A Programmable Logic Controller, PLC or Programmable Controller is a digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. PLCs are used in many industries and machines. http://en.wikipedia.org/wiki/Programmable_logic_controller
A HMI (Human Machine Interface) is the system by which people can interact with a machine. The user interface includes hardware (physical) and software (logical) components.