 Defining formula_5 as the controller output, the final form of the PID algorithm is

where

Equivalently, the transfer function in the Laplace domain of the PID controller is

where formula_27 is the complex frequency.The proportional term produces an output value that is proportional to the current error value.The proportional response can be adjusted by multiplying the error by a constant "K"p, called the proportional gain constant.