Integral Control

Integral control (I) continuously changes the MV in proportion to the time-integral of the error so as to eliminate the deviation.
Using the integral action, a user can eliminate the offset (deviation) caused by proportional action.

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Integral action is used with PI (Proportional + Integral) control or PID (Proportional + Integral + Derivative) control. The Integral Control cannot be used by itself.
It can be thought that proportional control alone is enough, but in reality when the controlled variable approaches the target value (SV),
the manipulated variable (MV) becomes smaller and disables it to control precisely.

As a result, there is this slight difference between the controlled variable (PV) and the target value (SV) over time, which is called "residual deviation".
In order to overcome this slight difference, the Integral Control is used to eliminate this residual deviation (offset).
Likewise, when the Proportional action is added with Integral action, it is called "PI Control".