Integral controller:
Integral action accumulates error as a function of time. It sums the error over time, multiplies that sum by a gain, and adds the result to the present controller output. If the error makes random excursions above and below zero, the net sum will be zero, so the integral action will not contribute. But if the error becomes positive or negative for an extended period of time, the integral action will begin to accumulate and make changes to the controller output.
Advantages:
i. The controller has the unique ability to return the process back to the exact setpoint.
ii. It can eliminate the offset in proportional control.
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