I have the following block diagram, and I want to find the transfer function \$\frac{\hat{\theta}}{\hat{T}}\$. I am not sure how to do this, I've got the rules of connection in a series or parallel, but I am stuck.

Block Diagram I started with the entrance of \$T\$ but got stuck, can someone please provide me some help?


This kind of block diagram doesn't have anything to do with the rules for parallel and series connections of impedances. It just represents a bunch of complex algebraic equations. Each of the rectangular boxes just produces an output variable by multiplying its input by a constant, given by the text in the box.

For example,

\$ V_m = \gamma(I_{ref}-I_m)\$ comes from the first box at the upper left.

\$ I_m = \dfrac{1}{Ls+R}(V_m - E_{emf})\$ comes from the next box to the right.

You can keep making equations like this for each variable in the diagram. At that point you should have a complete set of equations that you can reduce to get a relationship between \$\Omega\$ and T.

To do this for a complex system like yours, you may want to polish up your skills in a symbolic math package like Maple or Mathematica.

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