My Auber INS PID Controllers are only on/off. Maybe that have other models, but mine have a high and a low switch, but still only on/off as a function.
Example:
Temperature set to 150 degrees for mashing,
PID set to 150
PID LOW set to 148 "which wil turn my burner off at this temp because my system continues to heat up a couple of degrees even with the gas off"
PID High set to 155 " this does nothing on my system, but could be used to trigger heat exchanger to cool temp down".
Low Switch set to "ON" until temperature of 148 is reached.
Because of continual heating, the temperature continues to climb up to my 150 mark hopefully.
If Temp exceeds 155 degrees, then Alarm 2 or high limit is activated, which can start a chiller motor or heat exchanger of some sort to cool the unit. <~~ Not required, I don't personally use this function.
The Auber INS PID is very controllable and allows you to adjust those assumed curves such as shut off "relay, burner, heat exchanger, what ever" at 147 to assume climb to 150. If my burners failed get the temp to my 150 mark, I could adjust that curve to shut off burner at 148 degrees instead or any other .1 degree mark that I see fit. In other words, they do not only have to turn on and off at a preset mark, they can be used to design a curve to fit your system to control your temperature exactly.
Whether your system is HERMS or direct fire like mine, the controller would do the exact same routines for controlling the temperature. That control is ON/OFF. Heat on or heat off, that is the question. The only nice thing that I know about the Auber Ins PID controllers is that I have worked a little with them for my system and my burners so now I can control my HLT and MASH/Lauter Tun to 1/2 of 1 degree F.
The Auber PID is also very "Power Friendly" , it will take almost anything that you put into it. <~~ Another nice feature.
I would say PID is the way to go!