I practiced various examples of block algebra and I came across this example where I have to reduce the block diagram. The problem now is that I have there successively set branching points and sum points. How can I get rid of them?

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Here is how I came to this block diagram:

Starting point and first step:

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Second step:

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Third step:

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Final block diagram:

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Don't know what to do now... I thought to merge (G1G2) with (G5/G2 +1) and (G3G4) but again there isn't so much improvement.


1 Answer 1


I'm not going to write in the answers, but if I redraw your stuff just a little:

Starting redrawn

One of the things that might make it easier is to duplicate some of your boxes. Consider doubling up the H2*G2*G3 section:

Doubling up H2G2G3

If I redraw THAT just a little then it should show you how to clear up the middle section:

Resolve the middle

I'll just call whatever the middle resolves to "A" so I can keep going without needing to do the work:

Middle section resolved

The last tricky business is that summing junction in the middle of that feedback line. What I'd like to is to push the summing junction to the left so it can be with the second summing junction (from the start). Then you can split each branch of the summation into its own feedback line. To do that, first get that H1 out of the way:

Moving H1 behind the summing junction

Now distribute the negative from the second summing junction and reorganize:

Cleaning up the summing junction

And then finally split the group of summing junctions up into their own lines, which makes the feedback branches clearer.

Last difficult reduction

Now you just do like you'd do, resolve the feedback loops from inner to outer and you should have the reduction.


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