Process control basics: what is proportional (P) control, in terms of how the controller output responds to the error signal?

Introduction / Context:
Proportional (P) control is the foundation of many feedback systems. The controller compares a setpoint with a measured process variable to produce an error. In P control, the output is directly proportional to this error. This provides smooth, continuous actuation that increases or decreases in magnitude as the error grows or shrinks, improving stability and responsiveness compared to simple on–off control.

Given Data / Assumptions:

• Error = setpoint − process variable.
• Controller output u = Kp * error, possibly with limits.
• Actuation hardware supports a continuous command (or an equivalent time-proportional scheme).

Concept / Approach:
P control scales the output with error using proportional gain Kp. Because the output is continuous, the actuator can apply just enough correction to drive the process toward the setpoint. Pure P control often leaves a steady-state offset when disturbances or loads persist; integral action (I) is commonly added to remove offset, creating PI or PID control when needed.

Step-by-Step Solution:
Identify whether the controller output changes smoothly with error magnitude.Recognize that discrete outputs per error value describe on–off or step control, not P control.Note that “gain independent of offset error” is misleading; P control alone typically leaves offset.Select the statement that says the output varies continuously over a range.

Verification / Alternative check:
Plotting u versus error gives a straight line through the origin (subject to saturation). This linear, continuous mapping is the hallmark of proportional control.

Why Other Options Are Wrong:
Option A applies to on–off control. Option C is incorrect because P control does not eliminate offset; integral action is needed. “All” cannot be true if one statement is wrong.

Common Pitfalls:
Setting Kp too high (oscillation) or too low (sluggish response); forgetting that P alone leaves steady-state error in many processes.

Final Answer:
The controller output varies continuously over a range