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I have this block diagram which I already reduced pretty much:

enter image description here

Now I want to derive the transfer function from phi_o1 to q. However I have trouble with the feedback loops since they multiply with each other and I do not know how to reduce that.

How do I derive the transfer function?

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    \$\begingroup\$ Do you know Mason's rule?en.m.wikipedia.org/wiki/Mason's_gain_formula \$\endgroup\$
    – Bitrex
    May 16 '14 at 1:08
  • \$\begingroup\$ No I didn't :-) thanks for that link. I'm sure it will be of help in the future. \$\endgroup\$
    – WG-
    May 17 '14 at 14:18
  • \$\begingroup\$ Whew that solves it pretty well, too bad they haven't thought us that in my control courses. They even gave a scaled down assignments(in relation to this one) in the tests to do them manually (like I described in my answer). A lot of people were totally lost with that kind of thing, I'm almost a little angry because they didn't teach us this. I suggest you turn your comment into an answer! \$\endgroup\$
    – WalyKu
    May 21 '14 at 13:47
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My way of solving this would be to start at q and work down to phi_o1. Define a new variable for each of the points where the signal gets handed to somewhere else in the block diagramm. That way you have a less cumberstone diagramm, and you can work in a well defined way.

Now remove all feedbacks and write the variable names instead as if they were inputs. Repeat the process until you don't have any feedback loops. Now you can write down the solution.

To make the solution a function of phi_o1 only again, insert the earlier defined functions in their places. This time you should work from the input toward the output. You should be carefull not to forget the dependencies of each of the variables, so you don't lose any variables on the way.

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