# Can I Simplify a Block Diagram by Making Multiple G5 Blocks?

• mech-eng
In summary: If you do that, you can get rid of rational expressions, but you may not be able to write the transfer function easily.But if you do that, you can get rid of rational expressions, but you may not be able to write the transfer function easily.
mech-eng
I would like to ask why cannot I think G5 in series with G3(G4+G6G7) and then after muliplying them why I cannot think of G5*G3(G4+G6G7) in parallel to G2 so sum G2 and G5*G3(G4+G6G7) ?

Thank you.

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If you do that, what happens to G8 and C(s)?

G5 would be at the other side, by the way.

mech-eng said:
I would like to ask why cannot I think G5 in series with G3(G4+G6G7) and then after muliplying them why I cannot think of G5*G3(G4+G6G7) in parallel to G2 so sum G2 and G5*G3(G4+G6G7) ?
.
I suggest you review the definitions of serial and parallel and see how they apply in this case. It's completely clear from the definitions that what you want to be series isn't series.

mfb said:
If you do that, what happens to G8 and C(s)? G5 would be at the other side, by the way.

If you do that I would ignore the multiplication of G8 and G5 so the result would be incorrect. I cannot think of what happens to the C(s) ? Is that the same thing for G(8) i.e ignorance of multiplication? But problem is that is G5 also series with C(s) so when multiply G5 with G8 and (G4 +G6G7) should I also multiply G5 with C(s) ?

Thank you.

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phinds said:
I suggest you review the definitions of serial and parallel and see how they apply in this case. It's completely clear from the definitions that what you want to be series isn't series.

I try to still understand. Because there is a common point between G5, G8 and (G4 + G6G7), G5 cannot be only series with (G4 + G6G7) and the signal G5 is going to both G8 and (G4 + G6G7) so G5 is both series with them. When I do this result is correct but I think simpler.

Thank you.

You can make multiple G5 blocks, but I don't think that makes it simpler.

mfb said:
You can make multiple G5 blocks, but I don't think that makes it simpler.

But if I do that, I can get rid of rational expressions so I can write transfer function easily.

Thank you.

## What is a block diagram reduction?

A block diagram reduction is a method used to simplify a complex control system by reducing the number of blocks and connections in the diagram, while maintaining the original functionality.

## Why is block diagram reduction important?

Block diagram reduction is important because it allows scientists and engineers to analyze and design control systems more easily. By reducing the complexity of the diagram, it becomes easier to understand and troubleshoot the system.

## What are the steps to perform a block diagram reduction?

The steps to perform a block diagram reduction are:

1. Identify the input and output variables of the system.
2. Draw the original block diagram of the system.
3. Eliminate any unnecessary blocks or connections.
4. Combine series and parallel blocks to reduce the number of blocks.
5. Simplify the remaining blocks using algebraic rules.
6. Draw the final reduced block diagram.

## What are the algebraic rules used in block diagram reduction?

The algebraic rules used in block diagram reduction are:

• Series rule: Two or more blocks connected in series can be combined by multiplying their transfer functions.
• Parallel rule: Two or more blocks connected in parallel can be combined by adding their transfer functions.
• Feedback rule: A feedback loop can be reduced by using the formula 1/(1+GH), where G is the forward gain and H is the feedback gain.
• Mason's gain formula: This formula is used to calculate the overall transfer function of a complex system.

## Can block diagram reduction be used for any type of system?

Block diagram reduction can be used for linear, time-invariant systems. It is not applicable for non-linear or time-varying systems.

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