I really cannot understand how to derive the transfer function from the attached block diagram. It especially confuses me around the E-B-E loop.

Block Diagram


It helps if you label some internal states. For example lets call the signal coming out of block $A$ $x_1$ and the signal coming out of block $B$ $x_2$. From the block diagram it follows that,

$$ A\, (U - D\, x_2) = x_1, $$

$$ B\, (x_1 - E\, x_2) = x_2, $$

$$ Y = E\, x_2 - C\, x_1. $$

Assuming $U$ is known, than you have three linear equations and unknowns ($x_1$, $x_2$ and $Y$), which should be solvable.

  • $\begingroup$ I was able to solve it using the equations system. Did you follow any rule to label the internal states, or just intuition / common sense? $\endgroup$ – Pinco Pallino Apr 10 '17 at 0:26
  • $\begingroup$ @PincoPallino I mainly went by intuition, however I do think another definition should also work. For example define $x_2$ as the signal coming out of $E$. But you mainly want to add signals inside loops. Notice that my choice added one signal inside each loop of the block diagram. $\endgroup$ – Kwin van der Veen Apr 10 '17 at 0:52

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