Given this block diagram, I'm trying to derive the transfer function. I've tried moving the 2 branch to either side of the then getting something like this
But I'm not sure how to simplify it from there. Any guidance would be appreciated. Thank you.
Best Answer
Let \$g_1 = {10 \over s+1}, g_2 = {1 \over s}\$, and let \$w\$ be the output of the \$g_1\$ block.
You get \$w = g_1 (u - 2 w -g_2 w)\$, which gives \$w = {g_1 \over1 + 2 g_1 + g_1 g_2} u\$, and so \$y = {g_2 g_1 \over1 + 2 g_1 + g_1 g_2} u\$, or \$y = {1 \over 1+{2 \over g_2}+{1 \over g_1 g_2}} u\$ if you would prefer.
Substituting in the values for \$g_1, g_2\$ gives the transfer function you wanted.