I am looking to find the transfer function from w to z in this loop. I have been trying for a while looking all the relationships but just don't know how to express w in terms of r,d and n and then express it as a TF with z. I would appreciate a hint on how to solve this.
Regards
From the closed-loop in $v$ we have $$v=r-(n+d+GKv)$$ or equivalently $$v=(\mathbb{I}+GK)^{-1}(r-d-n)$$ Since $$z=-r+d+GKv$$ we have that $$z=\big[GK(\mathbb{I}+GK)^{-1}-\mathbb{I}\big]r-\big[GK(\mathbb{I}+GK)^{-1}-\mathbb{I}\big]d-GK(\mathbb{I}+GK)^{-1}n$$ that can be simplified to $$z=(\mathbb{I}+GK)^{-1}r-(\mathbb{I}+GK)^{-1}d-GK(\mathbb{I}+GK)^{-1}n$$