I'm trying to find the transfer function that represents the system shown below. Normally for Root Locus, yoou would find the 'open loop' tf. In this case there is the closed loop part to deal with? How do you deal with it?

System: https://app.box.com/s/lb7djxnuiwzer1he59rb
G(s): https://app.box.com/s/9egxf68k0n91hf0h892l

 

Which parameter for the gain variation K1 or K2?

 

Both are included and K1=K2.

 

Since one can only create a root locus for a single gain term you cannot investigate the inner and outer loop stability issues simultaneously. I would imagine one would set up a sequence of root loci in which the outer loop gain K1 is varied continuously whilst K2 is varied in steps over a range of sensible (stable?) values. So one obtains a series of root loci in which K1 is the primary variable with K2 fixed but different for each locus drawn. For each specific K2 value the inner loop would be replaced by the equivalent transfer function resulting from the inner loop being closed at that K2 value.
It will not be a trivial task.
I'm not sure if it has been mentioned before, but with your threads spread far and wide it's difficult to keep track of who said what - Are you familiar with the text "Automatic Control of Aircraft and Missiles" by John Blakelock? It gives many examples possibly relevant to your case.