Feedback loop element identification: Which is which? Non-Inverting Op amp circuit

General Control Loop block diagram:

Given schematic below, how to know which is which? Knowing which is which is critical, as it allows the use of theory to achieve the best result.

Equations that allowed us to identify corresponding blocks:

From simple voltage divider rule
vn = Ri/(Ri + Rf) * vout	eq 1
let α = Ri/(Ri+Rf)
vn = α * vout	eq 2
We see that vout is just opamp gain (Aamp) multiply by its input voltage
vout = (vp - vn) * Aamp
vout = (vin - α * vout) * Aamp
vout * ( 1 + α * Aamp) = vin * Aamp
vout / vin = Aamp / ( 1+ α * Aamp)	eq 3
From close loop equation of control theory:
vout/vin = TF = Aforward/(1 + Aforward*β)	eq 4
Comparing eq 3 with eq 4 , we see that
Aforward = Aamp
Aforward*β = α * Aamp
β = α = Ri/(Ri+Rf)
When loop gain (Aforward*β) is large enough, we see that
1 + Aforward*β ~= Aforward*β
TF = Aforward/ Aforward*β
TF = 1/β = (Ri + Rf)/Ri = 1 + (Rf/Ri)