matters

A steady-looking process can still have an actuator working unnecessarily hard. Check both measurement quality and the amount of output movement.

Keep the process and noise the same

Return to the delayed heater from the derivative lesson: 20 °C start, 50 °C target, 15 s lag, 5 s dead time, and 0–100% output. P stays at 2% output per °C and I at 0.12% output per (°C·s). Measurement noise is on.

Start with D = 3% output·s per °C and the filter at 0 s, which means off. Run the full 120 simulated seconds, inspect the blue output line, and save the trace. Predict what adding a filter will change before you restart.

Meet both operating requirements

Choose D and a filter time constant. The finished run must reach the target, peak no higher than 56 °C, and have average absolute error no greater than 0.6 °C over the final 24 s. Those limits are 20% and 2% of the 30 °C start-to-target span.

The output requirement is total absolute controller output (CV) travel divided by time no greater than 30 percentage points/s over those same final 24 s. Large repeated movements count even if the command ends where it started. This is a command-movement limit, not a physical actuator speed model.

Change one setting, use Restart, and finish another 120 s. Every restart uses the same noise sequence. First compare filter 0 s with 1 s while holding D fixed; then decide whether reducing D gives a better compromise.

What the filter changes

The measurement filter smooths the value used by the controller. The green measured process variable (PV) still shows the noisy sensor reading; the additional filtered PV line shows what the controller uses. It does not change the actual heater or repair a faulty sensor.

The filter time constant is in seconds. A larger value smooths more strongly but makes the controller's measurement respond more slowly. That extra delay can increase overshoot or slow correction, even when the output becomes quieter.

Diagnose before increasing the filter

Check sensor wiring, signal quality, scaling, and the noise source when the real measurement is poor. A filter can help with ordinary measurement noise, but smoothing a bad value does not make it a correct value. The shared filtering lesson develops that measurement concept.

Compare D = 0 as a valid alternative. The goal is to meet the operating requirements with an explainable response, rather than to use every controller term.

Hint 1 — Inspect the output scale

CV is in percent output. Repeated changes from 20% to 40% and back contribute 40 percentage points of command travel. A final CV near the right value can still have excessive travel along the way.

Hint 2 — Try a modest filter before a large one

Keep D at 3 and try 1 s of filtering. Compare the peak and ending travel with your unfiltered baseline. Then try D = 1 with 0.5 s of filtering as a separate trial.

Worked results after the comparisons

With D = 3, filter 0 s, ending travel is about 360 percentage points/s. With D unchanged and filter 1 s, it falls to about 23 percentage points/s, and the measured peak is about 53.6 °C. That filtered trial meets both limits.

D = 1 with filter 0.5 s also passes, at about 16 percentage points/s. D = 0 with the filter off passes too. By contrast, D = 3 with a 10 s filter makes the output quiet but exceeds the temperature peak limit by a wide margin.

The useful result is a measured compromise. Lower output travel alone does not prove that a filter setting is suitable.

Check your understanding

Record the D setting, filter time constant, peak, and ending output travel for two trials. Explain which meets both requirements and why increasing the filter indefinitely would be a poor method. The combined check can mark completion, and manual completion remains available.

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