The knobs can be included in the emulation. So that is to say, you model the unit as something having an audio input, and several controllers, such as knobs or switches. You then capture the behavior for all combinations of controller values, as part of the model. ("All combinations", for a potentiometer, might mean stepping it from 0 to 11 in increments of 1.)
The emulation ased on the model runs on a piece of hardware which has some generic controllers on it: some rotary encoders, a couple of switches and whatnot. These get assigned to the parameters of the model.
You could have a MIDI input on it, and use MIDI controllers, which would be cool. There are MIDI foot controllers that you can tilt with your foot to vary a parameter.
The different models could be assigned to MIDI program numbers. You could change the patch number with the foot controller, and vary the parameters with it also.
The foot controller might have, say, only two pedals, so you have to assign which ones you want: if the patch has five parameters, you have to fix the values of three of them and map the two important ones to the foot pedals you have. For the others, you can bend down and tweak the knobs on the unit itself.