What type of controller cannot always maintain the process variable exactly at the set-point?

A proportional-only controller is designed to maintain a process variable close to a set-point but cannot guarantee that it will match the set-point exactly. This type of controller adjusts its output in proportion to the error—the difference between the set-point and the process variable.

However, as the process variable gets closer to the set-point, the correction applied by the controller becomes smaller, which can lead to steady-state error, particularly in systems with varying loads or disturbances. In essence, while it can reduce the error, it does not eliminate it entirely; hence, the process variable may remain above or below the set-point consistently, especially in the presence of constant disturbances or load changes.

Other controllers mentioned, such as PID controllers, utilize proportional, integral, and derivative actions, helping to eliminate steady-state error due to the integral action. An On/Off controller will toggle based on predetermined thresholds but can achieve the set-point without maintaining stability. Feedforward controllers anticipate changes in the process and adjust proactively, allowing for more precise control in many situations.