In a PID controller, What happens to derivative output when error is constant?

Question:

In a PID controller, what happens to derivative output when error is constant?

Options:

A) Increases
B) Negative
C) Maximum
D) Zero


View Answer

:white_check_mark: Correct Answer: D) Zero


:magnifying_glass_tilted_right: Detailed Explanation

Derivative action depends on the rate of change of error:

image

If the error is constant:

image

Therefore:

image

The derivative term only responds when the error is changing.


:repeat_button: Practical Insight

  • Constant error → No derivative contribution
  • Rapidly changing error → Strong derivative action

This is why derivative does not affect steady-state behavior.


:cross_mark: Why Other Options Are Incorrect

A) Increases → Only if error is changing.
B) Negative → Sign depends on error trend, not constant value.
C) Maximum → Occurs only with rapid error change, not constant error.

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