Interesting discussion. Since I have some experience with PID functions and coffee roasting I think I might be able to help a little.
John is correct about D (derivative) not be used in coffee roasting because roasting is not that dynamic.
P and I are the two functions that you use to \"trim out\" your controls. But one cannot successfully be used without the other.
One set of PIDs will not be valid through an entire roast as the heat sources and the heat absorption rates of the coffee vary throughout the roast.
Additionally, the PID settings need to be different for different ranges of batch sizes.
In our case we use 3 sets of PID settings per roast, and have 4 sets for each roaster ( full, half, micro and pico) as each roaster has slightly different dynamics.
The above information would be true of systems using bean temperature as the control temperature- things are slightly different for those systems that use environment/drum temperature for control.
Finally, just buying a Watlow SD or anyother PID controller will not automatically give you the results you want. Furthermore, while buying a proportional modulating valve will certainly give you a wider range of control- without the burner being off- you must have some way for the controller to talk to the valve, usually via a signal conditioner. You cannot just hook one up to the other. With an On/Off valve you can control it with just a switched relay (a function that is in all PID controllers). Also, the techs at Watlow are awesome, but they are not coffee roasters and they do not understand the coffee roasting process. Meaning they may mislead you without actually trying to do so.