I assume you are talking about proportional-integral-derivative feedback controller. This kind of thing could be done with Arduino, depending on the type of sensors and actuators you have available, and the kind of system you are trying to control. For some applications, PID might be overkill; you might be able to get away with a simple thermostat model: if the vat of goo is too cold, turn on the heater... if it is too warm, turn it off... lather, rinse, repeat.
Why not post more details of the problem you are trying to solve. That will help get the conversation going!