Proportional control of a first-order process – effect of gain on offset A proportional controller with gain Kc regulates a first-order process. How does the steady-state offset change when Kc is varied?

Introduction / Context:
Steady-state offset is the nonzero difference between setpoint and controlled variable after the transients decay. In pure proportional control of most plants, offset persists after load disturbances. Understanding how proportional gain affects offset is crucial for tuning.

Given Data / Assumptions:

• First-order process with proportional (P-only) controller.
• Offset refers to steady-state error after a step load disturbance or setpoint change (with bias).
• No integral term is present unless stated.

Concept / Approach:
For a first-order plant under P-only control, the closed-loop steady-state error (offset) is inversely related to the loop gain. Higher proportional gain reduces the required error to produce the necessary controller output, thus reducing offset. Adding integral action eliminates offset by integrating error to drive steady-state error to zero.

Step-by-Step Solution:

Verification / Alternative check:
Classic control texts derive steady-state error constants showing proportional control yields finite error inversely proportional to gain, while integral control drives error to zero.

Why Other Options Are Wrong:

• Kc increased → offset increases: Opposite of correct relationship.
• Introducing integral action: Decreases offset to zero, not increase.
• Introducing derivative action: Affects transient response, not steady-state offset.

Common Pitfalls:
Increasing Kc excessively can destabilize the loop even though it reduces offset; practical tuning balances offset reduction with stability and noise amplification.

Final Answer:
Kc is reduced → offset increases