What type of controller cannot always maintain the process variable exactly on setpoint?

A proportional-only controller operates by producing an output that is directly proportional to the difference between the setpoint and the process variable, known as the error. This means that as the error decreases, the output also decreases, leading to a situation where the output will never fully eliminate the error. As a result, the process variable will oscillate around the setpoint without ever actually attaining it precisely. This behavior is due to the nature of proportional control, where a steady-state error persists because the controller cannot adjust output sufficiently to close the gap entirely.

In contrast, an integral controller—or a PID controller including integral action—has the ability to eliminate steady-state error over time by integrating the error. This continuous summation allows the controller to adjust its output even when the error is small, eventually driving the process variable to the setpoint. On/Off controllers, while simpler, entirely switch the output on or off based on whether the process variable is above or below the setpoint, leading to more significant deviations in the process variable but with less precision in maintaining it at the exact setpoint.

The fundamental characteristic of the proportional-only controller’s inability to hold the process variable exactly at the setpoint makes it the correct answer to this question.