Offset in a first-order process controlled by proportional (P-only) control with gain Kc: what modification to the control strategy most effectively eliminates steady-state offset without relying on extreme gain values?

Introduction / Context:
Proportional-only control of a load-disturbed process typically results in a steady-state error (offset) unless the process has integral action itself. Engineers often need to remove this bias so that the controlled variable exactly matches the set point at steady state.

Given Data / Assumptions:

• Process is well approximated by a first-order lag with nonzero steady-state gain.
• Controller is initially proportional only with gain Kc.
• Load disturbances or set-point changes can occur.

Concept / Approach:
With P-only control, the control signal at steady state is finite and requires a nonzero error to sustain the actuator output that balances the load—this is offset. Adding integral action introduces a term proportional to the time integral of the error, which accumulates until the steady-state error is driven to zero (for a stable, reachable operating point). Derivative action shapes dynamics but does not change the steady-state error for step loads.

Step-by-Step Solution:

Verification / Alternative check:
Closed-loop steady-state analysis shows that with PI control, the error for a step input is zero if the loop is stable and actuator limits are not hit.

Why Other Options Are Wrong:

Common Pitfalls:
Raising Kc excessively to reduce offset risks oscillation; integral action is the principled fix.

Final Answer:
Introducing integral (I) control