Conversion formulae and performance capabilities of two-degree-of-freedom PID control algorithms

The aim of the paper is to present two-degree-of-freedom (2DoF) proportional integral derivative (PID) control algorithms and conversion relations between their parameters. The Ideal PID with filter (PID_2F) is the more general PID controller. Restrictions to obtain equivalent 2DoF Standard or Series PID controllers are presented taking into account the derivative filter constant. Examples are used to illustrate when or when not equivalent controllers exist.