In literature various PID controller laws and types have been described. In industry two types prevail: the parallel form and the series form.

Parallel Form

A PID controller in parallel form (also known as standard form, ISA form or non-interacting form), has the control equation:

The controller actions (P, I and D) act independently as can be seen in the corresponding block diagram representation.

Series Form

A PID controller in series form (also known as interacting form), has the control equation:

The controller actions (P, I and D) act dependently as can be seen in the corresponding block diagram representation.

Note

P and PI controllers are the same in series and parallel form.