# IAM unable to solve these block diagrams

I need transfer functions for the block diagrams... IAM unable to solve those.. can I get help

• There are many questions with answers here about how to get the transfer function out of a block diagram, you should find something there. For example this one: engineering.stackexchange.com/questions/33790/… – OpticalResonator May 8 '20 at 10:42
• Thankyou for the answer. I'll answer the other block diagrams. Then I'll ask my doubts – Smiley May 9 '20 at 1:19

The step by step procedure is the following (at least how I like to do it)

$$\begin{gather} z = XG_o+Y \\\ w = zG_b \\\ \end{gather}$$ And by combining these two we get:

$$w = G_b[XG_o+Y]$$

$$\begin{gather} u = w+x \Rightarrow u = XG_bG_o+YG_b+X \end{gather}$$

And the last step which gives the overall transfer function:

$$Y = G_cu \Rightarrow Y=XG_bG_oG_c+YG_cG_b+XG_c$$

$$Y[1-G_cG_b]=X[G_bG_oG_c+G_c]$$

$$\frac{Y(s)}{X(s)}=T(s) = \frac{G_c(G_oG_b+1)}{1-G_cG_b}$$

• The equations add up, but there is some confusion in the indices, OPs question had Ga, Gb and Gc, your picture has twice Gc and once Gp, and the equations have Go, Gb and Gc. That should still be fixed, otherwise good answer. – OpticalResonator May 8 '20 at 11:45
• Fixed it. Thank you! – Teo Protoulis May 8 '20 at 11:49
• When you now still make all Gb in the equations into a Gp it's perfect – OpticalResonator May 8 '20 at 12:37
• That was funny :) Think everything is ok now. Changed the diagram! – Teo Protoulis May 8 '20 at 12:42
• Wonderful, have an upvote – OpticalResonator May 8 '20 at 13:15