Question:
Which PID term depends on the history of error over time?
Options:
A) Proportional
B) Integral
C) Derivative
D) Gain
View Answer
Correct Answer: B) Integral
Detailed Explanation
The Integral (I) term depends on the accumulated history of error over time.
Mathematically:
This means the controller:
- Continuously sums past error values
- Increases output if error persists
- Decreases output if error reverses
Even a small constant error, if present for a long time, will cause the integral term to grow until the steady-state error becomes zero.
Why This Is Important
Proportional control alone leaves steady-state offset.
Integral action eliminates this offset because it “remembers” past error and keeps correcting it.
Why Other Options Are Incorrect
A) Proportional → Depends only on present error.
C) Derivative → Depends on rate of change of error (future trend).
D) Gain → Is a tuning parameter, not a control action.
Quick Memory Trick:
- P → Present
- I → Past
- D → Future