GATE 2022 BT – Question 41
Which of the following statements are CORRECT for a controller? P. In a proportional controller, a control action is proportional to the error Q. In an integral controller, a control action is proportional to the derivative of the error R. There is no “offset” in the response of the closed-loop first-order process with a proportional controller S. There is no “offset” in the response of the closed-loop first-order process with a proportional-integral controller
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Correct answer: (C) P and S only
Explanation
Check each statement about controllers.
- **P. A proportional controller's action is proportional to the error.** True: $u=K_c\,e$. ✓
- **Q. An integral controller's action is proportional to the derivative of the error.** False. Integral action is proportional to the **integral** of the error (the derivative belongs to derivative action).
- **R. No offset with a proportional controller on a first-order process.** False. A P-only controller leaves a permanent steady-state error (offset) after a sustained disturbance or set-point change.
- **S. No offset with a proportional-integral controller.** True. Integral action keeps changing the output until the error is zero, so the offset is removed. ✓
Answer **P and S only** (C).