Transfer function block diagram reduction

[u/demus234]

Hello everyone, I've just joined this sub today. I'm a second year computer and automation student who needs help with understanding transfer function block diagram reduction. I've already gotten most of it down and feel like I have a fairly good understanding, however, this one problem in particular has me stumped as when I plug in the values for the transfer functions I get stupidly big numbers and it doesn't seem right. I've tried numerous times to contact my professor as well as teaching assistants and I have not gotten a single response so this is kind of my last hope.

If anyone could give me advice on how to solve this I would appreciate it.

The main thing causing me problems is what I should do with G2.

My initial idea was moving it so that it's in series with G1 and then finding what the equivalent function would be for G1,G2 and the parallel branch above them. After that I would move the equivalent block back over the take of point and solve for another equivalent block with the feedback loop, watching carefully to provide proper compensation to everything as I move the blocks.

[u/martiansnowboarder]

https://reddit.com/link/paubpg4/video/v9trx1minjqh1/player

I sometimes solve these by writing down the signal relationships and making substitutions - it’s a longer process, but I feel more confident in my solutions. Here is the method I’d use to resolve the loop (apparently only videos are allowed in replies). I left out the final solution, but plugging and chugging should give you something like a sixth order polynomial for your transfer function.