Integral and Derivative functions are used to:

The use of integral and derivative functions is fundamental in control theory, particularly in the context of maintaining process variables at a desired set-point. The integral function accumulates past errors over time, allowing the control system to adjust more effectively to persistent offsets. This helps in correcting situations where the process variable deviates from the set-point, ensuring that it arrives back at the desired level.

Meanwhile, the derivative function anticipates future errors based on the rate of change of the process variable. By measuring how quickly the variable is changing, the control system can react accordingly and apply corrective measures before the deviation becomes significant.

This combination of integral and derivative actions forms a robust approach in control mechanisms, often found in PID (Proportional-Integral-Derivative) controllers, which are designed specifically to keep process variables as close to their set-point as possible, even in the face of disturbances or changes in system dynamics.

In contrast, the other options focus on different aspects of control and monitoring. On-off control, for instance, is simpler and does not utilize integral or derivative operations, which are more sophisticated in approach. Monitoring energy usage typically involves tracking consumption metrics rather than directly manipulating process variables to stay at a set-point. Reducing disturbances, while related to system stability