Say you have for simplicity two TEC modules, something like:
each mounted on one side to a large aluminum plane of heatsink, large enough to be considered more-or-less infinite in extent from the perspective of the module. On the other you have a block cooler with cooling fluid piped through the two coolers in series, and a temperature sensor to sense the cooling block's temperature, and the cooling blocks are connected in series for fluid flow.
You want to feedback-control the two TEC modules via the temp sensors on the heatsink blocks to maximize the "exhaust" block temperature wrt the "input" block temperature for a given flow rate (I'm assuming that's the proper situation for maximal cooling of the working fluid input to output but please correct if not.)
Question I have is whether it's possible for the thermal coupling between them via the heatsink they're connected to to destabilize the individual feedback-control loops. my guess is yes it's possible it all depends on the particulars of the mounting geometry, the thermal resistances involved, and the speed of the individual electronic loops.
Is there a canonical method to analyze closed-loop systems that have both electrical and thermal feedback paths?