Evolution of Proportional Integral Derivative Controller

Proportional Integral Derivative order controller has been used in feedback mechanism since time immemorial. The paper introduces a novel form of proportional integral derivative (PID) controller termed as complex fractional order proportional integral derivative (CFOPID) controller of the form PI
^x+iy
D
^a+ib
. This variant of PID controller has more number of parameters than any of the PID and its derivatives. This work realizes a complex natured PID controller and exhibits the tuning of all the variants of PID controller utilizing Genetic Algorithm (starting from primitive Proportional controller to advanced CFOPID controller). It additionally relates the responses of each of the controllers and concludes the superior variant of PID controller.