Engineering Determine the transfer function of the block diagram

[icesalmon]

Homework Statement

Determine the transfer function of the block diagram

Relevant Equations

Equations for Block Diagram Algebra

Step 1: I first started by reducing the inside of the block diagram of picture "bd" (the portion with G₁ and the negative feedback G₂)
I obtained G₁/[1 + G₁G₂]
I'll call this term "F"

Step 2: Then I'm left with two terms feeding into a summing point:
F - G₃
I'll call this term "K"

I can reduce this diagram as I did in the first step:

T(s) = K / [1 - K*G₄ ]

The solution, on the other hand, is adding G₃ to F as indicated in the second picture I've attached
"bd2"
I am not sure if this is a mistake (to add G₃ instead of subtracting it) or if I'm not seeing something.
Any help is appreciated, apologies if I've left anything out or made my solution unclear in anyway.

 

[Jody]

Has your class covered Mason's gain formula?

 

[icesalmon]

No, we haven't covered that yet

 

[Jody]

Giving it another look... I personally agree with you with subtracting $G_3$.

 

[icesalmon]

Giving it another look... I personally agree with you with subtracting $G_3$.

any luck? I think the solution is making a mistake.