How to Simplify a Block Diagram to Obtain Y/R?

In summary, the block diagram contains a feedback loop that can be simplified to 1/(s+a1). The signal b1s can be obtained from the right loop, but there is difficulty in reaching that point. To construct an equation, one can trace the signals R and Y and use the left summation of b3R and a3Y, which is then multiplied by 1/s. This should equal Y on the right side.
  • #1
magnifik
360
0
I am having trouble trying to obtain Y/R from the block diagram below:
xf56cz.png


the only thing i understand so far is that the bottom right loop is a feedback loop and can be simplified to 1/(s+a1). i know b1s can be obtained from the right loop, but i am having trouble getting to that point. i know it has to do with moving the summer
 
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  • #2
Hi magnifik! :smile:

Trace the signals R and Y and construct an equation from them.

For instance, the left summation sums b3R and a3Y, which is then multiplied by 1/s.
This yields:
$$\frac 1 s (b_3 R + a_3 Y)$$

Can you complete the expression tracing it up to the right side, where it must be equal to Y?
 

Related to How to Simplify a Block Diagram to Obtain Y/R?

What is a block diagram simplification?

A block diagram simplification is the process of reducing a complex block diagram into a simpler one by eliminating unnecessary blocks, reducing the number of inputs and outputs, and rearranging the blocks to make the diagram easier to understand and work with.

Why is block diagram simplification important?

Block diagram simplification is important because it helps to reduce the complexity of a system, making it easier to analyze and design. It also helps to identify the main components and relationships within a system, making it easier to troubleshoot and improve.

What are the steps involved in block diagram simplification?

The steps involved in block diagram simplification are identifying the main components, reducing the number of inputs and outputs, eliminating unnecessary blocks, and rearranging the blocks to create a simpler and more organized diagram.

What tools or techniques can be used for block diagram simplification?

There are various tools and techniques that can be used for block diagram simplification, including signal flow graphs, Mason's gain formula, and block diagram algebra. These tools help to simplify the process and make it more efficient and accurate.

What are the benefits of block diagram simplification?

The benefits of block diagram simplification are improved understanding of a system, reduced complexity, easier analysis and design, and easier troubleshooting and improvement. It also helps to save time and effort in the overall system development process.

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