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A proportional-action controller (P controller) changes the manipulated variable M proportional
to the loop error. The P controller works immediately. By itself it cannot drive the loop error to
zero.
:Manipulated variable of the P controller at the time n
:Gain of the P controller
: Loop error at the time n
The following picture shows a jump in process value and step response of the controller:
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