Why is the derivative term in a PID controller often filtered, and what is the trade-off?

• A. Filter the derivative term to increase responsiveness.
• B. Do not filter; derivative kick remains.
• C. Filter the derivative term to reduce noise; reduces high-frequency sensitivity but adds lag.
• D. Filtering eliminates the derivative term.

Answer: (C)

The part of a PID that responds to how fast the error is changing is very good at anticipating future error, but it also amplifies high-frequency noise present in the measurement. In real sensors this noise shows up as rapid, small fluctuations, and the raw derivative term would chase that noise, causing jittery control actions, actuator wear, and even instability.

So we filter the derivative path with a low-pass filter. This keeps the helpful, smooth notion of “rate of change” while attenuating the high-frequency components that are just noise. The trade-off is that the filter introduces lag and phase shift in the derivative action, which makes the controller respond a bit more slowly to rapid changes and can reduce overall responsiveness or stability if the filter is too aggressive. In practice, a modest filter is chosen to balance noise reduction with preserving enough derivative action for good disturbance rejection.