Control systems block diagram reduction

[RIshen]

Homework Statement

Hi

I am having trouble simplifying the attached diagram with respect to the return summing block

Homework Equations

The Attempt at a Solution

there shouldn't be any superposition since there is only one input signal,
in the attached file I've simplified A to Be: G3/(G2-G2G3G4)
would it be correct to move the pick off lines as shown?
once the relevant block diagram rules are applied this is the point where i can't find a way to remove the summing block next to H1

 

[KataKoniK]

Dear student,

Thank you for your post. I understand that you are having trouble simplifying the attached diagram with respect to the return summing block. I will try my best to guide you through the process.

Firstly, you are correct in saying that there should not be any superposition since there is only one input signal. However, I would like to clarify that the term superposition is used to describe the principle of adding individual solutions of a linear system to obtain the overall solution. In this case, we are trying to simplify the diagram by using block diagram rules, not superposition.

Next, you have correctly simplified A to Be: G3/(G2-G2G3G4). This is a good start. Now, let's look at the pick-off lines. The pick-off lines should not be moved as shown. They should remain connected to the input and output of the summing block. Moving them would change the signal flow and alter the overall system.

Finally, you are correct in saying that the summing block next to H1 cannot be removed. This is because it represents the summing of the output of H1 and the input from the pick-off line. In order to simplify this further, you can use the summing junction rule, which states that the output of a summing junction is equal to the algebraic sum of its inputs. This means that you can replace the summing block with a transfer function that represents the sum of the two signals.

I hope this helps you in simplifying the diagram. If you have any further questions, please feel free to ask. Good luck with your studies!