Which controller action is directly proportional to the rate of change of the error and helps reduce overshoot and damp oscillations, but is sensitive to noise?

• A. Proportional Controller
• B. Derivative Controller
• C. Integral Controller
• D. On-Off Controller

Answer: (B)

The derivative action in a feedback controller uses the rate of change of the error to shape the control signal. By responding to how fast the error is changing, it adds a counteracting influence when the error starts to rise or fall quickly, which damps oscillations and reduces overshoot. This predictive feel helps smooth the response because you’re not just reacting to the current error but to its momentum.

However, differentiating amplifies high-frequency noise, so the derivative term can be sensitive to noisy measurements; practitioners often filter the signal or limit the derivative gain to keep noise from dominating the response.

In contrast, a proportional controller reacts only to the present error, giving an immediate but often insufficient response to damp oscillations. An integral controller reacts to the accumulated error over time, helping eliminate steady-state error but potentially causing slower response or overshoot. An on-off controller switches abruptly, which can introduce large oscillations and no smoothing.