hello.I'm a new comer to process control.i want to compare different algorithms used for the digital implementation of Pid controllers.my personal study tells me that i have to discretize the various pid models using different numerical methods.i would then write a computer program for the various discrete pid algorithms.but i can't find the mathematical model for any of the PID forms(parallel,series,noise suppressing etc).all i can see is either their continuous time function that expresses their output as a sum of the individual P,I,D terms or their transfer functions relationship.surely this aren't their models? i suppose their model should be in the form of a differential equation.please an explicit explanation coupled with model equations would be greatly appreciated.many thanks.