HW#10 prob.1 solution

Hello everyone,
I am aving trouble understanding the solution posted for HW10 prob. 1:

The solution states: Tc(fci) = (Rf*Gio*Ki/VM)*fo^2/(fz*fci) = 1. I do not understand how this expression was arrived at. It appears as though (Rf*Gio*Ki/VM) was assumed to be equal to the flat gain, say, Tco, of the compensator. I don't see how that is true. Even if it were true, I don't see how the rest of the expression makes sense.

I can see that (fci/fi)*(fi/fo)^2 = Tco, the flat gain of the compensated loop gain. However, one cannot know Tco without knowing the fi (the zero of thecompensator)….so there are three unknowns here (fi, fci and Tco).

My thinking would be: Choose fi first (say, for instance, fi = fci/10)….and assume fci = fs/5 = 200/5 = 40kHz. Then fi = 4kHz. Once we know fi, onlythen we can get Tco and then determine fci.

I would really appreciate if someone can shed light on this (or perhaps the grader or the student who did the solution).

Regards,
Nitish