Without knowing the specifics of your application or the specific controller you are looking at, I can only speak in general terms. PID controllers are analog devices which produce analog outputs (like you learned in class). To build an actual control system for an industrial application you would need to process the output in some way to run the output device typically an amp or a relay. If you were to build your own control system (i.e. purchasing the appropriate IC's and what not) then you could do whatever you wanted with the output. If you are buying something off the shelf the output will be processed in some way depending on the intended application of the device.
If you want to do temperature control on a fridge, PID control seems like a poor choice to me for a few reasons.
1. The compressor on a fridge should be run at 100% capacity or 0% capacity. This is a digital (binary) output. To do this you need to convert your analog output from the PID into a binary output which seems silly since there are other control systems which produce binary output as a default. You could do PWM, but this would be less efficient than running at 100%.
2. PID controllers can become unstable or oscillate if they are not tuned well. Repeatedly cycling a compressor can shorten the lifespan of the device. To effectively run the fridge you would need to really tune the control system well and I think you would still have problems (that is just my opinion based on building lots of control systems)
3. There are better, cheap, digital systems available to accomplish the desired task. For this type of temperature control, I personally would use an embedded microcontroller (there are many different systems available). Most systems have a built in ADC to convert your analog temperature input. You can easily customize you control system software to give better temperature control with minimal compressor cycling. Third your output is already binary (on/off), so you should only need a minimal amount of output signal processing to run you device. While I have never used the Arduino controller, but it looks like lots of people on this board are using it. I think there is even a thread were someone implemented a fridge temperature controller with it.
I noticed on your profile you have a Ph.D. in electrical engineering so I assume you realize there are many ways to implement a control system. I personally consider PIDs solely analog devices because that is how we treat them theoretically and that is how they were originally implemented. On the other hand, PID is also a control theory, where errors are corrected based on the current error, the sum of past errors, and the rate of change of error. The theory can be implemented easily on a digital device, but in my opinion this is not a true PID controller.
In any case I would love to hear more about you systems and if I can be of any help let me know.
Jake