PID Controller - PID Controller Theory

PID Controller Theory

This section describes the parallel or non-interacting form of the PID controller. For other forms please see the section Alternative nomenclature and PID forms.

The PID control scheme is named after its three correcting terms, whose sum constitutes the manipulated variable (MV). The proportional, integral, and derivative terms are summed to calculate the output of the PID controller. Defining as the controller output, the final form of the PID algorithm is:

where

: Proportional gain, a tuning parameter

: Integral gain, a tuning parameter

: Derivative gain, a tuning parameter

: Error

: Time or instantaneous time (the present)

: Variable of integration; takes on values from time 0 to the present .