block diagram reduction problem

kim24

Joined Mar 15, 2019
11
i have strugle to solve this problem and unable to do this question.
the question is.
a). find transfer function C(s)/R(s) using block diagram reduction
b). convert the diagram block into signal flow graph
c). find transfer function C(s)/R(s), D1(s)/R(s), and D2(s)/R(s) using mason's rule.

can someone help me? and tell me hpw to solve this step by step
thanks

ericgibbs

Joined Jan 29, 2010
12,215
hi kim,
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LvW

Joined Jun 13, 2013
1,212
kim, can you describe with words how block diagram reduction works in principle?

Papabravo

Joined Feb 24, 2006
15,464
A bi-directional flow between G2 and G3 makes no sense to me. How can this be reasonable?

MrAl

Joined Jun 17, 2014
8,063
A bi-directional flow between G2 and G3 makes no sense to me. How can this be reasonable?
There is only one way. Think about it.

MrAl

Joined Jun 17, 2014
8,063
kim, can you describe with words how block diagram reduction works in principle?
That's when you move connection points and blocks around with the intention of combining all blocks in the end to form one single path input to output. So it's not algebraic it is more physical although the blocks themselves combine algebraically.

Papabravo

Joined Feb 24, 2006
15,464
There is only one way. Think about it.
So there is an implied connection where the vertical and horizontal line cross. I'm used to seeing lines cross in diagrams without an actual connection being present, unless there is some visual indication of a connection.

MrAl

Joined Jun 17, 2014
8,063
So there is an implied connection where the vertical and horizontal line cross. I'm used to seeing lines cross in diagrams without an actual connection being present, unless there is some visual indication of a connection.
Yeah the way i reasoned is that there are other connections with no dots also, and there is no little "loop" jumper on the criss cross so i assumed it was a connection. Well that and the fact that there is no other way it could be unless they made another mistake on the diagram.

Papabravo

Joined Feb 24, 2006
15,464
Yeah the way i reasoned is that there are other connections with no dots also, and there is no little "loop" jumper on the criss cross so i assumed it was a connection. Well that and the fact that there is no other way it could be unless they made another mistake on the diagram.
Mistakes in textbooks and handout sheets are not entirely unheard of.

MrAl

Joined Jun 17, 2014
8,063
I started the block diagram reduction procedure just to illustrate. There is still a lot to do though.
Look at the original diagram and then the diagram at the top of this image then the bottom diagram of this image to see how the procedure went the way i started it. There could be other ways to start too i just happened to have seen these changes first.
Notice the empty block in the bottom diagram is easy to calculate i just did not write it in the block yet because i would have to make the block bigger to fit the text.
The main idea is that when we look at the top diagram we see a lower number of blocks in the diagram than in the original diagram and when we look at the bottom diagram we see even less. As the procedure progresses eventually we will end up with one single block with input on the left and output on the right although the expression inside that single block may be quite complicated.
This is sort of like reducing resistor networks by finding parallel and series combinations although in the block diagrams we are mainly concerned with the path transmittances and the rules for combining are different.

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