Rievtech xLogic ELC Series User Manual page 176

Summary
The P controller has the following characteristics:
It cannot correct faults with the control process > lasting loop error.
It reacts immediately to a change in the process value.
It is stable.
I Controller
An integral-action controller (I controller) changes the manipulated variable M proportional to the loop
error and to the time. The I controller works by delayed action. It completely remedies a loop error.
In order to calculate the value of the manipulated variable at a period of time n, the time up until this
period of time must be divided into small time slices. The loop errors at the end of each time slice must
be added up (integrated) and they are then entered in the calculation.
: Manipulated variable of the I controller at the time n
: Manipulated variable of the I controller at the time n-1; also called integral sum
: Gain of the I controller
: Sampling time, duration of a time slice
: Integral time: by means of this time, the influence of the integral part is controlled on the
manipulated variable, also known as integral-action time
: Loop error at the time n
: Loop error at the time n-1; etc.
: Loop error at the beginning of the calculations
The following picture shows a jump in process value and step response of the controller:
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