Actuators that modulate from fully open to fully closed as changes occur at the controller represent:

The correct answer is proportional control because actuators that modulate from fully open to fully closed in response to changes at the controller actively adjust their position in proportion to the signal they receive. This means that if a small change is detected, the actuator will make a corresponding small adjustment, and the same logic applies for larger changes.

Proportional control provides a continuous response rather than just switching between two states, which is characteristic of on/off control. This kind of control allows for finer regulation of systems, enabling the actuator to maintain the desired output effectively without overshooting or oscillating around the setpoint.

In contrast, integral and derivative controls serve different purposes within a control system. Integral control addresses accumulated errors over time, while derivative control anticipates future errors based on the rate of change. Neither of these approaches involves the direct modulation of position found in proportional control, which is why those options do not align with the described behavior of the actuators.