Block Diagram of Transfer function

[jahlin]

Homework Statement

Simplify the block diagram in figure and obtain the closed-loop transfer function. The first attachment is the question and the second attachment is the first step to the simplification of the block diagram.

Homework Equations

What i don't understand is how do you get rid off the summing point before the last block and replace it with the block( (1/G2(s))+1) in the first step. I don't understand the first step at all. any help would be appreciated. thanks.

The Attempt at a Solution

 

[Filip Larsen]

You mention two attachments, but I only see one. I am guessing that you "only" have trouble identifying which simple reductions that have been employed from first to second diagram, but without seeing both diagrams its probably hard for people here to give you help.

 

[jahlin]

heres the block diagram which i refer to in my original post.

the above attachment is the 1st step in reducing this block diagram.

 

[Filip Larsen]

Note, that the last sum node is not involved in any feed-back loops, so its input is simply two parallel blocks with a common input, which can be reduced to a single block with a sum. Picking the first hit I get when searching for "control block reduction" [1] as reference, the reduction can be seen as a case of applying rule 4. You should be able to find the reduction in your textbook if it has a similar list of rules.

[1] http://www.msubbu.in/sp/ctrl/BD-Rules.htm

 

[jahlin]

what i fail to figure out is (1/G2) + 1 where this +1 comes from.

thanks for your help.

 

[Filip Larsen]

The last sum node has two inputs: a line with a 1/G2 block and a line with no block. As you know, the diagram X --->A--- Y represents the equation Y = AX, that is, if you start with X and then multiply it with block A you get Y. Now think about what the diagram would mean if the line has no block, like X ------ Y (hint: it means Y=X) and what value of A would correspond to this diagram (hint: what value of A makes Y=AX equal to X=Y? Having this special value you can replace an empty line with a line that has a block with this special value).