This is often question. The answer is really simple. PLC is systems standalone. It recognizes inputs and base on the strategy, transmits outputs. These devices are being run by three different vendors PLCs. Through a system network, by correctly mapping of these three PLCs inputs and outputs, one can have a single centralized system control, known as Distributed control System (DCS). The DDC stand for Direct Digital Control was first utilized when process computers changed analog controllers, electrical circuits or even something that applied under pressure air.
The control actions are considered mathematically with DDC. This also permitted to apply other methods control as opposite of PID controllers. Some users do not consider a discrete controller of PID as DDC.
Currently we utilize DDC in the majority cases, but seldom mention it. The controllers of PID in a PC-based control or in a PLC at the old fashioned process computer such as HP2100, HP1000, or PDP-nn, or in a DCS no more utilizes analog circuits but computes the control from set point, current value and some previous values.
You can simply program a controller dead beat or a controller state space, probably with an observer, in a PLC modern. Even the majority tiny PLC frequently has enough power for processing. The PLC, DCS or even a PID controller with simple single loop made currently days all use the concept of DDC and perform Direct Digital Control.
Fundamentally PLC is ready industrial hardware which can be planned as per application logics with ladder programming. You can utilize ready made HMI or MMI as a user interface using PLC.
While DDC is not a ready made hardware solution but its fixed controller for any application. DDC can be operated from fundamental concept to design of product with design of hardware, firmware etc. You can design user interface configuration and calibration as an element of product in DDC, which will be stored in flash.