What is the integral term in a PID controller, and how does it affect steady-state error?

What is the integral term in a PID controller, and how does it affect steady-state error?

• A. It differentiates the current error to predict the future trend.
• B. It averages the error to smooth the response.
• C. It accumulates past errors over time and eliminates steady-state error in the ideal case.
• D. It provides a fixed bias to the control output.

Answer: (C)

The integral term collects past errors over time, producing a correction that grows as long as there is error. It adds a control signal proportional to the time integral of the error, Ki ∫ e(t) dt, so if the error persists, the integral action keeps increasing until the process variable reaches the reference. This is why, in an ideal continuous-time, properly tuned system with unity feedback, the integral action can eliminate steady-state error caused by constant biases or disturbances—the accumulated correction counteracts the persistent mismatch and drives the error toward zero. In real systems, though, this can lead to overshoot or slower settling and can cause windup if actuators saturate, so practical designs use anti-windup measures and careful tuning to reap the steady-state benefits without destabilizing the response.

The integral term collects past errors over time, producing a correction that grows as long as there is error. It adds a control signal proportional to the time integral of the error, Ki ∫ e(t) dt, so if the error persists, the integral action keeps increasing until the process variable reaches the reference. This is why, in an ideal continuous-time, properly tuned system with unity feedback, the integral action can eliminate steady-state error caused by constant biases or disturbances—the accumulated correction counteracts the persistent mismatch and drives the error toward zero. In real systems, though, this can lead to overshoot or slower settling and can cause windup if actuators saturate, so practical designs use anti-windup measures and careful tuning to reap the steady-state benefits without destabilizing the response.