How Does Moving the Summation Block Affect the Equation in Control Systems?

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SUMMARY

Moving the summation block in control systems affects the equation's structure significantly. When the summation block (H3) is placed before the gain block (G1), the entire result of the summation is multiplied by G1, altering the expression to (V1 - V3*H3) * G1. This contrasts with the original expression, V1*G1 - V3*H3, where the term V3*H3 remains independent of G1. Understanding this relationship is crucial for accurate control system modeling.

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  • Control systems fundamentals
  • Understanding of transfer functions
  • Knowledge of block diagram representation
  • Familiarity with gain blocks in control theory
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Control engineers, systems analysts, and students studying control theory will benefit from this discussion, particularly those focused on the mathematical modeling of dynamic systems.

LauraMorrison
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Hi there,

I am struggling to understand how moving the summation (with H3) to before G1 will cause H3 to have to be divided by G1. I tried writing down how the equations would work to make sense of it but I still can't see how it works out.

Please can someone explain this to me?

Thanks,
Laura Morrison
 
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If you move the summation block backwards, then the ENTIRE result of the summation block will be multiplied by G1, not just one of the termsyou are multiplying V3 by H3, then subtracting it from V1*G1, so your expression looks like
V1*G1-V3*H3

notice how the V3*H3 term is completely independent of the value of G1.

If you move the summation block before G1, then the expression will be

(V1-V3*H3)*G1 which is also V1*G1-V3*H3*G1

notice how the second term will change as G1 changes.

make sense?
 

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