Most Piping and Instrument Diagrams show to a certain extent the control loops.
But generally there is not room on the P&ID to show all the details of the loop. This is particularly true for multi purpose batch plants where loop configurations can change with the process, but even for continuous plants it is useful to draw loop diagrams.
Loop diagrams provide this detail without the clutter such as line sizes that are not relevant to the control of the process.
Loop diagrams are almost essential if your process includes cascade control, override controls, ratio control to name a few.
They come in various styles, this is based on SAMA.